source stringlengths 31 168 | text stringlengths 51 3k |
|---|---|
https://en.wikipedia.org/wiki/Jos%C3%A9%20Augusto%20S%C3%A1nchez%20P%C3%A9rez | José Augusto Sánchez Pérez (Madrid, 30 November 1882 – 13 November 1958) was a Spanish mathematician and member of the Spanish Royal Academy of Sciences.
He was professor of mathematics at the Instituto Beatriz de Galindo in Madrid. He published in the history of mathematics, in particular on Islamic mathematics in al-Andalus.
References
Ausejo Martínez, Elena. "José Augusto Sánceh Pérez" en Actas del IV Simposio Ciencia y Técnica en España de 1898 1 1945.
García Rúa, J. A. Sánchez Pérez. Gaceta matemática. 1ª serie, 11, págs. 3–5.
1882 births
1958 deaths
Historians of mathematics |
https://en.wikipedia.org/wiki/Orthodiagonal%20quadrilateral | In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles. In other words, it is a four-sided figure in which the line segments between non-adjacent vertices are orthogonal (perpendicular) to each other.
Special cases
A kite is an orthodiagonal quadrilateral in which one diagonal is a line of symmetry. The kites are exactly the orthodiagonal quadrilaterals that contain a circle tangent to all four of their sides; that is, the kites are the tangential orthodiagonal quadrilaterals.
A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram).
A square is a limiting case of both a kite and a rhombus.
Orthodiagonal equidiagonal quadrilaterals in which the diagonals are at least as long as all of the quadrilateral's sides have the maximum area for their diameter among all quadrilaterals, solving the n = 4 case of the biggest little polygon problem. The square is one such quadrilateral, but there are infinitely many others. An orthodiagonal quadrilateral that is also equidiagonal is a midsquare quadrilateral because its Varignon parallelogram is a square. Its area can be expressed purely in terms of its sides.
Characterizations
For any orthodiagonal quadrilateral, the sum of the squares of two opposite sides equals that of the other two opposite sides: for successive sides a, b, c, and d, we have
This follows from the Pythagorean theorem, by which either of these two sums of two squares can be expanded to equal the sum of the four squared distances from the quadrilateral's vertices to the point where the diagonals intersect. Conversely, any quadrilateral in which a2 + c2 = b2 + d2 must be orthodiagonal.
This can be proved in a number of ways, including using the law of cosines, vectors, an indirect proof, and complex numbers.
The diagonals of a convex quadrilateral are perpendicular if and only if the two bimedians have equal length.
According to another characterization, the diagonals of a convex quadrilateral ABCD are perpendicular if and only if
where P is the point of intersection of the diagonals. From this equation it follows almost immediately that the diagonals of a convex quadrilateral are perpendicular if and only if the projections of the diagonal intersection onto the sides of the quadrilateral are the vertices of a cyclic quadrilateral.
A convex quadrilateral is orthodiagonal if and only if its Varignon parallelogram (whose vertices are the midpoints of its sides) is a rectangle. A related characterization states that a convex quadrilateral is orthodiagonal if and only if the midpoints of the sides and the feet of the four maltitudes are eight concyclic points; the eight point circle. The center of this circle is the centroid of the quadrilateral. The quadrilateral formed by the feet of the maltitudes is called the principal orthic quadrilateral.
If the normals to the sides of a conv |
https://en.wikipedia.org/wiki/Daejeon%20Science%20High%20School%20for%20the%20Gifted | Daejeon Science High School for the Gifted (DSHS, ) is located in Daejeon, South Korea. It was founded in 1984. The school is for gifted students with talents in mathematics and sciences.
The graduates of the school usually go to science or engineering schools in Seoul National University, KAIST and other prestigious universities in Korea and in the world, and also medical schools in Korea.
History
November 21, 1983 Official permission of school foundation (6 classrooms, 60 students)
March 7, 1984 Opened school and took first entrance ceremony.
January 7, 1986 Opened dormitory Yeomyung-Gwan (黎明館)
June 11, 1992 Altering school regulations (9 classrooms in total)
May 6, 1994 School building newly constructed in new place and moved.
January 31, 2006 Altering school regulations (12 classrooms, 216 students)
March 1, 2009 Altering school regulations (15 classrooms, 270 students)
Facilities
Main Building 1 (Tamui-Gwan)
Center office, meeting rooms, office and classrooms of math, foreign language, Korean language, social studies
Each classroom is also operated as a major classroom for 2nd and 3rd graders.
5-story building
Main Building 2 (Ilshin-Gwan)
6 Classrooms (major classrooms for 1st graders), 4 reading rooms, library (Yeomyeongmaru), multimedia rooms, Seminar rooms, Soya art gallery, Yeomyeong story room etc.
4-story building
Hi-Tech Science Building (Dasan-Gwan)
The science building houses labs equipped with the latest facilities and devices
7-story building, astronomical telescopes in roof
A center for research the engages students and professors
Dormitories (Yeomyeong-Gwan)
69 rooms in the old building (A, for 2nd, 3rd male students), 68 rooms in the new building(B, for 1st grade male students, all female students)
1 Houseparent's room, 1 Exercising room, 4 Debating rooms, 2 Internet rooms (now removed)
A refrigerator on each floor
Cafeteria & Gym
200 seats cafeteria in 1st floor
Gym for basketball, badminton, table tennis, etc. in 2nd floor
See also
Education for the scientifically gifted in Korea
References
External links
Official website
Official website
Official Facebook page
Science high schools in South Korea
Schools in Daejeon
Educational institutions established in 1984
1984 establishments in South Korea |
https://en.wikipedia.org/wiki/Real%20Analysis%20Exchange | The Real Analysis Exchange (RAEX) is a biannual mathematics journal, publishing survey articles, research papers, and conference reports in real analysis and related topics. Its editor-in-chief is Paul D. Humke.
External links
The website of RAEX
Mathematics journals |
https://en.wikipedia.org/wiki/Inverse-variance%20weighting | In statistics, inverse-variance weighting is a method of aggregating two or more random variables to minimize the variance of the weighted average. Each random variable is weighted in inverse proportion to its variance, i.e., proportional to its precision.
Given a sequence of independent observations with variances , the inverse-variance weighted average is given by
The inverse-variance weighted average has the least variance among all weighted averages, which can be calculated as
If the variances of the measurements are all equal, then the inverse-variance weighted average becomes the simple average.
Inverse-variance weighting is typically used in statistical meta-analysis or sensor fusion to combine the results from independent measurements.
Context
Suppose an experimenter wishes to measure the value of a quantity, say the acceleration due to gravity of Earth, whose true value happens to be . A careful experimenter makes multiple measurements, which we denote with random variables . If they are all noisy but unbiased, i.e., the measuring device does not systematically overestimate or underestimate the true value and the errors are scattered symmetrically, then the expectation value . The scatter in the measurement is then characterised by the variance of the random variables , and if the measurements are performed under identical scenarios, then all the are the same, which we shall refer to by . Given the measurements, a typical estimator for , denoted as , is given by the simple average . Note that this empirical average is also a random variable, whose expectation value is but also has a scatter. If the individual measurements are uncorrelated, the square of the error in the estimate is given by
. Hence, if all the are equal, then the error in the estimate decreases with increase in as , thus making more observations preferred.
