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https://en.wikipedia.org/wiki/Albedo
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Albedo (; ) is the fraction of sunlight that is diffusely reflected by a body. It is measured on a scale from 0 (corresponding to a black body that absorbs all incident radiation) to 1 (corresponding to a body that reflects all incident radiation).
Surface albedo is defined as the ratio of radiosity Je to the irradiance Ee (flux per unit area) received by a surface. The proportion reflected is not only determined by properties of the surface itself, but also by the spectral and angular distribution of solar radiation reaching the Earth's surface. These factors vary with atmospheric composition, geographic location, and time (see position of the Sun). While bi-hemispherical reflectance is calculated for a single angle of incidence (i.e., for a given position of the Sun), albedo is the directional integration of reflectance over all solar angles in a given period. The temporal resolution may range from seconds (as obtained from flux measurements) to daily, monthly, or annual averages.
Unless given for a specific wavelength (spectral albedo), albedo refers to the entire spectrum of solar radiation. Due to measurement constraints, it is often given for the spectrum in which most solar energy reaches the surface (between 0.3 and 3 μm). This spectrum includes visible light (0.4–0.7 μm), which explains why surfaces with a low albedo appear dark (e.g., trees absorb most radiation), whereas surfaces with a high albedo appear bright (e.g., snow reflects most radiation).
Ice–albedo feedback is a positive feedback climate process where a change in the area of ice caps, glaciers, and sea ice alters the albedo and surface temperature of a planet. Ice is very reflective, therefore it reflects far more solar energy back to space than the other types of land area or open water. Ice–albedo feedback plays an important role in global climate change.
Albedo is an important concept in climatology, astronomy, and environmental management. The average albedo of the Earth from the upper
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https://en.wikipedia.org/wiki/Altruism
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Altruism is the principle and practice of concern for the well-being and/or happiness of other humans or animals. While objects of altruistic concern vary, it is an important moral value in many cultures and religions. It may be considered a synonym of selflessness, the opposite of selfishness.
The word altruism was popularized (and possibly coined) by the French philosopher Auguste Comte in French, as , for an antonym of egoism. He derived it from the Italian , which in turn was derived from Latin , meaning "other people" or "somebody else".
Altruism, as observed in populations of organisms, is when an individual performs an action at a cost to themselves (in terms of e.g. pleasure and quality of life, time, probability of survival or reproduction) that benefits, directly or indirectly, another individual, without the expectation of reciprocity or compensation for that action.
Altruism can be distinguished from feelings of loyalty or concern for the common good. The latter are predicated upon social relationships, whilst altruism does not consider relationships. Whether "true" altruism is possible in human psychology is a subject of debate. The theory of psychological egoism suggests that no act of sharing, helping, or sacrificing can be truly altruistic, as the actor may receive an intrinsic reward in the form of personal gratification. The validity of this argument depends on whether such intrinsic rewards qualify as "benefits".
The term altruism may also refer to an ethical doctrine that claims that individuals are morally obliged to benefit others. Used in this sense, it is usually contrasted with egoism, which claims individuals are morally obligated to serve themselves first.
Effective altruism is the use of evidence and reason to determine the most effective ways to benefit others.
The notion of altruism
The concept of altruism has a history in philosophical and ethical thought. The term was coined in the 19th century by the founding sociologist and ph
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https://en.wikipedia.org/wiki/Alain%20Connes
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Alain Connes (; born 1 April 1947 in Draguignan) is a French mathematician, known for his contributions to the study of operator algebras and noncommutative geometry. He is a professor at the , , Ohio State University and Vanderbilt University. He was awarded the Fields Medal in 1982.
Career
Alain Connes attended high school at in Marseille, and was then a student of the classes préparatoires in . Between 1966 and 1970 he studed at École normale supérieure in Paris, and in 1973 he obtained a PhD from Pierre and Marie Curie University, under the supervision of Jacques Dixmier.
From 1970 to 1974 he was research fellow at the French National Centre for Scientific Research and during 1975 he held a visiting position at Queen's University at Kingston in Canada.
In 1976 he returned to France and worked as professor at Pierre and Marie Curie University until 1980 and at CNRS between 1981 and 1984. Moreover, since 1979 he holds the Léon Motchane Chair at IHES. From 1984 until his retirement in 2017 he held the chair of Analysis and Geometry at Collège de France.
In parallel, he was awarded a distinguished professorship at Vanderbilt University between 2003 and 2012, and at Ohio State University between 2012 and 2021.
In 2000 he was an invited professor at the Conservatoire national des arts et métiers.
Research
Connes' main research interests revolved around operator algebras. Besides noncommutative geometry, he has applied his works in various areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.
In his early work on von Neumann algebras in the 1970s, he succeeded in obtaining the almost complete classification of injective factors. He also formulated the Connes embedding problem.
Following this, he made contributions in operator K-theory and index theory, which culminated in the Baum–Connes conjecture. He also introduced cyclic cohomology in the early 1980s as a first step in the study of noncommutativ
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https://en.wikipedia.org/wiki/Anthropology
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Anthropology is the scientific study of humanity, concerned with human behavior, human biology, cultures, societies, and linguistics, in both the present and past, including past human species. Social anthropology studies patterns of behavior, while cultural anthropology studies cultural meaning, including norms and values. A portmanteau term sociocultural anthropology is commonly used today. Linguistic anthropology studies how language influences social life. Biological or physical anthropology studies the biological development of humans.
Archaeological anthropology, often termed as "anthropology of the past," studies human activity through investigation of physical evidence. It is considered a branch of anthropology in North America and Asia, while in Europe, archaeology is viewed as a discipline in its own right or grouped under other related disciplines, such as history and palaeontology.
Etymology
The abstract noun anthropology is first attested in reference to history. Its present use first appeared in Renaissance Germany in the works of Magnus Hundt and Otto Casmann. Their Neo-Latin derived from the combining forms of the Greek words ánthrōpos (, "human") and lógos (, "study"). Its adjectival form appeared in the works of Aristotle. It began to be used in English, possibly via French , by the early 18th century.
Origin and development of the term
Through the 19th century
In 1647, the Bartholins, early scholars of the University of Copenhagen, defined as follows:
Sporadic use of the term for some of the subject matter occurred subsequently, such as the use by Étienne Serres in 1839 to describe the natural history, or paleontology, of man, based on comparative anatomy, and the creation of a chair in anthropology and ethnography in 1850 at the French National Museum of Natural History by Jean Louis Armand de Quatrefages de Bréau. Various short-lived organizations of anthropologists had already been formed. The Société Ethnologique de Paris, the first to
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https://en.wikipedia.org/wiki/ASCII
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ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of technical limitations of computer systems at the time it was invented, ASCII has just 128 code points, of which only 95 are , which severely limited its scope. Modern computer systems have evolved to use Unicode, which has millions of code points, but the first 128 of these are the same as the ASCII set.
The Internet Assigned Numbers Authority (IANA) prefers the name US-ASCII for this character encoding.
ASCII is one of the IEEE milestones.
Overview
ASCII was developed from telegraph code. Its first commercial use was in the Teletype Model 33 and the Teletype Model 35 as a seven-bit teleprinter code promoted by Bell data services. Work on the ASCII standard began in May 1961, with the first meeting of the American Standards Association's (ASA) (now the American National Standards Institute or ANSI) X3.2 subcommittee. The first edition of the standard was published in 1963, underwent a major revision during 1967, and experienced its most recent update during 1986. Compared to earlier telegraph codes, the proposed Bell code and ASCII were both ordered for more convenient sorting (i.e., alphabetization) of lists and added features for devices other than teleprinters.
The use of ASCII format for Network Interchange was described in 1969. That document was formally elevated to an Internet Standard in 2015.
Originally based on the (modern) English alphabet, ASCII encodes 128 specified characters into seven-bit integers as shown by the ASCII chart in this article. Ninety-five of the encoded characters are printable: these include the digits 0 to 9, lowercase letters a to z, uppercase letters A to Z, and punctuation symbols. In addition, the original ASCII specification included 33 non-printing control codes which originated wit
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https://en.wikipedia.org/wiki/Arithmetic%20mean
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In mathematics and statistics, the arithmetic mean ( ), arithmetic average, or just the mean or average (when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a survey. The term "arithmetic mean" is preferred in some mathematics and statistics contexts because it helps distinguish it from other types of means, such as geometric and harmonic.
In addition to mathematics and statistics, the arithmetic mean is frequently used in economics, anthropology, history, and almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.
While the arithmetic mean is often used to report central tendencies, it is not a robust statistic: it is greatly influenced by outliers (values much larger or smaller than most others). For skewed distributions, such as the distribution of income for which a few people's incomes are substantially higher than most people's, the arithmetic mean may not coincide with one's notion of "middle". In that case, robust statistics, such as the median, may provide a better description of central tendency.
Definition
Given a data set , the arithmetic mean (also mean or average), denoted (read bar), is the mean of the values .
The arithmetic mean is a data set's most commonly used and readily understood measure of central tendency. In statistics, the term average refers to any measurement of central tendency. The arithmetic mean of a set of observed data is equal to the sum of the numerical values of each observation, divided by the total number of observations. Symbolically, for a data set consisting of the values , the arithmetic mean is defined by the formula:
(For an explanation of the summation operator, see summation.)
For example, if the monthly salaries of employees are , then the arithmetic mean is:
If the data set is a s
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https://en.wikipedia.org/wiki/Algae
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Algae (, ; : alga ) is an informal term for a large and diverse group of photosynthetic, eukaryotic organisms. It is a polyphyletic grouping that includes species from multiple distinct clades. Included organisms range from unicellular microalgae, such as Chlorella, Prototheca and the diatoms, to multicellular forms, such as the giant kelp, a large brown alga which may grow up to in length. Most are aquatic and lack many of the distinct cell and tissue types, such as stomata, xylem and phloem that are found in land plants. The largest and most complex marine algae are called seaweeds, while the most complex freshwater forms are the Charophyta, a division of green algae which includes, for example, Spirogyra and stoneworts. Algae that are carried by water are plankton, specifically phytoplankton.
Algae constitute a polyphyletic group since they do not include a common ancestor, and although their plastids seem to have a single origin, from cyanobacteria, they were acquired in different ways. Green algae are examples of algae that have primary chloroplasts derived from endosymbiotic cyanobacteria. Diatoms and brown algae are examples of algae with secondary chloroplasts derived from an endosymbiotic red alga. Algae exhibit a wide range of reproductive strategies, from simple asexual cell division to complex forms of sexual reproduction.
Algae lack the various structures that characterize land plants, such as the phyllids (leaf-like structures) of bryophytes, rhizoids of non-vascular plants, and the roots, leaves, and other organs found in tracheophytes (vascular plants). Most are phototrophic, although some are mixotrophic, deriving energy both from photosynthesis and uptake of organic carbon either by osmotrophy, myzotrophy, or phagotrophy. Some unicellular species of green algae, many golden algae, euglenids, dinoflagellates, and other algae have become heterotrophs (also called colorless or apochlorotic algae), sometimes parasitic, relying entirely on external e
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https://en.wikipedia.org/wiki/Abacus
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The abacus (: abaci or abacuses), also called a counting frame, is a hand-operated calculating tool of unknown origin used since ancient times in the ancient Near East, Europe, China, and Russia, millennia before the adoption of the Hindu-Arabic numeral system.
The abacus consists of a two-dimensional array of slidable beads (or similar objects). In their earliest designs, the beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation.
Each rod typically represents one digit of a multi-digit number laid out using a positional numeral system such as base ten (though some cultures used different numerical bases). Roman and East Asian abacuses use a system resembling bi-quinary coded decimal, with a top deck (containing one or two beads) representing fives and a bottom deck (containing four or five beads) representing ones. Natural numbers are normally used, but some allow simple fractional components (e.g. , , and in Roman abacus), and a decimal point can be imagined for fixed-point arithmetic.
Any particular abacus design supports multiple methods to perform calculations, including addition, subtraction, multiplication, division, and square and cube roots. The beads are first arranged to represent a number, then are manipulated to perform a mathematical operation with another number, and their final position can be read as the result (or can be used as the starting number for subsequent operations).
In the ancient world, abacuses were a practical calculating tool. Although calculators and computers are commonly used today instead of abacuses, abacuses remain in everyday use in some countries. The abacus has an advantage of not requiring a writing implement and paper (needed for algorism) or an electric power source. Merchants, traders, and clerks in some parts of Eastern Europe, Russia, China, and Africa use abacuses. The abacus remains in common use as a scoring s
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https://en.wikipedia.org/wiki/Bitumen
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Bitumen (, ) is an immensely viscous constituent of petroleum. Depending on its exact composition it can be a sticky, black liquid or an apparently solid mass that behaves as a liquid over very large time scales. In the U.S., the material is commonly referred to as asphalt. Whether found in natural deposits or refined from petroleum, the substance is classed as a pitch. Prior to the 20th century the term asphaltum was in general use. The word derives from the ancient Greek ἄσφαλτος ásphaltos, which referred to natural bitumen or pitch. The largest natural deposit of bitumen in the world, estimated to contain 10 million tons, is the Pitch Lake of southwest Trinidad.
70% of annual bitumen production destined for road construction, its primary use. In this application bitumen is used to bind aggregate particles like gravel and forms a substance referred to as asphalt concrete, which is colloquially termed asphalt. Its other main uses lie in bituminous waterproofing products, such as roofing felt and roof sealant.
In material sciences and engineering the terms "asphalt" and "bitumen" are often used interchangeably and refer both to natural and manufactured forms of the substance, although there is regional variation as to which term is most common. Worldwide, geologists tend to favor the term "bitumen" for the naturally occurring material. For the manufactured material, which is a refined residue from the distillation process of selected crude oils, "bitumen" is the prevalent term in much of the world; however, in American English, "asphalt" is more commonly used. To help avoid confusion, the phrases "liquid asphalt", "asphalt binder", or "asphalt cement" are used in the U.S. Colloquially, various forms of asphalt are sometimes referred to as "tar", as in the name of the La Brea Tar Pits.
Naturally occurring bitumen is sometimes specified by the term "crude bitumen". Its viscosity is similar to that of cold molasses while the material obtained from the fractional di
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https://en.wikipedia.org/wiki/Astronaut
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An astronaut (from the Ancient Greek (), meaning 'star', and (), meaning 'sailor') is a person trained, equipped, and deployed by a human spaceflight program to serve as a commander or crew member aboard a spacecraft. Although generally reserved for professional space travelers, the term is sometimes applied to anyone who travels into space, including scientists, politicians, journalists, and tourists.
"Astronaut" technically applies to all human space travelers regardless of nationality. However, astronauts fielded by Russia or the Soviet Union are typically known instead as cosmonauts (from the Russian "kosmos" (космос), meaning "space", also borrowed from Greek ). Comparatively recent developments in crewed spaceflight made by China have led to the rise of the term taikonaut (from the Mandarin "tàikōng" (), meaning "space"), although its use is somewhat informal and its origin is unclear. In China, the People's Liberation Army Astronaut Corps astronauts and their foreign counterparts are all officially called hángtiānyuán (, meaning "heaven navigator" or literally "heaven-sailing staff").
Since 1961, 600 astronauts have flown in space. Until 2002, astronauts were sponsored and trained exclusively by governments, either by the military or by civilian space agencies. With the suborbital flight of the privately funded SpaceShipOne in 2004, a new category of astronaut was created: the commercial astronaut.
Definition
The criteria for what constitutes human spaceflight vary, with some focus on the point where the atmosphere becomes so thin that centrifugal force, rather than aerodynamic force, carries a significant portion of the weight of the flight object. The Fédération Aéronautique Internationale (FAI) Sporting Code for astronautics recognizes only flights that exceed the Kármán line, at an altitude of . In the United States, professional, military, and commercial astronauts who travel above an altitude of are awarded astronaut wings.
, 552 people from 3
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https://en.wikipedia.org/wiki/Atomic%20number
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The atomic number or nuclear charge number (symbol Z) of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (np) or the number of protons found in the nucleus of every atom of that element. The atomic number can be used to uniquely identify ordinary chemical elements. In an ordinary uncharged atom, the atomic number is also equal to the number of electrons.
For an ordinary atom which contains protons, neutrons and electrons, the sum of the atomic number Z and the neutron number N gives the atom's atomic mass number A. Since protons and neutrons have approximately the same mass (and the mass of the electrons is negligible for many purposes) and the mass defect of the nucleon binding is always small compared to the nucleon mass, the atomic mass of any atom, when expressed in daltons (making a quantity called the "relative isotopic mass"), is within 1% of the whole number A.
Atoms with the same atomic number but different neutron numbers, and hence different mass numbers, are known as isotopes. A little more than three-quarters of naturally occurring elements exist as a mixture of isotopes (see monoisotopic elements), and the average isotopic mass of an isotopic mixture for an element (called the relative atomic mass) in a defined environment on Earth determines the element's standard atomic weight. Historically, it was these atomic weights of elements (in comparison to hydrogen) that were the quantities measurable by chemists in the 19th century.
The conventional symbol Z comes from the German word 'number', which, before the modern synthesis of ideas from chemistry and physics, merely denoted an element's numerical place in the periodic table, whose order was then approximately, but not completely, consistent with the order of the elements by atomic weights. Only after 1915, with the suggestion and evidence that this Z number was also the nuclear charge and a physi
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https://en.wikipedia.org/wiki/Anatomy
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Anatomy () is the branch of biology concerned with the study of the structure of organisms and their parts. Anatomy is a branch of natural science that deals with the structural organization of living things. It is an old science, having its beginnings in prehistoric times. Anatomy is inherently tied to developmental biology, embryology, comparative anatomy, evolutionary biology, and phylogeny, as these are the processes by which anatomy is generated, both over immediate and long-term timescales. Anatomy and physiology, which study the structure and function of organisms and their parts respectively, make a natural pair of related disciplines, and are often studied together. Human anatomy is one of the essential basic sciences that are applied in medicine.
