source
stringlengths 31
207
| text
stringlengths 12
1.5k
|
|---|---|
https://en.wikipedia.org/wiki/Maw
|
Maw may refer to:
Biology
A human's or animal's stomach or gullet, a bird's crop
A fish's gas bladder (swim bladder)
Abomasum, the fourth stomach of a ruminant
Games
Maw (game), a card game
The Maw, a 2009 video game
The Maw, the main setting of the video game Little Nightmares
Maw, a character in the video game My Singing Monsters
People with the surname
Carlyle E. Maw (1903–1987), American lawyer and politician
Herbert B. Maw (1893–1990), American politician
Nicholas Maw (1935–2009), British composer
William Maw (1838–1924), British civil engineer
Other
Scottish and North American slang for "mother"
Maw (state), one of the Shan states of Southeast Asia
Maw language (disambiguation)
Mace (bludgeon), a weapon
Maw & Co, British manufacturer of ceramic tiles
See also
MAW (disambiguation)
Mawe (disambiguation)
|
https://en.wikipedia.org/wiki/J.%20J.%20C.%20Smart
|
John Jamieson Carswell Smart (16 September 1920 – 6 October 2012), was a British-Australian philosopher and was appointed as an Emeritus Professor by the Australian National University. He worked in the fields of metaphysics, philosophy of science, philosophy of mind, philosophy of religion, and political philosophy. He wrote multiple entries for the Stanford Encyclopedia of Philosophy.
Career
Born in Cambridge, England, of Scottish parents, Smart began his education locally, attending The Leys School, a leading independent boarding school. His younger brothers also became professors: Alastair (1922–1992) was Professor of Art History at Nottingham University; Ninian was a professor of religious studies and a pioneer in that field. Their father, William Marshall Smart, was John Couch Adams Astronomer at Cambridge University and later Regius Professor of Astronomy at Glasgow. In 1950, W. M. Smart was President of the Royal Astronomical Society. In 1946, Jack Smart graduated from the University of Glasgow with an MA, followed by a BPhil from Oxford University in 1948. He then worked as a Junior Research Fellow at Corpus Christi College, Oxford, for two years.
Smart served in the Second World War with the British Army where he was commissioned as a second lieutenant in the Royal Corps of Signals on 9 October 1941 and given the service number 212091. His war service was mainly in India and Burma. He was demobilised in April 1946 and in 1950 was granted the honorary rank of lieu
|
https://en.wikipedia.org/wiki/1869%20in%20science
|
The year 1869 in science and technology involved some significant events, listed below.
Events
November 4 – The first issue of scientific journal Nature is published in London, edited by Norman Lockyer.
Chemistry
March 6 – Dmitri Mendeleev makes a formal presentation of his periodic table to the Russian Chemical Society.
June 15 – John Wesley Hyatt patents celluloid, in Albany, New York.
July 15 – Hippolyte Mège-Mouriès files a patent for margarine (as oleomargarine) in France as a beef tallow and skimmed milk substitute for butter.
German chemist Lothar Meyer makes a formal presentation of the revised and expanded version of his independently-created 1864 periodic table, „Die Natur der chemischen Elemente als Funktion ihrer Atomgewichte".
Publication of Adolphe Wurtz's Dictionnaire de chimie pure et appliquée begins in Paris.
Life sciences
April 6 – The American Museum of Natural History is founded in New York.
June 24 – Sea Birds Preservation Act passed in the United Kingdom, preventing killing of designated species during the breeding season, the first Act to offer any protection to British wild birds.
Paul Langerhans discovers the pancreatic islets.
Friedrich Miescher discovers deoxyribonucleic acid (DNA) in the pus of discarded surgical bandages. Found in the nuclei of cells, Miescher names it "nuclein".
Neurasthenia is first published as a diagnosis in psychopathology by Michigan alienist E. H. Van Deusen of the Kalamazoo asylum followed a few months lat
|
https://en.wikipedia.org/wiki/1861%20in%20science
|
The year 1861 in science and technology involved some significant events, listed below.
Astronomy
May 13 – Comet C/1861 J1 (the "Great Comet of 1861") first observed from Australia by John Tebbutt.
Biology
Anton de Bary publishes his first work on fungi, describing sexual reproduction in Peronospora.
Charles Thorp, Archdeacon of Durham (d. 1862), arranges purchase of some of the Farne Islands off the north-east coast of England and employment of a warden to protect threatened seabird species.
Chemistry
March 30 – William Crookes announces his discovery of thallium.
Rubidium is discovered by Robert Bunsen and Gustav Kirchhoff, in Heidelberg, Germany, in the mineral lepidolite through the use of their spectroscope.
Aleksandr Butlerov is instrumental in creating the theory of chemical structure.
Josef Loschmidt publishes Chemische Studien, proposing two-dimensional representations for over 300 molecules and recognising variations in atomic size.
Ernest Solvay develops the Solvay process for the manufacture of soda ash (sodium carbonate).
Earth sciences
Eduard Suess proposes the former existence of the supercontinent Gondwana.
History of science and technology
Boulton and Watt rotative beam engine of 1788 from the makers' Soho Foundry in the west midlands of England is acquired for the Museum of Patents, predecessor of the Science Museum, London.
First volumes of Munk's Roll published.
Medicine and physiology
Paul Broca identifies the speech production center o
|
https://en.wikipedia.org/wiki/1857%20in%20science
|
The year 1857 in science and technology involved some significant events, listed below.
Astronomy
Peter Andreas Hansen's Tables of the Moon are published in London.
Biology
Rev. M. J. Berkeley publishes Introduction to Cryptogamic Botany.
Chemistry
Robert Bunsen invents apparatus for measuring effusion.
August Kekulé proposes that carbon is tetravalent, or forms exactly four chemical bonds.
Carl Wilhelm Siemens patents the Siemens cycle.
Earth sciences
January 9 – The 7.9 Fort Tejon earthquake shakes Central and Southern California with a maximum Mercalli intensity of IX (Violent). The event, which involves slip on the southern segment of the San Andreas Fault, leaves two people dead.
Friedrich Albert Fallou publishes Anfangsgründe der Bodenkunde [First Principles of Soil Science], laying the foundations for the modern study of soil science.
Exploration
May 16 – The British North American Exploring Expedition, led by Irish geographer Capt. John Palliser, sets off for a three-year exploration of Western Canada.
Galen Clark becomes the first European American to see the Mariposa Grove of giant sequoias in California.
History of science and technology
The Stockton and Darlington Railway's Locomotion No. 1 of 1825 is set aside for preservation in England.
Mathematics
William Rowan Hamilton invents the Icosian game.
Medicine
March 12 – Elizabeth Blackwell opens the New York Infirmary for Indigent Women and Children.
French surgeon Jean-Louis-Paul Denucé gives
|
https://en.wikipedia.org/wiki/1854%20in%20science
|
The year 1854 in science and technology involved some significant events, listed below.
Astronomy
July 22 – Discovery of the asteroid 30 Urania by John Russell Hind.
October c. – George Airy calculates the mean density of the Earth by measuring the gravity in a coal mine in South Shields.
Chemistry
Benjamin Silliman of Yale University is the first person to fractionate petroleum into its individual components by distillation.
Exploration
January 4 – First definite sighting of McDonald Islands in the Antarctic.
Mathematics
March 26 – Playfair cipher first demonstrated, by Charles Wheatstone.
George Boole's work on algebraic logic, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, published in London.
Arthur Cayley states the original version of Cayley's theorem and produces the first Cayley table.
Bernhard Riemann, a German mathematician, submits his habilitation thesis ("About the representability of a function by a trigonometric series"), in which he describes the Riemann integral. It is published by Richard Dedekind in 1867.
Medicine
April–May – Dr John Snow traces the source of one outbreak of cholera in London (which kills 500) to a single water pump, validating his theory that cholera is water-borne, and forming the starting point for epidemiology.
November – Florence Nightingale and her team of trained volunteer nurses arrive at Selimiye Barracks in Scutari in the Ottoman Empire to care for
|
https://en.wikipedia.org/wiki/1849%20in%20science
|
The year 1849 in science and technology involved some significant events, listed below.
Astronomy
Édouard Roche finds the limiting radius of tidal destruction and tidal creation for a body held together only by its self gravity, called the Roche limit, and uses it to explain why Saturn's rings do not condense into a satellite.
Biology
Arnold Adolph Berthold pioneers endocrinology with his observations on the operation of the testicles in roosters.
Nikolai Annenkov begins publication of Flora Mosquensis Exsiccata, the first Russian Flora.
Richard Owen publishes On the Nature of Limbs and begins publication of A History of British Fossil Reptiles.
William Thompson begins publication (in London) of The Natural History of Ireland with the first volume on birds.
Chemistry
Charles-Adolphe Wurtz obtains methylamine.
Louis Pasteur discovers that the racemic form of tartaric acid is a mixture of the levorotatory and dextrotatory forms, thus clarifying the nature of optical rotation and advancing the field of stereochemistry.
Mathematics
George Gabriel Stokes shows that solitary waves can arise from a combination of periodic waves.
Medicine
January 23 – English-born Elizabeth Blackwell is awarded her M.D. by the Medical Institute of Geneva, New York, becoming the first woman to qualify as a doctor in the United States.
British physician Dr. Thomas Addison first describes Addison’s disease in his On the Constitutional and Local Effects of Disease of the Suprarenal Capsule
|
https://en.wikipedia.org/wiki/Neuroevolution
|
Neuroevolution, or neuro-evolution, is a form of artificial intelligence that uses evolutionary algorithms to generate artificial neural networks (ANN), parameters, and rules. It is most commonly applied in artificial life, general game playing and evolutionary robotics. The main benefit is that neuroevolution can be applied more widely than supervised learning algorithms, which require a syllabus of correct input-output pairs. In contrast, neuroevolution requires only a measure of a network's performance at a task. For example, the outcome of a game (i.e., whether one player won or lost) can be easily measured without providing labeled examples of desired strategies. Neuroevolution is commonly used as part of the reinforcement learning paradigm, and it can be contrasted with conventional deep learning techniques that use gradient descent on a neural network with a fixed topology.
Features
Many neuroevolution algorithms have been defined. One common distinction is between algorithms that evolve only the strength of the connection weights for a fixed network topology (sometimes called conventional neuroevolution), and algorithms that evolve both the topology of the network and its weights (called TWEANNs, for Topology and Weight Evolving Artificial Neural Network algorithms).
A separate distinction can be made between methods that evolve the structure of ANNs in parallel to its parameters (those applying standard evolutionary algorithms) and those that develop them separat
|
https://en.wikipedia.org/wiki/John%20Olver
|
John Walter Olver (September 3, 1936 – February 23, 2023) was an American politician and chemist who was the U.S. representative for Massachusetts's 1st congressional district from 1991 to 2013. Raised on a farm in Pennsylvania, Olver graduated from college at the age of 18 and went on to earn a PhD in chemistry from the Massachusetts Institute of Technology and later taught chemistry at the University of Massachusetts Amherst for eight years.
He served in both chambers of the Massachusetts General Court, being elected to the Massachusetts House of Representatives in 1968 and the Massachusetts Senate in 1972. He ran in a 1991 special election to succeed 17-term Congressman Silvio O. Conte, who died in office. He was the first Democrat ever to represent the .
Olver announced he would not seek re-election in 2012 and retired at the end of his eleventh term in Congress.
Early life, education, and career
Olver was born on September 3, 1936, in Honesdale, Pennsylvania, the son of Helen Marguerite (née Fulleborn) and Thomas Horace Olver. His paternal grandparents were of English descent, and his maternal grandparents were German. Olver grew up on his father's farm, where the two tended cows, while his mother ran a boarding house which served families from Philadelphia and New York City. Olver graduated from high school when he was 15 and enrolled in Rensselaer Polytechnic Institute, where he earned a Bachelor of Science in chemistry at the age of 18. After earning his undergrad
|
https://en.wikipedia.org/wiki/Robert%20W.%20Wood
|
Robert Williams Wood (May 2, 1868 – August 11, 1955) was an American physicist and inventor who made pivotal contributions to the field of optics. He pioneered infrared and ultraviolet photography. Wood's patents and theoretical work inform modern understanding of the physics of ultraviolet light, and made possible myriad uses of UV fluorescence which became popular after World War I. He published many articles on spectroscopy, phosphorescence, diffraction, and ultraviolet light.
Early life and education
Robert W. Wood was born in Concord, Massachusetts to Robert Williams Wood, Senior. His father had been born in Massachusetts in 1803, was a physician in Maine until 1838, then a physician and pioneer in the sugar industry on the Hawaiian Islands until 1866, and also active in
the American Statistical Association.
Wood junior attended The Roxbury Latin School initially intending to become a priest. However, he decided to study optics instead when he witnessed a rare glowing aurora one night and believed the effect to be caused by "invisible rays". In his pursuit to find these "invisible rays", Wood studied and earned several degrees in physics from Harvard University, the Massachusetts Institute of Technology.
As a student at Harvard he swallowed marijuana as part of a self experiment, recorded the hallucinations he experienced in a report
for a course of psychology. A New York newspaper published the report. After he had received a bachelor’s degree in chemistry there, h
|
https://en.wikipedia.org/wiki/1844%20in%20science
|
The year 1844 in science and technology involved some significant events, listed below.
Astronomy
Friedrich Bessel explains the wobbling motions of Sirius and Procyon by suggesting that these stars have dark companions.
Biology
June 3 – The last definitely recorded pair of great auks (Pinguinus impennis) are killed on the Icelandic island of Eldey.
August 1 – Opening of Berlin Zoological Garden.
Gabriel Gustav Valentin notes the digestive activity of pancreatic juice.
George Robert Gray begins publication in London of The Genera of Birds.
Joseph Dalton Hooker begins publication of The Botany of the Antarctic Voyage of H.M. Discovery Ships Erebus and Terror ... 1839–1843 in London.
Chemistry
Karl Klaus discovers ruthenium.
Professor Gustaf Erik Pasch of Stockholm is granted the privilege of manufacturing a safety match.
French chemist Adolphe Wurtz reports the first synthesis of copper hydride, a well-known reducing agent and catalyst in organic chemistry.
Earth sciences
Robert Chambers publishes Vestiges of the Natural History of Creation (anonymously).
Mathematics
Joseph Liouville finds the first transcendental number
Hermann Grassmann studies vectors with more than three dimensions.
Medicine
Irish physician Francis Rynd utilises a hollow hypodermic needle to make the first recorded subcutaneous injections, specifically of a sedative to treat neuralgia.
Metrology
Joseph Whitworth introduces the thou.
Physics
William Robert Grove publishes The Correlati
|
https://en.wikipedia.org/wiki/Cold%20Spring%20Harbor%20Laboratory
|
Cold Spring Harbor Laboratory (CSHL) is a private, non-profit institution with research programs focusing on cancer, neuroscience, plant biology, genomics, and quantitative biology.
It is one of 68 institutions supported by the Cancer Centers Program of the U.S. National Cancer Institute (NCI) and has been an NCI-designated Cancer Center since 1987. The Laboratory is one of a handful of institutions that played a central role in the development of molecular genetics and molecular biology.