Instead of repeated measurements with one instrument, if the experimenter makes of the same quantity with different instruments with varying quality of measurements, then there is no reason to expect the different to be the same. Some instruments could be noisier than others. In the example of measuring the acceleration due to gravity, the different "instruments" could be measuring from a simple pendulum, from analysing a projectile motion etc. The simple average is no longer an optimal estimator, since the error in might actually exceed the error in the least noisy measurement if different measurements have very different errors. Instead of discarding the noisy measurements that increase the final error, the experimenter can combine all the measurements with appropriate weights so as to give more importance to the least noisy measurements and vice versa. Given the knowledge of , an optimal estimator to measure would be a weighted mean of the measurements , for the particular choice of the weights . The variance of the estimator , which for the optimal choice of the weights become
Note that sin |
https://en.wikipedia.org/wiki/N%20%3D%202%20superconformal%20algebra | In mathematical physics, the 2D N = 2 superconformal algebra is an infinite-dimensional Lie superalgebra, related to supersymmetry, that occurs in string theory and two-dimensional conformal field theory. It has important applications in mirror symmetry. It was introduced by as a gauge algebra of the U(1) fermionic string.
Definition
There are two slightly different ways to describe the N = 2 superconformal algebra, called the N = 2 Ramond algebra and the N = 2 Neveu–Schwarz algebra, which are isomorphic (see below) but differ in the choice of standard basis.
The N = 2 superconformal algebra is the Lie superalgebra with basis of even elements c, Ln, Jn, for n an integer, and odd elements G, G, where (for the Ramond basis) or (for the Neveu–Schwarz basis) defined by the following relations:
c is in the center
If in these relations, this yields the
N = 2 Ramond algebra; while if are half-integers, it gives the N = 2 Neveu–Schwarz algebra. The operators generate a Lie subalgebra isomorphic to the Virasoro algebra. Together with the operators , they generate a Lie superalgebra isomorphic to the super Virasoro algebra,
giving the Ramond algebra if are integers and the Neveu–Schwarz algebra otherwise. When represented as operators on a complex inner product space, is taken to act as multiplication by a real scalar, denoted by the same letter and called the central charge, and the adjoint structure is as follows:
Properties
The N = 2 Ramond and Neveu–Schwarz algebras are isomorphic by the spectral shift isomorphism of : with inverse:
In the N = 2 Ramond algebra, the zero mode operators , , and the constants form a five-dimensional Lie superalgebra. They satisfy the same relations as the fundamental operators in Kähler geometry, with corresponding to the Laplacian, the degree operator, and the and operators.
Even integer powers of the spectral shift give automorphisms of the N = 2 superconformal algebras, called spectral shift automorphisms. Another automorphism , of period two, is given by In terms of Kähler operators, corresponds to conjugating the complex structure. Since , the automorphisms and generate a group of automorphisms of the N = 2 superconformal algebra isomorphic to the infinite dihedral group .
Twisted operators were introduced by and satisfy: so that these operators satisfy the Virasoro relation with central charge 0. The constant still appears in the relations for and the modified relations
Constructions
Free field construction
give a construction using two commuting real bosonic fields ,
and a complex fermionic field
is defined to the sum of the Virasoro operators naturally associated with each of the three systems
where normal ordering has been used for bosons and fermions.
The current operator is defined by the standard construction from fermions
and the two supersymmetric operators by
This yields an N = 2 Neveu–Schwarz algebra with c = 3.
SU(2) supersymmetric coset construction
g |
https://en.wikipedia.org/wiki/VTG | VTG or Vtg may refer to:
Vitellogenin (VTG) a type of protein
Variable turbine geometry, in variable-geometry turbochargers
Airline code for Aviação Transportes Aéreos e Cargas, Angola
Virtual tributary group, in synchronous optical networking
An airport code for Vung Tau Airport, Vietnam
Victoria Tower Gardens, a park in London
See also
VTG-32, a type of video timer produced by FOR-A
VT Group, a privately held United States defense and services company |
https://en.wikipedia.org/wiki/Acta%20Numerica | Acta Numerica is a mathematics journal publishing research on numerical analysis. It was established in 1992 to publish widely accessible summaries of recent advances in the field.
One volume is published each year, consisting of review and survey articles from authors invited by the journal's editorial board.
The journal is indexed by Mathematical Reviews and Zentralblatt MATH. During the period of 2004–2009, it had an MCQ of 3.43, the highest of all journals indexed by Mathematical Reviews over that period of time.
References
Similar Journals
Mathematics of Computation (published by the American Mathematical Society)
Journal of Computational and Applied Mathematics
BIT Numerical Mathematics
Numerische Mathematik
Journals from the Society for Industrial and Applied Mathematics
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
External links
Mathematics journals
Annual journals
English-language journals
Cambridge University Press academic journals
Academic journals established in 1992 |
https://en.wikipedia.org/wiki/Advances%20in%20Mathematics | Advances in Mathematics is a peer-reviewed scientific journal covering research on pure mathematics. It was established in 1961 by Gian-Carlo Rota. The journal publishes 18 issues each year, in three volumes.
At the origin, the journal aimed at publishing articles addressed to a broader "mathematical community", and not only to mathematicians in the author's field. Herbert Busemann writes, in the preface of the first issue, "The need for expository articles addressing either all mathematicians or only those in somewhat related fields has long been felt, but little has been done outside of the USSR. The serial publication Advances in Mathematics was created in response to this demand."
Abstracting and indexing
The journal is abstracted and indexed in:
CompuMath Citation Index
Current Contents/Physical, Chemical & Earth Sciences
Mathematical Reviews
Science Citation Index
Scopus
Zentralblatt MATH
See also
List of periodicals published by Elsevier
References
External links
Mathematics journals
Academic journals established in 1961
English-language journals
Elsevier academic journals
Hybrid open access journals |
https://en.wikipedia.org/wiki/Thomas%20Bradley%20%28physician%29 | Thomas Bradley, M.D. (1751–1813) was an English physician.
Life
Bradley was a native of Worcester, where for some time he conducted a school in which mathematics formed a prominent study. About 1786 he withdrew from education, and, devoting himself to medical studies, went to Edinburgh, where he graduated M.D. in 1791.
He settled in London, and on 22 December 1791 was admitted licentiate of the College of Physicians. From 1794 to 1811 he was physician to the Westminster Hospital. In the practice of his profession he was not very successful.
Bradley died in St George's Fields at the close of 1813.
Works
His doctoral dissertation was published as De Epispasticorum Usu in variis morbis tractandis. For many years he acted as editor of the Medical and Physical Journal. He published a revised and enlarged edition of Joseph Fox the younger's Medical Dictionary, 1803, and also a Treatise on Worms and other Animals which infest the Human Body, 1813.
On the Prospectus for Rees's Cyclopædia he was credited with writing articles on medicine.
References
1751 births
1813 deaths
18th-century English medical doctors
Medical doctors from Worcester, England
English medical writers
18th-century English non-fiction writers
18th-century English male writers
18th-century English writers
19th-century English non-fiction writers
English editors
19th-century English medical doctors |
https://en.wikipedia.org/wiki/Euler%20calculus | Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently definable functions by integrating with respect to the Euler characteristic as a finitely-additive measure. In the presence of a metric, it can be extended to continuous integrands via the Gauss–Bonnet theorem. It was introduced independently by Pierre Schapira and Oleg Viro in 1988, and is useful for enumeration problems in computational geometry and sensor networks.
