source
stringlengths 31
207
| text
stringlengths 12
1.5k
|
|---|---|
https://en.wikipedia.org/wiki/Str%C3%B6mgren%20sphere
|
In theoretical astrophysics, there can be a sphere of ionized hydrogen (H II) around a young star of the spectral classes O or B. The theory was derived by Bengt Strömgren in 1937 and later named Strömgren sphere after him. The Rosette Nebula is the most prominent example of this type of emission nebula from the H II-regions.
The physics
Very hot stars of the spectral class O or B emit very energetic radiation, especially ultraviolet radiation, which is able to ionize the neutral hydrogen (H I) of the surrounding interstellar medium, so that hydrogen atoms lose their single electrons. This state of hydrogen is called H II. After a while, free electrons recombine with those hydrogen ions. Energy is re-emitted, not as a single photon, but rather as a series of photons of lesser energy. The photons lose energy as they travel outward from the star's surface, and are not energetic enough to again contribute to ionization. Otherwise, the entire interstellar medium would be ionized. A Strömgren sphere is the theoretical construct which describes the ionized regions.
The model
In its first and simplest form, derived by the Danish astrophysicist Bengt Strömgren in 1939, the model examines the effects of the electromagnetic radiation of a single star (or a tight cluster of similar stars) of a given surface temperature and luminosity on the surrounding interstellar medium of a given density. To simplify calculations, the interstellar medium is taken to be homogeneous and consistin
|
https://en.wikipedia.org/wiki/Residual%20strength
|
Residual strength is the load or force (usually mechanical) that a damaged object or material can still carry without failing. Material toughness, fracture size and geometry as well as its orientation all contribute to residual strength.
References
Materials science
|
https://en.wikipedia.org/wiki/Thomas%20J.%20Goreau
|
Thomas J. Goreau (Tom Goreau, * 1950 in Jamaica) is a biogeochemist and marine biologist. He is the son of two other renowned marine biologists, Thomas F. Goreau and Nora I. Goreau.
Education
After studying in Jamaican primary and secondary schools, he received an undergraduate degree in planetary physics from the Massachusetts Institute of Technology (BS, 1970). He went on to earn a Master of Science in planetary astronomy from the California Institute of Technology (1972) and a Ph.D. in biogeochemistry from Harvard University (1981).
Career
With his parents, he researched the coral reefs of Jamaica and continues to conduct research on the impacts of global climate change, pollution, and new diseases in reefs across the Caribbean, Indian Ocean, and Pacific. His current work focuses on coral reef restoration, fisheries restoration, shoreline protection, renewable energy, community-based coral reef management, mariculture, soil metabolism, soil carbon, and stabilization of global carbon dioxide. He was formerly Senior Scientific Affairs Officer at the United Nations Centre for Science and Technology for Development. He is currently President of the Global Coral Reef Alliance and Director of Remineralize The Earth.
See also
Biorock
Remineralize The Earth
References
External links
https://web.archive.org/web/20120318112219/http://oneworldgroup.org/2010/02/03/coral-reef-expert-thomas-goreau-talked-to-oneclimate-at-cop15-in-copenhagen/ Interview filmed at COP15 in Copen
|
https://en.wikipedia.org/wiki/Renato%20M.%20E.%20Sabbatini
|
Renato Marcos Endrizzi Sabbatini (born 20 February 1947, Campinas) is a retired professor at the Department of Biomedical Engineering and at the State University of Campinas Institute of Biology. He received a B.Sc. in Biomedical Sciences from Medical School of the University of São Paulo and a doctorate in behavioral neuroscience in 1977, followed by postdoctoral work at the Max Planck Institute of Psychiatry's Primate Behavior Department. He founded the Center for Biomedical Informatics,
and helped create the Brazilian Society for Health Informatics.
Sabbatini received the 1992 Prêmio José Reis de Divulgação Científica award for popular science writing,
and was named one of Info Exame Magazine's "50 Champions of Innovation" for 2007. He is currently president of the Edumed Institute for Education in Medicine and Health, a "not-for-profit educational, research and development institution."
Professor Sabbatini is a Fellow Elect (Inaugural Class) of the International Academy of Health Sciences Informatics, established by the International Medical Informatics Association (IMIA), and a Fellow Elect of the American College of Medical Informatics, established by the American Medical Informatics Association.
Selected publications
Sabbatini, R.M.E.: A multilayered neural network for processing 2D tomographic images in neurosurgery. Proceed. Nuclear Science Symposium and Medical Imaging Conference, IEEE, 1992
Ortiz J., Ghefter C.G., Silva C.E., Sabbatini R.M.E.: One-year mortali
|
https://en.wikipedia.org/wiki/Michael%20Sendivogius
|
Michael Sendivogius (; ; 2 February 1566 – 1636) was a Polish alchemist, philosopher, and medical doctor. A pioneer of chemistry, he developed ways of purification and creation of various acids, metals and other chemical compounds. He discovered that air is not a single substance and contains a life-giving substance—later called oxygen—170 years before Scheele's discovery of the element. He correctly identified this 'food of life' with the gas (also oxygen) given off by heating nitre (saltpetre). This substance, the 'central nitre', had a central position in Sendivogius' schema of the universe.
Biography
Little is known of his early life: he was born in a noble family that was part of the Clan of Ostoja. His father sent him to study in university of Kraków but Sendivogius visited also most of the European countries and universities; he studied at Vienna, Altdorf, Leipzig and Cambridge. His acquaintances included John Dee and Edward Kelley. It was thanks to him that King Stephen Báthory agreed to finance their experiments. In the 1590s he was active in Prague, at the famously open-minded court of Emperor Rudolf II.
In Poland he appeared at the court of King Sigismund III Vasa around 1600, and quickly achieved great fame, as the Polish king was himself an alchemy enthusiast and even conducted experiments with Sendivogius. In Kraków's Wawel castle, the chamber where his experiments were performed is still intact. The more conservative Polish nobles soon came to dislike him fo
|
https://en.wikipedia.org/wiki/Trans-Planckian%20problem
|
In black hole physics and inflationary cosmology, the trans-Planckian problem is the problem of the appearance of quantities beyond the Planck scale, which raise doubts on the physical validity of some results in these two areas, since one expects the physical laws to suffer radical modifications beyond the Planck scale.
In black hole physics, the original derivation of Hawking radiation involved field modes that, near the black hole horizon, have arbitrarily high frequencies—in particular, higher than the inverse Planck time, although these do not appear in the final results. A number of different alternative derivations have been proposed in order to overcome this problem.
The trans-Planckian problem can be conveniently considered in the framework of sonic black holes, condensed matter systems which can be described in a similar way as real black holes. In these systems, the analogue of the Planck scale is the interatomic scale, where the continuum description loses its validity. One can study whether in these systems the analogous process to Hawking radiation still occurs despite the short-scale cutoff represented by the interatomic distance.
The trans-Planckian problem also appears in inflationary cosmology. The cosmological scales that we nowadays observe correspond to length scales smaller than the Planck length at the onset of inflation.
Trans-Planckian problem in Hawking radiation
The trans-Planckian problem is the issue that Hawking's original calculation includ
|
https://en.wikipedia.org/wiki/AJP
|
AJP or ajp may refer to:
American Journal of Philology, published by Johns Hopkins University Press
American Journal of Psychiatry, published by the American Psychiatric Association
American Journal of Psychology, published by the University of Illinois Press
American Journal of Physics, published by the American Association of Physics Teachers and the American Institute of Physics
American Journal of Physiology, published by the American Physiological Society
Asian Jake Paul, single by American Youtuber IDubbbz
Australasian Journal of Philosophy, published by the Australasian Association of Philosophy
AJP Motos, a Portuguese motorcycle brand
Animal Justice Party, a political party in Australia focusing on animal rights
Apache JServ Protocol, protocol for computer servers
All Japan Pro Wrestling, Japanese professional wrestling promotion
South Levantine Arabic (deprecated ISO 639-3 code)
AJP6 and AJP8, TVR engines
|
https://en.wikipedia.org/wiki/Associated%20Legendre%20polynomials
|
In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation
or equivalently
where the indices ℓ and m (which are integers) are referred to as the degree and order of the associated Legendre polynomial respectively. This equation has nonzero solutions that are nonsingular on only if ℓ and m are integers with 0 ≤ m ≤ ℓ, or with trivially equivalent negative values. When in addition m is even, the function is a polynomial. When m is zero and ℓ integer, these functions are identical to the Legendre polynomials. In general, when ℓ and m are integers, the regular solutions are sometimes called "associated Legendre polynomials", even though they are not polynomials when m is odd. The fully general class of functions with arbitrary real or complex values of ℓ and m are Legendre functions. In that case the parameters are usually labelled with Greek letters.
The Legendre ordinary differential equation is frequently encountered in physics and other technical fields. In particular, it occurs when solving Laplace's equation (and related partial differential equations) in spherical coordinates. Associated Legendre polynomials play a vital role in the definition of spherical harmonics.
Definition for non-negative integer parameters and
These functions are denoted , where the superscript indicates the order and not a power of P. Their most straightforward definition is in terms
of derivatives of ordinary Legendre polynomials (m
|
https://en.wikipedia.org/wiki/Dominic%20Giampaolo
|
Dominic P. Giampaolo is a software developer who helped develop the Be File System for the Be Operating System (BeOS) and currently works at Apple Inc.
After graduating from Lewiston High School in Lewiston, Maine in 1987, he started studying political science at American University in Washington, D.C., but changed to computer science after one semester. After completing his bachelor's degree, he did a master's degree at Worcester Polytechnic Institute.
After graduating, he travelled to the west coast to work for Silicon Graphics in their Advanced Systems Division. There he worked in the group that ported IRIX to the 64-bit R8000 microprocessor chip set and worked on the RealityEngine and InfiniteReality graphics systems. While working for Silicon Graphics, he located and fixed a bug in Discreet Logic's Flame compositing system that was delaying post-production of the motion picture Speed.
In October 1995, Giampaolo heard about the BeBox from a friend at a poker game. Shortly after visiting the Be Inc. offices to see a demo of the computer, he began working on the BeOS, working initially in a number of areas including the kernel and the POSIX layer but most notably developing the Be File System alongside Cyril Meurillon, which replaced the Old Be File System written by Benoit Schillings which had itself replaced the original flat file system written by Meurillon. The Be File System included a number of advances compared to other personal computer filesystems in use at the
|
https://en.wikipedia.org/wiki/Top-down%20cosmology
|
In theoretical physics, top-down cosmology is a proposal to regard the many possible past histories of a given event as having real existence. This idea of multiple histories has been applied to cosmology, in a theoretical interpretation in which the universe has multiple possible cosmologies, and in which reasoning backwards from the current state of the universe to a quantum superposition of possible cosmic histories makes sense. Stephen Hawking has argued that the principles of quantum mechanics forbid a single cosmic history, and has proposed cosmological theories in which the lack of a past boundary condition naturally leads to multiple histories, called the 'no-boundary proposal', the proposed Hartle–Hawking state.
According to Hawking and Thomas Hertog, "The top-down approach we have described leads to a profoundly different view of cosmology, and the relation between cause and effect. Top down cosmology is a framework in which one essentially traces the histories backwards, from a spacelike surface at the present time. The noboundary histories of the universe thus depend on what is being observed, contrary to the usual idea that the universe has a unique, observer independent history."
See also
Consistent histories
Multiverse
Quantum cosmology
Hartle–Hawking state
References
Physical cosmology
Quantum measurement
|
https://en.wikipedia.org/wiki/Stefan%20Kaczmarz
|
Stefan Marian Kaczmarz (March 20, 1895 in Sambor, Galicia, Austria-Hungary – 1939) was a Polish mathematician. His Kaczmarz method provided the basis for many modern imaging technologies, including the CAT scan.
Kaczmarz was a professor of mathematics in the faculty of mechanical engineering of Jan Kazimierz University of Lwów from 1919 to 1939, where he collaborated with Stefan Banach.
The circumstances of Kaczmarz's death are unclear. In early September 1939, after World War II broke out, he was called up for Polish military service as a reserve lieutenant. He sent a letter to his wife on 4 September and was not heard from afterwards. Theories for his death include the possibility that he died soon after near Nisko (the source of his last letter to his wife) in a German bombing raid on a train he was traveling in, that he died later that month in combat against the Germans near Umiastów, or that he was murdered by the NKVD in April or May 1940 as part of the Katyń massacre.
References
External links
Biography of Stefan Kaczmarz (in Polish)
1895 births
1939 deaths
Lwów School of Mathematics
Polish military personnel killed in World War II
|
https://en.wikipedia.org/wiki/Codress%20message
|
In military cryptography, a codress message is an encrypted message whose address is also encrypted. This is usually done to prevent traffic analysis.
References
Cryptography
|
https://en.wikipedia.org/wiki/Robert%20Hyatt
|
Robert Morgan Hyatt (born 1948) is an American computer scientist and programmer. He co-authored the computer chess programs Crafty and Cray Blitz which won two World Computer Chess Championships in the 1980s. Hyatt was a computer science professor at the University of Southern Mississippi (1970–1985) and University of Alabama at Birmingham (1988–2016).
Early life and education
Hyatt was born in Laurel, Mississippi in 1948. He earned a bachelor's degree in 1970 and an M.S. in 1983, both from the University of Southern Mississippi. His master's dissertation was titled Cray Blitz: A Computer Chess Playing Program. Hyatt earned a Ph.D. in computer and information sciences at the University of Alabama at Birmingham in 1988. His thesis was titled A High-Performance Parallel Algorithm to Search Depth-First Game Trees. Bruce Wilsey Suter was Hyatt's doctoral advisor.
Career
Hyatt is co-author of the computer chess program Crafty and the co-author of Cray Blitz, a two-time winner of the World Computer Chess Championships. He has been actively involved in computer chess since he first started to program a computer to play chess in 1968. These efforts have been supported by various computer vendors such as Univac (1978), Cray Research (1980–1994), and more recently AMD via their developer's lab. Crafty is freely available both in executable form (from many different web sites) and in source form (from Hyatt's home page). Crafty presently participates in many computer chess tournam
|
https://en.wikipedia.org/wiki/Yoichiro%20Nambu
|
was a Japanese-American physicist and professor at the University of Chicago. Known for his contributions to the field of theoretical physics, he was awarded half of the Nobel Prize in Physics in 2008 for the discovery in 1960 of the mechanism of spontaneous broken symmetry in subatomic physics, related at first to the strong interaction's chiral symmetry and later to the electroweak interaction and Higgs mechanism. The other half was split equally between Makoto Kobayashi and Toshihide Maskawa "for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature."
Early life and education
Nambu was born in Tokyo, Japan, in 1921. After graduating from the then Fukui Secondary High School in Fukui City, he enrolled in the Imperial University of Tokyo and studied physics. He received his Bachelor of Science in 1942 and Doctorate of Science in 1952. In 1949 he was appointed to associate professor at Osaka City University and promoted to professorship the next year at the age of 29.