It has been home to eight scientists who have been awarded the Nobel Prize in Physiology or Medicine. CSHL is ranked among the leading basic research institutions in molecular biology and genetics, with Thomson Reuters ranking it #1 in the world. CSHL was also ranked #1 in research output worldwide by Nature. The Laboratory is led by Bruce Stillman, a biochemist and cancer researcher.
Since its inception in 1890, the institution's campus on the North Shore of Long Island has also been a center of biology education. Current CSHL educational programs serve professional scientists, doctoral students in biology, teachers of biology in the K–12 system, and students from the elementary grades through high school. In the past 10 years, CSHL conferences & courses have drawn over 81,000 scientists and students to the main campus. For this reason, many scientists consider CSHL a "crossroads of biological science." Since 2009 CSHL has partnered with the Suzhou Industrial Park in Suzhou, China to
|
https://en.wikipedia.org/wiki/Charles%20Algernon%20Parsons
|
Sir Charles Algernon Parsons, (13 June 1854 – 11 February 1931) was an Anglo-Irish engineer, best known for his invention of the compound steam turbine, and as the eponym of C. A. Parsons and Company. He worked as an engineer on dynamo and turbine design, and power generation, with great influence on the naval and electrical engineering fields. He also developed optical equipment for searchlights and telescopes.
Career and commercial activity
Parsons was born into an Anglo-Irish family in London as the youngest son of the famous astronomer William Parsons, 3rd Earl of Rosse. (The family seat is Birr Castle, County Offaly, Ireland, and the town of Birr was called Parsonstown, after the family, from 1620 to 1901.)
With his three brothers, Parsons was educated at home in Ireland by private tutors (including John Purser), all of whom were well versed in the sciences and also acted as practical assistants to the Earl in his astronomical work. (One of them later became, as Sir Robert Ball, Astronomer Royal for Ireland.) Parsons then read mathematics at Trinity College, Dublin and at St. John's College, Cambridge, graduating from the latter in 1877 with a first-class honours degree. He joined the Newcastle-based engineering firm of W.G. Armstrong as an apprentice, an unusual step for the son of an earl. Later he moved to Kitsons in Leeds, where he worked on rocket-powered torpedoes.
Steam turbine engine
In 1884 Parsons moved to Clarke, Chapman and Co., ship-engine manufactur
|
https://en.wikipedia.org/wiki/AstraZeneca
|
AstraZeneca plc () is an Anglo-Swedish multinational pharmaceutical and biotechnology company with its headquarters at the Cambridge Biomedical Campus in Cambridge, England. It has a portfolio of products for major diseases in areas including oncology, cardiovascular, gastrointestinal, infection, neuroscience, respiratory, and inflammation. It has been involved in developing the Oxford–AstraZeneca COVID-19 vaccine.
The company was founded in 1999 through the merger of the Swedish Astra AB and the British Zeneca Group (itself formed by the demerger of the pharmaceutical operations of Imperial Chemical Industries in 1993). Since the merger it has been among the world's largest pharmaceutical companies and has made numerous corporate acquisitions, including Cambridge Antibody Technology (in 2006), MedImmune (in 2007), Spirogen (in 2013) and Definiens (by MedImmune in 2014). It has its research and development concentrated in three strategic centres: Cambridge, England; Gothenburg, Sweden and Gaithersburg in Maryland, U.S.
AstraZeneca traces its earliest corporate history to 1913, when Astra AB was formed by a large group of doctors and apothecaries in Södertälje. Throughout the twentieth century, it grew into the largest pharmaceutical company in Sweden, and was considered a large company by the time of the merger. Its British counterpart, Zeneca PLC was formed in 1993 when ICI divested its pharmaceuticals businesses; Astra AB and Zeneca PLC merged six years later, with the c
|
https://en.wikipedia.org/wiki/Visual%20cryptography
|
Visual cryptography is a cryptographic technique which allows visual information (pictures, text, etc.) to be encrypted in such a way that the decrypted information appears as a visual image.
One of the best-known techniques has been credited to Moni Naor and Adi Shamir, who developed it in 1994. They demonstrated a visual secret sharing scheme, where an image was broken up into n shares so that only someone with all n shares could decrypt the image, while any shares revealed no information about the original image. Each share was printed on a separate transparency, and decryption was performed by overlaying the shares. When all n shares were overlaid, the original image would appear. There are several generalizations of the basic scheme including k-out-of-n visual cryptography, and using opaque sheets but illuminating them by multiple sets of identical illumination patterns under the recording of only one single-pixel detector.
Using a similar idea, transparencies can be used to implement a one-time pad encryption, where one transparency is a shared random pad, and another transparency acts as the ciphertext. Normally, there is an expansion of space requirement in visual cryptography. But if one of the two shares is structured recursively, the efficiency of visual cryptography can be increased to 100%.
Some antecedents of visual cryptography are in patents from the 1960s. Other antecedents are in the work on perception and secure communication.
Visual cryptography can
|
https://en.wikipedia.org/wiki/Axiom%20of%20dependent%20choice
|
In mathematics, the axiom of dependent choice, denoted by , is a weak form of the axiom of choice () that is still sufficient to develop most of real analysis. It was introduced by Paul Bernays in a 1942 article that explores which set-theoretic axioms are needed to develop analysis.
Formal statement
A homogeneous relation on is called a total relation if for every there exists some such that is true.
The axiom of dependent choice can be stated as follows:
For every nonempty set and every total relation on there exists a sequence in such that
for all
In fact, x0 may be taken to be any desired element of X. (To see this, apply the axiom as stated above to the set of finite sequences that start with x0 and in which subsequent terms are in relation , together with the total relation on this set of the second sequence being obtained from the first by appending a single term.)
If the set above is restricted to be the set of all real numbers, then the resulting axiom is denoted by
Use
Even without such an axiom, for any , one can use ordinary mathematical induction to form the first terms of such a sequence.
The axiom of dependent choice says that we can form a whole (countably infinite) sequence this way.
The axiom is the fragment of that is required to show the existence of a sequence constructed by transfinite recursion of countable length, if it is necessary to make a choice at each step and if some of those choices cannot be made independently of pre
|
https://en.wikipedia.org/wiki/Francisco%20%C3%81lvarez-Cascos
|
Francisco Álvarez–Cascos Fernández (born 1 October 1947) is a Spanish politician. He was Secretary-General of the ruling Partido Popular from 1989 to 1999 and the President of the Principality of Asturias from 2011 to 2012.
He studied civil engineering, and after working in an architect office and then for an architects association for a few years, he soon became a professional politician. In 1976 he joined Reforma Democrática, which later merged into Alianza Popular, both right-wing parties. He was the spokesman for the Gijón Council between 1979 and 1986, a county councilor and a member of the regional Pre-Autonomous Body.
In 1982, after Alianza Popular merged into the center-right People's Party, he was elected senator for Asturias, a position which he combined with that of spokesman for the People's Party Parliamentary Group in the General Junta of the Principate of Asturias (Asturias' regional legislature) from 1983 onwards. In 1986 he was elected deputy for Asturias and was re-elected in 1989, 1993, 1996 and 2000.
At the 9th National Congress of the People's Party, he was elected Secretary-General. He was confirmed three times in this office at the national congresses of the PP which took place in Seville (1990) and Madrid (1993 and 1996).
He was First Vice President of the Government and Minister of the Presidency for the 1996-2000 term, and Minister for Development for the 2000-2004 term.
In 2004, he resigned from Congress and left politics for a few years.
Pre
|
https://en.wikipedia.org/wiki/Computability
|
Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.
The most widely studied models of computability are the Turing-computable and μ-recursive functions, and the lambda calculus, all of which have computationally equivalent power. Other forms of computability are studied as well: computability notions weaker than Turing machines are studied in automata theory, while computability notions stronger than Turing machines are studied in the field of hypercomputation.
Problems
A central idea in computability is that of a (computational) problem, which is a task whose computability can be explored.
There are two key types of problems:
A decision problem fixes a set S, which may be a set of strings, natural numbers, or other objects taken from some larger set U. A particular instance of the problem is to decide, given an element u of U, whether u is in S. For example, let U be the set of natural numbers and S the set of prime numbers. The corresponding decision problem corresponds to primality testing.
A function problem consists of a function f from a set U to a set V. An instance of the problem is to compute, given an element u in U, the corresponding element f(u) in V. For example, U and V may be the set of all finite
|
https://en.wikipedia.org/wiki/Edward%20Felten
|
Edward William Felten (born March 25, 1963) is the Robert E. Kahn Professor of Computer Science and Public Affairs at Princeton University, where he was also the director of the Center for Information Technology Policy from 2007 to 2015 and from 2017 to 2019. On November 4, 2010, he was named Chief Technologist for the Federal Trade Commission, a position he officially assumed January 3, 2011. On May 11, 2015, he was named the Deputy U.S. Chief Technology Officer. In 2018, he was nominated to and began a term as Board Member of PCLOB.
Felten has done a variety of computer security research, including groundbreaking work on proof-carrying authentication and work on security related to the Java programming language, but he is perhaps best known for his paper on the Secure Digital Music Initiative (SDMI) challenge.
Biography
Felten attended the California Institute of Technology and graduated with a degree in physics in 1985. He worked as a staff programmer at Caltech from 1986 to 1989 on a parallel supercomputer project at Caltech. He then enrolled as a graduate student in computer science at the University of Washington. He was awarded a Master of Science degree in 1991 and a Ph.D. in 1993. His Ph.D. thesis was on developing an automated protocol for communication between parallel processors.
In 1993, he joined the faculty of Princeton University in the department of computer science as an assistant professor. He was promoted to associate professor in 1999 and to professor
|
https://en.wikipedia.org/wiki/Particle%20in%20a%20spherically%20symmetric%20potential
|
In quantum mechanics, a particle in a spherically symmetric potential is a system with a potential that depends only on the distance between the particle and a center. A particle in a spherically symmetric potential can be used as an approximation, for example, of the electron in a hydrogen atom or of the formation of chemical bonds.
In the general time-independent case, the dynamics of a particle in a spherically symmetric potential are governed by a Hamiltonian of the following form:
where is the mass of the particle, is the momentum operator, and the potential depends only on the vector magnitude of the position vector, that is, the radial distance from the origin (hence the spherical symmetry of the problem). The possible quantum states of the particle can be found by using the above Hamiltonian to solve the Schrödinger equation for its eigenvalues, which are the possible energies of the system, and their corresponding eigenstates, which are stationary states of the system.
To describe a particle in a spherically symmetric systems, it is convenient to use spherical coordinates , and . The time-independent Schrödinger equation for the system is then a separable, partial differential equation. This means solutions to the angular dimensions of the equation can be found independently of the radial dimension. This leaves an ordinary differential equation in terms only of the radius, , which determines the eigenstates for the particular potential, .
Structure of the eige
|
https://en.wikipedia.org/wiki/Claude%20Perrault
|
Claude Perrault (25 September 1613 – 9 October 1688) was a French physician and amateur architect, best known for his participation in the design of the east façade of the Louvre in Paris. He also designed the Paris Observatory and was an anatomist and author who wrote treatises on architecture, physics, and natural history.
His brother, Charles Perrault, is remembered as the classic reteller of the old story of Cinderella among other fables.
Biography
Perrault was born and died in Paris.
As physician and natural philosopher, who received a medical degree from the University of Paris in 1642, Perrault became one of the first members of the French Academy of Sciences when it was founded in 1666.
A committee commissioned by Louis XIV, the Petit Conseil, comprising Louis Le Vau, Charles Le Brun, and Perrault, designed the east façade of the Louvre. It was begun in 1667 and was essentially complete in 1674. By 1680, Louis XIV had abandoned the Louvre and focused his attention on the Palace of Versailles. The wing behind the east façade was not finished until the 19th century with the advent of Napoleon. The definitive design of the east façade is attributed to Perrault, who made the final alterations needed to accommodate a decision to double the width of the south wing. He also created projects for the joining of the Louvre with the Tuileries Palace and may have devised the use of iron tie rods behind the entablature of the east façade in order to solve engineering problems
|
https://en.wikipedia.org/wiki/Finite%20impulse%20response
|
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly samples (from first nonzero element through last nonzero element) before it then settles to zero.
FIR filters can be discrete-time or continuous-time, and digital or analog.
Definition
For a causal discrete-time FIR filter of order N, each value of the output sequence is a weighted sum of the most recent input values:
where:
is the input signal,
is the output signal,
is the filter order; an th-order filter has terms on the right-hand side
is the value of the impulse response at the ith instant for of an -order FIR filter. If the filter is a direct form FIR filter then is also a coefficient of the filter.
This computation is also known as discrete convolution.
The in these terms are commonly referred to as s, based on the structure of a tapped delay line that in many implementations or block diagrams provides the delayed inputs to the multiplication operations. One may speak of a 5th order/6-tap filter, for instance.
The impulse response of the filter as defined is nonz
|
https://en.wikipedia.org/wiki/Section%20%28biology%29
|
In biology a section () is a taxonomic rank that is applied differently in botany and zoology.
In botany
Within flora (plants), 'section' refers to a botanical rank below the genus, but above the species:
Domain > Kingdom > Division > Class > Order > Family > Tribe > Genus > Subgenus > Section > Subsection > Species
In zoology
Within fauna (animals), 'section' refers to a zoological rank below the order, but above the family:
Domain > Kingdom > Phylum > Class > Order > Section > Family > Tribe > Genus > Species
In bacteriology
The International Code of Nomenclature for Bacteria states that the Section rank is an informal one, between the subgenus and species (as in botany).
References
Botanical nomenclature
Plant taxonomy
Zoological nomenclature
Bacterial nomenclature
Taxa by rank
|
https://en.wikipedia.org/wiki/Covariant%20transformation
|
In physics, a covariant transformation is a rule that specifies how certain entities, such as vectors or tensors, change under a change of basis. The transformation that describes the new basis vectors as a linear combination of the old basis vectors is defined as a covariant transformation. Conventionally, indices identifying the basis vectors are placed as lower indices and so are all entities that transform in the same way. The inverse of a covariant transformation is a contravariant transformation. Whenever a vector should be invariant under a change of basis, that is to say it should represent the same geometrical or physical object having the same magnitude and direction as before, its components must transform according to the contravariant rule. Conventionally, indices identifying the components of a vector are placed as upper indices and so are all indices of entities that transform in the same way. The sum over pairwise matching indices of a product with the same lower and upper indices are invariant under a transformation.
A vector itself is a geometrical quantity, in principle, independent (invariant) of the chosen basis. A vector v is given, say, in components vi on a chosen basis ei. On another basis, say e′j, the same vector v has different components v′j and
As a vector, v should be invariant to the chosen coordinate system and independent of any chosen basis, i.e. its "real world" direction and magnitude should appear the same regardless of the basis vector
|
https://en.wikipedia.org/wiki/Sequence%20motif
|
In biology, a sequence motif is a nucleotide or amino-acid sequence pattern that is widespread and usually assumed to be related to biological function of the macromolecule. For example, an N-glycosylation site motif can be defined as Asn, followed by anything but Pro, followed by either Ser or Thr, followed by anything but Pro residue.