See also
Topological data analysis
References
Van den Dries, Lou. Tame Topology and O-minimal Structures, Cambridge University Press, 1998.
Arnold, V. I.; Goryunov, V. V.; Lyashko, O. V. Singularity Theory, Volume 1, Springer, 1998, p. 219.
External links
Ghrist, Robert. Euler Calculus video presentation, June 2009. published 30 July 2009.
Algebraic topology
Computational topology
Integral geometry
Measure theory |
https://en.wikipedia.org/wiki/Josip%20Pe%C4%8Dari%C4%87 | Josip Pečarić (born 2 September 1948) is a Croatian mathematician. He is a professor of mathematics in the Faculty of Textile Technology at the University of Zagreb, Croatia, and is a full member of the Croatian Academy of Sciences and Arts. He has written and co-authored over 1,200 mathematical publications. He has also published a number of works on history and politics that have been described as comprising historical negationism or Holocaust denial.
Education
Pečarić was born in Kotor, Montenegro (at the time part of Yugoslavia) on 2 September 1948, where he remained to attend elementary and high school. He studied at the University of Belgrade's Faculty of Electrical Engineering for his undergraduate and master's degrees, which he completed respectively in 1972 and 1975. The supervisor of his master's degree, mathematics professor, Dobrilo Tošić, inspired him to switch fields to mathematics.
Pečarić remained at the University of Belgrade, working on his PhD in mathematics from 1975 to 1982. He received it under the supervision of Petar Vasić. His dissertation was on Jensen's and related inequalities. He began working at the University of Zagreb in 1987.
Mathematics career
Pečarić is known for his work in the theory of inequalities. He has founded several journals, all published by Element in Zagreb: he is currently Editor-in-Chief at Mathematical Inequalities and Applications and at the Journal of Mathematical Inequalities, and also founded Operators and Matrices.
Pečarić has written and co-authored over 1,200 articles on mathematics in journals, books, and conference proceedings. He has also coauthored over 20 mathematical books, including 6 that are written in English.
Political views and historical negationism
In addition to his mathematical work, Pečarić has published more than 20 books and 40 articles on history and politics. This work is from a far-right point of view, and has been criticized as comprising historical negationism or Holocaust denial.
For example, Pečarić has advocated for the return of the World War II-era fascist salute Za dom spremni. This salute has been called the Croatian equivalent of the German Sieg Heil. His 2017 book General Praljak reinvents the war criminal Slobodan Praljak as a humanist and war hero. His books Serbian Myths about Jasenovac and The Jasenovac Lie Revealed, the latter coauthored with Stjepan Razum, argued that the Jasenovac concentration camp was a labor camp with much lower casualties than the commonly accepted figure, and that the bulk of its victims were Croats killed by Yugoslav communist authorities after the war. This last prompted the Simon Wiesenthal Centre to advocate the Croatian government to ban publications denying the war crimes of the Ustaša.
Honors and awards
Pečarić has received a number of honors and awards. He was awarded the Croatian National Science Award in 1996, and received the Order of Danica Hrvatska in 1999. Pečarić was appointed to full membersh |
https://en.wikipedia.org/wiki/Sheldon%20Axler | Sheldon Jay Axler (born November 6, 1949, Philadelphia) is an American mathematician and textbook author. He is a professor of mathematics and the Dean of the College of Science and Engineering at San Francisco State University.
He graduated from Miami Palmetto Senior High School in Miami, Florida in 1967. He obtained his AB in mathematics with highest honors at Princeton University (1971) and his PhD in mathematics, under professor Donald Sarason, from the University of California, Berkeley, with the dissertation "Subalgebras of " in 1975. As a postdoc, he was a C. L. E. Moore instructor at the Massachusetts Institute of Technology.
He taught for many years and became a full professor at Michigan State University. In 1997, Axler moved to San Francisco State University, where he became the chair of the Mathematics Department.
Axler received the Lester R. Ford Award for expository writing in 1996 from the Mathematical Association of America for a paper titled "Down with Determinants!" in which he shows how one can teach or learn linear algebra without the use of determinants. Axler later wrote a textbook, Linear Algebra Done Right (3rd ed. 2015), to the same effect.
In 2012, he became a fellow of the American Mathematical Society. He was an Associate Editor of the American Mathematical Monthly and the Editor-in-Chief of the Mathematical Intelligencer.
Books
Linear Algebra Done Right, third edition, Undergraduate Texts in Mathematics, Springer, 2015 (twelfth printing, 2009).
(with John E. McCarthy, and Donald Sarason) editors. Holomorphic Spaces, Cambridge University Press 1998.
(with Paul Bourdon, and Wade Ramey) Harmonic Function Theory, second edition, Graduate Texts in Mathematics, Springer, 2001.
Harmonic Function Theory software, a Mathematica package for symbolic manipulation of harmonic functions, version 7.00, released 1 January 2009 (previous versions released in 1992, 1993, 1994, 1996, 1999, 2000, 2001, 2002, 2003, and 2008).
Precalculus: A Prelude to Calculus, Wiley, 2009 (third printing, 2010).
(with Peter Rosenthal and Donald Sarason) editors. A Glimpse at Hilbert Space Operators, Birkhäuser, 2010.
College Algebra, John Wiley & Sons 2011.
Algebra & Trigonometry, John Wiley & Sons, January 2011.
Measure, Integration & Real Analysis (open access, updated 2020), Springer, November 2019.
References
External links
Axler's Home Page
College of Science & Engineering Newsletter from San Francisco State University.
Senior Fellow Sheldon Axler from California Council on Science and Technology.
Author profile in the database zbMATH
20th-century American mathematicians
21st-century American mathematicians
1949 births
Living people
San Francisco State University faculty
Fellows of the American Mathematical Society
Princeton University alumni
Place of birth missing (living people)
UC Berkeley College of Letters and Science alumni
People from Miami
Michigan State University faculty
Mathematicians from Philadelphia
Massachuset |
https://en.wikipedia.org/wiki/Topology%20and%20Its%20Applications | Topology and Its Applications is a peer-reviewed mathematics journal publishing research on topology. It was established in 1971 as General Topology and Its Applications, and renamed to its current title in 1980. The journal currently publishes 18 issues each year in one volume. It is indexed by Scopus, Mathematical Reviews, and Zentralblatt MATH. Its 2004–2008 MCQ was 0.38 and its 2020 impact factor was 0.617.
References
External links
Mathematics journals
English-language journals
Elsevier academic journals
Academic journals established in 1971 |
https://en.wikipedia.org/wiki/Maths%20Mansion | Maths Mansion is a British educational television series for school Years 4 to 6 (nine to eleven year olds) that ran from 19 September 2001 to 26 March 2003. Produced by Channel 4 by Open Mind, It follows the adventures of "Bad Man" taking kids to his mansion, Maths Mansion. There, the kids learn and are tested on maths every week; if they pass the quiz, they get a "Maths Card".
The kids are not allowed to leave the mansion until they get enough Maths Cards. They do not always pass the test, and this is shown in various episodes, one of them being Angleman!. Frequently interrupting each programme is another programme, about "Sad Man", who seems to be quite happy. He demonstrates maths with songs, puppets, and games.
