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https://en.wikipedia.org/wiki/Traffic%20equations | In queueing theory, a discipline within the mathematical theory of probability, traffic equations are equations that describe the mean arrival rate of traffic, allowing the arrival rates at individual nodes to be determined. Mitrani notes "if the network is stable, the traffic equations are valid and can be solved."
Jackson network
In a Jackson network, the mean arrival rate at each node i in the network is given by the sum of external arrivals (that is, arrivals from outside the network directly placed onto node i, if any), and internal arrivals from each of the other nodes on the network. If external arrivals at node i have rate , and the routing matrix is P, the traffic equations are, (for i = 1, 2, ..., m)
This can be written in matrix form as
and there is a unique solution of unknowns to this equation, so the mean arrival rates at each of the nodes can be determined given knowledge of the external arrival rates and the matrix P. The matrix I − P is surely non-singular as otherwise in the long run the network would become empty.
Gordon–Newell network
In a Gordon–Newell network there are no external arrivals, so the traffic equations take the form (for i = 1, 2, ..., m)
Notes
Queueing theory |
https://en.wikipedia.org/wiki/Masanori%20Ohya | is a Japanese mathematician.
After he received a Ph.D. in Mathematical Physics and Information Science and Dr.Sc., he continuously worked on operator algebra, quantum entropy, quantum information theory and bio-information. He achieved results in the fields of quantum information and mathematical physics. In particular, he proposed his version of quantum mutual entropy. Note this quantity is not the same as Holevo's chi quantity or coherent information, though each of them plays important role in quantum information theory. The information theoretic meaning of Ohya's quantum mutual information is still obscure.
He also proposed 'Information Dynamics' and 'Adaptive Dynamics', which he applied to the study of chaos theory, quantum information and biosciences as related fields.
Main research
Ohya studied multiple topics for more than thirty years, relating to quantum entropy, quantum information, chaos dynamics and life science. His main accomplishments are as follows:
Elucidation of Mathematical Bases of Quantum Channels,
Formulation of Quantum Mutual Information (Entropy),
Information Dynamics,
Analysis of Quantum Teleportation,
Quantum Algorithm,
Proposal of Adaptive Dynamics,
Applications to the life sciences.
They are explained in this book .
Academic and other appointments
Academic Appointments:
1987–present: Professor, Department of Information Sciences, Tokyo University of Science
2004–2006 Dean, Graduate School of Science and Technology, Tokyo University of Science
2002–2006 Committee, International Institute of Advanced Study in Kyoto
2006–present: Dean, Science and Technology, Tokyo University of Science
Università di Roma II, Copernicus University, Jena University and many others.
Member of the Editorial Board of International Journals:
Infinite Dimensional Analysis, Quantum Probability and Related Topics;
Reports on Mathematical Physics;
Editor-in-chief of the Editorial Board of the journal Open Systems & Information Dynamics
Amino Acid
Books (English only)
M.Ohya and D. Petz (1993) Quantum Entropy and its Use, Springer-Verlag, TMP Series.
R.S.Ingarden, A.Kossakowski and M.Ohya (1997), Information Dynamics and Open Systems, Kluwer Academic Publishers.
M.Ohya (1999), Mathematical foundation of quantum computer, Maruzen Publishing Company.
References
External links
Web page at Tokyo University of Science
20th-century Japanese mathematicians
21st-century Japanese mathematicians
1947 births
Living people |
https://en.wikipedia.org/wiki/Naturalizer | Naturalizer may refer to:
in mathematics, the naturalizer of an infranatural transformation
Naturalizer, a shoe brand of Caleres |
https://en.wikipedia.org/wiki/Semiorder | In order theory, a branch of mathematics, a semiorder is a type of ordering for items with numerical scores, where items with widely differing scores are compared by their scores and where scores within a given margin of error are deemed incomparable. Semiorders were introduced and applied in mathematical psychology by as a model of human preference. They generalize strict weak orderings, in which items with equal scores may be tied but there is no margin of error. They are a special case of partial orders and of interval orders, and can be characterized among the partial orders by additional axioms, or by two forbidden four-item suborders.
Utility theory
The original motivation for introducing semiorders was to model human preferences without assuming that incomparability is a transitive relation. For instance, suppose that , , and represent three quantities of the same material, and that is larger than by the smallest amount that is perceptible as a difference, while is halfway between the two of them. Then, a person who desires more of the material would prefer to , but would not have a preference between the other two pairs. In this example, and are incomparable in the preference ordering, as are and , but and are comparable, so incomparability does not obey the transitive law.
To model this mathematically, suppose that objects are given numerical utility values, by letting be any utility function that maps the objects to be compared (a set ) to real numbers. Set a numerical threshold (which may be normalized to 1) such that utilities within that threshold of each other are declared incomparable, and define a binary relation on the objects, by setting whenever . Then forms a semiorder.
If, instead, objects are declared comparable whenever their utilities differ, the result would be a strict weak ordering, for which incomparability of objects (based on equality of numbers) would be transitive.
Axiomatics
A semiorder, defined from a utility function as above, is a partially ordered set with the following two properties:
Whenever two disjoint pairs of elements are comparable, for instance as and , there must be an additional comparison among these elements, because would imply while would imply . Therefore, it is impossible to have two mutually incomparable two-point linear orders.
If three elements form a linear ordering , then every fourth point must be comparable to at least one of them, because would imply while would imply , in either case showing that is comparable to or to . So it is impossible to have a three-point linear order with a fourth incomparable point.
Conversely, every finite partial order that avoids the two forbidden four-point orderings described above can be given utility values making it into a semiorder.
Therefore, rather than being a consequence of a definition in terms of utility, these forbidden orderings, or equivalent systems of axioms, can be taken as a combinatorial definition of semi |
https://en.wikipedia.org/wiki/Heterogeneity%20%28disambiguation%29 | Heterogeneity is a diverseness of constituent structure.
Heterogeneity or heterogeneous may also refer to:
Data analysis
Heterogeneity in statistics
Heterogeneity in economics
Study heterogeneity, a concept in statistics
Heterogeneous relation
Biology and medicine
Heterogeneous conditions in medicine are those conditions which have several causes/etiologies
A heterogeneous taxon, a taxon that contains a great variety of individuals or sub-taxa; usually this implies that the taxon is an artificial grouping
Genetic heterogeneity, multiple origins causing the same disorder in different individuals.
Allelic heterogeneity, different mutations at the same locus causing the same disorder.
Chemistry
A heterogeneous reaction, a reaction in chemical kinetics that takes place at the interface of two or more phases, i.e. between a solid and a gas, a liquid and a gas, or a solid and a liquid
A heterogeneous catalysis, one in which the catalyst is in a different phase from the substrate
Ecology
Heterogeneity in landscape ecology, the measure of how different parts of a landscape are from one another.
Computer science
Heterogeneous computing, electronic systems that utilize a variety of different types of computational units
Semantic heterogeneity, where there are differences in meaning and interpretation across data sources and datasets
A data resource with multiple types of formats.
See also
Homogeneity and heterogeneity
Homogeneity (disambiguation)
Degeneracy |
https://en.wikipedia.org/wiki/Heptellated%208-simplexes | In eight-dimensional geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations (heptellation) from the regular 8-simplex.
There are 35 unique heptellations for the 8-simplex, including all permutations of truncations, cantellations, runcinations, sterications, pentellations, and hexications. The simplest heptellated 8-simplex is also called an expanded 8-simplex, with only the first and last nodes ringed, is constructed by an expansion operation applied to the regular 8-simplex. The highest form, the heptihexipentisteriruncicantitruncated 8-simplex is more simply called a omnitruncated 8-simplex with all of the nodes ringed.
Heptellated 8-simplex
Alternate names
Expanded 8-simplex
Small exated enneazetton (soxeb) (Jonathan Bowers)
Coordinates
The vertices of the heptellated 8-simplex can bepositioned in 8-space as permutations of (0,1,1,1,1,1,1,1,2). This construction is based on facets of the heptellated 9-orthoplex.
A second construction in 9-space, from the center of a rectified 9-orthoplex is given by coordinate permutations of:
(1,-1,0,0,0,0,0,0,0)
Root vectors
Its 72 vertices represent the root vectors of the simple Lie group A8.
Images
Omnitruncated 8-simplex
The symmetry order of an omnitruncated 8-simplex is 725760. The symmetry of a family of a uniform polytopes is equal to the number of vertices of the omnitruncation, being 362880 (9 factorial) in the case of the omnitruncated 8-simplex; but when the CD symbol is palindromic, the symmetry order is doubled, 725760 here, because the element corresponding to any element of the underlying 8-simplex can be exchanged with one of those corresponding to an element of its dual.
Alternate names
Heptihexipentisteriruncicantitruncated 8-simplex
Great exated enneazetton (goxeb) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the omnitruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,1,2,3,4,5,6,7,8). This construction is based on facets of the heptihexipentisteriruncicantitruncated 9-orthoplex, t0,1,2,3,4,5,6,7{37,4}
Images
Permutohedron and related tessellation
The omnitruncated 8-simplex is the permutohedron of order 9. The omnitruncated 8-simplex is a zonotope, the Minkowski sum of nine line segments parallel to the nine lines through the origin and the nine vertices of the 8-simplex.
Like all uniform omnitruncated n-simplices, the omnitruncated 8-simplex can tessellate space by itself, in this case 8-dimensional space with three facets around each ridge. It has Coxeter-Dynkin diagram of .
Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. |
https://en.wikipedia.org/wiki/Bernard%20Teissier | Bernard Teissier (; born 1945) is a French mathematician and a member of the Nicolas Bourbaki group. He has made major contributions to algebraic geometry and commutative algebra, specifically to singularity theory, multiplicity theory and valuation theory.
Teissier attained his doctorate from Paris Diderot University in 1973, under supervision of Heisuke Hironaka. He was a member and a leading figure of Nicolas Bourbaki. Along with Alain Connes, he gave the 1975/1976 Peccot Lectures. He was an invited speaker at the International Congress of Mathematics at Warsaw in 1983.
In 2012, he became a fellow of the American Mathematical Society.
References
External links
Website
1945 births
Living people
20th-century French mathematicians
21st-century French mathematicians
University of Paris alumni
Fellows of the American Mathematical Society
Nicolas Bourbaki |
https://en.wikipedia.org/wiki/All-Ireland%20Senior%20Football%20Championship%20records%20and%20statistics | This article contains records and statistics related to the All-Ireland Senior Football Championship, which has run since 1887.
General performances
a. London received a bye to the final in five seasons.
Provincial titles
Counties
By decade
The most successful team of each decade, judged by number of All-Ireland titles, is as follows:
1890s: 6 for Dublin (1891-92-94-97-98-99)
1900s: 5 for Dublin (1901-02-06-07-08)
1910s: 4 for Wexford (1915-16-17-18)
1920s: 3 each for Dublin (1921-22-23) and Kerry (1924-26-29)
1930s: 5 for Kerry (1930-31-32-37-39)
1940s: 3 for Kerry (1940-41-46)
1950s: 3 for Kerry (1953-55-59)
1960s: 3 each for Down (1960-61-68) and Galway (1964-65-66)
1970s: 4 for Kerry (1970-75-78-79)
1980s: 5 for Kerry (1980-81-84-85-86)
1990s: 2 each for Down (1991-94) and Meath (1996–99)
2000s: 5 for Kerry (2000-04-06-07-09)
2010s: 7 for Dublin (2011-13-15-16-17-18-19)
2020s: 1 each for Dublin (2020), Tyrone (2021) and Kerry (2022)
Consecutive wins
Sextuple
Dublin (2015, 2016, 2017, 2018, 2019, 2020)
Quadruple
Wexford (1915, 1916, 1917, 1918)
Kerry (1929, 1930, 1931, 1932)
Kerry (1978, 1979, 1980, 1981)
Treble
Dublin (1897, 1898, 1899)
Dublin (1906, 1907, 1908)
Dublin (1921, 1922, 1923)
Kerry (1939, 1940, 1941)
Galway (1964, 1965, 1966)
Kerry (1984, 1985, 1986)
Double
Dublin (1891, 1892)
Dublin (1901, 1902)
Kerry (1903, 1904)
Kerry (1913, 1914)
Kildare (1927, 1928)
Roscommon (1943, 1944)
Cavan (1947, 1948)
Mayo (1950, 1951)
Down (1960, 1961)
Kerry (1969, 1970)
Offaly (1971, 1972)
Dublin (1976, 1977)
Meath (1987, 1988)
Cork (1989, 1990)
Kerry (2006, 2007)
Single
Limerick (1887, 1896)
Tipperary (1889, 1895, 1900, 1920)
Cork (1890, 1911, 1945, 1973, 2010)
Wexford (1893)
Dublin (1894, 1942, 1958, 1963, 1974, 1983, 1995, 2011, 2013)
Kildare (1905, 1919)
Kerry (1909, 1924, 1926, 1937, 1946, 1953, 1955, 1959, 1962, 1975, 1997, 2000, 2004, 2009, 2014, 2022)
Louth (1910, 1912, 1957)
Galway (1925, 1934, 1938, 1956, 1998, 2001)
Cavan (1933, 1935, 1952)
Mayo (1936)
Meath (1949, 1954, 1967, 1996, 1999)
Down (1968, 1991, 1994)
Offaly (1982)
Donegal (1992, 2012)
Derry (1993)
Armagh (2002)
Tyrone (2003, 2005, 2008, 2021)
By semi-final appearances
As of 2 July 2023
Semi-final appearances (2001-)
By province
Most successful provinces
Cavan and Down are the Ulster teams with the most All-Ireland titles.
Dublin are the Leinster team with the most All-Ireland titles.
Galway are the Connacht team with the most All-Ireland titles.
Kerry are the Munster team with the most All-Ireland titles.
Provinces with highest number of different winning counties
The provinces providing the highest number of different winning counties are Leinster and Ulster, with six each. Dublin, Meath, Wexford, Kildare, Offaly and Louth from Leinster have won the title, while Cavan, Down, Tyrone, Donegal, Armagh and Derry are the successful Ulster sides. For Leinster's 12 counties, this represents a success rate o |
https://en.wikipedia.org/wiki/Dwight%20Duffus | Dwight Albert Duffus is a Canadian-American mathematician, the Goodrich C. White Professor of Mathematics & Computer Science at Emory University and editor-in-chief of the journal Order.
Duffus did his undergraduate studies at the University of Regina, graduating in 1974; he received his Ph.D. in 1978 from the University of Calgary under the supervision of Ivan Rival.
In 1986 Duffus received Emory University's Emory Williams Teaching Award, its highest award for teaching excellence. He served as chair of the Mathematics & Computer Science Department at Emory for many years, beginning in 1991.
References
Living people
20th-century American mathematicians
21st-century American mathematicians
Canadian mathematicians
University of Calgary alumni
University of Regina alumni
Emory University faculty
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Ivan%20Rival | Ivan Rival (March 15, 1947 – January 22, 2002 in Ottawa, Ontario, Canada) was a Canadian mathematician and computer scientist, a professor of mathematics at the University of Calgary and of computer science at the University of Ottawa.
Rival's Ph.D. thesis concerned lattice theory. After moving to Calgary he began to work more generally with partially ordered sets, and to study fixed point theorems for partially ordered structures. He was a frequent organizer of conferences in order theory, and in 1984 he founded the journal Order. As a computer scientist at Ottawa, he shifted research topics, applying his expertise in order theory to the study of data structures, computational geometry, and graph drawing.
Rival grew up in Hamilton, Ontario. He earned a bachelor's degree at McMaster University in 1969, and received his Ph.D. from the University of Manitoba in 1974 under the supervision of George Gratzer. After postdoctoral stints visiting Robert Dilworth at Caltech and Rudolf Wille at the Technische Hochschule Darmstadt, he took a faculty position at Calgary in 1975, and was promoted to full professor in 1981. In 1986, he moved to the University of Ottawa, where he became chair of the computer science department.
Rival's doctoral students included Dwight Duffus, the Goodrich C. White Professor of Mathematics & Computer Science at Emory University. Duffus took over the editorship of Order after the retirement (as editor) of William T. Trotter , who took over the editorship from Rival.
References
External links
The Ivan Rival Memorial Website
1947 births
2002 deaths
Canadian mathematicians
Academics from Hamilton, Ontario
McMaster University alumni
University of Manitoba alumni
Academic staff of the University of Calgary
Lattice theorists
Researchers in geometric algorithms
Academic staff of Technische Universität Darmstadt |
https://en.wikipedia.org/wiki/Fan%20chart | Fan chart may refer to:
Fan chart (genealogy), a way of depicting a family tree
Fan chart (time series), a way of depicting a past and future time series
Fan chart (statistics), a way of depicting dispersions according to two categorising dimensions |
https://en.wikipedia.org/wiki/Truncated%208-simplexes | In eight-dimensional geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-simplex.
There are four unique degrees of truncation. Vertices of the truncation 8-simplex are located as pairs on the edge of the 8-simplex. Vertices of the bitruncated 8-simplex are located on the triangular faces of the 8-simplex. Vertices of the tritruncated 8-simplex are located inside the tetrahedral cells of the 8-simplex.
Truncated 8-simplex
Alternate names
Truncated enneazetton (Acronym: tene) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the truncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,0,1,2). This construction is based on facets of the truncated 9-orthoplex.
Images
Bitruncated 8-simplex
Alternate names
Bitruncated enneazetton (Acronym: batene) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the bitruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,1,2,2). This construction is based on facets of the bitruncated 9-orthoplex.
Images
Tritruncated 8-simplex
Alternate names
Tritruncated enneazetton (Acronym: tatene) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the tritruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,2,2,2). This construction is based on facets of the tritruncated 9-orthoplex.
Images
Quadritruncated 8-simplex
The quadritruncated 8-simplex an isotopic polytope, constructed from 18 tritruncated 7-simplex facets.
Alternate names
Octadecazetton (18-facetted 8-polytope) (Acronym: be) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the quadritruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,2,2,2,2). This construction is based on facets of the quadritruncated 9-orthoplex.
