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https://en.wikipedia.org/wiki/Martin%20Lewis%20Perl
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Martin Lewis Perl (June 24, 1927 – September 30, 2014) was an American chemical engineer and physicist who won the Nobel Prize in Physics in 1995 for his discovery of the tau lepton.
Life and career
Perl was born in New York City, New York. His parents, Fay (née Resenthal), a secretary and bookkeeper, and Oscar Perl, a stationery salesman who founded a printing and advertising company, were Jewish immigrants to the US from the Polish area of Russia.
Perl was a 1948 chemical engineering graduate of Brooklyn Polytechnic Institute (now known as NYU-Tandon) in Brooklyn. After graduation, Perl worked for the General Electric Company, as a chemical engineer in a factory producing electron vacuum tubes. To learn about how the electron tubes worked, Perl signed up for courses in atomic physics and advanced calculus at Union College in Schenectady, New York, which led to his growing interest in physics, and eventually to becoming a graduate student in physics in 1950.
He received his Ph.D. from Columbia University in 1955, where his thesis advisor was I.I. Rabi. Perl's thesis described measurements of the nuclear quadrupole moment of sodium, using the atomic beam resonance method that Rabi had won the Nobel Prize in Physics for in 1944.
Following his Ph.D., Perl spent 8 years at the University of Michigan, where he worked on the physics of strong interactions, using bubble chambers and spark chambers to study the scattering of pions and later neutrons on protons.
While at Michi
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https://en.wikipedia.org/wiki/Row
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Row or ROW may refer to:
Exercise
Rowing, or a form of aquatic movement using oars
Row (weight-lifting), a form of weight-lifting exercise
Mathematics and informatics
Row vector, a 1 × n matrix in linear algebra
Row(s) in a table (information), a data arrangement with rows and columns
Row (database), a single, implicitly structured data item in a database table
Tone row, an arrangement of the twelve notes of the chromatic scale
Places
Rów, Pomeranian Voivodeship, north Poland
Rów, Warmian-Masurian Voivodeship, north Poland
Rów, West Pomeranian Voivodeship, northwest Poland
Roswell International Air Center's IATA code
Row, a former spelling of Rhu, Dunbartonshire, Scotland
The Row (Lyme, New York), a set of historic homes
The Row, Virginia, an unincorporated community
Rest of the world (RoW)
The Row or The Row Fulton Market, 900 West Randolph, a Chicago Skyscraper on Chicago's Restaurant Row
Other
Reality of Wrestling, an American professional wrestling promotion founded in 2005
Row (album), an album by Gerard
Right-of-way (transportation), ROW, also often R/O/W.
The Row (fashion label)
The Row (film), a 2018 Canadian-American film
See also
Skid row (disambiguation)
Rowing (disambiguation)
Rowe (disambiguation)
Roe (disambiguation)
Rho (disambiguation)
Line (disambiguation)
Column (disambiguation)
Controversy
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https://en.wikipedia.org/wiki/Quasisimple%20group
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In mathematics, a quasisimple group (also known as a covering group) is a group that is a perfect central extension E of a simple group S. In other words, there is a short exact sequence
such that , where denotes the center of E and [ , ] denotes the commutator.
Equivalently, a group is quasisimple if it is equal to its commutator subgroup and its inner automorphism group Inn(G) (its quotient by its center) is simple (and it follows Inn(G) must be non-abelian simple, as inner automorphism groups are never non-trivial cyclic). All non-abelian simple groups are quasisimple.
The subnormal quasisimple subgroups of a group control the structure of a finite insoluble group in much the same way as the minimal normal subgroups of a finite soluble group do, and so are given a name, component.
The subgroup generated by the subnormal quasisimple subgroups is called the layer, and along with the minimal normal soluble subgroups generates a subgroup called the generalized Fitting subgroup.
The quasisimple groups are often studied alongside the simple groups and groups related to their automorphism groups, the almost simple groups. The representation theory of the quasisimple groups is nearly identical to the projective representation theory of the simple groups.
Examples
The covering groups of the alternating groups are quasisimple but not simple, for
See also
Almost simple group
Schur multiplier
Semisimple group
References
External links
http://mathworld.wolfram.com/Quasis
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https://en.wikipedia.org/wiki/Symmetric%20space
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In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of symmetries contains an inversion symmetry about every point. This can be studied with the tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through Lie theory, which allowed Cartan to give a complete classification. Symmetric spaces commonly occur in differential geometry, representation theory and harmonic analysis.
In geometric terms, a complete, simply connected Riemannian manifold is a symmetric space if and only if its curvature tensor is invariant under parallel transport. More generally, a Riemannian manifold (M, g) is said to be symmetric if and only if, for each point p of M, there exists an isometry of M fixing p and acting on the tangent space as minus the identity (every symmetric space is complete, since any geodesic can be extended indefinitely via symmetries about the endpoints). Both descriptions can also naturally be extended to the setting of pseudo-Riemannian manifolds.
From the point of view of Lie theory, a symmetric space is the quotient G/H of a connected Lie group G by a Lie subgroup H which is (a connected component of) the invariant group of an involution of G. This definition includes more than the Riemannian definition, and reduces to it when H is compact.
Riemannian symmetric spaces arise in a wide variety of situations in both mathematics and physics. Their central role in
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https://en.wikipedia.org/wiki/Richard%20Goldschmidt
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Richard Benedict Goldschmidt (April 12, 1878 – April 24, 1958) was a German geneticist. He is considered the first to attempt to integrate genetics, development, and evolution. He pioneered understanding of reaction norms, genetic assimilation, dynamical genetics, sex determination, and heterochrony. Controversially, Goldschmidt advanced a model of macroevolution through macromutations popularly known as the "Hopeful Monster" hypothesis.
Goldschmidt also described the nervous system of the nematode, a piece of work that influenced Sydney Brenner to study the "wiring diagram" of Caenorhabditis elegans, winning Brenner and his colleagues the Nobel Prize in 2002.
Childhood and education
Goldschmidt was born in Frankfurt-am-Main, Germany to upper-middle class parents of Ashkenazi Jewish heritage. He had a classical education and entered the University of Heidelberg in 1896, where he became interested in natural history. From 1899 Goldschmidt studied anatomy and zoology at the University of Heidelberg with Otto Bütschli and Carl Gegenbaur. He received his Ph.D. under Bütschli in 1902, studying development of the trematode Polystomum.
Career
In 1903 Goldschmidt began working as an assistant to Richard Hertwig at the University of Munich, where he continued his work on nematodes and their histology, including studies of the nervous system development of Ascaris and the anatomy of Amphioxus. He founded the histology journal Archiv für Zellforschung while working in Hertwig's
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https://en.wikipedia.org/wiki/Joseph%20Sambrook
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Joseph Frank Sambrook (1 March 1939 – 14 June 2019) was a British molecular biologist known for his studies of DNA oncoviruses and the molecular biology of normal and cancerous cells.
Education and early career
Sambrook was educated at the University of Liverpool (BSc (hons) 1962) and obtained his PhD at the Australian National University in 1966. He did postdoctoral research at the MRC Laboratory of Molecular Biology (1966–67) and the Salk Institute for Biological Studies (1967–69). In 1969 he was hired by James D. Watson to work at the Cold Spring Harbor Laboratory in New York. Watson has been reported to say this was the best hiring decision he ever made. Joe was responsible for creating a combative creative environment at CSHL that fomented discovery. Subsequently, he worked at the University of Texas Southwestern Medical Center (Dallas).
Achievements
Sambrook is best known for his studies on DNA tumor viruses and the molecular biology of normal and neoplastic cells. His Tumour Virus Group at Cold Spring Harbor identified and mapped all of the major genes of adenoviruses and SV40, determined their transcriptional control in infected and transformed cells, and elucidated the mechanism of integration of these viruses into the genome of the host cell. He has also made important contributions to the understanding of intracellular traffic and protein folding and is an influential leader in the field of the molecular genetics of human cancer.
Sambrook is a former director
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https://en.wikipedia.org/wiki/Jos%C3%A9%20Leite%20Lopes
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José Leite Lopes (October 28, 1918 – June 12, 2006) was a Brazilian theoretical physicist who worked in the field of quantum field theory and particle physics.
Life
Leite Lopes began his university studies in 1935, enrolling in industrial chemistry at the Chemistry School of Pernambuco. In 1937, while presenting a paper to a scientific conference in Rio de Janeiro, the young student met Brazilian physicist Mário Schenberg and was introduced by him in São Paulo to Italian physicists Luigi Fantappiè and Gleb Wataghin. All three were working on research in physics at the then recently created University of São Paulo, amid a climate of great intellectual excitement and a breeding ground for a bright young generation of what would become the élite of Brazilian physics, such as César Lattes, Oscar Sala, Roberto Salmeron, Jayme Tiomno and Marcelo Damy de Souza Santos. Encouraged to study physics by what he saw, Leite Lopes moved to Rio de Janeiro after hist graduation in 1939. He took the entrance examinations to the National Faculty of Philosophy of the University of Brazil in 1940 and graduated a bachelor in physics in 1942. Accepting an invitation by Carlos Chagas Filho, Leite Lopes started to work in the same year the Institute of Biophysics of the Federal University of Rio de Janeiro, but soon moved to the University of São Paulo to take up graduate studies in quantum mechanics with his teacher, friend and sponsor, Mário Schenberg. His main work during this time was on the ca
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https://en.wikipedia.org/wiki/K%C5%8Dsaku%20Yosida
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was a Japanese mathematician who worked in the field of functional analysis. He is known for the Hille-Yosida theorem concerning C0-semigroups. Yosida studied mathematics at the University of Tokyo, and held posts at Osaka and Nagoya Universities. In 1955, Yosida returned to the University of Tokyo.
See also
Einar Carl Hille
Functional analysis
References
Kôsaku Yosida: Functional analysis. Grundlehren der mathematischen Wissenschaften 123, Springer-Verlag, 1971 (3rd ed.), 1974 (4th ed.), 1978 (5th ed.), 1980 (6th ed.)
External links
Photo
Kosaku Yosida / School of Mathematics and Statistics University of St Andrews, Scotland
94. Normed Rings and Spectral Theorems, II. By Kôsaku YOSIDA. Mathematical Inlstitute, Nagoya Imperial University. (Comm. by T.TAKAGMI, M.I.A. Oct.12,1943.)
Kosaku Yosida (1909 - 1990) - Biography - MacTutor
1909 births
1990 deaths
20th-century Japanese mathematicians
Mathematical analysts
Functional analysts
Operator theorists
Approximation theorists
University of Tokyo alumni
Academic staff of the University of Tokyo
Academic staff of Osaka University
Academic staff of Nagoya University
Laureates of the Imperial Prize
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https://en.wikipedia.org/wiki/%C3%98ystein%20Ore
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Øystein Ore (7 October 1899 – 13 August 1968) was a Norwegian mathematician known for his work in ring theory, Galois connections, graph theory, and the history of mathematics.
Life
Ore graduated from the University of Oslo in 1922, with a Cand.Real.degree in mathematics. In 1924, the University of Oslo awarded him the Ph.D. for a thesis titled Zur Theorie der algebraischen Körper, supervised by Thoralf Skolem. Ore also studied at Göttingen University, where he learned Emmy Noether's new approach to abstract algebra. He was also a fellow at the Mittag-Leffler Institute in Sweden, and spent some time at the University of Paris. In 1925, he was appointed research assistant at the University of Oslo.
Yale University’s James Pierpont went to Europe in 1926 to recruit research mathematicians. In 1927, Yale hired Ore as an assistant professor of mathematics, promoted him to associate professor in 1928, then to full professor in 1929. In 1931, he became a Sterling Professor (Yale's highest academic rank), a position he held until he retired in 1968.
Ore gave an American Mathematical Society Colloquium lecture in 1941 and was a plenary speaker at the International Congress of Mathematicians in 1936 in Oslo. He was also elected to the American Academy of Arts and Sciences and the Oslo Academy of Science. He was a founder of the Econometric Society.
Ore visited Norway nearly every summer. During World War II, he was active in the "American Relief for Norway" and "Free Norway" movem
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https://en.wikipedia.org/wiki/Gabriel%20Andrew%20Dirac
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Gabriel Andrew Dirac (13 March 1925 – 20 July 1984) was a Hungarian-British mathematician who mainly worked in graph theory. He served as Erasmus Smith's Professor of Mathematics at Trinity College Dublin from 1964 to 1966. In 1952, he gave a sufficient condition for a graph to contain a Hamiltonian circuit. The previous year, he conjectured that n points in the plane, not all collinear, must span at least two-point lines, where is the largest integer not exceeding . This conjecture was proven true when n is sufficiently large by Green and Tao in 2012.
Education
Dirac started his studies at St John's College, Cambridge in 1942, but in that same year the war saw him serving in the aircraft industry. He received his MA in 1949, and moved to the University of London, getting his Ph.D. "On the Colouring of Graphs: Combinatorial topology of Linear Complexes" there under Richard Rado.
Career
Dirac's main academic positions were at the King's College London (1948-1954), University of Toronto (1952-1953), University of Vienna (1954-1958), University of Hamburg (1958-1963), Trinity College Dublin (Erasmus Smith's Professor of Mathematics, 1964-1966), University of Wales at Swansea (1967-1970), and Aarhus University (1970-1984).
Family
He was born Balázs Gábor in Budapest, to Richárd Balázs, a military officer and businessman, and Margit "Manci" Wigner (sister of Eugene Wigner). When his mother married Paul Dirac in 1937, he and his sister resettled in England and were formally
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https://en.wikipedia.org/wiki/Einar%20Hille
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Carl Einar Hille (28 June 1894 – 12 February 1980) was an American mathematics professor and scholar. Hille authored or coauthored twelve mathematical books and a number of mathematical papers.
Early life and education
Hille was born in New York City. His parents were both immigrants from Sweden who separated before his birth. His father, Carl August Heuman, was a civil engineer. He was brought up by his mother, Edla Eckman, who took the surname Hille. When Einar was two years old, he and his mother returned to Stockholm. Hille spent the next 24 years of his life in Sweden, returning to the United States when he was 26 years old. Hille entered the University of Stockholm in 1911. Hille was awarded his first degree in mathematics in 1913 and the equivalent of a master's degree in the following year. He received a Ph.D. from Stockholm in 1918 for a doctoral dissertation entitled Some Problems Concerning Spherical Harmonics.
Career
In 1919 Hille was awarded the Mittag-Leffler Prize and was given the right to teach at the University of Stockholm. He subsequently taught at Harvard University, Princeton University, Stanford University and the University of Chicago. In 1933, he became an endowed professor on mathematics in the Graduate School of Yale University, retiring in 1962.
Hille's main work was on integral equations, differential equations, special functions, Dirichlet series and Fourier series. Later in his career his interests turned more towards functional analysis. H
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https://en.wikipedia.org/wiki/IEEE%20P1363
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IEEE P1363 is an Institute of Electrical and Electronics Engineers (IEEE) standardization project for public-key cryptography. It includes specifications for:
Traditional public-key cryptography (IEEE Std 1363-2000 and 1363a-2004)
Lattice-based public-key cryptography (IEEE Std 1363.1-2008)
Password-based public-key cryptography (IEEE Std 1363.2-2008)
Identity-based public-key cryptography using pairings (IEEE Std 1363.3-2013)
The chair of the working group as of October 2008 is William Whyte of NTRU Cryptosystems, Inc., who has served since August 2001. Former chairs were Ari Singer, also of NTRU (1999–2001), and Burt Kaliski of RSA Security (1994–1999).