Sad Man has a puppet called "Decimole", as for him being a mole. Decimole is known for attacking people; in the final episode, Bad Man digs up Decimole, and Decimole kills Bad Man. There were forty episodes in four seasons. Each episode is about ten minutes long and comes with a teacher's guide and activity book and three activity sheets of differing levels for kids to use in class.
Characters
The main characters of Maths Mansion (other than the several kids in each episode) are Bad Man and Sad Man. Bad Man is the game show host who traps the kids and does not let them leave until they acquire Maths Cards that are earned in his game show. One of Bad Man's catchphrases, "No Leaving Without Learning," sums up his attitude towards the kids and his role in the show.
Sad Man, a dated, uncharismatic, leather elbow patch wearing alter ego of Bad Man from the seventies, regularly interrupts Bad Man's programming with informational broadcasts that help the kids learn how to leave the mansion and teaches the lesson to the kids watching the show. Sad Man brings with him several minor characters such as Decimole and Snorter the Pig, a collection of puppets. Sad Man also occasionally has other alter egos himself such as Angleman, who is the namesake for one episode 5 of season 3.
Other than Bad Man, Sad Man, and the kids, other characters include:
Decimole
Miss Sniff
Angleman
Mr. Girhalf
Third Bird
Twelfth Elf
Not So Great Big Hen
Snorter
Thick Stick
Episodes
Season 1
Season 1 is an introduction to the number system and general mathematics.
Season 2
Season 2 is focused on doing simple mathematical calculations.
Season 3
Season 3 is focused on numbers and the number system, including natural numbers, integers, and rational numbers.
Season 4
Season 4 is focused on geometry, specifically shape, space, and problem solving using those ideas.
External links
Channel 4 Learning - Maths Mansion, an archive of the former official website.
References
Discovery Education Search
Episode 35, Angleman!
Mathematics education television series
British children's education television series |
https://en.wikipedia.org/wiki/Graph%20Style%20Sheets | GSS (Graph Style Sheets) in mathematics and computing, is an RDF (Resource Description Framework) vocabulary for representation of data in a model of labeled directed graph. Using it will make a relatively complex data resource modeled in RDF, much easier to understand by declaring simple styling and visibility instructions to be applied on selected resources, literals and properties.
Introduction
GSS (Graph Style Sheets) are proposed in order to visually transform the graphs: filtering information, providing alternative layouts for specific elements, and using all available visual variables to encode information, so as to visualise data in a way that better lends itself to human perception. In summary, GSS (Graph Style Sheets) have been designed for the purpose of filtering, grouping and styling of information elements through specification of declarative transformation rules.
GSS not only associate styles to node-edge representation of RDF models, but also can be used to hide part of the graph and offer alternative layouts for some intended elements. The language lets you change the shape (including bitmap icons) of nodes in the graph, change font attributes or stroke properties, and group some or all properties associated with a resource in a table and sort them. a relatively complex RDF model easier to understand by declaring simple styling and visibility instructions to be applied to selected resources and properties.
The GSS Language
GSS is a stylesheet language for styling data modeled in RDF and features a cascading mechanism. Its transformation model is loosely based on that of XSLT and its instructions resemble some existing W3C Recommendations such as CSS and SVG. In particular most of the GSS properties accept all values defined by the CSS 2 and SVG 1.0 Recommendations.
Any transformation rule of GSS is made of a selector-instruction pair. The left-hand side of a rule is called selector and the right-hand side is called the instruction. Such sets of rules are collected in a stylesheet (or several cascading stylesheets) and the application (a GSS engine) responsible for styling RDF model, evaluates relevant rules on data model (resources, literals and properties) while walking it; that is, if the selector of a rule matches a node (or edge) in the data model, its set of styling instructions are applied to that node (or edge). Conflicts between rules matching the same node (or edge) are resolved by giving different priority to rules in the stylesheets and most specific selector if conflicting rules are in the same stylesheet.
Tools for manipulating GSS
IsaViz 2.0 is equipped with a GSS Editor, which lets you create stylesheets without writing a single line of RDF.
References
Resource Description Framework |
https://en.wikipedia.org/wiki/Bousso%27s%20holographic%20bound | The Bousso bound captures a fundamental relation between quantum information and the geometry of space and time. It appears to be an imprint of a unified theory that combines quantum mechanics with Einstein's general relativity.
The study of black hole thermodynamics and the information paradox led to the idea of the holographic principle: the entropy of matter and radiation in a spatial region cannot exceed the Bekenstein–Hawking entropy of the boundary of the region, which is proportional to the boundary area. However, this "spacelike" entropy bound fails in cosmology; for example, it does not hold true in our universe.
Raphael Bousso showed that the spacelike entropy bound is violated more broadly in many dynamical settings. For example, the entropy of a collapsing star, once inside a black hole, will eventually exceed its surface area. Due to relativistic length contraction, even ordinary thermodynamic systems can be enclosed in an arbitrarily small area.
To preserve the holographic principle, Bousso proposed a different law, which does not follow from black hole physics: the covariant entropy bound or Bousso bound. Its central geometric object is a lightsheet, defined as a region traced out by non-expanding light-rays emitted orthogonally from an arbitrary surface B. For example, if B is a sphere at a moment of time in Minkowski space, then there are two lightsheets, generated by the past or future directed light-rays emitted towards the interior of the sphere at that time. If B is a sphere surrounding a large region in an expanding universe (an anti-trapped sphere), then there are again two light-sheets that can be considered. Both are directed towards the past, to the interior or the exterior. If B is a trapped surface, such as the surface of a star in its final stages of gravitational collapse, then the lightsheets are directed to the future.
The Bousso bound evades all known counterexamples to the spacelike bound. It was proven to hold when the entropy is approximately a local current, under weak assumptions. In weakly gravitating settings, the Bousso bound implies the Bekenstein bound and admits a formulation that can be proven to hold in any relativistic quantum field theory. The lightsheet construction can be inverted to construct holographic screens for arbitrary spacetimes.
A more recent proposal, the quantum focusing conjecture, implies the original Bousso bound and so can be viewed as a stronger version of it. In the limit where gravity is negligible, the quantum focusing conjecture predicts the quantum null energy condition, which relates the local energy density to a derivative of the entropy. This relation was later proven to hold in any relativistic quantum field theory, such as the Standard Model.
References
Quantum gravity |
https://en.wikipedia.org/wiki/Walter%20Brit | Walter Brit ( alternatively Brit, Brytte, or Brithus) (fl. 1390), was a fellow of Merton College, Oxford, and the reputed author of several works on astronomy and mathematics, as well as of a treatise on surgery. He has also been described as a follower of John Wycliffe, and as author of a book, De auferendis clero possessionibus.
Lollard identification issue
In the 17th century, Anthony Wood identified Brit with Walter Brut, a layman of the diocese of Hereford, whose trial before Bishop Thomas Trevenant of Hereford in 1391 is related by John Foxe. Current scholarship regards the matter as still open, however.
Foxe prints the articles of heresy with which Brut was charged, the speech in which he defended himself, and his ultimate submission of his opinions to the determination of the church. Thirty-seven articles were then drawn up and sent to the University of Cambridge to be confuted. Brut, however, appears to have escaped further molestation.