Overview
When a sequence motif appears in the exon of a gene, it may encode the "structural motif" of a protein; that is a stereotypical element of the overall structure of the protein. Nevertheless, motifs need not be associated with a distinctive secondary structure. "Noncoding" sequences are not translated into proteins, and nucleic acids with such motifs need not deviate from the typical shape (e.g. the "B-form" DNA double helix).
Outside of gene exons, there exist regulatory sequence motifs and motifs within the "junk", such as satellite DNA. Some of these are believed to affect the shape of nucleic acids (see for example RNA self-splicing), but this is only sometimes the case. For example, many DNA binding proteins that have affinity for specific DNA binding sites bind DNA in only its double-helical form. They are able to recognize motifs through contact with the double helix's major or minor groove.
Short coding motifs, which appear to lack secondary structure, include those that label proteins for delivery to particular parts of a cell, or mark them for phosphorylation.
Within a sequence or database of sequences, researchers sear
|
https://en.wikipedia.org/wiki/Simple%20ring
|
In abstract algebra, a branch of mathematics, a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. In particular, a commutative ring is a simple ring if and only if it is a field.
The center of a simple ring is necessarily a field. It follows that a simple ring is an associative algebra over this field. It is then called a simple algebra over this field.
Several references (e.g., Lang (2002) or Bourbaki (2012)) require in addition that a simple ring be left or right Artinian (or equivalently semi-simple). Under such terminology a non-zero ring with no non-trivial two-sided ideals is called quasi-simple.
Rings which are simple as rings but are not a simple module over themselves do exist: a full matrix ring over a field does not have any nontrivial two-sided ideals (since any ideal of is of the form with an ideal of ), but it has nontrivial left ideals (for example, the sets of matrices which have some fixed zero columns).
An immediate example of a simple ring is a division ring, where every nonzero element has a multiplicative inverse, for instance, the quaternions. Also, for any , the algebra of matrices with entries in a division ring is simple.
Joseph Wedderburn proved that if a ring is a finite-dimensional simple algebra over a field , it is isomorphic to a matrix algebra over some division algebra over . In particular, the only simple rings that are finite-dimensional algebras over the real numbers are rings of mat
|
https://en.wikipedia.org/wiki/Phagocyte
|
Phagocytes are cells that protect the body by ingesting harmful foreign particles, bacteria, and dead or dying cells. Their name comes from the Greek , "to eat" or "devour", and "-cyte", the suffix in biology denoting "cell", from the Greek kutos, "hollow vessel". They are essential for fighting infections and for subsequent immunity. Phagocytes are important throughout the animal kingdom and are highly developed within vertebrates. One litre of human blood contains about six billion phagocytes. They were discovered in 1882 by Ilya Ilyich Mechnikov while he was studying starfish larvae. Mechnikov was awarded the 1908 Nobel Prize in Physiology or Medicine for his discovery. Phagocytes occur in many species; some amoebae behave like macrophage phagocytes, which suggests that phagocytes appeared early in the evolution of life.
Phagocytes of humans and other animals are called "professional" or "non-professional" depending on how effective they are at phagocytosis. The professional phagocytes include many types of white blood cells (such as neutrophils, monocytes, macrophages, mast cells, and dendritic cells). The main difference between professional and non-professional phagocytes is that the professional phagocytes have molecules called receptors on their surfaces that can detect harmful objects, such as bacteria, that are not normally found in the body. Non-professional phagocytes do not have efficient phagocytic receptors, such as those for opsonins. Phagocytes are crucial i
|
https://en.wikipedia.org/wiki/Topological%20quantum%20field%20theory
|
In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.
Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry. Donaldson, Jones, Witten, and Kontsevich have all won Fields Medals for mathematical work related to topological field theory.
In condensed matter physics, topological quantum field theories are the low-energy effective theories of topologically ordered states, such as fractional quantum Hall states, string-net condensed states, and other strongly correlated quantum liquid states.
Overview
In a topological field theory, correlation functions do not depend on the metric of spacetime. This means that the theory is not sensitive to changes in the shape of spacetime; if spacetime warps or contracts, the correlation functions do not change. Consequently, they are topological invariants.
Topological field theories are not very interesting on flat Minkowski spacetime used in particle physics. Minkowski space can be contracted to a point, so a TQFT applied to Minkowski space results in trivial topological invariants. Consequently, TQFTs are usually applied to curved spacetimes, such as, for example, Riemann surfaces. Most of the known topological field theorie
|
https://en.wikipedia.org/wiki/Simon%20Newcomb
|
Simon Newcomb (March 12, 1835 – July 11, 1909) was a Canadian–American astronomer, applied mathematician, and autodidactic polymath. He served as Professor of Mathematics in the United States Navy and at Johns Hopkins University. Born in Nova Scotia, at the age of 19 Newcomb left an apprenticeship to join his father in Massachusetts, where the latter was teaching.
Though Newcomb had little conventional schooling, he completed a BSc at Harvard in 1858. He later made important contributions to timekeeping, as well as to other fields in applied mathematics, such as economics and statistics. Fluent in several languages, he also wrote and published several popular science books and a science fiction novel.
Biography
Early life
Simon Newcomb was born in the town of Wallace, Nova Scotia. His parents were John Burton Newcomb and his wife Emily Prince. His father was an itinerant school teacher, and frequently moved in order to teach in different parts of Canada, particularly in Nova Scotia and Prince Edward Island. Through his mother, Simon Newcomb was a distant cousin of William Henry Steeves, a Canadian Father of Confederation. Their immigrant ancestor in that line was Heinrich Stief, who immigrated from Germany and settled in New Brunswick about 1760.
Newcomb seems to have had little conventional schooling and was taught by his father. He also had a short apprenticeship in 1851 to Dr. Foshay, a charlatan herbalist in New Brunswick. But his father gave him an excellent foundati
|
https://en.wikipedia.org/wiki/Weierstrass%20function
|
In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve. It is named after its discoverer Karl Weierstrass.
The Weierstrass function has historically served the role of a pathological function, being the first published example (1872) specifically concocted to challenge the notion that every continuous function is differentiable except on a set of isolated points. Weierstrass's demonstration that continuity did not imply almost-everywhere differentiability upended mathematics, overturning several proofs that relied on geometric intuition and vague definitions of smoothness. These types of functions were denounced by contemporaries: Henri Poincaré famously described them as "monsters" and called Weierstrass' work "an outrage against common sense", while Charles Hermite wrote that they were a "lamentable scourge". The functions were difficult to visualize until the arrival of computers in the next century, and the results did not gain wide acceptance until practical applications such as models of Brownian motion necessitated infinitely jagged functions (nowadays known as fractal curves).
Construction
In Weierstrass's original paper, the function was defined as a Fourier series:
where , is a positive odd integer, and
The minimum value of for which there exists such that these constraints are satisfied is . This construction, along with the proof that th
|
https://en.wikipedia.org/wiki/Piecewise%20linear%20function
|
In mathematics and statistics, a piecewise linear, PL or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments.
Definition
A piecewise linear function is a function defined on a (possibly unbounded) interval of real numbers, such that there is a collection of intervals on each of which the function is an affine function. (Thus "piecewise linear" is actually defined to mean "piecewise affine".) If the domain of the function is compact, there needs to be a finite collection of such intervals; if the domain is not compact, it may either be required to be finite or to be locally finite in the reals.
Examples
The function defined by
is piecewise linear with four pieces. The graph of this function is shown to the right. Since the graph of an affine(*) function is a line, the graph of a piecewise linear function consists of line segments and rays. The x values (in the above example −3, 0, and 3) where the slope changes are typically called breakpoints, changepoints, threshold values or knots. As in many applications, this function is also continuous. The graph of a continuous piecewise linear function on a compact interval is a polygonal chain.
Other examples of piecewise linear functions include the absolute value function, the sawtooth function, and the floor function.
(*) A linear function satisfies by definition and therefore in particular ; functions whose graph is a straight line are affine rather than linear
|
https://en.wikipedia.org/wiki/Wolfgang%20Wahlster
|
Wolfgang Wahlster (born February 2, 1953) is a German artificial intelligence researcher. He was CEO and Scientific Director of the German Research Center for Artificial Intelligence and full professor of computer science at Saarland University, Saarbrücken. Wahlster remains Chief Executive Advisor of the German Research Center for Artificial Intelligence. In May 2019, he was honored by the Gesellschaft für Informatik as one of 10 most important heads of German artificial intelligence history. He is sometimes called the inventor of the "Industry 4.0" term.
Wahlster was one of the initiators of the Hermes Award, given each year since 2004 at the Hannover Messe and for many years was the Chairman of the Hermes Award Jury.
In 2016, he was elected to the University Council of the Technische Universität Darmstadt.
Education
Wahlster graduated from the Max-Planck Gymnasium in Delmenhorst. From 1972 to 1977 he studied computer science and theoretical linguistics at the University of Hamburg, where he received his diploma in 1977. In 1981 he received his doctorate in computer science from the University of Hamburg.
Awards and recognition
Wahlster was awarded the Deutscher Zukunftspreis ("German Future Award") in 2001 and has been a foreign member of the Class for Engineering Sciences of the Royal Swedish Academy of Sciences since 2003. In 2004, he was elected as a fellow of the Gesellschaft für Informatik.
In 2020, Wahlster was awarded an honorary title doctor honoris causa of
|
https://en.wikipedia.org/wiki/Weierstrass%20M-test
|
In mathematics, the Weierstrass M-test is a test for determining whether an infinite series of functions converges uniformly and absolutely. It applies to series whose terms are bounded functions with real or complex values, and is analogous to the comparison test for determining the convergence of series of real or complex numbers. It is named after the German mathematician Karl Weierstrass (1815-1897).
Statement
Weierstrass M-test.
Suppose that (fn) is a sequence of real- or complex-valued functions defined on a set A, and that there is a sequence of non-negative numbers (Mn) satisfying the conditions
for all and all , and
converges.
Then the series
converges absolutely and uniformly on A.
The result is often used in combination with the uniform limit theorem. Together they say that if, in addition to the above conditions, the set A is a topological space and the functions fn are continuous on A, then the series converges to a continuous function.
Proof
Consider the sequence of functions
Since the series converges and for every , then by the Cauchy criterion,
For the chosen ,
(Inequality (1) follows from the triangle inequality.)
The sequence is thus a Cauchy sequence in R or C, and by completeness, it converges to some number that depends on x. For n > N we can write
Since N does not depend on x, this means that the sequence of partial sums converges uniformly to the function S. Hence, by definition, the series converges uniformly.
Analogo
|
https://en.wikipedia.org/wiki/Plural%20quantification
|
In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular, values. As well as substituting individual objects such as Alice, the number 1, the tallest building in London etc. for x, we may substitute both Alice and Bob, or all the numbers between 0 and 10, or all the buildings in London over 20 stories.
The point of the theory is to give first-order logic the power of set theory, but without any "existential commitment" to such objects as sets. The classic expositions are Boolos 1984 and Lewis 1991.
History
The view is commonly associated with George Boolos, though it is older (see notably Simons 1982), and is related to the view of classes defended by John Stuart Mill and other nominalist philosophers. Mill argued that universals or "classes" are not a peculiar kind of thing, having an objective existence distinct from the individual objects that fall under them, but "is neither more nor less than the individual things in the class". (Mill 1904, II. ii. 2,also I. iv. 3).
A similar position was also discussed by Bertrand Russell in chapter VI of Russell (1903), but later dropped in favour of a "no-classes" theory. See also Gottlob Frege 1895 for a critique of an earlier view defended by Ernst Schroeder.
The general idea can be traced back to Leibniz. (Levey 2011, pp. 129–133)
Interest revived in plurals with work in linguistics in the 1970s by Remko Scha, Godehard Link, Fred Landman, Friederik
|
https://en.wikipedia.org/wiki/Jason%20Shiga
|
Jason Shiga (born 1976) is an American cartoonist who incorporates puzzles, mysteries and unconventional narrative techniques into his work.
Early life
Jason Shiga is from Oakland, California. His father, Seiji Shiga, was an animator who worked on the 1964 Rankin-Bass production Rudolph the Red-Nosed Reindeer. Jason Shiga was a pure mathematics major at the University of California at Berkeley, from which he graduated in 1998.
Career
Shiga is credited as the "Maze Specialist" for Issue #18 (Winter 2005/2006) of the literary journal McSweeney's Quarterly, which features a solved maze on the front cover and a (slightly different) unsolved maze on the back. The title page of each story in the journal is headed by a maze segment labeled with numbers leading to the first pages of other stories.
Shiga has also drawn and written several comics and illustrated features for Nickelodeon Magazine, some of which feature his original creations, and some starring Nickelodeon characters such as SpongeBob SquarePants and the Fairly OddParents.
Shiga makes a cameo appearance in the Derek Kirk Kim comic Ungrateful Appreciation as a Rubik's Cube-solving nerd.
Techniques and materials
According to the rear credits page of Empire State: A Love Story, Shiga, who was inspired by an actual Greyhound Bus trip from Oakland to New York to create that story, pencilled it with a yellow No. 2 pencil on copy paper. He then inked it with a lightbox and a 222 size Winsor & Newton brush, and lettered it
|
https://en.wikipedia.org/wiki/Philip%20Greenspun
|
Philip Greenspun (born September 28, 1963) is an American computer scientist, educator, early Internet entrepreneur, and pilot who was a pioneer in developing online communities like photo.net.
Biography
Greenspun was born on September 28, 1963, grew up in Bethesda, Maryland, and received a B.S. in Mathematics from MIT in 1982. After working for HP Labs in Palo Alto and Symbolics, he became a founder of ICAD, Inc. Greenspun returned to MIT to study electrical engineering and computer science, eventually receiving a Ph.D.
Working with Isaac Kohane of Boston Children's Hospital and Harvard Medical School, Greenspun was the developer of an early Web-based electronic medical record system. The system is described in "Building national electronic medical record systems via the World Wide Web" (1996). Greenspun and Kohane continue to work together on a medical informatics at Harvard Medical School.
In 1995, Greenspun was hired to lead development of Hearst Corporation's Internet services, which included early e-commerce sites. In 1997 he co-founded ArsDigita, a web services company which grew to $20 million in annual revenues by 2000.
Photo.net and ArsDigita
In 1993, Greenspun founded photo.net, an online community for people helping each other to improve their photographic skills. He seeded the community with "Travels with Samantha", a photo-illustrated account of a trip from Boston to Alaska and back. Photo.net became a business in 2000 with the help of some of his cofoun
|
https://en.wikipedia.org/wiki/Locally%20cyclic%20group
|
In mathematics, a locally cyclic group is a group (G, *) in which every finitely generated subgroup is cyclic.
Some facts
Every cyclic group is locally cyclic, and every locally cyclic group is abelian.
Every finitely-generated locally cyclic group is cyclic.