Images
Related polytopes
Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
x3x3o3o3o3o3o3o - tene, o3x3x3o3o3o3o3o - batene, o3o3x3x3o3o3o3o - tatene, o3o3o3x3x3o3o3o - be
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
8-polytopes |
https://en.wikipedia.org/wiki/Structured%20derivations | For mathematics education, Structured derivations (SD) is a logic-based format for presenting mathematical solutions and proofs created by Prof. Ralph-Johan Back and Joakim von Wright at Åbo Akademi University, Turku, Finland. The format was originally introduced as a way for presenting proofs in programming logic, but was later adapted to provide a practical approach to presenting proofs and derivations in mathematics education including exact formalisms. A structured derivation has a precise mathematical interpretation, and the syntax and the layout are precisely defined. The standardized syntax renders the format suitable for presenting and manipulating mathematics digitally.
SD is a further development of the calculational proof format introduced by Edsger W. Dijkstra and others in the early 1990s. In essence, three main extensions have been made. First, a mechanism for decomposing proofs through the use of subderivations has been added. The calculational approach is limited to writing proof fragments, and longer derivations are commonly decomposed into several separate subproofs. Using SD with subderivations, on the other hand, the presentation of a complete proof or solution is kept together, as subproofs can be presented exactly where they are needed. In addition, SD makes it possible to handle assumptions and observations in proofs. As such, the format can be seen as combining the benefits of the calculational style with the decomposition facilities of natural deduction.
Examples
The following three examples will be used to illustrate the most central features of structured derivations.
A simple equation
Solving a simple equation illustrates the basic structure of a structured derivation. The start of the solution is indicated by a bullet () followed by the task we are to solve (in this case the equation ).
Each step in the solution consists of two terms, a relation and a justification that explains why the relationship between the two terms hold. The justifications are given equal amount of space as the mathematical terms in order to indicate the importance of explanations in mathematics.
Assumptions and observations
Specifications of mathematical problems commonly contain information that can be used in the solution. When writing a proof or a solution as a structured derivation, all known information is listed in the beginning as assumptions. These assumptions can be used to create new information that will be useful for solving the problem. This information can be added as observations that build on the assumptions. The following example uses two assumptions ((a)–(b)) and two observations ([1]–[2]). The introductory part of the solution (the task, assumptions and observations) is separated from the proof part by the -symbol, denoting logical provability.
Sea water, where the mass-volume percentage of salt is 4.0%, is vaporized in a pool until its mass has decreased by 28%. What is the concentration of salt after the vaporizatio |
https://en.wikipedia.org/wiki/Kim%20Do-yeop | Kim Do-yeop (born November 26, 1988) is a South Korean football player who plays for K League 2 side Asan Mugunghwa. He changed his name from 'Kim In-han' in 2014.
Career statistics
Gyeongnam FC
Originally named as "Kim In-Han" was drafted to Gyeongnam FC from Sunmoon University as their 3rd choice in 2010 and since then, he only played for Gyeongnam FC, except for a period, where he went to Sangju Sangmu to serve mandatory military service in Korea.
External links
1988 births
Living people
People from Nonsan
Men's association football midfielders
South Korean men's footballers
Gyeongnam FC players
Gimcheon Sangmu FC players
Jeju United FC players
Seongnam FC players
Asan Mugunghwa FC players
K League 1 players
K League 2 players
Sportspeople from South Chungcheong Province
Sun Moon University alumni |
https://en.wikipedia.org/wiki/Hossein%20Emamian | Hossein Emamian is an Iranian footballer.
Club career
Emamian has played with Naft Tehran since 2009.
Club career statistics
Assists
References
Living people
Naft Tehran F.C. players
Iranian men's footballers
F.C. Nassaji Mazandaran players
Gol Gohar Sirjan F.C. players
Rah Ahan Tehran F.C. players
Men's association football wingers
Place of birth missing (living people)
1977 births |
https://en.wikipedia.org/wiki/Morgan%20Ward | Henry Morgan Ward (August 20, 1901 – June 26, 1963) was an American mathematician, a professor of mathematics at the California Institute of Technology.
Education and career
Ward was born in New York City. He studied at University of California, Berkeley, receiving his BA in 1924. He obtained his Ph.D. in mathematics from Caltech in 1928, with a dissertation entitled The Foundations of General Arithmetic; his advisor was Eric Temple Bell. He became a research fellow at Caltech, and then in 1929 a member of the faculty; he remained at Caltech until his death in 1963. Among his doctoral students was Robert P. Dilworth, who also became a Caltech professor. Ward is the academic ancestor of over 500 mathematicians and computer scientists through Dilworth and another of his students, Donald A. Darling.
Research
Ward's research interests included the study of recurrence relations and the divisibility properties of their solutions, diophantine equations including Euler's sum of powers conjecture and equations between monomials, abstract algebra, lattice theory and residuated lattices, functional equations and functional iteration, and numerical analysis. He also worked with the National Science Foundation on the reform of the elementary school mathematics curriculum, and with Clarence Ethel Hardgrove he wrote the textbook Modern Elementary Mathematics (Addison-Wesley, 1962).
Ward's works are collected in the Caltech library. A symposium in his memory was held at Caltech on November 21–22, 1963. Ward quasigroups are named after him, following his paper on alternative set of group axioms.
Personal life
Ward died of a heart attack in Duarte, California.
References
20th-century American mathematicians
Lattice theorists
California Institute of Technology alumni
California Institute of Technology faculty
1901 births
1963 deaths
California Institute of Technology fellows |
https://en.wikipedia.org/wiki/%CE%95-net%20%28computational%20geometry%29 | In computational geometry, an ε-net (pronounced epsilon-net) is the approximation of a general set by a collection of simpler subsets. In probability theory it is the approximation of one probability distribution by another.
Background
Let X be a set and R be a set of subsets of X; such a pair is called a range space or hypergraph, and the elements of R are called ranges or hyperedges. An ε-net of a subset P of X is a subset N of P such that any range r ∈ R with |r ∩ P| ≥ ε|P| intersects N. In other words, any range that intersects at least a proportion ε of the elements of P must also intersect the ε-net N.
For example, suppose X is the set of points in the two-dimensional plane, R is the set of closed filled rectangles (products of closed intervals), and P is the unit square [0, 1] × [0, 1]. Then the set N consisting of the 8 points shown in the adjacent diagram is a 1/4-net of P, because any closed filled rectangle intersecting at least 1/4 of the unit square must intersect one of these points. In fact, any (axis-parallel) square, regardless of size, will have a similar 8-point 1/4-net.
For any range space with finite VC dimension d, regardless of the choice of P, there exists an ε-net of P of size
because the size of this set is independent of P, any set P can be described using a set of fixed size.
This facilitates the development of efficient approximation algorithms. For example, suppose we wish to estimate an upper bound on the area of a given region, that falls inside a particular rectangle P. One can estimate this to within an additive factor of ε times the area of P by first finding an ε-net of P, counting the proportion of elements in the ε-net falling inside the region with respect to the rectangle P, and then multiplying by the area of P. The runtime of the algorithm depends only on ε and not P. One straightforward way to compute an ε-net with high probability is to take a sufficient number of random points, where the number of random points also depends only on ε. For example, in the diagram shown, any rectangle in the unit square containing at most three points in the 1/4-net has an area of at most 3/8 + 1/4 = 5/8.
ε-nets also provide approximation algorithms for the NP-complete hitting set and set cover problems.
Probability theory
Let be a probability distribution over some set . An -net for a class of subsets of is any subset such that
for any
Intuitively approximates the probability distribution.
A stronger notion is -approximation. An -approximation for class is a subset such that for any it holds
References
Computational geometry
Probability theory |
https://en.wikipedia.org/wiki/Crusaders%20Rugby%20League%20statistics%20and%20records | This page details statistics and records of the Crusaders Rugby League club.
Statistics
Seasons
Opposition
Attendance
Players
Records
Club
Super League
Appearances & Points
Tries & Goals
References
Statistics and records |
https://en.wikipedia.org/wiki/Vector%20algebra%20relations | The following are important identities in vector algebra. Identities that involve the magnitude of a vector , or the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension. Identities that use the cross product (vector product) A×B are defined only in three dimensions.
Magnitudes
The magnitude of a vector A can be expressed using the dot product:
In three-dimensional Euclidean space, the magnitude of a vector is determined from its three components using Pythagoras' theorem:
Inequalities
The Cauchy–Schwarz inequality:
The triangle inequality:
The reverse triangle inequality:
Angles
The vector product and the scalar product of two vectors define the angle between them, say θ:
To satisfy the right-hand rule, for positive θ, vector B is counter-clockwise from A, and for negative θ it is clockwise.
The Pythagorean trigonometric identity then provides:
If a vector A = (Ax, Ay, Az) makes angles α, β, γ with an orthogonal set of x-, y- and z-axes, then:
and analogously for angles β, γ. Consequently:
with unit vectors along the axis directions.
Areas and volumes
The area Σ of a parallelogram with sides A and B containing the angle θ is:
which will be recognized as the magnitude of the vector cross product of the vectors A and B lying along the sides of the parallelogram. That is:
(If A, B are two-dimensional vectors, this is equal to the determinant of the 2 × 2 matrix with rows A, B.) The square of this expression is:
where Γ(A, B) is the Gram determinant of A and B defined by:
In a similar fashion, the squared volume V of a parallelepiped spanned by the three vectors A, B, C is given by the Gram determinant of the three vectors:
Since A, B, C are three-dimensional vectors, this is equal to the square of the scalar triple product below.
This process can be extended to n-dimensions.
Addition and multiplication of vectors
Commutativity of addition: .
Commutativity of scalar product: .
Anticommutativity of cross product: .
Distributivity of multiplication by a scalar over addition: .
Distributivity of scalar product over addition: .
Distributivity of vector product over addition: .
Scalar triple product:
Vector triple product: .
Jacobi identity:
Binet-Cauchy identity:
Lagrange's identity: .
Vector quadruple product:
A consequence of the previous equation:
In 3 dimensions, a vector D can be expressed in terms of basis vectors {A,B,C} as:
See also
Vector space
Geometric algebra
Notes
References
Mathematical identities
Mathematics-related lists |
https://en.wikipedia.org/wiki/2001%20Lithuanian%20census | The 2001 Lithuania Census was carried out during April 6 - April 16 by the Lithuanian Department of Statistics. The results were published in 2002.
At the period of the census the country was subdivided as follows:
10 counties
60 municipalities
106 cities
464 rural elderships
21,500 rural settlements
Total population was 3,483,972, of which 2,332,098 were urban dwellers and 1,151,874 were rural dwellers.
References
2001
2001 censuses
Census |
https://en.wikipedia.org/wiki/Hodges%27%20estimator | In statistics, Hodges' estimator (or the Hodges–Le Cam estimator), named for Joseph Hodges, is a famous counterexample of an estimator which is "superefficient", i.e. it attains smaller asymptotic variance than regular efficient estimators. The existence of such a counterexample is the reason for the introduction of the notion of regular estimators.
Hodges' estimator improves upon a regular estimator at a single point. In general, any superefficient estimator may surpass a regular estimator at most on a set of Lebesgue measure zero.
Construction
Suppose is a "common" estimator for some parameter : it is consistent, and converges to some asymptotic distribution (usually this is a normal distribution with mean zero and variance which may depend on ) at the -rate:
Then the Hodges' estimator is defined as
This estimator is equal to everywhere except on the small interval , where it is equal to zero. It is not difficult to see that this estimator is consistent for , and its asymptotic distribution is
for any . Thus this estimator has the same asymptotic distribution as for all , whereas for the rate of convergence becomes arbitrarily fast. This estimator is superefficient, as it surpasses the asymptotic behavior of the efficient estimator at least at one point . In general, superefficiency may only be attained on a subset of Lebesgue measure zero of the parameter space .
Example
Suppose x1, ..., xn is an independent and identically distributed (IID) random sample from normal distribution with unknown mean but known variance. Then the common estimator for the population mean θ is the arithmetic mean of all observations: . The corresponding Hodges' estimator will be , where 1{...} denotes the indicator function.
The mean square error (scaled by n) associated with the regular estimator x is constant and equal to 1 for all θs. At the same time the mean square error of the Hodges' estimator behaves erratically in the vicinity of zero, and even becomes unbounded as . This demonstrates that the Hodges' estimator is not regular, and its asymptotic properties are not adequately described by limits of the form (θ fixed, ).
See also
James–Stein estimator
Notes
References
Estimator |
https://en.wikipedia.org/wiki/List%20of%20regions%20of%20Poland%20by%20gross%20regional%20product | This article is about the gross regional product of regions of the Poland, defined as Level 2 regions of the Nomenclature of Territorial Units for Statistics (NUTS 2), in nominal values. Values are shown in euros in the original source. All values are rounded to the nearest hundred. Except Warsaw metropolitan area, which is within Mazowieckie, all areas below are Voivodeships of Poland.
GRP per capita
This is a list of regions of Poland by gross regional product (GRP) per capita shown in euros. Statistics shown are for 2021 levels.
GRP
This is a list of regions of Poland by nominal gross regional product (GRP) shown in billion euros. Statistics shown are for 2021 levels.
See also
Poland A and B
References
GRP
GRP
Voivodeships by GRP per capita
Poland |
https://en.wikipedia.org/wiki/Hydrogamasellus%20calculus | Hydrogamasellus calculus is a species of mite in the family Ologamasidae.
References
Ologamasidae
Articles created by Qbugbot
Animals described in 1997 |
https://en.wikipedia.org/wiki/Cantellated%208-simplexes | In eight-dimensional geometry, a cantellated 8-simplex is a convex uniform 8-polytope, being a cantellation of the regular 8-simplex.
There are six unique cantellations for the 8-simplex, including permutations of truncation.
Cantellated 8-simplex
Alternate names
Small rhombated enneazetton (acronym: srene) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the cantellated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,1,1,2). This construction is based on facets of the cantellated 9-orthoplex.
Images
Bicantellated 8-simplex
Alternate names
Small birhombated enneazetton (acronym: sabrene) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the bicantellated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,1,2,2). This construction is based on facets of the bicantellated 9-orthoplex.
Images
Tricantellated 8-simplex
Alternate names
Small trirhombihexadecaexon (acronym: satrene) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the tricantellated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,1,2,2). This construction is based on facets of the tricantellated 9-orthoplex.
Images
Cantitruncated 8-simplex
Alternate names
Great rhombated enneazetton (acronym: grene) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the cantitruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,1,2,3). This construction is based on facets of the bicantitruncated 9-orthoplex.
Images
Bicantitruncated 8-simplex
Alternate names
Great birhombated enneazetton (acronym: gabrene) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the bicantitruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,2,3,3). This construction is based on facets of the bicantitruncated 9-orthoplex.
Images
Tricantitruncated 8-simplex
Great trirhombated enneazetton (acronym: gatrene) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the tricantitruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,2,3,3,3). This construction is based on facets of the bicantitruncated 9-orthoplex.
Images
Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polyt |
https://en.wikipedia.org/wiki/Runcinated%208-simplexes | In eight-dimensional geometry, a runcinated 8-simplex is a convex uniform 8-polytope with 3rd order truncations (runcination) of the regular 8-simplex.
There are eleven unique runcinations of the 8-simplex, including permutations of truncation and cantellation. The triruncinated 8-simplex and triruncicantitruncated 8-simplex have a doubled symmetry, showing [18] order reflectional symmetry in the A8 Coxeter plane.
Runcinated 8-simplex
Alternate names
Runcinated enneazetton
Small prismated enneazetton (Acronym: spene) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the runcinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,1,1,2). This construction is based on facets of the runcinated 9-orthoplex.
Images
Biruncinated 8-simplex
Alternate names
Biruncinated enneazetton
Small biprismated enneazetton (Acronym: sabpene) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the biruncinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,1,1,2,2). This construction is based on facets of the biruncinated 9-orthoplex.
Images
Triruncinated 8-simplex
Alternate names
Triruncinated enneazetton
Small triprismated enneazetton (Acronym: satpeb) (Jonathan Bowers)
Coordinates
The Cartesian coordinates of the vertices of the triruncinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,2,2,2). This construction is based on facets of the triruncinated 9-orthoplex.
Images
Runcitruncated 8-simplex
Images
Biruncitruncated 8-simplex
Images
Triruncitruncated 8-simplex
Images
Runcicantellated 8-simplex
Images
Biruncicantellated 8-simplex
Images
Runcicantitruncated 8-simplex
Images
Biruncicantitruncated 8-simplex
Images
Triruncicantitruncated 8-simplex
Images
Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
x3o3o3x3o3o3o3o - spene, o3x3o3o3x3o3o3o - sabpene, o3o3x3o3o3x3o3o - satpeb
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
8-polytopes |
https://en.wikipedia.org/wiki/Tibor%20Lad%C3%A1nyi | Tibor Ladányi (born 21 November 1991) is a Hungarian football player who currently plays for MTK Hungaria FC.
Club statistics
Updated to games played as of 1 June 2014.
External links
Profile at HLSZ
Profile at MLSZ
1991 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football midfielders
MTK Budapest FC players
Szigetszentmiklósi TK footballers
Budafoki MTE footballers
FC Dabas footballers
Nemzeti Bajnokság I players
Expatriate men's footballers in Austria
Expatriate men's footballers in Germany
Hungarian expatriate sportspeople in Austria
Hungarian expatriate sportspeople in Germany |
https://en.wikipedia.org/wiki/Stericated%208-simplexes | In eight-dimensional geometry, a stericated 8-simplex is a convex uniform 8-polytope with 4th order truncations (sterication) of the regular 8-simplex. There are 16 unique sterications for the 8-simplex including permutations of truncation, cantellation, and runcination.
Stericated 8-simplex
Coordinates
The Cartesian coordinates of the vertices of the stericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,1,1,1,2). This construction is based on facets of the stericated 9-orthoplex.
Images
Bistericated 8-simplex
Coordinates
The Cartesian coordinates of the vertices of the bistericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,1,2,2). This construction is based on facets of the bistericated 9-orthoplex.
Images
Steritruncated 8-simplex
Images
Bisteritruncated 8-simplex
Images
Stericantellated 8-simplex
Images
Bistericantellated 8-simplex
Images
Stericantitruncated 8-simplex
Images
Bistericantitruncated 8-simplex
Images
Steriruncinated 8-simplex
Images
Bisteriruncinated 8-simplex
Images
Steriruncitruncated 8-simplex
Images
Bisteriruncitruncated 8-simplex
Images
Steriruncicantellated 8-simplex
Images
Bisteriruncicantellated 8-simplex
Images
Steriruncicantitruncated 8-simplex
Images
Bisteriruncicantitruncated 8-simplex
Images
Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
x3o3o3o3x3o3o3o, o3x3o3o3o3x3o3o
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
8-polytopes |
https://en.wikipedia.org/wiki/Pentellated%208-simplexes | In eight-dimensional geometry, a pentellated 8-simplex is a convex uniform 8-polytope with 5th order truncations of the regular 8-simplex.