In 1952, he was invited by the Institute for Advanced Study in Princeton, New Jersey, United States, to study. He moved to the University of Chicago in 1954 and was promoted to professor in 1958. From 1974 to 1977 he was also Chairman of the Department of Physics. He became a United States citizen in 1970.
Career in physics
Nambu proposed the "color charge" of quantum chromodynamics,
having done early work on spontaneous symmetry br
|
https://en.wikipedia.org/wiki/Rossby%20parameter
|
The Rossby parameter (or simply beta ) is a number used in geophysics and meteorology which arises due to the meridional variation of the Coriolis force caused by the spherical shape of the Earth. It is important in the generation of Rossby waves. The Rossby parameter is given by
where is the Coriolis parameter, is the latitude, is the angular speed of the Earth's rotation, and is the mean radius of the Earth. Although both involve Coriolis effects, the Rossby parameter describes the variation of the effects with latitude (hence the latitudinal derivative), and should not be confused with the Rossby number.
See also
Beta plane
References
Atmospheric dynamics
|
https://en.wikipedia.org/wiki/Categorical%20logic
|
Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science.
In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor. The categorical framework provides a rich conceptual background for logical and type-theoretic constructions. The subject has been recognisable in these terms since around 1970.
Overview
There are three important themes in the categorical approach to logic:
Categorical semantics Categorical logic introduces the notion of structure valued in a category C with the classical model theoretic notion of a structure appearing in the particular case where C is the category of sets and functions. This notion has proven useful when the set-theoretic notion of a model lacks generality and/or is inconvenient. R.A.G. Seely's modeling of various impredicative theories, such as System F, is an example of the usefulness of categorical semantics.
It was found that the connectives of pre-categorical logic were more clearly understood using the concept of adjoint functor, and that the quantifiers were also best understood using adjoint functors.
Internal languages This can be seen as a formalization and generalization of proof by diagram chasing. One defines a suitable internal language naming relevant constituents of a category, and then applies categori
|
https://en.wikipedia.org/wiki/Leon%20Marchlewski
|
Leon Paweł Teodor Marchlewski (15 December 1869 in Włocławek – 16 January 1946 in Kraków, Poland) was a Polish chemist and an Honorary Member of the Polish Chemical Society.
He was one of the founders in the field of chlorophyll chemistry. The illustration on the right is of his diplomatic passport he used in 1927 to attend an international conference on chemistry in Paris.
References
External links
1869 births
1946 deaths
Burials at Rakowicki Cemetery
People from Włocławek
Polish senators
Polish chemists
Chemical pathologists
Members of the Lwów Scientific Society
Rectors of the Jagiellonian University
Commanders of the Order of Polonia Restituta
People from Congress Poland
|
https://en.wikipedia.org/wiki/Bohdan%20Szyszkowski
|
Bohdan Szyszkowski (born June 20, 1873, in Trybuchy, Podolia, Russia (now village in Ukraine) – August 13, 1931 in Myślenice, Poland) was a Polish chemist and member of PAU.
Szyszkowski published important papers on electrochemistry and surface chemistry.
See also
Szyszkowski equation
References
1873 births
1931 deaths
Polish chemists
Chemists from the Russian Empire
|
https://en.wikipedia.org/wiki/W%C5%82adys%C5%82aw%20Natanson
|
Władysław Natanson (1864–1937) was a Polish physicist.
Life
Natanson was head of Theoretical Physics at Kraków University from 1899 to 1935.
He published a series of papers on thermodynamically irreversible processes, gaining him recognition in the rapidly growing field. He was the first to consider the distinguishability of energy quanta in the statistical analysis of elementary processes, a precursor of the concept of quantum indistinguishability. He discovered a quantum statistics, rediscovered 11 years later by Satyendra Nath Bose and generalized by Albert Einstein though his derivation was not in terms of einstein's light quanta aka photons – the Bose–Einstein statistics.
See also
List of Poles (physicicsts)
Notes
Members of the Lwów Scientific Society
1864 births
1937 deaths
Academic staff of Jagiellonian University
Rectors of the Jagiellonian University
19th-century Polish physicists
20th-century Polish physicists
Physicists from Austria-Hungary
|
https://en.wikipedia.org/wiki/Electric%20blue
|
Electric blue may refer to:
Electric blue (color)
Biology
Electric blue crayfish (Procambarus alleni)
Electric blue gecko (Lygodactylus williamsi)
Sciaenochromis, a genus of haplochromine cichlid fish whose males are electric blue, including:
Electric blue hap (Sciaenochromis ahli)
Electric blue kande (Sciaenochromis psammophilu)
Music
Electric Blue (album), by Andy Bell, or the title song, 2005
"Electric Blue" (Icehouse song), 1987
"Electric Blue", a song by Arcade Fire from Everything Now, 2017
"Electric Blue", a song by the Cranberries from To the Faithful Departed, 1996
"Electric Blue", a song by Mars & Mystre, 2000
"Electric Blue", a song by Nicole Scherzinger from Big Fat Lie, 2014
Television
Electric Blue (TV series), a 1979–1987 British softcore pornography series
See also
Ionized-air glow
Electric Blues (disambiguation)
|
https://en.wikipedia.org/wiki/Occurs%20check
|
In computer science, the occurs check is a part of algorithms for syntactic unification. It causes unification of a variable V and a structure S to fail if S contains V.
Application in theorem proving
In theorem proving, unification without the occurs check can lead to unsound inference. For example, the Prolog goal
will succeed, binding X to a cyclic structure which has no counterpart in the Herbrand universe.
As another example,
without occurs-check, a resolution proof can be found for the non-theorem
: the negation of that formula has the conjunctive normal form , with and denoting the Skolem function for the first and second existential quantifier, respectively; the literals and are unifiable without occurs check, producing the refuting empty clause.
Rational tree unification
Prolog implementations usually omit the occurs check for reasons of efficiency, which can lead to circular data structures and looping.
By not performing the occurs check, the worst case complexity of unifying a term
with term
is reduced in many cases from
to
;
in the particular, frequent case of variable-term unifications, runtime shrinks to
.
Modern implementations, based on Colmerauer's Prolog II,
use rational tree unification to avoid looping. However it is difficult to keep the complexity time linear in the presence of cyclic terms. Examples where Colmerauers algorithm becomes quadratic can be readily constructed, but refinement proposals exist.
See image for an example ru
|
https://en.wikipedia.org/wiki/Oaklisp
|
Oaklisp is a portable object-oriented Scheme developed by Kevin J. Lang and Barak A. Pearlmutter while Computer Science PhD students at Carnegie Mellon University. Oaklisp uses a superset of Scheme syntax. It is based on generic operations rather than functions, and features anonymous classes, multiple inheritance, a strong error system, setters and locators for operations, and a facility for dynamic binding.
Version 1.2 includes an interface, bytecode compiler, run-time system and documentation.
References
External links
Oaklisp homepage
Scheme (programming language) implementations
Object-oriented programming languages
|
https://en.wikipedia.org/wiki/European%20Molecular%20Biology%20Laboratory
|
The European Molecular Biology Laboratory (EMBL) is an intergovernmental organization dedicated to molecular biology research and is supported by 28 member states, one prospect state, and one associate member state. EMBL was created in 1974 and is funded by public research money from its member states. Research at EMBL is conducted by approximately 110 independent research and service groups and teams covering the spectrum of molecular biology and bioinformatics. The list of Groups and Teams at EMBL can be found at . The Laboratory operates from six sites: the main laboratory in Heidelberg, and sites in Hinxton (the European Bioinformatics Institute (EBI), in England), Grenoble (France), Hamburg (Germany), Rome (Italy) and Barcelona (Spain). EMBL groups and laboratories perform basic research in molecular biology and molecular medicine as well as train scientists, students, and visitors. The organization aids in the development of services, new instruments and methods, and technology in its member states. Israel is the only full member state located outside Europe.
History
EMBL was the idea of Leó Szilárd, James Watson and John Kendrew. Their goal was to create an international research centre, similar to CERN, to rival the strongly American-dominated field of molecular biology. Kendrew served as the first Director-general of EMBL until 1982 and was succeeded by Lennart Philipson. From 1993 to 2005, Fotis Kafatos, served as director and was succeeded by Iain Mattaj, EMBL's
|
https://en.wikipedia.org/wiki/Le%20Lisp
|
Le Lisp (also Le_Lisp and Le-Lisp) is a programming language, a dialect of the language Lisp.
Programming language
It was developed at the French Institute for Research in Computer Science and Automation (INRIA), to be an implementation language for a very large scale integration (VLSI) workstation being designed under the direction of Jean Vuillemin. Le Lisp also had to run on various incompatible platforms (mostly running Unix operating systems) that were used by the project. The main goals for the language were to be a powerful post-Maclisp version of Lisp that would be portable, compatible, extensible, and efficient.
Jérôme Chailloux led the Le Lisp team, working with Emmanuel St. James, Matthieu Devin, and Jean-Marie Hullot in 1980. The dialect is historically noteworthy as one of the first Lisp implementations to be available on both the Apple II and the IBM PC.
On 2020-01-08, INRIA agreed to migrate the source code to the 2-clause BSD License which allowed few native ports from ILOG and Eligis to adopt this license model.
References
External links
, Eligis, for x86 processors
Le Lisp at Computer History Museum's Software Preservation Group
Le-Lisp Open Source repository on GitHub
Lisp programming language family
Lisp (programming language)
|
https://en.wikipedia.org/wiki/David%20King%20%28chemist%29
|
Sir David Anthony King (born 12 August 1939) is a South African-born British chemist, academic, and head of the Climate Crisis Advisory Group.
King first taught at Imperial College, London, the University of East Anglia, and was then Brunner Professor of Physical Chemistry (1974–1988) at the University of Liverpool. He held the 1920 Chair of Physical Chemistry at the University of Cambridge from 1988 to 2006, and was Master of Downing College, Cambridge, from 1995 to 2000: he is now emeritus professor. While at Cambridge, he was successively a fellow of St John's College, Downing College, and Queens' College. Moving to the University of Oxford, he was Director of the Smith School of Enterprise and the Environment from 2008 to 2012, and a Fellow of University College, Oxford, from 2009 to 2012. He was additionally President of Collegio Carlo Alberto in Turin, Italy (2008–2011), and Chancellor of the University of Liverpool (2010–2013).
Outside of academia, King was Chief Scientific Adviser to the UK Government and Head of the Government Office for Science from 2000 to 2007. He was then senior scientific adviser to UBS, a Swiss investment bank and financial services company, from 2008 to 2013. From 2013 to 2017, he returned to working with the UK Government as Special Representative for Climate Change to the Foreign Secretary. He was also Chairman of the government's Future Cities Catapult from 2013 to 2016.
Early life and education
King was born on 12 August 1939 in South
|
https://en.wikipedia.org/wiki/Ground%20and%20neutral
|
In electrical engineering, ground and neutral are circuit conductors used in alternating current (AC) electrical systems. The ground circuit is connected to earth, and neutral circuit is usually connected to ground. As the neutral point of an electrical supply system is often connected to earth ground, ground and neutral are closely related. Under certain conditions, a conductor used to connect to a system neutral is also used for grounding (earthing) of equipment and structures. Current carried on a grounding conductor can result in objectionable or dangerous voltages appearing on equipment enclosures, so the installation of grounding conductors and neutral conductors is carefully defined in electrical regulations. Where a neutral conductor is used also to connect equipment enclosures to earth, care must be taken that the neutral conductor never rises to a high voltage with respect to local ground.
Definitions
Ground or earth in a mains (AC power) electrical wiring system is a conductor that provides a low-impedance path to the earth to prevent hazardous voltages from appearing on equipment (high voltage spikes). The terms and are used synonymously in this section; is more common in North American English, and is more common in British English. Under normal conditions, a grounding conductor does not carry current. Grounding is also an integral path for home wiring because it causes circuit breakers to trip more quickly (ie, GFCI), which is safer. Adding new grounds req
|
https://en.wikipedia.org/wiki/Third%20grade
|
Third grade (also 3rd Grade or Grade 3) is the third year of formal or compulsory education. It is the third year of primary school. Children in third grade are usually 8-9 years old.
Examples of the American syllabus
In mathematics, students are usually introduced to multiplication and division facts, place value to thousands or ten thousands, and estimation. Depending on the elementary school, third grade students may even begin to work on long division, such as dividings in the double digits, hundreds, and thousands. Decimals (to tenths only) are sometimes introduced. Students begin to work on problem-solving skills working to explain their thinking in mathematical terms.
In science, third grade students are taught basic physics and chemistry. Weather and climate are also sometimes taught. The concept of atoms and molecules are common, the states of matter, and energy, along with basic chemical elements such as oxygen, hydrogen, gold, zinc, and iron. Nutrition is also sometimes taught in third grade along with chemistry.
Social studies sometimes begins a study of the culture of the United States and basic idea of the early part of the United States from the time of the Native Americans to the Civil War. Outward expansion and the gold rush are covered.
In reading and language arts, third grade students begin working more on text comprehension by using informational articles or different genre books than decoding strategies. Students also begin reading harder chapter bo
|
https://en.wikipedia.org/wiki/Real%20closed%20field
|
In mathematics, a real closed field is a field F that has the same first-order properties as the field of real numbers. Some examples are the field of real numbers, the field of real algebraic numbers, and the field of hyperreal numbers.
Definitions
A real closed field is a field F in which any of the following equivalent conditions is true:
F is elementarily equivalent to the real numbers. In other words, it has the same first-order properties as the reals: any sentence in the first-order language of fields is true in F if and only if it is true in the reals.
There is a total order on F making it an ordered field such that, in this ordering, every positive element of F has a square root in F and any polynomial of odd degree with coefficients in F has at least one root in F.
F is a formally real field such that every polynomial of odd degree with coefficients in F has at least one root in F, and for every element a of F there is b in F such that a = b2 or a = −b2.
F is not algebraically closed, but its algebraic closure is a finite extension.
F is not algebraically closed but the field extension is algebraically closed.
There is an ordering on F that does not extend to an ordering on any proper algebraic extension of F.
F is a formally real field such that no proper algebraic extension of F is formally real. (In other words, the field is maximal in an algebraic closure with respect to the property of being formally real.)
There is an ordering on F making it an ordered
|
https://en.wikipedia.org/wiki/Nubiology
|
Nubiology is the designation given to the primarily archaeological science that specialises in the scientific and historical study of Ancient Nubia and its antiquities.
It is sometimes also applied to scientists who study other ancient lands and cultures south of Ancient Egypt. The term was coined by Kazimierz Michałowski.