The IEEE Standard Association withdrew all of the 1363 standards except 1363.3-2013 on 7 November 2019.
Traditional public-key cryptography (IEEE Std 1363-2000 and 1363a-2004)
This specification includes key agreement, signature, and encryption
schemes using several mathematical approaches: integer factorization,
discrete logarithm, and elliptic curve discrete logarithm.
Key agreement schemes
DL/ECKAS-DH1 and DL/ECKAS-DH2 (Discrete Logarithm/Elliptic Curve Key Agreement Scheme, Diffie–Hellman version): This includes both traditional Diffie–Hellman and elliptic curve Diffie–Hellman.
DL/ECKAS-MQV (Discrete Logarithm/Elliptic Curve Key Agreement Scheme, Menezes–Qu–Vanstone version)
Signature schemes
DL/ECSSA (Discrete Logarithm/Elliptic Curve Signature Scheme with Appendix): Includes four main variants: DSA, ECD
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https://en.wikipedia.org/wiki/Refinement%20%28computing%29
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Refinement is a generic term of computer science that encompasses various approaches for producing correct computer programs and simplifying existing programs to enable their formal verification.
Program refinement
In formal methods, program refinement is the verifiable transformation of an abstract (high-level) formal specification into a concrete (low-level) executable program. Stepwise refinement allows this process to be done in stages. Logically, refinement normally involves implication, but there can be additional complications.
The progressive just-in-time preparation of the product backlog (requirements list) in agile software development approaches, such as Scrum, is also commonly described as refinement.
Data refinement
Data refinement is used to convert an abstract data model (in terms of sets for example) into implementable data structures (such as arrays). Operation refinement converts a specification of an operation on a system into an implementable program (e.g., a procedure). The postcondition can be strengthened and/or the precondition weakened in this process. This reduces any nondeterminism in the specification, typically to a completely deterministic implementation.
For example, x ∈ {1,2,3} (where x is the value of the variable x after an operation) could be refined to x ∈ {1,2}, then x ∈ {1}, and implemented as x := 1. Implementations of x := 2 and x := 3 would be equally acceptable in this case, using a different route for the refinement. However, we
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https://en.wikipedia.org/wiki/Frank%20Baron%20%28civil%20engineer%29
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Frank Martin Baron (July 7, 1914, Chicago, Illinois – October 17, 1994) served as professor of civil engineering at the University of California, Berkeley and held an international reputation as an expert in the fields of bridge and roof-structure design, and seismic and wind analysis. He was twice the recipient of the prized Leon S. Moisseiff Award issued annually by the American Society of Civil Engineers (ASCE), and among his manifold professional affiliations, served as chairman of the US Council of the International Association for Bridge and Structural Engineering.
Baron's research interests traced the current of cutting-edge theory in civil engineering design and construction. As an undergraduate architecture and engineering student and masters-level graduate student in structural engineering at the University of Illinois, Baron had the privilege of studying under two premier names in engineering design: H.M. Westergaard, known for his research on the use of reinforced concrete for pavement and dams, and Hardy Cross, an undisputed authority on contemporary structural frame analysis. He formed lasting bonds with both of these scholars, later reuniting with Westergaard at Harvard and Cross at Yale.
After receiving his Sc. D. in structures and mechanics at Harvard University and becoming assistant professor at Harvard, Baron accepted a position on the civil engineering faculty at Yale University as associate professor. While at Yale, Baron further explored his dissertat
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https://en.wikipedia.org/wiki/C0-semigroup
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{{DISPLAYTITLE:C0-semigroup }}
In mathematics, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function. Just as exponential functions provide solutions of scalar linear constant coefficient ordinary differential equations, strongly continuous semigroups provide solutions of linear constant coefficient ordinary differential equations in Banach spaces. Such differential equations in Banach spaces arise from e.g. delay differential equations and partial differential equations.
Formally, a strongly continuous semigroup is a representation of the semigroup (R+, +) on some Banach space X that is continuous in the strong operator topology. Thus, strictly speaking, a strongly continuous semigroup is not a semigroup, but rather a continuous representation of a very particular semigroup.
Formal definition
A strongly continuous semigroup on a Banach space is a map
such that
, (the identity operator on )
, as .
The first two axioms are algebraic, and state that is a representation of the semigroup ; the last is topological, and states that the map is continuous in the strong operator topology.
Infinitesimal generator
The infinitesimal generator A of a strongly continuous semigroup T is defined by
whenever the limit exists. The domain of A, D(A), is the set of x∈X for which this limit does exist; D(A) is a linear subspace and A is linear on this domain. The operator A is closed, although not necessari
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https://en.wikipedia.org/wiki/Valence%20%28chemistry%29
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In chemistry, the valence (US spelling) or valency (British spelling) of an atom is a measure of its combining capacity with other atoms when it forms chemical compounds or molecules. Valence is generally understood to be the number of chemical bonds that each atom of a given element typically forms. For a specified compound the valence of an atom is the number of bonds formed by the atom. Double bonds are considered to be two bonds, and triple bonds to be three. In most compounds, the valence of hydrogen is 1, of oxygen is 2, of nitrogen is 3, and of carbon is 4. Valence is not to be confused with the related concepts of the coordination number, the oxidation state, or the number of valence electrons for a given atom.
Description
The valence is the combining capacity of an atom of a given element, determined by the number of hydrogen atoms that it combines with. In methane, carbon has a valence of 4; in ammonia, nitrogen has a valence of 3; in water, oxygen has a valence of 2; and in hydrogen chloride, chlorine has a valence of 1. Chlorine, as it has a valence of one, can be substituted for hydrogen in many compounds. Phosphorus has a valence 3 in phosphine () and a valence of 5 in phosphorus pentachloride (), which shows that elements may have exhibit than one valence. The structural formula of a compound represents the connectivity of the atoms, with lines drawn between two atoms to represent bonds. The two tables below show examples of different compounds, their structur
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https://en.wikipedia.org/wiki/William%20Mitchell%20%28physicist%29
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Sir Edgar William John Mitchell, (September 25, 1925 – October 30, 2002) was a British physicist, professor of physics at Reading and Oxford, and he helped pioneer the field of neutron scattering.
Born in Kingsbridge, Devon, England, he studied physics at Sheffield University, which had become an important centre for research in radar and defence communications. In 1946 he took up a research position with Metropolitan-Vickers, leading to a secondment to Bristol University, where Nobel laureate Nevill Mott was head of the department. After gaining his PhD, he took a position at Reading University in 1951, becoming professor of physics in 1961, and later dean of science and deputy vice chancellor. In 1978 he was named Dr Lee's Professor of Experimental Philosophy at Oxford University and became the head of the Clarendon laboratory.
He was also a skilled administrator who served in many public capacities. He became chairman of SERC in 1985, at a time of conflict between the British government and higher education over funding and independence. He was vice-president of the European Science Foundation from 1989 to 1992 and president of CERN in 1991. Mitchell was also a member of the SEPP Board of Science Advisors. He won the Richard Glazebrook Medal and Prize in 1996.
References
1925 births
2002 deaths
English physicists
Fellows of the Royal Society
Commanders of the Order of the British Empire
Knights Bachelor
People from Kingsbridge
Academics of the University of Oxford
Peo
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https://en.wikipedia.org/wiki/Trigonal%20pyramidal%20molecular%20geometry
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In chemistry, a trigonal pyramid is a molecular geometry with one atom at the apex and three atoms at the corners of a trigonal base, resembling a tetrahedron (not to be confused with the tetrahedral geometry). When all three atoms at the corners are identical, the molecule belongs to point group C3v. Some molecules and ions with trigonal pyramidal geometry are the pnictogen hydrides (XH3), xenon trioxide (XeO3), the chlorate ion, , and the sulfite ion, . In organic chemistry, molecules which have a trigonal pyramidal geometry are sometimes described as sp3 hybridized. The AXE method for VSEPR theory states that the classification is AX3E1.
Trigonal pyramidal geometry in ammonia
The nitrogen in ammonia has 5 valence electrons and bonds with three hydrogen atoms to complete the octet. This would result in the geometry of a regular tetrahedron with each bond angle equal to cos−1(−) ≈ 109.5°. However, the three hydrogen atoms are repelled by the electron lone pair in a way that the geometry is distorted to a trigonal pyramid (regular 3-sided pyramid) with bond angles of 107°. In contrast, boron trifluoride is flat, adopting a trigonal planar geometry because the boron does not have a lone pair of electrons. In ammonia the trigonal pyramid undergoes rapid nitrogen inversion.
See also
VSEPR theory#AXE method
Molecular geometry
References
External links
Chem| Chemistry, Structures, and 3D Molecules
Indiana University Molecular Structure Center
Interactive molecular examples
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https://en.wikipedia.org/wiki/Margaret%20Oakley%20Dayhoff
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Margaret Belle (Oakley) Dayhoff (March 11, 1925 – February 5, 1983) was an American physical chemist and a pioneer in the field of bioinformatics. Dayhoff was a professor at Georgetown University Medical Center and a noted research biochemist at the National Biomedical Research Foundation, where she pioneered the application of mathematics and computational methods to the field of biochemistry. She dedicated her career to applying the evolving computational technologies to support advances in biology and medicine, most notably the creation of protein and nucleic acid databases and tools to interrogate the databases. She originated one of the first substitution matrices, point accepted mutations (PAM). The one-letter code used for amino acids was developed by her, reflecting an attempt to reduce the size of the data files used to describe amino acid sequences in an era of punch-card computing.
Her PhD degree was from Columbia University in the department of chemistry, where she devised computational methods to calculate molecular resonance energies of several organic compounds. She did postdoctoral studies at the Rockefeller Institute (now Rockefeller University) and the University of Maryland, and joined the newly established National Biomedical Research Foundation in 1959. She was the first woman to hold office in the Biophysical Society and the first person to serve as both secretary and eventually president.
Early life
Dayhoff was born an only child in Philadelphia,
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https://en.wikipedia.org/wiki/Generalized%20Kac%E2%80%93Moody%20algebra
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In mathematics, a generalized Kac–Moody algebra is a Lie algebra that is similar to a Kac–Moody algebra, except that it is allowed to have imaginary simple roots.
Generalized Kac–Moody algebras are also sometimes called GKM algebras, Borcherds–Kac–Moody algebras, BKM algebras, or Borcherds algebras. The best known example is the monster Lie algebra.
Motivation
Finite-dimensional semisimple Lie algebras have the following properties:
They have a nondegenerate symmetric invariant bilinear form (,).
They have a grading such that the degree zero piece (the Cartan subalgebra) is abelian.
They have a (Cartan) involution w.
(a, w(a)) is positive if a is nonzero.
For example, for the algebras of n by n matrices of trace zero, the bilinear form is (a, b) = Trace(ab), the Cartan involution is given by minus the transpose, and the grading can be given by "distance from the diagonal" so that the Cartan subalgebra is the diagonal elements.
Conversely one can try to find all Lie algebras with these properties (and satisfying a few other technical conditions). The answer is that one gets sums of finite-dimensional and affine Lie algebras.
The monster Lie algebra satisfies a slightly weaker version of the conditions above:
(a, w(a)) is positive if a is nonzero and has nonzero degree, but may be negative when a has degree zero. The Lie algebras satisfying these weaker conditions are more or less generalized Kac–Moody algebras.
They are essentially the same as algebras given by cert
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https://en.wikipedia.org/wiki/Opposite
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Opposite or Opposites may refer to:
Opposite (semantics), a word that means the reverse of a word
Opposite (leaf), an arrangement of leaves on a stem
Opposite (mathematics), the negative of a number; numbers that, when added, yield zero
"The Opposite", a 1994 episode of Seinfeld
Music
The Opposites, Dutch rap group
Opposites (album), 2013 album by Scottish alternative rock band Biffy Clyro
"Opposite" (song), 2013 song by Biffy Clyro
Opposites (EP), 2010 album by Tracey Thorn
"The Opposite", 1964 song by Johnny Burnette
See also
Opposite hitter, a position in volleyball
Antinomy, opposites in a certain form from Kant
Anti (disambiguation)
Contrary (disambiguation)
Flipside (disambiguation)
Inverse (disambiguation)
Opposite sex (disambiguation)
Opposition (disambiguation)
Polar opposite (disambiguation)
The House Opposite (disambiguation)
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https://en.wikipedia.org/wiki/Trigonal%20planar%20molecular%20geometry
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In chemistry, trigonal planar is a molecular geometry model with one atom at the center and three atoms at the corners of an equilateral triangle, called peripheral atoms, all in one plane. In an ideal trigonal planar species, all three ligands are identical and all bond angles are 120°. Such species belong to the point group D3h. Molecules where the three ligands are not identical, such as H2CO, deviate from this idealized geometry. Examples of molecules with trigonal planar geometry include boron trifluoride (BF3), formaldehyde (H2CO), phosgene (COCl2), and sulfur trioxide (SO3). Some ions with trigonal planar geometry include nitrate (), carbonate (), and guanidinium (). In organic chemistry, planar, three-connected carbon centers that are trigonal planar are often described as having sp2 hybridization.
Nitrogen inversion is the distortion of pyramidal amines through a transition state that is trigonal planar.
Pyramidalization is a distortion of this molecular shape towards a tetrahedral molecular geometry. One way to observe this distortion is in pyramidal alkenes.
See also
AXE method
Molecular geometry
VSEPR theory
References
External links
3D Chem Chemistry, Structures, and 3D Molecules
Indiana University Molecular Structure Center
Interactive molecular examples for point groups
Molecular Modeling
Animated Trigonal Planar Visual
Stereochemistry
Molecular geometry
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https://en.wikipedia.org/wiki/Friedrich%20Hasen%C3%B6hrl
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Friedrich Hasenöhrl (; 30 November 1874 – 7 October 1915) was an Austrian physicist.
Life
Friedrich Hasenöhrl was born in Vienna, Austria-Hungary in 1874. His father was a lawyer and his mother belonged to a prominent aristocratic family. After his elementary education, he studied natural science and mathematics at the University of Vienna under Joseph Stefan (1835–1893) and Ludwig Boltzmann (1844–1906). In 1896, he attained a doctorate under Franz-Serafin Exner with a thesis titled "Über den Temperaturkoeffizienten der Dielektrizitätskonstante in Flüssigkeiten und die Mosotti-Clausius'sche Formel".
He worked under Heike Kamerlingh Onnes in Leiden at the low temperature laboratory, and there he also befriended H. A. Lorentz.
In 1907 he became Boltzmann's successor at the University of Vienna as the head of the Department of Theoretical Physics. He had a number of illustrious pupils there and had an especially significant impact on Erwin Schrödinger, who later won the Nobel Prize for Physics for his contributions to quantum mechanics.
In an autobiography, Schrödinger claimed "no other human being had a greater influence on me than Fritz Hasenöhrl, except perhaps my father Rudolph".