Every subgroup and quotient group of a locally cyclic group is locally cyclic.
Every homomorphic image of a locally cyclic group is locally cyclic.
A group is locally cyclic if and only if every pair of elements in the group generates a cyclic group.
A group is locally cyclic if and only if its lattice of subgroups is distributive .
The torsion-free rank of a locally cyclic group is 0 or 1.
The endomorphism ring of a locally cyclic group is commutative.
Examples of locally cyclic groups that are not cyclic
Examples of abelian groups that are not locally cyclic
The additive group of real numbers (R, +); the subgroup generated by 1 and (comprising all numbers of the form a + b) is isomorphic to the direct sum Z + Z, which is not cyclic.
References
.
.
Abelian group theory
Properties of groups
|
https://en.wikipedia.org/wiki/1788%20in%20science
|
The year 1788 in science and technology involved some significant events.
Astronomy
December 21 – Caroline Herschel discovers the periodic comet 35P/Herschel–Rigollet.
Biology
Dr. Edward Jenner publishes his observation that it is the newly hatched common cuckoo which pushes its host's eggs and chicks out of the nest.
James E. Smith founds the Linnean Society of London.
Utamaro publishes Ehon Mushi Erami ("Picture Book of Crawling Creatures") in Japan with color illustrations.
Thomas Walter publishes Flora Caroliniana, the first flora of North America to follow Linnaean taxonomy.
Gilbert White publishes The Natural History and Antiquities of Selborne, in the County of Southampton (dated 1789), a pioneering observational study of English ecology.
Earth sciences
James Hutton's Theory of the Earth; or an Investigation of the Laws observable in the Composition, Dissolution, and Restoration of Land upon the Globe is published for the first time, in Transactions of the Royal Society of Edinburgh.
Mechanics
Lagrange's Mécanique analytique is published in Paris, introducing Lagrangian mechanics.
Medicine
December 5 – Rev. Dr. Francis Willis is called in to advise on treatment of the mental condition of King George III of the United Kingdom.
Technology
February 1 – Isaac Briggs and William Longstreet patent a steamboat in the United States.
October 14 – William Symington demonstrates a paddle steamer on Dalswinton Loch in Scotland.
Awards
Copley Medal: Charles Blagd
|
https://en.wikipedia.org/wiki/1786%20in%20science
|
The year 1786 in science and technology involved some significant events.
Astronomy
January 17 – Pierre Méchain first observes Comet Encke, from Paris.
August 1 – Caroline Herschel becomes the first woman to discover a comet.
Biology
Subfossil bones of the Rodrigues solitaire are discovered.
Linguistics
February 2 – In a speech before The Asiatic Society in Calcutta, Sir William Jones notes the formal resemblances between Latin, Greek, and Sanskrit, laying the foundation for comparative linguistics and Indo-European studies.
Mathematics
Erland Samuel Bring publishes , proposing algebraic solutions to quintic functions.
Lagrange moves from Prussia to Paris under the patronage of Louis XVI of France.
William Playfair produces the first line and bar charts.
Technology
August – James Rumsey tests his first steamboat in the Potomac river at Shepherdstown, Virginia.
Ignaz von Born introduces a method of extracting metals using the patio process in his Ueber des Anquicken der gold- und silberhältigen Erze, published in Vienna.
Scottish millwright Andrew Meikle invents a practical threshing machine.
Awards
Copley Medal: Not awarded
Births
January 5 – Thomas Nuttall, English naturalist (died 1859)
February 26 – François Arago, French mathematician, physicist and astronomer (died 1853)
February 28 – Christian Ramsay, Scottish botanist (died 1839)
April 16 – Thomas Sewall, American anatomist (died 1845)
April 28 – Elizabeth Andrew Warren, Cornish botanist and mari
|
https://en.wikipedia.org/wiki/1784%20in%20science
|
The year 1784 in science and technology involved some significant events.
Astronomy
September 10 – Edward Pigott identifies the variable star Eta Aquilae from York, England.
October 19 – John Goodricke begins his observations of the variable star Delta Cephei from York.
Biology
Publication of the Annals of Agriculture edited by Arthur Young begins in Great Britain.
Peter Simon Pallas begins publication of Flora Rossica, the first Flora of Russia.
Chemistry
L'Abbé René Just Haüy states the geometrical law of crystallization.
Antoine Lavoisier pioneers stoichiometry.
Citric acid is first isolated by Carl Wilhelm Scheele, who crystallizes it from lemon juice.
Cholesterol is isolated.
History of science
Publication of David Bourgeois' Recherches sur l'art de voler, depuis la plus haute antiquité jusque'a ce jour in Paris, the earliest work on the history of flight.
Mathematics
Carl Friedrich Gauss, at the age of seven, pioneers the field of summation with the formula summing 1:n as (n(n+1))/2.
Medicine
11 February – Royal College of Surgeons in Ireland chartered.
12 March — Appointment of the French Royal Commission on Animal Magnetism (the Commission's Report was presented to King Louis XVI on 11 August 1784).
Madame du Coudray, pioneer of modern midwifery in France, retires.
Benjamin Franklin makes the first known specific reference (in a letter) to the wearing of bifocal spectacles.
John Hunter first describes the condition phlebitis.
Paleontology
The fi
|
https://en.wikipedia.org/wiki/1780%20in%20science
|
The year 1780 in science and technology involved some significant events.
Biology
Clément Joseph Tissot publishes Gymnastique médicinale et chirurgicale, ou, essai sur l'utilité du mouvement, ou des différens exercices du corps, et du repos dans la cure des malades in Paris, the first text on the therapeutic benefits of physical exercise.
Lazzaro Spallanzani publishes Dissertationi di fisica animale e vegetale, first interpreting the process of animal digestion as a chemical process in the stomach, by action of gastric juice. He also carries out important researches on animal fertilization.
Chemistry
Lactose is identified as a sugar by Carl Wilhelm Scheele.
Physics
Jean-Paul Marat publishes Recherches physiques sur le feu (Research into the Physics of Fire) and Découvertes de M. Marat sur la lumière (Mr Marat's Discoveries on Light).
History of science
Dr John Aikin publishes his Biographical Memoirs of Medicine in Great Britain, the first English language historical dictionary of physicians.
Technology
Aimé Argand invents the Argand lamp.
Thomas Earnshaw devises the spring detent escapement for marine chronometers.
Awards
Copley Medal: Samuel Vince
Births
January 13 – Pierre Jean Robiquet, French chemist (died 1840).
March 10 – William Charles Ellis, English psychiatric physician (died 1839).
April 13 – Alexander Mitchell, Irish engineer and inventor of the screw-pile lighthouse (died 1868).
September 5 - Clarke Abel, British surgeon and naturalist (died 1
|
https://en.wikipedia.org/wiki/Pi%20function
|
In mathematics, three different functions are known as the pi or Pi function:
(pi function) – the prime-counting function
(Pi function) – the gamma function when offset to coincide with the factorial
Rectangular function
You might also be looking for:
– the Infinite product of a sequence
Capital pi notation
|
https://en.wikipedia.org/wiki/1774%20in%20science
|
The year 1774 in science and technology involved some significant events.
Astronomy
Johann Elert Bode discovers the galaxy Messier 81.
Lagrange publishes a paper on the motion of the nodes of a planet's orbit.
Biology
Italian physicist Abbé Bonaventura Corti publishes Osservazioni microscopiche sulla tremella e sulla circulazione del fluido in una pianta acquajuola in Lucca, including his discovery of cyclosis in plant cells.
French physician Antoine Parmentier publishes Examen chymique des pommes de terres in Paris, analysing the nutritional value of the potato.
Chemistry
August 1 – Joseph Priestley, working at Bowood House, Wiltshire, England, isolates oxygen in the form of a gas, which he calls "dephlogisticated air".
Antoine Lavoisier publishes his first book, a literature review on the composition of air, Opuscules physiques et chimiques.
Carl Wilhelm Scheele discovers "dephlogisticated muriatic acid" (chlorine), manganese and barium.
Exploration
Second voyage of James Cook
June 16/17 – English explorer Captain Cook becomes the first European to sight (and name) Palmerston Island in the Pacific Ocean.
September 4 – Cook becomes the first European to sight (and name) the island of New Caledonia in Melanesia.
October 10 – Cook becomes the first European to sight (and name) Norfolk Island in the Pacific Ocean, uninhabited at this date.
Mathematics
P.-S. Laplace publishes Mémoire sur la probabilité des causes par les événements, including a restatement of B
|
https://en.wikipedia.org/wiki/1770%20in%20science
|
The year 1770 in science and technology involved some significant events.
Astronomy
July 1 – Lexell's Comet passes closer to the Earth than any other comet in recorded history, approaching to a distance of 0.015 AU. It is observed by Charles Messier between June 14 and October 3.
Biology
Arthur Young publishes A Course of Experimental Agriculture in England.
Chemistry
Benjamin Rush publishes Syllabus of a Course of Lectures on Chemistry in Philadelphia, the first chemistry textbook in North America.
Exploration
March 26 – First voyage of James Cook: English explorer Captain James Cook and his crew aboard complete the circumnavigation of New Zealand.
April 18 (April 19 by Cook's log) – Captain Cook and his crew become the first recorded Europeans to encounter the eastern coastline of the Australian continent.
April 28 (April 29 by Cook's log) – Captain Cook drops anchor in a wide bay about 16 km (10 mi) south of the present city of Sydney, Australia. Because the young botanist on board the ship, Joseph Banks, discovers 30,000 specimens of plant life in the area, 1,600 of them unknown to European science, Cook names the place Botany Bay on May 7.
August 22 (August 23 by Cook's log) – Captain Cook determines that New Holland (Australia) is not contiguous with New Guinea.
Mathematics
French mathematician and political scientist Jean-Charles de Borda formulates the ranked preferential electoral system which becomes known as the Borda count.
Lagrange discusses repres
|
https://en.wikipedia.org/wiki/Polylogarithmic%20function
|
In mathematics, a polylogarithmic function in is a polynomial in the logarithm of ,
The notation is often used as a shorthand for , analogous to for .
In computer science, polylogarithmic functions occur as the order of time or memory used by some algorithms (e.g., "it has polylogarithmic order"), such as in the definition of QPTAS (see PTAS).
All polylogarithmic functions of are for every exponent (for the meaning of this symbol, see small o notation), that is, a polylogarithmic function grows more slowly than any positive exponent. This observation is the basis for the soft O notation .
References
Mathematical analysis
Polynomials
Analysis of algorithms
|
https://en.wikipedia.org/wiki/Von%20Neumann%20universe
|
In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is often used to provide an interpretation or motivation of the axioms of ZFC. The concept is named after John von Neumann, although it was first published by Ernst Zermelo in 1930.
The rank of a well-founded set is defined inductively as the smallest ordinal number greater than the ranks of all members of the set. In particular, the rank of the empty set is zero, and every ordinal has a rank equal to itself. The sets in V are divided into the transfinite hierarchy Vα, called the cumulative hierarchy, based on their rank.
Definition
The cumulative hierarchy is a collection of sets Vα
indexed by the class of ordinal numbers; in particular, Vα is the set of all sets having ranks less than α. Thus there is one set Vα for each ordinal number α. Vα may be defined by transfinite recursion as follows:
Let V0 be the empty set:
For any ordinal number β, let Vβ+1 be the power set of Vβ:
For any limit ordinal λ, let Vλ be the union of all the V-stages so far:
A crucial fact about this definition is that there is a single formula φ(α,x) in the language of ZFC that states "the set x is in Vα".
The sets Vα are called stages or ranks.
The class V is defined to be the union of all the V-stages:
An equivalent definition sets
for eac
|
https://en.wikipedia.org/wiki/1764%20in%20science
|
The year 1764 in science and technology involved some significant events.
Astronomy
Lagrange publishes on the libration of the Moon, and an explanation as to why the same face is always turned to the Earth, a problem which he treats with the aid of virtual work, containing the germ of his idea of generalized equations of motion.
Physics
Specific and latent heats are described by Joseph Black.
Technology
The spinning jenny, a multi-spool spinning wheel, is invented by James Hargreaves in Stanhill, near Blackburn, Lancashire, England.
Awards
Copley Medal: John Canton
Births
Early – James Smithson, British mineralogist, chemist and benefactor (died 1829)
April 3 – John Abernethy, English surgeon (died 1831)
May 4 – Joseph Carpue, English surgeon (died 1846)
September 17 – John Goodricke, English astronomer (died 1786)
October – William Symington, Scottish mechanical engineer and steamboat pioneer (died 1831)
November 10 – Andrés Manuel del Río, Spanish chemist (died 1849)
Maria Medina Coeli, Italian physician (died 1846)
Approx. date – Alexander Mackenzie, Scottish explorer (died 1820)
Deaths
March 17
William Oliver, English physician (born 1695)
George Parker, 2nd Earl of Macclesfield, English astronomer (born c. 1696)
September 2 – Rev. Nathaniel Bliss, English Astronomer Royal (born 1700)
November 20 – Christian Goldbach, Prussian mathematician (born 1690)
References
18th century in science
1760s in science
|
https://en.wikipedia.org/wiki/1760%20in%20science
|
The year 1760 in science and technology involved some significant events.
Chemistry
Louis Claude Cadet de Gassicourt investigates inks based on cobalt salts and isolates cacodyl from cobalt mineral containing arsenic, pioneering work in organometallic chemistry.
Geology
John Michell suggests earthquakes are caused by one layer of rocks rubbing against another.
Medicine
April 30 – Swiss mathematician Daniel Bernoulli presents a paper at the French Academy of Sciences in Paris in which "a mathematical model was used for the first time to study the population dynamics of infectious disease."
Samuel-Auguste Tissot publishes L'Onanisme in Lausanne, a treatise on the supposed ill-effects of masturbation.
Physics
Johann Heinrich Lambert publishes Photometria, a pioneering work in photometry, including a formulation of the Beer–Lambert law on light absorption and the introduction of the albedo as a reflection coefficient.
Events
Mathematician Leonhard Euler begins writing his Letters to a German Princess (Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie) to Friederike Charlotte of Brandenburg-Schwedt and her younger sister Louise.
Awards
Copley Medal: Benjamin Wilson
Births
April 13 – Thomas Beddoes, reforming English physician (died 1808)
June 5 – Johan Gadolin, Finnish chemist and mineralogist (died 1852)
October 23 – Hanaoka Seishū, Japanese surgeon (died 1835)
Clelia Durazzo Grimaldi, Italian botanist (died 1830)
Deaths
Septe
|
https://en.wikipedia.org/wiki/Constructible%20set
|
In mathematics, constructible set may refer to either:
a notion in Gödel's constructible universe.
a union of locally closed set in a topological space. See constructible set (topology).
|
https://en.wikipedia.org/wiki/Synthetic
|
Synthetic things are composed of multiple parts, often with the implication that they are artificial. In particular, 'synthetic' may refer to:
Science
Synthetic biology
Synthetic chemical or compound, produced by the process of chemical synthesis
Synthetic elements, chemical elements that are not naturally found on Earth and therefore have to be created in experiments
Synthetic organic compounds synthetic chemical compounds based on carbon (organic compounds).