External links
Website Study of Nubiology at the Polish Academy of Sciences
History of Nubia
Area studies by ancient history
Archaeology of Egypt
Archaeology of Sudan
|
https://en.wikipedia.org/wiki/C9
|
C9, C09 or C-9 may refer to:
Biology, medicine, and chemistry
C9 (Complement component 9), a protein
ATC code C09, a subgroup of the Anatomical Therapeutic Chemical Classification System
C09, ICD-10 code for malignant neoplasm of tonsil
Carbon-9 (C-9 or 9C), an isotope of carbon
Military and weapons
Hi-Point Models C9 and C9 Comp handguns
C9 LMG, Canadian light machine gun
C9, an ID for the German Nachtjagdgeschwader 5 air squadron in World War II
Music
C9, a note five octaves above Middle C
C9, a C ninth chord
Organizations
Cloud9, an American esports organization
C9 League, an association of Chinese universities
The Council of Cardinal Advisers, an advisory body to the pope, originally comprising nine members
C9 Entertainment, a South Korean entertainment company and record label
Transportation
Cierva C.9, a 1927 British experimental autogyro
HMS C9, a British submarine
Ford C-9, a US military designation for the Ford Trimotor aircraft
McDonnell Douglas C-9, a US Air Force transport aircraft based on the civilian DC-9
USS Montgomery (C-9), a US Navy cruiser
C9, the IATA code for Cirrus Airlines
Sauber C9, a Le Mans racing car
C9 engine, by Caterpillar Inc.
C-9 (Cercanías Madrid), a commuter rail line in Madrid
LNER Class C9, a class of 2 British steam locomotives rebuilt from C7s in 1931
Other uses
C9, an ISO 216 standard paper size
C9, a holiday light bulb size
C9, a sportswear line by Champion
See also
9C (disambiguation)
|
https://en.wikipedia.org/wiki/Characteristic%20%28algebra%29
|
In mathematics, the characteristic of a ring , often denoted , is defined to be the smallest positive number of copies of the ring's multiplicative identity () that will sum to the additive identity (). If no such number exists, the ring is said to have characteristic zero.
That is, is the smallest positive number such that:
if such a number exists, and otherwise.
Motivation
The special definition of the characteristic zero is motivated by the equivalent definitions characterized in the next section, where the characteristic zero is not required to be considered separately.
The characteristic may also be taken to be the exponent of the ring's additive group, that is, the smallest positive integer such that:
for every element of the ring (again, if exists; otherwise zero). This definition applies in the more general class of a rngs (see ); for (unital) rings the two definitions are equivalent due to their distributive law.
Equivalent characterizations
The characteristic is the natural number such that is the kernel of the unique ring homomorphism from to .
The characteristic is the natural number such that contains a subring isomorphic to the factor ring , which is the image of the above homomorphism.
When the non-negative integers are partially ordered by divisibility, then is the smallest and is the largest. Then the characteristic of a ring is the smallest value of for which . If nothing "smaller" (in this ordering) than will suffice, then t
|
https://en.wikipedia.org/wiki/Salem%20number
|
In mathematics, a Salem number is a real algebraic integer whose conjugate roots all have absolute value no greater than 1, and at least one of which has absolute value exactly 1. Salem numbers are of interest in Diophantine approximation and harmonic analysis. They are named after Raphaël Salem.
Properties
Because it has a root of absolute value 1, the minimal polynomial for a Salem number must be reciprocal. This implies that is also a root, and that all other roots have absolute value exactly one. As a consequence α must be a unit in the ring of algebraic integers, being of norm 1.
Every Salem number is a Perron number (a real algebraic number greater than one all of whose conjugates have smaller absolute value).
Relation with Pisot–Vijayaraghavan numbers
The smallest known Salem number is the largest real root of Lehmer's polynomial (named after Derrick Henry Lehmer)
which is about : it is conjectured that it is indeed the smallest Salem number, and the smallest possible Mahler measure of an irreducible non-cyclotomic polynomial.
Lehmer's polynomial is a factor of the shorter 12th-degree polynomial,
all twelve roots of which satisfy the relation
Salem numbers can be constructed from Pisot–Vijayaraghavan numbers. To recall, the smallest of the latter is the unique real root of the cubic polynomial,
known as the plastic number and approximately equal to 1.324718. This can be used to generate a family of Salem numbers including the smallest one found so far. T
|
https://en.wikipedia.org/wiki/Formally%20real%20field
|
In mathematics, in particular in field theory and real algebra, a formally real field is a field that can be equipped with a (not necessarily unique) ordering that makes it an ordered field.
Alternative definitions
The definition given above is not a first-order definition, as it requires quantifiers over sets. However, the following criteria can be coded as (infinitely many) first-order sentences in the language of fields and are equivalent to the above definition.
A formally real field F is a field that also satisfies one of the following equivalent properties:
−1 is not a sum of squares in F. In other words, the Stufe of F is infinite. (In particular, such a field must have characteristic 0, since in a field of characteristic p the element −1 is a sum of 1s.) This can be expressed in first-order logic by , , etc., with one sentence for each number of variables.
There exists an element of F that is not a sum of squares in F, and the characteristic of F is not 2.
If any sum of squares of elements of F equals zero, then each of those elements must be zero.
It is easy to see that these three properties are equivalent. It is also easy to see that a field that admits an ordering must satisfy these three properties.
A proof that if F satisfies these three properties, then F admits an ordering uses the notion of prepositive cones and positive cones. Suppose −1 is not a sum of squares; then a Zorn's Lemma argument shows that the prepositive cone of sums of squares can be
|
https://en.wikipedia.org/wiki/Brucine
|
Brucine, is an alkaloid closely related to strychnine, most commonly found in the Strychnos nux-vomica tree. Brucine poisoning is rare, since it is usually ingested with strychnine, and strychnine is more toxic than brucine. In synthetic chemistry, it can be used as a tool for stereospecific chemical syntheses.
Brucine is named from the genus Brucea, named after James Bruce who brought back Brucea antidysenterica from Ethiopia.
History
Brucine was discovered in 1819 by Pelletier and Caventou in the bark of the Strychnos nux-vomica tree. While its structure was not deduced until much later, it was determined that it was closely related to strychnine in 1884, when the chemist Hanssen converted both strychnine and brucine into the same molecule.
Identification
Brucine can be detected and quantified using liquid chromatography-mass spectrometry. Historically, brucine was distinguished from strychnine by its reactivity toward chromic acid.
Applications
Chemical applications
Since brucine is a large chiral molecule, it has been used in chiral resolution. Fisher first reported its use as a resolving agent in 1899, and it was the first natural product used as an organocatalyst in a reaction resulting in an enantiomeric enrichment by Marckwald, in 1904. Its bromide salt has been used as the stationary phase in HPLC in order to selectively bind one of two anionic enantiomers. Brucine has also been used in fractional distillation in acetone in order to resolve dihydroxy fatty ac
|
https://en.wikipedia.org/wiki/Hilbert%E2%80%93Speiser%20theorem
|
In mathematics, the Hilbert–Speiser theorem is a result on cyclotomic fields, characterising those with a normal integral basis. More generally, it applies to any finite abelian extension of , which by the Kronecker–Weber theorem are isomorphic to subfields of cyclotomic fields.
Hilbert–Speiser Theorem. A finite abelian extension has a normal integral basis if and only if it is tamely ramified over .
This is the condition that it should be a subfield of where is a squarefree odd number. This result was introduced by in his Zahlbericht and by .
In cases where the theorem states that a normal integral basis does exist, such a basis may be constructed by means of Gaussian periods. For example if we take a prime number , has a normal integral basis consisting of all the -th roots of unity other than . For a field contained in it, the field trace can be used to construct such a basis in also (see the article on Gaussian periods). Then in the case of squarefree and odd, is a compositum of subfields of this type for the primes dividing (this follows from a simple argument on ramification). This decomposition can be used to treat any of its subfields.
proved a converse to the Hilbert–Speiser theorem:
Each finite tamely ramified abelian extension of a fixed number field has a relative normal integral basis if and only if .
There is an elliptic analogue of the theorem proven by .
It is now called the Srivastav-Taylor theorem .
References
Cyclotomic fields
Theo
|
https://en.wikipedia.org/wiki/Telos
|
Telos (; ) is a term used by philosopher Aristotle to refer to the final cause of a natural organ or entity, or of human art. Telos is the root of the modern term teleology, the study of purposiveness or of objects with a view to their aims, purposes, or intentions. Teleology is central in Aristotle's work on plant and animal biology, and human ethics, through his theory of the four causes. Aristotle's notion that everything has a telos also gave rise to epistemology.
In Aristotle
Telos has been consistently used in the writings of Aristotle, in which the term, on several occasions, denotes 'goal'. It is considered synonymous to teleute ('end'), particularly in Aristotle's discourse about the plot-structure in Poetics. The philosopher went as far as to say that telos can encompass all forms of human activity. One can say, for instance, that the telos of warfare is victory, or the telos of business is the creation of wealth. Within this conceptualization, there are telos that are subordinate to other telos, as all activities have their own, respective goals.
For Aristotle, these subordinate telos can become the means to achieve more fundamental telos. Through this concept, for instance, the philosopher underscored the importance of politics and that all other fields are subservient to it. He explained that the telos of the blacksmith is the production of a sword, while that of the swordsman's, which uses the weapon as a tool, is to kill or incapacitate an enemy. On the oth
|
https://en.wikipedia.org/wiki/Monthly%20Notices%20of%20the%20Royal%20Astronomical%20Society
|
Monthly Notices of the Royal Astronomical Society (MNRAS) is a peer-reviewed scientific journal covering research in astronomy and astrophysics. It has been in continuous existence since 1827 and publishes letters and papers reporting original research in relevant fields. Despite the name, the journal is no longer monthly, nor does it carry the notices of the Royal Astronomical Society.
History
The first issue of MNRAS was published on 9 February 1827 as Monthly Notices of the Astronomical Society of London and it has been in continuous publication ever since. It took its current name from the second volume, after the Astronomical Society of London became the Royal Astronomical Society (RAS). Until 1960 it carried the monthly notices of the RAS, at which time these were transferred to the newly established Quarterly Journal of the Royal Astronomical Society (1960–1996) and then to its successor journal Astronomy & Geophysics (since 1997). Until 1965, MNRAS was published in-house by the society; from 1965 to 2012 it was published by Blackwell Publishing (later part of Wiley-Blackwell) on behalf of the RAS. From 2013, MNRAS is published by Oxford University Press (OUP).
The journal is no longer monthly, with thirty-six issues a year divided into nine volumes. The Letters section had originally appeared on pink paper in the print edition, but moved online only in the early 2000s. Print publication ceased after the April 2020 volume, during the COVID-19 pandemic, with the jour
|
https://en.wikipedia.org/wiki/L%C3%A9vy%27s%20constant
|
In mathematics Lévy's constant (sometimes known as the Khinchin–Lévy constant) occurs in an expression for the asymptotic behaviour of the denominators of the convergents of continued fractions.
In 1935, the Soviet mathematician Aleksandr Khinchin showed that the denominators qn of the convergents of the continued fraction expansions of almost all real numbers satisfy
Soon afterward, in 1936, the French mathematician Paul Lévy found the explicit expression for the constant, namely
The term "Lévy's constant" is sometimes used to refer to (the logarithm of the above expression), which is approximately equal to 1.1865691104… The value derives from the asymptotic expectation of the logarithm of the ratio of successive denominators, using the Gauss-Kuzmin distribution. In particular, the ratio has the asymptotic density function
for and zero otherwise. This gives Lévy's constant as
.
The base-10 logarithm of Lévy's constant, which is approximately 0.51532041…, is half of the reciprocal of the limit in Lochs' theorem.
See also
Khinchin's constant
References
Further reading
External links
Continued fractions
Mathematical constants
Paul Lévy (mathematician)
|
https://en.wikipedia.org/wiki/Two-level%20scheduling
|
Two-level scheduling is a computer science term to describe a method to more efficiently perform process scheduling that involves swapped out processes.
Consider this problem: A system contains 50 running processes all with equal priority. However, the system's memory can only hold 10 processes in memory simultaneously. Therefore, there will always be 40 processes swapped out written on virtual memory on the hard disk. The time taken to swap out and swap in a process is 50 ms respectively.
With straightforward Round-robin scheduling, every time a context switch occurs, a process would need to be swapped in (because only the 10 least recently used processes are swapped in). Choosing randomly among the processes would diminish the probability to 80% (40/50). If that occurs, then obviously a process also need to be swapped out. Swapping in and out of is costly, and the scheduler would waste much of its time doing unneeded swaps.
That is where two-level scheduling enters the picture. It uses two different schedulers, one lower-level scheduler which can only select among those processes in memory to run. That scheduler could be a Round-robin scheduler. The other scheduler is the higher-level scheduler whose only concern is to swap in and swap out processes from memory. It does its scheduling much less often than the lower-level scheduler since swapping takes so much time.
Thus, the higher-level scheduler selects among those processes in memory that have run for a long time
|
https://en.wikipedia.org/wiki/Apparent%20weight
|
In physics, apparent weight is a property of objects that corresponds to how heavy an object appears to be. The apparent weight of an object will differ from the ordinary weight of an object whenever the force of gravity acting on the object is not balanced by an equal but opposite normal force. By definition, the weight of an object is equal to the magnitude of the force of gravity acting on it. This means that even a "weightless" astronaut in low Earth orbit, with an apparent weight of zero, has almost the same weight as he would have while standing on the ground; this is due to the force of gravity in low Earth orbit and on the ground being almost the same.
An object that rests on the ground is subject to a normal force exerted by the ground. The normal force acts only on the boundary of the object that is in contact with the ground. This ground reaction force is transferred into the body; the force of gravity on every part of the body is balanced by stress forces acting on that part. A "weightless" astronaut feels weightless due to the absence of these stress forces.
By defining the apparent weight of an object in terms of normal forces, one can capture this effect of the stress forces. A common definition is "the force the body exerts on whatever it rests on."
The apparent weight can also differ from weight when an object is "partially or completely immersed in a fluid", where there is an "upthrust" from the fluid that is working against the force of gravity. Another
|
https://en.wikipedia.org/wiki/Sign%20bit
|
In computer science, the sign bit is a bit in a signed number representation that indicates the sign of a number. Although only signed numeric data types have a sign bit, it is invariably located in the most significant bit position, so the term may be used interchangeably with "most significant bit" in some contexts.
Almost always, if the sign bit is 0, the number is non-negative (positive or zero). If the sign bit is 1 then the number is negative, although formats other than two's complement integers allow a signed zero: distinct "positive zero" and "negative zero" representations, the latter of which does not correspond to the mathematical concept of a negative number.
In the two's complement representation, the sign bit has the weight where is the number of bits. In the ones' complement representation, the most negative value is , but there are two representations of zero, one for each value of the sign bit. In a sign-and-magnitude representation of numbers, the value of the sign bit determines whether the numerical value is positive or negative.