Anatomy is a complex and dynamic field that is constantly evolving as new discoveries are made. In recent years, there has been a significant increase in the use of advanced imaging techniques, such as MRI and CT scans, which allow for more detailed and accurate visualizations of the body's structures.
The discipline of anatomy is divided into macroscopic and microscopic parts. Macroscopic anatomy, or gross anatomy, is the examination of an animal's body parts using unaided eyesight. Gross anatomy also includes the branch of superficial anatomy. Microscopic anatomy involves the use of optical instruments in the study of the tissues of various structures, known as histology, and also in the study of cells.
The history of anatomy is characterized by a progressive understanding of the functions of the organs and structures of the human body. Methods have also improved dramatically, advancing from the examination of animals by dissection of carcasses and cadavers (corpses) to 20th-century medical imaging techniques, including X-ray, ultrasound, and magnetic resonance imaging.
Etymology and definition
Derived from the Greek anatomē "dissection" (from anatémnō "I cut up, cut open" from ἀνά aná "up", and τέμνω té
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https://en.wikipedia.org/wiki/Ambiguity
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Ambiguity is the type of meaning in which a phrase, statement, or resolution is not explicitly defined, making several interpretations plausible. A common aspect of ambiguity is uncertainty. It is thus an attribute of any idea or statement whose intended meaning cannot be definitively resolved, according to a rule or process with a finite number of steps. (The prefix ambi- reflects the idea of "two," as in "two meanings.")
The concept of ambiguity is generally contrasted with vagueness. In ambiguity, specific and distinct interpretations are permitted (although some may not be immediately obvious), whereas with vague information it is difficult to form any interpretation at the desired level of specificity.
Linguistic forms
Lexical ambiguity is contrasted with semantic ambiguity. The former represents a choice between a finite number of known and meaningful context-dependent interpretations. The latter represents a choice between any number of possible interpretations, none of which may have a standard agreed-upon meaning. This form of ambiguity is closely related to vagueness.
Ambiguity in human language is argued to reflect principles of efficient communication. Languages that communicate efficiently will avoid sending information that is redundant with information provided in the context. This can be shown mathematically to result in a system which is ambiguous when context is neglected. In this way, ambiguity is viewed as a generally useful feature of a linguistic system.
Linguistic ambiguity can be a problem in law, because the interpretation of written documents and oral agreements is often of paramount importance.
Lexical ambiguity
The lexical ambiguity of a word or phrase applies to it having more than one meaning in the language to which the word belongs. "Meaning" here refers to whatever should be represented by a good dictionary. For instance, the word "bank" has several distinct lexical definitions, including "financial institution" and "edge of
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https://en.wikipedia.org/wiki/Algorithms%20%28journal%29
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Algorithms is a monthly peer-reviewed open-access scientific journal of mathematics, covering design, analysis, and experiments on algorithms. The journal is published by MDPI and was established in 2008. The founding editor-in-chief was Kazuo Iwama (Kyoto University). From May 2014 to September 2019, the editor-in-chief was Henning Fernau (Universität Trier). The current editor-in-chief is Frank Werner (Otto-von-Guericke-Universität Magdeburg).
Abstracting and indexing
According to the Journal Citation Reports, the journal has a 2022 impact factor of 2.3.
The journal is abstracted and indexed in:
See also
Journals with similar scope include:
ACM Transactions on Algorithms
Algorithmica
Journal of Algorithms (Elsevier)
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https://en.wikipedia.org/wiki/Algorithm
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In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually. Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus".
In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result.
As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.
History
Ancient algorithms
Since antiquity, step-by-step procedures for solving mathematical problems have been attested. This includes Babylonian mathematics (around 2500 BC), Egyptian mathematics (around 1550 BC), Indian mathematics (around 800 BC and later; e.g. Shulba Sutras, Kerala School, and Brāhmasphuṭasiddhānta), The Ifa Oracle (around 500 BC), Greek mathematics (around 240 BC, e.g. sieve of Eratosthenes and Euclidean algorithm), and Arabic mathematics (9th century, e.g. cryptographic algorithms for
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https://en.wikipedia.org/wiki/Apple%20Inc.
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Apple Inc. is an American multinational technology company headquartered in Cupertino, California. , Apple is the world's biggest company by market capitalization, and with the largest technology company by 2022 revenue. , Apple is the fourth-largest personal computer vendor by unit sales; the largest manufacturing company by revenue; and the second-largest mobile phone manufacturer in the world. It is considered one of the Big Five American information technology companies, alongside Alphabet (parent company of Google), Amazon, Meta Platforms, and Microsoft.
Apple was founded as Apple Computer Company on April 1, 1976, by Steve Wozniak, Steve Jobs and Ronald Wayne to develop and sell Wozniak's Apple I personal computer. It was incorporated by Jobs and Wozniak as Apple Computer, Inc. in 1977. The company's second computer, the Apple II, became a best seller and one of the first mass-produced microcomputers. Apple went public in 1980 to instant financial success. The company developed computers featuring innovative graphical user interfaces, including the 1984 original Macintosh, announced that year in a critically acclaimed advertisement called "1984". By 1985, the high cost of its products, and power struggles between executives, caused problems. Wozniak stepped back from Apple and pursued other ventures, while Jobs resigned and founded NeXT, taking some Apple employees with him.
As the market for personal computers expanded and evolved throughout the 1990s, Apple lost considerable market share to the lower-priced duopoly of the Microsoft Windows operating system on Intel-powered PC clones (also known as "Wintel"). In 1997, weeks away from bankruptcy, the company bought NeXT to resolve Apple's unsuccessful operating system strategy and entice Jobs back to the company. Over the next decade, Jobs guided Apple back to profitability through a number of tactics including introducing the iMac, iPod, iPhone and iPad to critical acclaim, launching the "Think different"
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https://en.wikipedia.org/wiki/ABBA
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ABBA ( , ; formerly named Björn & Benny, Agnetha & Anni-Frid or Björn & Benny, Agnetha & Frida) are a Swedish pop supergroup formed in Stockholm in 1972 by Agnetha Fältskog, Björn Ulvaeus, Benny Andersson, and Anni-Frid Lyngstad. The group's name is an acronym of the first letters of their first names arranged as a palindrome. They are one of the most popular and successful musical groups of all time, and are one of the best-selling music acts in the history of popular music, topping the charts worldwide from 1974 to 1982, and in 2022.
In , ABBA were 's first winner of the Eurovision Song Contest with the song "Waterloo", which in 2005 was chosen as the best song in the competition's history as part of the 50th anniversary celebration of the contest. During the band's main active years, it consisted of two married couples: Fältskog and Ulvaeus, and Lyngstad and Andersson. With the increase of their popularity, their personal lives suffered, which eventually resulted in the collapse of both marriages. The relationship changes were reflected in the group's music, with later compositions featuring darker and more introspective lyrics. After ABBA disbanded in December 1982, Andersson and Ulvaeus continued their success writing music for multiple audiences including stage, musicals and movies, while Fältskog and Lyngstad pursued solo careers.
Ten years after the group broke up, a compilation, ABBA Gold, was released becoming a worldwide best-seller. In 1999, ABBA's music was adapted into Mamma Mia!, a stage musical that toured worldwide and, as of April 2022, is still in the top-ten longest running productions on both Broadway (closed in 2015) and the West End (still running). A film of the same name, released in 2008, became the highest-grossing film in the United Kingdom that year. A sequel, Mamma Mia! Here We Go Again, was released in 2018.
In 2016, the group reunited and started working on a digital avatar concert tour. Newly recorded songs were announced in 2018
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https://en.wikipedia.org/wiki/Argon
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Argon is a chemical element with the symbol Ar and atomic number 18. It is in group 18 of the periodic table and is a noble gas. Argon is the third-most abundant gas in Earth's atmosphere, at 0.934% (9340 ppmv). It is more than twice as abundant as water vapor (which averages about 4000 ppmv, but varies greatly), 23 times as abundant as carbon dioxide (400 ppmv), and more than 500 times as abundant as neon (18 ppmv). Argon is the most abundant noble gas in Earth's crust, comprising 0.00015% of the crust.
Nearly all of the argon in Earth's atmosphere is radiogenic argon-40, derived from the decay of potassium-40 in Earth's crust. In the universe, argon-36 is by far the most common argon isotope, as it is the most easily produced by stellar nucleosynthesis in supernovas.
The name "argon" is derived from the Greek word , neuter singular form of meaning 'lazy' or 'inactive', as a reference to the fact that the element undergoes almost no chemical reactions. The complete octet (eight electrons) in the outer atomic shell makes argon stable and resistant to bonding with other elements. Its triple point temperature of 83.8058 K is a defining fixed point in the International Temperature Scale of 1990.
Argon is extracted industrially by the fractional distillation of liquid air. Argon is mostly used as an inert shielding gas in welding and other high-temperature industrial processes where ordinarily unreactive substances become reactive; for example, an argon atmosphere is used in graphite electric furnaces to prevent the graphite from burning. Argon is also used in incandescent, fluorescent lighting, and other gas-discharge tubes. Argon makes a distinctive blue-green gas laser. Argon is also used in fluorescent glow starters.
Characteristics
Argon has approximately the same solubility in water as oxygen and is 2.5 times more soluble in water than nitrogen. Argon is colorless, odorless, nonflammable and nontoxic as a solid, liquid or gas. Argon is chemically inert under
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https://en.wikipedia.org/wiki/Arsenic
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Arsenic is a chemical element with the symbol As and atomic number 33. Arsenic occurs in many minerals, usually in combination with sulfur and metals, but also as a pure elemental crystal. Arsenic is a metalloid. It has various allotropes, but only the grey form, which has a metallic appearance, is important to industry.
The primary use of arsenic is in alloys of lead (for example, in car batteries and ammunition). Arsenic is a common n-type dopant in semiconductor electronic devices. It is also a component of the III–V compound semiconductor gallium arsenide. Arsenic and its compounds, especially the trioxide, are used in the production of pesticides, treated wood products, herbicides, and insecticides. These applications are declining with the increasing recognition of the toxicity of arsenic and its compounds.
A few species of bacteria are able to use arsenic compounds as respiratory metabolites. Trace quantities of arsenic are an essential dietary element in rats, hamsters, goats, chickens, and presumably other species. A role in human metabolism is not known. However, arsenic poisoning occurs in multicellular life if quantities are larger than needed. Arsenic contamination of groundwater is a problem that affects millions of people across the world.
The United States' Environmental Protection Agency states that all forms of arsenic are a serious risk to human health. The United States' Agency for Toxic Substances and Disease Registry ranked arsenic as number 1 in its 2001 Priority List of Hazardous Substances at Superfund sites. Arsenic is classified as a Group-A carcinogen.
Characteristics
Physical characteristics
The three most common arsenic allotropes are grey, yellow, and black arsenic, with grey being the most common. Grey arsenic (α-As, space group Rm No. 166) adopts a double-layered structure consisting of many interlocked, ruffled, six-membered rings. Because of weak bonding between the layers, grey arsenic is brittle and has a relatively low Mo
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https://en.wikipedia.org/wiki/Atom
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An atom is a particle that consists of a nucleus of protons and neutrons surrounded by an electromagnetically-bound cloud of electrons. The atom is the basic particle of the chemical elements, and the chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. The number of neutrons defines the isotope of the element.
Atoms are extremely small, typically around 100 picometers across. A human hair is about a million carbon atoms wide. This is smaller than the shortest wavelength of visible light, which means humans cannot see atoms with conventional microscopes. Atoms are so small that accurately predicting their behavior using classical physics is not possible due to quantum effects.
More than 99.94% of an atom's mass is in the nucleus. Each proton has a positive electric charge, while each electron has a negative charge, and the neutrons, if any are present, have no electric charge. If the numbers of protons and electrons are equal, as they normally are, then the atom is electrically neutral. If an atom has more electrons than protons, then it has an overall negative charge, and is called a negative ion (or anion). Conversely, if it has more protons than electrons, it has a positive charge, and is called a positive ion (or cation).
The electrons of an atom are attracted to the protons in an atomic nucleus by the electromagnetic force. The protons and neutrons in the nucleus are attracted to each other by the nuclear force. This force is usually stronger than the electromagnetic force that repels the positively charged protons from one another. Under certain circumstances, the repelling electromagnetic force becomes stronger than the nuclear force. In this case, the nucleus splits and leaves behind different elements. This is a form of nuclear decay.
Atoms can attach to one or more other atoms by chemical bonds to
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https://en.wikipedia.org/wiki/Aluminium
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Aluminium (aluminum in North American English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals; about one-third that of steel. It has a great affinity towards oxygen, forming a protective layer of oxide on the surface when exposed to air. Aluminium visually resembles silver, both in its color and in its great ability to reflect light. It is soft, nonmagnetic and ductile. It has one stable isotope: 27Al, which is highly abundant, making aluminium the twelfth-most common element in the universe. The radioactivity of 26Al is used in radiometric dating.
Chemically, aluminium is a post-transition metal in the boron group; as is common for the group, aluminium forms compounds primarily in the +3 oxidation state. The aluminium cation Al3+ is small and highly charged; as such, it has more polarizing power, and bonds formed by aluminium have a more covalent character. The strong affinity of aluminium for oxygen leads to the common occurrence of its oxides in nature. Aluminium is found on Earth primarily in rocks in the crust, where it is the third-most abundant element, after oxygen and silicon, rather than in the mantle, and virtually never as the free metal. It is obtained industrially by mining bauxite, a sedimentary rock rich in aluminium minerals.
The discovery of aluminium was announced in 1825 by Danish physicist Hans Christian Ørsted. The first industrial production of aluminium was initiated by French chemist Henri Étienne Sainte-Claire Deville in 1856. Aluminium became much more available to the public with the Hall–Héroult process developed independently by French engineer Paul Héroult and American engineer Charles Martin Hall in 1886, and the mass production of aluminium led to its extensive use in industry and everyday life. In World Wars I and II, aluminium was a crucial strategic resource for aviation. In 1954, aluminium became the most produced non-ferrous metal, surpassing coppe
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https://en.wikipedia.org/wiki/Andrey%20Markov
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Andrey Andreyevich Markov (14 June 1856 – 20 July 1922) was a Russian mathematician best known for his work on stochastic processes. A primary subject of his research later became known as the Markov chain. He was also a strong, close to master-level chess player.
Markov and his younger brother Vladimir Andreevich Markov (1871–1897) proved the Markov brothers' inequality.
His son, another Andrey Andreyevich Markov (1903–1979), was also a notable mathematician, making contributions to constructive mathematics and recursive function theory.
Biography
Andrey Markov was born on 14 June 1856 in Russia. He attended the St. Petersburg Grammar School, where some teachers saw him as a rebellious student. In his academics he performed poorly in most subjects other than mathematics. Later in life he attended Saint Petersburg Imperial University (now Saint Petersburg State University). Among his teachers were Yulian Sokhotski (differential calculus, higher algebra), Konstantin Posse (analytic geometry), Yegor Zolotarev (integral calculus), Pafnuty Chebyshev (number theory and probability theory), Aleksandr Korkin (ordinary and partial differential equations), Mikhail Okatov (mechanism theory), Osip Somov (mechanics), and Nikolai Budajev (descriptive and higher geometry). He completed his studies at the university and was later asked if he would like to stay and have a career as a Mathematician. He later taught at high schools and continued his own mathematical studies. In this time he found a practical use for his mathematical skills. He figured out that he could use chains to model the alliteration of vowels and consonants in Russian literature. He also contributed to many other mathematical aspects in his time. He died at age 66 on 20 July 1922.
Timeline
In 1877, Markov was awarded a gold medal for his outstanding solution of the problem
About Integration of Differential Equations by Continued Fractions with an Application to the Equation .
During the following year,
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https://en.wikipedia.org/wiki/Axiom
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An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.
The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning.
In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom". Logical axioms are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (A and B) implies A), while non-logical axioms (e.g., ) are substantive assertions about the elements of the domain of a specific mathematical theory, such as arithmetic.
Non-logical axioms may also be called "postulates" or "assumptions". In most cases, a non-logical axiom is simply a formal logical expression used in deduction to build a mathematical theory, and might or might not be self-evident in nature (e.g., the parallel postulate in Euclidean geometry). To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms), and there are typically many ways to axiomatize a given mathematical domain.
Any axiom is a statement that serves as a starting point from which other statements are logically derived. Whether it is meaningful (and, if so, what it means) for an axiom to be "true" is a subject of debate in the philosophy of mathematics.
Etymology
The word axiom comes from the Greek word (axíōma), a verbal noun from the verb (axioein), meaning "to deem worthy", but also "to require", which in turn comes from (áxios), meaning "being in balance", and hence "having (the same) value (as)", "worthy", "proper". Among the ancient Greek philosophers an a
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https://en.wikipedia.org/wiki/Acute%20disseminated%20encephalomyelitis
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Acute disseminated encephalomyelitis (ADEM), or acute demyelinating encephalomyelitis, is a rare autoimmune disease marked by a sudden, widespread attack of inflammation in the brain and spinal cord. As well as causing the brain and spinal cord to become inflamed, ADEM also attacks the nerves of the central nervous system and damages their myelin insulation, which, as a result, destroys the white matter. The cause is often a trigger such as from viral infection or vaccinations.
ADEM's symptoms resemble the symptoms of multiple sclerosis (MS), so the disease itself is sorted into the classification of the multiple sclerosis borderline diseases. However, ADEM has several features that distinguish it from MS. Unlike MS, ADEM occurs usually in children and is marked with rapid fever, although adolescents and adults can get the disease too. ADEM consists of a single flare-up whereas MS is marked with several flare-ups (or relapses), over a long period of time. Relapses following ADEM are reported in up to a quarter of patients, but the majority of these 'multiphasic' presentations following ADEM likely represent MS. ADEM is also distinguished by a loss of consciousness, coma and death, which is very rare in MS, except in severe cases.