Synthetic peptide
Synthetic population
Synthetic population (biology)
Industry
Synthetic fuel
Synthetic oil
Synthetic marijuana
Synthetic diamond
Synthetic fibers, cloth or other material made from other substances than natural (animal, plant) materials
Other
Synthetic position, a concept in finance
Synthetic-aperture radar, a type or radar
Analytic–synthetic distinction, in philosophy
Synthetic language in linguistics, inflected or agglutinative languages
Synthetic intelligence a term emphasizing that true intelligence expressed by computing machines is not an imitation or "artificial."
Synthetic or constructed language, such as Esperanto
Synthetic music, produced by a synthesizer, a machine to create artificial sound and music
Synthetic chord in music theory
Synthetic person or legal personality, characteristic of a non-human entity regarded by law as having the status of a person
Synthetic data, are any data applicable to a given situation that are not obtained by direct measurement or from l
|
https://en.wikipedia.org/wiki/L2
|
L2, L2, L02, L II, L.2 or L-2 may refer to:
Astronomy
L2 point, second Lagrangian point in a two body orbiting system
L2 Puppis, star which is also known as HD 56096
Advanced Telescope for High Energy Astrophysics, a proposed X-ray telescope
Biology
Haplogroup L2 (mtDNA) in human genetics
ATC code L02 Endocrine therapy, a subgroup of the Anatomical Therapeutic Chemical Classification System
the second lumbar vertebrae of the vertebral column in human anatomy
the second larval stage in the Caenorhabditis elegans worm development
Computing
L2 cache, the Level-2 CPU cache in a computer
Layer 2 of the OSI model, in computer networking
L2 (operating system), or Liedtke 2 (a.k.a. EUMEL/ELAN), a persistent microkernel operating system developed by German computer scientist Jochen Liedtke
L2 (programming language)
ISO/IEC 8859-2 (Latin-2), an 8-bit character encoding
Entertainment
L2 (music group), an American pop duo
Leprechaun 2, 1994 film
Lineage II, a MMO game
Lumines II, a puzzle game
Mathematics
The L2 space of square-integrable functions
L2 norm
The ℓ2 space of square-summable sequences
L2 cohomology, a cohomology theory for smooth non-compact manifolds with Riemannian metric
Technology and weapons
a variety of low-alloy special purpose steel
a L-carrier cable system developed by AT&T
a series of fragmentation hand grenades used by the British armed forces (American M61 copies), before being replaced by the L109 grenade
the L designation given
|
https://en.wikipedia.org/wiki/Alignment
|
Alignment may refer to:
Archaeology
Alignment (archaeology), a co-linear arrangement of features or structures with external landmarks
Stone alignment, a linear arrangement of upright, parallel megalithic standing stones
Biology
Structural alignment, establishing similarities in the 3D structure of protein molecules
Sequence alignment, in bioinformatics, arranging the sequences of DNA, RNA, or protein to identify similarities
Alignment program, software used in sequence alignment
Engineering
Road alignment, the route of a road, defined as a series of horizontal tangents and curves, as defined by planners and surveyors
Railway alignment, three-dimensional geometry of track layouts
Transfer alignment, a process for initializing and calibrating the inertial navigation system on a missile or torpedo
Shaft alignment, in mechanical engineering, aligning two or more shafts with each other
Wheel alignment, automobile wheel and suspension angles which affect performance and tire wear
Technology
AI alignment, steering artificial intelligence systems towards the intended objective
Alignment level, an audio recording/engineering term for a selected point in the audio that represents a reasonable sound level
Business–IT alignment, how well an organization is able to use Information Technology to achieve objectives
Data structure alignment, arranging data in computer memory to fit machine design, also known more simply as an alignment structure
Music alignment, linking
|
https://en.wikipedia.org/wiki/Josephson%20effect
|
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. The effect is named after the British physicist Brian Josephson, who predicted in 1962 the mathematical relationships for the current and voltage across the weak link. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mechanics are observable at ordinary, rather than atomic, scale. The Josephson effect has many practical applications because it exhibits a precise relationship between different physical measures, such as voltage and frequency, facilitating highly accurate measurements.
The Josephson effect produces a current, known as a supercurrent, that flows continuously without any voltage applied, across a device known as a Josephson junction (JJ). These consist of two or more superconductors coupled by a weak link. The weak link can be a thin insulating barrier (known as a superconductor–insulator–superconductor junction, or S-I-S), a short section of non-superconducting metal (S-N-S), or a physical constriction that weakens the superconductivity at the point of contact (S-c-S).
Josephson junctions have important applications in quantum-mechanical circuits, such as SQUIDs, superconducting qubits, and RSFQ digital electronics. The NIST standard for one volt is achieved by an array of 20,208 Josephson junctions in series.
History
The DC Josephson effect had been seen in experiments
|
https://en.wikipedia.org/wiki/360%20%28number%29
|
360 (three hundred sixty) is the natural number following 359 and preceding 361.
In mathematics
360 is a highly composite number and one of only seven numbers such that no number less than twice as much has more divisors; the others are 1, 2, 6, 12, 60, and 2520 .
360 is also a superior highly composite number, a colossally abundant number, a refactorable number, a 5-smooth number, and a Harshad number in decimal since the sum of its digits (9) is a divisor of 360.
360 is divisible by the number of its divisors (24), and it is the smallest number divisible by every natural number from 1 to 10, except for 7. Furthermore, one of the divisors of 360 is 72, which is the number of primes below it.
360 is the sum of twin primes (179 + 181) and the sum of four consecutive powers of 3 (9 + 27 + 81 + 243).
The sum of Euler's totient function φ(x) over the first thirty-four integers is 360.
360 is a triangular matchstick number.
A circle is divided into 360 degrees for angular measurement. is also called a round angle. This unit choice divides round angles into equal sectors measured in integer rather than fractional degrees. Many angles commonly appearing in planimetrics have an integer number of degrees. For a simple non-intersecting polygon, the sum of the internal angles of a quadrilateral always equals 360 degrees.
Integers from 361 to 369
361
361 = 192, centered triangular number, centered octagonal number, centered decagonal number, member of the Mian–Chowla seque
|
https://en.wikipedia.org/wiki/Dedekind%20eta%20function
|
In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane of complex numbers, where the imaginary part is positive. It also occurs in bosonic string theory.
Definition
For any complex number with , let ; then the eta function is defined by,
Raising the eta equation to the 24th power and multiplying by gives
where is the modular discriminant. The presence of 24 can be understood by connection with other occurrences, such as in the 24-dimensional Leech lattice.
The eta function is holomorphic on the upper half-plane but cannot be continued analytically beyond it.
The eta function satisfies the functional equations
In the second equation the branch of the square root is chosen such that when .
More generally, suppose are integers with , so that
is a transformation belonging to the modular group. We may assume that either , or and . Then
where
Here is the Dedekind sum
Because of these functional equations the eta function is a modular form of weight and level 1 for a certain character of order 24 of the metaplectic double cover of the modular group, and can be used to define other modular forms. In particular the modular discriminant of Weierstrass can be defined as
and is a modular form of weight 12. Some authors omit the factor of , so that the series expansion has integral coefficients.
The Jacobi triple product implies that the eta is (up to a factor) a Jac
|
https://en.wikipedia.org/wiki/Dirichlet%20eta%20function
|
In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having real part > 0:
This Dirichlet series is the alternating sum corresponding to the Dirichlet series expansion of the Riemann zeta function, ζ(s) — and for this reason the Dirichlet eta function is also known as the alternating zeta function, also denoted ζ*(s). The following relation holds:
Both Dirichlet eta function and Riemann zeta function are special cases of polylogarithm.
While the Dirichlet series expansion for the eta function is convergent only for any complex number s with real part > 0, it is Abel summable for any complex number. This serves to define the eta function as an entire function. (The above relation and the facts that the eta function is entire and together show the zeta function is meromorphic with a simple pole at s = 1, and possibly additional poles at the other zeros of the factor , although in fact these hypothetical additional poles do not exist.)
Equivalently, we may begin by defining
which is also defined in the region of positive real part ( represents the gamma function). This gives the eta function as a Mellin transform.
Hardy gave a simple proof of the functional equation for the eta function, which is
From this, one immediately has the functional equation of the zeta function also, as well as another means to extend the definition of eta to the entire complex p
|
https://en.wikipedia.org/wiki/Weierstrass%20elliptic%20function
|
In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions are also referred to as ℘-functions and they are usually denoted by the symbol ℘, a uniquely fancy script p. They play an important role in the theory of elliptic functions. A ℘-function together with its derivative can be used to parameterize elliptic curves and they generate the field of elliptic functions with respect to a given period lattice.
Symbol for Weierstrass -function
Definition
Let be two complex numbers that are linearly independent over and let be the lattice generated by those numbers. Then the -function is defined as follows:
This series converges locally uniformly absolutely in . Oftentimes instead of only is written.
The Weierstrass -function is constructed exactly in such a way that it has a pole of the order two at each lattice point.
Because the sum alone would not converge it is necessary to add the term .
It is common to use and in the upper half-plane as generators of the lattice. Dividing by maps the lattice isomorphically onto the lattice with . Because can be substituted for , without loss of generality we can assume , and then define .
Motivation
A cubic of the form , where are complex numbers with , cannot be rationally parameterized. Yet one still wants to find a way to parameterize it.
For the quadric , the unit circle, there exists a (non-rational) p
|
https://en.wikipedia.org/wiki/Graphical%20model
|
A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning.
Types of graphical models
Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a distribution over a multi-dimensional space and a graph that is a compact or factorized representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, Bayesian networks and Markov random fields. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce.
Undirected Graphical Model
The undirected graph shown may have one of several interpretations; the common feature is that the presence of an edge implies some sort of dependence between the corresponding random variables. From this graph we might deduce that are all mutually independent, once is known, or (equivalently in this case) that
for some non-negative functions .
Bayesian network
If the network structure of the model is a directed acyclic graph, the model represents a factorization of the joint probability of all random variabl
|
https://en.wikipedia.org/wiki/Revaz%20Dogonadze
|
Revaz Dogonadze ( November 21, 1931 – May 13, 1985) was a notable Georgian scientist, Corresponding Member of the Georgian National Academy of Sciences (GNAS) (1982), Doctor of Physical & Mathematical Sciences (Full Doctor) (1966), Professor (1972), one of the founders of Quantum electrochemistry,
Life and works
He was born in 1931, in Tbilisi, Georgia. His father, Dr.Sc. Roman I. Dogonadze (1905–1970) was a professor of Agrarian Sciences. In 1955 Revaz Dogonadze graduated from the Moscow Engineering Physics Institute. He was Scientific Fellow (1958–1962) and Senior Scientific Fellow – Head of the Group of Quantum Electrochemistry (1962–1978) of the Department of Theoretical Investigations of the Moscow Institute of Electrochemistry (now Frumkin Institute of Electrochemistry of the Russian Academy of Science). He was Associate Professor (1963–1969) and Full Professor (1969–1973) of the Moscow State University. In 1961 he received a PhD degree, in 1966 a degree of Doctor of Sciences (Full Doctor).
Dogonadze was the first to view a chemical electron-transfer process as a quantum-mechanical transition between two separate electronic states, induced by weak electrostatic interactions between the molecular entities represented by the states. His group attracted students from Moscow State University and the Moscow Engineering Physics Institute, and foreign scientists as well; he was advisor for 13 PhD and 5 Dr.Sci. theses. Work of this group through the 1970s dealt with the rela
|
https://en.wikipedia.org/wiki/Deborah%20S.%20Jin
|
Deborah Shiu-lan Jin (; November 15, 1968 – September 15, 2016) was an American physicist and fellow with the National Institute of Standards and Technology (NIST); Professor Adjunct, Department of Physics at the University of Colorado; and a fellow of the JILA, a NIST joint laboratory with the University of Colorado.
She was considered a pioneer in polar molecular quantum chemistry. From 1995 to 1997 she worked with Eric Cornell and Carl Wieman at JILA, where she was involved in some of the earliest studies of dilute gas Bose-Einstein condensates. In 2003, Dr. Jin's team at JILA made the first fermionic condensate, a new form of matter. She used magnetic traps and lasers to cool fermionic atomic gases to less than 100 billionths of a degree above zero, successfully demonstrating quantum degeneracy and the formation of a molecular Bose-Einstein condensate. Jin was frequently mentioned as a strong candidate for the Nobel Prize in Physics. In 2002, Discover magazine recognized her as one of the 50 most important women in science.
Biography
Early life
Jin was born in Santa Clara County, California, Jin was one of three children, and grew up in Indian Harbour Beach, Florida. Her father was a physicist and her mother a physicist working as an engineer. Her father Ron Jin was born in Fuzhou in 1933 and passed away in 2010.
Education
Jin graduated magna cum laude from Princeton University in 1990, receiving an A.B. in physics after completing a senior thesis titled "A Condens
|
https://en.wikipedia.org/wiki/Algebraic%20function%20field
|
In mathematics, an algebraic function field (often abbreviated as function field) of n variables over a field k is a finitely generated field extension K/k which has transcendence degree n over k. Equivalently, an algebraic function field of n variables over k may be defined as a finite field extension of the field K = k(x1,...,xn) of rational functions in n variables over k.
Example
As an example, in the polynomial ring k[X,Y] consider the ideal generated by the irreducible polynomial Y2 − X3 and form the field of fractions of the quotient ring k[X,Y]/(Y2 − X3). This is a function field of one variable over k; it can also be written as (with degree 2 over ) or as (with degree 3 over ). We see that the degree of an algebraic function field is not a well-defined notion.
Category structure
The algebraic function fields over k form a category; the morphisms from function field K to L are the ring homomorphisms f : K → L with f(a) = a for all a in k. All these morphisms are injective. If K is a function field over k of n variables, and L is a function field in m variables, and n > m, then there are no morphisms from K to L.
Function fields arising from varieties, curves and Riemann surfaces
The function field of an algebraic variety of dimension n over k is an algebraic function field of n variables over k.
Two varieties are birationally equivalent if and only if their function fields are isomorphic. (But note that non-isomorphic varieties may have the same function field!)
|
https://en.wikipedia.org/wiki/De%20Morgan
|
De Morgan or de Morgan is a surname, and may refer to:
Augustus De Morgan (1806–1871), British mathematician and logician.
De Morgan's laws (or De Morgan's theorem), a set of rules from propositional logic.
The De Morgan Medal, a triennial mathematics prize awarded by the London Mathematical Society.
William De Morgan (1839–1917), English designer, potter, ceramics-worker, and novelist.
Evelyn De Morgan (1855–1919), English pre-Raphaelite painter.