When the war broke out in 1914, he volunteered at once into the Austria-Hungarian army. He fought as Oberleutnant against the Italians in Tyrol. He was wounded, recovered and returned to the front. He was then killed by a grenade in an attack on Mount Plaut (Folgaria) on 7 October 1915 at the
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https://en.wikipedia.org/wiki/Bond%20energy
|
In chemistry, bond energy (BE), also called the mean bond enthalpy or average bond enthalpy is a measure of bond strength in a chemical bond. IUPAC defines bond energy as the average value of the gas-phase bond-dissociation energy (usually at a temperature of 298.15 K) for all bonds of the same type within the same chemical species.
The bond dissociation energy (enthalpy) is also referred to as
bond disruption energy, bond energy, bond strength, or binding
energy (abbreviation: BDE, BE, or D). It is defined as the standard
enthalpy change of the following fission: R - X → R + X. The BDE,
denoted by Dº(R - X), is usually derived by the thermochemical
equation,
The enthalpy of formation ΔHfº of a large number of atoms, free radicals, ions,
clusters and compounds is available from the websites of NIST,
NASA, CODATA, and IUPAC. Most authors prefer to use the
BDE values at 298.15 K.
For example, the carbon–hydrogen bond energy in methane BE(C–H) is the enthalpy change (∆H) of breaking one molecule of methane into a carbon atom and four hydrogen radicals, divided by four. The exact value for a certain pair of bonded elements varies somewhat depending on the specific molecule, so tabulated bond energies are generally averages from a number of selected typical chemical species containing that type of bond.
Bond energy (BE) is the average of all bond-dissociation energies of a single type of bond in a given molecule. The bond-dissociation energies of several different bonds of th
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https://en.wikipedia.org/wiki/Mathematics%2C%20Engineering%2C%20Science%20Achievement
|
Mathematics, Engineering, Science Achievement (MESA) is an academic preparation program for pre-college, community college and university-level students. Established in 1970 in California, the program provides academic support to students from educationally disadvantaged backgrounds throughout the education pathway so they will excel in math and science and ultimately attain four-year degrees in science, technology, engineering or math (STEM) fields. The program has successfully been replicated in over a dozen other states.
Locations and partners
MESA, while administered by the University of California, is an intersegmental program, with centers located at all major statewide education institutions (California Department of Education, University of California, California State University, California Community Colleges, the Association of Independent California Colleges and Universities). MESA has established an active partnership with industry and STEM leaders such as AT&T, Chevron, Google, HP, Sempra Energy, and PG&E. These partners supply expertise, volunteers, internship and opportunities for students to visit companies and learn about career options in STEM fields. The strong relationship with industry has resulted in MESA incorporating many elements of industry culture into its approaches and activities.
A partnership of MESA programs in eleven states (Arizona, California, Colorado, Maryland, New Mexico, Nevada, Oregon, Utah and Washington) has established a network c
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https://en.wikipedia.org/wiki/Homolysis%20%28chemistry%29
|
In chemistry, homolysis () or homolytic fission is the dissociation of a molecular bond by a process where each of the fragments (an atom or molecule) retains one of the originally bonded electrons. During homolytic fission of a neutral molecule with an even number of electrons, two free radicals will be generated. That is, the two electrons involved in the original bond are distributed between the two fragment species. Bond cleavage is also possible by a process called heterolysis.
The energy involved in this process is called bond dissociation energy (BDE). BDE is defined as the "enthalpy (per mole) required to break a given bond of some specific molecular entity by homolysis," symbolized as D. BDE is dependent on the strength of the bond, which is determined by factors relating to the stability of the resulting radical species.
Because of the relatively high energy required to break bonds in this manner, homolysis occurs primarily under certain circumstances:
Light (i.e. ultraviolet radiation)
Heat
Certain intramolecular bonds, such as the O–O bond of a peroxide, are weak enough to spontaneously homolytically dissociate with a small amount of heat.
High temperatures in the absence of oxygen (pyrolysis) can induce homolytic elimination of carbon compounds.
Most bonds homolyse at temperatures above 200°C.
Additionally, in some cases pressure can induce the formation of radicals. These conditions excite electrons to the next highest molecular orbital, thus creating a
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https://en.wikipedia.org/wiki/Heterolysis%20%28chemistry%29
|
In chemistry, heterolysis or heterolytic fission () is the process of cleaving/breaking a covalent bond where one previously bonded species takes both original bonding electrons from the other species. During heterolytic bond cleavage of a neutral molecule, a cation and an anion will be generated. Most commonly the more electronegative atom keeps the pair of electrons becoming anionic while the more electropositive atom becomes cationic.
Heterolytic fission almost always happens to single bonds; the process usually produces two fragment species.
The energy required to break the bond is called the heterolytic bond dissociation energy, which is similar (but not equivalent) to homolytic bond dissociation energy commonly used to represent the energy value of a bond.
One example of the differences in the energies is the energy required to break a bond
{|
| H2 -> 2H. || || ΔH = 104 kcal/mol
|-
| H2 -> H+ + H- || || ΔH = 66 kcal/mol (in water)
|}
History
The discovery and categorization of heterolytic bond fission was clearly dependent on the discovery and categorization of the chemical bond.
In 1916, chemist Gilbert N. Lewis developed the concept of the electron-pair bond, in which two atoms share one to six electrons, thus forming the single electron bond, a single bond, a double bond, or a triple bond. This became the model for a covalent bond.
In 1932 Linus Pauling first proposed the concept of electronegativity, which also introduced the idea that ele
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https://en.wikipedia.org/wiki/No-arbitrage%20bounds
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In financial mathematics, no-arbitrage bounds are mathematical relationships specifying limits on financial portfolio prices. These price bounds are a specific example of good–deal bounds, and are in fact the greatest extremes for good–deal bounds.
The most frequent nontrivial example of no-arbitrage bounds is put–call parity for option prices. In incomplete markets, the bounds are given by the subhedging and superhedging prices.
The essence of no-arbitrage in mathematical finance is excluding the possibility of "making money out of nothing" in the financial market. This is necessary because the existence of arbitrage is not only unrealistic, but also contradicts the possibility of an economic equilibrium. All mathematical models of financial markets have to satisfy a no-arbitrage condition to be realistic models.
See also
Box spread
Indifference price
References
Mathematical finance
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https://en.wikipedia.org/wiki/Michael%20addition%20reaction
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In organic chemistry, the Michael reaction or Michael 1,4 addition is a reaction between a Michael donor (an enolate or other nucleophile) and a Michael acceptor (usually an α,β-unsaturated carbonyl) to produce a Michael adduct by creating a carbon-carbon bond at the acceptor's β-carbon. It belongs to the larger class of conjugate additions and is widely used for the mild formation of carbon-carbon bonds.
The Michael addition is an important atom-economical method for diastereoselective and enantioselective C–C bond formation, and many asymmetric variants exist
In this general Michael addition scheme, either or both of R and R' on the nucleophile (the Michael donor) represent electron-withdrawing substituents such as acyl, cyano, nitro, or sulfone groups, which make the adjacent methylene hydrogen acidic enough to form a carbanion when reacted with the base, B:. For the alkene (the Michael acceptor), the R" substituent is usually a carbonyl, which makes the compound an α,β-unsaturated carbonyl compound (either an enone or an enal), or R" may be any electron withdrawing group.
Definition
As originally defined by Arthur Michael, the reaction is the addition of an enolate of a ketone or aldehyde to an α,β-unsaturated carbonyl compound at the β carbon. The current definition of the Michael reaction has broadened to include nucleophiles other than enolates. Some examples of nucleophiles include doubly stabilized carbon nucleophiles such as beta-ketoesters, malonates, and beta-c
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https://en.wikipedia.org/wiki/Principle%20of%20equivalence
|
Principle of equivalence may refer to:
The relativistic equivalence principle
Carl Jung's second principle relating to the libido#Analytical psychology
The principle of nuclear equivalence, in genetics
Wolfram's principle of computational equivalence, discussed in A New Kind of Science
See also
Doctrine of cash equivalence
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https://en.wikipedia.org/wiki/Timothy%20J.%20Hickey
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Timothy J. Hickey (born July 24, 1955) is a professor of computer science and former Chair of the Computer Science and Internet Studies Program (INET) at Brandeis University.
Hickey's specialties include analysis of algorithms, logic programming and parallel processing, symbolic manipulation, and groupware. His current research involved the study of Educational Technology, Brain-Computer Interfaces and Game-based Learning. He is the co-creator and lead developer of the JScheme programming language and the GrewpEdit collaborative editor.
Hickey graduated summa cum laude with a B.A. in Mathematics from Brandeis University and holds an M.S. and Ph.D. in Mathematics from the University of Chicago.
References
External links
Professor Hickey's website
GrewpEdit website
JScheme website
Brandeis University faculty
American computer scientists
Brandeis University alumni
1955 births
Living people
University of Chicago alumni
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https://en.wikipedia.org/wiki/Random%20matrix
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In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathematically as matrix problems. For example, the thermal conductivity of a lattice can be computed from the dynamical matrix of the particle-particle interactions within the lattice.
Applications
Physics
In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms. Wigner postulated that the spacings between the lines in the spectrum of a heavy atom nucleus should resemble the spacings between the eigenvalues of a random matrix, and should depend only on the symmetry class of the underlying evolution. In solid-state physics, random matrices model the behaviour of large disordered Hamiltonians in the mean-field approximation.
In quantum chaos, the Bohigas–Giannoni–Schmit (BGS) conjecture asserts that the spectral statistics of quantum systems whose classical counterparts exhibit chaotic behaviour are described by random matrix theory.
In quantum optics, transformations described by random unitary matrices are crucial for demonstrating the advantage of quantum over classical computation (see, e.g., the boson sampling model). Moreover, such random unitary transformations can be directly implemented in an optical circuit, by mapping their parameters to optical circuit components (that is beam splitte
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https://en.wikipedia.org/wiki/List%20of%20Guggenheim%20Fellowships%20awarded%20in%201970
|
List of Guggenheim Fellowship winners for 1970.
United States and Canadian fellows
Patrick Ahern, professor of mathematics, University of Wisconsin–Madison.
Michael M. Ames, former director and professor emeritus, Museum of Anthropology, University of British Columbia.
Albert K. Ando, professor of economics and finance, University of Pennsylvania.
Jon Howard Appleton, composer; Arthur R. Virgin Professor of Music, Dartmouth College.
Giuseppe Attardi, professor of biology, California Institute of Technology: 1970, 1986.
James M. Banner, Jr., independent historian, Washington, D.C..
Thomas G. Barnes, professor of history, University of California, Berkeley.
Samuel Haskell Baron, alumni distinguished professor emeritus of history, University of North Carolina at Chapel Hill: 1970.
Romare Bearden, deceased. Fine arts.
Max Beberman, deceased. Education.
Jonathan Beckwith, American Cancer Society Research Professor of Microbiology and Molecular Genetics, Harvard Medical School.
Charles Franklin Bennett, professor of biogeography, University of California, Los Angeles.
Malcolm Bersohn, associate professor of chemistry, University of Toronto.
Alexander M. Bickel, deceased. Law.
Peter J. Bickel, chair, professor of statistics, University of California, Berkeley.
James Bishop, artist, New York City.
Ronald Bladen, deceased. Fine Arts.
John McDonald Blakely, professor of materials science and engineering, Cornell University.
Henry David Block, deceased. Computer sc
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https://en.wikipedia.org/wiki/Ariel%20Rubinstein
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Ariel Rubinstein (Hebrew: אריאל רובינשטיין; born April 13, 1951) is an Israeli economist who works in economic theory, game theory and bounded rationality.
Biography
Ariel Rubinstein is a professor of economics at the School of Economics at Tel Aviv University and the Department of Economics at New York University. He studied mathematics and economics at the Hebrew University of Jerusalem, 1972–1979 (B.Sc. Mathematics, Economics and Statistics, 1974;
M.A. Economics, 1975; M.Sc Mathematics, 1976; Ph.D. Economics, 1979).
In 1982, he published "Perfect equilibrium in a bargaining model", an important contribution to the theory of bargaining. The model is known also as a Rubinstein bargaining model. It describes two-person bargaining as an extensive game with perfect information in which the players alternate offers. A key assumption is that the players are impatient. The main result gives conditions under which the game has a unique subgame perfect equilibrium and characterizes this equilibrium.
Honours and awards
Rubinstein was elected a member of the Israel Academy of Sciences and Humanities (1995), a Foreign Honorary Member of the American Academy of Arts and Sciences in (1994) and the American Economic Association (1995). In 1985 he was elected a fellow of the Econometric Society, and served as its president in 2004.
In 2002, he was awarded an honorary doctorate by the Tilburg University.
He has received the Bruno Prize (2000), the Israel Prize for economics (2002),
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https://en.wikipedia.org/wiki/Richard%20Schroeppel
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Richard C. Schroeppel (born 1948) is an American mathematician born in Illinois. His research has included magic squares, elliptic curves, and cryptography. In 1964, Schroeppel won first place in the United States among over 225,000 high school students in the Annual High School Mathematics Examination, a contest sponsored by the Mathematical Association of America and the Society of Actuaries. In both 1966 and 1967, Schroeppel scored among the top 5 in the U.S. in the William Lowell Putnam Mathematical Competition. In 1973 he discovered that there are 275,305,224 normal magic squares of order 5. In 1998–1999 he designed the Hasty Pudding Cipher, which was a candidate for the Advanced Encryption Standard, and he is one of the designers of the SANDstorm hash, a submission to the NIST SHA-3 competition.
Among other contributions, Schroeppel was the first to recognize the sub-exponential running time of certain integer factoring algorithms. While not entirely rigorous, his proof that Morrison and Brillhart's continued fraction factoring algorithm ran in roughly steps was an important milestone in factoring and laid a foundation for much later work, including the current "champion" factoring algorithm, the number field sieve.
Schroeppel analyzed Morrison and Brillhart's algorithm, and saw how to cut the run time to roughly by modifications that allowed sieving. This improvement doubled the size of numbers that could be factored in a given amount of time. Coming around the tim
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https://en.wikipedia.org/wiki/Deadband
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A deadband or dead-band (also known as a dead zone or a neutral zone) is a band of input values in the domain of a transfer function in a control system or signal processing system where the output is zero (the output is 'dead' - no action occurs). Deadband regions can be used in control systems such as servoamplifiers to prevent oscillation or repeated activation-deactivation cycles (called 'hunting' in proportional control systems). A form of deadband that occurs in mechanical systems, compound machines such as gear trains is backlash.
Voltage regulators
In some power substations there are regulators that keep the voltage within certain predetermined limits, but there is a range of voltage in-between during which no changes are made, such as between 112 and 118 volts (the deadband is 6 volts), or between 215 to 225 volts (deadband is 10 volts).
Backlash
Gear teeth with slop (backlash) exhibit deadband. There is no drive from the input to the output shaft in either direction while the teeth are not meshed. Leadscrews generally also have backlash and hence a deadband, which must be taken into account when making position adjustments, especially with CNC systems. If mechanical backlash eliminators are not available, the control can compensate for backlash by adding the deadband value to the position vector whenever direction is reversed.