It affects about 8 per 1,000,000 people per year. Although it occurs in all ages, most reported cases are in children and adolescents, with the average age around 5 to 8 years old. The disease affects males and females almost equally. ADEM shows seasonal variation with higher incidence in winter and spring months which may coincide with higher viral infections during these months. The mortality rate may be as high as 5%; however, full recovery is seen in 50 to 75% of cases with increase in survival rates up to 70 to 90% with figures including minor residual disability as well. The average time to recover from ADEM flare-ups is one to six months.
ADEM produces multiple inflammatory lesions in the brain and spinal cord, particularly in the
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https://en.wikipedia.org/wiki/Ada%20Lovelace
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Augusta Ada King, Countess of Lovelace (née Byron; 10 December 1815 – 27 November 1852) was an English mathematician and writer, chiefly known for her work on Charles Babbage's proposed mechanical general-purpose computer, the Analytical Engine. She was the first to recognise that the machine had applications beyond pure calculation.
Ada Byron was the only legitimate child of poet Lord Byron and reformer Lady Byron. All Lovelace's half-siblings, Lord Byron's other children, were born out of wedlock to other women. Byron separated from his wife a month after Ada was born and left England forever. He died in Greece when Ada was eight. Her mother remained bitter and promoted Ada's interest in mathematics and logic in an effort to prevent her from developing her father's perceived insanity. Despite this, Ada remained interested in him, naming her two sons Byron and Gordon. Upon her death, she was buried next to him at her request. Although often ill in her childhood, Ada pursued her studies assiduously. She married William King in 1835. King was made Earl of Lovelace in 1838, Ada thereby becoming Countess of Lovelace.
Her educational and social exploits brought her into contact with scientists such as Andrew Crosse, Charles Babbage, Sir David Brewster, Charles Wheatstone, Michael Faraday, and the author Charles Dickens, contacts which she used to further her education. Ada described her approach as "poetical science" and herself as an "Analyst (& Metaphysician)".
When she was eighteen, her mathematical talents led her to a long working relationship and friendship with fellow British mathematician Charles Babbage, who is known as "the father of computers". She was in particular interested in Babbage's work on the Analytical Engine. Lovelace first met him in June 1833, through their mutual friend, and her private tutor, Mary Somerville.
Between 1842 and 1843, Ada translated an article by the military engineer Luigi Menabrea (later Prime Minister of Italy) about the A
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https://en.wikipedia.org/wiki/Absolute%20value
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In mathematics, the absolute value or modulus of a real number , is the non-negative value without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and For example, the absolute value of 3 and the absolute value of −3 is The absolute value of a number may be thought of as its distance from zero.
Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.
Terminology and notation
In 1806, Jean-Robert Argand introduced the term module, meaning unit of measure in French, specifically for the complex absolute value, and it was borrowed into English in 1866 as the Latin equivalent modulus. The term absolute value has been used in this sense from at least 1806 in French and 1857 in English. The notation , with a vertical bar on each side, was introduced by Karl Weierstrass in 1841. Other names for absolute value include numerical value and magnitude. In programming languages and computational software packages, the absolute value of is generally represented by abs(x), or a similar expression.
The vertical bar notation also appears in a number of other mathematical contexts: for example, when applied to a set, it denotes its cardinality; when applied to a matrix, it denotes its determinant. Vertical bars denote the absolute value only for algebraic objects for which the notion of an absolute value is defined, notably an element of a normed division algebra, for example a real number, a complex number, or a quaternion. A closely related but distinct notation is the use of vertical bars for either the Euclidean norm or sup norm of a vector although double vertical bars with subscripts respe
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https://en.wikipedia.org/wiki/Analog%20signal
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An analog signal is any continuous-time signal representing some other quantity, i.e., analogous to another quantity. For example, in an analog audio signal, the instantaneous signal voltage varies continuously with the pressure of the sound waves.
In contrast, a digital signal represents the original time-varying quantity as a sampled sequence of quantized values. Digital sampling imposes some bandwidth and dynamic range constraints on the representation and adds quantization error.
The term analog signal usually refers to electrical signals; however, mechanical, pneumatic, hydraulic, and other systems may also convey or be considered analog signals.
Representation
An analog signal uses some property of the medium to convey the signal's information. For example, an aneroid barometer uses rotary position as the signal to convey pressure information. In an electrical signal, the voltage, current, or frequency of the signal may be varied to represent the information.
Any information may be conveyed by an analog signal; such a signal may be a measured response to changes in a physical variable, such as sound, light, temperature, position, or pressure. The physical variable is converted to an analog signal by a transducer. For example, sound striking the diaphragm of a microphone induces corresponding fluctuations in the current produced by a coil in an electromagnetic microphone or the voltage produced by a condenser microphone. The voltage or the current is said to be an analog of the sound.
Noise
An analog signal is subject to electronic noise and distortion introduced by communication channels, recording and signal processing operations, which can progressively degrade the signal-to-noise ratio (SNR). As the signal is transmitted, copied, or processed, the unavoidable noise introduced in the signal path will accumulate as a generation loss, progressively and irreversibly degrading the SNR, until in extreme cases, the signal can be overwhelmed. Noise can sho
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https://en.wikipedia.org/wiki/Aspect%20ratio
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The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangle is oriented as a "landscape".
The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal fraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, and 1.6 are all ways of representing the same aspect ratio.
In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side.
Applications and uses
The term is most commonly used with reference to:
Graphic / image
Image aspect ratio
Display aspect ratio
Paper size
Standard photographic print sizes
Motion picture film formats
Standard ad size
Pixel aspect ratio
Photolithography: the aspect ratio of an etched, or deposited structure is the ratio of the height of its vertical side wall to its width.
HARMST High Aspect Ratios allow the construction of tall microstructures without slant
Tire code
Tire sizing
Turbocharger impeller sizing
Wing aspect ratio of an aircraft or bird
Astigmatism of an optical lens
Nanorod dimensions
Shape factor (image analysis and microscopy)
Finite Element Analysis
Aspect ratios of simple shapes
Rectangles
For a rectangle, the aspect ratio denotes the ratio of the width to the height of the rectangle. A square has the smallest possible aspect ratio of 1:1.
Examples:
4:3 = 1.: Some (not all) 20th century computer monitors (VGA, XGA, etc.), standard-definition television
: international paper sizes (ISO 216)
3:2 = 1.5: 35mm still camera film, iPhone (until iPhone 5) displays
16:10 = 1.6: commonly used widescreen computer displays (WXGA)
Φ:1 = 1.618...: golden ratio, close to 16:10
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https://en.wikipedia.org/wiki/Algorithms%20for%20calculating%20variance
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Algorithms for calculating variance play a major role in computational statistics. A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
Naïve algorithm
A formula for calculating the variance of an entire population of size N is:
Using Bessel's correction to calculate an unbiased estimate of the population variance from a finite sample of n observations, the formula is:
Therefore, a naïve algorithm to calculate the estimated variance is given by the following:
Let
For each datum :
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.
Because and can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation. Thus this algorithm should not be used in practice, and several alternate, numerically stable, algorithms have been proposed. This is particularly bad if the standard deviation is small relative to the mean.
Computing shifted data
The variance is invariant with respect to changes in a location parameter, a property which can be used to avoid the catastrophic cancellation in this formula.
with any constant, which leads to the new formula
the closer is to the mean value the more accurate the result will be, but just choosing a value inside the
samples range will guarantee the desired stability. If the values are small then there are no problems with the sum of its squares, on the contrary, if they are large it necessarily means that the variance is large as well. In any case the second term in the formula is always smaller than the first one therefore no cancellation may occur.
If just the first sample is taken as the algorithm can be written in Py
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https://en.wikipedia.org/wiki/Analysis
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Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development.
The word comes from the Ancient Greek (analysis, "a breaking-up" or "an untying;" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses.
As a formal concept, the method has variously been ascribed to Alhazen, René Descartes (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name).
The converse of analysis is synthesis: putting the pieces back together again in a new or different whole.
Applications
Science
The field of chemistry uses analysis in three ways: to identify the components of a particular chemical compound (qualitative analysis), to identify the proportions of components in a mixture (quantitative analysis), and to break down chemical processes and examine chemical reactions between elements of matter. For an example of its use, analysis of the concentration of elements is important in managing a nuclear reactor, so nuclear scientists will analyze neutron activation to develop discrete measurements within vast samples. A matrix can have a considerable effect on the way a chemical analysis is conducted and the quality of its results. Analysis can be done manually or with a device.
Types of Analysis:
A) Qualitative Analysis: It is concerned with which components are in a given sample or compound.
Example: Precipitation reaction
B) Quantitative Analysis: It is to determine the quantity of individual component present in a given sample or compound.
Example: To find concentration by uv-spectrophotometer.
Isotopes
Chemists can use isotope analysis to assist analysts with i
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https://en.wikipedia.org/wiki/Augustin-Jean%20Fresnel
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Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theory, from the late 1830s until the end of the 19th century. He is perhaps better known for inventing the catadioptric (reflective/refractive) Fresnel lens and for pioneering the use of "stepped" lenses to extend the visibility of lighthouses, saving countless lives at sea. The simpler dioptric (purely refractive) stepped lens, first proposed by Count Buffon and independently reinvented by Fresnel, is used in screen magnifiers and in condenser lenses for overhead projectors.
By expressing Huygens's principle of secondary waves and Young's principle of interference in quantitative terms, and supposing that simple colors consist of sinusoidal waves, Fresnel gave the first satisfactory explanation of diffraction by straight edges, including the first satisfactory wave-based explanation of rectilinear propagation. Part of his argument was a proof that the addition of sinusoidal functions of the same frequency but different phases is analogous to the addition of forces with different directions. By further supposing that light waves are purely transverse, Fresnel explained the nature of polarization, the mechanism of chromatic polarization, and the transmission and reflection coefficients at the interface between two transparent isotropic media. Then, by generalizing the direction-speed-polarization relation for calcite, he accounted for the directions and polarizations of the refracted rays in doubly-refractive crystals of the biaxial class (those for which Huygens's secondary wavefronts are not axisymmetric). The period between the first publication of his pure-transverse-wave hypothesis, and the submission of his first correct solution to the biaxial problem, was less than a year.
Later, he coined the terms linear polarization, circular
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https://en.wikipedia.org/wiki/Ardipithecus
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Ardipithecus is a genus of an extinct hominine that lived during the Late Miocene and Early Pliocene epochs in the Afar Depression, Ethiopia. Originally described as one of the earliest ancestors of humans after they diverged from the chimpanzees, the relation of this genus to human ancestors and whether it is a hominin is now a matter of debate. Two fossil species are described in the literature: A. ramidus, which lived about 4.4 million years ago during the early Pliocene, and A. kadabba, dated to approximately 5.6 million years ago (late Miocene). Initial behavioral analysis indicated that Ardipithecus could be very similar to chimpanzees, however more recent analysis based on canine size and lack of canine sexual dimorphism indicates that Ardipithecus was characterised by reduced aggression, and that they more closely resemble bonobos.
Some analyses describe Australopithecus as being sister to Ardipithecus ramidus specifically. This means that Australopithecus is distinctly closer related to Ardipithecus ramidus than Ardipithecus kadabba. Cladistically, then, Australopithecus (and eventually Homo sapiens) indeed emerged within the Ardipithecus lineage, and this lineage is not literally extinct.
Ardipithecus ramidus
A. ramidus was named in September 1994. The first fossil found was dated to 4.4 million years ago on the basis of its stratigraphic position between two volcanic strata: the basal Gaala Tuff Complex (G.A.T.C.) and the Daam Aatu Basaltic Tuff (D.A.B.T.). The name Ardipithecus ramidus stems mostly from the Afar language, in which Ardi means "ground/floor" and ramid means "root". The pithecus portion of the name is from the Greek word for "ape".
Like most hominids, but unlike all previously recognized hominins, it had a grasping hallux or big toe adapted for locomotion in the trees. It is not confirmed how many other features of its skeleton reflect adaptation to bipedalism on the ground as well. Like later hominins, Ardipithecus had reduced canine
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https://en.wikipedia.org/wiki/Algebraic%20number
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An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial . That is, it is a value for x for which the polynomial evaluates to zero. As another example, the complex number is algebraic because it is a root of .
All integers and rational numbers are algebraic, as are all roots of integers. Real and complex numbers that are not algebraic, such as and , are called transcendental numbers.
The set of algebraic numbers is countably infinite and has measure zero in the Lebesgue measure as a subset of the uncountable complex numbers. In that sense, almost all complex numbers are transcendental.
Examples
All rational numbers are algebraic. Any rational number, expressed as the quotient of an integer and a (non-zero) natural number , satisfies the above definition, because is the root of a non-zero polynomial, namely .
Quadratic irrational numbers, irrational solutions of a quadratic polynomial with integer coefficients , , and , are algebraic numbers. If the quadratic polynomial is monic (), the roots are further qualified as quadratic integers.
Gaussian integers, complex numbers for which both and are integers, are also quadratic integers. This is because and are the two roots of the quadratic .
A constructible number can be constructed from a given unit length using a straightedge and compass. It includes all quadratic irrational roots, all rational numbers, and all numbers that can be formed from these using the basic arithmetic operations and the extraction of square roots. (By designating cardinal directions for +1, −1, +, and −, complex numbers such as are considered constructible.)
Any expression formed from algebraic numbers using any combination of the basic arithmetic operations and extraction of th roots gives another algebraic number.
Polynomial roots that canno
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https://en.wikipedia.org/wiki/Automorphism
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In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object.
Definition
In the context of abstract algebra, a mathematical object is an algebraic structure such as a group, ring, or vector space. An automorphism is simply a bijective homomorphism of an object with itself. (The definition of a homomorphism depends on the type of algebraic structure; see, for example, group homomorphism, ring homomorphism, and linear operator.)
The identity morphism (identity mapping) is called the trivial automorphism in some contexts. Respectively, other (non-identity) automorphisms are called nontrivial automorphisms.
The exact definition of an automorphism depends on the type of "mathematical object" in question and what, precisely, constitutes an "isomorphism" of that object. The most general setting in which these words have meaning is an abstract branch of mathematics called category theory. Category theory deals with abstract objects and morphisms between those objects.
In category theory, an automorphism is an endomorphism (i.e., a morphism from an object to itself) which is also an isomorphism (in the categorical sense of the word, meaning there exists a right and left inverse endomorphism).
This is a very abstract definition since, in category theory, morphisms are not necessarily functions and objects are not necessarily sets. In most concrete settings, however, the objects will be sets with some additional structure and the morphisms will be functions preserving that structure.
Automorphism group
If the automorphisms of an object form a set (instead of a proper class), then they form a group under composition of morphisms. This group is called the automorphism group
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https://en.wikipedia.org/wiki/Artificial%20intelligence
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Artificial intelligence (AI) is the intelligence of machines or software, as opposed to the intelligence of humans or animals. It is also the field of study in computer science that develops and studies intelligent machines. "AI" may also refer to the machines themselves.
AI technology is widely used throughout industry, government and science. Some high-profile applications are: advanced web search engines (e.g., Google Search), recommendation systems (used by YouTube, Amazon, and Netflix), understanding human speech (such as Siri and Alexa), self-driving cars (e.g., Waymo), generative or creative tools (ChatGPT and AI art), and competing at the highest level in strategic games (such as chess and Go).
Artificial intelligence was founded as an academic discipline in 1956. The field went through multiple cycles of optimism followed by disappointment and loss of funding, but after 2012, when deep learning surpassed all previous AI techniques, there was a vast increase in funding and interest.
The various sub-fields of AI research are centered around particular goals and the use of particular tools. The traditional goals of AI research include reasoning, knowledge representation, planning, learning, natural language processing, perception, and support for robotics. General intelligence (the ability to solve an arbitrary problem) is among the field's long-term goals.
To solve these problems, AI researchers have adapted and integrated a wide range of problem-solving techniques, including search and mathematical optimization, formal logic, artificial neural networks, and methods based on statistics, operations research, and economics. AI also draws upon psychology, linguistics, philosophy, neuroscience and many other fields.
Goals
The general problem of simulating (or creating) intelligence has been broken down into sub-problems. These consist of particular traits or capabilities that researchers expect an intelligent system to display. The traits described below hav
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https://en.wikipedia.org/wiki/Abbreviation
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An abbreviation (from Latin , meaning short) is a shortened form of a word or phrase, by any method. It may consist of a group of letters or words taken from the full version of the word or phrase; for example, the word abbreviation itself can be abbreviated as abbr., abbrv., or abbrev.; NPO, for nil (or nothing) per (by) os (mouth) is an abbreviated medical instruction. It may also consist of initials only, a mixture of initials and words, or words or letters representing words in another language (for example, e.g., i.e. or RSVP). Some types of abbreviations are acronyms (some pronounceable, some initialisms) or grammatical contractions or crasis.
An abbreviation is a shortening by any of these or other methods.
Types
Acronyms, initialisms, contractions and crasis share some semantic and phonetic functions, and all four are connected by the term "abbreviation" in loose parlance.
An initialism is an abbreviation pronounced by spelling out each letter, i.e. FBI (), USA (), IBM (), BBC ()
A contraction is a reduction in the length of a word or phrase made by omitting certain of its letters or syllables. Consequently, contractions are a subset of abbreviations. Often, but not always, the contraction includes the first and last letters or elements. Examples of contractions are "li'l" (for "little"), "I'm" (for "I am"), and "he'd've" (for "he would have").