Attribution of scientific writings
The work most frequently cited as Brit's is the Theorica Planetarum, which bears his name in two manuscripts in the Bodleian Library (Digby, xv. ff. 58 b-92, and Wood, 8 d, f. 93); it has also been claimed for Simon Bredon. Pederson considers it as Brit's.
The work in question, which begins with the words: , is further to be distinguished from another treatise with the same title, of which the opening words are , and of which the authorship is shown by the notices collected by Baldassarre Boncompagni ( in Della Vita e delle Opere di Gherardo Cremonese e di Gherardo di Sabbionetta) to be really due to the younger Gerard of Cremona (Gerardus de Sabloneto) in the thirteenth century. The latter has been repeatedly confounded with the Theorica indifferently assigned by the bibliographers to Brit and Bredon.
Another treatise mentioned by John Bale as the composition of Brit is the Theoremata Planetarum, which Thomas Tanner cites as that existing in the Digby MS. exc. f. 190 b (now f. 169 b). This manuscript dates from about the year 1300, and the work is by Johannes de Sacrobosco.
Finally, the Cirurgia Walteri Brit named in the ancient table of contents in another Digby MS. (xcviii. f. 1 b) has nothing corresponding to it in the volume itself but a set of English medical receipts whose author is not stated (f. 257).
Notes
External links
The Bodleian Library: Digby manuscripts
Year of birth missing
Year of death missing
English surgeons
Fellows of Merton College, Oxford
14th-century English mathematicians
14th-century English astronomers
14th-century English medical doctors
14th-century English writers
14th-century writers in Latin |
https://en.wikipedia.org/wiki/Hilbert%27s%20inequality | In analysis, a branch of mathematics, Hilbert's inequality states that
for any sequence of complex numbers. It was first demonstrated by David Hilbert with the constant instead of ; the sharp constant was found by Issai Schur. It implies that the discrete Hilbert transform is a bounded operator in .
Formulation
Let be a sequence of complex numbers. If the sequence is infinite, assume that it is square-summable:
Hilbert's inequality (see ) asserts that
Extensions
In 1973, Montgomery & Vaughan reported several generalizations of Hilbert's inequality, considering the bilinear forms
and
where are distinct real numbers modulo 1 (i.e. they belong to distinct classes in the quotient group ) and are distinct real numbers. Montgomery & Vaughan's generalizations of Hilbert's inequality are then given by
and
where
is the distance from to the nearest integer, and denotes the smallest positive value. Moreover, if
then the following inequalities hold:
and
References
Online book chapter Hilbert’s Inequality and Compensating Difficulties extracted from .
External links
Inequalities
Complex analysis
Number theory |
https://en.wikipedia.org/wiki/Jovica%20Vasili%C4%87 | Jovica Vasilić (Serbian Cyrillic: Јовица Василић; born 8 July 1990) is a Serbian footballer who plays as a right-back.
Career statistics
External links
Utakmica profile
Srbijafudbal profile
1990 births
Living people
People from Priboj
Footballers from Zlatibor District
Serbian men's footballers
Men's association football defenders
FK Sloga Kraljevo players
FK Sloboda Užice players
FK Novi Pazar players
OFK Beograd players
FK Vojvodina players
Serbian First League players
Serbian SuperLiga players |
https://en.wikipedia.org/wiki/1995%20S%C3%A3o%20Paulo%20FC%20season | The 1995 season was São Paulo's 66th season since club's existence.
Statistics
Scorers
Overall
{|class="wikitable"
|-
|Games played || 86 (36 Campeonato Paulista, 7 Copa do Brasil, 23 Campeonato Brasileiro, 6 Supercopa Libertadores, 14 Friendly match)
|-
|Games won || 39 (17 Campeonato Paulista, 3 Copa do Brasil, 9 Campeonato Brasileiro, 4 Supercopa Libertadores, 6 Friendly match)
|-
|Games drawn || 24 (10 Campeonato Paulista, 3 Copa do Brasil, 6 Campeonato Brasileiro, 0 Supercopa Libertadores, 5 Friendly match)
|-
|Games lost || 23 (9 Campeonato Paulista, 1 Copa do Brasil, 8 Campeonato Brasileiro, 2 Supercopa Libertadores, 3 Friendly match)
|-
|Goals scored || 116
|-
|Goals conceded || 89
|-
|Goal difference || +26
|-
|Best result || 4–1 (H) v Novorizontino – Campeonato Paulista – 1995.02.044–1 (A) v Náutico – Copa do Brasil – 1995.03.144–1 (H) v Ponte Preta – Campeonato Paulista – 1995.04.20
|-
|Worst result || 1–4 (A) v Werder Bremen – Friendly match – 1995.08.07
|-
|Most appearances ||
|-
|Top scorer || Bentinho (22)
|-
Friendlies
Trofeo Achille e Cesare Bortolotti
Torneio Rei Dadá
Copa dos Campeões Mundiais
Official competitions
Campeonato Paulista
Matches
Record
Copa do Brasil
Record
Campeonato Brasileiro
First round
Chave B
Matches
Second round
Chave B
Matches
Record
Supercopa Sudamericana
Record
References
External links
official website
Sao Paulo
São Paulo FC seasons |
https://en.wikipedia.org/wiki/List%20of%20Ariane%20launches%20%282000%E2%80%932009%29 | This is a list of launches performed by Ariane carrier rockets between 2000 and 2009. During this period, the Ariane 4 was retired from service in favour of the Ariane 5.
Launch statistics
Rocket configurations
Launch outcomes
Launch history
References |
https://en.wikipedia.org/wiki/Straightening%20theorem%20for%20vector%20fields | In differential calculus, the domain-straightening theorem states that, given a vector field on a manifold, there exist local coordinates such that in a neighborhood of a point where is nonzero. The theorem is also known as straightening out of a vector field.
The Frobenius theorem in differential geometry can be considered as a higher-dimensional generalization of this theorem.
Proof
It is clear that we only have to find such coordinates at 0 in . First we write where is some coordinate system at . Let . By linear change of coordinates, we can assume Let be the solution of the initial value problem and let
(and thus ) is smooth by smooth dependence on initial conditions in ordinary differential equations. It follows that
,
and, since , the differential is the identity at . Thus, is a coordinate system at . Finally, since , we have: and so
as required.
References
Theorem B.7 in Camille Laurent-Gengoux, Anne Pichereau, Pol Vanhaecke. Poisson Structures, Springer, 2013.
Differential calculus |
https://en.wikipedia.org/wiki/Ivan%20Fesenko | Ivan Fesenko is a mathematician working in number theory and its interaction with other areas of modern mathematics.
Education
Fesenko was educated at St. Petersburg State University where he was awarded a PhD in 1987.
Career and research
Fesenko was awarded the Prize of the Petersburg Mathematical Society in 1992. Since 1995, he is professor in pure mathematics at University of Nottingham.
He contributed to several areas of number theory such as class field theory and its generalizations, as well as to various related developments in pure mathematics.
Fesenko contributed to explicit formulas for the generalized Hilbert symbol on local fields and higher local field, higher class field theory, p-class field theory, arithmetic noncommutative local class field theory.
He coauthored a textbook on local fields and a volume on higher local fields.