Jacques de Morgan (1857–1924), French archaeologist.
|
https://en.wikipedia.org/wiki/Beryciformes
|
The Beryciformes are a poorly-understood order of carnivorous ray-finned fishes consisting of 7 families, 30 genera, and 161 species. They feed on small fish and invertebrates. Beyond this, little is known about the biology of most member species because of their nocturnal habits and deepwater habitats. All beryciform species are marine and most live in tropical to temperate, deepwater environments. Most live on the continental shelf and continental slope, with some species being found as deep as . Some species move closer to the surface at night, while others live entirely in shallow water and are nocturnal, hiding in rock crevices and caves during the day. Several species are mesopelagic and bathypelagic. Beryciformes' bodies are deep and mildly compressed, typically with large eyes that help them see in darker waters. Colors range from red to yellow and brown to black, and sizes range from . Member genera include the alfonsinos, squirrelfishes, flashlight fishes, fangtooth fishes, spinyfins, pineconefishes, redfishes, roughies, and slimeheads. A number of member species are caught commercially, including the alfonsino, the splendid alfonsino, and the orange roughy, the latter being much more economically important. Some species have bioluminescent bacteria contained in pockets of skin or in light organs near the eyes, including the anomalopids and monocentrids.
Taxonomy and phylogeny
Beryciforms first appeared during the Late Cretaceous period and have survived to today
|
https://en.wikipedia.org/wiki/Almost%20disjoint%20sets
|
In mathematics, two sets are almost disjoint if their intersection is small in some sense; different definitions of "small" will result in different definitions of "almost disjoint".
Definition
The most common choice is to take "small" to mean finite. In this case, two sets are almost disjoint if their intersection is finite, i.e. if
(Here, '|X|' denotes the cardinality of X, and '< ∞' means 'finite'.) For example, the closed intervals [0, 1] and [1, 2] are almost disjoint, because their intersection is the finite set {1}. However, the unit interval [0, 1] and the set of rational numbers Q are not almost disjoint, because their intersection is infinite.
This definition extends to any collection of sets. A collection of sets is pairwise almost disjoint or mutually almost disjoint if any two distinct sets in the collection are almost disjoint. Often the prefix "pairwise" is dropped, and a pairwise almost disjoint collection is simply called "almost disjoint".
Formally, let I be an index set, and for each i in I, let Ai be a set. Then the collection of sets {Ai : i in I} is almost disjoint if for any i and j in I,
For example, the collection of all lines through the origin in R2 is almost disjoint, because any two of them only meet at the origin. If {Ai} is an almost disjoint collection consisting of more than one set, then clearly its intersection is finite:
However, the converse is not true—the intersection of the collection
is empty, but the collection is not almost
|
https://en.wikipedia.org/wiki/Heisenberg%20group
|
In mathematics, the Heisenberg group , named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form
under the operation of matrix multiplication. Elements a, b and c can be taken from any commutative ring with identity, often taken to be the ring of real numbers (resulting in the "continuous Heisenberg group") or the ring of integers (resulting in the "discrete Heisenberg group").
The continuous Heisenberg group arises in the description of one-dimensional quantum mechanical systems, especially in the context of the Stone–von Neumann theorem. More generally, one can consider Heisenberg groups associated to n-dimensional systems, and most generally, to any symplectic vector space.
The three-dimensional case
In the three-dimensional case, the product of two Heisenberg matrices is given by:
As one can see from the term {{math|ab}}, the group is non-abelian.
The neutral element of the Heisenberg group is the identity matrix, and inverses are given by
The group is a subgroup of the 2-dimensional affine group Aff(2): acting on corresponds to the affine transform .
There are several prominent examples of the three-dimensional case.
Continuous Heisenberg group
If , are real numbers (in the ring R) then one has the continuous Heisenberg group H3(R).
It is a nilpotent real Lie group of dimension 3.
In addition to the representation as real 3×3 matrices, the continuous Heisenberg group also has several different representations in terms of functi
|
https://en.wikipedia.org/wiki/1759%20in%20science
|
The year 1759 in science and technology involved several significant events.
Astronomy
Halley's Comet returns; a team of three mathematicians, Alexis Clairaut, Jérome Lalande and Nicole Reine Lepaute, have – for the first time – predicted the date.
Biology
Caspar Friedrich Wolff's dissertation at the University of Halle Theoria Generationis supports the theory of epigenesis.
Botany
Kew Gardens established in England by Augusta of Saxe-Coburg, the mother of George III.
Geology
Giovanni Arduino proposes dividing the geological history of Earth into four periods: Primitive, Secondary, Tertiary and Volcanic, or Quaternary.
Medicine
June 15 – The first vascular surgery in history is performed by a Dr. Hallowell at Newcastle upon Tyne in England, who uses suture repair rather than a tying off with a ligature to repair an aneurysm on a patient's brachial artery. The new procedure of reconstructing a damaged artery replaces the practice of ligation that had risked the amputation of a limb or organ failure.
Angélique du Coudray publishes Abrégé de l'art des accouchements ("The Art of Obstetrics").
Physics
Posthumous publication of Émilie du Châtelet's French translation and commentary on Newton's Principia, Principes mathématiques de la philosophie naturelle.
Technology
English clockmaker John Harrison produces his "No. 1 sea watch" ("H4"), the first successful marine chronometer.
Transport
James Brindley is engaged by the Duke of Bridgewater to construct a canal to
|
https://en.wikipedia.org/wiki/1758%20in%20science
|
The year 1758 in science and technology involved some significant events.
Astronomy
Comet Halley reappears as predicted by Edmond Halley in 1705.
Chemistry
John Champion patents a process for calcining zinc sulphide into an oxide usable in the retort process.
Medicine
Angélique du Coudray demonstrates the first obstetric mannequin.
Scottish physician Francis Home makes the first attempt to deliver a measles vaccine.
Physics
Ruđer Bošković publishes his atomic theory in Philosophiæ naturalis theoria redacta ad unicam legem virium in natura existentium ("Theory of natural philosophy reduced to one law of the forces existing in nature").
John Dolland presents his "Account of some experiments concerning the different refrangibility of light" (Philosophical Transactions of the Royal Society (London)) describing the discovery of a means of constructing doublet achromatic lenses by the combination of crown and flint glasses, reducing chromatic aberration.
Zoology
January 1 – Swedish biologist Carl Linnaeus (Carl von Linné) publishes in Stockholm the first volume (Animalia) of the 10th edition of Systema Naturae, the starting point of modern zoological nomenclature, introducing binomial nomenclature for animals to his established system of Linnaean taxonomy. Among the first examples of his system of identifying an organism by genus and then species, Linnaeus identifies the lamprey with the name Petromyzon marinus. He introduces the term Homo sapiens. (Date of January 1 as
|
https://en.wikipedia.org/wiki/1755%20in%20science
|
The year 1755 in science and technology involved some significant events.
Astronomy
Immanuel Kant develops the nebular hypothesis in his Universal Natural History and Theory of Heaven (Allgemeine Naturgeschichte und Theorie des Himmels).
Chemistry
June – Joseph Black's discovery of carbon dioxide ("fixed air") and magnesium is communicated in a paper to the Philosophical Society of Edinburgh.
Earth sciences
November 1 – An earthquake in Lisbon kills 30,000 inhabitants.
Publication of De Litteraria expeditione per pontificiam ditionem ad dimetiendos duos meridiani gradus a PP, a description of the measurement of a meridian arc carried out in the Papal States by Ruđer Bošković with Christopher Maire in 1750–52.
Mathematics
Leonhard Euler's Institutiones calculi differentialis is published.
Technology
December 2 – The second Eddystone Lighthouse (1709–1755), with a wooden cone, catches fire and burns to the ground; it will be rebuilt in stone.
While serving as Postmaster General of the northern American colonies, Benjamin Franklin invents a simple odometer, attached to his horse carriage, to help analyze the best routes for delivering the mail.
approx. date – Thomas Mudge invents the lever escapement for timepieces.
Awards
Copley Medal: John Huxham
Births
January 28 – Samuel Thomas von Sömmerring, Prussian physician, anatomist, paleontologist and inventor (died 1830).
April 11 – James Parkinson, English surgeon (died 1824).
June 15 – Antoine François, French c
|
https://en.wikipedia.org/wiki/Simon%20Singh
|
Simon Lehna Singh, (born 19 September 1964) is a British popular science author, theoretical and particle physicist. His written works include Fermat's Last Theorem (in the United States titled Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem), The Code Book (about cryptography and its history), Big Bang (about the Big Bang theory and the origins of the universe), Trick or Treatment? Alternative Medicine on Trial (about complementary and alternative medicine, co-written by Edzard Ernst) and The Simpsons and Their Mathematical Secrets (about mathematical ideas and theorems hidden in episodes of The Simpsons and Futurama). In 2012 Singh founded the Good Thinking Society, through which he created the website "Parallel" to help students learn mathematics.
Singh has also produced documentaries and works for television to accompany his books, is a trustee of the National Museum of Science and Industry, a patron of Humanists UK, founder of the Good Thinking Society, and co-founder of the Undergraduate Ambassadors Scheme.
Early life and education
Singh was born in a Sikh family to parents who emigrated from Punjab, India to Britain in 1950. He is the youngest of three brothers, his eldest brother being Tom Singh, the founder of the UK New Look chain of stores. Singh grew up in Wellington, Somerset, attending Wellington School, and went on to Imperial College London, where he studied physics. He was active in the student union, becoming President
|
https://en.wikipedia.org/wiki/Cyclic%20permutation
|
In mathematics, and in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation has k elements, it may be called a k-cycle. Some authors widen this definition to include permutations with fixed points in addition to at most one non-trivial cycle. In cycle notation, cyclic permutations are denoted by the list of their elements enclosed with parentheses, in the order to which they are permuted.
For example, the permutation (1 3 2 4) that sends 1 to 3, 3 to 2, 2 to 4 and 4 to 1 is a 4-cycle, and the permutation (1 3 2)(4) that sends 1 to 3, 3 to 2, 2 to 1 and 4 to 4 is considered a 3-cycle by some authors. On the other hand, the permutation (1 3)(2 4) that sends 1 to 3, 3 to 1, 2 to 4 and 4 to 2 is not a cyclic permutation because it separately permutes the pairs {1, 3} and {2, 4}.
The set of elements that are not fixed by a cyclic permutation is called the orbit of the cyclic permutation. Every permutation on finitely many elements can be decomposed into cyclic permutations on disjoint orbits.
The individual cyclic parts of a permutation are also called cycles, thus the second example is composed of a 3-cycle and a 1-cycle (or fixed point) and the third is composed of two 2-cycles.
Definition
There is not widespread consensus about the precise definition of a cyclic permutation. Some authors define a permutation of a set to be cyclic if "successiv
|
https://en.wikipedia.org/wiki/Horseshoe%20map
|
In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator. The action of the map is defined geometrically by squishing the square, then stretching the result into a long strip, and finally folding the strip into the shape of a horseshoe.
Most points eventually leave the square under the action of the map. They go to the side caps where they will, under iteration, converge to a fixed point in one of the caps. The points that remain in the square under repeated iteration form a fractal set and are part of the invariant set of the map.
The squishing, stretching and folding of the horseshoe map are typical of chaotic systems, but not necessary or even sufficient.
In the horseshoe map, the squeezing and stretching are uniform. They compensate each other so that the area of the square does not change. The folding is done neatly, so that the orbits that remain forever in the square can be simply described.
For a horseshoe map:
there are an infinite number of periodic orbits;
periodic orbits of arbitrarily long period exist;
the number of periodic orbits grows exponentially with the period; and
close to any point of the fractal invariant set there is a point of a periodic orbit.
The horseshoe map
The horseshoe map is a diffeomorphism defined f
|
https://en.wikipedia.org/wiki/List%20of%20ciphertexts
|
Some famous ciphertexts (or cryptograms), in chronological order by date, are:
See also
Undeciphered writing systems (cleartext, natural-language writing of unknown meaning)
External links
Elonka Dunin's list of famous unsolved codes and ciphers
Cryptography lists and comparisons
History of cryptography
Undeciphered historical codes and ciphers
|
https://en.wikipedia.org/wiki/1750%20in%20science
|
The year 1750 in science and technology involved some significant events.
Astronomy
Thomas Wright suggests that the Milky Way Galaxy is a disk-shaped system of stars with the Solar System near the centre.
Exploration
April 1 – Pehr Osbeck sets out on a primarily botanical expedition to China.
Physics
January 17 – John Canton reads a paper before the Royal Society on a method of making artificial magnets.
Approx. date – Leonhard Euler and Daniel Bernoulli develop the Euler–Bernoulli beam equation.
Technology
November 18 – Westminster Bridge across the River Thames in London, designed by the Swiss-born engineer Charles Labelye, is officially opened.
Publications
Historia Plantarum, originally written by Conrad Gessner between 1555 and 1565.
Awards
Copley Medal: George Edwards
Births
March 16 – Caroline Herschel, German-born English astronomer (died 1848)
July 2 – François Huber, Swiss naturalist (died 1831)
July 5 – Ami Argand, Genevan physicist and chemist (died 1803)
September 22 – Christian Konrad Sprengel, German botanist (died 1816)
October 25 – Marie Le Masson Le Golft, French naturalist (died 1826)
Aaron Arrowsmith, English cartographer (died 1823)
Jean Nicolas Fortin, French physicist and instrument maker who invented a portable mercury barometer in 1800 (died 1831)
Deaths
December 1 – Johann Gabriel Doppelmayr, German mathematician, astronomer, and cartographer (born 1677)
References
18th century in science
1750s in science
|
https://en.wikipedia.org/wiki/Bilinear%20form
|
In mathematics, a bilinear form is a bilinear map on a vector space (the elements of which are called vectors) over a field K (the elements of which are called scalars). In other words, a bilinear form is a function that is linear in each argument separately:
and
and
The dot product on is an example of a bilinear form.
The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms.
When is the field of complex numbers , one is often more interested in sesquilinear forms, which are similar to bilinear forms but are conjugate linear in one argument.
Coordinate representation
Let be an -dimensional vector space with basis .
The matrix A, defined by is called the matrix of the bilinear form on the basis .
If the matrix represents a vector with respect to this basis, and similarly, the matrix represents another vector , then:
A bilinear form has different matrices on different bases. However, the matrices of a bilinear form on different bases are all congruent. More precisely, if is another basis of , then
where the form an invertible matrix . Then, the matrix of the bilinear form on the new basis is .
Maps to the dual space
Every bilinear form on defines a pair of linear maps from to its dual space . Define by
This is often denoted as
where the dot ( ⋅ ) indicates the slot into which the argument for the resulting linear functional is to be placed (see Currying).
For a fi
|
https://en.wikipedia.org/wiki/%E2%88%921
|
In mathematics, −1 (negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0.
Algebraic properties
Multiplication
Multiplying a number by −1 is equivalent to changing the sign of the number – that is, for any we have . This can be proved using the distributive law and the axiom that 1 is the multiplicative identity:
.
Here we have used the fact that any number times 0 equals 0, which follows by cancellation from the equation
.
In other words,
,
so is the additive inverse of , i.e. , as was to be shown.
Square of −1
The square of −1, i.e. −1 multiplied by −1, equals 1. As a consequence, a product of two negative numbers is positive.