History
Abbreviations have a long history. They were created to avoid spelling out whole words. This might be done to save time and space (given that many inscriptions were carved in stone) and also to provide secrecy. In both Greece and Rome the reduction of words to single letters was common. In Roman inscriptions, "Words were commonly abbreviated by using the initial letter or letters of words, and most inscriptions have at least one abbreviation". However, "some could have more than one meaning, depending on their context. (For example, can be an abbreviation for many words, such as , , , , , , and .)" Ma
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https://en.wikipedia.org/wiki/Angle
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In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Angles formed by two rays are also known as plane angles as they lie in the plane that contains the rays. Angles are also formed by the intersection of two planes; these are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
The magnitude of an angle is called an angular measure or simply "angle". Angle of rotation is a measure conventionally defined as the ratio of a circular arc length to its radius, and may be a negative number. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.
History and etymology
The word angle comes from the Latin word , meaning "corner." Cognate words include the Greek () meaning "crooked, curved" and the English word "ankle." Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow."
Euclid defines a plane angle as the inclination to each other, in a plane, of two lines that meet each other and do not lie straight with respect to each other. According to the Neoplatonic metaphysician Proclus, an angle must be either a quality, a quantity, or a relationship. The first concept, angle as quality, was used by Eudemus of Rhodes, who regarded an angle as a deviation from a straight line; the second, angle as quality, by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third: angle as a relationship.
Identifying angles
In mathematical expressions, it is common to use Greek letters (α, β, γ, θ, φ, . . . ) as variables denoting the size of some angle (to avoid confusion with its other meaning, t
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https://en.wikipedia.org/wiki/Acoustics
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Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries.
Hearing is one of the most crucial means of survival in the animal world and speech is one of the most distinctive characteristics of human development and culture. Accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound and hearing as a key element of mating rituals or for marking territories. Art, craft, science and technology have provoked one another to advance the whole, as in many other fields of knowledge. Robert Bruce Lindsay's "Wheel of Acoustics" is a well accepted overview of the various fields in acoustics.
History
Etymology
The word "acoustic" is derived from the Greek word ἀκουστικός (akoustikos), meaning "of or for hearing, ready to hear" and that from ἀκουστός (akoustos), "heard, audible", which in turn derives from the verb ἀκούω(akouo), "I hear".
The Latin synonym is "sonic", after which the term sonics used to be a synonym for acoustics and later a branch of acoustics. Frequencies above and below the audible range are called "ultrasonic" and "infrasonic", respectively.
Early research in acoustics
In the 6th century BC, the ancient Greek philosopher Pythagoras wanted to know why some combinations of musical sounds seemed more beautiful than others, and he found answers in terms of numerical ratios representing the harmonic overtone series on a string. He is reputed to have observed that when the length
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https://en.wikipedia.org/wiki/Atomic%20physics
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Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned with the way in which electrons are arranged around the nucleus and
the processes by which these arrangements change. This comprises ions, neutral atoms and, unless otherwise stated, it can be assumed that the term atom includes ions.
The term atomic physics can be associated with nuclear power and nuclear weapons, due to the synonymous use of atomic and nuclear in standard English. Physicists distinguish between atomic physics—which deals with the atom as a system consisting of a nucleus and electrons—and nuclear physics, which studies nuclear reactions and special properties of atomic nuclei.
As with many scientific fields, strict delineation can be highly contrived and atomic physics is often considered in the wider context of atomic, molecular, and optical physics. Physics research groups are usually so classified.
Isolated atoms
Atomic physics primarily considers atoms in isolation. Atomic models will consist of a single nucleus that may be surrounded by one or more bound electrons. It is not concerned with the formation of molecules (although much of the physics is identical), nor does it examine atoms in a solid state as condensed matter. It is concerned with processes such as ionization and excitation by photons or collisions with atomic particles.
While modelling atoms in isolation may not seem realistic, if one considers atoms in a gas or plasma then the time-scales for atom-atom interactions are huge in comparison to the atomic processes that are generally considered. This means that the individual atoms can be treated as if each were in isolation, as the vast majority of the time they are. By this consideration, atomic physics provides the underlying theory in plasma physics and atmospheric physics, even though
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https://en.wikipedia.org/wiki/Atomic%20orbital
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In atomic theory and quantum mechanics, an atomic orbital () is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. The term atomic orbital may also refer to the physical region or space where the electron can be calculated to be present, as predicted by the particular mathematical form of the orbital.
Each orbital in an atom is characterized by a set of values of the three quantum numbers , , and , which respectively correspond to the electron's energy, its angular momentum, and an angular momentum vector component (magnetic quantum number). As an alternative to the magnetic quantum number, the orbitals are often labeled by the associated harmonic polynomials (e.g., xy, ). Each such orbital can be occupied by a maximum of two electrons, each with its own projection of spin . The simple names s orbital, p orbital, d orbital, and f orbital refer to orbitals with angular momentum quantum number and respectively. These names, together with the value of , are used to describe the electron configurations of atoms. They are derived from the description by early spectroscopists of certain series of alkali metal spectroscopic lines as sharp, principal, diffuse, and fundamental. Orbitals for > 3 continue alphabetically (g, h, i, k, ...), omitting j because some languages do not distinguish between the letters "i" and "j".
Atomic orbitals are the basic building blocks of the atomic orbital model (or electron cloud or wave mechanics model), a modern framework for visualizing the submicroscopic behavior of electrons in matter. In this model the electron cloud of an atom may be seen as being built up (in approximation) in an electron configuration that is a product of simpler hydrogen-like atomic orbitals. The repeating periodicity of blocks of 2, 6, 10, and 14 elements within sections of the periodic ta
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https://en.wikipedia.org/wiki/Amino%20acid
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Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although over 500 amino acids exist in nature, by far the most important are the 22 α-amino acids incorporated into proteins. Only these 22 appear in the genetic code of all life.
Amino acids can be classified according to the locations of the core structural functional groups, as alpha- (α-), beta- (β-), gamma- (γ-) or delta- (δ-) amino acids; other categories relate to polarity, ionization, and side chain group type (aliphatic, acyclic, aromatic, containing hydroxyl or sulfur, etc.). In the form of proteins, amino acid residues form the second-largest component (water being the largest) of human muscles and other tissues. Beyond their role as residues in proteins, amino acids participate in a number of processes such as neurotransmitter transport and biosynthesis. It is thought that they played a key role in enabling life on Earth and its emergence.
Amino acids are formally named by the IUPAC-IUBMB Joint Commission on Biochemical Nomenclature in terms of the fictitious "neutral" structure shown in the illustration. For example, the systematic name of alanine is 2-aminopropanoic acid, based on the formula . The Commission justified this approach as follows:
The systematic names and formulas given refer to hypothetical forms in which amino groups are unprotonated and carboxyl groups are undissociated. This convention is useful to avoid various nomenclatural problems but should not be taken to imply that these structures represent an appreciable fraction of the amino-acid molecules.
History
The first few amino acids were discovered in the early 1800s. In 1806, French chemists Louis-Nicolas Vauquelin and Pierre Jean Robiquet isolated a compound from asparagus that was subsequently named asparagine, the first amino acid to be discovered. Cystine was discovered in 1810, although its monomer, cysteine, remained undiscovered until 1884. Glycine and leucine were discovere
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https://en.wikipedia.org/wiki/Alan%20Turing
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Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. He is widely considered to be the father of theoretical computer science and artificial intelligence.
Born in Maida Vale, London, Turing was raised in southern England. He graduated at King's College, Cambridge, with a degree in mathematics. Whilst he was a fellow at Cambridge, he published a proof demonstrating that some purely mathematical yes–no questions can never be answered by computation. He defined a Turing machine and proved that the halting problem for Turing machines is undecidable. In 1938, he obtained his PhD from the Department of Mathematics at Princeton University. During the Second World War, Turing worked for the Government Code and Cypher School at Bletchley Park, Britain's codebreaking centre that produced Ultra intelligence. For a time he led Hut 8, the section that was responsible for German naval cryptanalysis. Here, he devised a number of techniques for speeding the breaking of German ciphers, including improvements to the pre-war Polish bomba method, an electromechanical machine that could find settings for the Enigma machine. Turing played a crucial role in cracking intercepted coded messages that enabled the Allies to defeat the Axis powers in many crucial engagements, including the Battle of the Atlantic.
After the war, Turing worked at the National Physical Laboratory, where he designed the Automatic Computing Engine, one of the first designs for a stored-program computer. In 1948, Turing joined Max Newman's Computing Machine Laboratory at the Victoria University of Manchester, where he helped develop the Manchester computers and became
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https://en.wikipedia.org/wiki/Astronomical%20unit
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The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits the Sun, from a maximum (aphelion) to a minimum (perihelion) and back again once each year. The astronomical unit was originally conceived as the average of Earth's aphelion and perihelion; however, since 2012 it has been defined as exactly .
The astronomical unit is used primarily for measuring distances within the Solar System or around other stars. It is also a fundamental component in the definition of another unit of astronomical length, the parsec.
History of symbol usage
A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union (IAU) had used the symbol A to denote a length equal to the astronomical unit. In the astronomical literature, the symbol AU was (and remains) common. In 2006, the International Bureau of Weights and Measures (BIPM) had recommended ua as the symbol for the unit, from the French "unité astronomique". In the non-normative Annex C to ISO 80000-3:2006 (now withdrawn), the symbol of the astronomical unit was also ua.
In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au". The scientific journals published by the American Astronomical Society and the Royal Astronomical Society subsequently adopted this symbol. In the 2014 revision and 2019 edition of the SI Brochure, the BIPM used the unit symbol "au". ISO 80000-3:2019, which replaces ISO 80000-3:2006, does not mention the astronomical unit.
Development of unit definition
Earth's orbit around the Sun is an ellipse. The semi-major axis of this elliptic orbit is defined to be half of the straight line segment that joins the perihelion and aphelion. The centre of the Sun lies on this stra
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https://en.wikipedia.org/wiki/Acoustic%20theory
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Acoustic theory is a scientific field that relates to the description of sound waves. It derives from fluid dynamics. See acoustics for the engineering approach.
For sound waves of any magnitude of a disturbance in velocity, pressure, and density we have
In the case that the fluctuations in velocity, density, and pressure are small, we can approximate these as
Where is the perturbed velocity of the fluid, is the pressure of the fluid at rest, is the perturbed pressure of the system as a function of space and time, is the density of the fluid at rest, and is the variance in the density of the fluid over space and time.
In the case that the velocity is irrotational (), we then have the acoustic wave equation that describes the system:
Where we have
Derivation for a medium at rest
Starting with the Continuity Equation and the Euler Equation:
If we take small perturbations of a constant pressure and density:
Then the equations of the system are
Noting that the equilibrium pressures and densities are constant, this simplifies to
A Moving Medium
Starting with
We can have these equations work for a moving medium by setting , where is the constant velocity that the whole fluid is moving at before being disturbed (equivalent to a moving observer) and is the fluid velocity.
In this case the equations look very similar:
Note that setting returns the equations at rest.
Linearized Waves
Starting with the above given equations of motion for a medium at rest:
Let us now take to all be small quantities.
In the case that we keep terms to first order, for the continuity equation, we have the term going to 0. This similarly applies for the density perturbation times the time derivative of the velocity. Moreover, the spatial components of the material derivative go to 0. We thus have, upon rearranging the equilibrium density:
Next, given that our sound wave occurs in an ideal fluid, the motion is adiabatic, and then we can relate the small
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https://en.wikipedia.org/wiki/Ada%20%28programming%20language%29
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Ada is a structured, statically typed, imperative, and object-oriented high-level programming language, inspired by Pascal and other languages. It has built-in language support for design by contract (DbC), extremely strong typing, explicit concurrency, tasks, synchronous message passing, protected objects, and non-determinism. Ada improves code safety and maintainability by using the compiler to find errors in favor of runtime errors. Ada is an international technical standard, jointly defined by the International Organization for Standardization (ISO), and the International Electrotechnical Commission (IEC). , the standard, called Ada 2012 informally, is ISO/IEC 8652:2012.
Ada was originally designed by a team led by French computer scientist Jean Ichbiah of Honeywell under contract to the United States Department of Defense (DoD) from 1977 to 1983 to supersede over 450 programming languages used by the DoD at that time. Ada was named after Ada Lovelace (1815–1852), who has been credited as the first computer programmer.
Features
Ada was originally designed for embedded and real-time systems. The Ada 95 revision, designed by S. Tucker Taft of Intermetrics between 1992 and 1995, improved support for systems, numerical, financial, and object-oriented programming (OOP).
Features of Ada include: strong typing, modular programming mechanisms (packages), run-time checking, parallel processing (tasks, synchronous message passing, protected objects, and nondeterministic select statements), exception handling, and generics. Ada 95 added support for object-oriented programming, including dynamic dispatch.
The syntax of Ada minimizes choices of ways to perform basic operations, and prefers English keywords (such as "or else" and "and then") to symbols (such as "||" and "&&"). Ada uses the basic arithmetical operators "+", "-", "*", and "/", but avoids using other symbols. Code blocks are delimited by words such as "declare", "begin", and "end", where the "end" (in most
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https://en.wikipedia.org/wiki/Advanced%20Encryption%20Standard
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The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.
AES is a variant of the Rijndael block cipher developed by two Belgian cryptographers, Joan Daemen and Vincent Rijmen, who submitted a proposal to NIST during the AES selection process. Rijndael is a family of ciphers with different key and block sizes. For AES, NIST selected three members of the Rijndael family, each with a block size of 128 bits, but three different key lengths: 128, 192 and 256 bits.
AES has been adopted by the U.S. government. It supersedes the Data Encryption Standard (DES), which was published in 1977. The algorithm described by AES is a symmetric-key algorithm, meaning the same key is used for both encrypting and decrypting the data.
In the United States, AES was announced by the NIST as U.S. FIPS PUB 197 (FIPS 197) on November 26, 2001. This announcement followed a five-year standardization process in which fifteen competing designs were presented and evaluated, before the Rijndael cipher was selected as the most suitable.
AES is included in the ISO/IEC 18033-3 standard. AES became effective as a U.S. federal government standard on May 26, 2002, after approval by U.S. Secretary of Commerce Donald Evans. AES is available in many different encryption packages, and is the first (and only) publicly accessible cipher approved by the U.S. National Security Agency (NSA) for top secret information when used in an NSA approved cryptographic module.
Definitive standards
The Advanced Encryption Standard (AES) is defined in each of:
FIPS PUB 197: Advanced Encryption Standard (AES)
ISO/IEC 18033-3: Block ciphers
Description of the ciphers
AES is based on a design principle known as a substitution–permutation network, and is efficient in both software and hardware. Unlike its predecessor DES, AES does not use a Feiste
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https://en.wikipedia.org/wiki/Anisotropy
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Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different properties when measured along different axes: physical or mechanical properties (absorbance, refractive index, conductivity, tensile strength, etc.).
An example of anisotropy is light coming through a polarizer. Another is wood, which is easier to split along its grain than across it because of the directional non-uniformity of the grain (the grain is the same in one direction, not all directions).
Fields of interest
Computer graphics
In the field of computer graphics, an anisotropic surface changes in appearance as it rotates about its geometric normal, as is the case with velvet.
Anisotropic filtering (AF) is a method of enhancing the image quality of textures on surfaces that are far away and steeply angled with respect to the point of view. Older techniques, such as bilinear and trilinear filtering, do not take into account the angle a surface is viewed from, which can result in aliasing or blurring of textures. By reducing detail in one direction more than another, these effects can be reduced easily.
Chemistry
A chemical anisotropic filter, as used to filter particles, is a filter with increasingly smaller interstitial spaces in the direction of filtration so that the proximal regions filter out larger particles and distal regions increasingly remove smaller particles, resulting in greater flow-through and more efficient filtration.
In fluorescence spectroscopy, the fluorescence anisotropy, calculated from the polarization properties of fluorescence from samples excited with plane-polarized light, is used, e.g., to determine the shape of a macromolecule. Anisotropy measurements reveal the average angular displacement of the fluorophore that occurs between absorption and subsequent emission of a photo
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https://en.wikipedia.org/wiki/Alpha%20decay
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Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms or 'decays' into a different atomic nucleus, with a mass number that is reduced by four and an atomic number that is reduced by two. An alpha particle is identical to the nucleus of a helium-4 atom, which consists of two protons and two neutrons. It has a charge of and a mass of . For example, uranium-238 decays to form thorium-234.
While alpha particles have a charge , this is not usually shown because a nuclear equation describes a nuclear reaction without considering the electrons – a convention that does not imply that the nuclei necessarily occur in neutral atoms.
Alpha decay typically occurs in the heaviest nuclides. Theoretically, it can occur only in nuclei somewhat heavier than nickel (element 28), where the overall binding energy per nucleon is no longer a maximum and the nuclides are therefore unstable toward spontaneous fission-type processes. In practice, this mode of decay has only been observed in nuclides considerably heavier than nickel, with the lightest known alpha emitter being the second lightest isotope of antimony, 104Sb. Exceptionally, however, beryllium-8 decays to two alpha particles.
Alpha decay is by far the most common form of cluster decay, where the parent atom ejects a defined daughter collection of nucleons, leaving another defined product behind. It is the most common form because of the combined extremely high nuclear binding energy and relatively small mass of the alpha particle. Like other cluster decays, alpha decay is fundamentally a quantum tunneling process. Unlike beta decay, it is governed by the interplay between both the strong nuclear force and the electromagnetic force.
Alpha particles have a typical kinetic energy of 5 MeV (or ≈ 0.13% of their total energy, 110 TJ/kg) and have a speed of about 15,000,000 m/s, or 5% of the speed of light. There is surprisingly small variat
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https://en.wikipedia.org/wiki/Analytical%20engine
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The analytical engine was a proposed mechanical general-purpose computer designed by English mathematician and computer pioneer Charles Babbage. It was first described in 1837 as the successor to Babbage's difference engine, which was a design for a simpler mechanical calculator.