Fesenko discovered a higher Haar measure and integration on various higher local and adelic objects. He pioneered the study of zeta functions in higher dimensions by developing his theory of higher adelic zeta integrals. These integrals are defined using the higher Haar measure and objects from higher class field theory. Fesenko generalized the Iwasawa-Tate theory from 1-dimensional global fields to 2-dimensional arithmetic surfaces such as proper regular models of elliptic curves over global fields. His theory led to three further developments.
The first development is the study of functional equation and meromorphic continuation of the Hasse zeta function of a proper regular model of an elliptic curve over a global field. This study led Fesenko to introduce a new mean-periodicity correspondence between the arithmetic zeta functions and mean-periodic elements of the space of smooth functions on the real line of not more than exponential growth at infinity. This correspondence can be viewed as a weaker version of the Langlands correspondence, where L-functions and replaced by zeta functions and automorphicity is replaced by mean-periodicity. This work was followed by a joint work with Suzuki and Ricotta.
The second development is an application to the generalized Riemann hypothesis, which in this higher theory is reduced to a certain positivity property of small derivatives of the boundary function and to the properties of the spectrum of the Laplace transform of the boundary function.
The third development is a higher adelic study of relations between the arithmetic and analytic ranks of an elliptic curve over a global field, which in conjectural form are stated in the Birch and Swinnerton-Dyer conjecture for the zeta function of elliptic surfaces. This new method uses FIT theory, two adelic structures: the geometric additive adelic structure and the arithmetic multiplicative adelic structure and an interplay between them motivated by higher class field theory. These two adelic structures have some similarity to two symmetries in inter-universal Teichmüller theory of Mochizuki.
His contributi |
https://en.wikipedia.org/wiki/Biot%E2%80%93Tolstoy%E2%80%93Medwin%20diffraction%20model | In applied mathematics, the Biot–Tolstoy–Medwin (BTM) diffraction model describes edge diffraction. Unlike the uniform theory of diffraction (UTD), BTM does not make the high frequency assumption (in which edge lengths and distances from source and receiver are much larger than the wavelength). BTM sees use in acoustic simulations.
Impulse response
The impulse response according to BTM is given as follows:
The general expression for sound pressure is given by the convolution integral
where represents the source signal, and represents the impulse response at the receiver position. The BTM gives the latter in terms of
the source position in cylindrical coordinates where the -axis is considered to lie on the edge and is measured from one of the faces of the wedge.
the receiver position
the (outer) wedge angle and from this the wedge index
the speed of sound
as an integral over edge positions
where the summation is over the four possible choices of the two signs, and are the distances from the point to the source and receiver respectively, and is the Dirac delta function.
where
See also
Uniform theory of diffraction
Notes
References
Calamia, Paul T. and Svensson, U. Peter, "Fast time-domain edge-diffraction calculations for interactive acoustic simulations," EURASIP Journal on Advances in Signal Processing, Volume 2007, Article ID 63560.
Signal processing |
https://en.wikipedia.org/wiki/Bernstein%27s%20problem | In differential geometry, Bernstein's problem is as follows: if the graph of a function on Rn−1 is a minimal surface in Rn, does this imply that the function is linear?
This is true for n at most 8, but false for n at least 9. The problem is named for Sergei Natanovich Bernstein who solved the case n = 3 in 1914.
Statement
Suppose that f is a function of n − 1 real variables. The graph of f is a surface in Rn, and the condition that this is a minimal surface is that f satisfies the minimal surface equation
Bernstein's problem asks whether an entire function (a function defined throughout Rn−1 ) that solves this equation is necessarily a degree-1 polynomial.
History
proved Bernstein's theorem that a graph of a real function on R2 that is also a minimal surface in R3 must be a plane.
gave a new proof of Bernstein's theorem by deducing it from the fact that there is no non-planar area-minimizing cone in R3.
showed that if there is no non-planar area-minimizing cone in Rn−1 then the analogue of Bernstein's theorem is true for graphs in Rn, which in particular implies that it is true in R4.
showed there are no non-planar minimizing cones in R4, thus extending Bernstein's theorem to R5.
showed there are no non-planar minimizing cones in R7, thus extending Bernstein's theorem to R8. He also showed that the surface defined by
is a locally stable cone in R8, and asked if it is globally area-minimizing.
showed that Simons' cone is indeed globally minimizing, and that in Rn for n≥9 there are graphs that are minimal, but not hyperplanes. Combined with the result of Simons, this shows that the analogue of Bernstein's theorem is true in Rn for n≤8, and false in higher dimensions.
References
German translation in
External links
Encyclopaedia of Mathematics article on the Bernstein theorem
Minimal surfaces
Functions and mappings
Dimension
Theorems in differential geometry |
https://en.wikipedia.org/wiki/Bernstein%27s%20theorem | In mathematics, Bernstein's theorem may refer to:
Bernstein's theorem about the Sato–Bernstein polynomial
Bernstein's problem about minimal surfaces
Bernstein's theorem on monotone functions
Bernstein's theorem (approximation theory)
Bernstein's theorem (polynomials)
Bernstein's lethargy theorem
Bernstein–von Mises theorem
Cantor–Bernstein–Schroeder theorem in set theory. |
https://en.wikipedia.org/wiki/Multivariate%20stable%20distribution | The multivariate stable distribution is a multivariate probability distribution that is a multivariate generalisation of the univariate stable distribution. The multivariate stable distribution defines linear relations between stable distribution marginals. In the same way as for the univariate case, the distribution is defined in terms of its characteristic function.
The multivariate stable distribution can also be thought as an extension of the multivariate normal distribution. It has parameter, α, which is defined over the range 0 < α ≤ 2, and where the case α = 2 is equivalent to the multivariate normal distribution. It has an additional skew parameter that allows for non-symmetric distributions, where the multivariate normal distribution is symmetric.
Definition
Let be the unit sphere in . A random vector, , has a multivariate stable distribution - denoted as -, if the joint characteristic function of is
where 0 < α < 2, and for
This is essentially the result of Feldheim, that any stable random vector can be characterized by a spectral measure (a finite measure on ) and a shift vector .
Parametrization using projections
Another way to describe a stable random vector is in terms of projections. For any vector , the projection is univariate stable with some skewness , scale and some shift . The notation is used if X is stable with
for every . This is called the projection parameterization.
The spectral measure determines the projection parameter functions by:
Special cases
There are special cases where the multivariate characteristic function takes a simpler form. Define the characteristic function of a stable marginal as
Isotropic multivariate stable distribution
The characteristic function is
The spectral measure is continuous and uniform, leading to radial/isotropic symmetry.
For the multinormal case , this corresponds to independent components, but so is not the case when . Isotropy is a special case of ellipticity (see the next paragraph) – just take to be a multiple of the identity matrix.
Elliptically contoured multivariate stable distribution
The elliptically contoured multivariate stable distribution is a special symmetric case of the multivariate stable distribution.
If X is α-stable and elliptically contoured, then it has joint characteristic function
for some shift vector (equal to the mean when it exists) and some positive definite matrix (akin to a correlation matrix, although the usual definition of correlation fails to be meaningful).
Note the relation to characteristic function of the multivariate normal distribution: obtained when α = 2.