Floating-point numbers, such as IEEE format, IBM format, VAX format, and even the format used by the Zuse Z1 and Z3 use a sign-and-magnitude representation.
When using a complement representation, to convert a signed number to a wider format the additional bits must be filled with copies of the sign bit in order to preserve its numerical value, a process called sign extension or sign propagation.
References
Binary ari
|
https://en.wikipedia.org/wiki/Sphecidae
|
The Sphecidae are a cosmopolitan family of wasps of the suborder Apocrita that includes sand wasps, mud daubers, and other thread-waisted wasps.
The name Sphecidae was formerly given to a much larger grouping of wasps. This was found to be paraphyletic, so most of the old subfamilies have been moved to the Crabronidae.
Biology
The biology of the Sphecidae, even under the restricted definition, is still fairly diverse; some sceliphrines even display rudimentary forms of sociality, and some sphecines rear multiple larvae in a single large brood cell. Many nest in pre-existing cavities, or dig simple burrows in the soil, but some species construct free-standing nests of mud and even (in one genus) resin. All are predatory and parasitoidal, but the type of prey ranges from spiders to various dictyopterans, orthopteroids and larvae of either Lepidoptera or other Hymenoptera; the vast majority practice mass provisioning, providing all the prey items prior to laying the egg.
Phylogeny
This phylogenetic tree is based on Sann et al., 2018, which used phylogenomics to demonstrate that both the bees (Anthophila) and the Sphecidae arose from within the former Crabronidae, which is therefore paraphyletic, and which they suggested should be split into several families; the former family Heterogynaidae nests within the Bembicidae, as here defined. These findings differ in several details from studies published by two other sets of authors in 2017, though all three studies demonstrate a
|
https://en.wikipedia.org/wiki/Thaddeus%20Mann
|
Thaddeus Robert Rudolph Mann CBE FRS (4 December 1908 – 27 November 1993) was a biochemist who made significant contributions to the field of reproductive biology. Mann was born in Lwow, Austria-Hungary (now Ukraine) and was educated at Lwow University. He studied medicine at the Johannes Casimirus University in Lwow, obtaining the degrees of Physician in 1932 and Doctor of Medicine in 1934.
He continued his education at the Molteno Institute, Cambridge on a Rockefeller Fellowship, 1935-1937, and remained at the University of Cambridge during the rest of his career. He died in Cambridge.
Mann began his career in the laboratory of Professor Jacob Karol Parnas (1884-1949) in Poland, where he was involved in research on glycolysis and muscle energy metabolism.
He was elected a Fellow of the Royal Society in 1951.
He was married to Cecilia Lutwak-Mann, an endocrinologist and physiologist.
Publications
Thaddeus Mann published more than 250 papers, and several books.
Further reading
Ostrowski WS (1990) Thaddeus Mann. Life and work. Andrologia. 1990;22 Suppl 1:3–9.
References
External links
1993 deaths
1908 births
Fellows of the Royal Society
|
https://en.wikipedia.org/wiki/Cohomology%20ring
|
In mathematics, specifically algebraic topology, the cohomology ring of a topological space X is a ring formed from the cohomology groups of X together with the cup product serving as the ring multiplication. Here 'cohomology' is usually understood as singular cohomology, but the ring structure is also present in other theories such as de Rham cohomology. It is also functorial: for a continuous mapping of spaces one obtains a ring homomorphism on cohomology rings, which is contravariant.
Specifically, given a sequence of cohomology groups Hk(X;R) on X with coefficients in a commutative ring R (typically R is Zn, Z, Q, R, or C) one can define the cup product, which takes the form
The cup product gives a multiplication on the direct sum of the cohomology groups
This multiplication turns H•(X;R) into a ring. In fact, it is naturally an N-graded ring with the nonnegative integer k serving as the degree. The cup product respects this grading.
The cohomology ring is graded-commutative in the sense that the cup product commutes up to a sign determined by the grading. Specifically, for pure elements of degree k and ℓ; we have
A numerical invariant derived from the cohomology ring is the cup-length, which means the maximum number of graded elements of degree ≥ 1 that when multiplied give a non-zero result. For example a complex projective space has cup-length equal to its complex dimension.
Examples
where .
where .
where .
where .
where .
where .
By the Künneth formula, t
|
https://en.wikipedia.org/wiki/Divide
|
Divide may refer to:
Mathematics
Division (mathematics)
Divides, redirects to Divisor
Geography
Drainage divide, a line separating two drainage basins
Great Divide Basin, in Wyoming
Places
Divide, Saskatchewan, Canada
Divide, Colorado, community
Divide, Illinois, an unincorporated community
Divide, Montana, a rural community
Divide, Oregon, an unincorporated community
Divide, West Virginia, an unincorporated community
Divide County, North Dakota
Music
"Divide", a song by All That Remains from The Order of Things
"Divide", a song by Bastille from Doom Days
"Divide", a song by Disturbed from Indestructible
"Divide", a song by Vision of Disorder from Vision of Disorder
÷ (album), a 2017 album by Ed Sheeran
Divides, album by The Virginmarys 2016
The Continental Divide (album)
The Divide, album by Tom Waits and Scott Vestal 2011
See also
Continental divide (disambiguation)
Div (disambiguation)
Divided (disambiguation)
Division (disambiguation)
Division sign (÷)
The Divide (disambiguation)
Vertical line (dividing line)
|
https://en.wikipedia.org/wiki/Total%20derivative
|
In mathematics, the total derivative of a function at a point is the best linear approximation near this point of the function with respect to its arguments. Unlike partial derivatives, the total derivative approximates the function with respect to all of its arguments, not just a single one. In many situations, this is the same as considering all partial derivatives simultaneously. The term "total derivative" is primarily used when is a function of several variables, because when is a function of a single variable, the total derivative is the same as the ordinary derivative of the function.
The total derivative as a linear map
Let be an open subset. Then a function is said to be (totally) differentiable at a point if there exists a linear transformation such that
The linear map is called the (total) derivative or (total) differential of at . Other notations for the total derivative include and . A function is (totally) differentiable if its total derivative exists at every point in its domain.
Conceptually, the definition of the total derivative expresses the idea that is the best linear approximation to at the point . This can be made precise by quantifying the error in the linear approximation determined by . To do so, write
where equals the error in the approximation. To say that the derivative of at is is equivalent to the statement
where is little-o notation and indicates that is much smaller than as . The total derivative is the uniq
|
https://en.wikipedia.org/wiki/Magnon
|
A magnon is a quasiparticle, a collective excitation of the spin structure of an electron in a crystal lattice. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave. Magnons carry a fixed amount of energy and lattice momentum, and are spin-1, indicating they obey boson behavior.
Brief history
The concept of a magnon was introduced in 1930 by Felix Bloch in order to explain the reduction of the spontaneous magnetization in a ferromagnet. At absolute zero temperature (0 K), a Heisenberg ferromagnet reaches the state of lowest energy (so-called ground state), in which all of the atomic spins (and hence magnetic moments) point in the same direction. As the temperature increases, more and more spins deviate randomly from the alignment, increasing the internal energy and reducing the net magnetization. If one views the perfectly magnetized state at zero temperature as the vacuum state of the ferromagnet, the low-temperature state with a few misaligned spins can be viewed as a gas of quasiparticles, in this case magnons. Each magnon reduces the total spin along the direction of magnetization by one unit of (reduced Planck's constant) and the magnetization by , where is the gyromagnetic ratio. This leads to Bloch's law for the temperature dependence of spontaneous magnetization:
where is the (material dependent) critical temperature, and is the magnitude of the spontaneous magnetization.
The quantitative theory of magnons,
|
https://en.wikipedia.org/wiki/Glossary%20of%20cryptographic%20keys
|
This glossary lists types of keys as the term is used in cryptography, as opposed to door locks. Terms that are primarily used by the U.S. National Security Agency are marked (NSA). For classification of keys according to their usage see cryptographic key types.
40-bit key - key with a length of 40 bits, once the upper limit of what could be exported from the U.S. and other countries without a license. Considered very insecure. See key size for a discussion of this and other lengths.
authentication key - Key used in a keyed-hash message authentication code, or HMAC.
benign key - (NSA) a key that has been protected by encryption or other means so that it can be distributed without fear of its being stolen. Also called BLACK key.
content-encryption key (CEK) a key that may be further encrypted using a KEK, where the content may be a message, audio, image, video, executable code, etc.
crypto ignition key An NSA key storage device (KSD-64) shaped to look like an ordinary physical key.
cryptovariable - NSA calls the output of a stream cipher a key or key stream. It often uses the term cryptovariable for the bits that control the stream cipher, what the public cryptographic community calls a key.
data encryption key (DEK) used to encrypt the underlying data.
derived key - keys computed by applying a predetermined hash algorithm or key derivation function to a password or, better, a passphrase.
DRM key - A key used in Digital Rights Management to protect media
electronic
|
https://en.wikipedia.org/wiki/Sweet%20Tooth
|
A sweet tooth is a fondness or craving for sweet foods.
Sweet Tooth may also refer to:
Biology
The "sweet tooth" behavioral phenotype (i.e., a fondness or craving for sweet foods), caused by a single nucleotide polymorphism of the FGF21 gene
Fictional characters
Sweet Tooth, a character in the video game series Twisted Metal
Sweet Tooth, A villain in the 1977 animated TV series The New Adventures of Batman
Sweet-Tooth Jangala, a character in the PlayStation 2 port of the 2008 racing video game Speed Racer: The Videogame
Sweet Tooth, A villain in the 2012 musical Holy Musical B@man!
Dr. Sweet Tooth, a character in The 7D
Sweet Tooth, a character in the defunct online MMPORG game Moshi Monsters
Literature
Sweet Tooth (comics), a comic strip in the British comic Whizzer and Chips
A 1989 story by Lin Carter
Sweet Tooth (novel), a 2012 novel by Ian McEwan
Sweet Tooth (Vertigo), an American comic book limited series by Jeff Lemire
Television or movies
Sweet Tooth (TV series), an American fantasy drama series based on the comic book
Music
Halloween: Sweet Tooth, a 2007 album in the Halloween series by Mannheim Steamroller
Sweet Tooth, a 1990s British band that included Justin Broadrick
Sweet Tooth, a 2007 album by The Electric Confectionaires
"Sweet Tooth", a song by the band Free from Tons of Sobs
"Sweet Tooth", a song by Marilyn Manson from Portrait of an American Family
"Sweet Tooth", a song by Raheem DeVaughn from The Love Experience
"Sweet Tooth"
|
https://en.wikipedia.org/wiki/Claudio%20Sillero-Zubiri
|
Claudio Sillero-Zubiri is an Argentine-born British zoologist. He is a Professor of Conservation Biology at Oxford University's WildCRU, the Wildlife Conservation Research Unit, and Bill Travers Fellow at Lady Margaret Hall. He is the Chair of the IUCN/SSC Canid Specialist Group, and Chief Scientist of the Born Free Foundation. He is internationally recognized for his work with carnivore conservation, and in particular the endangered Ethiopian wolf (Canis simensis).
He studied at the Universidad Nacional de La Plata, then obtained his Ph.D. at Oxford University in 1994 with a study on the behavioural ecology of the Ethiopian wolf. Academic interests are the behavioural ecology of carnivores, conservation biology, population biology and disease dynamics, with a particular interest in the Canidae.
His work includes the conservation of endangered species, protected areas management, and wildlife surveys for 35 years spanning four continents. In 1998 he received the Whitley Award for Animal Conservation from the Royal Geographical Society for his work in Ethiopia.
Becoming increasingly involved in the relationships between protected areas and their surrounding rural communities, he is now working with biodiversity conservation policies and practices, particularly in South America, India and Ethiopia.
His work with the IUCN Canid Specialist Group began in 1995 assisting with various conservation programmes and coordinating the Ethiopian Wolf Conservation Programme (EWCP). He i
|
https://en.wikipedia.org/wiki/Median%20%28disambiguation%29
|
Median may refer to:
Mathematics and statistics
Median (statistics), in statistics, a number that separates the lowest- and highest-value halves
Median (geometry), in geometry, a line joining a vertex of a triangle to the midpoint of the opposite side
Median (graph theory), a vertex m(a,b,c) that belongs to shortest paths between each pair of a, b, and c
Median algebra, an algebraic triple product generalising the algebraic properties of the majority function
Median graph, undirected graph in which every three vertices a, b, and c have a unique median
Geometric median, a point minimizing the sum of distances to a given set of points
People
Median (rapper), a rapper from the U.S. city of Raleigh, North Carolina
Science and technology
Median (biology), an anatomical term of location, meaning at or towards the central plane of a bilaterally symmetrical organism or structure
Median filter, a nonlinear digital filtering technique used to reduce noise in images
Median nerve, a nerve in humans and other animals located in the upper limb, one of the five main nerves originating from the brachial plexus
Other
Median language, the extinct Northwestern Iranian language of the Medes people
Median Empire or Median Kingdom, an ancient Iranian empire predating the First Persian Empire
Median consonant, a consonant sound that is produced when air flows across the center of the mouth over the tongue
Median strip, the portion of a divided roadway used to separate opposing traf
|
https://en.wikipedia.org/wiki/Grothendieck%20universe
|
In mathematics, a Grothendieck universe is a set U with the following properties:
If x is an element of U and if y is an element of x, then y is also an element of U. (U is a transitive set.)
If x and y are both elements of U, then is an element of U.
If x is an element of U, then P(x), the power set of x, is also an element of U.
If is a family of elements of U, and if is an element of U, then the union is an element of U.
A Grothendieck universe is meant to provide a set in which all of mathematics can be performed. (In fact, uncountable Grothendieck universes provide models of set theory with the natural ∈-relation, natural powerset operation etc.). Elements of a Grothendieck universe are sometimes called small sets. The idea of universes is due to Alexander Grothendieck, who used them as a way of avoiding proper classes in algebraic geometry.
The existence of a nontrivial Grothendieck universe goes beyond the usual axioms of Zermelo–Fraenkel set theory; in particular it would imply the existence of strongly inaccessible cardinals.
Tarski–Grothendieck set theory is an axiomatic treatment of set theory, used in some automatic proof systems, in which every set belongs to a Grothendieck universe.
The concept of a Grothendieck universe can also be defined in a topos.
Properties
As an example, we will prove an easy proposition.
Proposition. If and , then .
Proof. because . because , so .
It is similarly easy to prove that any Grothendieck universe U contains:
|
https://en.wikipedia.org/wiki/Subordination
|
Subordination may refer to
Subordination in a hierarchy (in military, society, etc.)