There are two unique pentellations of the 8-simplex. Including truncations, cantellations, runcinations, and sterications, there are 32 more pentellations. These polytopes are a part of a family 135 uniform 8-polytopes with A8 symmetry. A8, [37] has order 9 factorial symmetry, or 362880. The bipentalled form is symmetrically ringed, doubling the symmetry order to 725760, and is represented the double-bracketed group [[37]]. The A8 Coxeter plane projection shows order [9] symmetry for the pentellated 8-simplex, while the bipentellated 8-simple is doubled to [18] symmetry.
Pentellated 8-simplex
Coordinates
The Cartesian coordinates of the vertices of the pentellated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,1,1,1,2). This construction is based on facets of the pentellated 9-orthoplex.
Images
Bipentellated 8-simplex
Coordinates
The Cartesian coordinates of the vertices of the bipentellated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,1,1,1,1,1,2,2). This construction is based on facets of the bipentellated 9-orthoplex.
Images
Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
x3o3o3o3o3x3o3o, o3x3o3o3o3o3x3o
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
8-polytopes |
https://en.wikipedia.org/wiki/Hexicated%208-simplexes | In eight-dimensional geometry, a hexicated 8-simplex is a uniform 8-polytope, being a hexication (6th order truncation) of the regular 8-simplex.
Coordinates
The Cartesian coordinates of the vertices of the hexicated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,1,1,2). This construction is based on facets of the hexicated 9-orthoplex.
Images
Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, PhD
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
8-polytopes |
https://en.wikipedia.org/wiki/D%C3%A1vid%20Kelemen | Dávid Kelemen (born 24 May 1992) is a Hungarian professional football player who plays for Romanian Liga II club Csíkszereda, which he captains.
Club statistics
Updated to games played as of 28 October 2023.
Honours
MTK Budapest
Magyar Kupa runner-up: 2011–12
References
External links
Profile at HLSZ
1992 births
Living people
Footballers from Békéscsaba
Hungarian men's footballers
Men's association football defenders
Hungary men's youth international footballers
Hungary men's under-21 international footballers
MTK Budapest FC players
Hapoel Tel Aviv F.C. players
Paksi FC players
Békéscsaba 1912 Előre footballers
Nyíregyháza Spartacus FC players
Vasas SC players
Szombathelyi Haladás footballers
FK Csíkszereda Miercurea Ciuc players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Israeli Premier League players
Liga II players
Expatriate men's footballers in Israel
Expatriate men's footballers in Romania
Hungarian expatriate sportspeople in Israel
Hungarian expatriate sportspeople in Romania |
https://en.wikipedia.org/wiki/Series-parallel%20partial%20order | In order-theoretic mathematics, a series-parallel partial order is a partially ordered set built up from smaller series-parallel partial orders by two simple composition operations.
The series-parallel partial orders may be characterized as the N-free finite partial orders; they have order dimension at most two. They include weak orders and the reachability relationship in directed trees and directed series–parallel graphs. The comparability graphs of series-parallel partial orders are cographs.
Series-parallel partial orders have been applied in job shop scheduling, machine learning of event sequencing in time series data, transmission sequencing of multimedia data, and throughput maximization in dataflow programming.
Series-parallel partial orders have also been called multitrees; however, that name is ambiguous: multitrees also refer to partial orders with no four-element diamond suborder and to other structures formed from multiple trees.
Definition
Consider and , two partially ordered sets. The series composition of and , written , , or ,is the partially ordered set whose elements are the disjoint union of the elements of and . In , two elements and that both belong to or that both belong to have the same order relation that they do in or respectively. However, for every pair , where belongs to and belongs to , there is an additional order relation in the series composition. Series composition is an associative operation: one can write as the series composition of three orders, without ambiguity about how to combine them pairwise, because both of the parenthesizations and describe the same partial order. However, it is not a commutative operation, because switching the roles of and will produce a different partial order that reverses the order relations of pairs with one element in and one in .
The parallel composition of and , written , , or , is defined similarly, from the disjoint union of the elements in and the elements in , with pairs of elements that both belong to or both to having the same order as they do in or respectively. In , a pair , is incomparable whenever belongs to and belongs to . Parallel composition is both commutative and associative.
The class of series-parallel partial orders is the set of partial orders that can be built up from single-element partial orders using these two operations. Equivalently, it is the smallest set of partial orders that includes the single-element partial order and is closed under the series and parallel composition operations.
A weak order is the series parallel partial order obtained from a sequence of composition operations in which all of the parallel compositions are performed first, and then the results of these compositions are combined using only series compositions.
Forbidden suborder characterization
The partial order with the four elements , , , and and exactly the three order relations is an example of a fence or zigzag poset; its Hass |
https://en.wikipedia.org/wiki/Multivariate%20kernel%20density%20estimation | Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics. It can be viewed as a generalisation of histogram density estimation with improved statistical properties. Apart from histograms, other types of density estimators include parametric, spline, wavelet and Fourier series. Kernel density estimators were first introduced in the scientific literature for univariate data in the 1950s and 1960s and subsequently have been widely adopted. It was soon recognised that analogous estimators for multivariate data would be an important addition to multivariate statistics. Based on research carried out in the 1990s and 2000s, multivariate kernel density estimation has reached a level of maturity comparable to its univariate counterparts.
Motivation
We take an illustrative synthetic bivariate data set of 50 points to illustrate the construction of histograms. This requires the choice of an anchor point (the lower left corner of the histogram grid). For the histogram on the left, we choose (−1.5, −1.5): for the one on the right, we shift the anchor point by 0.125 in both directions to (−1.625, −1.625). Both histograms have a binwidth of 0.5, so any differences are due to the change in the anchor point only. The colour-coding indicates the number of data points which fall into a bin: 0=white, 1=pale yellow, 2=bright yellow, 3=orange, 4=red. The left histogram appears to indicate that the upper half has a higher density than the lower half, whereas the reverse is the case for the right-hand histogram, confirming that histograms are highly sensitive to the placement of the anchor point.
One possible solution to this anchor point placement problem is to remove the histogram binning grid completely. In the left figure below, a kernel (represented by the grey lines) is centred at each of the 50 data points above. The result of summing these kernels is given on the right figure, which is a kernel density estimate. The most striking difference between kernel density estimates and histograms is that the former are easier to interpret since they do not contain artifices induced by a binning grid.
The coloured contours correspond to the smallest region which contains the respective probability mass: red = 25%, orange + red = 50%, yellow + orange + red = 75%, thus indicating that a single central region contains the highest density.
The goal of density estimation is to take a finite sample of data and to make inferences about the underlying probability density function everywhere, including where no data are observed. In kernel density estimation, the contribution of each data point is smoothed out from a single point into a region of space surrounding it. Aggregating the individually smoothed contributions gives an overall picture of the structure of the data and its density function. In the details to follow, we show that this approach l |
https://en.wikipedia.org/wiki/Example%20choice | Example choice is a teaching method that has been developed and explored at the University of Bergen. The main objective is to make mathematics and science teaching more interesting and relevant to the daily life of students. One study by Perkins, Gratny, Adams, Finkelstein, and Wieman found that interest in physics declined during a semester-long introductory calculus-based mechanics course. Whereas 19% of the students reported increased interest in physics, 45% reported that their interest in physics decreased. When interest increased, the leading reason was that students reported to see a connection between physics and the real world. Example choice aims to highlight the connection between formal principles and their relevance for everyday life in order to make school instruction a relevant experience for the child, as already John Dewey called for in his book "School and Society". For him, connecting instructional content to everyday life was the only legitimate way to make things interesting, as noted in his essay "Interest and Effort".
In traditional teaching, formal principles (laws, formula, problem solving procedures) in mathematics and science are often taught abstractly and then illustrated by an example. In example choice, by contrast, students are given multiple example tasks that all can be solved using the formal principle. The examples pertain to different topics, and each student is instructed to choose the most interesting example. This example is used to explain the formal principle.
For example, when teaching the joint probability of two independent events, teachers often explain the abstract procedure (p1 * p2) first and illustrate this procedure with an example (e.g., throwing a die twice). In example choice, by contrast, teachers first collect or construct examples from topics that are of potential interest to high school students, such as contracting hereditary diseases, contraception, or winning in a two-step lottery to meet one's favorite artist. After the students selected the example that interests them most, they are given a problem related to the chosen example that they have to try to solve. After the solution attempt, the principle behind the joint probability of two independent events will be explained, using the chosen example. Teachers may then use the other examples in order to deepen the understanding of joint probabilities, for example by using worked examples.
A study observed that example choice increased interest in learning an abstract principle, and participants in the study invested more time to learn. In other words, students are the producers of learning.
Example choice is difficult to use in traditional teaching because teachers often do not know the interests of their students. Even if they know these interests, a teacher would need much time and effort to find examples. With new technologies, teachers and students can help build a database of examples that users can retrieve when the formal pr |
https://en.wikipedia.org/wiki/North%20Carolina%20Science%20Olympiad | North Carolina Science Olympiad (NCSO) is a nonprofit organization with the mission to attract and retain the pool of K–12 students entering science, technology, engineering, and mathematics (STEM) degrees and careers in North Carolina. Every year NCSO hosts tournaments on university, community college, and public school campuses across the state. These tournaments are rigorous academic interscholastic competitions that consist of a series of different hands-on, interactive, challenging and inquiry-based events that are well balanced between the various disciplines of biology, earth science, environmental science, chemistry, physics, engineering and technology. NCSO is housed at The Science House at NC State University.
History
The first recorded Science Olympiad was held on Saturday, November 23, 1974, at St. Andrews Presbyterian College in Laurinburg, North Carolina. Dr. Donald Barnes and Dr. David Wetmore were the originators of this event. Fifteen schools from North and South Carolina participated in this event. This Olympiad was a day-long affair, with competitions and demonstrations for high school students in the areas of biology, chemistry, and physics. There were four event periods during this day, and each event period had one fun event (like beaker race or paper airplane), one demonstration (like glassblowing and holography), and one serious event (like periodic table quiz or Science Bowl). An article was published in the Journal of Chemical Education in January 1978 documenting the success of recruiting students through Science Olympiad. St. Andrews continues to host a Science Olympiad tournament to this day.
John C. "Jack" Cairns was a teacher at Dover High School in Delaware in the 1970s when he learned about Science Olympiad taking place in North Carolina. He shared this information with Dr. Douglas R. Macbeth, the Delaware State Science Supervisor. Cairns was appointed to a steering committee to organize the first Olympiad in Delaware which took place at Delaware State University in the Spring of 1977.
By 1982, word about Science Olympiad continued to spread, and caught the attention of Dr. Gerard Putz in Macomb County, Michigan. Putz invited Cairns to share the success of the Delaware Science Olympiad with Macomb County. As a result, Michigan hosted their first two tournaments in 1983 and 1984 while at the same time Delaware hosted eight similar tournaments. Putz and Cairns then decided to share the program with the rest of the nation.
Competition
Score is calculated by giving 1 point for a first-place finish, 2 points for a second-place finish, etc.
In final events standings, (D) denotes defending champions.
NCSO competitions are run in a style similar to a track meet. Each competitor has individual events that they compete in, instead of shot put and javelin, a competitor would participate in Forensics and Tower Building. Competitors receive individual rankings in each individual event they compete in, and at the end of |
https://en.wikipedia.org/wiki/Emil%20Artin%20Junior%20Prize%20in%20Mathematics | Established in 2001, the Emil Artin Junior Prize in Mathematics is presented usually every year to a former student of an Armenian university, who is under the age of thirty-five, for outstanding contributions in algebra, geometry, topology,
and number theory. The award is announced in the Notices of the American Mathematical Society. The prize is named after Emil Artin, who was of Armenian descent. Although eligibility for the prize is not fully international, as the recipient has to have studied in Armenia, awards are made only for specific outstanding publications in leading international journals.
Recipient of the Emil Artin Junior Prize
2001 Vahagn Mikaelian
2002 Artur Barkhudaryan
2004 Gurgen R. Asatryan
2005 Mihran Papikian
2007 Ashot Minasyan
2008 Nansen Petrosyan
2009 Grigor Sargsyan
2010 Hrant Hakobyan
2011 Lilya Budaghyan
2014 Sevak Mkrtchyan
2015 Anush Tserunyan
2016 Lilit Martirosyan
2018 Davit Harutyunyan
2019 Vahagn Aslanyan
2020 Levon Haykazyan
2021 Arman Darbinyan
2022 Diana Davidova
2023 Davit Karagulyan
See also
List of mathematics awards
References
Mathematics awards |
https://en.wikipedia.org/wiki/Logit-normal%20distribution | In probability theory, a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution. If Y is a random variable with a normal distribution, and t is the standard logistic function, then X = t(Y) has a logit-normal distribution; likewise, if X is logit-normally distributed, then Y = logit(X)= log (X/(1-X)) is normally distributed. It is also known as the logistic normal distribution, which often refers to a multinomial logit version (e.g.).
A variable might be modeled as logit-normal if it is a proportion, which is bounded by zero and one, and where values of zero and one never occur.
Characterization
Probability density function
The probability density function (PDF) of a logit-normal distribution, for 0 < x < 1, is:
where μ and σ are the mean and standard deviation of the variable’s logit (by definition, the variable’s logit is normally distributed).
The density obtained by changing the sign of μ is symmetrical, in that it is equal to f(1-x;-μ,σ), shifting the mode to the other side of 0.5 (the midpoint of the (0,1) interval).
Moments
The moments of the logit-normal distribution have no analytic solution. The moments can be estimated by numerical integration, however numerical integration can be prohibitive when the values of are such that the density function diverges to infinity at the end points zero and one. An alternative is to use the observation that the logit-normal is a transformation of a normal random variable. This allows us to approximate the -th moment via the following quasi Monte Carlo estimate
where is the standard logistic function, and is the inverse cumulative distribution function of a normal distribution with mean and variance .
Mode or modes
When the derivative of the density equals 0 then the location of the mode x satisfies the following equation:
For some values of the parameters there are two solutions, i.e. the distribution is bimodal.
Multivariate generalization
The logistic normal distribution is a generalization of the logit–normal distribution to D-dimensional probability vectors by taking a logistic transformation of a multivariate normal distribution.
Probability density function
The probability density function is:
where denotes a vector of the first (D-1) components of and denotes the simplex of D-dimensional probability vectors. This follows from applying the additive logistic transformation to map a multivariate normal random variable to the simplex:
The unique inverse mapping is given by:
.
This is the case of a vector x which components sum up to one. In the case of x with sigmoidal elements, that is, when
we have
where the log and the division in the argument are taken element-wise. This is because the Jacobian matrix of the transformation is diagonal with elements .
Use in statistical analysis
The logistic normal distribution is a more flexible alternative to the Dirichlet distribution in that it can |
https://en.wikipedia.org/wiki/Quadruple%20product | In mathematics, the quadruple product is a product of four vectors in three-dimensional Euclidean space. The name "quadruple product" is used for two different products, the scalar-valued scalar quadruple product and the vector-valued vector quadruple product or vector product of four vectors.
Scalar quadruple product
The scalar quadruple product is defined as the dot product of two cross products:
where a, b, c, d are vectors in three-dimensional Euclidean space. It can be evaluated using the identity:
or using the determinant:
Proof
We first prove that
This can be shown by straightforward matrix algebra using the correspondence between elements of and , given by
, where
It then follows from the properties of skew-symmetric matrices that
We also know from vector triple products that
Using this identity along with the one we have just derived, we obtain the desired identity:
Vector quadruple product
The vector quadruple product is defined as the cross product of two cross products:
where a, b, c, d are vectors in three-dimensional Euclidean space. It can be evaluated using the identity:
using the notation for the triple product:
Equivalent forms can be obtained using the identity:
This identity can also be written using tensor notation and the Einstein summation convention as follows:
where is the Levi-Civita symbol.
Application
The quadruple products are useful for deriving various formulas in spherical and plane geometry. For example, if four points are chosen on the unit sphere, A, B, C, D, and unit vectors drawn from the center of the sphere to the four points, a, b, c, d respectively, the identity:
in conjunction with the relation for the magnitude of the cross product:
and the dot product:
where a = b = 1 for the unit sphere, results in the identity among the angles attributed to Gauss:
where x is the angle between a × b and c × d, or equivalently, between the planes defined by these vectors.
Josiah Willard Gibbs's pioneering work on vector calculus provides several other examples.
See also
Binet–Cauchy identity
Lagrange's identity
Notes
References
Operations on vectors
Vector calculus |
https://en.wikipedia.org/wiki/Mirsky%27s%20theorem | In mathematics, in the areas of order theory and combinatorics, Mirsky's theorem characterizes the height of any finite partially ordered set in terms of a partition of the order into a minimum number of antichains. It is named for and is closely related to Dilworth's theorem on the widths of partial orders, to the perfection of comparability graphs, to the Gallai–Hasse–Roy–Vitaver theorem relating longest paths and colorings in graphs, and to the Erdős–Szekeres theorem on monotonic subsequences.
The theorem
The height of a partially ordered set is defined to be the maximum cardinality of a chain, a totally ordered subset of the given partial order. For instance, in the set of positive integers from 1 to N, ordered by divisibility, one of the largest chains consists of the powers of two that lie within that range, from which it follows that the height of this partial order is .
Mirsky's theorem states that, for every finite partially ordered set, the height also equals the minimum number of antichains (subsets in which no pair of elements are ordered) into which the set may be partitioned. In such a partition, every two elements of the longest chain must go into two different antichains, so the number of antichains is always greater than or equal to the height; another formulation of Mirsky's theorem is that there always exists a partition for which the number of antichains equals the height. Again, in the example of positive integers ordered by divisibility, the numbers can be partitioned into the antichains {1}, {2,3}, {4,5,6,7}, etc. There are sets in this partition, and within each of these sets, every pair of numbers forms a ratio less than two, so no two numbers within one of these sets can be divisible.
To prove the existence of a partition into a small number of antichains for an arbitrary finite partially ordered set, consider for every element x the chains that have x as their largest element, and let N(x) denote the size of the largest of these x-maximal chains. Then each set N−1(i), consisting of elements that have equal values of N, is an antichain, and these antichains partition the partial order into a number of antichains equal to the size of the largest chain. In his original proof, Mirsky constructs the same partition inductively, by choosing an antichain of the maximal elements of longest chains, and showing that the length of the longest chain among the remaining elements is reduced by one.