The analytical engine incorporated an arithmetic logic unit, control flow in the form of conditional branching and loops, and integrated memory, making it the first design for a general-purpose computer that could be described in modern terms as Turing-complete. In other words, the structure of the analytical engine was essentially the same as that which has dominated computer design in the electronic era. The analytical engine is one of the most successful achievements of Charles Babbage.
Babbage was never able to complete construction of any of his machines due to conflicts with his chief engineer and inadequate funding. It was not until 1941 that Konrad Zuse built the first general-purpose computer, Z3, more than a century after Babbage had proposed the pioneering analytical engine in 1837.
Design
Babbage's first attempt at a mechanical computing device, the Difference Engine, was a special-purpose machine designed to tabulate logarithms and trigonometric functions by evaluating finite differences to create approximating polynomials. Construction of this machine was never completed; Babbage had conflicts with his chief engineer, Joseph Clement, and ultimately the British government withdrew its funding for the project.
During this project, Babbage realised that a much more general design, the analytical engine, was possible. The work on the design of the analytical engine started around 1833.
The input, consisting of programs ("formulae") and data, was to be provided to the machine via punched cards, a method being used at the time to direct mechanical looms such as the Jacquard loom. For output, the machine would have a printer, a curve plotter, and a bell. The machine would also
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https://en.wikipedia.org/wiki/Almost%20all
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In mathematics, the term "almost all" means "all but a negligible quantity". More precisely, if is a set, "almost all elements of " means "all elements of but those in a negligible subset of ". The meaning of "negligible" depends on the mathematical context; for instance, it can mean finite, countable, or null.
In contrast, "almost no" means "a negligible quantity"; that is, "almost no elements of " means "a negligible quantity of elements of ".
Meanings in different areas of mathematics
Prevalent meaning
Throughout mathematics, "almost all" is sometimes used to mean "all (elements of an infinite set) except for finitely many". This use occurs in philosophy as well. Similarly, "almost all" can mean "all (elements of an uncountable set) except for countably many".
Examples:
Almost all positive integers are greater than 1012.
Almost all prime numbers are odd (2 is the only exception).
Almost all polyhedra are irregular (as there are only nine exceptions: the five platonic solids and the four Kepler–Poinsot polyhedra).
If P is a nonzero polynomial, then P(x) ≠ 0 for almost all x (if not all x).
Meaning in measure theory
When speaking about the reals, sometimes "almost all" can mean "all reals except for a null set". Similarly, if S is some set of reals, "almost all numbers in S" can mean "all numbers in S except for those in a null set". The real line can be thought of as a one-dimensional Euclidean space. In the more general case of an n-dimensional space (where n is a positive integer), these definitions can be generalised to "all points except for those in a null set" or "all points in S except for those in a null set" (this time, S is a set of points in the space). Even more generally, "almost all" is sometimes used in the sense of "almost everywhere" in measure theory, or in the closely related sense of "almost surely" in probability theory.
Examples:
In a measure space, such as the real line, countable sets are null. The set of rational numbers is
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https://en.wikipedia.org/wiki/Antimatter
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In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding particles in "ordinary" matter, and can be thought of as matter with reversed charge, parity, and time, known as CPT reversal. Antimatter occurs in natural processes like cosmic ray collisions and some types of radioactive decay, but only a tiny fraction of these have successfully been bound together in experiments to form antiatoms. Minuscule numbers of antiparticles can be generated at particle accelerators; however, total artificial production has been only a few nanograms. No macroscopic amount of antimatter has ever been assembled due to the extreme cost and difficulty of production and handling. Nonetheless, antimatter is an essential component of widely-available applications related to beta decay, such as positron emission tomography, radiation therapy, and industrial imaging.
In theory, a particle and its antiparticle (for example, a proton and an antiproton) have the same mass, but opposite electric charge, and other differences in quantum numbers.
A collision between any particle and its anti-particle partner leads to their mutual annihilation, giving rise to various proportions of intense photons (gamma rays), neutrinos, and sometimes less-massive particleantiparticle pairs. The majority of the total energy of annihilation emerges in the form of ionizing radiation. If surrounding matter is present, the energy content of this radiation will be absorbed and converted into other forms of energy, such as heat or light. The amount of energy released is usually proportional to the total mass of the collided matter and antimatter, in accordance with the notable mass–energy equivalence equation, .
Antiparticles bind with each other to form antimatter, just as ordinary particles bind to form normal matter. For example, a positron (the antiparticle of the electron) and an antiproton (the antiparticle of the proton) can form an antihydrogen atom.
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https://en.wikipedia.org/wiki/Antiparticle
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In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antielectron). While the electron has a negative electric charge, the positron has a positive electric charge, and is produced naturally in certain types of radioactive decay. The opposite is also true: the antiparticle of the positron is the electron.
Some particles, such as the photon, are their own antiparticle. Otherwise, for each pair of antiparticle partners, one is designated as the normal particle (the one that occurs in matter usually interacted with in daily life). The other (usually given the prefix "anti-") is designated the antiparticle.
Particle–antiparticle pairs can annihilate each other, producing photons; since the charges of the particle and antiparticle are opposite, total charge is conserved. For example, the positrons produced in natural radioactive decay quickly annihilate themselves with electrons, producing pairs of gamma rays, a process exploited in positron emission tomography.
The laws of nature are very nearly symmetrical with respect to particles and antiparticles. For example, an antiproton and a positron can form an antihydrogen atom, which is believed to have the same properties as a hydrogen atom. This leads to the question of why the formation of matter after the Big Bang resulted in a universe consisting almost entirely of matter, rather than being a half-and-half mixture of matter and antimatter. The discovery of charge parity violation helped to shed light on this problem by showing that this symmetry, originally thought to be perfect, was only approximate.
Because charge is conserved, it is not possible to create an antiparticle without either destroying another particle of the same charge (as is for instance the case when antiparticles are produced naturally via beta decay or the collis
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https://en.wikipedia.org/wiki/Associative%20property
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In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.
Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is (after rewriting the expression with parentheses and in infix notation if necessary), rearranging the parentheses in such an expression will not change its value. Consider the following equations:
Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real numbers, it can be said that "addition and multiplication of real numbers are associative operations".
Associativity is not the same as commutativity, which addresses whether the order of two operands affects the result. For example, the order does not matter in the multiplication of real numbers, that is, , so we say that the multiplication of real numbers is a commutative operation. However, operations such as function composition and matrix multiplication are associative, but not (generally) commutative.
Associative operations are abundant in mathematics; in fact, many algebraic structures (such as semigroups and categories) explicitly require their binary operations to be associative.
However, many important and interesting operations are non-associative; some examples include subtraction, exponentiation, and the vector cross product. In contrast to the theoretical properties of real numbers, the addition of floating point numbers in computer science is not associative, and the choice of how to associate an expression can have a significant effect on rounding error.
Definition
Formally,
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https://en.wikipedia.org/wiki/Atanasoff%E2%80%93Berry%20computer
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The Atanasoff–Berry computer (ABC) was the first automatic electronic digital computer. Limited by the technology of the day, and execution, the device has remained somewhat obscure. The ABC's priority is debated among historians of computer technology, because it was neither programmable, nor Turing-complete. Conventionally, the ABC would be considered the first electronic ALU (arithmetic logic unit) which is integrated into every modern processor's design.
Its unique contribution was to make computing faster by being the first to use vacuum tubes to do the arithmetic calculations. Prior to this, slower electro-mechanical methods were used by Konrad Zuse's Z1 computer, and the simultaneously developed Harvard Mark I. The first electronic, programmable, digital machine, the Colossus computer from 1943 to 1945, used similar tube-based technology as ABC.
Overview
Conceived in 1937, the machine was built by Iowa State College mathematics and physics professor John Vincent Atanasoff with the help of graduate student Clifford Berry. It was designed only to solve systems of linear equations and was successfully tested in 1942. However, its intermediate result storage mechanism, a paper card writer/reader, was not perfected, and when John Vincent Atanasoff left Iowa State College for World War II assignments, work on the machine was discontinued. The ABC pioneered important elements of modern computing, including binary arithmetic and electronic switching elements, but its special-purpose nature and lack of a changeable, stored program distinguish it from modern computers. The computer was designated an IEEE Milestone in 1990.
Atanasoff and Berry's computer work was not widely known until it was rediscovered in the 1960s, amid patent disputes over the first instance of an electronic computer. At that time ENIAC, that had been created by John Mauchly and J. Presper Eckert, was considered to be the first computer in the modern sense, but in 1973 a U.S. District Court in
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https://en.wikipedia.org/wiki/Ammonia
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Ammonia is an inorganic chemical compound of nitrogen and hydrogen with the formula . A stable binary hydride and the simplest pnictogen hydride, ammonia is a colourless gas with a distinct pungent smell. Biologically, it is a common nitrogenous waste, and it contributes significantly to the nutritional needs of terrestrial organisms by serving as a precursor to fertilisers. Around 70% of ammonia produced industrially is used to make fertilisers in various forms and composition, such as urea and diammonium phosphate. Ammonia in pure form is also applied directly into the soil.
Ammonia, either directly or indirectly, is also a building block for the synthesis of many pharmaceutical products and is used in many commercial cleaning products. It is mainly collected by downward displacement of both air and water.
Although common in nature—both terrestrially and in the outer planets of the Solar System—and in wide use, ammonia is both caustic and hazardous in its concentrated form. In many countries it is classified as an extremely hazardous substance, and is subject to strict reporting requirements by facilities that produce, store, or use it in significant quantities.
The global industrial production of ammonia in 2021 was 235 million tonnes. Industrial ammonia is sold either as ammonia liquor (usually 28% ammonia in water) or as pressurised or refrigerated anhydrous liquid ammonia transported in tank cars or cylinders.
For fundamental reasons, the production of ammonia from the elements hydrogen and nitrogen is difficult, requiring high pressures and high temperatures. The Haber process that enabled industrial production was invented at the beginning of the 20th century, revolutionizing agriculture.
boils at at a pressure of one atmosphere, so the liquid must be stored under pressure or at low temperature. Household ammonia or ammonium hydroxide is a solution of in water. The concentration of such solutions is measured in units of the Baumé scale (density), wi
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https://en.wikipedia.org/wiki/Assembly%20language
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In computer programming, assembly language (alternatively assembler language or symbolic machine code), often referred to simply as assembly and commonly abbreviated as ASM or asm, is any low-level programming language with a very strong correspondence between the instructions in the language and the architecture's machine code instructions. Assembly language usually has one statement per machine instruction (1:1), but constants, comments, assembler directives, symbolic labels of, e.g., memory locations, registers, and macros are generally also supported.
The first assembly code in which a language is used to represent machine code instructions is found in Kathleen and Andrew Donald Booth's 1947 work, Coding for A.R.C.. Assembly code is converted into executable machine code by a utility program referred to as an assembler. The term "assembler" is generally attributed to Wilkes, Wheeler and Gill in their 1951 book The Preparation of Programs for an Electronic Digital Computer, who, however, used the term to mean "a program that assembles another program consisting of several sections into a single program". The conversion process is referred to as assembly, as in assembling the source code. The computational step when an assembler is processing a program is called assembly time.
Because assembly depends on the machine code instructions, each assembly language is specific to a particular computer architecture.
Sometimes there is more than one assembler for the same architecture, and sometimes an assembler is specific to an operating system or to particular operating systems. Most assembly languages do not provide specific syntax for operating system calls, and most assembly languages can be used universally with any operating system, as the language provides access to all the real capabilities of the processor, upon which all system call mechanisms ultimately rest. In contrast to assembly languages, most high-level programming languages are generally portable ac
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https://en.wikipedia.org/wiki/Amber
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Amber is fossilized tree resin that has been appreciated for its color and natural beauty since Neolithic times. Much valued from antiquity to the present as a gemstone, amber is made into a variety of decorative objects. Amber is used in jewelry and has been used as a healing agent in folk medicine.
There are five classes of amber, defined on the basis of their chemical constituents. Because it originates as a soft, sticky tree resin, amber sometimes contains animal and plant material as inclusions. Amber occurring in coal seams is also called resinite, and the term ambrite is applied to that found specifically within New Zealand coal seams.
Etymology
The English word amber derives from Arabic (ultimately from Middle Persian ambar) via Middle Latin ambar and Middle French ambre. The word referred to what is now known as ambergris (ambre gris or "grey amber"), a solid waxy substance derived from the sperm whale. The word, in its sense of "ambergris," was adopted in Middle English in the 14th century.
In the Romance languages, the sense of the word was extended to Baltic amber (fossil resin) from as early as the late 13th century. At first called white or yellow amber (ambre jaune), this meaning was adopted in English by the early 15th century. As the use of ambergris waned, this became the main sense of the word.
The two substances ("yellow amber" and "grey amber") conceivably became associated or confused because they both were found washed up on beaches. Ambergris is less dense than water and floats, whereas amber is too dense to float, though less dense than stone.
The classical names for amber, Latin electrum and Ancient Greek (ēlektron), are connected to a term ἠλέκτωρ (ēlektōr) meaning "beaming Sun". According to myth, when Phaëton son of Helios (the Sun) was killed, his mourning sisters became poplar trees, and their tears became elektron, amber. The word elektron gave rise to the words electric, electricity, and their relatives because of amber's abil
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https://en.wikipedia.org/wiki/AOL
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AOL (stylized as Aol., formerly a company known as AOL Inc. and originally known as America Online) is an American web portal and online service provider based in New York City. It is a brand marketed by the current incarnation of Yahoo! Inc.
The service traces its history to an online service known as PlayNET. PlayNET licensed its software to Quantum Link (Q-Link), that went online in November 1985. A new IBM PC client was launched in 1988, and eventually renamed as America Online in 1989. AOL grew to become the largest online service, displacing established players like CompuServe and The Source. By 1995, AOL had about three million active users.
AOL was one of the early pioneers of the Internet in the early-1990s, and the most recognized brand on the web in the United States. It originally provided a dial-up service to millions of Americans, pioneered instant messaging, and in 1993 began adding internet access. In 1998, AOL purchased Netscape for US$4.2 billion. In 2001, at the height of its popularity, it purchased the media conglomerate Time Warner in the largest merger in U.S. history. AOL rapidly shrank thereafter, partly due to the decline of dial-up and rise of broadband. AOL was eventually spun off from Time Warner in 2009, with Tim Armstrong appointed the new CEO. Under his leadership, the company invested in media brands and advertising technologies.
On June 23, 2015, AOL was acquired by Verizon Communications for $4.4 billion. On May 3, 2021, Verizon announced it would sell Yahoo and AOL to private equity firm Apollo Global Management for $5 billion. On September 1, 2021, AOL became part of the new Yahoo! Inc.
History
1983–1991: early years
AOL began in 1983, as a short-lived venture called Control Video Corporation (CVC), founded by William von Meister. Its sole product was an online service called GameLine for the Atari 2600 video game console, after von Meister's idea of buying music on demand was rejected by Warner Bros. Subscribers bought a m
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https://en.wikipedia.org/wiki/Absolute%20zero
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Absolute zero is the lowest limit of the thermodynamic temperature scale; a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.15 degrees on the Celsius scale (International System of Units), which equals −459.67 degrees on the Fahrenheit scale (United States customary units or imperial units). The corresponding Kelvin and Rankine temperature scales set their zero points at absolute zero by definition.
It is commonly thought of as the lowest temperature possible, but it is not the lowest enthalpy state possible, because all real substances begin to depart from the ideal gas when cooled as they approach the change of state to liquid, and then to solid; and the sum of the enthalpy of vaporization (gas to liquid) and enthalpy of fusion (liquid to solid) exceeds the ideal gas's change in enthalpy to absolute zero. In the quantum-mechanical description, matter at absolute zero is in its ground state, the point of lowest internal energy.
The laws of thermodynamics indicate that absolute zero cannot be reached using only thermodynamic means, because the temperature of the substance being cooled approaches the temperature of the cooling agent asymptotically. Even a system at absolute zero, if it could somehow be achieved, would still possess quantum mechanical zero-point energy, the energy of its ground state at absolute zero; the kinetic energy of the ground state cannot be removed.
Scientists and technologists routinely achieve temperatures close to absolute zero, where matter exhibits quantum effects such as Bose–Einstein condensate, superconductivity and superfluidity.
Thermodynamics near absolute zero
At temperatures near , n
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https://en.wikipedia.org/wiki/Adiabatic%20process
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In thermodynamics, an adiabatic process (Greek: adiábatos, "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, an adiabatic process transfers energy to the surroundings only as work. As a key concept in thermodynamics, the adiabatic process supports the theory that explains the first law of thermodynamics.
Some chemical and physical processes occur too rapidly for energy to enter or leave the system as heat, allowing a convenient "adiabatic approximation". For example, the adiabatic flame temperature uses this approximation to calculate the upper limit of flame temperature by assuming combustion loses no heat to its surroundings.
In meteorology and oceanography, adiabatic expanding produces condensation of moisture or salinity, oversaturating the parcel. Therefore, the excess must be removed. There, the process becomes a pseudo-adiabatic process whereby the liquid water or salt that condenses is assumed to be removed upon formation by idealized instantaneous precipitation. The pseudoadiabatic process is only defined for expansion because a compressed parcel becomes warmer and remains undersaturated.
Description
A process without transfer of heat to or from a system, so that , is called adiabatic, and such a system is said to be adiabatically isolated. The simplifying assumption frequently made is that a process is adiabatic. For example, the compression of a gas within a cylinder of an engine is assumed to occur so rapidly that on the time scale of the compression process, little of the system's energy can be transferred out as heat to the surroundings. Even though the cylinders are not insulated and are quite conductive, that process is idealized to be adiabatic. The same can be said to be true for the expansion process of such a system.