For an algebraic proof of this result, start with the equation
.
The first equality follows from the above result, and the second follows from the definition of −1 as additive inverse of 1: it is precisely that number which when added to 1 gives 0. Now, using the distributive law, it can be seen that
.
The third equality follows from the fact that 1 is a multiplicative identity. But now adding 1 to both sides of this last equation implies
.
The above arguments hold in any ring, a concept of abstract algebra generalizing integers and real numbers.
Square roots of −1
Although there are no real square roots of −1, the complex number satisfies , and as such can be considered a
|
https://en.wikipedia.org/wiki/Fixed%20point%20%28mathematics%29
|
{{hatnote|1=Fixed points in mathematics are not to be confused with other uses of "fixed point", or stationary points where {{math|1=f(x) = 0}}.}}
In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically, for functions, a fixed point is an element that is mapped to itself by the function.
Fixed point of a function
Formally, is a fixed point of a function if belongs to both the domain and the codomain of , and .
For example, if is defined on the real numbers by
then 2 is a fixed point of , because .
Not all functions have fixed points: for example, , has no fixed points, since is never equal to for any real number. In graphical terms, a fixed-point means the point is on the line , or in other words the graph of has a point in common with that line.
Fixed point iteration
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. Specifically, given a function with the same domain and codomain, a point in the domain of , the fixed-point iteration is
which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of .
The notions of attracting fixed points, repelling fixed points, and periodic points are defined with respect to fixed-point iteration.
Fixed-point theorems
A fixed-poi
|
https://en.wikipedia.org/wiki/Theta%20function
|
In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theory.
The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables (conventionally called ), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions, making it a quasiperiodic function. In the abstract theory this quasiperiodicity comes from the cohomology class of a line bundle on a complex torus, a condition of descent.
One interpretation of theta functions when dealing with the heat equation is that "a theta function is a special function that describes the evolution of temperature on a segment domain subject to certain boundary conditions".
Throughout this article, should be interpreted as (in order to resolve issues of choice of branch).
Jacobi theta function
There are several closely related functions called Jacobi theta functions, and many different and incompatible systems of notation for them.
One Jacobi theta function (named after Carl Gustav Jacob Jacobi) is a function defined for two complex variables and , where can be any complex number and is the half-period ratio, confined to the upper half-plane, which means it has positive imaginary part. It is given by the
|
https://en.wikipedia.org/wiki/Key%20derivation%20function
|
In cryptography, a key derivation function (KDF) is a cryptographic algorithm that derives one or more secret keys from a secret value such as a master key, a password, or a passphrase using a pseudorandom function (which typically uses a cryptographic hash function or block cipher). KDFs can be used to stretch keys into longer keys or to obtain keys of a required format, such as converting a group element that is the result of a Diffie–Hellman key exchange into a symmetric key for use with AES. Keyed cryptographic hash functions are popular examples of pseudorandom functions used for key derivation.
History
The first deliberately slow (key stretching) password-based key derivation function was called "crypt" (or "crypt(3)" after its man page), and was invented by Robert Morris in 1978. It would encrypt a constant (zero), using the first 8 characters of the user's password as the key, by performing 25 iterations of a modified DES encryption algorithm (in which a 12-bit number read from the real-time computer clock is used to perturb the calculations). The resulting 64-bit number is encoded as 11 printable characters and then stored in the Unix password file. While it was a great advance at the time, increases in processor speeds since the PDP-11 era have made brute-force attacks against crypt feasible, and advances in storage have rendered the 12-bit salt inadequate. The crypt function's design also limits the user password to 8 characters, which limits the keyspace and make
|
https://en.wikipedia.org/wiki/Jacobi%20elliptic%20functions
|
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation for . The Jacobi elliptic functions are used more often in practical problems than the Weierstrass elliptic functions as they do not require notions of complex analysis to be defined and/or understood. They were introduced by . Carl Friedrich Gauss had already studied special Jacobi elliptic functions in 1797, the lemniscate elliptic functions in particular, but his work was published much later.
Overview
There are twelve Jacobi elliptic functions denoted by , where and are any of the letters , , , and . (Functions of the form are trivially set to unity for notational completeness.) is the argument, and is the parameter, both of which may be complex. In fact, the Jacobi elliptic functions are meromorphic in both and . The distribution of the zeros and poles in the -plane is well-known. However, questions of the distribution of the zeros and poles in the -plane remain to be investigated.
In the complex plane of the argument , the twelve functio
|
https://en.wikipedia.org/wiki/Subgraph%20isomorphism%20problem
|
In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a subgraph that is isomorphic to H.
Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. However certain other cases of subgraph isomorphism may be solved in polynomial time.
Sometimes the name subgraph matching is also used for the same problem. This name puts emphasis on finding such a subgraph as opposed to the bare decision problem.
Decision problem and computational complexity
To prove subgraph isomorphism is NP-complete, it must be formulated as a decision problem. The input to the decision problem is a pair of graphs G and H. The answer to the problem is positive if H is isomorphic to a subgraph of G, and negative otherwise.
Formal question:
Let , be graphs. Is there a subgraph such that ? I. e., does there exist a bijection such that ?
The proof of subgraph isomorphism being NP-complete is simple and based on reduction of the clique problem, an NP-complete decision problem in which the input is a single graph G and a number k, and the question is whether G contains a complete subgraph with k vertices. To translate this to a subgraph isomorphism problem, simply let H be the complete graph Kk; then the answer to the subgraph isomorphism problem for G and H is e
|
https://en.wikipedia.org/wiki/1748%20in%20science
|
The year 1748 in science and technology involved some significant events.
Archaeology
Rediscovery of the ruins of Pompeii.
Chemistry
Thomas Frye of the Bow porcelain factory in London produces bone china.
Earth sciences
Publication in Amsterdam of the Neptunian theory of French diplomat Benoît de Maillet (died 1738) in Telliamed, ou entretiens d’un philosophe indien avec un missionnaire françois, sur la diminution de la mer, la formation de la terre, l’origine de l’homme... as edited by Abbé Jean Baptiste de Mascrier.
Mathematics
Leonhard Euler publishes Introductio in analysin infinitorum, an introduction to pure analytical mathematics, in Berlin. He calculates the mathematical constant e to 23 digits and presents Euler's formula. Euler's fifth paper on nautical topics, E137, is also written in this year but not published until 1750.
Maria Agnesi publishes Instituzioni analitiche ad uso della gioventù italiana in Milan, "regarded as the best introduction extant to the works of Euler".
approx. date – Thomas Bayes originates Bayes' theorem.
Medicine
John Fothergill publishes Account of the Sore Throat, attended with Ulcers, an early description of diphtheria.
Technology
Pierre Le Roy invents the detent escapement in watchmaking.
Lewis Paul invents a hand machine for wool-carding.
Publications
Publication in Madrid of Jorge Juan and Antonio de Ulloa's Relación Histórica del Viage a la América Meridionale, including Ulloa's account of platinum.
Publication of M
|
https://en.wikipedia.org/wiki/CBA
|
CBA may refer to:
Maths and science
Casei Bifidus Acidophilus, a bacterium
Colicin, activity protein
Complete Boolean algebra, a concept from mathematics
Cytometric Bead Array, a bead-based immunoassay
Cell Based Assay, also a kind of immunoassay
4-Carboxybenzaldehyde, a byproduct in the industrial production of terephthalic acid
Congenital bronchial atresia, a rare congenital abnormality
Organizations
Academic
Catholic Biblical Association
Center for Bits and Atoms, a research institution at the Massachusetts Institute of Technology, United States
Christian Brothers Academy, schools run by the Institute of the Brothers of the Christian Schools, including:
Christian Brothers Academy (New Jersey), in Lincroft, New Jersey
Christian Brothers Academy (Albany, New York)
Christian Brothers Academy (Syracuse, New York)
College of Business Administration (Saudi Arabia), private college in Saudi Arabia
Corby Business Academy, in Corby, England
Banks
Central Bank of Armenia
Centrale Bank van Aruba, the central bank of Aruba
Commercial Bank of Africa, headquartered in Nairobi, Kenya
Commercial Bank of Australia (1866–1982), merged into the Wales bank to form Westpac
Commonwealth Bank of Australia
Professional and interest
California Bluegrass Association
Cambridge Buddhist Association
Canadian Bankers Association
Canadian Bar Association
CBA (Christian trade association), established in 1950 by bookstores
Chicago Bar Association
Chinese Benevolent Ass
|
https://en.wikipedia.org/wiki/Thorin
|
Thorin may refer to:
Thorin II Oakenshield, a Dwarf in J. R. R. Tolkien's The Hobbit
Thorin (chemistry), an organic arsenic compound used in the determination of thorium and barium
Donald E. Thorin (1934–2016), American cinematographer
Olof Thorin (1912–2004), Swedish mathematician
Thorin, Germanic name for males, representing the Germanic God Thor
|
https://en.wikipedia.org/wiki/Elliptic%20Curve%20Digital%20Signature%20Algorithm
|
In cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography.
Key and signature-size
As with elliptic-curve cryptography in general, the bit size of the private key believed to be needed for ECDSA is about twice the size of the security level, in bits. For example, at a security level of 80 bits—meaning an attacker requires a maximum of about operations to find the private key—the size of an ECDSA private key would be 160 bits. On the other hand, the signature size is the same for both DSA and ECDSA: approximately bits, where is the exponent in the formula , that is, about 320 bits for a security level of 80 bits, which is equivalent to operations.
Signature generation algorithm
Suppose Alice wants to send a signed message to Bob. Initially, they must agree on the curve parameters . In addition to the field and equation of the curve, we need , a base point of prime order on the curve; is the multiplicative order of the point .
The order of the base point must be prime. Indeed, we assume that every nonzero element of the ring is invertible, so that must be a field. It implies that must be prime (cf. Bézout's identity).
Alice creates a key pair, consisting of a private key integer , randomly selected in the interval ; and a public key curve point . We use to denote elliptic curve point multiplication by a scalar.
For Alice to sign a message , she follows
|
https://en.wikipedia.org/wiki/Schnorr%20signature
|
In cryptography, a Schnorr signature is a digital signature produced by the Schnorr signature algorithm that was described by Claus Schnorr. It is a digital signature scheme known for its simplicity, among the first whose security is based on the intractability of certain discrete logarithm problems. It is efficient and generates short signatures. It was covered by which expired in February 2008.
Algorithm
Choosing parameters
All users of the signature scheme agree on a group, , of prime order, , with generator, , in which the discrete log problem is assumed to be hard. Typically a Schnorr group is used.
All users agree on a cryptographic hash function .
Notation
In the following,
Exponentiation stands for repeated application of the group operation
Juxtaposition stands for multiplication on the set of congruence classes or application of the group operation (as applicable)
Subtraction stands for subtraction on the set of congruence classes
, the set of finite bit strings
, the set of congruence classes modulo
, the multiplicative group of integers modulo (for prime , )
.
Key generation
Choose a private signing key, , from the allowed set.
The public verification key is .
Signing
To sign a message, :
Choose a random from the allowed set.
Let .
Let , where denotes concatenation and is represented as a bit string.
Let .
The signature is the pair, .
Note that ; if , then the signature representation can fit into 40 bytes.
Verifying
Let
Let
If then the signatur
|
https://en.wikipedia.org/wiki/Zero-knowledge%20proof
|
In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true, while avoiding conveying to the verifier any information beyond the mere fact of the statement's truth. The intuition underlying zero-knowledge proofs is that it is trivial to prove the possession of certain information by simply revealing it; the challenge is to prove this possession without revealing the information, or any aspect of it whatsoever.
In light of the fact that one should be able to generate a proof of some statement only when in possession of certain secret information connected to the statement, the verifier, even after having become convinced of the statement's truth, should nonetheless remain unable to prove the statement to third parties.
In the plain model, nontrivial zero-knowledge proofs (i.e., those for languages outside of BPP) demand interaction between the prover and the verifier. This interaction usually entails the selection of one or more random challenges by the verifier; the random origin of these challenges, together with the prover's successful responses to them notwithstanding, jointly convince the verifier that the prover does possess the claimed knowledge. If interaction weren't present, then the verifier, having obtained the protocol's execution transcript—that is, the prover's one and only message—could replay that transcript to a third party, thereby co
|
https://en.wikipedia.org/wiki/Femtochemistry
|
Femtochemistry is the area of physical chemistry that studies chemical reactions on extremely short timescales (approximately 10−15 seconds or one femtosecond, hence the name) in order to study the very act of atoms within molecules (reactants) rearranging themselves to form new molecules (products). In a 1988 issue of the journal Science, Ahmed Hassan Zewail published an article using this term for the first time, stating "Real-time femtochemistry, that is, chemistry on the femtosecond timescale...". Later in 1999, Zewail received the Nobel Prize in Chemistry for his pioneering work in this field showing that it is possible to see how atoms in a molecule move during a chemical reaction with flashes of laser light.
Application of femtochemistry in biological studies has also helped to elucidate the conformational dynamics of stem-loop RNA structures.
Many publications have discussed the possibility of controlling chemical reactions by this method, but this remains controversial. The steps in some reactions occur in the femtosecond timescale and sometimes in attosecond timescales, and will sometimes form intermediate products. These reaction intermediates cannot always be deduced from observing the start and end products.
Pump–probe spectroscopy
The simplest approach and still one of the most common techniques is known as pump–probe spectroscopy. In this method, two or more optical pulses with variable time delay between them are used to investigate the processes happen
|
https://en.wikipedia.org/wiki/Field%20norm
|
In mathematics, the (field) norm is a particular mapping defined in field theory, which maps elements of a larger field into a subfield.
Formal definition
Let K be a field and L a finite extension (and hence an algebraic extension) of K.
The field L is then a finite dimensional vector space over K.
Multiplication by α, an element of L,
,
is a K-linear transformation of this vector space into itself.
The norm, NL/K(α), is defined as the determinant of this linear transformation.
If L/K is a Galois extension, one may compute the norm of α ∈ L as the product of all the Galois conjugates of α:
where Gal(L/K) denotes the Galois group of L/K. (Note that there may be a repetition in the terms of the product.)
For a general field extension L/K, and nonzero α in L, let σ(α), ..., σ(α) be the roots of the minimal polynomial of α over K (roots listed with multiplicity and lying in some extension field of L); then
.
If L/K is separable, then each root appears only once in the product (though the exponent, the degree [L:K(α)], may still be greater than 1).
Examples
Quadratic field extensions
One of the basic examples of norms comes from quadratic field extensions where is a square-free integer.
Then, the multiplication map by on an element is
The element can be represented by the vector
since there is a direct sum decomposition as a -vector space.
The matrix of is then
and the norm is , since it is the determinant of this matrix.
Norm of Q(√2)
Consider the numb
|
https://en.wikipedia.org/wiki/Running%20key%20cipher
|
In classical cryptography, the running key cipher is a type of polyalphabetic substitution cipher in which a text, typically from a book, is used to provide a very long keystream. Usually, the book to be used would be agreed ahead of time, while the passage to be used would be chosen randomly for each message and secretly indicated somewhere in the message.