Related results
Dilworth's theorem
Mirsky was inspired by Dilworth's theorem, stating that, for every partially ordered set, the maximum size of an antichain equals the minimum number of chains in a partition of the set into chains. For sets of order dimension two, the two theorems coincide (a chain in the majorization ordering of points in general position in the plane is an antichain in the set of points formed by a 90° rotation from the original set, and vice versa) but for more general partial orders the two theorems differ, and |
https://en.wikipedia.org/wiki/List%20of%20Puebla%20F.C.%20records%20and%20statistics | Mexican association football team Puebla F.C. has competed in the Primera División de México, Segunda División de México and Liga de Ascenso divisions. This article documents their statistics and club records.
Year by Year standings
First division
After the 1955–56 season, Puebla F.C. folded. It was reformed in the 1964-65 season, starting in the second division.
Second division
In 1970 the First Division was expanded from 16 to 18 teams; the Second Division champion Zacatepec was promoted and a playoff was held
for the remaining place. The teams competing for the place were Nacional, Naucalpan, Puebla and Union de Curtidores. Puebla won the playoff and was promoted.
First Division
This last total does not include the 92-93 season.
Short Tournaments
Primera A
First Division
Clubs Records
First goal in the first division (Cup)Guadalupe Velásquez 1944
First goal in the first division (League) Eladio Aschetto 1944
Largest win 8-1 against Tampico Madero 1986-87
Most goals scored Ricardo Alvarez 87 goles
Most goals score in long tournament Jorge Orlando Aravena 1988-89 (28)
Most goals scored in short tournament Carlos Muñoz 1996 (15)
Fastes goal score in a game Nicolás Olivera 2009 (11 sec against Cruz Azul)
Most titles as manager Manuel Lapuente (5)League 82-83,89-90,Cup Mexico 89-90,cup champions in champions 89-90,League champions concacaf 1991
Most games won 1945–47 and 1988–89 won 20
Most game won in short tournament 1996 9
Most points obtain in a long tournament 1988-89 (69)
Most points obtain in a short tournament 1996 (31)
Most games played with the club Arturo Alvarez (346) league games only
All time top goalscorers
Since the 1950s, when Ricardo Alvarez scored his 86th and last goal with the club, no one else has accomplished this feat. It was on May 21, 1959 when Alvarez scored his last goals with Puebla before leaving the club to join Veracruz. Alvarez left a record of 86 goals in 125 games through a career that spanned 5 years. Half a century later, the name of "La Changa" Alvarez is still the best goal scorer ever in the history of Puebla F.C. in first division. Even with the club's constancy in first division, playing a total of 54 championships, no other player has reached Alvarez's number of goals scored and only one player has obtained the league goal scoring title in 1996.
It was the Spanish Carlos Muñoz who gave Puebla F.C. their only one goal scoring title in 1996 with 15 goals. Thanks to 4 good tournaments, Muñoz placed himself in the list of the best goal scorers in the club's history but still far from the 86 scored by Ricardo Alvarez.
Two players were close to beat Alvarez's record: Silvio Fogel in The 1970s and Carlos Poblete in the 1980s. Silvio Fogel scored 84 goals and now is the scoring runner-up in Puebla's history. Carlos Poblete scored 83 and now is third place in the all-time scoring list. Carlos Poblete is at the top of the list in goals scored in playoffs with 15 goals scored. Carlos and Silvio score |
https://en.wikipedia.org/wiki/List%20of%20Russian%20scientists |
Polymaths
Karl Ernst von Baer, polymath naturalist, formulated the geological Baer's law on river erosion and embryological Baer's laws, founder of the Russian Entomological Society, co-founder of the Russian Geographical Society
Alexander Borodin, chemist and composer, author of the famous opera Prince Igor, discovered Borodin reaction, co-discovered Aldol reaction
Alexander Chizhevsky, interdisciplinary scientist, biophysicist, philosopher and artist, founder of heliobiology and modern air ionification, Russian cosmist
Johann Gottlieb Georgi, naturalist, chemist, mineralogist, ethnographer and explorer, the first to describe omul fish of Baikal, published the first full-scale work on ethnography of indigenous peoples of Russia
Mikhail Lomonosov, polymath scientist, artist and inventor; founder of the Moscow State University; proposed the law of conservation of matter; disproved the phlogiston theory; invented coaxial rotor and the first helicopter; invented the night vision telescope and off-axis reflecting telescope; discovered the atmosphere of Venus; suggested the organic origin of soil, peat, coal, petroleum and amber; pioneered the research of atmospheric electricity; coined the term physical chemistry; the first to record the freezing of mercury; co-developed Russian porcelain, re-discovered smalt and created a number of mosaics dedicated to Petrine era; author of an early account of Russian history and the first opponent of the Normanist theory; reformed Russian literary language by combining Old Church Slavonic with vernacular tongue in his early grammar; influenced Russian poetry through his odes
Nikolay Lvov, polymath artist, geologist, philologist and ethnographer, compiled the first major collection of Russian folk songs, adapted rammed earth technology for northern climate and built the Priory Palace in Gatchina, pioneered HVAC technology, invented carton-pierre
Alexander Middendorf, zoologist and explorer, discoverer of Putorana Plateau, founder of permafrost science, studied the influence of permafrost on living beings, coined the term radula, prominent hippologist and horse breeder
Vladimir Obruchev, geologist, paleontologist, geographer and explorer of Siberia and Central Asia, author of the comprehensive Geology of Siberia and two popular science fiction novels, Plutonia and Sannikov Land
Peter Simon Pallas, polymath naturalist, geographer, ethnographer, philologist, explorer of European Russia and Siberia, discoverer of the first pallasite meteorite (Krasnojarsk) and multiple animals, including the Pallas's cat, Pallas's squirrel, and Pallas's gull
Yakov Perelman, a founder of popular science, author of many popular books, including the Physics Can Be Fun and Mathematics Can Be Fun
Nicholas Roerich, artist, writer, philosopher, archeologist, explorer of Central Asia, public figure, initiator of the international Roerich's Pact on the defense of cultural objects, author of over 7000 paintings
Pyotr Semyonov-Tyan-Shansky, ge |
https://en.wikipedia.org/wiki/2010%E2%80%9311%20Sun%20Hei%20SC%20season | The 2010–11 season is the 17th season of Sun Hei SC in Hong Kong First Division League. The team is coached by Brazilian coach José Ricardo Rambo.
Squad statistics
Statistics accurate as of match played 26 September 2010
Matches
Competitive
Hong Kong First Division League
Hong Kong Senior Challenge Shield
References
Sun Hei
Sun Hei SC seasons |
https://en.wikipedia.org/wiki/2004%E2%80%9305%20Sun%20Hei%20SC%20season | The 2004–05 Sun Hei SC season is the 11th season of Sun Hei SC in Hong Kong First Division League. The team was coached by Malaysian coach Koo Luam Khen.
Squad statistics
Statistics accurate as of match played 31 May 2005
Matches
Competitive
Hong Kong First Division League
Hong Kong Senior Challenge Shield
Hong Kong FA Cup
Hong Kong League Cup
References
Sun Hei SC seasons
Sun Hei |
https://en.wikipedia.org/wiki/1995%E2%80%9396%20Golden%20season | The 1995–96 season is the second season of Golden, the preceder of Sun Hei SC in Hong Kong First Division League.
Squad statistics
Statistics accurate as of match played 31 May 1996
Matches
Competitive
References
Sun Hei SC seasons
Gold |
https://en.wikipedia.org/wiki/Hermann%20Flaschka | Hermann Flaschka (25 March 1945 – 18 March 2021) was an Austrian-American mathematical physicist and Professor of Mathematics at the University of Arizona, known for his important contributions in completely integrable systems (soliton equations).
Childhood
Flaschka had lived in the USA since his family immigrated when he was a teenager. They lived in Atlanta, GA. His father Hermenegild Arved Flaschka (1915 - 1999) taught Chemistry at Georgia Tech. Hermann graduated from Druid Hills High School with the class of 1962 and received his Bachelor's degree at Georgia Tech in 1967.
Among other achievements there he also received the "William Gilmer Perry Awards for Freshman English" in 1963, despite the fact that he's not a native speaker.
Career
He received his Ph.D. from the Massachusetts Institute of Technology in 1970. His advisor was Gilbert Strang and the title of his thesis Asymptotic Expansions and Hyperbolic Equations with Multiple Characteristics.
He then worked as post-doc at the Carnegie Mellon University until 1972. He was a professor at the University of Arizona until his retirement in 2017.
He lectured as visiting professor at several institutions, among them the Clarkson University (1978/79), the Kyoto RIMS (1980/81) and the École Polytechnique Fédérale de Lausanne (2002).
In 1995 he received the Norbert Wiener Prize in Applied Mathematics. In 2012 he became a fellow of the American Mathematical Society.
Work
He made important contributions to the theory of completely integrable systems in particular the Toda lattice and the Korteweg–de Vries equation.
In 1980 he co-founded Physica D: Nonlinear Phenomena for which he also served as co-editor for many years. Publisher Elsevier now lists him as honorary editor.
References
External links
1995 Norbert Wiener Prize in Applied Mathematics, Notices AMS
Homepage
1945 births
2021 deaths
20th-century American mathematicians
21st-century American mathematicians
Austrian mathematicians
University of Arizona faculty
Georgia Tech alumni
Fellows of the American Mathematical Society
Massachusetts Institute of Technology alumni |
https://en.wikipedia.org/wiki/Sergio%20Albeverio | Sergio Albeverio (born 17 January 1939) is a Swiss mathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis (including infinite dimensional, non-standard, and stochastic analysis), mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences.
He initiated (with Raphael Høegh-Krohn) a systematic mathematical theory of Feynman path integrals and of infinite dimensional Dirichlet forms and associated stochastic processes (with applications particularly in quantum mechanics, statistical mechanics and quantum field theory). He also gave essential contributions to the development of areas such as p-adic functional and stochastic analysis as well as to the singular perturbation theory for differential operators. Other important contributions concern constructive quantum field theory and representation theory of infinite dimensional groups. He also initiated a new approach to the study of galaxy and planets formation inspired by stochastic mechanics.
Life and career
Albeverio is the son of Olivetta Albeverio Brighenti (1910–1968) and Luigi (Gino) Albeverio (1905–1968). He grew up in Lugano, Switzerland. He is married to Solvejg Albeverio Manzoni (painter and writer) since 1970. They have a daughter, Mielikki Albeverio (dipl. socialsc.).
Study of mathematics and physics at the ETH Zürich with a Diploma Thesis (1962) under the direction of Markus Fierz and David Ruelle, and a PhD Thesis (1966) under the direction of Res Jost and Markus Fierz.
Assistant at ETH Zürich (1962–67), visiting lecturer at Imperial College (1967–68, R. F. Streater). Invitation by Irving Segal as co-worker (MIT, 1968–69), replaced by a year stay as teacher at Liceo Cantonale, Lugano, due to family reasons.
Research Fellowship at Princeton University (1970–72, A. S. Wightman). Visiting Professorships at University of Oslo (1973–77, R. Høegh-Krohn), University of Naples (1973–74, G. F. Dell'Antonio), University of Aix-Marseille II (1976–77, D. Kastler, R. Stora).
Since 1977 permanent professorships in Germany:
1977–79 University of Bielefeld
1979–97 Titular of Chair for Probability and Mathematical Physics, Ruhr-University Bochum
Since 1997: Titular of Chair for Probability and Mathematical Statistics, University of Bonn (Emeritus since 2008). Member of the Hausdorff Center for Mathematics since its foundation (2006).
1997–2009: Professor and Director of Mathematics Section at Accademia di Architettura, USI, Mendrisio; 2011–2015 Chair Professorship in Mathematics, KFUPM, Dhahran.
Longer research and invited professorship positions at many universities and research centers in Europe, China, Japan, Mexico, USSR/Russia, USA.
Research interests
Albeverio's main research interests include probability theory (stochastic processes; stochastic analysis; SPDEs); analysis (function |
https://en.wikipedia.org/wiki/Abstract%20logic%20%28disambiguation%29 | Abstract logic is a formal system consisting of a class of sentences and a satisfaction relation with specific properties.
Abstract logic may also refer to:
Abstract algebraic logic, the study of the algebraization of deductive systems arising as an abstraction of the Lindenbaum-Tarski algebra
Abstract Logic (album), a 1995 album by Jonas Hellborg and Shawn Lane |
https://en.wikipedia.org/wiki/Lars%20Grorud | Lars Grorud (born 2 July 1983) is a retired Norwegian football defender.
He joined Brann at the start of the 2011 season.
Career statistics
Club
References
1983 births
Living people
Footballers from Tønsberg
Norwegian men's footballers
Men's association football defenders
FK Eik Tønsberg players
FK Tønsberg players
Sogndal Fotball players
SK Brann players
Fredrikstad FK players
Sandefjord Fotball players
Norwegian First Division players
Eliteserien players |
https://en.wikipedia.org/wiki/Schneider%E2%80%93Lang%20theorem | In mathematics, the Schneider–Lang theorem is a refinement by of a theorem of about the transcendence of values of meromorphic functions. The theorem implies both the Hermite–Lindemann and Gelfond–Schneider theorems, and implies the transcendence of some values of elliptic functions and elliptic modular functions.
Statement
Fix a number field and meromorphic , of which at least two are algebraically independent and have orders and , and such that for any . Then there are at most
distinct complex numbers such that for all combinations of and .
Examples
If and then the theorem implies the Hermite–Lindemann theorem that is transcendental for nonzero algebraic : otherwise, would be an infinite number of values at which both and are algebraic.
Similarly taking and for irrational algebraic implies the Gelfond–Schneider theorem that if and are algebraic, then }: otherwise, would be an infinite number of values at which both and are algebraic.
Recall that the Weierstrass P function satisfies the differential equation
Taking the three functions to be , , shows that, for any algebraic , if and are algebraic, then is transcendental.
Taking the functions to be and for a polynomial of degree shows that the number of points where the functions are all algebraic can grow linearly with the order .
Proof
To prove the result Lang took two algebraically independent functions from , say, and , and then created an auxiliary function . Using Siegel's lemma, he then showed that one could assume vanished to a high order at the . Thus a high-order derivative of takes a value of small size at one such s, "size" here referring to an algebraic property of a number. Using the maximum modulus principle, Lang also found a separate estimate for absolute values of derivatives of . Standard results connect the size of a number and its absolute value, and the combined estimates imply the claimed bound on .
Bombieri's theorem
and generalized the result to functions of several variables. Bombieri showed that if K is an algebraic number field and f1, ..., fN are meromorphic functions of d complex variables of order at most ρ generating a field K(f1, ..., fN) of transcendence degree at least d + 1 that is closed under all partial derivatives, then the set of points where all the functions fn have values in K is contained in an algebraic hypersurface in Cd of degree at most
gave a simpler proof of Bombieri's theorem, with a slightly stronger bound of d(ρ1 + ... + ρd+1)[K:Q] for the degree, where the ρj are the orders of d + 1 algebraically independent functions. The special case d = 1 gives the Schneider–Lang theorem, with a bound of (ρ1 + ρ2)[K:Q] for the number of points.
Example
If is a polynomial with integer coefficients then the functions are all algebraic at a dense set of points of the hypersurface .
References
Diophantine approximation
Transcendental numbers |
https://en.wikipedia.org/wiki/Charles%20Hadcock | Charles William George Hadcock is a British sculptor (born 1965 in Derby, England) known for his monumental sculptures that incorporate elements of geology, engineering, and mathematics. Hadcock's work also draws inspiration from music, philosophy, and poetry. He is a Deputy Lieutenant of Lancashire.
Charles Hadcock sculptures can be found in a variety of public and private collections around the world. His works are often large in scale and are made from a variety of materials, including steel, stone, and bronze. Two sculptures, "Helisphere" and "Torsion II", are exhibited in Canary Wharf Art Trail, London.
Education
Charles Hadcock studied at Ampleforth College 1979–1983, Derby College of Art & Technology 1983–1984, Cheltenham College of Art 1984–1987, Royal College of Art 1987–1989.
Career
Aspects of the natural world, geology and engineering lie in combination within Charles Hadcock's work openly, or as hidden jewels. Finding that the mathematical formulas for shapes observed within the natural world are often the source for solving engineering design problems, Hadcock has incorporated these ideas both at first and at second hand into components for his sculptures. His direct observation of rocks becomes a source for the surface of his sculptures while mathematics inform how a sculpture may be achieved with multiple castings of a single form. Hadcock's works are imbued with a visual vitality so that the sculptures remain free, dynamic, unrestrained, and immediate.
Hadcock prefers to work on his own sculpture rather than rely on production facilities so that the eye and hand of the artist is apparent in every work. His belief is that his knowledge, skill, and techniques are constantly evolving, informing each piece he makes.
Investigating Multiples, a 1996 solo exhibition in London at Reed's Wharf Gallery followed the siting of Caesura IV at Sculpture at Goodwood. His first monumental public commission in 1997, Passacaglia, came after a national competition for a permanent work to be installed on Brighton Beach. Controversial initially, Passacaglia is now an iconic feature of the Brighton beachfront.
A 1999 exhibition of Hadcock's drawings and maquettes If in doubt, ask at London's Imperial College was part of a drive by the university to encourage engineering students to learn about the arts. There is 1 in all of us was a collaboration with soundscape engineers at the Gardner Arts Centre, University of Sussex, whilst the Peter Scott Gallery at Lancaster University had to find additional exhibition space outside the gallery in 2006.
Hadcock was included in the 1999 exhibition of British sculptors Shape of the Century at Salisbury Cathedral and Canary Wharf, which was followed by inclusion in Bronze: Contemporary British Sculpture, a group show to celebrate the millennium and the tradition of siting bronze sculptures in London parks. Hadcock's monumental bronze, Caesura VI, was installed and remains in situ in Holland Park, Lond |
https://en.wikipedia.org/wiki/Latt%C3%A8s%20map | In mathematics, a Lattès map is a rational map f = ΘLΘ−1 from the complex sphere to itself such that Θ is a holomorphic map from a complex torus to the complex sphere and L is an affine map z → az + b from the complex torus to itself.