Insubordination, disobedience
Subordination (linguistics)
Subordination (finance)
Subordination agreement, a legal document used to deprecate the claim of one party in favor of another
Subordination (horse), a Thoroughbred racehorse
In mathematics
Littlewood subordination theorem
Subordinate partition of unity in paracompact space
|
https://en.wikipedia.org/wiki/Habitable%20zone
|
In astronomy and astrobiology, the habitable zone (HZ), or more precisely the circumstellar habitable zone (CHZ), is the range of orbits around a star within which a planetary surface can support liquid water given sufficient atmospheric pressure. The bounds of the HZ are based on Earth's position in the Solar System and the amount of radiant energy it receives from the Sun. Due to the importance of liquid water to Earth's biosphere, the nature of the HZ and the objects within it may be instrumental in determining the scope and distribution of planets capable of supporting Earth-like extraterrestrial life and intelligence.
The habitable zone is also called the Goldilocks zone, a metaphor, allusion and antonomasia of the children's fairy tale of "Goldilocks and the Three Bears", in which a little girl chooses from sets of three items, ignoring the ones that are too extreme (large or small, hot or cold, etc.), and settling on the one in the middle, which is "just right".
Since the concept was first presented in 1953, many stars have been confirmed to possess an HZ planet, including some systems that consist of multiple HZ planets. Most such planets, being either super-Earths or gas giants, are more massive than Earth, because massive planets are easier to detect. On November 4, 2013, astronomers reported, based on Kepler data, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of Sun-like stars and red dwarfs in the Milky Way. About
|
https://en.wikipedia.org/wiki/Superacid
|
In chemistry, a superacid (according to the original definition) is an acid with an acidity greater than that of 100% pure sulfuric acid (), which has a Hammett acidity function (H0) of −12. According to the modern definition, a superacid is a medium in which the chemical potential of the proton is higher than in pure sulfuric acid. Commercially available superacids include trifluoromethanesulfonic acid (), also known as triflic acid, and fluorosulfuric acid (), both of which are about a thousand times stronger (i.e. have more negative H0 values) than sulfuric acid. Most strong superacids are prepared by the combination of a strong Lewis acid and a strong Brønsted acid. A strong superacid of this kind is fluoroantimonic acid. Another group of superacids, the carborane acid group, contains some of the strongest known acids. Finally, when treated with anhydrous acid, zeolites (microporous aluminosilicate minerals) will contain superacidic sites within their pores. These materials are used on massive scale by the petrochemical industry in the upgrading of hydrocarbons to make fuels.
History
The term superacid was originally coined by James Bryant Conant in 1927 to describe acids that were stronger than conventional mineral acids. This definition was refined by Ronald Gillespie in 1971, as any acid with an H0 value lower than that of 100% sulfuric acid (−11.93). George A. Olah prepared the so-called "magic acid", so named for its ability to attack hydrocarbons, by mixing anti
|
https://en.wikipedia.org/wiki/Kernel%20%28linear%20algebra%29
|
In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the linear subspace of the domain of the map which is mapped to the zero vector. That is, given a linear map between two vector spaces and , the kernel of is the vector space of all elements of such that , where denotes the zero vector in , or more symbolically:
Properties
The kernel of is a linear subspace of the domain .
In the linear map two elements of have the same image in if and only if their difference lies in the kernel of , that is,
From this, it follows that the image of is isomorphic to the quotient of by the kernel:
In the case where is finite-dimensional, this implies the rank–nullity theorem:
where the term refers the dimension of the image of , while refers to the dimension of the kernel of ,
That is,
so that the rank–nullity theorem can be restated as
When is an inner product space, the quotient can be identified with the orthogonal complement in of This is the generalization to linear operators of the row space, or coimage, of a matrix.
Application to modules
The notion of kernel also makes sense for homomorphisms of modules, which are generalizations of vector spaces where the scalars are elements of a ring, rather than a field. The domain of the mapping is a module, with the kernel constituting a submodule. Here, the concepts of rank and nullity do not necessarily apply.
In functional analysis
If V and W are topological vector spaces
|
https://en.wikipedia.org/wiki/Johan%20Gadolin
|
Johan Gadolin (5 June 176015 August 1852) was a Finnish chemist, physicist and mineralogist. Gadolin discovered a "new earth" containing the first rare-earth compound yttrium, which was later determined to be a chemical element. He is also considered the founder of Finnish chemistry research, as the second holder of the Chair of Chemistry at the Royal Academy of Turku (or Åbo Kungliga Akademi). Gadolin was ennobled for his achievements and awarded the Order of Saint Vladimir and the Order of Saint Anna.
Early life and education
Johan Gadolin was born in Åbo (Finnish name Turku), Finland (then a part of Sweden). Johan was the son of Jakob Gadolin, professor of physics and theology at Åbo. Johan began to study mathematics at the Royal Academy of Turku (Åbo Kungliga Akademi) when he was fifteen. Later he changed his major to chemistry, studying with Pehr Adrian Gadd, the first chair of chemistry at Åbo.
In 1779 Gadolin moved to Uppsala University. In 1781, he published his dissertation Dissertatio chemica de analysi ferri ("Chemical dissertation on the analysis of iron"), under the direction of Torbern Bergman. Bergman founded an important research school, and many of his students, including Gadolin, Johan Gottlieb Gahn, and Carl Wilhelm Scheele, became close friends.
Career
Gadolin was fluent in Latin, Finnish, Russian, German, English and French in addition to his native Swedish. He was a candidate for the chair of chemistry at Uppsala in 1784, but Johann Afzelius was s
|
https://en.wikipedia.org/wiki/Eilenberg%E2%80%93MacLane%20space
|
In mathematics, specifically algebraic topology, an Eilenberg–MacLane space is a topological space with a single nontrivial homotopy group.
Let G be a group and n a positive integer. A connected topological space X is called an Eilenberg–MacLane space of type , if it has n-th homotopy group isomorphic to G and all other homotopy groups trivial. Assuming that G is abelian in the case that , Eilenberg–MacLane spaces of type always exist, and are all weak homotopy equivalent. Thus, one may consider as referring to a weak homotopy equivalence class of spaces. It is common to refer to any representative as "a " or as "a model of ". Moreover, it is common to assume that this space is a CW-complex (which is always possible via CW approximation).
The name is derived from Samuel Eilenberg and Saunders Mac Lane, who introduced such spaces in the late 1940s.
As such, an Eilenberg–MacLane space is a special kind of topological space that in homotopy theory can be regarded as a building block for CW-complexes via fibrations in a Postnikov system. These spaces are important in many contexts in algebraic topology, including computations of homotopy groups of spheres, definition of cohomology operations, and for having a strong connection to singular cohomology.
A generalised Eilenberg–Maclane space is a space which has the homotopy type of a product of Eilenberg–Maclane spaces
.
Examples
The unit circle is a .
The infinite-dimensional complex projective space is a model of .
|
https://en.wikipedia.org/wiki/Sigma-additive%20set%20function
|
In mathematics, an additive set function is a function mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, If this additivity property holds for any two sets, then it also holds for any finite number of sets, namely, the function value on the union of k disjoint sets (where k is a finite number) equals the sum of its values on the sets. Therefore, an additive set function is also called a finitely additive set function (the terms are equivalent). However, a finitely additive set function might not have the additivity property for a union of an infinite number of sets. A σ-additive set function is a function that has the additivity property even for countably infinite many sets, that is,
Additivity and sigma-additivity are particularly important properties of measures. They are abstractions of how intuitive properties of size (length, area, volume) of a set sum when considering multiple objects. Additivity is a weaker condition than σ-additivity; that is, σ-additivity implies additivity.
The term modular set function is equivalent to additive set function; see modularity below.
Additive (or finitely additive) set functions
Let be a set function defined on an algebra of sets with values in (see the extended real number line). The function is called or , if whenever and are disjoint sets in then
A consequence of this is that an additive function cannot take both and as valu
|
https://en.wikipedia.org/wiki/Brown%27s%20representability%20theorem
|
In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy category Hotc of pointed connected CW complexes, to the category of sets Set, to be a representable functor.
More specifically, we are given
F: Hotcop → Set,
and there are certain obviously necessary conditions for F to be of type Hom(—, C), with C a pointed connected CW-complex that can be deduced from category theory alone. The statement of the substantive part of the theorem is that these necessary conditions are then sufficient. For technical reasons, the theorem is often stated for functors to the category of pointed sets; in other words the sets are also given a base point.
Brown representability theorem for CW complexes
The representability theorem for CW complexes, due to Edgar H. Brown, is the following. Suppose that:
The functor F maps coproducts (i.e. wedge sums) in Hotc to products in Set:
The functor F maps homotopy pushouts in Hotc to weak pullbacks. This is often stated as a Mayer–Vietoris axiom: for any CW complex W covered by two subcomplexes U and V, and any elements u ∈ F(U), v ∈ F(V) such that u and v restrict to the same element of F(U ∩ V), there is an element w ∈ F(W) restricting to u and v, respectively.
Then F is representable by some CW complex C, that is to say there is an isomorphism
F(Z) ≅ HomHotc(Z, C)
for any CW complex Z, which is natural in Z in that for any morphism from Z to
|
https://en.wikipedia.org/wiki/Barry%20Commoner
|
Barry Commoner (May 28, 1917 – September 30, 2012) was an American cellular biologist, college professor, and politician. He was a leading ecologist and among the founders of the modern environmental movement. He was the director of the Center for Biology of Natural Systems and its Critical Genetics Project. He ran as the Citizens Party candidate in the 1980 U.S. presidential election. His work studying the radioactive fallout from nuclear weapons testing led to the Nuclear Test Ban Treaty of 1963.
Early life
Commoner was born in Brooklyn, New York, on May 28, 1917, the son of Jewish immigrants from Russia. He received his bachelor's degree in zoology from Columbia University in 1937 and his master's and doctoral degrees from Harvard University in 1938 and 1941, respectively.
Career in academia
After serving as a lieutenant in the US Navy during World War II, Commoner moved to St. Louis, Missouri, and he became an associate editor for Science Illustrated from 1946 to 1947. He became a professor of plant physiology at Washington University in St. Louis in 1947 and taught there for 34 years. During this period, in 1966, he founded the Center for the Biology of Natural Systems to study "the science of the total environment". Commoner was on the founding editorial board of the Journal of Theoretical Biology in 1961.
In the late 1950s, Commoner became known for his opposition to nuclear weapons testing, becoming part of the team which conducted the Baby Tooth Survey, demonstr
|
https://en.wikipedia.org/wiki/Dedekind-infinite%20set
|
In mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A. Explicitly, this means that there exists a bijective function from A onto some proper subset B of A. A set is Dedekind-finite if it is not Dedekind-infinite (i.e., no such bijection exists). Proposed by Dedekind in 1888, Dedekind-infiniteness was the first definition of "infinite" that did not rely on the definition of the natural numbers.
A simple example is , the set of natural numbers. From Galileo's paradox, there exists a bijection that maps every natural number n to its square n2. Since the set of squares is a proper subset of , is Dedekind-infinite.
Until the foundational crisis of mathematics showed the need for a more careful treatment of set theory, most mathematicians assumed that a set is infinite if and only if it is Dedekind-infinite. In the early twentieth century, Zermelo–Fraenkel set theory, today the most commonly used form of axiomatic set theory, was proposed as an axiomatic system to formulate a theory of sets free of paradoxes such as Russell's paradox. Using the axioms of Zermelo–Fraenkel set theory with the originally highly controversial axiom of choice included (ZFC) one can show that a set is Dedekind-finite if and only if it is finite in the usual sense. However, there exists a model of Zermelo–Fraenkel set theory without the axiom of choice (ZF) in which there exists an infinite, Dedekind-finit
|
https://en.wikipedia.org/wiki/George%20Kistiakowsky
|
George Bogdanovich Kistiakowsky (, ; – December 7, 1982) was a Ukrainian-American physical chemistry professor at Harvard who participated in the Manhattan Project and later served as President Dwight D. Eisenhower's Science Advisor.
Born in Boyarka in the old Russian Empire, into "an old Ukrainian Cossack family which was part of the intellectual elite in pre-revolutionary Russia", Kistiakowsky fled his homeland during the Russian Civil War. He made his way to Germany, where he earned his PhD in physical chemistry under the supervision of Max Bodenstein at the University of Berlin. He emigrated to the United States in 1926, where he joined the faculty of Harvard University in 1930, and became a citizen in 1933.
During World War II, Kistiakowsky was the head of the National Defense Research Committee (NDRC) section responsible for the development of explosives, and the technical director of the Explosives Research Laboratory (ERL), where he oversaw the development of new explosives, including RDX and HMX. He was involved in research into the hydrodynamic theory of explosions, and the development of shaped charges. In October 1943, he was brought into the Manhattan Project as a consultant. He was soon placed in charge of X Division, which was responsible for the development of the explosive lenses necessary for an implosion-type nuclear weapon. In July 1945, he watched the first atomic explosion in the Trinity test. A few weeks later, another implosion-type weapon (Fat Man)
|
https://en.wikipedia.org/wiki/Joan%20Saura
|
Joan Saura i Laporta is a Green ICV Spanish politician in Catalonia. He was born in Barcelona, Catalonia, in 1950. He studied at the Escola d'Enginyeria Tècnica (Technical Engineering School), where he specialized in Industrial Chemistry. In the beginning, he was devoted to the trade union and the neighbourhood: he enrolled into the Workers' Commissions (CCOO) in 1973, while he was working for the electrics company FECSA, and cofounded the La Florida Neighbourhood Association, in L'Hospitalet de Llobregat, 1974.
Municipal policy
He became town councillor in L'Hospitalet de Llobregat for the Unified Socialist Party of Catalonia (PSUC) in the first democratic local elections in 1979, where he participated in the formation of the government, and remained a councillor until 1991.
He also chaired (from 1983 to 1987) the Public Transport commission in Barcelona.
Parliament of Catalonia
He was elected for the third and fourth Legislatures (1988 to 1995) as deputy for Barcelona in the Catalan Parliament for the Iniciativa per Catalunya Verds (ICV) party. He was the spokesperson of his party's group and became its president in 1993.
In this Parliament he has held several positions, including membership in the Economy, Finances and Budget commission, in the Industry commission, Territorial Politics as well as various others.
Congress of the Deputies
On 3 March 1996 he was elected to the Spanish Congress of Deputies representing Barcelona Province and was re-elected at the subsequ
|
https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan%20coefficients
|
In physics, the Clebsch–Gordan (CG) coefficients are numbers that arise in angular momentum coupling in quantum mechanics. They appear as the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. In more mathematical terms, the CG coefficients are used in representation theory, particularly of compact Lie groups, to perform the explicit direct sum decomposition of the tensor product of two irreducible representations (i.e., a reducible representation into irreducible representations, in cases where the numbers and types of irreducible components are already known abstractly). The name derives from the German mathematicians Alfred Clebsch and Paul Gordan, who encountered an equivalent problem in invariant theory.