Independent components
The marginals are independent with , then the
characteristic function is
Observe that when α = 2 this reduces again to the multivariate normal; note that the iid case and the isotropic case do not coincide when α < 2.
Independent components is a special case of discrete spectral measure (see next paragraph), with the spectral measu |
https://en.wikipedia.org/wiki/Cyclic%20number%20%28group%20theory%29 | A cyclic number is a natural number n such that n and φ(n) are coprime. Here φ is Euler's totient function. An equivalent definition is that a number n is cyclic if and only if any group of order n is cyclic.
Any prime number is clearly cyclic. All cyclic numbers are square-free.
Let n = p1 p2 … pk where the pi are distinct primes, then φ(n) = (p1 − 1)(p2 − 1)...(pk – 1). If no pi divides any (pj – 1), then n and φ(n) have no common (prime) divisor, and n is cyclic.
The first cyclic numbers are 1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 35, 37, 41, 43, 47, 51, 53, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 123, 127, 131, 133, 137, 139, 141, 143, 145, 149, ... .
References
Number theory |
https://en.wikipedia.org/wiki/Quasitoric%20manifold | In mathematics, a quasitoric manifold is a topological analogue of the nonsingular projective toric variety of algebraic geometry. A smooth -dimensional manifold is a quasitoric manifold if it admits a smooth, locally standard action of an -dimensional torus, with orbit space an -dimensional simple convex polytope.
Quasitoric manifolds were introduced in 1991 by M. Davis and T. Januszkiewicz, who called them "toric manifolds". However, the term "quasitoric manifold" was eventually adopted to avoid confusion with the class of compact smooth toric varieties, which are known to algebraic geometers as toric manifolds.
Quasitoric manifolds are studied in a variety of contexts in algebraic topology, such as complex cobordism theory, and the other oriented cohomology theories.
Definitions
Denote the -th subcircle of the -torus by so that . Then coordinate-wise multiplication of on is called the standard representation.
Given open sets in and in , that are closed under the action of , a -action on is defined to be locally isomorphic to the standard representation if , for all in , in , where is a homeomorphism , and is an automorphism of .
Given a simple convex polytope with facets, a -manifold is a quasitoric manifold over if,
the -action is locally isomorphic to the standard representation,
there is a projection that maps each -dimensional orbit to a point in the interior of an -dimensional face of , for .
The definition implies that the fixed points of under the -action are mapped to the vertices of by , while points where the action is free project to the interior of the polytope.
The dicharacteristic function
A quasitoric manifold can be described in terms of a dicharacteristic function and an associated dicharacteristic matrix. In this setting it is useful to assume that the facets of are ordered so that the intersection is a vertex of , called the initial vertex.
A dicharacteristic function is a homomorphism , such that if is a codimension- face of , then is a monomorphism on restriction to the subtorus in .
The restriction of λ to the subtorus corresponding to the initial vertex is an isomorphism, and so can be taken to be a basis for the Lie algebra of . The epimorphism of Lie algebras associated to λ may be described as a linear transformation , represented by the dicharacteristic matrix given by
The th column of is a primitive vector in , called the facet vector. As each facet vector is primitive, whenever the facets meet in a vertex, the corresponding columns form a basis of , with determinant equal to . The isotropy subgroup associated to each facet is described by
for some in .
In their original treatment of quasitoric manifolds, Davis and Januskiewicz introduced the notion of a characteristic function that mapped each facet of the polytope to a vector determining the isotropy subgroup of the facet, but this is only defined up to sign. In more recent studies of quasitoric manifolds, |
https://en.wikipedia.org/wiki/Advances%20in%20Applied%20Mathematics | Advances in Applied Mathematics is a peer-reviewed mathematics journal publishing research on applied mathematics. Its founding editor was Gian-Carlo Rota (Massachusetts Institute of Technology); from 1980 to 1999, Joseph P. S. Kung (University of North Texas) served as managing editor. It is currently published by Elsevier with eight issues per year and edited by Hal Schenck (Auburn University) and Catherine Yan (Texas A&M University).
Abstracting and indexing
The journal is abstracted and indexed by:
ACM Guide to Computing Literature
CompuMath Citation Index
Current Contents/Physics, Chemical, & Earth Sciences
Mathematical Reviews
Science Citation Index
Scopus
According to the Journal Citation Reports, the journal has a 2020 impact factor of 0.848.
See also
List of periodicals published by Elsevier
References
External links
Mathematics journals
Academic journals established in 1980
English-language journals
Elsevier academic journals
8 times per year journals |
https://en.wikipedia.org/wiki/Pankaj%20K.%20Agarwal | Pankaj Kumar Agarwal is an Indian computer scientist and mathematician researching algorithms in computational geometry and related areas. He is the RJR Nabisco Professor of Computer Science and Mathematics at Duke University, where he has been chair of the computer science department since 2004. He obtained his Doctor of Philosophy (Ph.D.) in computer science in 1989 from the Courant Institute of Mathematical Sciences, New York University, under the supervision of Micha Sharir.
Books
Agarwal is the author or co-author of:
Intersection and Decomposition Algorithms for Planar Arrangements (Cambridge University Press, 1991, ). The topics of this book are algorithms for, and the combinatorial geometry of, arrangements of lines and arrangements of more general types of curves in the Euclidean plane and the real projective plane. The topics covered in this monograph include Davenport–Schinzel sequences and their application to the complexity of single cells in arrangements, levels in arrangements, algorithms for building arrangements in part or in whole, and ray shooting in arrangements.
Davenport–Schinzel Sequences and Their Geometric Applications (with Micha Sharir, Cambridge University Press, 1995, ). This book concerns Davenport–Schinzel sequences, sequences of symbols drawn from a given alphabet with the property that no subsequence of more than some finite length consists of two alternating symbols. As the book discusses, these sequences and combinatorial bounds on their length have many applications in combinatorial and computational geometry, including bounds on lower envelopes of sets of functions, single cells in arrangements, shortest paths, and dynamically changing geometric structures.
Combinatorial Geometry (with János Pach, Wiley, 1995, ). This book, less specialized than the prior two, is split into two sections. The first, on packing and covering problems, includes topics such as Minkowski's theorem, sphere packing, the representation of planar graphs by tangent circles, the planar separator theorem. The second section, although mainly concerning arrangements, also includes topics from extremal graph theory, Vapnik–Chervonenkis dimension, and discrepancy theory.
Awards and honors
Agarwal was elected as a fellow of the Association for Computing Machinery in 2002. He is also former Duke Bass Fellow and an Alfred P. Sloan Fellow. He was the recipient of a National Young Investigator Award in 1993. Before holding the RJR Nabisco Professorship, he was the Earl D. Mclean Jr. Professor of Computer Science at Duke.
References
External links
, Duke University
Department page at Duke University
Year of birth missing (living people)
Living people
Courant Institute of Mathematical Sciences alumni
Duke University faculty
Researchers in geometric algorithms
Fellows of the Association for Computing Machinery
20th-century Indian mathematicians |
https://en.wikipedia.org/wiki/Eugene%20Seneta | Eugene Seneta is Professor Emeritus, School of Mathematics and Statistics, University of Sydney, known for his work in probability and non-negative matrices, applications and history. He is known for the variance gamma model in financial mathematics (the Madan–Seneta process). He was Professor, School of Mathematics and Statistics at the University of Sydney from 1979 until retirement, and an Elected Fellow since 1985 of the Australian Academy of Science. In 2007 Seneta was awarded the Hannan Medal in Statistical Science
by the Australian Academy of Science, for his seminal work in probability and statistics; for his work connected with branching processes, history of probability and statistics, and many other areas.