Hysteresis versus Deadband
Deadband is different from hysteresis. With hysteresis, there is no deadband and so the output is always in
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https://en.wikipedia.org/wiki/Appell%20sequence
|
In mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence satisfying the identity
and in which is a non-zero constant.
Among the most notable Appell sequences besides the trivial example are the Hermite polynomials, the Bernoulli polynomials, and the Euler polynomials. Every Appell sequence is a Sheffer sequence, but most Sheffer sequences are not Appell sequences. Appell sequences have a probabilistic interpretation as systems of moments.
Equivalent characterizations of Appell sequences
The following conditions on polynomial sequences can easily be seen to be equivalent:
For ,
and is a non-zero constant;
For some sequence of scalars with ,
For the same sequence of scalars,
where
For ,
Recursion formula
Suppose
where the last equality is taken to define the linear operator on the space of polynomials in . Let
be the inverse operator, the coefficients being those of the usual reciprocal of a formal power series, so that
In the conventions of the umbral calculus, one often treats this formal power series as representing the Appell sequence . One can define
by using the usual power series expansion of the and the usual definition of composition of formal power series. Then we have
(This formal differentiation of a power series in the differential operator is an instance of Pincherle differentiation.)
In the case of Hermite polynomials, this reduces to the conventional recursion formula for that sequence.
Sub
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https://en.wikipedia.org/wiki/Pr%C3%BCfer%20sequence
|
In combinatorial mathematics, the Prüfer sequence (also Prüfer code or Prüfer numbers) of a labeled tree is a unique sequence associated with the tree. The sequence for a tree on n vertices has length n − 2, and can be generated by a simple iterative algorithm. Prüfer sequences were first used by Heinz Prüfer to prove Cayley's formula in 1918.
Algorithm to convert a tree into a Prüfer sequence
One can generate a labeled tree's Prüfer sequence by iteratively removing vertices from the tree until only two vertices remain. Specifically, consider a labeled tree T with vertices {1, 2, ..., n}. At step i, remove the leaf with the smallest label and set the ith element of the Prüfer sequence to be the label of this leaf's neighbour.
The Prüfer sequence of a labeled tree is unique and has length n − 2.
Both coding and decoding can be reduced to integer radix sorting and parallelized.
Example
Consider the above algorithm run on the tree shown to the right. Initially, vertex 1 is the leaf with the smallest label, so it is removed first and 4 is put in the Prüfer sequence. Vertices 2 and 3 are removed next, so 4 is added twice more. Vertex 4 is now a leaf and has the smallest label, so it is removed and we append 5 to the sequence. We are left with only two vertices, so we stop. The tree's sequence is {4,4,4,5}.
Algorithm to convert a Prüfer sequence into a tree
Let {a[1], a[2], ..., a[n]} be a Prüfer sequence:
The tree will have n+2 nodes, numbered from 1 to n+2.
For
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https://en.wikipedia.org/wiki/Magnetic%20switchable%20device
|
A magnetic switchable device (often called a magnetic base) is a magnetic fixture that uses one or more permanent magnets in a configuration that allows the external field to be turned on or off. They are used in many applications including optics, metalworking, lifting, and robotics, to attach items to metal surfaces in a secure but temporary way.
The magnetic base may have a V cut into the bottom of the base or the back. This V allows the base to be attached to a round bar such as the column of a drill press or a pipe.
One type of magnetic switchable device is made from two blocks of iron, with a round cavity bored through the centre. The halves are joined together with a non-ferrous material such as brass or aluminium. A round permanent magnet is inserted into the bored hole and a handle is attached to allow rotation of the magnet. This act of rotation changes the orientation of the magnetic field.
In the off position, the poles are oriented towards the non-ferrous core. The iron blocks act as keepers by bridging between both poles.
In the on position, the poles are each in one iron half, which then acts as an extension. The field is effectively passing across an air gap (at the base and top). If this gap is bridged with a piece of iron, it becomes part of the magnetic circuit and will be attracted with the full strength of the magnet.
A magnetic base can therefore be attached in a variety of positions to any ferrous surface, allowing the base to be positioned in t
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https://en.wikipedia.org/wiki/Galvanoluminescence
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Galvanoluminescence Is the emission of light produced by the passage of an electric current through an appropriate electrolyte in which an electrode, made of certain metals such as aluminium or tantalum, has been immersed. An example being the electrolysis of sodium bromide (NaBr).
Luminescence
Materials science
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https://en.wikipedia.org/wiki/Locally%20compact%20group
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In mathematics, a locally compact group is a topological group G for which the underlying topology is locally compact and Hausdorff. Locally compact groups are important because many examples of groups that arise throughout mathematics are locally compact and such groups have a natural measure called the Haar measure. This allows one to define integrals of Borel measurable functions on G so that standard analysis notions such as the Fourier transform and spaces can be generalized.
Many of the results of finite group representation theory are proved by averaging over the group. For compact groups, modifications of these proofs yields similar results by averaging with respect to the normalized Haar integral. In the general locally compact setting, such techniques need not hold. The resulting theory is a central part of harmonic analysis. The representation theory for locally compact abelian groups is described by Pontryagin duality.
Examples and counterexamples
Any compact group is locally compact.
In particular the circle group T of complex numbers of unit modulus under multiplication is compact, and therefore locally compact. The circle group historically served as the first topologically nontrivial group to also have the property of local compactness, and as such motivated the search for the more general theory, presented here.
Any discrete group is locally compact. The theory of locally compact groups therefore encompasses the theory of ordinary groups since any group c
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https://en.wikipedia.org/wiki/Hendrik%20Casimir
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Hendrik Brugt Gerhard Casimir (15 July 1909 – 4 May 2000) was a Dutch physicist who made significant contributions to the field of quantum mechanics and quantum electrodynamics. He is best known for his work on the Casimir effect, which describes the attractive force between two uncharged plates in a vacuum due to quantum fluctuations of the electromagnetic field.
Hendrik Casimir is also known for his research on the two-fluid model of superconductors (together with C. J. Gorter) in 1934.
Biography
Casimir was born 15 July 1909. He studied theoretical physics at the University of Leiden under Paul Ehrenfest, where he received his Ph.D. in 1931. His Ph.D. thesis dealt with the quantum mechanics of a rigid spinning body and the group theory of the rotations of molecules. During that time he also spent some time in Copenhagen with Niels Bohr, where he helped Bohr support the latter's hypothesis of the "gunslinger effect" with mock shoot-outs on campus.
From 1932 to mid-1933, Casimir worked as an assistant to Wolfgang Pauli at ETH Zurich. During this period, he worked on the relativistic theory of the electron, in particular, evaluating deviations of the Klein-Nishina equation in the case of bound electrons. To attack the problem, he invented a number of mathematical tools. One in particular is still referred to as the “Casimir Trick": in particle interaction calculations, it is a familiar procedure of trace formation and projections using products of Dirac matrices.
In 1938
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https://en.wikipedia.org/wiki/Biomedical%20cybernetics
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Biomedical cybernetics investigates signal processing, decision making and control structures in living organisms. Applications of this research field are in biology, ecology and health sciences.
Fields
Biological cybernetics
Medical cybernetics
Methods
Connectionism
Decision theory
Information theory
Systeomics
Systems theory
See also
Cybernetics
Prosthetics
List of biomedical cybernetics software
References
Kitano, H. (Hrsg.) (2001). Foundations of Systems Biology. Cambridge (Massachusetts), London, MIT Press, .
External links
ResearchGate topic on biomedical cybernetics
Cybernetics
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https://en.wikipedia.org/wiki/Berezinskii%E2%80%93Kosterlitz%E2%80%93Thouless%20transition
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The Berezinskii–Kosterlitz–Thouless (BKT) transition is a phase transition of the two-dimensional (2-D) XY model in statistical physics. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. Thouless. BKT transitions can be found in several 2-D systems in condensed matter physics that are approximated by the XY model, including Josephson junction arrays and thin disordered superconducting granular films. More recently, the term has been applied by the 2-D superconductor insulator transition community to the pinning of Cooper pairs in the insulating regime, due to similarities with the original vortex BKT transition.
Work on the transition led to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz; Berezinskii died in 1980.
XY model
The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. This system is not expected to possess a normal second-order phase transition. This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size.
This is a specific case of what is called the Mermin–Wagner theorem in spin systems.
Rigorously the transition is not completely understoo
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https://en.wikipedia.org/wiki/Niemeier%20lattice
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In mathematics, a Niemeier lattice is one of the 24
positive definite even unimodular lattices of rank 24,
which were classified by . gave a simplified proof of the classification. In the 1970s, has a sentence mentioning that he found more than 10 such lattices in the 1940s, but gives no further details. One example of a Niemeier lattice is the Leech lattice found in 1967.
Classification
Niemeier lattices are usually labelled by the Dynkin diagram of their
root systems. These Dynkin diagrams have rank either 0 or 24, and all of their components have the same Coxeter number. (The Coxeter number, at least in these cases, is
the number of roots divided by the dimension.) There are exactly 24 Dynkin diagrams with these properties, and there turns out to be a unique Niemeier
lattice for each of these Dynkin diagrams.
The complete list of Niemeier lattices is given in the following table.
In the table,
G0 is the order of the group generated by reflections
G1 is the order of the group of automorphisms fixing all components of the Dynkin diagram
G2 is the order of the group of automorphisms of permutations of components of the Dynkin diagram
G∞ is the index of the root lattice in the Niemeier lattice, in other words, the order of the "glue code". It is the square root of the discriminant of the root lattice.
G0×G1×G2 is the order of the automorphism group of the lattice
G∞×G1×G2 is the order of the automorphism group of the corresponding deep hole.
The neighborhood graph o
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https://en.wikipedia.org/wiki/Genetic%20anthropomorphism
|
In evolutionary biology, genetic anthropomorphism refers to "thinking like a gene". The central question is "if I were a gene, what would I do in order to reproduce myself". The question is an obvious fallacy since genes are incapable of thought. However, natural selection does act in such a way that those that are most successful at reproducing themselves (by following the optimum strategy) prosper. Thinking like a gene enables the results to be visualised. This is related to a philosophical tool known as the intentional stance.
The most notable genetic anthropomorphist was the British biologist, W. D. Hamilton. Hamilton's friend, Richard Dawkins, popularised the idea.
Anthropomorphism has been criticised on a number of grounds, including that it is reductionist.
Evolutionary biology
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https://en.wikipedia.org/wiki/Toru%20Kumon
|
was a Japanese mathematics educator, born in Kōchi Prefecture, Japan. He graduated from the College of Science at Osaka University with a degree in mathematics and taught high school mathematics in his home town of Osaka. In 1954, his son, Takeshi, performed poorly in a Year 2 mathematics test. Prompted by his wife, Teiko, Toru closely examined Takeshi's textbooks and believed they lacked the proper opportunity for a child to practice and master a topic. As a result, he began to handwrite worksheets each day for his son. By the time Takeshi was in Year 6, he was able to solve differential and integral calculus usually seen in the final years of high school. This was the beginning of the Kumon Method of Learning.
As a result of Takeshi's progress, other parents became interested in Kumon's ideas, and in 1955, the first Kumon Center was opened in Osaka, Japan. In 1958, Toru Kumon founded the Kumon Institute of Education, which set the standards for the Kumon Centers that began to open around the world.
The Kumon Programs are designed to strengthen a student's fundamental maths and language skills by studying worksheets tailored to a student's ability. The method also aims for students to learn independently and to study advanced material beyond their school grade level.
Students progress once they demonstrate mastery of a topic. Kumon defined mastery as being able to achieve an excellent score on the material in a given time. Kumon strongly emphasised the concepts of ti
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https://en.wikipedia.org/wiki/Cellularization
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In evolutionary biology, the term cellularization (cellularisation) has been used in theories to explain the evolution of cells, for instance in the pre-cell theory, dealing with the evolution of the first cells on this planet, and in the syncytial theory attempting to explain the origin of Metazoa from unicellular organisms.
Processes of cell development in multinucleate cells (syncytium, plural syncytia) of animals and plants are also termed cellularization, often called syncytium cellularization.
The pre-cell theory
According to Otto Kandler's pre-cell theory, early evolution of life and primordial metabolism (see Iron-Sulfur world hypothesis - metabolism first scenario, according to Wächtershäuser) led to the early diversification of life through the evolution of a multiphenotypical population of pre-cells, from which the three founder groups A, B, C and then, from them, the precursor cells (here named proto-cells) of the three domains of life emerged successively.
In this scenario the three domains of life did not originate from an ancestral nearly complete “first cell“ nor a cellular organism often defined as the last universal common ancestor (LUCA), but from a population of evolving pre-cells. Kandler introduced the term cellularization for his concept of a successive evolution of cells by a process of evolutionary improvements.
His concept may explain the quasi-random distribution of evolutionarily important features among the three domains and, at the same ti
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https://en.wikipedia.org/wiki/Robinson%20annulation
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The Robinson annulation is a chemical reaction used in organic chemistry for ring formation. It was discovered by Robert Robinson in 1935 as a method to create a six membered ring by forming three new carbon–carbon bonds. The method uses a ketone and a methyl vinyl ketone to form an α,β-unsaturated ketone in a cyclohexane ring by a Michael addition followed by an aldol condensation. This procedure is one of the key methods to form fused ring systems.
Formation of cyclohexenone and derivatives are important in chemistry for their application to the synthesis of many natural products and other interesting organic compounds such as antibiotics and steroids. Specifically, the synthesis of cortisone is completed through the use of the Robinson annulation.
The initial paper on the Robinson annulation was published by William Rapson and Robert Robinson while Rapson studied at Oxford with professor Robinson. Before their work, cyclohexenone syntheses were not derived from the α,β-unsaturated ketone component. Initial approaches coupled the methyl vinyl ketone with a naphthol to give a naphtholoxide, but this procedure was not sufficient to form the desired cyclohexenone. This was attributed to unsuitable conditions of the reaction.
Robinson and Rapson found in 1935 that the interaction between cyclohexanone and α,β-unsaturated ketone afforded the desired cyclohexenone. It remains one of the key methods for the construction of six membered ring compounds. Since it is so widely used
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https://en.wikipedia.org/wiki/Evolutionary%20arms%20race
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In evolutionary biology, an evolutionary arms race is an ongoing struggle between competing sets of co-evolving genes, phenotypic and behavioral traits that develop escalating adaptations and counter-adaptations against each other, resembling the geopolitical concept of an arms race. These are often described as examples of positive feedback. The co-evolving gene sets may be in different species, as in an evolutionary arms race between a predator species and its prey (Vermeij, 1987), or a parasite and its host. Alternatively, the arms race may be between members of the same species, as in the manipulation/sales resistance model of communication (Dawkins & Krebs, 1979) or as in runaway evolution or Red Queen effects. One example of an evolutionary arms race is in sexual conflict between the sexes, often described with the term Fisherian runaway. Thierry Lodé emphasized the role of such antagonistic interactions in evolution leading to character displacements and antagonistic coevolution.