Lattès maps are named after French mathematician Samuel Lattès, who wrote about them in 1918.
References
Dynamical systems |
https://en.wikipedia.org/wiki/Equichordal%20point | In geometry, an equichordal point is a point defined relative to a convex plane curve such that all chords passing through the point are equal in length. Two common figures with equichordal points are the circle and the limaçon. It is impossible for a curve to have more than one equichordal point.
Equichordal curves
A curve is called equichordal when it has an equichordal point. Such a curve may be constructed as the pedal curve of a curve of constant width. For instance, the pedal curve of a circle is either another circle (when the center of the circle is the pedal point) or a limaçon; both are equichordal curves.
Multiple equichordal points
In 1916 Fujiwara proposed the question of whether a curve could have two equichordal points (offering in the same paper a proof that three or more is impossible). Independently, a year later, Blaschke, Rothe and Weitzenböck posed the same question. The problem remained unsolved until it was finally proven impossible in 1996 by Marek Rychlik. Despite its elementary formulation, the equichordal point problem was difficult to solve. Rychlik's theorem is proved by methods of advanced complex analysis and algebraic geometry and it is 72 pages long.
References
External links
Curves
Geometry |
https://en.wikipedia.org/wiki/Compound%20probability%20distribution | In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables.
If the parameter is a scale parameter, the resulting mixture is also called a scale mixture.
The compound distribution ("unconditional distribution") is the result of marginalizing (integrating) over the latent random variable(s) representing the parameter(s) of the parametrized distribution ("conditional distribution").
Definition
A compound probability distribution is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution with an unknown parameter that is again distributed according to some other distribution . The resulting distribution is said to be the distribution that results from compounding with . The parameter's distribution is also called the mixing distribution or latent distribution. Technically, the unconditional distribution results from marginalizing over , i.e., from integrating out the unknown parameter(s) . Its probability density function is given by:
The same formula applies analogously if some or all of the variables are vectors.
From the above formula, one can see that a compound distribution essentially is a special case of a marginal distribution: The joint distribution of and is given by
, and the compound results as its marginal distribution:
.
If the domain of is discrete, then the distribution is again a special case of a mixture distribution.
Properties
General
The compound distribution will depend on the specific expression of each distribution, as well as which parameter of is distributed according to the distribution , and the parameters of will include any parameters of that are not marginalized, or integrated, out.
The support of is the same as that of , and if the latter is a two-parameter distribution parameterized with the mean and variance, some general properties exist.
Mean and variance
The compound distribution's first two moments are given by the law of total expectation and the law of total variance:
If the mean of is distributed as , which in turn has mean and variance the expressions above imply and , where is the variance of .
Proof
let and be probability distributions parameterized with mean a variance asthen denoting the probability density functions as and respectively, and being the probability density of we haveand we have from the parameterization and thatand therefore the mean of the compound distribution as per the expression for its first moment above.
The variance of is given by , andgiven the fact that and . Finally we get
Applications
Testing
Distributions of common test statistics result as compound distr |
https://en.wikipedia.org/wiki/List%20of%20career%20achievements%20by%20Hakeem%20Olajuwon | This page details the career achievements of Nigerian American basketball player Hakeem Olajuwon.
NBA statistics
Averages
Totals
Career highs
Top shot-blocking efforts
Regular season
Playoffs
NBA regular season leader
Blocks per game: 1990 (4.6), 1991 (3.9), 1993 (4.2)
Rebounds per game: 1989 (13.5), 1990 (14.0)
Offensive rebounds: 1985 (440)
Defensive rebounds: 1989 (767), 1990 (850)
Total rebounds: 1989 (1,105), 1990 (1,149)
Blocks: 1990 (376), 1993 (342)
Personal fouls: 1985 (344)
Field goal attempts: 1994 (1,694)
Games played: 1985 (82), 1989 (82), 1990 (82), 1999 (50)
Achievements
2× NBA champion (1994, '95)
2× NBA Finals MVP (1994, '95)
1× NBA MVP (1994)
2× Defensive Player of Year (1993, '94)
6× All-NBA First Team (1987, '88, '89, '93, '94, '97)
3× All-NBA Second Team ('86, '90, '96)
3× All-NBA Third Team (1991, '95, '99)
5× All-Defensive First Team ('87, '88, '90, '93, '94)
4× All-Defensive Second Team ('85, '91, '96, '97)
12× All-Star
Olympic gold medalist (1996)
Named one of the 50 Greatest Players in NBA History (1996).
Olajuwon ended his career in the top ten all-time in blocks, scoring, rebounding, and steals. He is the only player in NBA history to retire in the top ten for all four categories (he is now 11th all-time in rebounding).
Olajuwon was elected to the Naismith Memorial Basketball Hall of Fame as a member of the class of 2008.
Ranked #10 in ESPN'''s All-Time #NBArank: Counting down the greatest players ever (published in 2016)
Ranked #12 in SLAM Magazines 2018 revision of the top 100 greatest players of all time (published in the January 2018 issue)
NBA records
Regular seasonMost points scored without free throw attempt in a game: Houston Rockets (109) vs. Denver Nuggets (113),
48 points - 24/40 FG%
Broken by Jamal Murray in ()Third player in NBA history to record a quadruple-double in a game: Houston Rockets (120) vs. Milwaukee Bucks (94),
18 points, 16 rebounds, 10 assists, 11 blocks (and 1 steal) in 40 minutes
Nate Thurmond, Alvin Robertson and David Robinson are the only other players to achieve this.Seasons leading the league in defensive rebounds: 2 (—)
Broken by Dennis Rodman in Consecutive seasons leading the league in defensive rebounds: 2 (—)
Broken by Kevin Garnett in Blocked shots, career: 3,830Consecutive seasons leading the league in blocked shots: 2 (—)
Broken by Dikembe Mutombo in Steals by a center, career: 2,162Steals by a center, season: 213 ()
Also holds second (see below)Five by fives, career: 6Only player in NBA history to record 200 blocks and 200 steals in the same season: 282 blocks, 213 steals ()Seasons with 200 blocks and 100 steals: 11 (—)
Only twelve players in NBA history have achieved this feat in the same season.Third player in NBA history to lead the league in blocks and rebounding in the same season: 14.0 rebounds and 4.6 blocks per game ()
Also achieved by Kareem Abdul-Jabbar (Los Angeles Lakers, ), Bill Walton (Portland Trail Blazers, ), Ben Wallace (Detroit Piston |
https://en.wikipedia.org/wiki/Concomitant%20%28statistics%29 | In statistics, the concept of a concomitant, also called the induced order statistic, arises when one sorts the members of a random sample according to corresponding values of another random sample.
Let (Xi, Yi), i = 1, . . ., n be a random sample from a bivariate distribution. If the sample is ordered by the Xi, then the Y-variate associated with Xr:n will be denoted by Y[r:n] and termed the concomitant of the rth order statistic.
Suppose the parent bivariate distribution having the cumulative distribution function F(x,y) and its probability density function f(x,y), then the probability density function of rth concomitant for is
If all are assumed to be i.i.d., then for , the joint density for is given by
That is, in general, the joint concomitants of order statistics is dependent, but are conditionally independent given for all k where . The conditional distribution of the joint concomitants can be derived from the above result by comparing the formula in marginal distribution and hence
References
Theory of probability distributions |
https://en.wikipedia.org/wiki/Mechanical%20testing | Mechanical testing covers a wide range of tests, which can be divided broadly into two types:
those that aim to determine a material's mechanical properties, independent of geometry.
those that determine the response of a structure to a given action, e.g. testing of composite beams, aircraft structures to destruction, etc.
Mechanical testing of materials
There exists a large number of tests, many of which are standardized, to determine the various mechanical properties of materials. In general, such tests set out to obtain geometry-independent properties; i.e. those intrinsic to the bulk material. In practice this is not always feasible, since even in tensile tests, certain properties can be influenced by specimen size and/or geometry. Here is a listing of some of the most common tests:
Hardness Testing
Vickers hardness test (HV), which has one of the widest scales
Brinell hardness test (HB)
Knoop hardness test (HK), for measurement over small areas
Janka hardness test, for wood
Meyer hardness test
Rockwell hardness test (HR), principally used in the USA
Shore durometer hardness, used for polymers
Barcol hardness test, for composite materials
Tensile testing, used to obtain the stress-strain curve for a material, and from there, properties such as Young modulus, yield (or proof) stress, tensile stress and % elongation to failure.
Impact testing
Izod test
Charpy test
Fracture toughness testing
Linear-elastic (KIc)
K–R curve
Elastic plastic (JIc, CTOD)
Creep Testing, for the mechanical behaviour of materials at high temperatures (relative to their melting point)
Fatigue Testing, for the behaviour of materials under cyclic loading
Load-controlled smooth specimen tests
Strain-controlled smooth specimen tests
Fatigue crack growth testing
Non-Destructive Testing
References
General references
Materials science
Materials testing
Tests |
https://en.wikipedia.org/wiki/Leifur%20Magnusson | Leifur Magnusson (7 July 1882 – 15 February 1960) was an Icelandic American economist with the Bureau of Labor Statistics and the International Labour Organization.
Biography
He was born in Iceland on 7 July 1882. He died in a traffic accident in Claremont, California on 15 February 1960.
References
1960 deaths
1882 births
Icelandic emigrants to the United States
International Labour Organization people
Road incident deaths in California |
https://en.wikipedia.org/wiki/Baumslag%E2%80%93Gersten%20group | In the mathematical subject of geometric group theory, the Baumslag–Gersten group, also known as the Baumslag group, is a particular one-relator group exhibiting some remarkable properties regarding its finite quotient groups, its Dehn function and the complexity of its word problem.
The group is given by the presentation
Here exponential notation for group elements denotes conjugation, that is, for .
History
The Baumslag–Gersten group G was originally introduced in a 1969 paper of Gilbert Baumslag, as an example of a non-residually finite one-relator group with an additional remarkable property that all finite quotient groups of this group are cyclic. Later, in 1992, Stephen Gersten showed that G, despite being a one-relator group given by a rather simple presentation, has the Dehn function growing very quickly, namely faster than any fixed iterate of the exponential function. This example remains the fastest known growth of the Dehn function among one-relator groups. In 2011 Alexei Myasnikov, Alexander Ushakov, and Dong Wook Won proved that G has the word problem solvable in polynomial time.
Baumslag-Gersten group as an HNN extension
The Baumslag–Gersten group G can also be realized as an HNN extension of the Baumslag–Solitar group with stable letter t and two cyclic associated subgroups:
Properties of the Baumslag–Gersten group G
Every finite quotient group of G is cyclic. In particular, the group G is not residually finite.
An endomorphism of G is either an automorphism or its image is a cyclic subgroup of G. In particular the group G is Hopfian and co-Hopfian.
The outer automorphism group Out(G) of G is isomorphic to the additive group of dyadic rationals and in particular is not finitely generated.
Gersten proved that the Dehn function f(n) of G grows faster than any fixed iterate of the exponential. Subsequently A. N. Platonov proved that f(n) is equivalent to
Myasnikov, Ushakov, and Won, using compression methods of ``power circuits" arithmetics, proved that the word problem in G is solvable in polynomial time. Thus the group G exhibits a large gap between the growth of its Dehn function and the complexity of its word problem.
The conjugacy problem in G is known to be decidable, but the only known worst-case upper bound estimate for the complexity of the conjugacy problem, due to Janis Beese, is elementary recursive. It is conjectured that this estimate is sharp, based on some reductions to power circuit division problems. There is a strongly generically polynomial time solution of the conjugacy problem for G.
Generalizations
Andrew Brunner considered one-relator groups of the form
where
and generalized many of Baumslag's original results in that context.
Mahan Mitra considered a word-hyperbolic analog G of the Baumslag–Gersten group, where Mitra's group possesses a rank three free subgroup that is highly distorted in G, namely where the subgroup distortion is higher than any fixed iterated power of the exponent |
https://en.wikipedia.org/wiki/Dirac%20spectrum | In mathematics, a Dirac spectrum, named after Paul Dirac, is the spectrum of eigenvalues of a Dirac operator on a Riemannian manifold with a spin structure. The isospectral problem for the Dirac spectrum asks whether two Riemannian spin manifolds have identical spectra. The Dirac spectrum depends on the spin structure in the sense that there exists a Riemannian manifold with two different spin structures that have different Dirac spectra.
See also
Can you hear the shape of a drum?
Dirichlet eigenvalue
Spectral asymmetry
Angle-resolved photoemission spectroscopy
References
Spectral theory
Quantum mechanics |
https://en.wikipedia.org/wiki/Hamilton%20Tiger-Cats%20all-time%20records%20and%20statistics | The following is a list of Hamilton Tiger-Cats all time records and statistics for players current to the 2023 CFL season. This list includes all seasons since the Hamilton Tiger-Cats' inception in 1950 and does not include lineage figures from the Hamilton Tigers nor the Hamilton Wildcats. Each category lists the top six players, where known, except for when the sixth place player is tied in which case all players with the same number are listed. Aside from Grey Cup championship games played and won, this list includes only regular season statistics.
For records by head coaches, see List of Hamilton Tiger-Cats head coaches.
Grey Cup championships
Grey Cup games won
4 – Angelo Mosca, Tommy Grant, John Barrow, Chet Miksza, Garney Henley, Bob Krouse
3 – Pete Neumann, Zeno Karcz, Bill Danychuk, Joe Zuger, Gene Ceppetelli, Ellison Kelly, Hal Patterson
Grey Cup games played in
9 – John Barrow, Tommy Grant
8 – Angelo Mosca, Chet Miksza
7 – Pete Neumann, Garney Henley, Ralph Goldston, Zeno Karcz, Geno DeNobile
Tenure
Most Games Played
296 – Paul Osbaldiston – (1986-2003)
216 – Garney Henley – (1960-75)
204 – Rocky DiPietro – (1978-91)
200 – Rob Hitchcock – (1995-2006)
192 – John Barrow – (1957-70)
184 – Pete Newmann – (1951-64)
Most Seasons Played
18 – Paul Osbaldiston – (1986-2003)
16 – Garney Henley – (1960-75)
15 – Chet Miksza – (1952-65, 68)
14 – Pete Newmann – (1951-64)
14 – John Barrow – (1957-70)
14 – Rocky DiPietro – (1978-91)
Scoring
Most Points – Career
2856 – Paul Osbaldiston – (1986-2003)
1069 – Bernie Ruoff – (1980-87)
603 – Tommy Joe Coffey – (1967-72)
561 – Justin Medlock – (2011, 2014-15)
522 – Earl Winfield – (1987-97)
476 – Nick Setta – (2007-09)
Most Points – Season
233 – Paul Osbaldiston – 1989
212 – Paul Osbaldiston – 1990
203 – Paul Osbaldiston – 1999
197 – Justin Medlock – 2011
196 – Paul Osbaldiston – 1992
189 – Paul Osbaldiston – 1994
Most Points – Game
26 – Terry Evanshen – versus Ottawa Rough Riders, September 7, 1975
24 – Garney Henley – versus Saskatchewan Roughriders, October 15, 1962
24 – Kalin Hall – versus BC Lions, October 15, 1995
24 – Paul Osbaldiston – versus Ottawa Rough Riders, September 22, 1996
24 – Tony Akins – versus Winnipeg Blue Bombers, October 10, 1999
24 – Justin Medlock – versus BC Lions, October 22, 2011
Most Touchdowns – Career
87 – Earl Winfield – (1987-97)
62 – Brandon Banks – (2013-19, 2021)
56 – Garney Henley – (1960-75)
54 – Tommy Grant – (1956-68)
50 – Dave Flemming – (1965-74)
46 – Ronald Williams – (1998-2001)
Most Touchdowns – Season
17 – Chris Williams – 2012
16 – Brandon Banks – 2019
15 – Tony Champion – 1989
15 – Ronald Williams – 1999
15 – Ronald Williams – 2000
13 – Terry Evanshen – 1975
13 – Steve Stapler – 1987
13 – Earl Winfield – 1988
13 – Earl Winfield – 1990
13 – Earl Winfield – 1995
13 – Ronald Williams – 1998
Most Touchdowns – Game
4 – Garney Henley – versus Saskatchewan Roughriders, October 15, 1962
4 – Terry Evanshen – versus Ottawa Rough Riders, September 7, 1975 |
https://en.wikipedia.org/wiki/Saskatchewan%20Roughriders%20all-time%20records%20and%20statistics | The following is a list of Saskatchewan Roughriders all-time records and statistics current to the 2023 CFL season. Each category lists the top five players, where known, except for when the fifth place player is tied in which case all players with the same number are listed.