The assumption of adiabatic isolation is useful and often combined with other such idealizations to
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https://en.wikipedia.org/wiki/Acacia%20sensu%20lato
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Acacia s.l. (pronounced or ), known commonly as mimosa, acacia, thorntree or wattle, babul [India/hindi] is a polyphyletic genus of shrubs and trees belonging to the subfamily Mimosoideae of the family Fabaceae. It was described by the Swedish botanist Carl Linnaeus in 1773 based on the African species Acacia nilotica. Many non-Australian species tend to be thorny, whereas the majority of Australian acacias are not. All species are pod-bearing, with sap and leaves often bearing large amounts of tannins and condensed tannins that historically found use as pharmaceuticals and preservatives.
The genus Acacia constitutes, in its traditional circumspection, the second largest genus in Fabaceae (Astragalus being the largest), with roughly 1,300 species, about 960 of them native to Australia, with the remainder spread around the tropical to warm-temperate regions of both hemispheres, including Europe, Africa, southern Asia, and the Americas (see List of Acacia species). The genus was divided into five separate genera under the tribe "Acacieae". The genus now called Acacia represents the majority of the Australian species and a few native to southeast Asia, Réunion, and Pacific Islands. Most of the species outside Australia, and a small number of Australian species, are classified into Vachellia and Senegalia. The two final genera, Acaciella and Mariosousa, each contain about a dozen species from the Americas (but see "Classification" below for the ongoing debate concerning their taxonomy).
Classification
English botanist and gardener Philip Miller adopted the name Acacia in 1754. The generic name is derived from (), the name given by early Greek botanist-physician Pedanius Dioscorides (middle to late first century) to the medicinal tree A. nilotica in his book Materia Medica. This name derives from the Ancient Greek word for its characteristic thorns, (; "thorn"). The species name nilotica was given by Linnaeus from this tree's best-known range along the Nile river.
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https://en.wikipedia.org/wiki/APL%20%28programming%20language%29
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APL (named after the book A Programming Language) is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the multidimensional array. It uses a large range of special graphic symbols to represent most functions and operators, leading to very concise code. It has been an important influence on the development of concept modeling, spreadsheets, functional programming, and computer math packages. It has also inspired several other programming languages.
History
Mathematical notation
A mathematical notation for manipulating arrays was developed by Kenneth E. Iverson, starting in 1957 at Harvard University. In 1960, he began work for IBM where he developed this notation with Adin Falkoff and published it in his book A Programming Language in 1962. The preface states its premise:
This notation was used inside IBM for short research reports on computer systems, such as the Burroughs B5000 and its stack mechanism when stack machines versus register machines were being evaluated by IBM for upcoming computers.
Iverson also used his notation in a draft of the chapter A Programming Language, written for a book he was writing with Fred Brooks, Automatic Data Processing, which would be published in 1963.
In 1979, Iverson received the Turing Award for his work on APL.
Development into a computer programming language
As early as 1962, the first attempt to use the notation to describe a complete computer system happened after Falkoff discussed with William C. Carter his work to standardize the instruction set for the machines that later became the IBM System/360 family.
In 1963, Herbert Hellerman, working at the IBM Systems Research Institute, implemented a part of the notation on an IBM 1620 computer, and it was used by students in a special high school course on calculating transcendental functions by series summation. Students tested their code in Hellerman's lab. This implementation of a part of the notation was called Personalized
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https://en.wikipedia.org/wiki/AWK
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AWK (awk ) is a domain-specific language designed for text processing and typically used as a data extraction and reporting tool. Like sed and grep, it is a filter, and is a standard feature of most Unix-like operating systems.
The AWK language is a data-driven scripting language consisting of a set of actions to be taken against streams of textual data – either run directly on files or used as part of a pipeline – for purposes of extracting or transforming text, such as producing formatted reports. The language extensively uses the string datatype, associative arrays (that is, arrays indexed by key strings), and regular expressions. While AWK has a limited intended application domain and was especially designed to support one-liner programs, the language is Turing-complete, and even the early Bell Labs users of AWK often wrote well-structured large AWK programs.
AWK was created at Bell Labs in the 1970s, and its name is derived from the surnames of its authors: Alfred Aho, Peter Weinberger, and Brian Kernighan. The acronym is pronounced the same as the name of the bird species auk, which is illustrated on the cover of The AWK Programming Language. When written in all lowercase letters, as awk, it refers to the Unix or Plan 9 program that runs scripts written in the AWK programming language.
History
AWK was initially developed in 1977 by Alfred Aho (author of egrep), Peter J. Weinberger (who worked on tiny relational databases), and Brian Kernighan. AWK takes its name from their respective initials. According to Kernighan, one of the goals of AWK was to have a tool that would easily manipulate both numbers and strings.
AWK was also inspired by Marc Rochkind's programming language that was used to search for patterns in input data, and was implemented using yacc.
As one of the early tools to appear in Version 7 Unix, AWK added computational features to a Unix pipeline besides the Bourne shell, the only scripting language available in a standard Unix environment.
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https://en.wikipedia.org/wiki/Alfred%20Russel%20Wallace
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Alfred Russel Wallace (8 January 1823 – 7 November 1913) was an English naturalist, explorer, geographer, anthropologist, biologist and illustrator. He independently conceived the theory of evolution through natural selection; his 1858 paper on the subject was published that year alongside extracts from Charles Darwin's earlier writings on the topic. It spurred Darwin to set aside the "big species book" he was drafting and quickly write an abstract of it, which was published in 1859 as On the Origin of Species.
Wallace did extensive fieldwork, starting in the Amazon River basin. He then did fieldwork in the Malay Archipelago, where he identified the faunal divide now termed the Wallace Line, which separates the Indonesian archipelago into two distinct parts: a western portion in which the animals are largely of Asian origin, and an eastern portion where the fauna reflect Australasia. He was considered the 19th century's leading expert on the geographical distribution of animal species, and is sometimes called the "father of biogeography", or more specifically of zoogeography.
Wallace was one of the leading evolutionary thinkers of the 19th century, working on warning coloration in animals and reinforcement (sometimes known as the Wallace effect), a way that natural selection could contribute to speciation by encouraging the development of barriers against hybridisation. Wallace's 1904 book Man's Place in the Universe was the first serious attempt by a biologist to evaluate the likelihood of life on other planets. He was one of the first scientists to write a serious exploration of whether there was life on Mars.
Aside from scientific work, he was a social activist, critical of what he considered to be an unjust social and economic system in 19th-century Britain. His advocacy of spiritualism and his belief in a non-material origin for the higher mental faculties of humans strained his relationship with other scientists. He was one of the first prominent scientist
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https://en.wikipedia.org/wiki/Acupuncture
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Acupuncture is a form of alternative medicine and a component of traditional Chinese medicine (TCM) in which thin needles are inserted into the body. Acupuncture is a pseudoscience; the theories and practices of TCM are not based on scientific knowledge, and it has been characterized as quackery.
There is a range of acupuncture variants which originated in different philosophies, and techniques vary depending on the country in which it is performed. However, it can be divided into two main foundational philosophical applications and approaches; the first form being the modern standardized form called eight principles TCM and the second an older system that is based on the ancient Daoist wuxing, better known as the five elements or phases in the West. Acupuncture is most often used to attempt pain relief, though acupuncturists say that it can also be used for a wide range of other conditions. Acupuncture is generally used only in combination with other forms of treatment.
The global acupuncture market was worth US$24.55 billion in 2017. The market was led by Europe with a 32.7% share, followed by Asia-Pacific with a 29.4% share and the Americas with a 25.3% share. It was estimated in 2021 that the industry would reach a market size of $55bn by 2023.
The conclusions of trials and systematic reviews of acupuncture generally provide no good evidence of benefit, which suggests that it is not an effective method of healthcare. Acupuncture is generally safe when done by appropriately trained practitioners using clean needle technique and single-use needles. When properly delivered, it has a low rate of mostly minor adverse effects. When accidents and infections do occur, they are associated with neglect on the part of the practitioner, particularly in the application of sterile techniques. A review conducted in 2013 stated that reports of infection transmission increased significantly in the preceding decade. The most frequently reported adverse events were pneumothora
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https://en.wikipedia.org/wiki/Amaranth
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Amaranthus is a cosmopolitan genus of annual or short-lived perennial plants collectively known as amaranths. Some amaranth species are cultivated as leaf vegetables, pseudocereals, and ornamental plants. Catkin-like cymes of densely packed flowers grow in summer or fall. Amaranth varies in flower, leaf, and stem color with a range of striking pigments from the spectrum of maroon to crimson and can grow longitudinally from tall with a cylindrical, succulent, fibrous stem that is hollow with grooves and bracteoles when mature.
There are approximately 75 species in the genus, 10 of which are dioecious and native to North America with the remaining 65 monoecious species endemic to every continent (except Antarctica) from tropical lowlands to the Himalayas. Members of this genus share many characteristics and uses with members of the closely related genus Celosia. Amaranth grain is collected from the genus. The leaves of some species are also eaten.
Description
Amaranth is a herbaceous plant or shrub that is either annual or perennial across the genus. Flowers vary interspecifically from the presence of 3 or 5 tepals and stamens, whereas a 7-porate pollen grain structure remains consistent across the family. Species across the genus contain concentric rings of vascular bundles, and fix carbon efficiently with a C4 photosynthetic pathway. Leaves are approximately and of oval or elliptical shape that are either opposite or alternate across species, although most leaves are whole and simple with entire margins.
Amaranth has a primary root with deeper spreading secondary fibrous root structures. Inflorescences are in the form a large panicle that varies from terminal to axial, color, and sex. The tassel of fluorescence is either erect or bent and varies in width and length between species. Flowers are radially symmetric and either bisexual or unisexual with very small, bristly perianth and pointy bracts. Species in this genus are either monecious (e.g. A. hybridus,) o
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https://en.wikipedia.org/wiki/Aquaculture
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Aquaculture (less commonly spelled aquiculture), also known as aquafarming, is the controlled cultivation ("farming") of aquatic organisms such as fish, crustaceans, mollusks, algae and other organisms of value such as aquatic plants (e.g. lotus). Aquaculture involves cultivating freshwater, brackish water and saltwater populations under controlled or semi-natural conditions, and can be contrasted with commercial fishing, which is the harvesting of wild fish. Mariculture, commonly known as marine farming, refers specifically to aquaculture practiced in seawater habitats and lagoons, as opposed to freshwater aquaculture. Pisciculture is a type of aquaculture that consists of fish farming to obtain fish products as food.
Aquaculture can also be defined as the breeding, growing, and harvesting of fish and other aquatic plants, also known as farming in water. It is an environmental source of food and commercial product which help to improve healthier habitats and used to reconstruct population of endangered aquatic species. Technology has increased the growth of fish in coastal marine waters and open oceans due to the increased demand for seafood.
Aquaculture can be conducted in completely artificial facilities built on land (onshore aquaculture), as in the case of fish tank, ponds, aquaponics or raceways, where the living conditions rely on human control such as water quality (oxygen), feed, temperature. Alternatively, they can be conducted on well-sheltered shallow waters nearshore of a body of water (inshore aquaculture), where the cultivated species are subjected to a relatively more naturalistic environments; or on fenced/enclosed sections of open water away from the shore (offshore aquaculture), where the species are either cultured in cages, racks or bags, and are exposed to more diverse natural conditions such as water currents (such as ocean currents), diel vertical migration and nutrient cycles.
According to the Food and Agriculture Organization (FAO), aqu
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https://en.wikipedia.org/wiki/Kolmogorov%20complexity
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In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It is named after Andrey Kolmogorov, who first published on the subject in 1963 and is a generalization of classical information theory.
The notion of Kolmogorov complexity can be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem.
In particular, no program P computing a lower bound for each text's Kolmogorov complexity can return a value essentially larger than P's own length (see section ); hence no single program can compute the exact Kolmogorov complexity for infinitely many texts.
Definition
Consider the following two strings of 32 lowercase letters and digits:
abababababababababababababababab , and
4c1j5b2p0cv4w1x8rx2y39umgw5q85s7
The first string has a short English-language description, namely "write ab 16 times", which consists of 17 characters. The second one has no obvious simple description (using the same character set) other than writing down the string itself, i.e., "write 4c1j5b2p0cv4w1x8rx2y39umgw5q85s7" which has 38 characters. Hence the operation of writing the first string can be said to have "less complexity" than writing the second.
More formally, the complexity of a string is the length of the shortest possible description of the string in some fixed universal description language (the sensitivity of complexity relative to the choice of description language is discussed below). It can be shown that the Kolmogorov complexity of any string cannot
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https://en.wikipedia.org/wiki/Ibn%20al-Haytham
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Ḥasan Ibn al-Haytham (Latinized as Alhazen; ; full name ; ) was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq. Referred to as "the father of modern optics", he made significant contributions to the principles of optics and visual perception in particular. His most influential work is titled Kitāb al-Manāẓir (Arabic: , "Book of Optics"), written during 1011–1021, which survived in a Latin edition. The works of Alhazen were frequently cited during the scientific revolution by Isaac Newton, Johannes Kepler, Christiaan Huygens, and Galileo Galilei.
Ibn al-Haytham was the first to correctly explain the theory of vision, and to argue that vision occurs in the brain, pointing to observations that it is subjective and affected by personal experience. He also stated the principle of least time for refraction which would later become the Fermat's principle. He made major contributions to catoptrics and dioptrics by studying reflection, refraction and nature of images formed by light rays. Ibn al-Haytham was an early proponent of the concept that a hypothesis must be supported by experiments based on confirmable procedures or mathematical reasoning—an early pioneer in the scientific method five centuries before Renaissance scientists. On account of this, he is sometimes described as the world's "first true scientist". He was also a polymath, writing on philosophy, theology and medicine.
Born in Basra, he spent most of his productive period in the Fatimid capital of Cairo and earned his living authoring various treatises and tutoring members of the nobilities. Ibn al-Haytham is sometimes given the byname al-Baṣrī after his birthplace, or al-Miṣrī ("the Egyptian"). Al-Haytham was dubbed the "Second Ptolemy" by Abu'l-Hasan Bayhaqi and "The Physicist" by John Peckham. Ibn al-Haytham paved the way for the modern science of physical optics.
Biography
Ibn al-Haytham (Alhazen) was born c. 965 to a family of Arab or Persian o
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https://en.wikipedia.org/wiki/Alexander%20Anderson%20%28mathematician%29
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Alexander Anderson ( in Aberdeen – in Paris) was a Scottish mathematician.
Life
He was born in Aberdeen, possibly in 1582, according to a print which suggests he was aged 35 in 1617. It is unknown where he was educated, but it is likely that he initially studied writing and philosophy (the "belles lettres") in his home city of Aberdeen.
He then went to the continent, and was a professor of mathematics in Paris by the start of the seventeenth century. There he published or edited, between the years 1612 and 1619, various geometric and algebraic tracts. He described himself as having "more wisdom than riches" in the dedication of Vindiciae Archimedis (1616).
He was first cousin of David Anderson of Finshaugh, a celebrated mathematician, and David Anderson's daughter was the mother of mathematician James Gregory.
Work
He was selected by the executors of François Viète to revise and edit Viète's manuscript works. Viète died in 1603, and it is unclear if Anderson knew him, but his eminence was sufficient to attract the attention of the dead man's executors. Anderson corrected and expanded upon Viète's manuscripts, which extended known geometry to the new algebra, which used general symbols to represent quantities.
Publications
The known works of Anderson amount to six thin quarto volumes, and as the last of them was published in 1619, it is probable that the author died soon after that year, but the precise date is unknown. He wrote other works that have since been lost. From his last work it appears he wrote another piece, "A Treatise on the Mensuration of Solids," and copies of two other works, Ex. Math. and Stereometria Triangulorum Sphæricorum, were in the possession of Sir Alexander Hume until the after the middle of the seventeenth century.
1612: Supplementum Apollonii Redivivi
1615: Ad Angularum Sectionem Analytica Theoremata F. Vieta
1615: Pro Zetetico Apolloniani
1615: Francisci Vietae Fontenaeensis
1616: Vindiciae Archimedis
1619: Alexandri Andersoni Exe
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https://en.wikipedia.org/wiki/Arthritis
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Arthritis is a term often used to mean any disorder that affects joints. Symptoms generally include joint pain and stiffness. Other symptoms may include redness, warmth, swelling, and decreased range of motion of the affected joints. In some types of arthritis, other organs are also affected. Onset can be gradual or sudden.
There are over 100 types of arthritis. The most common forms are osteoarthritis (degenerative joint disease) and rheumatoid arthritis. Osteoarthritis usually occurs with age and affects the fingers, knees, and hips. Rheumatoid arthritis is an autoimmune disorder that often affects the hands and feet. Other types include gout, lupus, fibromyalgia, and septic arthritis. They are all types of rheumatic disease.
Treatment may include resting the joint and alternating between applying ice and heat. Weight loss and exercise may also be useful. Recommended medications may depend on the form of arthritis. These may include pain medications such as ibuprofen and paracetamol (acetaminophen). In some circumstances, a joint replacement may be useful.
Osteoarthritis affects more than 3.8% of people, while rheumatoid arthritis affects about 0.24% of people. Gout affects about 1–2% of the Western population at some point in their lives. In Australia about 15% of people are affected by arthritis, while in the United States more than 20% have a type of arthritis. Overall the disease becomes more common with age. Arthritis is a common reason that people miss work and can result in a decreased quality of life. The term is derived from arthr- (meaning 'joint') and -itis (meaning 'inflammation').
Classification
There are several diseases where joint pain is primary, and is considered the main feature. Generally when a person has "arthritis" it means that they have one of these diseases, which include:
Hemarthrosis
Osteoarthritis
Rheumatoid arthritis
Gout and pseudo-gout
Septic arthritis
Ankylosing spondylitis
Juvenile idiopathic arthritis
Still's disease
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https://en.wikipedia.org/wiki/Adenosine%20triphosphate
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Adenosine triphosphate (ATP) is an organic compound that provides energy to drive and support many processes in living cells, such as muscle contraction, nerve impulse propagation, condensate dissolution, and chemical synthesis. Found in all known forms of life, ATP is often referred to as the "molecular unit of currency" of intracellular energy transfer. When consumed in metabolic processes, it converts either to adenosine diphosphate (ADP) or to adenosine monophosphate (AMP). Other processes regenerate ATP. It is also a precursor to DNA and RNA, and is used as a coenzyme. A human adult processes around 50 kg of ATP daily.