Symmetrical versus asymmetrical arms races
Arms races may be classified as either symmetrical or asymmetrical. In a symmetrical arms race, selection pressure acts on participants in the same direction. An example of this is trees growing taller as a result of competition for light, where the selective advantage for either species is increased height. An asymmetrical arms race involves contrasting selection pressures, such as the case of cheetahs and gazelles, where cheetahs evolve to be
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https://en.wikipedia.org/wiki/Parasite%20load
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Parasite load is a measure of the number and virulence of the parasites that a host organism harbours. Quantitative parasitology deals with measures to quantify parasite loads in samples of hosts and to make statistical comparisons of parasitism across host samples.
In evolutionary biology, parasite load has important implications for sexual selection and the evolution of sex, as well as openness to experience.
Infection and distribution
A single parasite species usually has an aggregated distribution across host individuals, which means that most hosts harbor few parasites, while a few hosts carry the vast majority of parasite individuals. This poses considerable problems for students of parasite ecology: use of parametric statistics should be avoided. Log-transformation of data before the application of parametric test, or the use of non-parametric statistics is often recommended. However, this can give rise to further problems. Therefore, modern day quantitative parasitology is based on more advanced biostatistical methods.
In vertebrates, males frequently carry higher parasite loads than females. Differences in movement patterns, habitat choice, diet, body size, and ornamentation are all thought to contribute to this sex bias observed in parasite loads. Often males have larger habitat ranges and thus are likely to encounter more parasite-dense areas than female conspecifics. Whenever sexual dimorphism is exhibited in species, the larger sex is thought to tolerate
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https://en.wikipedia.org/wiki/Solvolysis
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In chemistry, solvolysis is a type of nucleophilic substitution (S1/S2) or elimination where the nucleophile is a solvent molecule. Characteristic of S1 reactions, solvolysis of a chiral reactant affords the racemate. Sometimes however, the stereochemical course is complicated by intimate ion pairs, whereby the leaving anion remains close to the carbocation, effectively shielding it from an attack by the nucleophile. Particularly fast reactions can occur by neighbour group participation, with nonclassical ions as intermediates or transition states.
Examples
For certain nucleophiles, solvolysis reactions are classified. Solvolysis involving water is called hydrolysis. Related terms are alcoholysis (alcohols) and specifically methanolysis (methanol), acetolysis, ammonolysis (ammonia), and aminolysis (alkyl amines). Glycolysis is however an older term for the multistep conversion of glucose to pyruvate.
Hydrolysis
While solvolysis often refers to an organic chemistry context, hydrolysis is common throughout inorganic chemistry, where aqua complexes of metal ions react with solvent molecules due to the Lewis acidity of the metal center. For example, aqueous solutions of aluminium chloride are acidic due to the aqua-aluminium complex losing protons to water molecules, giving hydronium ions which lowers the pH.
In organic chemistry, hydrolysis reactions often give two fragments from an initial substrate. For example, the hydrolysis of amides give carboxylic acids and amines; t
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https://en.wikipedia.org/wiki/Intimate%20ion%20pair
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In chemistry, the intimate ion pair concept, introduced by Saul Winstein, describes the interactions between a cation, anion and surrounding solvent molecules. In ordinary aqueous solutions of inorganic salts, an ion is completely solvated and shielded from the counterion. In less polar solvents, two ions can still be connected to some extent. In a tight, intimate, or contact ion pair, there are no solvent molecules between the two ions. When solvation increases, ionic bonding decreases and a loose or solvent-shared ion pair results. The ion pair concept explains stereochemistry in solvolysis.
The concept of intimate ion pairs is used to explain the slight tendency for inversion of stereochemistry during an S1 reaction. It is proposed that solvent or other ions in solution may assist in the removal of a leaving group to form a carbocation which reacts in an S1 fashion; similarly, the leaving group may associate loosely with the cationic intermediate. The association of solvent or an ion with the leaving group effectively blocks one side of the incipient carbocation, while allowing the backside to be attacked by a nucleophile. This leads to a slight excess of the product with inverted stereochemistry, whereas a purely S1 reaction should lead to a racemic product. Intimate ion pairs are also invoked in the Si mechanism. Here, part of the leaving group detaches and attacks from the same face, leading to retention.
See also
Ion association
Asymmetric ion-pairing catalysis
Re
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https://en.wikipedia.org/wiki/Ajoene
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Ajoene is an organosulfur compound found in garlic (Allium sativum) extracts. It is a colorless liquid that contains sulfoxide and disulfide functional groups. The name (and pronunciation) is derived from "ajo", the Spanish word for garlic. It is found as a mixture of up to four stereoisomers, which differ in terms of the stereochemistry of the central alkene (E- vs Z-) and the chirality of the sulfoxide sulfur (R- vs S-).
History and syntheses
The structure of ajoene was determined and it was synthesized based on biosynthetic considerations in 1984, correcting an incorrect structure published in 1983. A short, scalable total synthesis of ajoene was reported in 2018 by Wirth and coworkers while a biosynthetically modeled synthesis of trifluoroajoene from difluoroallicin was published in 2017. Syntheses of various ajoene analogues have also been reported. The chemistry of ajoene has been extensively investigated.
When a garlic clove is crushed or finely chopped, allicin is released, with subsequent formation of ajoene when the material is dissolved in various solvents including edible oils. Ajoene is also found in garlic extract. Ajoene is most stable and most abundant in macerate of garlic (chopped garlic in edible oil).
The reaction sequence that forms ajoene (2 in the diagram) involves two molecules of allicin. First, one allicin molecule (1 in the diagram) fragments to form 2-propenesulfenic acid and thioacrolein. These two react in separate stages with another allicin
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https://en.wikipedia.org/wiki/Method%20of%20undetermined%20coefficients
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In mathematics, the method of undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and recurrence relations. It is closely related to the annihilator method, but instead of using a particular kind of differential operator (the annihilator) in order to find the best possible form of the particular solution, an ansatz or 'guess' is made as to the appropriate form, which is then tested by differentiating the resulting equation. For complex equations, the annihilator method or variation of parameters is less time-consuming to perform.
Undetermined coefficients is not as general a method as variation of parameters, since it only works for differential equations that follow certain forms.
Description of the method
Consider a linear non-homogeneous ordinary differential equation of the form
where denotes the i-th derivative of , and denotes a function of .
The method of undetermined coefficients provides a straightforward method of obtaining the solution to this ODE when two criteria are met:
are constants.
g(x) is a constant, a polynomial function, exponential function , sine or cosine functions or , or finite sums and products of these functions (, constants).
The method consists of finding the general homogeneous solution for the complementary linear homogeneous differential equation
and a particular integral of the linear non-homogeneous ordinary differential equation based on . Then th
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https://en.wikipedia.org/wiki/Antrum
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This is a disambiguation page for the biological term. For the 2018 horror movie, see Antrum (film)
In biology, antrum is a general term for a cavity or chamber, which may have specific meaning in reference to certain organs or sites in the body.
In vertebrates, it may refer specifically to:
Antrum follicularum, the cavity in the epithelium that envelops the oocyte
Mastoid antrum, a cavity between the middle ear and temporal bone in the skull
Stomach antrum, either
Pyloric antrum, the lower portion of the stomach. This is what is usually referred to as "antrum" in stomach-related topics
or Antrum cardiacum, a dilation that occurs in the esophagus near the stomach (forestomach)
Maxillary antrum or antrum of Highmore, the maxillary sinus, a cavity in the maxilla and the largest of the paranasal sinuses
In invertebrates, it may refer specifically to:
Antrum of female lepidoptera genitalia
Anatomy
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https://en.wikipedia.org/wiki/Philip%20Hall
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Philip Hall FRS (11 April 1904 – 30 December 1982), was an English mathematician. His major work was on group theory, notably on finite groups and solvable groups.
Biography
He was educated first at Christ's Hospital, where he won the Thompson Gold Medal for mathematics, and later at King's College, Cambridge. He was elected a Fellow of the Royal Society in 1951 and awarded its Sylvester Medal in 1961. He was President of the London Mathematical Society in 1955–1957, and awarded its Berwick Prize in 1958 and De Morgan Medal in 1965.
Publications
See also
Abstract clone
Commutator collecting process
Isoclinism of groups
Regular p-group
Three subgroups lemma
Hall algebra, and Hall polynomials
Hall subgroup
Hall–Higman theorem
Hall–Littlewood polynomial
Hall's universal group
Hall's marriage theorem
Hall word
Hall–Witt identity
Irwin–Hall distribution
Zappa–Szép product
References
1904 births
1982 deaths
20th-century English mathematicians
Algebraists
Group theorists
People educated at Christ's Hospital
Alumni of King's College, Cambridge
Fellows of the Royal Society
Bletchley Park people
Presidents of the London Mathematical Society
Sadleirian Professors of Pure Mathematics
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https://en.wikipedia.org/wiki/Heinz%20Pr%C3%BCfer
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Ernst Paul Heinz Prüfer (10 November 1896 – 7 April 1934) was a German Jewish mathematician born in Wilhelmshaven. His major contributions were on abelian groups, graph theory, algebraic numbers, knot theory and Sturm–Liouville theory.
In 1915 he began his university studies in mathematics, Physics and Chemistry in Berlin. After that he started his doctorate degree with Issai Schur as his advisor at Friedrich Wilhelm University, Berlin. In 1921 he obtained his doctorate degree. His thesis was named Unendliche Abelsche Gruppen von Elementen endlicher Ordnung (Infinite abelian groups of elements of finite order). This thesis set the road for his contributions on abelian groups. In 1922 he worked with mathematician Paul Koebe in the University of Jena, and in 1923 he obtained tenure and was at this university until 1927. In that year he moved to Münster University where he worked until the end of his life. His final work was about projective geometry, but it was posthumously completed by his students Gustav Fleddermann and Gottfried Köthe.
Heinz Prüfer was married, but never had children. He died prematurely at 37 years of age in 1934 in Münster Germany, due to lung cancer.
Mathematical contributions
Heinz Prüfer created the following mathematical notions that were later named after him:
Prüfer sequence (also known as a Prüfer code; it has broad applications in graph theory and network theory).
Prüfer domain. Also see Bézout domain, which is a Prüfer domain
Prüfer rank
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https://en.wikipedia.org/wiki/Ticket%20lock
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In computer science, a ticket lock is a synchronization mechanism, or locking algorithm, that is a type of spinlock that uses "tickets" to control which thread of execution is allowed to enter a critical section.
Overview
The basic concept of a ticket lock is similar to the ticket queue management system. This is the method that many bakeries and delis use to serve customers in the order that they arrive, without making them stand in a line. Generally, there is some type of dispenser from which customers pull sequentially numbered tickets upon arrival. The dispenser usually has a sign above or near it stating something like "Please take a number". There is also typically a dynamic sign, usually digital, that displays the ticket number that is now being served. Each time the next ticket number (customer) is ready to be served, the "Now Serving" sign is incremented and the number called out. This allows all of the waiting customers to know how many people are still ahead of them in the queue or line.
Like this system, a ticket lock is a first in first out (FIFO) queue-based mechanism. It adds the benefit of fairness of lock acquisition and works as follows; there are two integer values which begin at 0. The first value is the queue ticket, the second is the dequeue ticket. The queue ticket is the thread's position in the queue, and the dequeue ticket is the ticket, or queue position, that now has the lock (Now Serving).
When a thread arrives, it atomically obtains
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https://en.wikipedia.org/wiki/Zerah%20Colburn
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Zerah Colburn may refer to:
Zerah Colburn (mental calculator) (1804–1840), American mathematics prodigy
Zerah Colburn (locomotive designer) (1832–1870), American steam locomotive designer and railroad author
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https://en.wikipedia.org/wiki/1023%20%28number%29
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1023 (one thousand [and] twenty-three) is the natural number following 1022 and preceding 1024.
In mathematics
1023 is the tenth Mersenne number of the form .
In binary, it is also the tenth repdigit 11111111112 as all Mersenne numbers in decimal are repdigits in binary.
It is equal to the sum of five consecutive prime numbers 193 + 197 + 199 + 211 + 223.
It is the number of three-dimensional polycubes with 7 cells.
1023 is the number of elements in the 9-simplex, as well as the number of uniform polytopes in the tenth-dimensional hypercubic family , and the number of noncompact solutions in the family of paracompact honeycombs that shares symmetries with .
In other fields
Computing
Floating-point units in computers often run a IEEE 754 64-bit, floating-point excess-1023 format in 11-bit binary. In this format, also called binary64, the exponent of a floating-point number (e.g. 1.009001 E1031) appears as an unsigned binary integer from 0 to 2047, where subtracting 1023 from it gives the actual signed value.
1023 is the number of dimensions or length of messages of an error-correcting Reed-Muller code made of 64 block codes.
Technology
The Global Positioning System (GPS) works on a ten-digit binary counter that runs for 1023 weeks, at which point an integer overflow causes its internal value to roll over to zero again.
1023 being , is the maximum number that a 10-bit ADC converter can return when measuring the highest voltage in range.
See also
The year AD 1023
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https://en.wikipedia.org/wiki/Feit%E2%80%93Thompson%20theorem
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In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved by .
History
conjectured that every nonabelian finite simple group has even order. suggested using the centralizers of involutions of simple groups as the basis for the classification of finite simple groups, as the Brauer–Fowler theorem shows that there are only a finite number of finite simple groups with given centralizer of an involution. A group of odd order has no involutions, so to carry out Brauer's program it is first necessary to show that non-cyclic finite simple groups never have odd order. This is equivalent to showing that odd order groups are solvable, which is what Feit and Thompson proved.
The attack on Burnside's conjecture was started by , who studied CA groups; these are groups such that the Centralizer of every non-trivial element is Abelian. In a pioneering paper he showed that all CA groups of odd order are solvable. (He later classified all the simple CA groups, and more generally all simple groups such that the centralizer of any involution has a normal 2-Sylow subgroup, finding an overlooked family of simple groups of Lie type in the process, that are now called Suzuki groups.)
extended Suzuki's work to the family of CN groups; these are groups such that the Centralizer of every non-trivial element is Nilpotent. They showed that every CN group of odd order is solvable. Their proof is similar to Suzuki's p
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https://en.wikipedia.org/wiki/Larkin%20Kerwin
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John Larkin Kerwin (June 22, 1924 – May 1, 2004) was a Canadian physicist.
Born in Quebec City, he studied physics at St. Francis Xavier University and obtained his master's degree in physics at the Massachusetts Institute of Technology. His received his D.Sc. from Université Laval. He was Chairman of the Department of Physics from 1961 to 1967. He was the first lay Rector of Université Laval, holding this position from 1972 to 1977.
From 1954 to 1955 he was the president of the Canadian Association of Physicists. From 1980 to 1989 he was President of the National Research Council of Canada and was the first president of the Canadian Space Agency and coined the term Canadarm. In 1982 he received the Gold Medal from the Canadian Council of Professional Engineers. In 1987 he was awarded the Outstanding Achievement Award of the Public Service of Canada. In 1989 he was president of the Canadian Academy of Engineering. Kerwin also served at an international level, he was president of the International Union of Pure and Applied Physics (IUPAP) from 1987–1990.