Grey Cup Championships
Most by a Player
2 - Darian Durant
2 - John Chick
2 - Mike McCullough
2 - Neal Hughes
2 - Chris Getzlaf
Games
Most Games
284 – Gene Makowsky
271 – Roger Aldag
246 – Ron Lancaster
238 – Reg Whitehouse
237 – Ron Atchison
Most Regular Seasons Played
17 – Ron Atchison – 1952–1968
17 – Roger Aldag – 1976–1992
17 – Gene Makowsky – 1995–2011
16 – Ron Lancaster – 1963–1978
15 – Fred Wilson – 1911–1926
15 – Bill Clarke – 1951–1965
15 – Reg Whitehouse – 1952–1966
Scoring
Most Points – Career
2374 – Dave Ridgway
1613 – Paul McCallum
863 – Jack Abendschan
823 – George Reed
757 – Luca Congi
Most Points – Season
233 – Dave Ridgway – 1990
216 – Dave Ridgway – 1989
216 – Dave Ridgway – 1991
215 – Dave Ridgway – 1988
198 – Brett Lauther – 2018
Most Points – Game
30 – Ferd Burkett – versus Winnipeg Blue Bombers, October 26, 1959
28 – Dave Ridgway – versus Ottawa Rough Riders, July 29, 1984
25 – Dave Ridgway – versus Edmonton Eskimos, August 19, 1984
24 – Several tied
Most Touchdowns – Career
137 – George Reed
78 – Ray Elgaard
75 – Don Narcisse
60 – Hugh Campbell
55 – Ken Carpenter
55 – Weston Dressler
Most Touchdowns – Season
18 – Ken Carpenter – 1955
17 – Hugh Campbell – 1966
17 – Craig Ellis – 1985
16 – Jack Hill – 1958
16 – George Reed – 1968
16 – Wes Cates – 2010
Most Touchdowns – Game
5 – Ferd Burkett – versus Winnipeg Blue Bombers, October 26, 1959
4 – Brian Timmis – versus Saskatoon Quakers, October 30, 1920
4 – George Reed – versus Edmonton Eskimos, October 30, 1968
4 – Milson Jones – versus Winnipeg Blue Bombers, August 31, 1988
Most Rushing Touchdowns – Career
134 – George Reed
41 – Wes Cates
34 – Kent Austin
32 – Chris Szarka
30 – Milson Jones
Most Rushing Touchdowns – Season
16 – George Reed – 1968
15 – George Reed – 1967
15 – Wes Cates – 2010
14 – Craig Ellis – 1985
13 – George Reed – 1972
Most Rushing Touchdowns – Game
4 – Ferd Burkett – versus Winnipeg Blue Bombers, October 26, 1959
4 – George Reed – versus Edmonton Eskimos, October 30, 1968
4 – Milson Jones – versus Winnipeg Blue Bombers, August 31, 1988
Most Touchdown Receptions – Career
78 – Ray Elgaard
75 – Don Narcisse
60 – Hugh Campbell
53 – Jeff Fairholm
50 – Weston Dressler
Most Touchdown Receptions – Season
17 – Hugh Campbell – 1966
14 – Jack Hill – 1958
14 – Joey Walters – 1981
13 – Jeff Fairholm – 1991
13 – Weston Dressler – 2012
Most Touchdown Receptions – Game
3 – several tied, most recently Samuel Emilus – versus Winnipeg Blue Bombers, June 16, 2023
Most Kickoff Return Touchdowns – Career
2 – Mario Alford (2022–23)
2 – Demetris Bendross (2000–02)
2 – Marcus Thigpen (2009, 2017–19)
Most Kickoff Return Touchdowns – Season
2 – Mario Alford – 2022
2 – Demetris Bendross – |
https://en.wikipedia.org/wiki/Consistent%20pricing%20process | A consistent pricing process (CPP) is any representation of (frictionless) "prices" of assets in a market. It is a stochastic process in a filtered probability space such that at time the component can be thought of as a price for the asset.
Mathematically, a CPP in a market with d-assets is an adapted process in if Z is a martingale with respect to the physical probability measure , and if at all times such that is the solvency cone for the market at time .
The CPP plays the role of an equivalent martingale measure in markets with transaction costs. In particular, there exists a 1-to-1 correspondence between the CPP and the EMM .
References
Financial risk modeling
Mathematical finance |
https://en.wikipedia.org/wiki/Edmonton%20Elks%20all-time%20records%20and%20statistics | The following is a select list of Edmonton Elks all-time records and statistics current to the 2023 CFL season.
Grey Cup championships
Won, as a player:
7 – Bill Stevenson - (, -, )
6 – Dave Cutler - (, -)
6 – Dave Fennell - (, -)
6 – Larry Highbaugh - (, -)
6 – Dan Kepley - (, -)
6 – Dale Potter - (, -)
6 – Tom Towns - (, -)
Grey Cup games played in:
9 – Dave Cutler - (-, -)
9 – Larry Highbaugh - (-, -)
8 – Ron Estay - (-, -)
8 – Bob Howes - (-, -)
8 – Tom Wilkinson - (-, -)
8 – Dave Fennell - (-, -)
8 – Dale Potter - (-, -)
8 – Bill Stevenson - (, -, )
Won, as a Head Coach:
5 – Hugh Campbell - (-)
3 – Pop Ivy - (-)
Grey Cup appearances for a Head Coach:
6 – Hugh Campbell - (-)
3 – Pop Ivy - (-)
3 – Ray Jauch - (-)
Coaching
Seasons
11 – William Deacon White
7 – Ray Jauch
7 – Ron Lancaster
Games
126 – Ron Lancaster
112 – Ray Jauch
96 – Hugh Campbell
96 – Neill Armstrong
Wins
83 – Ron Lancaster
70 – Hugh Campbell
65 – Ray Jauch
Best Winning Percentage (min. 30 games)
.781 – Pop Ivy
.755 – Hugh Campbell
.667 – Ron Lancaster
Losses
56 – Neill Armstrong
43 – Ray Jauch
43 – Ron Lancaster
Worst Winning Percentage (min. 30 games)
.398 – Neill Armstrong
.407 – Kavis Reed
.444 – Don Matthews
.444 – Richie Hall
Games played
274 – Rod Connop
268 – Sean Fleming
254 - Dave Cutler
Scoring
Most points – Career
2,571 – Sean Fleming
2,237 – Dave Cutler
756 – Sean Whyte
677 – Jackie Parker
Most Points – Season
224 – Jerry Kauric -
207 – Sean Fleming -
204 – Sean Fleming -
195 – Dave Cutler -
Most Points – Game
30 – Eric Blount – vs. Winnipeg Blue Bombers, Sept. 15, 1995
24 – Jim Germany - vs. Hamilton Tiger-Cats, Aug. 1, 1981
24 – Brian Kelly - vs. Ottawa Rough Riders, June 30, 1984
24 – Sean Fleming - @ BC Lions, Oct. 29, 1993
24 – Kez McCorvey - vs. Winnipeg Blue Bombers, July 21, 2000
Touchdowns
Most Touchdowns – Career
97 – Brian Kelly
79 – Jackie Parker
77 – Norman Kwong
Most Touchdowns – Season
20 – Blake Marshall -
19 – Jim Germany -
18 – Brian Kelly -
Most Touchdowns – Game
5 – Eric Blount - vs. Winnipeg Blue Bombers, Sept. 15, 1995
4 – Jim Germany - vs. Hamilton Tiger-Cats, Aug. 1, 1981
4 – Brian Kelly - vs. Ottawa Rough Riders, June 30, 1984
4 – Kez McCorvey - vs. Winnipeg Blue Bombers, July 21, 2000
Kicking
Most Converts – Career
713 – Sean Fleming
627 – Dave Cutler
170 – Jerry Kauric
Most Converts – Season
70 – Jerry Kauric -
64 – Ray Macoritti -
63 – Sean Fleming -
Most Converts - Game
9 – Sean Fleming - vs. Winnipeg Blue Bombers, Sept. 15, 1995
8 – Dave Cutler - vs. Montreal Alouettes, Sept. 26, 1981
8 – Dave Cutler - vs. Toronto Argonauts, Oct. 24, 1981
Most Field Goals – Career
553 – Sean Fleming
464 – Dave Cutler
195 – Sean Whyte
Most Field Goals – Season
50 – Dave Cutler -
47 – Sean Fleming -
47 – Sean Whyte -
45 – Jerry Kauric -
45 – Sean Fleming -
45 – Sean Whyte -
Most Field Goals – Game
7 – Sean Whyte - @ Winnipeg Blue Bombers, June 27, 2019
7 – Sean Whyte - vs. Winnipeg Blue Bombers, Aug. 23, |
https://en.wikipedia.org/wiki/Topic%20model | In statistics and natural language processing, a topic model is a type of statistical model for discovering the abstract "topics" that occur in a collection of documents. Topic modeling is a frequently used text-mining tool for discovery of hidden semantic structures in a text body. Intuitively, given that a document is about a particular topic, one would expect particular words to appear in the document more or less frequently: "dog" and "bone" will appear more often in documents about dogs, "cat" and "meow" will appear in documents about cats, and "the" and "is" will appear approximately equally in both. A document typically concerns multiple topics in different proportions; thus, in a document that is 10% about cats and 90% about dogs, there would probably be about 9 times more dog words than cat words. The "topics" produced by topic modeling techniques are clusters of similar words. A topic model captures this intuition in a mathematical framework, which allows examining a set of documents and discovering, based on the statistics of the words in each, what the topics might be and what each document's balance of topics is.
Topic models are also referred to as probabilistic topic models, which refers to statistical algorithms for discovering the latent semantic structures of an extensive text body. In the age of information, the amount of the written material we encounter each day is simply beyond our processing capacity. Topic models can help to organize and offer insights for us to understand large collections of unstructured text bodies. Originally developed as a text-mining tool, topic models have been used to detect instructive structures in data such as genetic information, images, and networks. They also have applications in other fields such as bioinformatics and computer vision.
History
An early topic model was described by Papadimitriou, Raghavan, Tamaki and Vempala in 1998. Another one, called probabilistic latent semantic analysis (PLSA), was created by Thomas Hofmann in 1999. Latent Dirichlet allocation (LDA), perhaps the most common topic model currently in use, is a generalization of PLSA. Developed by David Blei, Andrew Ng, and Michael I. Jordan in 2002, LDA introduces sparse Dirichlet prior distributions over document-topic and topic-word distributions, encoding the intuition that documents cover a small number of topics and that topics often use a small number of words. Other topic models are generally extensions on LDA, such as Pachinko allocation, which improves on LDA by modeling correlations between topics in addition to the word correlations which constitute topics. Hierarchical latent tree analysis (HLTA) is an alternative to LDA, which models word co-occurrence using a tree of latent variables and the states of the latent variables, which correspond to soft clusters of documents, are interpreted as topics.
Topic models for context information
Approaches for temporal information include Block and Newman's determinati |
https://en.wikipedia.org/wiki/Jon%20Deeks | Jon Deeks is a professor of biostatistics at the University of Birmingham, England. He was elected a Fellow of the Academy of Medical Sciences in 2021.
References
Living people
Academics of the University of Birmingham
Biostatisticians
Year of birth missing (living people)
NIHR Senior Investigators |
https://en.wikipedia.org/wiki/String%20group | In topology, a branch of mathematics, a string group is an infinite-dimensional group introduced by as a -connected cover of a spin group. A string manifold is a manifold with a lifting of its frame bundle to a string group bundle. This means that in addition to being able to define holonomy along paths, one can also define holonomies for surfaces going between strings. There is a short exact sequence of topological groupswhere is an Eilenberg–MacLane space and is a spin group. The string group is an entry in the Whitehead tower (dual to the notion of Postnikov tower) for the orthogonal group:It is obtained by killing the homotopy group for , in the same way that is obtained from by killing . The resulting manifold cannot be any finite-dimensional Lie group, since all finite-dimensional compact Lie groups have a non-vanishing . The fivebrane group follows, by killing .
More generally, the construction of the Postnikov tower via short exact sequences starting with Eilenberg–MacLane spaces can be applied to any Lie group G, giving the string group String(G).
Intuition for the string group
The relevance of the Eilenberg-Maclane space lies in the fact that there are the homotopy equivalencesfor the classifying space , and the fact . Notice that because the complex spin group is a group extensionthe String group can be thought of as a "higher" complex spin group extension, in the sense of higher group theory since the space is an example of a higher group. It can be thought of the topological realization of the groupoid whose object is a single point and whose morphisms are the group . Note that the homotopical degree of is , meaning its homotopy is concentrated in degree , because it comes from the homotopy fiber of the mapfrom the Whitehead tower whose homotopy cokernel is . This is because the homotopy fiber lowers the degree by .
Understanding the geometry
The geometry of String bundles requires the understanding of multiple constructions in homotopy theory, but they essentially boil down to understanding what -bundles are, and how these higher group extensions behave. Namely, -bundles on a space are represented geometrically as bundle gerbes since any -bundle can be realized as the homotopy fiber of a map giving a homotopy squarewhere . Then, a string bundle must map to a spin bundle which is -equivariant, analogously to how spin bundles map equivariantly to the frame bundle.
Fivebrane group and higher groups
The fivebrane group can similarly be understood by killing the group of the string group using the Whitehead tower. It can then be understood again using an exact sequence of higher groupsgiving a presentation of it terms of an iterated extension, i.e. an extension by by . Note map on the right is from the Whitehead tower, and the map on the left is the homotopy fiber.
See also
Gerbe
N-group (category theory)
Elliptic cohomology
String bordism
References
External links
From Loop Groups to 2-groups - gives a c |
https://en.wikipedia.org/wiki/Waxahachie%20Global%20High%20School | Waxahachie Global High School is a high school in Waxahachie, Texas, founded in 2007 on the historic T.C. Wilemon campus. It is one of only 91 STEM (science, technology, engineering, and mathematics) academies in the state of Texas. It was additionally granted Early College High School status in 2009 through a partnership with Navarro College, allowing students to earn an associate degree along with their high school diploma. Recently, as of the start of the 2013-2014 school year, Global High made a partnership with UT Tyler for all the STEM-based college courses offered at Global. As a public charter school, students from Ellis County and surrounding areas can attend regardless of zoning. Many students commute from surrounding cities such as Waxahachie, Red Oak, Ennis, Maypearl, Midlothian, Palmer, Italy, Cedar Hill, and Desoto. In 2014, Waxahachie Global was named the "Best High School" by the U.S. News & World Report. Starting in the 2018-19 school year, the Global campus is located in the Billy R. Hancock Building (formerly the Ninth Grade Academy).
School structure and graduation requirements
As both a T-STEM academy and Early College High School, Global has a unique structure. Students are fully enrolled in Navarro College after passing the Accuplacer tests or earning sufficient STAAR scores. Tuition is paid by the college with no cost to Global families, and as such, qualifying students are encouraged to fully utilize Navarro's resources. In addition to dual credit classes offered during the school day, students may take zero and ninth hour (before and after school) courses on Global's campus, and select evening and summer courses on Navarro's Midlothian or Waxahachie campus.
To graduate with an associate degree, students must earn 63 credit hours in select fields mandated by Navarro College. Global students who complete all the required courses in good standing are eligible to receive an Associate's of Science (AS) or an Associate's of Art (AA) degree. Any credit hours earned, regardless of degree completion status, may be transferred to participating four-year universities. This enables even non-degree earning students to transfer a minimum amount of credits to their continuing education without having to pay for the courses.
Global offers a variety of upper level science classes, engineering electives, mathematics from Geometry through college Calculus II, and a wide assortment of technical computer courses to fulfill its STEM standing. To fill unique graduation requirements, all students are required to take an engineering course in addition to two technology courses. Other graduation requirements follow the Texas standards.
The third pillar of Global's structure is project-based learning. This method teaches teamwork, responsibility, presentation skills, time management and more. Each teacher assigns around 5 projects per school year; often more in the case of engineering and technology courses. Popular projects have included des |
https://en.wikipedia.org/wiki/Geometry%20Expert | Geometry Expert (GEX) is a Chinese software package for dynamic diagram drawing and automated geometry theorem proving and discovering.
There's a new Chinese version of Geometry Expert, called MMP/Geometer.
Java Geometry Expert is free under GNU General Public License.
External links
GEX Official website
Java GEX (old, new) on Wichita State University
Java GEX Documentation on Wichita State University
Theorem proving software systems
Automated theorem proving
Interactive geometry software |
https://en.wikipedia.org/wiki/Olga%20Kharlampovich | Olga Kharlampovich (born March 25, 1960 in Sverdlovsk) is a Russian-Canadian mathematician working in the area of group theory. She is the Mary P. Dolciani Professor of Mathematics at the CUNY Graduate Center and Hunter College.
Contributions
Kharlampovich is known for her example of a finitely presented 3-step solvable group with unsolvable word problem (solution of the Novikov–Adian problem) and for the solution together with A. Myasnikov of the Tarski conjecture (from 1945) about equivalence of first-order theories of finitely generated non-abelian free groups (also solved by Zlil Sela) and decidability of this common theory.
Algebraic geometry for groups, introduced by Baumslag, Myasnikov, Remeslennikov, and Kharlampovich
became one of the new research directions in combinatorial group theory.
Education and career
She received her Ph.D. from the Leningrad State University in 1984 (her doctoral advisor was Lev Shevrin) and Russian “Doctor of Science” in 1990 from the Moscow Steklov Institute of Mathematics.
Prior to her current appointment at CUNY, she held a position at Ural State University, Ekaterinburg, Russia, and was a Professor of Mathematics at McGill University, Montreal, Canada, where she had been working since 1990.
As of August 2011 she moved to Hunter College of the City University of New York as the Mary P. Dolciani Professor of Mathematics, where she is the inaugural holder of the first endowed professorship in the Department of Mathematics and Statistics.
Recognition
For her undergraduate work on the Novikov–Adian problem she was awarded in 1981 a Medal from the Soviet Academy of Sciences. She received an Ural Mathematical Society Award in 1984 for the solution of the Malcev–Kargapolov problem posed in 1965 about the algorithmic decidability of the universal theory of the class of all finite nilpotent groups.
Kharlampovich was awarded in 1996 the Krieger–Nelson Prize of the Canadian Mathematical Society for her work on algorithmic problems in varieties of groups and Lie algebras (the description of this work can be found in the survey paper with Sapir and on the prize web site).
She was awarded the 2015 Mal'cev Prize for the series of works on fundamental model-theoretic problems in algebra.
She was elected a Fellow of the American Mathematical Society in the 2020 class "for contributions to algorithmic and geometric group theory, algebra and logic."
Selected publications
References
External links
Hunter webpage
McGill home page
Canadian mathematicians
Women mathematicians
Academic staff of McGill University
City University of New York faculty
CUNY Graduate Center faculty
Living people
1958 births
Academic staff of Ural State University
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Flavia%20Pennetta%20career%20statistics | This is a list of the main career statistics of professional Italian tennis player Flavia Pennetta
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup and Olympic Games are included in win–loss records.
Singles
Doubles
Significant finals
Grand Slam tournaments
Singles: 1 (1 title)
Doubles: 3 (1 title, 2 runner-ups)
WTA Finals finals
Doubles: 1 (1 title)
WTA Premier Mandatory & 5 finals
Singles: 1 (1 title)
Doubles: 10 (4 titles, 6 runner-ups)
WTA career finals
Singles: 25 (11 titles, 14 runner-ups)
Doubles: 34 (17 titles, 17 runner-ups)
ITF Circuit finals
Singles: 10 (7 titles, 3 runner-ups)
Doubles: 15 (9 titles, 6 runner-ups)
Record against top 10 players
Pennetta's match record against players who have been ranked in the top 10. Active players are in boldface.
No. 1 wins
Top 10 wins
Notes
External links
Unofficial website
Tennis career statistics |
https://en.wikipedia.org/wiki/Andrzej%20Alexiewicz | Andrzej Alexiewicz (11 February 1917, Lwów, Poland – 11 July 1995) was a Polish mathematician, a disciple of the Lwow School of Mathematics. Alexiewicz was an expert at functional analysis and continued and edited the work of Stefan Banach.