From the perspective of biochemistry, ATP is classified as a nucleoside triphosphate, which indicates that it consists of three components: a nitrogenous base (adenine), the sugar ribose, and the triphosphate.
Structure
ATP consists of an adenine attached by the 9-nitrogen atom to the 1′ carbon atom of a sugar (ribose), which in turn is attached at the 5' carbon atom of the sugar to a triphosphate group. In its many reactions related to metabolism, the adenine and sugar groups remain unchanged, but the triphosphate is converted to di- and monophosphate, giving respectively the derivatives ADP and AMP. The three phosphoryl groups are labeled as alpha (α), beta (β), and, for the terminal phosphate, gamma (γ).
In neutral solution, ionized ATP exists mostly as ATP4−, with a small proportion of ATP3−.
Binding of metal cations to ATP
Being polyanionic and featuring a potentially chelating polyphosphate group, ATP binds metal cations with high affinity. The binding constant for is (). The binding of a divalent cation, almost always magnesium, strongly affects the interaction of ATP with various proteins. Due to the strength of the ATP-Mg2+ interaction, ATP exists in the cell mostly as a complex with bonded to the phosphate oxygen centers.
A second magnesium ion is critical for ATP binding in the kinase domain. The presence of Mg2+ regulates kin
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https://en.wikipedia.org/wiki/Antibiotic
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An antibiotic is a type of antimicrobial substance active against bacteria. It is the most important type of antibacterial agent for fighting bacterial infections, and antibiotic medications are widely used in the treatment and prevention of such infections. They may either kill or inhibit the growth of bacteria. A limited number of antibiotics also possess antiprotozoal activity. Antibiotics are not effective against viruses such as the common cold or influenza; drugs which inhibit growth of viruses are termed antiviral drugs or antivirals rather than antibiotics. They are also not effective against fungi; drugs which inhibit growth of fungi are called antifungal drugs.
Sometimes, the term antibiotic—literally "opposing life", from the Greek roots ἀντι anti, "against" and βίος bios, "life"—is broadly used to refer to any substance used against microbes, but in the usual medical usage, antibiotics (such as penicillin) are those produced naturally (by one microorganism fighting another), whereas non-antibiotic antibacterials (such as sulfonamides and antiseptics) are fully synthetic. However, both classes have the same goal of killing or preventing the growth of microorganisms, and both are included in antimicrobial chemotherapy. "Antibacterials" include antiseptic drugs, antibacterial soaps, and chemical disinfectants, whereas antibiotics are an important class of antibacterials used more specifically in medicine and sometimes in livestock feed.
Antibiotics have been used since ancient times. Many civilizations used topical application of moldy bread, with many references to its beneficial effects arising from ancient Egypt, Nubia, China, Serbia, Greece, and Rome. The first person to directly document the use of molds to treat infections was John Parkinson (1567–1650). Antibiotics revolutionized medicine in the 20th century. Alexander Fleming (1881–1955) discovered modern day penicillin in 1928, the widespread use of which proved significantly beneficial during wa
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https://en.wikipedia.org/wiki/Allotropy
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Allotropy or allotropism () is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of the elements. Allotropes are different structural modifications of an element: the atoms of the element are bonded together in different manners.
For example, the allotropes of carbon include diamond (the carbon atoms are bonded together to form a cubic lattice of tetrahedra), graphite (the carbon atoms are bonded together in sheets of a hexagonal lattice), graphene (single sheets of graphite), and fullerenes (the carbon atoms are bonded together in spherical, tubular, or ellipsoidal formations).
The term allotropy is used for elements only, not for compounds. The more general term, used for any compound, is polymorphism, although its use is usually restricted to solid materials such as crystals. Allotropy refers only to different forms of an element within the same physical phase (the state of matter, such as a solid, liquid or gas). The differences between these states of matter would not alone constitute examples of allotropy. Allotropes of chemical elements are frequently referred to as polymorphs or as phases of the element.
For some elements, allotropes have different molecular formulae or different crystalline structures, as well as a difference in physical phase; for example, two allotropes of oxygen (dioxygen, O2, and ozone, O3) can both exist in the solid, liquid and gaseous states. Other elements do not maintain distinct allotropes in different physical phases; for example, phosphorus has numerous solid allotropes, which all revert to the same P4 form when melted to the liquid state.
History
The concept of allotropy was originally proposed in 1840 by the Swedish scientist Baron Jöns Jakob Berzelius (1779–1848). The term is derived . After the acceptance of Avogadro's hypothesis in 1860, it was understood that elements could exist as polyatomic molecules, and two allotropes of oxygen were recog
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https://en.wikipedia.org/wiki/Augustin-Louis%20Cauchy
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Baron Augustin-Louis Cauchy ( , , ; 21 August 178923 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors. He (nearly) single-handedly founded complex analysis and the study of permutation groups in abstract algebra.
A profound mathematician, Cauchy had a great influence over his contemporaries and successors; Hans Freudenthal stated: "More concepts and theorems have been named for Cauchy than for any other mathematician (in elasticity alone there are sixteen concepts and theorems named for Cauchy)." Cauchy was a prolific writer; he wrote approximately eight hundred research articles and five complete textbooks on a variety of topics in the fields of mathematics and mathematical physics.
Biography
Youth and education
Cauchy was the son of Louis François Cauchy (1760–1848) and Marie-Madeleine Desestre. Cauchy had two brothers: Alexandre Laurent Cauchy (1792–1857), who became a president of a division of the court of appeal in 1847 and a judge of the court of cassation in 1849, and Eugene François Cauchy (1802–1877), a publicist who also wrote several mathematical works.
Cauchy married Aloise de Bure in 1818. She was a close relative of the publisher who published most of Cauchy's works. They had two daughters, Marie Françoise Alicia (1819) and Marie Mathilde (1823).
Cauchy's father was a highly ranked official in the Parisian Police of the
Ancien Régime, but lost this position due to the French Revolution (July 14, 1789), which broke out one month before Augustin-Louis was born. The Cauchy family survived the revolution and the following Reign of Terror (1793–94) by escaping to Arcueil, where Cauchy received his first education, from his father. After the execution of R
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https://en.wikipedia.org/wiki/Archimedes
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Archimedes of Syracuse (, ; ) was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems. These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral.
Archimedes' other mathematical achievements include deriving an approximation of pi, defining and investigating the Archimedean spiral, and devising a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, working on statics and hydrostatics. Archimedes' achievements in this area include a proof of the law of the lever, the widespread use of the concept of center of gravity, and the enunciation of the law of buoyancy or Archimedes' principle. He is also credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.
Archimedes died during the siege of Syracuse, when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting Archimedes' tomb, which was surmounted by a sphere and a cylinder that Archimedes requested be placed there to represent his mathematical discoveries.
Unlike his inventions, Archimedes' mathematical writings were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensi
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https://en.wikipedia.org/wiki/Alternative%20medicine
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Alternative medicine is any practice that aims to achieve the healing effects of medicine despite lacking biological plausibility, testability, repeatability or evidence of effectiveness. Unlike modern medicine, which employs the scientific method to test plausible therapies by way of responsible and ethical clinical trials, producing repeatable evidence of either effect or of no effect, alternative therapies reside outside of medical science and do not originate from using the scientific method, but instead rely on testimonials, anecdotes, religion, tradition, superstition, belief in supernatural "energies", pseudoscience, errors in reasoning, propaganda, fraud, or other unscientific sources. Frequently used terms for relevant practices are New Age medicine, pseudo-medicine, unorthodox medicine, holistic medicine, fringe medicine, and unconventional medicine, with little distinction from quackery.
Some alternative practices are based on theories that contradict the established science of how the human body works; others resort to the supernatural or superstitious to explain their effect or lack thereof. In others, the practice has plausibility but lacks a positive risk–benefit outcome probability. Research into alternative therapies often fails to follow proper research protocols (such as placebo-controlled trials, blind experiments and calculation of prior probability), providing invalid results. History has shown that if a method is proven to work, it eventually ceases to be alternative and becomes mainstream medicine.
Much of the perceived effect of an alternative practice arises from a belief that it will be effective (the placebo effect), or from the treated condition resolving on its own (the natural course of disease). This is further exacerbated by the tendency to turn to alternative therapies upon the failure of medicine, at which point the condition will be at its worst and most likely to spontaneously improve. In the absence of this bias, especially fo
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https://en.wikipedia.org/wiki/Abzyme
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An abzyme (from antibody and enzyme), also called catmab (from catalytic monoclonal antibody), and most often called catalytic antibody or sometimes catab, is a monoclonal antibody with catalytic activity. Abzymes are usually raised in lab animals immunized against synthetic haptens, but some natural abzymes can be found in normal humans (anti-vasoactive intestinal peptide autoantibodies) and in patients with autoimmune diseases such as systemic lupus erythematosus, where they can bind to and hydrolyze DNA. To date abzymes display only weak, modest catalytic activity and have not proved to be of any practical use. They are, however, subjects of considerable academic interest. Studying them has yielded important insights into reaction mechanisms, enzyme structure and function, catalysis, and the immune system itself.
Enzymes function by lowering the activation energy of the transition state of a chemical reaction, thereby enabling the formation of an otherwise less-favorable molecular intermediate between the reactant(s) and the product(s). If an antibody is developed to bind to a molecule that is structurally and electronically similar to the transition state of a given chemical reaction, the developed antibody will bind to, and stabilize, the transition state, just like a natural enzyme, lowering the activation energy of the reaction, and thus catalyzing the reaction. By raising an antibody to bind to a stable transition-state analog, a new and unique type of enzyme is produced.
So far, all catalytic antibodies produced have displayed only modest, weak catalytic activity. The reasons for low catalytic activity for these molecules have been widely discussed. Possibilities indicate that factors beyond the binding site may play an important role, in particular through protein dynamics. Some abzymes have been engineered to use metal ions and other cofactors to improve their catalytic activity.
History
The possibility of catalyzing a reaction by means of an antibody
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https://en.wikipedia.org/wiki/Adaptive%20radiation
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In evolutionary biology, adaptive radiation is a process in which organisms diversify rapidly from an ancestral species into a multitude of new forms, particularly when a change in the environment makes new resources available, alters biotic interactions or opens new environmental niches. Starting with a single ancestor, this process results in the speciation and phenotypic adaptation of an array of species exhibiting different morphological and physiological traits. The prototypical example of adaptive radiation is finch speciation on the Galapagos ("Darwin's finches"), but examples are known from around the world.
Characteristics
Four features can be used to identify an adaptive radiation:
A common ancestry of component species: specifically a recent ancestry. Note that this is not the same as a monophyly in which all descendants of a common ancestor are included.
A phenotype-environment correlation: a significant association between environments and the morphological and physiological traits used to exploit those environments.
Trait utility: the performance or fitness advantages of trait values in their corresponding environments.
Rapid speciation: presence of one or more bursts in the emergence of new species around the time that ecological and phenotypic divergence is underway.
Conditions
Adaptive radiations are thought to be triggered by an ecological opportunity or a new adaptive zone. Sources of ecological opportunity can be the loss of antagonists (competitors or predators), the evolution of a key innovation or dispersal to a new environment. Any one of these ecological opportunities has the potential to result in an increase in population size and relaxed stabilizing (constraining) selection. As genetic diversity is positively correlated with population size the expanded population will have more genetic diversity compared to the ancestral population. With reduced stabilizing selection phenotypic diversity can also increase. In addition, intraspecific
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https://en.wikipedia.org/wiki/Agarose%20gel%20electrophoresis
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Agarose gel electrophoresis is a method of gel electrophoresis used in biochemistry, molecular biology, genetics, and clinical chemistry to separate a mixed population of macromolecules such as DNA or proteins in a matrix of agarose, one of the two main components of agar. The proteins may be separated by charge and/or size (isoelectric focusing agarose electrophoresis is essentially size independent), and the DNA and RNA fragments by length. Biomolecules are separated by applying an electric field to move the charged molecules through an agarose matrix, and the biomolecules are separated by size in the agarose gel matrix.
Agarose gel is easy to cast, has relatively fewer charged groups, and is particularly suitable for separating DNA of size range most often encountered in laboratories, which accounts for the popularity of its use. The separated DNA may be viewed with stain, most commonly under UV light, and the DNA fragments can be extracted from the gel with relative ease. Most agarose gels used are between 0.7–2% dissolved in a suitable electrophoresis buffer.
Properties of agarose gel
Agarose gel is a three-dimensional matrix formed of helical agarose molecules in supercoiled bundles that are aggregated into three-dimensional structures with channels and pores through which biomolecules can pass. The 3-D structure is held together with hydrogen bonds and can therefore be disrupted by heating back to a liquid state. The melting temperature is different from the gelling temperature, depending on the sources, agarose gel has a gelling temperature of 35–42 °C and a melting temperature of 85–95 °C. Low-melting and low-gelling agaroses made through chemical modifications are also available.
Agarose gel has large pore size and good gel strength, making it suitable as an anticonvection medium for the electrophoresis of DNA and large protein molecules. The pore size of a 1% gel has been estimated from 100 nm to 200–500 nm, and its gel strength allows gels as dilute
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https://en.wikipedia.org/wiki/Allele
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An allele is a variation of the same sequence of nucleotides at the same place on a long DNA molecule, as described in leading textbooks on genetics and evolution. The word is a short form of "allelomorph".
"The chromosomal or genomic location of a gene or any other genetic element is called a locus (plural: loci) and alternative DNA sequences at a locus are called alleles."
The simplest alleles are single nucleotide polymorphisms (SNP), but they can also be insertions and deletions of up to several thousand base pairs.
Most alleles observed result in little or no change in the function of the gene product it codes for. However, sometimes different alleles can result in different observable phenotypic traits, such as different pigmentation. A notable example of this is Gregor Mendel's discovery that the white and purple flower colors in pea plants were the result of a single gene with two alleles.
Nearly all multicellular organisms have two sets of chromosomes at some point in their biological life cycle; that is, they are diploid. In this case, the chromosomes can be paired. Each chromosome in the pair contains the same genes in the same order, and place, along the length of the chromosome. For a given gene, if the two chromosomes contain the same allele, they, and the organism, are homozygous with respect to that gene. If the alleles are different, they, and the organism, are heterozygous with respect to that gene.
Popular definitions of 'allele' typically refer only to different alleles within genes. For example, the ABO blood grouping is controlled by the ABO gene, which has six common alleles (variants). In population genetics, nearly every living human's phenotype for the ABO gene is some combination of just these six alleles.
Etymology
The word "allele" is a short form of allelomorph ("other form", a word coined by British geneticists William Bateson and Edith Rebecca Saunders) in the 1920s, which was used in the early days of genetics to describe varia
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https://en.wikipedia.org/wiki/Antimicrobial%20resistance
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Antimicrobial resistance (AMR) occurs when microbes evolve mechanisms that protect them from the effects of antimicrobials (drugs used to treat infections). All classes of microbes can evolve resistance where the drugs are no longer effective. Fungi evolve antifungal resistance. Viruses evolve antiviral resistance. Protozoa evolve antiprotozoal resistance, and bacteria evolve antibiotic resistance. Together all of these come under the umbrella of antimicrobial resistance. Microbes resistant to multiple antimicrobials are called multidrug resistant (MDR) and are sometimes referred to as superbugs. Although antimicrobial resistance is a naturally occurring process, it is often the result of improper usage of the drugs and management of the infections.
Antibiotic resistance is a major subset of AMR, that applies specifically to bacteria that become resistant to antibiotics. Resistance in bacteria can arise naturally by genetic mutation, or by one species acquiring resistance from another. Resistance can appear spontaneously because of random mutations, but also arises through spreading of resistant genes through horizontal gene transfer. However, extended use of antibiotics appears to encourage selection for mutations which can render antibiotics ineffective. Antifungal resistance is a subset of AMR, that specifically applies to fungi that have become resistant to antifungals. Resistance to antifungals can arise naturally, for example by genetic mutation or through aneuploidy. Extended use of antifungals leads to development of antifungal resistance through various mechanisms.
Clinical conditions due to infections caused by microbes containing AMR cause millions of deaths each year. In 2019 there were around 1.27 million deaths globally caused by bacterial AMR. Infections caused by resistant microbes are more difficult to treat, requiring higher doses of antimicrobial drugs, more expensive antibiotics, or alternative medications which may prove more toxic. These appr
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https://en.wikipedia.org/wiki/Antigen
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In immunology, an antigen (Ag) is a molecule, moiety, foreign particulate matter, or an allergen, such as pollen, that can bind to a specific antibody or T-cell receptor. The presence of antigens in the body may trigger an immune response.
Antigens can be proteins, peptides (amino acid chains), polysaccharides (chains of simple sugars), lipids, or nucleic acids. Antigens exist on normal cells, cancer cells, parasites, viruses, fungi, and bacteria.
Antigens are recognized by antigen receptors, including antibodies and T-cell receptors. Diverse antigen receptors are made by cells of the immune system so that each cell has a specificity for a single antigen. Upon exposure to an antigen, only the lymphocytes that recognize that antigen are activated and expanded, a process known as clonal selection. In most cases, antibodies are antigen-specific, meaning that an antibody can only react to and bind one specific antigen; in some instances, however, antibodies may cross-react to bind more than one antigen. The reaction between an antigen and an antibody is called the antigen-antibody reaction.
Antigen can originate either from within the body ("self-protein" or "self antigens") or from the external environment ("non-self"). The immune system identifies and attacks "non-self" external antigens. Antibodies usually do not react with self-antigens due to negative selection of T cells in the thymus and B cells in the bone marrow. The diseases in which antibodies react with self antigens and damage the body's own cells are called autoimmune diseases.