In 1976, he received an honorary doctorate from Concordia University, one of 15 from various universities. In 1978 he was made an Officer of the Order of Canada and was promoted to Companion in 1980. In 1988 he was made an Officer of the National Order of Quebec. He was elected Fellow of the Royal Society of Canada and was president from 1976 to 1977. He was made an Officer of the Légion d'honneur de France.
He died in Qu
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https://en.wikipedia.org/wiki/Robert%20Plot
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Robert Plot (13 December 1640 – 30 April 1696) was an English naturalist, first Professor of Chemistry at the University of Oxford, and the first keeper of the Ashmolean Museum.
Early life and education
Born in Borden, Kent to parents Robert Plot and Elisabeth Patenden, and baptised on 13 December 1640, Plot was educated at the Wye Free School in Kent. He entered Magdalen Hall, Oxford in 1658 where he graduated with a BA in 1661 and an MA in 1664. Plot subsequently taught and served as dean and vice principal at Magdalen Hall while preparing for his BCL and DCL, which he received in 1671 before moving to University College in 1676.
Natural history and chemistry
By this time, Plot had already developed an interest in the systematic study of natural history and antiquities. In June 1674, with patronage from John Fell, the bishop of Oxford, and Ralph Bathurst, vice-chancellor of the university, Plot began studying and collecting artefacts throughout the nearby countryside, publishing his findings three years later in The Natural History of Oxford-shire. In this work, he described and illustrated various rocks, minerals and fossils, including the first known illustration of a dinosaur bone which he attributed to a giant human (later recognised as the femur of a Megalosaurus), but believed that most fossils were not remains of living organisms but rather crystallisations of mineral salts with a coincidental zoological form.
The favourable reception of his findings not only ea
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https://en.wikipedia.org/wiki/Rick%20Sternbach
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Richard Michael Sternbach (born 1951) is an illustrator who is best known for his space illustrations and his work on the Star Trek television series.
Early years
Born in Bridgeport, Connecticut, in 1969 Sternbach enrolled at the University of Connecticut with an art major, but after a couple of years switched to marine biology. After leaving University, he became an illustrator for books and magazines, with his first cover illustration published on the October 1973 issue of Analog magazine. Sternbach became a friend of science fiction writer Greg Bear, after his illustration of "A Martian Ricorso" featured in the cover of the February 1976 issue of Analog.
During 1974 to 1976 he produced several original works of art for the Gengras Planetarium, part of the Children's Museum of West Hartford, in Connecticut. The works included airbrush paintings of the Earth as a primeval planet. It is unknown if these works are still in possession of CMWH, the original owner and client of Sternbach.
In 1976 he helped found the Association of Science Fiction and Fantasy Artists (ASFA), to give legal advice to science fiction and fantasy artists on contracts and copyrights.
In 1977, inspired by the story of artist Ralph McQuarrie's move from working in the aerospace industry to working for George Lucas on Star Wars, Sternbach moved to California to seek illustration work in the film and television industry.
Movie work
After some work for Disney and PBS, in April 1978, Sternbach was of
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https://en.wikipedia.org/wiki/Robotrek
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Robotrek, known in Japan as , is a role-playing video game (RPG) for the Super Nintendo Entertainment System (SNES). It was developed by Quintet and published by Enix in both Japan and North America in 1994. Set on the fictional planet Quintenix, the game puts the player in control of a budding robotics expert who is the son of a famous inventor.
As its Japanese name implies, Robotrek was intended as a humorous game. Designed to appeal to a younger audience, Robotrek'''s main focus is on allowing the player to raise up to three robots which are built from spare parts that may be found, gained through battles, or generated by the player by means of the game's item combination system.Robotrek sold poorly and was given mostly average reviews upon its release. The game's combination of traditional RPG mechanics with the ability to build customizable robots and invent items was positively received. Mixed criticism was directly at its graphics, music, and overall presentation. Some sources have noted gameplay similarities between Robotrek and the later released Pokémon and Robopon RPG franchises.
GameplayRobotrek has similar gameplay to that of most RPG video games, with the notable exception that the main character is not the combatant; rather, the robots he invents are, making it more similar to Pokémon and Dragon Quest Monsters. The robots are highly customizable, in aspects such as equipment, special attacks, body color and name. The player is allowed to build a maximum of th
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https://en.wikipedia.org/wiki/Edge-of-the-wedge%20theorem
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In mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the same continuous function on the edge. It is used in quantum field theory to construct the analytic continuation of Wightman functions. The formulation and the first proof of the theorem were presented by Nikolay Bogoliubov at the International Conference on Theoretical Physics, Seattle, USA (September, 1956) and also published in the book Problems in the Theory of Dispersion Relations. Further proofs and generalizations of the theorem were given by R. Jost and H. Lehmann (1957), F. Dyson (1958), H. Epstein (1960), and by other researchers.
The one-dimensional case
Continuous boundary values
In one dimension, a simple case of the edge-of-the-wedge theorem can be stated as follows.
Suppose that f is a continuous complex-valued function on the complex plane that is holomorphic on the upper half-plane, and on the lower half-plane. Then it is holomorphic everywhere.
In this example, the two wedges are the upper half-plane and the lower half plane, and their common edge is the real axis. This result can be proved from Morera's theorem. Indeed, a function is holomorphic provided its integral round any contour vanishes; a contour which crosses the real axis can be broken up into contours in the upper and lower half-planes and the integral round these vanishes by hypothesis.
Distrib
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https://en.wikipedia.org/wiki/Scorpionate%20ligand
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In coordination chemistry, a scorpionate ligand is a tridentate (three-donor-site) ligand that binds to a central atom in a fac manner. The most popular class of scorpionates are the hydrotris(pyrazolyl)borates or Tp ligands. These were also the first to become popular. These ligands first appeared in journals in 1966 from the then little-known DuPont chemist of Ukrainian descent, Swiatoslaw Trofimenko. Trofimenko called this discovery "a new and fertile field of remarkable scope".
The term scorpionate comes from the fact that the ligand can bind a metal with two donor sites like the pincers of a scorpion; the third and final donor site reaches over the plane formed by the metal and the other two donor atoms to bind to the metal. The binding can be thought of as being like a scorpion grabbing the metal with two pincers before stinging it.
While many scorpionate ligands are of the Tp class, many other scorpionate ligands are known. For example, the Tm and tripodal phosphine classes have an equally good claim to be scorpionate ligands. Many of the scorpionate ligands have a central boron atom which bears a total of four groups, but it is possible to create ligands which use other central atoms.
Homoscorpionates vs. heteroscorpionates
Trofimenko's initial work in the field was with the homoscorpionates where three pyrazolyl groups are attached to a boron. Since this work a range of ligands have been reported where more than one type of metal binding group is attached to the
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https://en.wikipedia.org/wiki/Direction%20of%20arrival
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In signal processing, direction of arrival (DOA) denotes the direction from which usually a propagating wave arrives at a point, where usually a set of sensors are located. These set of sensors forms what is called a sensor array. Often there is the associated technique of beamforming which is estimating the signal from a given direction. Various engineering problems addressed in the associated literature are:
Find the direction relative to the array where the sound source is located
Direction of different sound sources around you are also located by you using a process similar to those used by the algorithms in the literature
Radio telescopes use these techniques to look at a certain location in the sky
Recently beamforming has also been used in radio frequency (RF) applications such as wireless communication. Compared with the spatial diversity techniques, beamforming is preferred in terms of complexity. On the other hand, beamforming in general has much lower data rates. In multiple access channels (code-division multiple access (CDMA), frequency-division multiple access (FDMA), time-division multiple access (TDMA)), beamforming is necessary and sufficient
Various techniques for calculating the direction of arrival, such as angle of arrival (AoA), time difference of arrival (TDOA), frequency difference of arrival (FDOA), or other similar associated techniques.
Limitations on the accuracy of estimation of direction of arrival signals in digital antenna arrays are associated
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https://en.wikipedia.org/wiki/Biological%20psychiatry
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Biological psychiatry or biopsychiatry is an approach to psychiatry that aims to understand mental disorder in terms of the biological function of the nervous system. It is interdisciplinary in its approach and draws on sciences such as neuroscience, psychopharmacology, biochemistry, genetics, epigenetics and physiology to investigate the biological bases of behavior and psychopathology. Biopsychiatry is the branch of medicine which deals with the study of the biological function of the nervous system in mental disorders.
There is some overlap with neurology, which focuses on disorders where gross or visible pathology of the nervous system is apparent, such as epilepsy, cerebral palsy, encephalitis, neuritis, Parkinson's disease and multiple sclerosis. There is also some overlap with neuropsychiatry, which typically deals with behavioral disturbances in the context of apparent brain disorder. In contrast biological psychiatry describes the basic principles and then delves deeper into various disorders. It is structured to follow the organisation of the DSM-IV, psychiatry's primary diagnostic and classification guide. The contributions of this field explore functional neuroanatomy, imaging, and neuropsychology and pharmacotherapeutic possibilities for depression, anxiety and mood disorders, substance abuse and eating disorders, schizophrenia and psychotic disorders, and cognitive and personality disorders.
Biological psychiatry and other approaches to mental illness are not
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https://en.wikipedia.org/wiki/Adrian%20Bejan
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Adrian Bejan is a Romanian-American professor who has made contributions to modern thermodynamics and developed his constructal law. He is J. A. Jones Distinguished Professor of Mechanical Engineering at Duke University and author of the books Design in Nature, The Physics of Life , Freedom and Evolution and Time And Beauty: Why Time Flies And Beauty Never Dies
Early life and education
Bejan was born in Galaţi, a city on the Danube in Romania.
His mother, Marioara Bejan (1914–1998), was a pharmacist. His father, Dr. Anghel Bejan (1910–1976), was a veterinarian. Bejan showed an early talent in drawing, and his parents enrolled him in art school. He also excelled in basketball, which earned him a position on the Romanian national basketball team.
At age 19 Bejan won a scholarship to the United States and entered Massachusetts Institute of Technology in Cambridge, Massachusetts. In 1972 he was awarded BS and MS degrees as a member of the Honors Course in Mechanical Engineering. He graduated in 1975 with a PhD from MIT with a thesis titled "Improved thermal design of the cryogenic cooling system for a superconducting synchronous generator". His advisor was Joseph L. Smith Jr.
Career
From 1976 to 1978 Bejan was a Miller research fellow in at the University of California Berkeley working with Chang-Lin Tien. In 1978 he moved to Colorado and joined the faculty of the Department of Mechanical Engineering at the University of Colorado in Boulder. In 1982 Bejan published his first
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https://en.wikipedia.org/wiki/Miguel%20Nicolelis
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Miguel Ângelo Laporta Nicolelis, M.D., Ph.D. (, born March 7, 1961), is a Brazilian scientist, physician and Duke School of Medicine Professor in Neuroscience at Duke University, best known for his pioneering work surrounding brain-computer interface (also known as "brain-machine interface") technology.
Biography
Nicolelis holds a medical degree from the University of São Paulo (1984), a doctorate in Sciences (General Physiology) from the University of São Paulo (1989) and a PhD in Physiology and Biophysics from Hahnemann University (now Drexel University College of Medicine). He is a full professor in the Department of Neurobiology and Co-Director of the Neuroengineering Center at Duke University (USA). Founder of the Alberto Santos Dumont Association for Research Support (AASDAP) and the Santos Dumont Institute (ISD), he proposed the use of science as an agent of social and economic transformation. Nicolelis is a Researcher at the International Institute of Neurosciences Edmond and Lily Safra (IIN-ELS) and Coordinator of the Andar de Novo Project, developed at AASDAP in São Paulo.
He and his colleagues at Duke University implanted electrode arrays into a monkey's brain that were able to detect the monkey's motor intent and thus able to control reaching and grasping movements performed by a robotic arm. This was possible by decoding signals of hundreds of neurons recorded in volitional areas of the cerebral cortex while the monkey played with a hand-held joystick to move
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https://en.wikipedia.org/wiki/Narrabri%20Stellar%20Intensity%20Interferometer
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The Narrabri Stellar Intensity Interferometer (NSII) was the first astronomical instrument to measure the diameters of a large number of stars at visible wavelengths. It was designed by (amongst others) Robert Hanbury Brown, who received the Hughes Medal in 1971 for this work. It was built by University of Sydney School of Physics and was located near the town of Narrabri in north-central New South Wales, Australia. Many of the components were constructed in the UK. The design was based on an earlier optical intensity interferometer built by Hanbury Brown and Richard Q. Twiss at Jodrell Bank in the UK. Whilst the original device had a maximum baseline of 10m, the NSII device consisted of a large circular track that allowed the detectors to be separated from 10 to 188m. The NSII operated from 1963 until 1974, and was used to measure the angular diameters of 32 stars.
See also
Lists of telescopes
References
The angular diameters of 32 stars, Mon. Not. R. Astron. Soc. Volume 167 pp 121–136 (1974)
Hanbury Brown R, The intensity interferometer – its application to astronomy, Taylor & Francis, 1974
Telescopes
Interferometric telescopes
Science and technology in New South Wales
Astronomical observatories in New South Wales
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https://en.wikipedia.org/wiki/Integral%20%28disambiguation%29
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Integral is a concept in calculus.
Integral may also refer to:
in mathematics
Integer, a number
Integral symbol
Integral (measure theory), or Lebesgue integration
Integral element
in computer science
Integral data type, a data type that represents some range of mathematical integers
in philosophy and spirituality
Integral humanism (India), political philosophy in Hindu nationalism
Integral theory, an area of discourse emanating from Ken Wilber's thought on spiritual evolution, methodology and ontology. Also known under other names, including integral philosophy, integral worldview, etc.
Integral Culture, transmodern subculture referred to by sociologist Paul H. Ray
as a proper name
INTEGRAL, the International Gamma-Ray Astrophysics Laboratory
Intégral: The Journal of Applied Musical Thought, a music-theory journal
"Integral (song)", a Pet Shop Boys song from Fundamental
The Integral, a glass spaceship in Yevgeny Zamyatin's novel We
Integral (horse), a British Thoroughbred racehorse
Integral, an extended play by The Sixth Lie
Integral (album)
Integral (train), diesel multiple unit train type
See also
Integralism, ideology according to which a nation is an organic unity
Integrality, in commutative algebra, the notions of an element integral over a ring
Integration (disambiguation)
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https://en.wikipedia.org/wiki/Initiation%20%28chemistry%29
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In chemistry, initiation is a chemical reaction that triggers one or more secondary reactions. Initiation creates a reactive centre on a molecule which produces a chain reaction. The reactive centre generated by initiation is usually a radical, but can also be cations or anions. Once the reaction is initiated, the species goes through propagation where the reactive species reacts with stable molecules, producing stable species and reactive species. This process can produce very long chains of molecules called polymers, which are the building blocks for many materials. After propagation, the reaction is then terminated. There are different types of initiation, with the two main ways being thermal initiation and photo-initiation (light).
Thermal initiation
Thermal initiation involves initiating a reaction in the presence of heat, usually at very high temperatures. Heating a reaction can result in radical initiation of the substrate(s). In the presence of heat, a monomer can self-initiate and react with other monomers or pairs of monomers. This process is called spontaneous polymerization and requires a lot of heat to occur (up to 200°C). For monomers to initiate and polymerize with the same type of monomer (called Homopolymerization), ~180°C is needed for the monomers to initiate. Copolymerization, which is when different kinds of monomers are initiated and react with each other, is more stable and can happen at lower temperatures than Homopolymerization. Self-initiation betw
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https://en.wikipedia.org/wiki/Ketone%20halogenation
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In organic chemistry, α-keto halogenation is a special type of halogenation.