See also
Alexiewicz norm
External links
Alexiewicz Biography
Andrzej Alexiewicz (1917-1995), a biography by Julian Musielak and Witold Wnuk
1917 births
1995 deaths
Lwów School of Mathematics |
https://en.wikipedia.org/wiki/Tytus%20Babczy%C5%84ski | Titus Babczyński (1830 in Warsaw – 1910) was a Polish mathematician and physicist. He graduated from the School of Fine Arts in Warsaw, then studied physics and mathematics. In 1872, he was a doctor at the University of St. Petersburg.
In the period (1857–1862), he was a professor of higher mathematics and mechanics at the School of Fine Arts in Warsaw and eventually the University of Warsaw (1862–1887). He wrote the acclaimed papers: "On the phenomena of induction," which was awarded a gold medal at the University of St. Petersburg, as well as "higher algebra lectures and calculus," "Introduction to higher growth," Method of multiplication and algebraic functions of symmetric rational."
Polish mathematicians
1830 births
1910 deaths
Mathematicians from the Russian Empire |
https://en.wikipedia.org/wiki/A%20Treatise%20on%20Probability | A Treatise on Probability is a book published by John Maynard Keynes while at Cambridge University in 1921. The Treatise attacked the classical theory of probability and proposed a "logical-relationist" theory instead. In a 1922 review, Bertrand Russell, the co-author of Principia Mathematica, called it "undoubtedly the most important work on probability that has appeared for a very long time," and said that the "book as a whole is one which it is impossible to praise too highly."
The Treatise is fundamentally philosophical in nature despite extensive mathematical formulations. The Treatise presented an approach to probability that was more subject to variation with evidence than the highly quantified classical version. Keynes's conception of probability is that it is a strictly logical relation between evidence and hypothesis, a degree of partial implication. Keynes's Treatise is the classic account of the logical interpretation of probability (or probabilistic logic), a view of probability that has been continued by such later works as Carnap's Logical Foundations of Probability and E.T. Jaynes Probability Theory: The Logic of Science.
Keynes saw numerical probabilities as special cases of probability, which did not have to be quantifiable or even comparable.
Keynes, in chapter 3 of the "A Treatise on Probability", used the example of taking an umbrella in case of rain to express the idea of uncertainty that he dealt with by the use of interval estimates in chapters 3, 15, 16, and 17 of the "A Treatise on Probability". Intervals that overlap are not greater than, less than or equal to each other. They can't be compared.
Is our expectation of rain, when we start out for a walk, always more likely than not, or less likely than not, or as likely as not? I am prepared to argue that on some occasions none of these alternatives hold, and that it will be an arbitrary matter to decide for or against the umbrella. If the barometer is high, but the clouds are black, it is not always rational that one should prevail over the other in our minds, or even that we should balance them, though it will be rational to allow caprice to determine us and to waste no time on the debate.
References
Keynesian economics
Probability books
1921 non-fiction books
Books by John Maynard Keynes
Macmillan Publishers books
Treatises |
https://en.wikipedia.org/wiki/Takefumi%20Toma | is a Japanese retired football player.
Japan U-21
Toma was selected for the Japan Under-21 squad for the 2010 Asian Games held in Guangzhou, China PR.
Club statistics
Updated to 24 February 2019.
References
External links
Profile at Matsumoto Yamaga
1989 births
Living people
Association football people from Okinawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
Kashima Antlers players
Tochigi SC players
Montedio Yamagata players
Matsumoto Yamaga FC players
FC Gifu players
Asian Games medalists in football
Footballers at the 2010 Asian Games
Medalists at the 2010 Asian Games
Asian Games gold medalists for Japan
Men's association football defenders |
https://en.wikipedia.org/wiki/Special%20group%20%28finite%20group%20theory%29 | In group theory, a discipline within abstract algebra, a special group is a finite group of prime power order that is either elementary abelian itself or of class 2 with its derived group, its center, and its Frattini subgroup all equal and elementary abelian . A special group of order pn that has class 2 and whose derived group has order p is called an extra special group.
References
Finite groups
P-groups |
https://en.wikipedia.org/wiki/P%C3%B3lya%20urn%20model | In statistics, a Pólya urn model (also known as a Pólya urn scheme or simply as Pólya's urn), named after George Pólya, is a family of urn models that can be used to interpret many commonly used statistical models.
The model represents objects of real interest (such as atoms, people, cars, etc.) as colored balls in an urn. In the basic Pólya urn model, the experimenter puts x white and y black balls into an urn. At each step, one ball is drawn uniformly at random from the urn, and its color observed; it is then returned in the urn, and an additional ball of the same color is added to the urn.
If by random chance, more black balls are drawn than white balls in the initial few draws, it would make it more likely for more black balls to be drawn later. Similarly for the white balls. Thus the urn has a self-reinforcing property ("the rich get richer"). It is the opposite of sampling without replacement, where every time a particular value is observed, it is less likely to be observed again, whereas in a Pólya urn model, an observed value is more likely to be observed again. In a Pólya urn model, successive acts of measurement over time have less and less effect on future measurements, whereas in sampling without replacement, the opposite is true: After a certain number of measurements of a particular value, that value will never be seen again.
It is also different from sampling with replacement, where the ball is returned to the urn but without adding new balls. In this case, there is neither self-reinforcing nor anti-self-reinforcing
Basic results
Questions of interest are the evolution of the urn population and the sequence of colors of the balls drawn out.
After draws, the probability that the urn contains white balls and black balls is , where the overbar denotes rising factorial. This can be proved by drawing the Pascal's triangle of all possible configurations.
More generally, if the urn starts with balls of color , with , then after draws, the probability that the urn contains balls of color iswhere we use the multinomial coefficient.
Conditional on the urn ending up with balls of color after draws, there are different trajectories that could have led to such an end-state. The conditional probability of each trajectory is the same: .
Interpretation
One of the reasons for interest in this particular rather elaborate urn model (i.e. with duplication and then replacement of each ball drawn) is that it provides an example in which the count (initially x black and y white) of balls in the urn is not concealed, which is able to approximate the correct updating of subjective probabilities appropriate to a different case in which the original urn content is concealed while ordinary sampling with replacement is conducted (without the Pólya ball-duplication). Because of the simple "sampling with replacement" scheme in this second case, the urn content is now static, but this greater simplicity is compensated for by the assumption t |
https://en.wikipedia.org/wiki/Emil%20Petkov | Emil Petkov (; born 16 July 1980) is a former Bulgarian footballer, who played as a midfielder.
Club statistics
As of 22 July 2012
References
1980 births
Living people
Bulgarian men's footballers
First Professional Football League (Bulgaria) players
FC Marek Dupnitsa players
FC Rodopa Smolyan players
FC Lyubimets players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Henry%20Martyn%20Andrew | Henry Martyn Andrew (3 January 1845 – 18 September 1888) was an English-born professor of mathematics and natural philosophy at the Royal Agricultural College, Cirencester, and later professor of Natural Philosophy at the Melbourne University.
Andrew, son of Rev. Matthew Andrew and his wife Louisa, née Job, was born at Bridgnorth, Shropshire, England. He was educated at several English and Continental schools, and after his arrival in Victoria in 1857, at the Church of England grammar school, Melbourne, under the Rev. Dr. Bromby. He entered the University of Melbourne in 1861, and graduated B.A. in 1864, with the scholarship in mathematics and natural philosophy, and first-class honours in natural science. He was appointed in June of that year lecturer on civil engineering, being the first graduate of Melbourne to be appointed to office in the University, and resigned the position in June 1868 on his departure for England. He also resigned the second mastership of Wesley College, Melbourne, which he had accepted in 1866; and on his arrival in England in Oct. 1868 he entered St. John's College, Cambridge, where in 1870 he was second foundation scholar and a Wright's prizeman. He graduated BA as 27th wrangler in Jan. 1872, accepted the professorship of mathematics and natural philosophy at the Royal Agricultural College, Cirencester, took his M.A. degree in 1875, returned to Wesley College, Melbourne, in the same year as second master under Professor Irving, whom he succeeded as head master at Christmas 1875. In 1882 he left Wesley College to succeed Mr. Pirani as Lecturer on Natural Philosophy in Melbourne University, where he became first professor on the establishment of the chair on that subject, and continued in this position until his death at Suez on 18 September 1888, whilst on leave. Professor Andrew was author of a paper on "Brain Waves," joint author with the late Mr. F. J. Pirani, M.A., C.E., of an edition of the first three books of Euclid, graduated M.A. at Melbourne University in 1867, and acted as joint secretary of the University Senate. He was three times elected a member of the University Council between and 1886. Professor Andrew was ensign in the St. John's company of the Cambridge University Volunteer Corps, and captain of the Melbourne University company; and both as a musician and a contributor to the press he did valuable work. His widow has adopted the dramatic profession, under the name of Miss Constance Edwards.
References
1845 births
1888 deaths
Academic staff of the University of Melbourne
University of Melbourne alumni
Academics of the Royal Agricultural University |
https://en.wikipedia.org/wiki/Bal%C3%A1zs%20Balogh%20%28footballer%2C%20born%201990%29 | Balázs Balogh (, born 11 June 1990) is a Hungarian footballer who currently plays as a midfielder for Paks.
Club statistics
Updated to games played as of 15 May 2021.
Honours
Újpest
Hungarian Cup (1): 2013–14
References
External links
Profile
1990 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football midfielders
Empoli FC players
US Lecce players
Újpest FC players
Puskás Akadémia FC players
Paksi FC players
Nemzeti Bajnokság I players
Hungarian expatriate men's footballers
Expatriate men's footballers in Italy
Hungarian expatriate sportspeople in Italy
Hungary men's international footballers
Hungary men's under-21 international footballers
21st-century Hungarian people |
https://en.wikipedia.org/wiki/Concentration%20parameter | In probability theory and statistics, a concentration parameter is a special kind of numerical parameter of a parametric family of probability distributions. Concentration parameters occur in two kinds of distribution: In the Von Mises–Fisher distribution, and in conjunction with distributions whose domain is a probability distribution, such as the symmetric Dirichlet distribution and the Dirichlet process. The rest of this article focuses on the latter usage.
The larger the value of the concentration parameter, the more evenly distributed is the resulting distribution (the more it tends towards the uniform distribution). The smaller the value of the concentration parameter, the more sparsely distributed is the resulting distribution, with most values or ranges of values having a probability near zero (in other words, the more it tends towards a distribution concentrated on a single point, the degenerate distribution defined by the Dirac delta function).
Dirichlet distribution
In the case of multivariate Dirichlet distributions, there is some confusion over how to define the concentration parameter. In the topic modelling literature, it is often defined as the sum of the individual Dirichlet parameters, when discussing symmetric Dirichlet distributions (where the parameters are the same for all dimensions) it is often defined to be the value of the single Dirichlet parameter used in all dimensions. This second definition is smaller by a factor of the dimension of the distribution.
A concentration parameter of 1 (or k, the dimension of the Dirichlet distribution, by the definition used in the topic modelling literature) results in all sets of probabilities being equally likely, i.e., in this case the Dirichlet distribution of dimension k is equivalent to a uniform distribution over a k-1-dimensional simplex. This is not the same as what happens when the concentration parameter tends towards infinity. In the former case, all resulting distributions are equally likely (the distribution over distributions is uniform). In the latter case, only near-uniform distributions are likely (the distribution over distributions is highly peaked around the uniform distribution). Meanwhile, in the limit as the concentration parameter tends towards zero, only distributions with nearly all mass concentrated on one of their components are likely (the distribution over distributions is highly peaked around the k possible Dirac delta distributions centered on one of the components, or in terms of the k-dimensional simplex, is highly peaked at corners of the simplex).
Sparse prior
An example of where a sparse prior (concentration parameter much less than 1) is called for, consider a topic model, which is used to learn the topics that are discussed in a set of documents, where each "topic" is described using a categorical distribution over a vocabulary of words. A typical vocabulary might have 100,000 words, leading to a 100,000-dimensional categorical distribu |
https://en.wikipedia.org/wiki/2006%E2%80%9307%20Xiangxue%20Sun%20Hei%20season | The 2006–07 season is the 11th season of Sun Hei SC in Hong Kong First Division League. The team was coached by Malaysian coach Koo Luam Khen.
Squad statistics
Statistics accurate as of match played 31 May 2007
Matches
Competitive
References
Sun Hei SC seasons
Sun Hei |
https://en.wikipedia.org/wiki/1989%E2%80%9390%20Saudi%20First%20Division | Statistics of the 1989–90 Saudi First Division.
External links
Saudi Arabia Football Federation
Saudi League Statistics
Al Jazirah 21 Feb 1990 issue 6355
Saudi First Division League seasons
Saudi Professional League
2 |
https://en.wikipedia.org/wiki/Farthest%20neighbor | Farthest neighbor may refer to:
Farthest neighbor graph in geometry
The farthest neighbor method for calculating distances between clusters in hierarchical clustering.
See also
Nearest neighbor (disambiguation) |
https://en.wikipedia.org/wiki/Fabien%20Morel | Fabien Morel (born 22 January 1965, in Reims) is a French algebraic geometer and key developer of A¹ homotopy theory with Vladimir Voevodsky. Among his accomplishments is the proof of the Friedlander conjecture, and the proof of the complex case of the Milnor conjecture stated in Milnor's 1983 paper 'On the homology of Lie groups made discrete'. This result was presented at the Second Abel Conference, held in January–February 2012.
In 2006 he was an invited speaker with talk A1-algebraic topology at the International Congress of Mathematicians in Madrid.
Selected publications
A1-algebraic topology over a field. (= Lecture Notes in Mathematics. 2052). Springer, 2012, .
with Marc Levine: Algebraic Cobordism. Springer, 2007, .
Homotopy theory of Schemes. American Mathematical Society, 2006 (French original published by Société Mathématique de France 1999)
References
1965 births
Living people
Scientists from Reims
20th-century French mathematicians
21st-century French mathematicians
Algebraic geometers |
https://en.wikipedia.org/wiki/List%20of%20Watford%20F.C.%20records%20and%20statistics | Watford Football Club is an English association football club from Watford, Hertfordshire. The club was formed in 1898 from the amalgamation of West Herts and Watford St. Mary's. As of the 2022–23 season, it competes in the EFL Championship, the second division of English football.
Honours and achievements
Between 1896 and 1920, West Herts (and later Watford) competed in the Southern League, along with many future Football League sides from Southern England and Wales. The team won the league title in 1914–15, and finished as runners-up to Portsmouth on goal average in 1919–20. Watford joined the Football League in 1920, and since then have won the Third Division twice, and the Fourth Division once. They have achieved promotion to the top level of English football on four occasions; as runners-up of the Second Division in 1981–82, and winners of the play-off final (often considered the richest game in football) in 1999 and 2006. They also gained automatic promotion in 2015, finishing second in the Championship. Their highest finish in the Football League was second in the First Division, achieved in 1982–83.
Watford's best performances in the FA Cup came in the 1984 FA Cup and 2019 FA cup, when they reached the final whilst suffering the biggest ever score line defeat in 2019. They have reached the semi-finals on four further occasions, and have also reached the semi-finals of the Football League Cup twice. On Watford's only appearance in a major European cup competition to date, they reached the third round of the UEFA Cup in 1983–84. They also won the Third Division South Cup in 1937; which was shared with Millwall after being level 3–3 over two legs.
The Football League
Before the Premier League
First Division: Runners-up 1982–83
Second Division: Runners-up 1981–82
Third Division: Champions 1968–69
Third Division: Runners-up 1978–79
Third Division South: Highest finish: Fourth 1936–37, 1937–38, 1938–39, 1955–54
Fourth Division: Champions 1977–78
Fourth Division: Fourth place promotion 1959–60
After the formation of the Premier League
Championship: Runners-up 2014–15, 2020–21
Championship: Play-off winners 1998–99, 2005–06
Division Two: Champions 1997–98
National cup competitions
FA Cup
Finalists: 1983–84, 2018–19
Semi-Finalists: 1969–70, 1986–87, 2002–03, 2006–07, 2015–16
League Cup
Semi-finalists: 1978–79, 2004–05
Other honours
Southern League
First Division: Champions 1914–15
First Division: Runners-up 1919–20
Second Division: Champions 1899–1900, 1903–04
UEFA Cup
Third round: 1983–84
Football League Third Division South Cup
Winners 1936–37 (shared)
Runners-up 1934–35
Records and statistics
All statistics correct as of 30 August 2023.
Highest Attendances
Football League: 27,968 vs. Queens Park Rangers Second Division, 20 August 1969.
FA Cup: 34,099 vs. Manchester United (4th round), 3 February 1969.
Football League Cup: 27,656 vs. Nottingham Forest (semi-final, 2nd leg), 30 January 1979.
UEFA Cup: 21,457 vs. 1. FC Kaiserslautern |
https://en.wikipedia.org/wiki/Anastasia%20Pavlyuchenkova%20career%20statistics | This is a list of career statistics of Russian tennis player Anastasia Pavlyuchenkova. To date, Pavlyuchenkova has won 12 WTA singles titles (finishing runner-up in nine other finals) and six WTA doubles titles (including two WTA 1000 titles), as well as five ITF singles titles and eight ITF doubles titles. She has reached one Grand Slam singles final at the 2021 French Open, as well as an additional 12 Grand Slam quarterfinals (six apiece in both singles and doubles) across all four major tournaments.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup, United Cup, Hopman Cup and Olympic Games are included in win–loss records.
Singles
Current after the 2023 US Open.
Doubles
Current after the 2023 Madrid Open.
Significant finals
Grand Slam tournaments
Singles: 1 (runner-up)
Olympic Games
Mixed doubles: 1 (gold medal)
WTA 1000 tournaments
Doubles: 2 (2 titles)
WTA career finals
Singles: 21 (12 titles, 9 runner-ups)
Doubles: 10 (6 titles, 4 runner-ups)
WTA Challenger finals
Singles: 1 (runner-up)
ITF Circuit finals
Singles: 6 (5 titles, 1 runner-up)
Doubles: 10 (8 titles, 2 runner-ups)
WTA rankings
*as of 6 June 2022.