Vaccines are examples of antigens in an immunogenic form, which are intentionally administered to a recipient to induce the memory function of the adaptive immune system towards antigens of the pathogen invading that recipient. The vaccine for seasonal influenza is a common example.
Etymology
Paul Ehrlich coined the term antibody () in his side-chain theory at the end of the 19th century. In 1899, Ladislas Deutsch (László Detr
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https://en.wikipedia.org/wiki/Autosome
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An autosome is any chromosome that is not a sex chromosome. The members of an autosome pair in a diploid cell have the same morphology, unlike those in allosomal (sex chromosome) pairs, which may have different structures. The DNA in autosomes is collectively known as atDNA or auDNA.
For example, humans have a diploid genome that usually contains 22 pairs of autosomes and one allosome pair (46 chromosomes total). The autosome pairs are labeled with numbers (1–22 in humans) roughly in order of their sizes in base pairs, while allosomes are labelled with their letters. By contrast, the allosome pair consists of two X chromosomes in females or one X and one Y chromosome in males. Unusual combinations of XYY, XXY, XXX, XXXX, XXXXX or XXYY, among other Salome combinations, are known to occur and usually cause developmental abnormalities.
Autosomes still contain sexual determination genes even though they are not sex chromosomes. For example, the SRY gene on the Y chromosome encodes the transcription factor TDF and is vital for male sex determination during development. TDF functions by activating the SOX9 gene on chromosome 17, so mutations of the SOX9 gene can cause humans with an ordinary Y chromosome to develop as females.
All human autosomes have been identified and mapped by extracting the chromosomes from a cell arrested in metaphase or prometaphase and then staining them with a type of dye (most commonly, Giemsa). These chromosomes are typically viewed as karyograms for easy comparison. Clinical geneticists can compare the karyogram of an individual to a reference karyogram to discover the cytogenetic basis of certain phenotypes. For example, the karyogram of someone with Patau Syndrome would show that they possess three copies of chromosome 13. Karyograms and staining techniques can only detect large-scale disruptions to chromosomes—chromosomal aberrations smaller than a few million base pairs generally cannot be seen on a karyogram.
Autosomal genetic disorde
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https://en.wikipedia.org/wiki/Alessandro%20Volta
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Alessandro Giuseppe Antonio Anastasio Volta (, ; 18 February 1745 – 5 March 1827) was an Italian physicist and chemist who was a pioneer of electricity and power and is credited as the inventor of the electric battery and the discoverer of methane. He invented the voltaic pile in 1799, and reported the results of his experiments in 1800 in a two-part letter to the president of the Royal Society. With this invention Volta proved that electricity could be generated chemically and debunked the prevalent theory that electricity was generated solely by living beings. Volta's invention sparked a great amount of scientific excitement and led others to conduct similar experiments, which eventually led to the development of the field of electrochemistry.
Volta also drew admiration from Napoleon Bonaparte for his invention, and was invited to the Institute of France to demonstrate his invention to the members of the institute. Throughout his life, Volta enjoyed a certain amount of closeness with the emperor who conferred upon him numerous honours.
Volta held the chair of experimental physics at the University of Pavia for nearly 40 years and was widely idolised by his students. Despite his professional success, Volta was inclined towards domestic life and this was more apparent in his later years when he tended to live secluded from public life and more for the sake of his family. He died in 1827 from a series of illnesses which began in 1823. The SI unit of electric potential is named the volt in his honour.
Personal life
Volta was born in Como, a town in northern Italy, on 18 February 1745. His father, Filippo Volta, was of noble lineage. His mother, Donna Maddalena, came from the family of the Inzaghis. In 1794, Volta married an aristocratic lady also from Como, Teresa Peregrini, with whom he raised three sons: Zanino, Flaminio, and Luigi.
Career
In 1774, he became a professor of physics at the Royal School in Como. A year later, he improved and popularised the elect
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https://en.wikipedia.org/wiki/Aeon
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The word aeon , also spelled eon (in American and Australian English), originally meant "life", "vital force" or "being", "generation" or "a period of time", though it tended to be translated as "age" in the sense of "ages", "forever", "timeless" or "for eternity". It is a Latin transliteration from the ancient Greek word (), from the archaic () meaning "century". In Greek, it literally refers to the timespan of one hundred years. A cognate Latin word or (cf. ) for "age" is present in words such as longevity and mediaeval.
Although the term aeon may be used in reference to a period of a billion years (especially in geology, cosmology and astronomy), its more common usage is for any long, indefinite period. Aeon can also refer to the four aeons on the geologic time scale that make up the Earth's history, the Hadean, Archean, Proterozoic, and the current aeon, Phanerozoic.
Astronomy and cosmology
In astronomy, an aeon is defined as a billion years (109 years, abbreviated AE).
Roger Penrose uses the word aeon to describe the period between successive and cyclic Big Bangs within the context of conformal cyclic cosmology.
Philosophy and mysticism
In Buddhism, an "aeon" or (Sanskrit: ) is often said to be 1,334,240,000 years, the life cycle of the world.
Christianity's idea of "eternal life" comes from the word for life, (), and a form of (), which could mean life in the next aeon, the Kingdom of God, or Heaven, just as much as immortality, as in .
According to Christian universalism, the Greek New Testament scriptures use the word () to mean a long period and the word () to mean "during a long period"; thus, there was a time before the aeons, and the aeonian period is finite. After each person's mortal life ends, they are judged worthy of aeonian life or aeonian punishment. That is, after the period of the aeons, all punishment will cease and death is overcome and then God becomes the all in each one (). This contrasts with the conventional Christian b
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https://en.wikipedia.org/wiki/American%20Civil%20Liberties%20Union
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The American Civil Liberties Union (ACLU) is an American nonprofit human rights organization founded in 1920. The organization strives "to defend and preserve the individual rights and liberties guaranteed to every person in this country by the Constitution and laws of the United States". The ACLU works through litigation and lobbying and has over 1,800,000 members as of July 2018, with an annual budget of over $300 million. Affiliates of the ACLU are active in all 50 states, Washington, D.C., and Puerto Rico. The ACLU provides legal assistance in cases where it considers civil liberties at risk. Legal support from the ACLU can take the form of direct legal representation or preparation of amicus curiae briefs expressing legal arguments when another law firm is already providing representation.
In addition to representing persons and organizations in lawsuits, the ACLU lobbies for policy positions established by its board of directors. Current positions of the ACLU include opposing the death penalty; supporting same-sex marriage and the right of LGBT people to adopt; supporting reproductive rights such as birth control and abortion rights; eliminating discrimination against women, minorities, and LGBT people; decarceration in the United States; protecting housing and employment rights of veterans; reforming sex offender registries and protecting housing and employment rights of convicted first-time offenders; supporting the rights of prisoners and opposing torture; and upholding the separation of church and state by opposing government preference for religion over non-religion or for particular faiths over others.
Legally, the ACLU consists of two separate but closely affiliated nonprofit organizations, namely the American Civil Liberties Union, a 501(c)(4) social welfare group; and the ACLU Foundation, a 501(c)(3) public charity. Both organizations engage in civil rights litigation, advocacy, and education, but only donations to the 501(c)(3) foundation are tax d
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https://en.wikipedia.org/wiki/Apparent%20magnitude
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Apparent magnitude () is a measure of the brightness of a star or other astronomical object. An object's apparent magnitude depends on its intrinsic luminosity, its distance, and any extinction of the object's light caused by interstellar dust along the line of sight to the observer.
The word magnitude in astronomy, unless stated otherwise, usually refers to a celestial object's apparent magnitude. The magnitude scale dates back to the ancient Roman astronomer Claudius Ptolemy, whose star catalog listed stars from 1st magnitude (brightest) to 6th magnitude (dimmest). The modern scale was mathematically defined in a way to closely match this historical system.
The scale is reverse logarithmic: the brighter an object is, the lower its magnitude number. A difference of 1.0 in magnitude corresponds to a brightness ratio of , or about 2.512. For example, a star of magnitude 2.0 is 2.512 times as bright as a star of magnitude 3.0, 6.31 times as bright as a star of magnitude 4.0, and 100 times as bright as one of magnitude 7.0.
Differences in astronomical magnitudes can also be related to another logarithmic ratio scale, the decibel: an increase of one astronomical magnitude is exactly equal to a decrease of 4 decibels (dB).
The brightest astronomical objects have negative apparent magnitudes: for example, Venus at −4.2 or Sirius at −1.46. The faintest stars visible with the naked eye on the darkest night have apparent magnitudes of about +6.5, though this varies depending on a person's eyesight and with altitude and atmospheric conditions. The apparent magnitudes of known objects range from the Sun at −26.832 to objects in deep Hubble Space Telescope images of magnitude +31.5.
The measurement of apparent magnitude is called photometry. Photometric measurements are made in the ultraviolet, visible, or infrared wavelength bands using standard passband filters belonging to photometric systems such as the UBV system or the Strömgren uvbyβ system.
Absolute magnitude is a
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https://en.wikipedia.org/wiki/Algebraic%20geometry
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Algebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.
The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular points, inflection points and points at infinity. More advanced questions involve the topology of the curve and the relationship between curves defined by different equations.
Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. As a study of systems of polynomial equations in several variables, the subject of algebraic geometry begins with finding specific solutions via equation solving, and then proceeds to understand the intrinsic properties of the totality of solutions of a system of equations. This understanding requires both conceptual theory and computational technique.
In the 20th century, algebraic geometry split into several subareas.
The mainstream of algebraic geometry is devoted to the study of the complex points of the algebraic varieties and more generally to the points with coordinates in an algebraically closed field.
Real algebraic geometry is the study of the real algebraic varieties.
Diophantine geometry and, more generally, arithmetic geometry is the study of algebraic
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https://en.wikipedia.org/wiki/Comparison%20of%20American%20and%20British%20English
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The English language was introduced to the Americas by British colonisation, beginning in the late 16th and early 17th centuries. The language also spread to numerous other parts of the world as a result of British trade and colonisation and the spread of the former British Empire, which, by 1921, included 470–570 million people, about a quarter of the world's population. Note that in England, Wales, Ireland and especially parts of Scotland there are differing varieties of the English language, so the term 'British English' is an oversimplification. Written forms of 'British' and American English as found in newspapers and textbooks vary little in their essential features, with only occasional noticeable differences.
Over the past 400 years, the forms of the language used in the Americas—especially in the United States—and that used in the United Kingdom have diverged in a few minor ways, leading to the versions now often referred to as American English and British English. Differences between the two include pronunciation, grammar, vocabulary (lexis), spelling, punctuation, idioms, and formatting of dates and numbers. However, the differences in written and most spoken grammar structure tend to be much fewer than in other aspects of the language in terms of mutual intelligibility. A few words have completely different meanings in the two versions or are even unknown or not used in one of the versions. One particular contribution towards formalising these differences came from Noah Webster, who wrote the first American dictionary (published 1828) with the intention of showing that people in the United States spoke a different dialect from those spoken in the UK, much like a regional accent.
This divergence between American English and British English has provided opportunities for humorous comment: e.g. in fiction George Bernard Shaw says that the United States and United Kingdom are "two countries divided by a common language"; and Oscar Wilde says that "We have
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https://en.wikipedia.org/wiki/Arbor%20Day
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Arbor Day (or Arbour Day in some countries) is a secular day of observance in which individuals and groups are encouraged to plant trees. Today, many countries observe such a holiday. Though usually observed in the spring, the date varies, depending on climate and suitable planting season.
Origins and history
First Arbor Day
The Spanish village of Mondoñedo held the first documented arbor plantation festival in the world organized by its mayor in 1594. The place remains as Alameda de los Remedios and it is still planted with lime and horse-chestnut trees. A humble granite marker and a bronze plate recall the event. Additionally, the small Spanish village of Villanueva de la Sierra held the first modern Arbor Day, an initiative launched in 1805 by the local priest with the enthusiastic support of the entire population.
First American Arbor Day
The first American Arbor Day was originated by J. Sterling Morton of Nebraska City, Nebraska, at an annual meeting of the Nebraska State board of agriculture held in Lincoln. On April 10, 1872, an estimated one million trees were planted in Nebraska.
In 1883, the American Forestry Association made Northrop the Chairman of the committee to campaign for Arbor Day nationwide. Birdsey Northrop of Connecticut was responsible for globalizing the idea when he visited Japan in 1895 and delivered his Arbor Day and Village Improvement message. He also brought his enthusiasm for Arbor Day to Australia, Canada, and Europe.
McCreight and Theodore Roosevelt
Beginning in 1906, Pennsylvania conservationist Major Israel McCreight of DuBois, Pennsylvania, argued that President Theodore Roosevelt’s conservation speeches were limited to businessmen in the lumber industry and recommended a campaign of youth education and a national policy on conservation education. McCreight urged Roosevelt to make a public statement to school children about trees and the destruction of American forests. Conservationist Gifford Pinchot, Chief of the Unite
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https://en.wikipedia.org/wiki/A.%20J.%20Ayer
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Sir Alfred Jules "Freddie" Ayer ( ; 29 October 1910 – 27 June 1989), usually cited as A. J. Ayer, was an English philosopher known for his promotion of logical positivism, particularly in his books Language, Truth, and Logic (1936) and The Problem of Knowledge (1956).
Ayer was educated at Eton College and the University of Oxford, after which he studied the philosophy of logical positivism at the University of Vienna. From 1933 to 1940 he lectured on philosophy at Christ Church, Oxford.
During the Second World War Ayer was a Special Operations Executive and MI6 agent.
Ayer was Grote Professor of the Philosophy of Mind and Logic at University College London from 1946 until 1959, after which he returned to Oxford to become Wykeham Professor of Logic at New College. He was president of the Aristotelian Society from 1951 to 1952 and knighted in 1970. He was known for his advocacy of humanism, and was the second president of the British Humanist Association (now known as Humanists UK).
Ayer was president of the Homosexual Law Reform Society for a time; he remarked, "as a notorious heterosexual I could never be accused of feathering my own nest."
Life
Ayer was born in St John's Wood, in north west London, to Jules Louis Cyprien Ayer and Reine (née Citroen), wealthy parents from continental Europe. His mother was from the Dutch-Jewish family that founded the Citroën car company in France; his father was a Swiss Calvinist financier who worked for the Rothschild family, including for their bank and as secretary to Alfred Rothschild.
Ayer was educated at Ascham St Vincent's School, a former boarding preparatory school for boys in the seaside town of Eastbourne in Sussex, where he started boarding at the relatively early age of seven for reasons to do with the First World War, and at Eton College, where he was a King's Scholar. At Eton Ayer first became known for his characteristic bravado and precocity. Though primarily interested in his intellectual pursuits, he was
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https://en.wikipedia.org/wiki/Atle%20Selberg
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Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician known for his work in analytic number theory and the theory of automorphic forms, and in particular for bringing them into relation with spectral theory. He was awarded the Fields Medal in 1950 and an honorary Abel Prize in 2002.
Early years
Selberg was born in Langesund, Norway, the son of teacher Anna Kristina Selberg and mathematician Ole Michael Ludvigsen Selberg. Two of his three brothers, Sigmund and Henrik, were also mathematicians. His other brother, Arne, was a professor of engineering.
While he was still at school he was influenced by the work of Srinivasa Ramanujan and he found an exact analytical formula for the partition function as suggested by the works of Ramanujan; however, this result was first published by Hans Rademacher.
He studied at the University of Oslo and completed his PhD in 1943.
World War II
During World War II, Selberg worked in isolation due to the German occupation of Norway. After the war, his accomplishments became known, including a proof that a positive proportion of the zeros of the Riemann zeta function lie on the line .
During the war, he fought against the German invasion of Norway, and was imprisoned several times.
Post-war in Norway
After the war, he turned to sieve theory, a previously neglected topic which Selberg's work brought into prominence. In a 1947 paper he introduced the Selberg sieve, a method well adapted in particular to providing auxiliary upper bounds, and which contributed to Chen's theorem, among other important results.
In 1948 Selberg submitted two papers in Annals of Mathematics in which he proved by elementary means the theorems for primes in arithmetic progression and the density of primes. This challenged the widely held view of his time that certain theorems are only obtainable with the advanced methods of complex analysis. Both results were based on his work on the asymptotic formula
where
for primes . He establish
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https://en.wikipedia.org/wiki/Andrew%20Wiles
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Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal by the Royal Society. He was appointed Knight Commander of the Order of the British Empire in 2000, and in 2018, was appointed the first Regius Professor of Mathematics at Oxford. Wiles is also a 1997 MacArthur Fellow.
Education and early life
Wiles was born on 11 April 1953 in Cambridge, England, the son of Maurice Frank Wiles (1923–2005) and Patricia Wiles (née Mowll). From 1952 to 1955, his father worked as the chaplain at Ridley Hall, Cambridge, and later became the Regius Professor of Divinity at the University of Oxford.
Wiles began his formal schooling in Nigeria, while living there as a very young boy with his parents. However, according to letters written by his parents, for at least the first several months after he was supposed to be attending classes, he refused to go. From that fact, Wiles himself concluded that he was not in his earliest years enthusiastic about spending time in academic institutions. He trusts the letters, though he could not remember himself a time when he did not enjoy solving mathematical problems.
Wiles attended King's College School, Cambridge, and The Leys School, Cambridge. Wiles states that he came across Fermat's Last Theorem on his way home from school when he was 10 years old. He stopped at his local library where he found a book The Last Problem, by Eric Temple Bell, about the theorem. Fascinated by the existence of a theorem that was so easy to state that he, a ten-year-old, could understand it, but that no one had proven, he decided to be the first person to prove it. However, he soon realised that his knowledge was too limited, so he abandoned his childhood dream until it was brought back to his attention at the age of 33 by Ken
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