From a vector calculus perspective, the CG coefficients associated with the SO(3) group can be defined simply in terms of integrals of products of spherical harmonics and their complex conjugates. The addition of spins in quantum-mechanical terms can be read directly from this approach as spherical harmonics are eigenfunctions of total angular momentum and projection thereof onto an axis, and the integrals correspond to the Hilbert space inner product. From the formal definition of angular momentum, recursion relations for the Clebsch–Gordan coefficients can be found. There also exist complicated explicit formulas for their direct calculation.
The formulas below use Dirac's bra–ket notation and the Condon–Shortley phase
|
https://en.wikipedia.org/wiki/Lamb%20shift
|
In physics the Lamb shift, named after Willis Lamb, refers to an anomalous difference in energy between two electron orbitals in a hydrogen atom. The difference was not predicted by theory and it cannot be derived from the Dirac equation, which predicts identical energies. Hence the Lamb shift refers to a deviation from theory seen in the differing energies contained by the 2S1/2 and 2P1/2 orbitals of the hydrogen atom.
The Lamb shift is caused by interactions between the virtual photons created through vacuum energy fluctuations and the electron as it moves around the hydrogen nucleus in each of these two orbitals. The Lamb shift has since played a significant role through vacuum energy fluctuations in theoretical prediction of Hawking radiation from black holes.
This effect was first measured in 1947 in the Lamb–Retherford experiment on the hydrogen microwave spectrum and this measurement provided the stimulus for renormalization theory to handle the divergences. It was the harbinger of modern quantum electrodynamics developed by Julian Schwinger, Richard Feynman, Ernst Stueckelberg, Sin-Itiro Tomonaga and Freeman Dyson. Lamb won the Nobel Prize in Physics in 1955 for his discoveries related to the Lamb shift.
Importance
In 1978, on Lamb's 65th birthday, Freeman Dyson addressed him as follows: "Those years, when the Lamb shift was the central theme of physics, were golden years for all the physicists of my generation. You were the first to see that this tiny shift, so
|
https://en.wikipedia.org/wiki/Cluster%20decomposition
|
In physics, the cluster decomposition property states that experiments carried out far from each other cannot influence each other. Usually applied to quantum field theory, it requires that vacuum expectation values of operators localized in bounded regions factorize whenever these regions becomes sufficiently distant from each other. First formulated by Eyvind Wichmann and James H. Crichton in 1963 in the context of the S-matrix, it was conjectured by Steven Weinberg that in the low energy limit the cluster decomposition property, together with Lorentz invariance and quantum mechanics, inevitably lead to quantum field theory. String theory satisfies all three of the conditions and so provides a counter-example against this being true at all energy scales.
Formulation
The S-matrix describes the amplitude for a process with an initial state evolving into a final state . If the initial and final states consist of two clusters, with and close to each other but far from the pair and , then the cluster decomposition property requires the S-matrix to factorize
as the distance between the two clusters increases. The physical interpretation of this is that any two spatially well separated experiments and cannot influence each other. This condition is fundamental to the ability to doing physics without having to know the state of the entire universe. By expanding the S-matrix into a sum of a product of connected S-matrix elements , which at the perturbative level are equiva
|
https://en.wikipedia.org/wiki/Interactome
|
In molecular biology, an interactome is the whole set of molecular interactions in a particular cell. The term specifically refers to physical interactions among molecules (such as those among proteins, also known as protein–protein interactions, PPIs; or between small molecules and proteins) but can also describe sets of indirect interactions among genes (genetic interactions).
The word "interactome" was originally coined in 1999 by a group of French scientists headed by Bernard Jacq. Mathematically, interactomes are generally displayed as graphs. Though interactomes may be described as biological networks, they should not be confused with other networks such as neural networks or food webs.
Molecular interaction networks
Molecular interactions can occur between molecules belonging to different biochemical families (proteins, nucleic acids, lipids, carbohydrates, etc.) and also within a given family. Whenever such molecules are connected by physical interactions, they form molecular interaction networks that are generally classified by the nature of the compounds involved. Most commonly, interactome refers to protein–protein interaction (PPI) network (PIN) or subsets thereof. For instance, the Sirt-1 protein interactome and Sirt family second order interactome is the network involving Sirt-1 and its directly interacting proteins where as second order interactome illustrates interactions up to second order of neighbors (Neighbors of neighbors). Another extensively studied t
|
https://en.wikipedia.org/wiki/Polyakov%20action
|
In physics, the Polyakov action is an action of the two-dimensional conformal field theory describing the worldsheet of a string in string theory. It was introduced by Stanley Deser and Bruno Zumino and independently by L. Brink, P. Di Vecchia and P. S. Howe in 1976, and has become associated with Alexander Polyakov after he made use of it in quantizing the string in 1981. The action reads:
where is the string tension, is the metric of the target manifold, is the worldsheet metric, its inverse, and is the determinant of . The metric signature is chosen such that timelike directions are + and the spacelike directions are −. The spacelike worldsheet coordinate is called , whereas the timelike worldsheet coordinate is called . This is also known as the nonlinear sigma model.
The Polyakov action must be supplemented by the Liouville action to describe string fluctuations.
Global symmetries
N.B.: Here, a symmetry is said to be local or global from the two dimensional theory (on the worldsheet) point of view. For example, Lorentz transformations, that are local symmetries of the space-time, are global symmetries of the theory on the worldsheet.
The action is invariant under spacetime translations and infinitesimal Lorentz transformations
where , and is a constant. This forms the Poincaré symmetry of the target manifold.
The invariance under (i) follows since the action depends only on the first derivative of . The proof of the invariance under (ii) is as follows:
Lo
|
https://en.wikipedia.org/wiki/Vitali%E2%80%93Hahn%E2%80%93Saks%20theorem
|
In mathematics, the Vitali–Hahn–Saks theorem, introduced by , , and , proves that under some conditions a sequence of measures converging point-wise does so uniformly and the limit is also a measure.
Statement of the theorem
If is a measure space with and a sequence of complex measures. Assuming that each is absolutely continuous with respect to and that a for all the finite limits exist Then the absolute continuity of the with respect to is uniform in that is, implies that uniformly in Also is countably additive on
Preliminaries
Given a measure space a distance can be constructed on the set of measurable sets with This is done by defining
where is the symmetric difference of the sets
This gives rise to a metric space by identifying two sets when Thus a point with representative is the set of all such that
Proposition: with the metric defined above is a complete metric space.
Proof: Let
Then
This means that the metric space can be identified with a subset of the Banach space .
Let , with
Then we can choose a sub-sequence such that exists almost everywhere and . It follows that for some (furthermore if and only if for large enough, then we have that the limit inferior of the sequence) and hence Therefore, is complete.
Proof of Vitali-Hahn-Saks theorem
Each defines a function on by taking . This function is well defined, this is it is independent on the representative of the class due to the absolute continuity of wit
|
https://en.wikipedia.org/wiki/NSA%20cryptography
|
The vast majority of the National Security Agency's work on encryption is classified, but from time to time NSA participates in standards processes or otherwise publishes information about its cryptographic algorithms. The NSA has categorized encryption items into four product types, and algorithms into two suites. The following is a brief and incomplete summary of public knowledge about NSA algorithms and protocols.
Type 1 Product
A Type 1 Product refers to an NSA endorsed classified or controlled cryptographic item for classified or sensitive U.S. government information, including cryptographic equipment, assembly or component classified or certified by NSA for encrypting and decrypting classified and sensitive national security information when appropriately keyed.
Type 2 Product
A Type 2 Product refers to an NSA endorsed unclassified cryptographic equipment, assemblies or components for sensitive but unclassified U.S. government information.
Type 3 Product
Unclassified cryptographic equipment, assembly, or component used, when appropriately keyed, for encrypting or decrypting unclassified sensitive U.S. Government or commercial information, and to protect systems requiring protection mechanisms consistent with standard commercial practices. A Type 3 Algorithm refers to NIST endorsed algorithms, registered and FIPS published, for sensitive but unclassified U.S. government and commercial information.
Type 4 Product
A Type 4 Algorithm refers to algorithms that are r
|
https://en.wikipedia.org/wiki/Hahn%20embedding%20theorem
|
In mathematics, especially in the area of abstract algebra dealing with ordered structures on abelian groups, the Hahn embedding theorem gives a simple description of all linearly ordered abelian groups. It is named after Hans Hahn.
Overview
The theorem states that every linearly ordered abelian group G can be embedded as an ordered subgroup of the additive group ℝΩ endowed with a lexicographical order, where ℝ is the additive group of real numbers (with its standard order), Ω is the set of Archimedean equivalence classes of G, and ℝΩ is the set of all functions from Ω to ℝ which vanish outside a well-ordered set.
Let 0 denote the identity element of G. For any nonzero element g of G, exactly one of the elements g or −g is greater than 0; denote this element by |g|. Two nonzero elements g and h of G are Archimedean equivalent if there exist natural numbers N and M such that N|g| > |h| and M|h| > |g|. Intuitively, this means that neither g nor h is "infinitesimal" with respect to the other. The group G is Archimedean if all nonzero elements are Archimedean-equivalent. In this case, Ω is a singleton, so ℝΩ is just the group of real numbers. Then Hahn's Embedding Theorem reduces to Hölder's theorem (which states that a linearly ordered abelian group is Archimedean if and only if it is a subgroup of the ordered additive group of the real numbers).
gives a clear statement and proof of the theorem. The papers of and together provide another proof. See also .
See al
|
https://en.wikipedia.org/wiki/Wave%20mechanics
|
Wave mechanics may refer to:
the mechanics of waves
the application of the quantum wave equation, especially in position and momentum spaces.
See also
Quantum mechanics
Wave equation
Quantum state
Matter wave
|
https://en.wikipedia.org/wiki/Generalized%20signal%20averaging
|
Within signal processing, in many cases only one image with noise is available, and averaging is then realized in a local neighbourhood. Results are acceptable if the noise is smaller in size than the smallest objects of interest in the image, but blurring of edges is a serious disadvantage. In the case of smoothing within a single image, one has to assume that there are no changes in the gray levels of the underlying image data. This assumption is clearly violated at locations of image edges, and edge blurring is a direct consequence of violating the assumption.
Description
Averaging is a special case of discrete convolution. For a 3 by 3 neighbourhood, the convolution mask M is:
The significance of the central pixel may be increased, as it approximates the properties of noise with a Gaussian probability distribution:
A suitable page for beginners about matrices is at:
https://web.archive.org/web/20060819141930/http://www.gamedev.net/reference/programming/features/imageproc/page2.asp
The whole article starts on page: https://web.archive.org/web/20061019072001/http://www.gamedev.net/reference/programming/features/imageproc/
References
Signal processing
Noise (graphics)
Radio technology
|
https://en.wikipedia.org/wiki/Crown%20ether
|
In organic chemistry, crown ethers are cyclic chemical compounds that consist of a ring containing several ether groups (). The most common crown ethers are cyclic oligomers of ethylene oxide, the repeating unit being ethyleneoxy, i.e., . Important members of this series are the tetramer (n = 4), the pentamer (n = 5), and the hexamer (n = 6). The term "crown" refers to the resemblance between the structure of a crown ether bound to a cation, and a crown sitting on a person's head. The first number in a crown ether's name refers to the number of atoms in the cycle, and the second number refers to the number of those atoms that are oxygen. Crown ethers are much broader than the oligomers of ethylene oxide; an important group are derived from catechol.
Crown ethers strongly bind certain cations, forming complexes. The oxygen atoms are well situated to coordinate with a cation located at the interior of the ring, whereas the exterior of the ring is hydrophobic. The resulting cations often form salts that are soluble in nonpolar solvents, and for this reason crown ethers are useful in phase transfer catalysis. The denticity of the polyether influences the affinity of the crown ether for various cations. For example, 18-crown-6 has high affinity for potassium cation, 15-crown-5 for sodium cation, and 12-crown-4 for lithium cation. The high affinity of 18-crown-6 for potassium ions contributes to its toxicity. The smallest crown ether still capable of binding cations is 8-cro
|
https://en.wikipedia.org/wiki/The%20Road%20to%20Reality
|
The Road to Reality: A Complete Guide to the Laws of the Universe is a book on modern physics by the British mathematical physicist Roger Penrose, published in 2004. It covers the basics of the Standard Model of particle physics, discussing general relativity and quantum mechanics, and discusses the possible unification of these two theories.
Overview
The book discusses the physical world. Many fields that 19th century scientists believed were separate, such as electricity and magnetism, are aspects of more fundamental properties. Some texts, both popular and university level, introduce these topics as separate concepts, and then reveal their combination much later. The Road to Reality reverses this process, first expounding the underlying mathematics of space–time, then showing how electromagnetism and other phenomena fall out fully formed.
The book is just over 1100 pages, of which the first 383 are dedicated to mathematics—Penrose's goal is to acquaint inquisitive readers with the mathematical tools needed to understand the remainder of the book in depth. Physics enters the discussion on page 383 with the topic of spacetime. From there it moves on to fields in spacetime, deriving the classical electrical and magnetic forces from first principles; that is, if one lives in spacetime of a particular sort, these fields develop naturally as a consequence. Energy and conservation laws appear in the discussion of Lagrangians and Hamiltonians, before moving on to a full discussi
|
https://en.wikipedia.org/wiki/David%20Albert
|
David Z. Albert (born 1954) is Frederick E. Woodbridge Professor of Philosophy and Director of the MA Program in The Philosophical Foundations of Physics at Columbia University in New York.
Education and career
He received his bachelor's degree in physics from Columbia College (1976) and his PhD in theoretical physics from The Rockefeller University (1981) under Professor Nicola Khuri. Afterwards he worked with Yakir Aharonov of Tel Aviv University. He has spent most of his career in the philosophy department at Columbia University, although he has also been a frequent visiting professor of philosophy at Rutgers University. In 2015, he was elected a Fellow of the American Academy of Arts & Sciences.
Philosophical work
Albert has published four books—Quantum Mechanics and Experience (1992), Time and Chance (2000), After Physics (2015), and A Guess at the Riddle (2023)—as well as numerous articles on quantum mechanics. His books have been both praised and criticized for their informal, conversational style.
Public philosophy
Appearance in What the Bleep Do We Know!?
Albert appeared in the controversial movie What the Bleep Do We Know!? (2004). According to an article published in Popular Science, he was "outraged at the final product." The article states that Albert granted the filmmakers a near-four hour interview about quantum mechanics being unrelated to consciousness or spirituality. His interview was then edited and incorporated into the film in a way that misrep
|
https://en.wikipedia.org/wiki/Polyketide
|
In organic chemistry, polyketides are a class of natural products derived from a precursor molecule consisting of a chain of alternating ketone (, or its reduced forms) and methylene () groups: . First studied in the early 20th century, discovery, biosynthesis, and application of polyketides has evolved. It is a large and diverse group of secondary metabolites caused by its complex biosynthesis which resembles that of fatty acid synthesis. Because of this diversity, polyketides can have various medicinal, agricultural, and industrial applications. Many polyketides are medicinal or exhibit acute toxicity. Biotechnology has enabled discovery of more naturally-occurring polyketides and evolution of new polyketides with novel or improved bioactivity.