WTA Tour career earnings
as of 15 November 2021
Grand Slam tournament seedings
Tennis Leagues
League finals: 1 (first place)
Fed Cup participation
Singles: 18 (9–9)
Doubles: 7 (5–2)
Head-to-head records
Record against top 10 players
Pavlyuchenkova's record against certain players who have been ranked in the top 10 are as follows. Active players are in boldface:
No. 1 wins
Top 10 wins
Double bagel matches (6–0, 6–0)
Exhibition Finals
Notes
References
External links
Pavlyuchenkova, Anastasia |
https://en.wikipedia.org/wiki/Maria%20Kirilenko%20career%20statistics | This is a list of the main career statistics of Russian professional tennis player Maria Kirilenko. She has won six singles and 12 doubles titles on the WTA Tour. At the Grand Slams, in singles, she reached three different quarterfinals; the 2010 Australian Open, 2012 Wimbledon Championships and 2013 French Open, respectively. In doubles, she reached a couple of quarterfinals and semifinals, along with two finals (the 2011 Australian Open and 2012 French Open). On the WTA Rankings, in both competition, she entered top 10. In singles, she has No. 10 as her career-highest and No. 5 in doubles.
She also left her mark at the national competitions for Russia, reaching semifinals of the 2012 Summer Olympics in London, but lost bronze medal match to Victoria Azarenka. However, in doubles, she won bronze medal alongside Nadia Petrova. At the Fed Cup, in 2011, with her Russian team, she reached final but lost to Czech Republic 2–3. Her biggest title in doubles is the 2012 WTA Tour Championships that she won alongside her compatriot Petrova.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup and Olympic Games are included in win–loss records.
Singles
Doubles
Grand Slam finals
Doubles: 2 runner-ups
Other significant finals
Olympics finals
Singles: 1 bronze medal match (0–1)
Doubles: 1 bronze medal match (1–0)
Year-end championships finals
Doubles: 1 (1 title)
WTA Premier Mandatory & 5 finals
Doubles: 7 (3 titles, 4 runner-ups)
WTA career finals
Singles: 12 (6 titles, 6 runner-ups)
Doubles: 25 (12 titles, 13 runner-ups)
WTA Tour career earnings
{|cellpadding=3 cellspacing=0 border=1 style=border:#aaa;solid:1px;border-collapse:collapse;text-align:center;
|-style=background:#eee;font-weight:bold
|width="90"|Year
|width="100"|Grand Slam <br/ >titles'|width="100"|WTA <br/ >titles
|width="100"|Total <br/ >titles
|width="120"|Earnings ($)
|width="100"|Money list rank
|-
|2003
|0
|0
|0
| align="right" |55,550
|155
|-
|2004
|0
|1
|1
| align="right" |107,444
|112
|-
|2005
|0
|2
|2
| align="right" |382,559
|35
|-
|2006
|0
|0
|0
| align="right" |431,467
|31
|-
|2007
|0
|2
|2
| align="right" |451,756
|34
|-
|2008
|0
|5
|5
| align="right" |455,770
|39
|-
|2009
|0
|1
|1
| align="right" |444,704
|50
|-
|2010
|0
|2
|2
| align="right" |912,925
|21
|-
|2011
|0
|2
|2
| align="right" |1,001,417
|16
|-
|2012
|0
|2
|2
| align="right" |1,327,054
|14
|-
|2013
|0
|1
|1
| align="right" |995,357
|20
|-
|2014*
|0
|0
|0
| align="right" |230,216
|>100
|-
|Career*
|0
|18
|18
| align="right" |6,526,615
|43
|}
*As of Feb 28, 2013
Fed Cup participations
Singles (5)
Doubles (2)
Record against other players
Record against top 10 playersKirilenko's record against players who have been ranked in the top 10. Active players are in boldface.''
No. 1 wins
Top 10 wins
Notes
References
External links
Kirilenko, Maria |
https://en.wikipedia.org/wiki/Ana%20Ivanovic%20career%20statistics | This is a list of the main career statistics of Serbian professional tennis player, Ana Ivanovic. Ivanovic won fifteen WTA singles titles including one grand slam singles title at the 2008 French Open and three WTA Tier I singles titles. She was also the runner-up at the 2007 French Open and 2008 Australian Open and a semi-finalist at the 2007 Wimbledon Championships and 2007 WTA Tour Championships. On June 9, 2008, Ivanovic became the world No. 1 for the first time in her career.
Career achievements
Ivanovic reached her first grand slam singles quarterfinal at the 2005 French Open, defeating third seed Amélie Mauresmo en route before losing in straight sets to seventh seed, Nadia Petrova. The following year, Ivanovic won her first major title at the 2006 Rogers Cup, defeating former world No. 1 Martina Hingis in the final in straight sets. Ivanovic subsequently won the US Open Series that year.
In January 2007, Ivanovic recorded her first win over a reigning world No. 1 at the Toray Pan Pacific Open when Maria Sharapova retired whilst down a set in their semi-final match. In May 2007, Ivanovic cracked the top ten of the WTA rankings for the first time in her career, rising to a then career high of world No. 8 after winning the Qatar Telecom German Open by defeating world No. 4 Svetlana Kuznetsova in three sets in the final. At the 2007 French Open, Ivanovic reached her first grand slam singles final, defeating Kuznetsova in the quarterfinals and world No. 2 Maria Sharapova in the semi-finals before losing in straight sets to world No. 1 and two-time defending champion Justine Henin in the final. At the 2007 Wimbledon Championships, Ivanovic reached her second consecutive grand slam singles semi-final but lost in straight sets to the eventual champion, Venus Williams. Later that year, Ivanovic won her fourth career singles title at the East West Bank Classic and as a result, achieved a new career high singles ranking of world No. 4. Ivanovic's results throughout the year allowed her to qualify for the year-ending WTA Tour Championships for the first time in her career. She progressed to the semi-finals where she lost in straight sets to the world No. 1 Justine Henin. Ivanovic finished the year ranked world No. 4, the best year-end ranking of her career.
In January 2008, Ivanovic reached her first Australian Open final and second grand slam singles final overall but lost in straight sets to Maria Sharapova. However, Ivanovic achieved a new career high singles ranking of world No. 2 following the event. Later that year, Ivanovic reached her third grand slam singles final by defeating Jelena Janković in three sets in the semi-finals and thus ensured that she would become the world No. 1 for the first time in her career. Ivanovic then defeated first-time grand slam singles finalist Dinara Safina in the final in straight sets to win her first and only grand slam singles title.
At the 2012 US Open, Ivanovic defeated Tsvetana Pironkova in the four |
https://en.wikipedia.org/wiki/Marion%20Bartoli%20career%20statistics | This is a list of the main career statistics of retired French tennis player Marion Bartoli. Bartoli reached a career-high singles ranking of No. 7 in the world on 30 January 2012, and won the women's singles title at the 2013 Wimbledon Championships. Overall, Bartoli won eight singles titles and three doubles titles on the WTA Tour.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup and Olympic Games are included in win–loss records.
Singles
Doubles
Significant finals
Grand Slam tournamentss
Singles: 2 (1 title, 1 runner-up)
WTA Tournament of Champions
Singles: 1 (runner-up)
WTA Premier Mandatory & 5 finals
Singles: 1 (runner-up)
WTA career finals
Singles: 19 (8 titles, 11 runner-ups)
Doubles: 7 (3 titles, 4 runner-ups)
ITF Circuit finals
Singles: 6 titles
Doubles: 2 (1 title, 1 runner-up)
Best Grand Slam results details
Grand Slam winners are in boldface, and runner-ups are in italics.
WTA Tour career earnings
Bartoli earned more than 11 million dollars during her career.
Head-to-head records
Record against top 10 players
Bartoli's record against players who have been ranked in the top 10. Active players are in boldface.
No. 1 wins
Top 10 wins
Notes
References
Bartoli, Marion |
https://en.wikipedia.org/wiki/Hall%E2%80%93Higman%20theorem | In mathematical group theory, the Hall–Higman theorem, due to , describes the possibilities for the minimal polynomial of an element of prime power order for a representation of a p-solvable group.
Statement
Suppose that G is a p-solvable group with no normal p-subgroups, acting faithfully on a vector space over a field of characteristic p.
If x is an element of order pn of G then the minimal polynomial is of the form (X − 1)r for some r ≤ pn. The Hall–Higman theorem states that one of the following 3 possibilities holds:
r = pn
p is a Fermat prime and the Sylow 2-subgroups of G are non-abelian and r ≥ pn −pn−1
p = 2 and the Sylow q-subgroups of G are non-abelian for some Mersenne prime q = 2m − 1 less than 2n and r ≥ 2n − 2n−m.
Examples
The group SL2(F3) is 3-solvable (in fact solvable) and has an obvious 2-dimensional representation over a field of characteristic p=3, in which the elements of order 3 have minimal polynomial (X−1)2 with r=3−1.
References
Theorems in group theory
Number theory |
https://en.wikipedia.org/wiki/Vladimir%20Lifschitz | Vladimir Lifschitz (born 30 May 1947) is the Gottesman Family Centennial Professor in Computer Sciences at the University of Texas at Austin. He received a degree in mathematics from the Steklov Institute of Mathematics in Russia in 1971 and emigrated to the United States in 1976. Lifschitz's research interests are in the areas of computational logic and knowledge representation. He is a Fellow of the Association for the Advancement of Artificial Intelligence, the Editor-in-Chief of the ACM Transactions on Computational Logic, and an Editorial Advisor of the journal Theory and Practice of Logic Programming.
He, together with Michael Gelfond, defined stable model semantics for logic programs, which later became the theoretical foundation for Answer Set Programming, a new declarative programming paradigm.
References
External links
Vladimir Lifschitz's homepage at University of Texas at Austin
Vladimir Lifschitz's publications on DBLP
Living people
American computer scientists
University of Texas at Austin faculty
Logic programming researchers
Fellows of the Association for the Advancement of Artificial Intelligence
1947 births |
https://en.wikipedia.org/wiki/Mamba%20%28Chunya%29 | Mamba is an administrative ward in the Chunya district of the Mbeya Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 10,563 people in the ward, from 15,462 in 2012.
Villages / vitongoji
The ward has 3 villages and 13 vitongoji.
Mamba
Kisalasi C
Kisalasi D
Mamba A
Mamba B
Mandumbwi
Mtande
Ijiwa
Mabatini
Magunga
Mamba F
Mamba G
Mapinduzi
Mamba E
Mapinduzi
Ngwangu
References
Wards of Mbeya Region |
https://en.wikipedia.org/wiki/Otjiwarongo%20Secondary%20School | Otjiwarongo Secondary School is a high school in Otjiwarongo. It frequently produces good results compared to other schools in Namibia.
In 2009 the Biology, English, and Mathematics results were among the best in the country. In 2012 Otjiwarongo Secondary School was the 23rd best-performing High School in Namibia, in 2013 it occupied rank 12.
See also
List of schools in Namibia
Education in Namibia
References
Schools in Otjozondjupa Region
Otjiwarongo |
https://en.wikipedia.org/wiki/Bruno%20Formigoni | Bruno Leonardo Formigoni (born April 18, 1990), is a Brazilian defensive midfielder. He currently plays for Inter de Limeira.
Career
Career statistics
As of 10 September 2010
Honours
Contract
References
External links
Bruno Formigoni at ZeroZero
1990 births
Living people
Sportspeople from Sorocaba
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Brazilian expatriate sportspeople in Japan
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Campeonato Brasileiro Série D players
J2 League players
São Paulo FC players
Cerezo Osaka players
Paulista Futebol Clube players
Figueirense FC players
Guaratinguetá Futebol players
Red Bull Bragantino II players
União Recreativa dos Trabalhadores players
São José Esporte Clube players
Clube Atlético Bragantino players
América Futebol Clube (RN) players
Esporte Clube XV de Novembro (Piracicaba) players
Clube Atlético Linense players
Batatais Futebol Clube players
Rio Claro Futebol Clube players
Associação Atlética Internacional (Limeira) players
Men's association football midfielders
Footballers from São Paulo (state) |
https://en.wikipedia.org/wiki/List%20of%20Crusaders%20Rugby%20League%20players | This page details the honours and statistics of individual players of the Crusaders Rugby League club.
2011 Squad
2010 Squad
Player Of The Year
The award is determined by fans votes and is usually presented in December or January.
Award Honours
Welsh Internationals
A total of 18 players have won caps with the Wales national rugby league team whilst playing for the Crusaders.
Other Internationals
Anthony Seibold - Germany
Jason Chan - Papua New Guinea
References
Crusaders |
https://en.wikipedia.org/wiki/Quantum%20algebra | Quantum algebra is one of the top-level mathematics categories used by the arXiv. It is the study of noncommutative analogues and generalizations of commutative algebras, especially those arising in Lie theory.
Subjects include:
Quantum groups
Skein theories
Operadic algebra
Diagrammatic algebra
Quantum field theory
Racks and quandles
See also
Coherent states in mathematical physics
Glossary of areas of mathematics
Mathematics Subject Classification
Ordered type system, a substructural type system
Outline of mathematics
Quantum logic
References
External links
Quantum algebra at arxiv.org
Quantum groups |
https://en.wikipedia.org/wiki/Ormiston%20Venture%20Academy | Ormiston Venture Academy (formerly Oriel Specialist Mathematics and Computing College) is a secondary school with academy status located in Oriel Avenue, Gorleston in the English county of Norfolk. The school educates children aged 11 to 16. It is housed in a block constructed in 2008 and a second newer building that stands where the original building, constructed in 1954, was located. The present facility includes a new reception area, Learning Resource Centre, and classrooms; it was opened in March 2014 by alumnus Callum Cooke.
History
Originally named Great Yarmouth Technical High School, it was opened in 1954 to replace the old Technical High School located in Southtown. It has gone through many different names, including Oriel Grammar School, Oriel High School and Oriel Specialist Maths and Computing College. In c 2007, its houses were: Trinity, Magdalen, Girton and Pembroke. Previously, when the Technical High School and the Oriel Grammar School the houses were Blue - Perebourne, Red - Fastolff, Yellow - Grenfell, and Green - Paget. Also Middleton were black and Nelson wearing white.
The current principal as of February 2013 is Simon Gilbert-Barnham. A new building was added to the site, by Net Zero Buildings, to accommodate the Humanities department. The school is sponsored by the Ormiston Academies Trust.
Gresham's Scholarship
The school has a connection with the privately-funded, boarding school Gresham's in Holt, North Norfolk – whereby one student per academic year is offered a fully-funded scholarship to study at Gresham's for two years. There have been 10 scholars so far.
References
External links
Official website
Educational institutions established in 1954
Academies in Norfolk
Gorleston-on-Sea
Secondary schools in Norfolk
1954 establishments in England
Ormiston Academies |
https://en.wikipedia.org/wiki/The%20Mathematics%20of%20Magic | "The Mathematics of Magic" is a fantasy novella by American writers L. Sprague de Camp and Fletcher Pratt, the second story in their Harold Shea series. It was first published in the August 1940 issue of the fantasy pulp magazine Unknown. It first appeared in book form, together with the preceding novella, "The Roaring Trumpet", in the collection The Incomplete Enchanter, issued in hardcover by Henry Holt and Company in 1941, and in paperback by Pyramid Books in 1960. It has since been reprinted in various collections by numerous other publishers, including The Compleat Enchanter (1975), The Incompleat Enchanter (1979), The Complete Compleat Enchanter (1989), and The Mathematics of Magic: The Enchanter Stories of L. Sprague de Camp and Fletcher Pratt (2007). It has been translated into Dutch and Italian. In 2016, the story was shortlisted for the Retro Hugo Award for Best Novella.
The Harold Shea stories are parallel world tales in which universes where magic works coexist with our own, and in which those based on the mythologies, legends, and literary fantasies of our world and can be reached by aligning one's mind to them by a system of symbolic logic. In "The Mathematics of Magic", Shea visits his second such world, that of Edmund Spenser's epic poem The Faerie Queene.
Plot summary
Psychologist Harold Shea's accidental visit to the world of Norse mythology has confirmed his colleague Reed Chalmer's speculation that alternate universes can be reached by employing a system of symbolic logic encoding their basic assumptions. Encouraged at his theory's validation but pessimistic as to the prospects of it being taken seriously by their profession, Chalmers proposes to join Shea in a second expedition, more carefully planned, to a world in which they can achieve the fame and fortune that they are unlikely to gain in their own. He suggests the world represented by Spenser's The Faerie Queene.
Outfitting themselves appropriately, they make the attempt and are successful in reaching their target world. They soon encounter the Lady Britomart, one of Queen Gloriana's knights, in whose company they attend a tournament at the castle of Satyrane. At the feast afterward Chalmers becomes smitten by a magical simulacrum of the Lady Florimel, only to lose her in the confusion engendered by a sorcerous disruption of the proceedings. Later he and Shea undertake to find the root of the trouble, a secret brotherhood of enchanters they theorize has been tipping the balance against the forces of good, and which they hope to infiltrate and subvert. They meet the woodland huntress Belphebe, with whom Shea becomes enamored, and face the peril of the Blatant Beast, summoned up by Chalmers in a spell gone wrong.
Finally, the two succeed in infiltrating the enchanters' cabal, Chalmers as a magician and Shea as his apprentice. Chalmers, bringing a systematic and scientific approach to bear on the study of magic, fits right in—a bit too well, in Shea's opinion. The secr |
https://en.wikipedia.org/wiki/Icosidodecahedral%20prism | In geometry, an icosidodecahedral prism is a convex uniform polychoron (four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of parallel Platonic solids or Archimedean solids.
Alternative names
Icosidodecahedral dyadic prism (Norman W. Johnson)
Iddip (Jonathan Bowers: for icosidodecahedral prism)
Icosidodecahedral hyperprism
External links
4-polytopes |
https://en.wikipedia.org/wiki/Truncated%20dodecahedral%20prism | In geometry, a truncated dodecahedral prism is a convex uniform polychoron (four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.
Alternative names
Truncated-dodecahedral dyadic prism (Norman W. Johnson)
Tiddip (Jonathan Bowers: for truncated-dodecahedral prism)
Truncated-dodecahedral hyperprism
See also
Truncated 120-cell,
External links
4-polytopes |
https://en.wikipedia.org/wiki/Rhombicosidodecahedral%20prism | In geometry, a rhombicosidodecahedral prism or small rhombicosidodecahedral prism is a convex uniform polychoron (four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.
Alternative names
(small) rhombicosidodecahedral dyadic prism (Norman W. Johnson)
Sriddip (Jonathan Bowers: for small-rhombicosidodecahedral prism)
(small) rhombicosidodecahedral hyperprism
External links
4-polytopes |
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