The reaction may be carried out under either acidic or basic conditions in an aqueous medium with the corresponding elemental halogen. In this way, chloride, bromide, and iodide (but notably not fluoride) functionality can be inserted selectively in the alpha position of a ketone.
The position alpha to the carbonyl group () in a ketone is easily halogenated. This is due to its ability to form an enolate () in basic solution, or an enol () in acidic solution. An example of alpha halogenation is the mono-bromination of acetone (), carried out under either acidic or basic conditions, to give bromoacetone:
Acidic (in acetic acid):
Basic (in aqueous NaOH):
In acidic solution, usually only one alpha hydrogen is replaced by a halogen, as each successive halogenation is slower than the first. The halogen decreases the basicity of the carbonyl oxygen, thus making protonation less favorable. However, in basic solutions, successive halogenation is more rapid due to inductive electron withdrawal by the halogen. This makes the remaining hydrogens more acidic. In the case of methyl ketones, this reaction often occurs a third time to form a ketone trihalide, which can undergo rapid substitution with water to form a carboxylate () in what is known as the haloform reaction.
The regioselectivity also differs: The halogenation of an unsymmetrical ketone in acid results in the more substituted alkyl group being ha
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https://en.wikipedia.org/wiki/Moshe%20Wolman
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Moshe Wolman (November 10, 1914 – September 5, 2009) was an Israeli neuropathologist. He is considered one of the fathers of histochemistry. In 1954, he described Wolman's disease.
Biography
Moshe Wolman was born in 1914 in Warsaw, Poland. He immigrated to Mandate Palestine in 1925. He grew up in Tel Aviv and graduated from the prestigious Herzliya Gymnasium (academic secondary school). He studied medicine in Italy (Florence 1932-1935 and Rome, 1935–1938). In 1939, he married Brigitte "Bigi" Koebbel with whom he had four children: filmmaker Dan Wolman, philosopher Ruth Manor (1944–2005), psychiatrist Naomi Oren, and composer Amnon Wolman.
Medical career
From 1938 to 1940, he worked in the Cancer Research Institute of the Hebrew University and did residency at the department of Internal Medicine of the Hadassah Hospital. In the 1940s, he volunteered to serve in the British Army and joined the 101 Military Mission (the famous Gideon Force of Orde Wingate). He was involved in the operation in 1941 that brought Emperor Haile Selassie back to occupied Ethiopia and was in charge of a medical ward and clinical laboratory in the Menelik Hospital in Addis Ababa in 1941-1944. In 1944, he was posted in the Central Pathology Laboratory of the Middle East Forces located in Cairo, Egypt. In 1945 he was appointed as head of the Pathology Laboratory of the 27th General Hospital in Tel-El-Kabir, Egypt.
After his release from the army in 1946, Wolman joined the department of Pathology of
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https://en.wikipedia.org/wiki/Electrophilic%20halogenation
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In organic chemistry, an electrophilic aromatic halogenation is a type of electrophilic aromatic substitution. This organic reaction is typical of aromatic compounds and a very useful method for adding substituents to an aromatic system.
A few types of aromatic compounds, such as phenol, will react without a catalyst, but for typical benzene derivatives with less reactive substrates, a Lewis acid is required as a catalyst. Typical Lewis acid catalysts include , , and . These work by forming a highly electrophilic complex which is attacked by the benzene ring.
Reaction mechanism
The reaction mechanism for chlorination of benzene is the same as bromination of benzene. Iron(III) bromide and iron(III) chloride become inactivated if they react with water, including moisture in the air. Therefore, they are generated by adding iron filings to bromine or chlorine. Here is the mechanism of this reaction:
The mechanism for iodination is slightly different: iodine (I2) is treated with an oxidizing agent such as nitric acid to obtain the electrophilic iodine ("I+", probably IONO2). Other conditions for iodination include I2, HIO3, H2SO4, and N-iodosuccinimide, H2SO4. These conditions are successful for highly deactivated arenes, including nitroaromatics.
In a series of studies, the powerful reagent obtained by using a mixture of iodine and potassium iodate dissolved in concentrated sulfuric acid was used. Here the iodinating agent is the triiodine cation I3+ and the base is HSO4−
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https://en.wikipedia.org/wiki/Clugston%20Group
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The Clugston Group was a privately owned business involved in construction and civil engineering, property development and logistics. The group was based in Scunthorpe, North Lincolnshire in England. On 5 December 2019, the group and its construction businesses filed for administration, with debts of £64m.
History
The company was founded by Leonard Clugston in 1937 in Lincolnshire, as Clugston Cawood. Initially, it pioneered the development and use of recycled blast furnace slag from Scunthorpe’s iron and steel plants. This was used in the construction of runways for the RAF in the Second World War, and led the company into civil engineering, road construction and the building of sea defences on the east coast.
In June 2009, the then company CEO Stephen Martin went 'undercover' at the company for the television series of Channel 4, Undercover Boss.
Martin described the experience as extremely positive, and implemented a number of new measures as a result. In February 2017, Martin left to become director general of the Institute of Directors, and was replaced by Bob Vickers (formerly a director of Carillion Construction Services). Vickers resigned as CEO in June 2019; Glynn Thomas became interim CEO.
Administration
The company filed a notice of intention to appoint administrators from KPMG on 5 December 2019, for Clugston Group Ltd, Clugston Construction Ltd and Clugston Services Ltd. The group reportedly collapsed owing over £40m (a figure later revised to £64m), and was
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https://en.wikipedia.org/wiki/Complete%20active%20space
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In quantum chemistry, a complete active space is a type of classification of molecular orbitals. Spatial orbitals are classified as belonging to three classes:
core, always hold two electrons
active, partially occupied orbitals
virtual, always hold zero electrons
This classification allows one to develop a set of Slater determinants for the description of the wavefunction as a linear combination of these determinants. Based on the freedom left for the occupation in the active orbitals, a certain number of electrons are allowed to populate all the active orbitals in appropriate combinations, developing a finite-size space of determinants. The resulting wavefunction is of multireference nature, and is blessed by additional properties if compared to other selection schemes.
The active classification can theoretically be extended to all the molecular orbitals, to obtain a full CI treatment. In practice, this choice is limited, due to the high computational cost needed to optimize a large CAS wavefunction on medium and large molecular systems.
A Complete Active Space wavefunction is used to obtain a first approximation of the so-called static correlation, which represents the contribution needed to describe bond dissociation processes correctly. This requires a wavefunction that includes a set of electronic configurations with high and very similar importance. Dynamic correlation, representing the contribution to the energy brought by the instantaneous interaction between e
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https://en.wikipedia.org/wiki/Sch%C3%B6niger%20oxidation
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In chemistry, the Schöniger oxidation (also known as the Schöniger flask test or the oxygen flask method) is a method of elemental analysis developed by Wolfgang Schöniger.
The test is conducted in an Erlenmeyer flask, or in a separatory funnel. It involves the combustion of a sample in pure oxygen, followed by the absorption of the combustion products by a solution of sodium hydroxide.
It allows quantitative determination of elemental chlorine, nitrogen and sulfur in a sample.
References
Further reading
Chemical tests
Elemental analysis
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https://en.wikipedia.org/wiki/Juda%20Hirsch%20Quastel
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Juda Hirsch Quastel, (October 2, 1899 – October 15, 1987) was a British-Canadian biochemist who pioneered diverse research in neurochemistry, soil metabolism, cellular metabolism, and cancer.
Biography
Quastel, also known as "Harry" or "Q," was born at Ecclesall Road in Sheffield the son of Jonas Quastel, a confectioner, and his wife, Flora Itcovitz. His parents had come to Britain in 1897 from Tarnopol in Galicia (Eastern Europe) and were married in Britain. He was named after his grandfather,
Juda Quastel, a chemist in Tarnapol.
He was educated at Sheffield Central Secondary School. In the First World War, he served with the British Army as a Laboratory Assistant at St George's Hospital from 1917 to 1919.
Electing to study chemistry, Quastel received a baccalaureate from Imperial College London in 1921. Pursuing graduate work at the University of Cambridge, Quastel studied with Frederick Gowland Hopkins, the leading figure in British biochemistry and a future Nobel Prize recipient for his work on the nutritional importance of vitamins. Under Hopkins, Quastel received a Doctor of Philosophy degree from the University of Cambridge in biochemistry in 1924 and, not long after, was made a Fellow of Trinity College, Cambridge.
Quastel remained in Hopkins’ department as a demonstrator and lecturer from 1923 to 1929, during which he pioneered the research of microbial enzymology. He obtained a doctorate of science from Cambridge in 1926 and received a Beit Memorial Fellowship
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https://en.wikipedia.org/wiki/Accretion%20%28astrophysics%29
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In astrophysics, accretion is the accumulation of particles into a massive object by gravitationally attracting more matter, typically gaseous matter, into an accretion disk. Most astronomical objects, such as galaxies, stars, and planets, are formed by accretion processes.
Overview
The accretion model that Earth and the other terrestrial planets formed from meteoric material was proposed in 1944 by Otto Schmidt, followed by the protoplanet theory of William McCrea (1960) and finally the capture theory of Michael Woolfson. In 1978, Andrew Prentice resurrected the initial Laplacian ideas about planet formation and developed the modern Laplacian theory. None of these models proved completely successful, and many of the proposed theories were descriptive.
The 1944 accretion model by Otto Schmidt was further developed in a quantitative way in 1969 by Viktor Safronov. He calculated, in detail, the different stages of terrestrial planet formation. Since then, the model has been further developed using intensive numerical simulations to study planetesimal accumulation. It is now accepted that stars form by the gravitational collapse of interstellar gas. Prior to collapse, this gas is mostly in the form of molecular clouds, such as the Orion Nebula. As the cloud collapses, losing potential energy, it heats up, gaining kinetic energy, and the conservation of angular momentum ensures that the cloud forms a flattened disk—the accretion disk.
Accretion of galaxies
A few hundred thou
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https://en.wikipedia.org/wiki/%C3%81lvaro%20de%20Campos
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Álvaro de Campos (; October 15, 1890 – November 30, 1935) was one of the poet Fernando Pessoa's various heteronyms, widely known by his powerful and wrathful writing style. According to his author, this alter ego was born in Tavira, Portugal, studied mechanical engineering and finally graduated in ship engineering in Glasgow. After a journey in Ireland, Campos sailed to the Orient and wrote his poem "Opiario" in the Suez Canal "onboard". He worked in 'Barrow-on-Furness' (sic) (which Pessoa wrote a poem about) and Newcastle-on-Tyne (1922). Unemployed, Campos returned to Lisbon in 1926 (he wrote then the poem "Lisbon Revisited"), where he lived ever since. He was born in October, 1890, but Pessoa didn't put an end to the life of Campos, so he would have survived his author who died in November, 1935. Campos' works may be split in three phases: the decadent phase, the futuristic phase and the decadent (sad) phase. He chose Whitman and Marinetti as masters, showing some similarities with their works, mainly in the second phase: hymns like "Ode Triunfal", "Ode Marítima", and "Ultimatum" praise the power of the rising technology, the strength of the machines, the dark side of the industrial civilization, and an enigmatic love for the machines. The first phase (marked by the poem Opiário) shared some of its pessimism with Pessoa's friend Mário de Sá-Carneiro, one of his co-workers in Orpheu magazine. In the last phase, Pessoa drops the mask, and reveals through Campos all the empti
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https://en.wikipedia.org/wiki/Boris%20Tsirelson
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Boris Semyonovich Tsirelson (May 4, 1950 – January 21, 2020) (, ) was a Russian–Israeli mathematician and Professor of Mathematics at Tel Aviv University in Israel, as well as a Wikipedia editor.
Biography
Tsirelson was born in Leningrad to a Russian Jewish family. From his father Simeon's side, he was the great-nephew of rabbi Yehuda Leib Tsirelson, chief rabbi of Bessarabia from 1918 to 1941, and a prominent posek and Jewish leader. He obtained his Master of Science from the University of Leningrad and remained there to pursue graduate studies. He obtained his Ph.D. in 1975, with thesis "General properties of bounded Gaussian processes and related questions" written under the direction of Ildar Abdulovich Ibragimov.
Later, he participated in the refusenik movement, but only received permission to emigrate to Israel in 1991. From then until 2017, he was a professor at Tel-Aviv University.
In 1998 he was an Invited Speaker at the International Congress of Mathematicians in Berlin.
Contributions to mathematics
Tsirelson made notable contributions to probability theory and functional analysis. These include:
Tsirelson's bound, in quantum mechanics, is an inequality, related to the issue of quantum nonlocality.
Tsirelson space is an example of a reflexive Banach space in which neither a l p space nor a c0 space can be embedded.
The Tsirelson's drift, a counterexample in the theory of stochastic differential equations, it's a SDE which has a weak solution but no strong s
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https://en.wikipedia.org/wiki/Green%20computing
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Green computing, green IT (Information Technology), or ICT sustainability, is the study and practice of environmentally sustainable computing or IT.
The goals of green computing are similar to green chemistry: reduce the use of hazardous materials, maximize energy efficiency during the product's lifetime, increase the recyclability or biodegradability of defunct products and factory waste. Green computing is important for all classes of systems, ranging from handheld systems to large-scale data centers. Many corporate IT departments have green computing initiatives to reduce the environmental effect of their IT operations. Yet it is also clear that the environmental footprint of the sector is significant, estimated at 5-9% of the world's total electricity use and more than 2% of all emissions. Data centres and telecommunications will need to become more energy efficient, reuse waste energy, and use more renewable energy sources to stay competitive. Some believe they can and should become climate neutral by 2030.
Origins
In 1992, the U.S. Environmental Protection Agency launched Energy Star, a voluntary labeling program that is designed to promote and recognize the energy efficiency in monitors, climate control equipment, and other technologies. This resulted in the widespread adoption of sleep mode among consumer electronics. Concurrently, the Swedish organization TCO Development launched the TCO Certified program to promote low magnetic and electrical emissions from CRT-b
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https://en.wikipedia.org/wiki/NCSE
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NCSE may refer to:
Education
National Center for Science Education, United States, promotes the teaching of evolutionary biology and climate science
National Council for Special Education, Ireland, supports students with disabilities
National Certificate of Secondary Education, Trinidad and Tobago, a school qualification
Other
Cognistat, formerly known as the Neurobehavioral Cognitive Status Examination (NCSE), a cognitive screening test
National Council for Science and the Environment, United States, a business-research alliance for environmental policy
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https://en.wikipedia.org/wiki/Margaret%20Harrington
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Margaret Helen Harrington (born October 4, 1945) is a Canadian teacher and former politician in Ontario, Canada. She was a New Democratic Party member of the Legislative Assembly of Ontario from 1990 to 1995.