History
Naturally produced polyketides by various plants and organisms have been used by humans since before studies on them began in the 19th and 20th century. In 1893, J. Norman Collie synthesized detectable amounts of orcinol by heating dehydracetic acid with barium hydroxide causing the pyrone ring to open into a triketide. Further studies in 1903 by Collie on the triketone polyketide intermediate noted the condensation occurring amongst compounds with multiple keten groups coining the term polyketides.
It wasn't until 1955 that the biosynthesis of polyketides were understood. Arthur Birch used radioisotope labeling of carbon in acetate to trace the biosynthesis of 2-hydroxy-6-methylbenzoic acid in Penicillium patulum and dem
|
https://en.wikipedia.org/wiki/E.%20W.%20Hobson
|
Ernest William Hobson FRS (27 October 1856 – 19 April 1933) was an English mathematician, now remembered mostly for his books, some of which broke new ground in their coverage in English of topics from mathematical analysis. He was Sadleirian Professor of Pure Mathematics at the University of Cambridge from 1910 to 1931.
Life
He was born in Derby, and was educated at Derby School, the Royal School of Mines, and Christ's College, Cambridge, graduating Senior Wrangler in 1878.
He was the brother of the economist John A. Hobson.
He became a Fellow of Christ's almost immediately after graduation. He made his way into research mathematics only gradually, becoming an expert in the theory of spherical harmonics.
His 1907 work on real analysis was something of a watershed in the British mathematical tradition; and was lauded by G. H. Hardy. It included material on general topology and Fourier series that was topical at the time; and included mistakes that were picked up later (for example by R. L. Moore).
From 1924 to 1927, Robert Pollock Gillespie studied under him.
He is buried in the Parish of the Ascension Burial Ground in Cambridge, with his wife Seline, born 25 March 1860, died 10 June 1940, by whom he had four sons, one of whom Walter William (1894 - 1930) is buried with them in the same grave.
Works
A Treatise on Trigonometry (1891)
Theory of Functions of a Real Variable (1907)
Vol. I, 3rd edition (1927)
Mathematics, from the points of view of the Mathematician a
|
https://en.wikipedia.org/wiki/Robert%20Lee%20Moore
|
Robert Lee Moore (November 14, 1882 – October 4, 1974) was an American mathematician who taught for many years at the University of Texas. He is known for his work in general topology, for the Moore method of teaching university mathematics, and for his racist treatment of African-American mathematics students.
Life
Although Moore's father was reared in New England and was of New England ancestry, he fought in the American Civil War on the side of the Confederacy. After the war, he ran a hardware store in Dallas, then little more than a railway stop, and raised six children, of whom Robert, named after the commander of the Confederate Army of Northern Virginia, was the fifth.
Moore entered the University of Texas at the unusually youthful age of 15, in 1898, already knowing calculus thanks to self-study. He completed the B.Sc. in three years instead of the usual four; his teachers included G. B. Halsted and L. E. Dickson. After a year as a teaching fellow at Texas, he taught high school for a year in Marshall, Texas.
An assignment of Halsted's led Moore to prove that one of Hilbert's axioms for geometry was redundant. When E. H. Moore (no relation), who headed the Department of Mathematics at the University of Chicago, and whose research interests were on the foundations of geometry, heard of Robert's feat, he arranged for a scholarship that would allow Robert to study for a doctorate at Chicago. Oswald Veblen supervised Moore's 1905 thesis, titled Sets of Metrical Hypoth
|
https://en.wikipedia.org/wiki/Spin%20quantum%20number
|
In physics, the spin quantum number is a quantum number (designated ) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. It has the same value for all particles of the same type, such as = for all electrons. It is an integer for all bosons, such as photons, and a half-odd-integer for all fermions, such as electrons and protons. The component of the spin along a specified axis is given by the spin magnetic quantum number, conventionally written . The value of is the component of spin angular momentum, in units of the reduced Planck constant , parallel to a given direction (conventionally labelled the –axis). It can take values ranging from + to − in integer increments. For an electron, can be either or .
The phrase spin quantum number was originally used to describe the fourth of a set of quantum numbers (the principal quantum number , the azimuthal quantum number , the magnetic quantum number , and the spin magnetic quantum number ), which completely describe the quantum state of an electron in an atom.
Some introductory chemistry textbooks describe as the spin quantum number, and is not mentioned since its value is a fixed property of the electron, sometimes using the variable in place of . Some authors discourage this usage as it causes confusion. At a more advanced level where quantum mechanical operators or coupled spins are introduced, is referred to as the spin quantum number, and is d
|
https://en.wikipedia.org/wiki/E.%20T.%20Whittaker
|
Sir Edmund Taylor Whittaker (24 October 1873 – 24 March 1956) was a British mathematician, physicist, and historian of science. Whittaker was a leading mathematical scholar of the early 20th-century who contributed widely to applied mathematics and was renowned for his research in mathematical physics and numerical analysis, including the theory of special functions, along with his contributions to astronomy, celestial mechanics, the history of physics, and digital signal processing.
Among the most influential publications in Whittaker's bibliography, he authored several popular reference works in mathematics, physics, and the history of science, including A Course of Modern Analysis (better known as Whittaker and Watson), Analytical Dynamics of Particles and Rigid Bodies, and A History of the Theories of Aether and Electricity. Whittaker is also remembered for his role in the relativity priority dispute, as he credited Henri Poincaré and Hendrik Lorentz with developing special relativity in the second volume of his History, a dispute which has lasted several decades, though scientific consensus has remained with Einstein. Whittaker served as the Royal Astronomer of Ireland early in his career, a position he held from 1906 through 1912, before moving on to the chair of mathematics at the University of Edinburgh for the next three decades and, towards the end of his career, received the Copley Medal and was knighted. The School of Mathematics of the University of Edinburgh h
|
https://en.wikipedia.org/wiki/Paul%20J.%20Crutzen
|
Paul Jozef Crutzen (; 3 December 1933 – 28 January 2021) was a Dutch meteorologist and atmospheric chemist. He and Mario Molina and Frank Sherwood Rowland were awarded the Nobel Prize in Chemistry in 1995 for their work on atmospheric chemistry and specifically for his efforts in studying the formation and decomposition of atmospheric ozone. In addition to studying the ozone layer and climate change, he popularized the term Anthropocene to describe a proposed new epoch in the Quaternary period when human actions have a drastic effect on the Earth. He was also amongst the first few scientists to introduce the idea of a nuclear winter to describe the potential climatic effects stemming from large-scale atmospheric pollution including smoke from forest fires, industrial exhausts, and other sources like oil fires.
He was a member of the Royal Swedish Academy of Sciences and an elected foreign member of the Royal Society in the United Kingdom.
Early life and education
Crutzen was born in Amsterdam, the son of Anna (Gurk) and Josef Crutzen. In September 1940, the same year Germany invaded The Netherlands, Crutzen entered his first year of elementary school. After many delays and school switches caused by events in the war, Crutzen graduated from elementary school and moved onto "Hogere Burgerschool" (Higher Citizens School) in 1946, where he became fluent in French, English, and German. Along with languages he also focused on natural sciences in this school, from which he graduat
|
https://en.wikipedia.org/wiki/Catechin
|
Catechin is a flavan-3-ol, a type of secondary metabolite providing antioxidant roles in plants. It belongs to the subgroup of polyphenols called flavonoids.
The name of the catechin chemical family derives from catechu, which is the tannic juice or boiled extract of Mimosa catechu (Acacia catechu L.f).
Chemistry
Catechin possesses two benzene rings (called the A and B rings) and a dihydropyran heterocycle (the C ring) with a hydroxyl group on carbon 3. The A ring is similar to a resorcinol moiety while the B ring is similar to a catechol moiety. There are two chiral centers on the molecule on carbons 2 and 3. Therefore, it has four diastereoisomers. Two of the isomers are in trans configuration and are called catechin and the other two are in cis configuration and are called epicatechin.
The most common catechin isomer is (+)-catechin. The other stereoisomer is (−)-catechin or ent-catechin. The most common epicatechin isomer is (−)-epicatechin (also known under the names L-epicatechin, epicatechol, (−)-epicatechol, L-acacatechin, L-epicatechol, epicatechin, 2,3-cis-epicatechin or (2R,3R)-(−)-epicatechin).
The different epimers can be separated using chiral column chromatography.
Making reference to no particular isomer, the molecule can just be called catechin. Mixtures of the different enantiomers can be called (±)-catechin or DL-catechin and (±)-epicatechin or DL-epicatechin.
Catechin and epicatechin are the building blocks of the proanthocyanidins, a type of cond
|
https://en.wikipedia.org/wiki/BEST%20Robotics
|
BEST (Boosting Engineering, Science, and Technology) is a national six-week robotics competition in the United States held each fall, designed to help interest middle school and high school students in possible engineering careers. The games are similar in scale to those of the FIRST Tech Challenge.
History
The idea for a BEST (Boosting Engineering, Science, and Technology) competition originated in 1993 when two Texas Instruments (TI) engineers, Ted Mahler and Steve Marum, were serving as guides for Engineering Day at their company site in Sherman, Texas. Together with a group of high school students, they watched a video of freshmen building a robot in Woodie Flowers's class at Massachusetts Institute of Technology. The high school students were so interested that Mahler and Marum said, "Why don't we do this?"
With enthusiastic approval from TI management, North Texas BEST was born. The first competition was held in 1993 with 14 schools and 221 students (including one team from San Antonio).
After learning that a San Antonio group had formed a non-profit organization to support a BEST event, North Texas BEST mentored them in providing their own BEST competition. Thus, San Antonio BEST, the second BEST competition site (or "hub"), was started in 1994. The two groups - North Texas and San Antonio - decided to meet for Texas BEST, a state playoff at Howard Payne University in Brownwood, Texas. The competition has also been held at Texas A&M University, Southern Methodist Un
|
https://en.wikipedia.org/wiki/Pharmacophore
|
In medicinal chemistry and molecular biology, a pharmacophore is an abstract description of molecular features that are necessary for molecular recognition of a ligand by a biological macromolecule. IUPAC defines a pharmacophore to be "an ensemble of steric and electronic features that is necessary to ensure the optimal supramolecular interactions with a specific biological target and to trigger (or block) its biological response". A pharmacophore model explains how structurally diverse ligands can bind to a common receptor site. Furthermore, pharmacophore models can be used to identify through de novo design or virtual screening novel ligands that will bind to the same receptor.
Features
Typical pharmacophore features include hydrophobic centroids, aromatic rings, hydrogen bond acceptors or donors, cations, and anions. These pharmacophobic points may be located on the ligand itself or may be projected points presumed to be located in the receptor.
The features need to match different chemical groups with similar properties, in order to identify novel ligands. Ligand-receptor interactions are typically "polar positive", "polar negative" or "hydrophobic". A well-defined pharmacophore model includes both hydrophobic volumes and hydrogen bond vectors.
Model development
The process for developing a pharmacophore model generally involves the following steps:
Select a training set of ligands – Choose a structurally diverse set of molecules that will be used for developi
|
https://en.wikipedia.org/wiki/Margaret%20Gatty
|
Margaret Gatty ( Scott; 3 June 1809 – 4 October 1873) was an English children's author and writer on marine biology. In some writings she argues against Charles Darwin's Origin of Species. She became a popular writer of tales for young people, which she hoped would influence adult minds as well. Among her other books are Parables from Nature, Worlds not Realized, Proverbs Illustrated, and Aunt Judy's Tales. She edited Aunt Judy's Magazine, a family publication written by various family members.
Science
Gatty became fascinated by marine biology through contact with a second cousin, Charles Henry Gatty, a Royal Society member. There may also have been influence from William Henry Harvey, whom she met while convalescing in Hastings in 1848. She corresponded with many great marine biologists of her day including George Johnston, George Busk and Robert Brown. She wrote British Sea Weeds, a book that was more accessible than previous ones on the subject. This illustrated book, published in 1872, was the outcome of 14 years' work and described 200 species. It continued to be used into the 1950s.
Gatty's other collecting and scientific interests included sundials, which led to an 1872 book on 350 of them, focusing on their artistry and literary nature rather than their astronomical aspects, although it discussed historical developments. The coverage of sundials on mainland Europe and some illustrations were major contributions from a friend, Eleanor Lloyd.
Children's literature
Wh
|
https://en.wikipedia.org/wiki/Herbrand%E2%80%93Ribet%20theorem
|
In mathematics, the Herbrand–Ribet theorem is a result on the class group of certain number fields. It is a strengthening of Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity if and only if p divides the numerator of the n-th Bernoulli number Bn
for some n, 0 < n < p − 1. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an Bn.
Statement
The Galois group Δ of the cyclotomic field of pth roots of unity for an odd prime p, Q(ζ) with ζp = 1, consists of the p − 1 group elements σa, where . As a consequence of Fermat's little theorem, in the ring of p-adic integers we have p − 1 roots of unity, each of which is congruent mod p to some number in the range 1 to p − 1; we can therefore define a Dirichlet character ω (the Teichmüller character) with values in by requiring that for n relatively prime to p, ω(n) be congruent to n modulo p. The p part of the class group is a -module (since it is p-primary), hence a module over the group ring . We now define idempotent elements of the group ring for each n from 1 to p − 1, as
It is easy to see that and where is the Kronecker delta. This allows us to break up the p part of the ideal class group G of Q(ζ) by means of the idempotents; if G is the p-primary part of the ideal class group, then, letting Gn = εn(G), we have .
The Herbrand–Ribet theorem states that for odd n, Gn is nontrivial if and only if p divides the Ber
|
https://en.wikipedia.org/wiki/Morpholino
|
A Morpholino, also known as a Morpholino oligomer and as a phosphorodiamidate Morpholino oligomer (PMO), is a type of oligomer molecule (colloquially, an oligo) used in molecular biology to modify gene expression. Its molecular structure contains DNA bases attached to a backbone of methylenemorpholine rings linked through phosphorodiamidate groups. Morpholinos block access of other molecules to small (~25 base) specific sequences of the base-pairing surfaces of ribonucleic acid (RNA). Morpholinos are used as research tools for reverse genetics by knocking down gene function.
This article discusses only the Morpholino antisense oligomers, which are nucleic acid analogs. The word "Morpholino" can occur in other chemical names, referring to chemicals containing a six-membered morpholine ring. To help avoid confusion with other morpholine-containing molecules, when describing oligos "Morpholino" is often capitalized as a trade name, but this usage is not consistent across scientific literature. Morpholino oligos are sometimes referred to as PMO (for phosphorodiamidate morpholino oligomer), especially in medical literature. Vivo-Morpholinos and PPMO are modified forms of Morpholinos with chemical groups covalently attached to facilitate entry into cells.