Example
The text used is The C Programming Language (1978 edition), and the tabula recta is the tableau. The plaintext is "Flee at once".
Page 63, line 1 is selected as the running key:
errors can occur in several places. A label has...
The running key is then written under the plaintext:
The message is then sent as "JCVSR LQNPS". However, unlike a Vigenère cipher, if the message is extended, the key is not repeated; the key text itself is used as the key. If the message is extended, such as, "Flee at once. We are discovered", then the running key continues as before:
To determine where to find the running key, a fake block of five ciphertext characters is subsequently added, with three denoting the page number, and two the line number, using A=0, B=1 etc. to encode digits. Such a block is called an indicator block. The indicator block will be inserted as the second last of each message. (Many other schemes are possible for hiding indicator blocks.) Thus page 63, line 1 encodes as "AGDAB" (06301).
This yields a final message of "JCVSR LQNPS YGUIM QAWXS AGDAB MECTO".
Variants
Modern variants of the running key c
|
https://en.wikipedia.org/wiki/Susan%20Watts
|
Susan Janet Watts (born 13 July 1962) is a science journalist. She was science editor of the BBC's Newsnight programme, from January 1995 to November 2013.
Education
Watts was educated at Haberdashers' Aske's Hatcham Girls' School. She has a Bachelor of Science degree in Physics from Imperial College London and a Diploma in Journalism from City University London
Career
Watts spent ten years in print journalism specialising in scientific topics. She worked for Computer Weekly from 1985-9, New Scientist from 1989-91 and The Independent from 1991-5, before moving into television. She won a BAFTA for her reporting of the BSE "Mad Cow" crisis in British farming. In 2013 she was made redundant from Newsnight when incoming editor Ian Katz decided that the programme no longer required a dedicated science editor.
In 2015 Watts became Head of Public Engagement and Communications at the MRC London Institute of Medical Sciences, Imperial College London.
Hutton Tribunal
Watts came into the limelight in Summer 2003 during the Hutton Inquiry, a judicial inquiry into the death of Biological Weapons expert David Kelly. Kelly had died by suicide after his exposure as the source for a controversial report by fellow BBC journalist Andrew Gilligan, in which it was claimed that the British government had deliberately exaggerated the threat posed by Iraq's Weapons of Mass Destruction in order to justify a war.
On 2 June 2003, Susan Watts broadcast a report in which she extensively quoted a "s
|
https://en.wikipedia.org/wiki/Jacobi
|
Jacobi may refer to:
People with the surname Jacobi
Mathematics:
Jacobi sum, a type of character sum
Jacobi method, a method for determining the solutions of a diagonally dominant system of linear equations
Jacobi eigenvalue algorithm, a method for calculating the eigenvalues and eigenvectors of a real symmetric matrix
Jacobi elliptic functions, a set of doubly-periodic functions
Jacobi polynomials, a class of orthogonal polynomials
Jacobi symbol, a generalization of the Legendre symbol
Jacobi coordinates, a simplification of coordinates for an n-body system
Jacobi identity for non-associative binary operations
Jacobi's formula for the derivative of the determinant of a matrix
Jacobi triple product an identity in the theory of theta functions
Jacobi's theorem (disambiguation) (various)
Other:
Jacobi Medical Center, New York
Jacobi (grape), another name for the French/German wine grape Pinot Noir Précoce
Jacobi (crater), a lunar impact crater in the southern highlands on the near side of the Moon
Software_for_handling_chess_problems#Jacobi, chess software
See also
Jacoby (disambiguation)
Jacob
Jakob (disambiguation)
Jacobs (disambiguation)
Jacobite (disambiguation)
|
https://en.wikipedia.org/wiki/Rita%20R.%20Colwell
|
Rita Rossi Colwell (born November 23, 1934) is an American environmental microbiologist and scientific administrator. Colwell holds degrees in bacteriology, genetics, and oceanography and studies infectious diseases. Colwell is the founder and Chair of CosmosID, a bioinformatics company. From 1998 to 2004, she was the 11th Director and 1st female Director of the National Science Foundation. She has served on the board of directors of EcoHealth Alliance since 2012.
Early life and education
Colwell was born on November 23, 1934 in Beverly, Massachusetts. Her parents, Louis and Louise Rossi, had eight children, Rita being the seventh child born into the Rossi household. Neither her mother nor her father were from scientific backgrounds. In 1956, Rita obtained a B.S. in bacteriology from Purdue University. She also received her M.S. in genetics from Purdue in 1957. Colwell obtained her Ph.D. from the University of Washington in aquatic microbiology under the direction of microbiologist John Liston in 1961. She participated in a post-doctoral fellowship at the Canadian National Research Council in Ottawa.
Career
Colwell is recognized for her study of global infectious disease spread through water sources and its impacts on global health. Through this research, she has developed an international network that has brought attention to the emergence of new infectious diseases in drinking/bathing water, pertaining mostly to its role on the developing world.
Cholera research
Durin
|
https://en.wikipedia.org/wiki/American%20Society%20for%20Microbiology
|
The American Society for Microbiology (ASM), originally the Society of American Bacteriologists, is a professional organization for scientists who study viruses, bacteria, fungi, algae, and protozoa as well as other aspects of microbiology. It was founded in 1899. The Society publishes a variety of scientific journals, textbooks, and other educational materials related to microbiology and infectious diseases. ASM organizes annual meetings, as well as workshops and professional development opportunities for its members.
History
ASM was founded in 1899 under the name the "Society of American Bacteriologists." In December 1960, it was renamed the "American Society for Microbiology."
Mission
ASM's mission is "to promote and advance the microbial sciences." The society seeks to accomplish this mission through:
Publishing highly cited publications
Running multi-disciplinary meetings
Deploying resources and expertise around the world
Advocating for scientific research
Fostering a deeper public understanding of microbiology
Membership
ASM has more than 30,000 members, including researchers, educators and health professionals. Membership is open to all and is offered at a discounted rate to students, postdoctoral fellows and emeritus faculty. Members pay annual dues to support the activities of ASM. ASM's newest Clinical Lab Scientist membership category was established in 2019.
ASM provides professional development opportunities and supports microbiology professionals throu
|
https://en.wikipedia.org/wiki/Avida
|
Avida is an artificial life software platform to study the evolutionary biology of self-replicating and evolving computer programs (digital organisms). Avida is under active development by Charles Ofria's Digital Evolution Lab at Michigan State University; the first version of Avida was designed in 1993 by Ofria, Chris Adami and C. Titus Brown at Caltech, and has been fully reengineered by Ofria on multiple occasions since then. The software was originally inspired by the Tierra system.
Design principles
Tierra simulated an evolutionary system by introducing computer programs that competed for computer resources, specifically processor (CPU) time and access to main memory. In this respect it was similar to Core Wars, but differed in that the programs being run in the simulation were able to modify themselves, and thereby evolve. Tierra's programs were artificial life organisms.
Unlike Tierra, Avida assigns every digital organism its own protected region of memory, and executes it with a separate virtual CPU. By default, other digital organisms cannot access this memory space, neither for reading nor for writing, and cannot execute code that is not in their own memory space.
A second major difference is that the virtual CPUs of different organisms can run at different speeds, such that one organism executes, for example, twice as many instructions in the same time interval as another organism. The speed at which a virtual CPU runs is determined by a number of factors, bu
|
https://en.wikipedia.org/wiki/Random%20oracle
|
In cryptography, a random oracle is an oracle (a theoretical black box) that responds to every unique query with a (truly) random response chosen uniformly from its output domain. If a query is repeated, it responds the same way every time that query is submitted.
Stated differently, a random oracle is a mathematical function chosen uniformly at random, that is, a function mapping each possible query to a (fixed) random response from its output domain.
Random oracles as a mathematical abstraction were first used in rigorous cryptographic proofs in the 1993 publication by Mihir Bellare and Phillip Rogaway (1993). They are typically used when the proof cannot be carried out using weaker assumptions on the cryptographic hash function. A system that is proven secure when every hash function is replaced by a random oracle is described as being secure in the random oracle model, as opposed to secure in the standard model of cryptography.
Applications
Random oracles are typically used as an idealised replacement for cryptographic hash functions in schemes where strong randomness assumptions are needed of the hash function's output. Such a proof often shows that a system or a protocol is secure by showing that an attacker must require impossible behavior from the oracle, or solve some mathematical problem believed hard in order to break it. However, it only proves such properties in the random oracle model, making sure no major design flaws are present. It is in general not true
|
https://en.wikipedia.org/wiki/National%20Solar%20Observatory
|
The National Solar Observatory (NSO) is a United States federally funded research and development center to advance the knowledge of the physics of the Sun. NSO studies the Sun both as an astronomical object and as the dominant external influence on Earth.
NSO is headquartered in Boulder and operates facilities at a number of locations - at the 4-meter Daniel K. Inouye Solar Telescope in the Haleakala Observatory on the island of Maui, at Sacramento Peak near Sunspot in New Mexico, and six sites around the world for the Global Oscillations Network Group one of which is shared with the Synoptic Optical Long-term Investigations of the Sun.
NSO provides its observations to the scientific community. It operates facilities, develops advanced instrumentation both in-house and through partnerships, conducts solar research, and carries out educational and public outreach.
Visiting the observatories
The National Solar Observatory HQ is located on the campus of the University of Colorado, Boulder. It also has some staff on Maui, and Sacramento Peak.
Telescopes operated by the observatory
Big Bear Solar Observatory
Synoptic Optical Long-term Investigations of the Sun
Haleakala Observatory
Daniel K. Inouye Solar Telescope
Sacramento Peak
See Sunspot Solar Observatory for the telescopes located there
Global
Global Oscillation Network Group
Directors
A list of all NSO directors since the founding of the observatory is given below.
History
The Sacramento Peak observator
|
https://en.wikipedia.org/wiki/MESSENGER
|
MESSENGER was a NASA robotic space probe that orbited the planet Mercury between 2011 and 2015, studying Mercury's chemical composition, geology, and magnetic field. The name is a backronym for "Mercury Surface, Space Environment, Geochemistry, and Ranging", and a reference to the messenger god Mercury from Roman mythology.
MESSENGER was launched aboard a Delta II rocket in August 2004. Its path involved a complex series of flybys – the spacecraft flew by Earth once, Venus twice, and Mercury itself three times, allowing it to decelerate relative to Mercury using minimal fuel. During its first flyby of Mercury in January 2008, MESSENGER became the second mission, after Mariner 10 in 1975, to reach Mercury.
MESSENGER entered orbit around Mercury on March 18, 2011, becoming the first spacecraft to do so. It successfully completed its primary mission in 2012. Following two mission extensions, the spacecraft used the last of its maneuvering propellant to deorbit, impacting the surface of Mercury on April 30, 2015.
Mission overview
MESSENGERs formal data collection mission began on April 4, 2011. The primary mission was completed on March 17, 2012, having collected close to 100,000 images. MESSENGER achieved 100% mapping of Mercury on March 6, 2013, and completed its first year-long extended mission on March 17, 2013. The probe's second extended mission lasted for over two years, but as its low orbit degraded, it required reboosts to avoid impact. It conducted its final reboo
|
https://en.wikipedia.org/wiki/IPS
|
IPS, ips, or iPS may refer to:
Science and technology
Biology and medicine
Ips (beetle), a genus of bark beetle
Induced pluripotent stem cell or iPS cells
Intermittent photic stimulation, a neuroimaging technique
Intraparietal sulcus, a region of the brain
Computing
IPS panel, screen technology for liquid-crystal displays
Image Packaging System, OpenSolaris software
Instructions per second, a measure of a computer's processor speed
Internet Provider Security
Interpreter for Process Structures, used in AMSAT satellites
International Patching System file extension, see ROM hacking
Indoor positioning system, for wireless location indoors
Intrusion prevention system, network security appliance
Mathematics
Inner product space, a vector space with an additional structure called an inner product
Units of measure
Inch per second, a unit of speed
Inch–pound–second system of units, a system of measurement sometimes used in engineering (i.e. CAD design)
Iron pipe size
Other uses in science and technology
Inboard propulsion system, for watercraft by Volvo Penta
Inclined plate settler, a type of clarifier used in water purification; See Lamella clarifier
Interplanetary Superhighway, a collection of gravitationally determined pathways through the Solar system
Introductory Physical Science
IPS/UPS, an electric power transmission grid of some CIS countries
Organizations
International
Industrial and provident society, in the UK, Ireland, and New Zealand
Industri
|
https://en.wikipedia.org/wiki/1742%20in%20science
|
The year 1742 in science and technology involved some significant events.
Astronomy
January 14 – Death of Edmond Halley; James Bradley succeeds him as Astronomer Royal in Great Britain.
Mathematics
June – Christian Goldbach produces Goldbach's conjecture.
Colin Maclaurin publishes his Treatise on Fluxions in Great Britain, the first systematic exposition of Newton's methods.
Metrology
Anders Celsius publishes his proposal for a centigrade temperature scale originated in 1741.
Physiology and medicine
Surgeon Joseph Hurlock publishes his A Practical Treatise upon Dentition, or The breeding of teeth in children in London, the first treatise in English on dentition.
Technology
Benjamin Robins publishes his New Principles of Gunnery, containing the determination of the force of gun-powder and an investigation of the difference in the resisting power of the air to swift and slow motions in London, containing a description of his ballistic pendulum and the results of his scientific experiments into improvements in ballistics.
The first large (12 ft focal length) reflecting telescope is made, in Gregorian form, by James Short, for use by Charles Spencer, 3rd Duke of Marlborough, in London.
Awards
Copley Medal: Christopher Middleton.
Births
March 15 (bapt.) – John Stackhouse, English botanist (died 1819).
May 18 – Lionel Lukin, English inventor (died 1834).
December 3 – James Rennell, English geographer, historian and oceanographer (died 1830).
December 9 – Carl Wil
|
https://en.wikipedia.org/wiki/J-invariant
|
In mathematics, Felix Klein's -invariant or function, regarded as a function of a complex variable , is a modular function of weight zero for defined on the upper half-plane of complex numbers. It is the unique such function which is holomorphic away from a simple pole at the cusp such that
Rational functions of are modular, and in fact give all modular functions. Classically, the -invariant was studied as a parameterization of elliptic curves over , but it also has surprising connections to the symmetries of the Monster group (this connection is referred to as monstrous moonshine).
Definition
The -invariant can be defined as a function on the upper half-plane
with the third definition implying can be expressed as a cube, also since 1728.
The given functions are the modular discriminant , Dedekind eta function , and modular invariants,
where , are Fourier series,
and , are Eisenstein series,
and (the square of the nome). The -invariant can then be directly expressed in terms of the Eisenstein series as,
with no numerical factor other than 1728. This implies a third way to define the modular discriminant,
For example, using the definitions above and , then the Dedekind eta function has the exact value,
implying the transcendental numbers,
but yielding the algebraic number (in fact, an integer),
In general, this can be motivated by viewing each as representing an isomorphism class of elliptic curves. Every elliptic curve over is a complex torus, and th
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.