Background
Harrington was educated at Queen's University in Kingston, Ontario, receiving a Bachelor of Science degree in Biochemistry. She worked as a secondary school teacher in Niagara Falls after her graduation, and served as city councillor of the Niagara Falls City Council. In 1988, she was named Niagara Falls Woman of the Year. Her husband, Dick Harrington, ran for the federal and provincial New Democratic Party on three occasions. She and her husband had two children, Kevin and Jennifer.
Politics
Harrington ran for the Ontario legislature in the 1987 provincial election, and finished second against Liberal Vince Kerrio in the riding of Niagara Falls. She lost by 5,664 votes. Three years later, in the 1990 provincial election, she defeated Liberal candidate Wayne Campbell by almost 6,000 votes in the same riding. The NDP won a majority government and Harrington was appointed as parliamentary assistant to the Minister of Housing from 1990 to 1993. She was then appointed as a Deputy Speaker.
Shortly after the election, Harrington was accused of improprieties on voting day. She admitted to improperly adding two names to the voter's list. She claimed that she was mistaken about the rules for adding names to the list. The Ontario Elections Act states people may be a
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https://en.wikipedia.org/wiki/Strain%20theory
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Strain theory can refer to;
In chemistry:
Baeyer strain theory
In social sciences:
Strain theory (sociology), the theory that social structures within society may pressure citizens to commit crime
Value-added theory, the assumption that certain conditions are needed for the development of a social movement
See also
General strain theory, a theory of criminology developed by Robert Agnew
Role strain, a concept in role theory in sociology
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https://en.wikipedia.org/wiki/Mapping%20cylinder
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In mathematics, specifically algebraic topology, the mapping cylinder of a continuous function between topological spaces and is the quotient
where the denotes the disjoint union, and ∼ is the equivalence relation generated by
That is, the mapping cylinder is obtained by gluing one end of to via the map . Notice that the "top" of the cylinder is homeomorphic to , while the "bottom" is the space . It is common to write for , and to use the notation or for the mapping cylinder construction. That is, one writes
with the subscripted cup symbol denoting the equivalence. The mapping cylinder is commonly used to construct the mapping cone , obtained by collapsing one end of the cylinder to a point. Mapping cylinders are central to the definition of cofibrations.
Basic properties
The bottom Y is a deformation retract of .
The projection splits (via ), and the deformation retraction is given by:
(where points in stay fixed because for all ).
The map is a homotopy equivalence if and only if the "top" is a strong deformation retract of . An explicit formula for the strong deformation retraction can be worked out.
Examples
Mapping cylinder of a fiber bundle
For a fiber bundle with fiber , the mapping cylinder
has the equivalence relation
for . Then, there is a canonical map sending a point
to the point , giving a fiber bundle
whose fiber is the cone . To see this, notice the fiber over a point is the quotient space
where every point in is equivalent.
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https://en.wikipedia.org/wiki/Prime%20model
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In mathematics, and in particular model theory, a prime model is a model that is as simple as possible. Specifically, a model is prime if it admits an elementary embedding into any model to which it is elementarily equivalent (that is, into any model satisfying the same complete theory as ).
Cardinality
In contrast with the notion of saturated model, prime models are restricted to very specific cardinalities by the Löwenheim–Skolem theorem. If is a first-order language with cardinality and is a complete theory over then this theorem guarantees a model for of cardinality Therefore no prime model of can have larger cardinality since at the very least it must be elementarily embedded in such a model. This still leaves much ambiguity in the actual cardinality. In the case of countable languages, all prime models are at most countably infinite.
Relationship with saturated models
There is a duality between the definitions of prime and saturated models. Half of this duality is discussed in the article on saturated models, while the other half is as follows. While a saturated model realizes as many types as possible, a prime model realizes as few as possible: it is an atomic model, realizing only the types that cannot be omitted and omitting the remainder. This may be interpreted in the sense that a prime model admits "no frills": any characteristic of a model that is optional is ignored in it.
For example, the model is a prime model of the theory of the natural
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https://en.wikipedia.org/wiki/Louis%20M%C3%A9nard
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Louis-Nicolas Ménard (19 October 1822 – 9 February 1901) was a French man of letters also known for his early discoveries on collodion.
Biography
He was born in Paris. His versatile genius occupied itself in turn with chemistry, poetry, painting and history. In 1843 he published, under the pseudonym of L. de Senneville, a translation of Prométhée délivré. Turning to chemistry, he discovered collodion in 1846, but its value was not recognized at the time; and its application later to surgery and photography brought him no advantage.
Ménard was a socialist, always in advance of the reform movements of his time. After 1848 he was condemned to imprisonment for his Prologue d'une révolution. He escaped to London, returning to Paris only in 1852. Until 1860 he occupied himself with classical studies, the fruits of which are to be seen in his Poèmes (1855), Polythéisme hellénique (1863), and two academic theses, De sacra poesi graecorum and La Morale avant les philosophes (1860).
The next ten years Ménard spent chiefly among the Barbizon artists, and he exhibited several pictures. He was in London at the time of the Paris Commune, and defended it with his pen. In 1887 he became professor at the École des Arts décoratifs, and in 1895 professor of universal history at the Hôtel de Ville in Paris. Ménard died in Paris on 9 February 1901.
His works include: Histoire des anciens peuples de l'Orient (1882); Histoire des Israélites d'après l'exégèse biblique (1883), and Histoire des Gr
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https://en.wikipedia.org/wiki/Thane%20Gustafson
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Thane Gustafson (born 1944) is a professor of political science at Georgetown University, Washington, D.C., United States. He specializes in comparative politics and the political history of Russia and the former USSR.
Gustafson holds degrees in both political science and chemistry from the University of Illinois, and a doctorate from Harvard University. He is a former professor at Harvard, and a former analyst for RAND Corporation. He is Senior Director of Russian and Caspian Energy for IHS Cambridge Energy Research Associates (IHS CERA).
Gustafson is the author of Capitalism Russian Style, Crisis amid Plenty: The Politics of Soviet Energy under Brezhnev and Gorbachev (which was awarded the Marshall Shulman Book Prize as the best book on Soviet affairs), coauthor (with Daniel Yergin) of Russia 2010 and What It Means for the World, and Wheel of Fortune: The Battle for Oil and Power in Russia. Served as a Peace Corps volunteer in Côte d'Ivoire From 1966 to 1968 with his wife Ruth Gustafson.
Works
Capitalism Russian-style Cambridge, England ; New York : Cambridge University Press, 1999.
Wheel of fortune : the battle for oil and power in Russia, Cambridge, Massachusetts ; London, England : The Belknap Press of Harvard University Press, 2012.
Crisis amid plenty., Princeton University Press, 2016.
The Bridge Harvard University Press, 2020.
Klimat: Russia in the Age of Climate Change. Harvard University Press, 2021.
References
External links
Living people
Georgetown
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https://en.wikipedia.org/wiki/Multimap
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In computer science, a multimap (sometimes also multihash, multidict or multidictionary) is a generalization of a map or associative array abstract data type in which more than one value may be associated with and returned for a given key. Both map and multimap are particular cases of containers (for example, see C++ Standard Template Library containers). Often the multimap is implemented as a map with lists or sets as the map values.
Examples
In a student enrollment system, where students may be enrolled in multiple classes simultaneously, there might be an association for each enrollment of a student in a course, where the key is the student ID and the value is the course ID. If a student is enrolled in three courses, there will be three associations containing the same key.
The index of a book may report any number of references for a given index term, and thus may be coded as a multimap from index terms to any number of reference locations or pages.
Querystrings may have multiple values associated with a single field. This is commonly generated when a web form allows multiple check boxes or selections to be chosen in response to a single form element.
Language support
C++
C++'s Standard Template Library provides the multimap container for the sorted multimap using a self-balancing binary search tree, and SGI's STL extension provides the hash_multimap container, which implements a multimap using a hash table.
As of C++11, the Standard Template Library provides the u
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https://en.wikipedia.org/wiki/Nettie%20Stevens
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Nettie Maria Stevens (July 7, 1861 – May 4, 1912) was an American geneticist who discovered sex chromosomes. In 1905, soon after the rediscovery of Mendel's paper on genetics in 1900, she observed that male mealworms produced two kinds of sperm, one with a large chromosome and one with a small chromosome. When the sperm with the large chromosome fertilized eggs, they produced female offspring, and when the sperm with the small chromosome fertilized eggs, they produced male offspring. The pair of sex chromosomes that she studied later became known as the X and Y chromosomes.
Early life
Nettie Maria Stevens was born on July 7, 1861, in Cavendish, Vermont, to Julia (née Adams) and Ephraim Stevens. In 1863, after the death of her mother, her father remarried and the family moved to Westford, Massachusetts. Her father worked as a carpenter and earned enough money to provide Nettie and her sister, Emma, with a strong education through high school.
Education
During her education, Stevens was near the top of her class. She and her sister Emma were 2 of the 3 women to graduate from Westford Academy between 1872 and 1883. After graduating in 1880, Stevens moved to Lebanon, New Hampshire to teach high school zoology, physiology, mathematics, English, and Latin. After three years, she returned to Vermont to continue her studies.
Stevens continued her education at Westfield Normal School (now Westfield State University) She completed the four-year course in two years and graduated with
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https://en.wikipedia.org/wiki/Mereotopology
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In formal ontology, a branch of metaphysics, and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts.
History and motivation
Mereotopology begins in philosophy with theories articulated by A. N. Whitehead in several books and articles he published between 1916 and 1929, drawing in part on the mereogeometry of De Laguna (1922). The first to have proposed the idea of a point-free definition of the concept of topological space in mathematics was Karl Menger in his book Dimensionstheorie (1928) -- see also his (1940). The early historical background of mereotopology is documented in Bélanger and Marquis (2013) and Whitehead's early work is discussed in Kneebone (1963: ch. 13.5) and Simons (1987: 2.9.1). The theory of Whitehead's 1929 Process and Reality augmented the part-whole relation with topological notions such as contiguity and connection. Despite Whitehead's acumen as a mathematician, his theories were insufficiently formal, even flawed. By showing how Whitehead's theories could be fully formalized and repaired, Clarke (1981, 1985) founded contemporary mereotopology. The theories of Clarke and Whitehead are discussed in Simons (1987: 2.10.2), and Lucas (2000: ch. 10). The entry Whitehead's point-free geometry includes two contemporary treatments of Whitehead's theories, due to Giangiacomo Gerla, each different from the
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https://en.wikipedia.org/wiki/Edmund%20Beecher%20Wilson
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Edmund Beecher Wilson (October 19, 1856 – March 3, 1939) was a pioneering American zoologist and geneticist. He wrote one of the most influential textbooks in modern biology, The Cell. He discovered the chromosomal XY sex-determination system in 1905—that human males have XY and females XX sex chromosomes. Nettie Stevens independently made the same discovery the same year and published shortly thereafter.
Career
Wilson was born in Geneva, Illinois, the son of Isaac G. Wilson, a judge, and his wife, Carioline Clark.
He graduated from Yale University in biology in 1878. He earned his Ph.D. in biology at Johns Hopkins in 1881.
He was a lecturer at Williams College in 1883–84 and at the Massachusetts Institute of Technology in 1884–85. He served as professor of biology at Bryn Mawr College from 1885 to 1891.
In 1888, he was elected as a member to the American Philosophical Society.
He spent the balance of his career at Columbia University where he was successively adjunct professor of biology (1891–94), professor of invertebrate zoology (1894–1897), and professor of zoology (from 1897).
Wilson is credited as America's first cell biologist. In 1898 he used the similarity in embryos to describe phylogenetic relationships. By observing spiral cleavage in molluscs, flatworms and annelids he concluded that the same organs came from the same group of cells and concluded that all these organisms must have a common ancestor. He was elected a Fellow of the American Academy of Arts
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https://en.wikipedia.org/wiki/Abiotic%20component
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In biology and ecology, abiotic components or abiotic factors are non-living chemical and physical parts of the environment that affect living organisms and the functioning of ecosystems. Abiotic factors and the phenomena associated with them underpin biology as a whole. They affect a plethora of species, in all forms of environmental conditions, such as marine or land animals. Humans can make or change abiotic factors in a species' environment. For instance, fertilizers can affect a snail's habitat, or the greenhouse gases which humans utilize can change marine pH levels.
Abiotic components include physical conditions and non-living resources that affect living organisms in terms of growth, maintenance, and reproduction. Resources are distinguished as substances or objects in the environment required by one organism and consumed or otherwise made unavailable for use by other organisms.
Component degradation of a substance occurs by chemical or physical processes, e.g. hydrolysis. All non-living components of an ecosystem, such as atmospheric conditions and water resources, are called abiotic components.
Factors
In biology, abiotic factors can include water, light, radiation, temperature, humidity, atmosphere, acidity, salinity, precipitation altitude, minerals, tides, rain, dissolved oxygen nutrients, and soil. The macroscopic climate often influences each of the above. Pressure and sound waves may also be considered in the context of marine or sub-terrestrial environm
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https://en.wikipedia.org/wiki/Pullback%20bundle
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In mathematics, a pullback bundle or induced bundle is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle and a continuous map one can define a "pullback" of by as a bundle over . The fiber of over a point in is just the fiber of over . Thus is the disjoint union of all these fibers equipped with a suitable topology.
Formal definition
Let be a fiber bundle with abstract fiber and let be a continuous map. Define the pullback bundle by
and equip it with the subspace topology and the projection map given by the projection onto the first factor, i.e.,
The projection onto the second factor gives a map
such that the following diagram commutes:
If is a local trivialization of then is a local trivialization of where
It then follows that is a fiber bundle over with fiber . The bundle is called the pullback of E by or the bundle induced by . The map is then a bundle morphism covering .
Properties
Any section of over induces a section of , called the pullback section , simply by defining
for all .
If the bundle has structure group with transition functions (with respect to a family of local trivializations ) then the pullback bundle also has structure group . The transition functions in are given by
If is a vector bundle or principal bundle then so is the pullback . In the case of a principal bundle the right action of on is given by
It then follows that the map covering is equivariant and so defines a
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https://en.wikipedia.org/wiki/AA%20tree
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An AA tree in computer science is a form of balanced tree used for storing and retrieving ordered data efficiently. AA trees are named after their originator, Swedish computer scientist Arne Andersson.
AA trees are a variation of the red–black tree, a form of binary search tree which supports efficient addition and deletion of entries. Unlike red–black trees, red nodes on an AA tree can only be added as a right subchild. In other words, no red node can be a left sub-child. This results in the simulation of a 2–3 tree instead of a 2–3–4 tree, which greatly simplifies the maintenance operations. The maintenance algorithms for a red–black tree need to consider seven different shapes to properly balance the tree:
An AA tree on the other hand only needs to consider two shapes due to the strict requirement that only right links can be red:
Balancing rotations
Whereas red–black trees require one bit of balancing metadata per node (the color), AA trees require O(log(log(N))) bits of metadata per node, in the form of an integer "level". The following invariants hold for AA trees:
The level of every leaf node is one.
The level of every left child is exactly one less than that of its parent.
The level of every right child is equal to or one less than that of its parent.
The level of every right grandchild is strictly less than that of its grandparent.
Every node of level greater than one has two children.
A link where the child's level is equal to that of its parent is call
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