Gene knockdown is achieved by reducing the expression of a particular gene in a cell. In the case of protein-coding genes, this usually leads to a reduction in the quantity of the corresponding protein in the cell. Knocking d
|
https://en.wikipedia.org/wiki/Open%20quantum%20system
|
In physics, an open quantum system is a quantum-mechanical system that interacts with an external quantum system, which is known as the environment or a bath. In general, these interactions significantly change the dynamics of the system and result in quantum dissipation, such that the information contained in the system is lost to its environment. Because no quantum system is completely isolated from its surroundings, it is important to develop a theoretical framework for treating these interactions in order to obtain an accurate understanding of quantum systems.
Techniques developed in the context of open quantum systems have proven powerful in fields such as quantum optics, quantum measurement theory, quantum statistical mechanics, quantum information science, quantum thermodynamics, quantum cosmology, quantum biology, and semi-classical approximations.
Quantum system and environment
A complete description of a quantum system requires the inclusion of the environment. Completely describing the resulting combined system then requires the inclusion of its environment, which results in a new system that can only be completely described if its environment is included and so on. The eventual outcome of this process of embedding is the state of the whole universe described by a wavefunction . The fact that every quantum system has some degree of openness also means that no quantum system can ever be in a pure state. A pure state is unitary equivalent to a zero-temperature gro
|
https://en.wikipedia.org/wiki/Raja%20Rao
|
Raja Rao (8 November 1908 – 8 July 2006) was an Indian-American writer of English-language novels and short stories, whose works are deeply rooted in metaphysics. The Serpent and the Rope (1960), a semi-autobiographical novel recounting a search for spiritual truth in Europe and India, established him as one of the finest Indian prose stylists and won him the Sahitya Akademi Award in 1963. For the entire body of his work, Rao was awarded the Neustadt International Prize for Literature in 1988. Rao's wide-ranging body of work, spanning a number of genres, is seen as a varied and significant contribution to Indian English literature, as well as World literature as a whole.
Biography
Early life
Raja Rao was born on 8 November 1908 in Hassan, in the princely state of Mysore (now in Karnataka in South India) into a Kannada-speaking Brahmin family and was the eldest of 9 siblings, with seven sisters and a brother named Yogeshwara Ananda. His father, H.V. Krishnaswamy, taught Kannada, the native language of Karnataka, and Mathematics at Nizam College in Hyderabad. His mother, Gauramma, was a homemaker who died when Raja Rao was 4 years old.
The death of his mother when he was four left a lasting impression on the novelist – the absence of a mother and orphanhood are recurring themes in his work. Another influence from early life was his grandfather, with whom he lived in Hassan and Harihalli or Harohalli).
Rao was educated at a Muslim school, the Madarsa-e-Aliya in Hyderabad. Af
|
https://en.wikipedia.org/wiki/MBP
|
MBP or mbp may refer to:
Science and technology
Münchausen syndrome by proxy, a disorder wherein a caregiver acts as if their patient has health problems
MacBook Pro, a line of Macintosh portable computers by Apple Inc.
Modbus Plus, an extended version of the Modbus serial communications protocol published by Modicon in 1979
Biology
Mega base pairs (Mbp)
Major basic protein, a protein which in humans is encoded by the PRG2 gene
Maltose-binding protein, a part of the maltose/maltodextrin system of Escherichia coli
4-Methyl-2,4-bis(4-hydroxyphenyl)pent-1-ene, a metabolite of bisphenol A
Milk basic protein, a milk protein fraction
Myc-binding protein-1, a protein encoded by the alpha-enolase glycolytic enzyme
Myelin basic protein, a protein believed to be important in the process of myelination of nerves in the central nervous system
Mannan-binding lectin (also mannose- or mannan-binding protein), an important factor in innate immunity
Media
"ManBearPig", the sixth episode of the tenth season of Comedy Central's South Park
Million Book Project, a book digitization project, led by Carnegie Mellon University
Murder by Pride, the eighth studio album by Stryper
Organisations
McDonough Bolyard Peck, an American construction management company
Marquette Branch Prison, a prison in Michigan, US
Ministry of Public Security (Poland) (Polish: Ministerstwo Bezpieczeństwa Publicznego) 1945-1954
MBP Moto, an Italian motorcycle brand based in Bologna and owned by the Qian
|
https://en.wikipedia.org/wiki/Isozyme
|
In biochemistry, isozymes (also known as isoenzymes or more generally as multiple forms of enzymes) are enzymes that differ in amino acid sequence but catalyze the same chemical reaction. Isozymes usually have different kinetic parameters (e.g. different KM values), or are regulated differently. They permit the fine-tuning of metabolism to meet the particular needs of a given tissue or developmental stage.
In many cases, isozymes are encoded by homologous genes that have diverged over time. Strictly speaking, enzymes with different amino acid sequences that catalyse the same reaction are isozymes if encoded by different genes, or allozymes if encoded by different alleles of the same gene; the two terms are often used interchangeably.
Introduction
Isozymes were first described by R. L. Hunter and Clement Markert (1957) who defined them as different variants of the same enzyme having identical functions and present in the same individual. This definition encompasses (1) enzyme variants that are the product of different genes and thus represent different loci (described as isozymes) and (2) enzymes that are the product of different alleles of the same gene (described as allozymes).
Isozymes are usually the result of gene duplication, but can also arise from polyploidisation or nucleic acid hybridization. Over evolutionary time, if the function of the new variant remains identical to the original, then it is likely that one or the other will be lost as mutations accumulate
|
https://en.wikipedia.org/wiki/Dirac%20operator
|
In mathematics and quantum mechanics, a Dirac operator is a differential operator that is a formal square root, or half-iterate, of a second-order operator such as a Laplacian. The original case which concerned Paul Dirac was to factorise formally an operator for Minkowski space, to get a form of quantum theory compatible with special relativity; to get the relevant Laplacian as a product of first-order operators he introduced spinors. It was first published in 1928.
Formal definition
In general, let D be a first-order differential operator acting on a vector bundle V over a Riemannian manifold M. If
where ∆ is the Laplacian of V, then D is called a Dirac operator.
In high-energy physics, this requirement is often relaxed: only the second-order part of D2 must equal the Laplacian.
Examples
Example 1
D = −i ∂x is a Dirac operator on the tangent bundle over a line.
Example 2
Consider a simple bundle of notable importance in physics: the configuration space of a particle with spin confined to a plane, which is also the base manifold. It is represented by a wavefunction
where x and y are the usual coordinate functions on R2. χ specifies the probability amplitude for the particle to be in the spin-up state, and similarly for η. The so-called spin-Dirac operator can then be written
where σi are the Pauli matrices. Note that the anticommutation relations for the Pauli matrices make the proof of the above defining property trivial. Those relations define the notion of
|
https://en.wikipedia.org/wiki/C.%20H.%20Waddington
|
Conrad Hal Waddington (8 November 1905 – 26 September 1975) was a British developmental biologist, paleontologist, geneticist, embryologist and philosopher who laid the foundations for systems biology, epigenetics, and evolutionary developmental biology.
Although his theory of genetic assimilation had a Darwinian explanation, leading evolutionary biologists including Theodosius Dobzhansky and Ernst Mayr considered that Waddington was using genetic assimilation to support so-called Lamarckian inheritance, the acquisition of inherited characteristics through the effects of the environment during an organism's lifetime.
Waddington had wide interests that included poetry and painting, as well as left-wing political leanings. In his book The Scientific Attitude (1941), he touched on political topics such as central planning, and praised Marxism as a "profound scientific philosophy".
Life
Conrad Waddington, known as "Wad" to his friends and "Con" to family, was born in Evesham to Hal and Mary Ellen (Warner) Waddington, on 8 November 1905.
His family moved to India and until nearly three years of age, Waddington lived in India, where his father worked on a tea estate in the Wayanad district of Kerala. In 1910, at the age of four, he was sent to live with family in England including his aunt, uncle, and Quaker grandmother. His parents remained in India until 1928. During his childhood, he was particularly attached to a local druggist and distant relation, Dr. Doeg. Doeg, whom Wa
|
https://en.wikipedia.org/wiki/Inter-University%20Centre%20for%20Astronomy%20and%20Astrophysics
|
The Inter-University Centre for Astronomy and Astrophysics (IUCAA) is an autonomous institution set up by the University Grants Commission of India to promote nucleation and growth of active groups in astronomy and astrophysics in Indian universities. IUCAA is located in the University of Pune campus next to the National Centre for Radio Astrophysics, which operates the Giant Metrewave Radio Telescope. IUCAA has a campus designed by Indian architect Charles Correa.
History
After the founding of the Giant Metrewave Radio Telescope (GMRT) by Prof. Govind Swarup, a common research facility for astronomy and astrophysics was proposed by Dr. Yash Pal of the planning commission. Working on this idea, astrophysicist Prof. Jayant Narlikar, along with Ajit Kembhavi and Naresh Dadhich set up IUCAA within the Pune University campus in 1988.
In 2002, IUCAA initiated a nationwide campaign to popularize astronomy and astrophysics in colleges and universities. IUCAA arranged visitor programs for universities in Nagpur (Maharashtra), Thiruvalla (Kerala), Siliguri (West Bengal) and others, along with a tie-up with the Ferguson college, Pune.
In 2004, IUCAA set up the Muktangan Vidnyan Shodhika (Exlporatorium), a science popularization initiative, with a grant from the Pu La Deshpande foundation. The center is open to all school students from Pune. IUCAA was declared the nodal center for India to coordinate the year-long celebrations for the International Year of Astronomy.
IUCAA was heade
|
https://en.wikipedia.org/wiki/Jean-Fran%C3%A7ois%20Pil%C3%A2tre%20de%20Rozier
|
Jean-François Pilâtre de Rozier () was a French chemistry and physics teacher, and one of the first pioneers of aviation. He made the first manned free balloon flight with François Laurent d'Arlandes on 21 November 1783, in a Montgolfier balloon. He later died when his balloon crashed near Wimereux in the Pas-de-Calais during an attempt to fly across the English Channel. His companion Pierre Romain and he thus became the first known fatalities in an air crash.
Early life
He was born in Metz, the third son of Magdeleine Wilmard and Mathurin Pilastre, known as "de Rozier", a former soldier who became an innkeeper. His interests in the chemistry of drugs had been awakened in the military hospital of Metz, an important garrison town on the border of France. He made his way to Paris at the age of 18, then taught physics and chemistry at the Academy in Reims, which brought him to the attention of the Comte de Provence, brother of King Louis XVI.
He returned to Paris, where he was put in charge of Monsieur's cabinet of natural history and made a valet de chambre to Monsieur's wife, Madame, which brought him his ennobled name, Pilâtre de Rozier. He opened his own museum in the Marais quarter of Paris on 11 December 1781, where he undertook experiments in physics, and provided demonstrations to nobles. He researched the new field of gases, and invented a respirator.
Flight pioneer
In June 1783, he witnessed the first public demonstration of a balloon by the Montgolfier broth
|
https://en.wikipedia.org/wiki/Physics%20of%20skiing
|
The physics of skiing refers to the analysis of the forces acting on a person while skiing.
The motion of a skier is determined by the physical principles of the conservation of energy and the frictional forces acting on the body. For example, in downhill skiing, as the skier is accelerated down the hill by the force of gravity, their gravitational potential energy is converted to kinetic energy, the energy of motion. In the ideal case, all of the potential energy would be converted into kinetic energy; in reality, some of the energy is lost to heat due to friction.
One type of friction acting on the skier is the kinetic friction between the skis and snow. The force of friction acts in the direction opposite to the direction of motion, resulting in a lower velocity and hence less kinetic energy. The kinetic friction can be reduced by applying wax to the bottom of the skis which reduces the coefficient of friction. Different types of wax are manufactured for different temperature ranges because the snow quality changes depending on the current weather conditions and thermal history of the snow. The shape and construction material of a ski can also greatly impact the forces acting on a skier. Skis designed for use in powder condition are very different from skis designed for use on groomed trails. These design differences can be attributed to the differences in the snow quality.
An illustration of how snow quality can be different follows. In an area which experienc
|
https://en.wikipedia.org/wiki/Heberto%20Castillo
|
Heberto Castillo Martínez (August 23, 1928 – April 5, 1997) was a Mexican civil engineer and political activist.
Castillo was born in Ixhuatlán de Madero, Veracruz, and received a bachelor's degree in civil engineering from the National Autonomous University. An accomplished engineer, he taught several courses at the UNAM and at the National Polytechnic Institute, wrote several textbooks and invented the tridilosa.
He became a political activist and got involved in several workers' rights struggles, leading to imprisonment by the federal government in the infamous Lecumberri Penitentiary. Castillo was one of the first among leading left-wing politicians to express dismay at the dictatorial nature of Soviet-bloc governments, starting a movement towards a social democracy-based left wing and away from a Moscow-based left leaning opposition in Mexico.
During his lifetime he co-founded three political parties: the Mexican Workers' Party (Partido Mexicano de los Trabajadores, PMT), the Mexican Socialist Party (Partido Mexicano Socialista, PMS) and the Party of the Democratic Revolution (Partido de la Revolución Democrática, PRD). In his last years in politics he became a staunch critic of the Zapatista rebellion in Chiapas and, crucially, voluntarily withdrew from the presidential race in 1988 to support the unified candidacy of Cuauhtémoc Cárdenas.
He died on April 5, 1997 at the age of 68, in Mexico City and received the Belisario Domínguez Medal of Honor (postmortem) that s
|
https://en.wikipedia.org/wiki/Lava%20dome
|
In volcanology, a lava dome is a circular, mound-shaped protrusion resulting from the slow extrusion of viscous lava from a volcano. Dome-building eruptions are common, particularly in convergent plate boundary settings. Around 6% of eruptions on Earth are lava dome forming. The geochemistry of lava domes can vary from basalt (e.g. Semeru, 1946) to rhyolite (e.g. Chaiten, 2010) although the majority are of intermediate composition (such as Santiaguito, dacite-andesite, present day) The characteristic dome shape is attributed to high viscosity that prevents the lava from flowing very far. This high viscosity can be obtained in two ways: by high levels of silica in the magma, or by degassing of fluid magma. Since viscous basaltic and andesitic domes weather fast and easily break apart by further input of fluid lava, most of the preserved domes have high silica content and consist of rhyolite or dacite.
Existence of lava domes has been suggested for some domed structures on the Moon, Venus, and Mars, e.g. the Martian surface in the western part of Arcadia Planitia and within Terra Sirenum.
Dome dynamics
Lava domes evolve unpredictably, due to non-linear dynamics caused by crystallization and outgassing of the highly viscous lava in the dome's conduit. Domes undergo various processes such as growth, collapse, solidification and erosion.
Lava domes grow by endogenic dome growth or exogenic dome growth. The former implies the enlargement of a lava dome due to the influx of magm
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.