References
E. Seneta (2004). Fitting the variance-gamma model to financial data, Stochastic methods and their applications, J. Appl. Probab. 41A, 177–187.
E. Seneta (2001). Characterization by orthogonal polynomial systems of finite Markov chains, J. Appl. Probab., 38A, 42–52.
Madan D, Seneta E. (1990). The variance gamma (v.g.) model for share market returns, Journal of Business, 63 (1990), 511–524.
P. Hall and E. Seneta (1988). Products of independent normally attracted random variables, Probability Theory and Related Fields, 78, 135–142.
E. Seneta (1974). Regularly varying functions in the theory of simple branching processes, Advances in Applied Probability, 6, 408–420.
E. Seneta (1973). The simple branching process with infinite mean, I, Journal of Applied Probability, 10, 206–212.
E. Seneta (1973). A Tauberian theorem of R. Landau and W. Feller, The Annals of Probability, 1, 1057–1058.
External links
Eugene Seneta faculty page at U. of Sydney and list of publications.
Probability theorists
Australian statisticians
Fellows of the Australian Academy of Science
Living people
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Almamell%C3%A9k | Almamellék () is a village in Baranya County, Hungary.
References
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Alm%C3%A1skereszt%C3%BAr | Almáskeresztúr is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Als%C3%B3szentm%C3%A1rton | Alsószentmárton is a village in Baranya county, Hungary. It is located near the border with Croatia.
The population is composed of the Romani people.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Ap%C3%A1tvarasd | Apátvarasd () is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County
Hungarian German communities |
https://en.wikipedia.org/wiki/Babarcsz%C5%91l%C5%91s | Babarcszőlős is a village in Baranya county, Hungary. It is very small in terms of population with only little over 100 people living in the village.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/B%C3%A1nfa | Bánfa is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Baranyah%C3%ADdv%C3%A9g | Baranyahídvég is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Bics%C3%A9rd | Bicsérd is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Birj%C3%A1n | Birján is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Bodolyab%C3%A9r | Bodolyabér is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Bog%C3%A1d | Bogád is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Bog%C3%A1dmindszent | Bogádmindszent is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/B%C3%BCkk%C3%B6sd | Bükkösd is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/B%C3%BCr%C3%BCs | Bürüs is a village in Baranya county, Hungary.
History
According to László Szita the settlement was completely Hungarian in the 18th century.
References
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Cs%C3%A1nyoszr%C3%B3 | Csányoszró is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Csarn%C3%B3ta | Csarnóta is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Cseb%C3%A9ny | Csebény () is a village in Baranya County, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Cserk%C3%BAt | Cserkút is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Csert%C5%91 | Csertő is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Dencsh%C3%A1za | Dencsháza is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Di%C3%B3sviszl%C3%B3 | Diósviszló is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Dr%C3%A1vacsehi | Drávacsehi is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Dr%C3%A1vacsepely | Drávacsepely is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Dr%C3%A1vafok | Drávafok is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Dr%C3%A1vaiv%C3%A1nyi | Drávaiványi is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Dr%C3%A1vapalkonya | Drávapalkonya is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Dr%C3%A1vapiski | Drávapiski is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Dr%C3%A1vaszabolcs | Drávaszabolcs is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Dr%C3%A1vaszerdahely | Drávaszerdahely is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Dr%C3%A1vaszt%C3%A1ra | Drávasztára () is a village in Baranya County, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Eger%C3%A1g | Egerág is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Egyh%C3%A1zasharaszti | Egyházasharaszti is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Endr%C5%91c | Endrőc is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Erd%C5%91sm%C3%A1rok | Erdősmárok is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Fels%C5%91szentm%C3%A1rton | Felsőszentmárton () is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Gar%C3%A9 | Garé is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Ger%C3%A9nyes | Gerényes is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Gilv%C3%A1nfa | Gilvánfa is a village in Baranya county, Hungary. The village has an almost entirely Roma population.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/G%C3%B6rcs%C3%B6nydoboka | Görcsönydoboka is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Gy%C3%B3d | Gyód is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Gy%C3%B6ngyfa | Gyöngyfa is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Hegyh%C3%A1tmar%C3%B3c | Hegyhátmaróc is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Hegyszentm%C3%A1rton | Hegyszentmárton is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Homor%C3%BAd | Homorúd is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Horv%C3%A1thertelend | Horváthertelend is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Huszt%C3%B3t | Husztót is a village in Baranya county, Hungary.
External links
Local statistics
Populated places in Baranya County |
https://en.wikipedia.org/wiki/Primary%20extension | In field theory, a branch of algebra, a primary extension L of K is a field extension such that the algebraic closure of K in L is purely inseparable over K.
Properties
An extension L/K is primary if and only if it is linearly disjoint from the separable closure of K over K.
A subextension of a primary extension is primary.
A primary extension of a primary extension is primary (transitivity).
Any extension of a separably closed field is primary.
An extension is regular if and only if it is separable and primary.
A primary extension of a perfect field is regular.
References
Field (mathematics) |
https://en.wikipedia.org/wiki/Orthogonal%20symmetric%20Lie%20algebra | In mathematics, an orthogonal symmetric Lie algebra is a pair consisting of a real Lie algebra and an automorphism of of order such that the eigenspace of s corresponding to 1 (i.e., the set of fixed points) is a compact subalgebra. If "compactness" is omitted, it is called a symmetric Lie algebra. An orthogonal symmetric Lie algebra is said to be effective if intersects the center of trivially. In practice, effectiveness is often assumed; we do this in this article as well.
The canonical example is the Lie algebra of a symmetric space, being the differential of a symmetry.
Let be effective orthogonal symmetric Lie algebra, and let denotes the -1 eigenspace of . We say that is of compact type if is compact and semisimple. If instead it is noncompact, semisimple, and if is a Cartan decomposition, then is of noncompact type. If is an Abelian ideal of , then is said to be of Euclidean type.
Every effective, orthogonal symmetric Lie algebra decomposes into a direct sum of ideals , and , each invariant under and orthogonal with respect to the Killing form of , and such that if , and denote the restriction of to , and , respectively, then , and are effective orthogonal symmetric Lie algebras of Euclidean type, compact type and noncompact type.
References
Lie algebras |
https://en.wikipedia.org/wiki/West%20Watta | {
"type": "FeatureCollection",
"features": [
{
"type": "Feature",
"properties": {},
"geometry": {
"type": "Point",
"coordinates": [
81.112747192383,
6.6693815775734
]
}
}
]
}
West Watta is a village in Sri Lanka. It is located within Central Province, slightly southeast. The A2 road runs through the village; it is close to the Kinkini Wehera Raja Maha Viharaya Buddhist Temple and next to the Kirindi Oya River.
See also
List of towns in Central Province, Sri Lanka
External links
Populated places in Matale District |
https://en.wikipedia.org/wiki/List%20of%20Philippine%20Basketball%20Association%20career%20assists%20leaders | This is a list of Philippine Basketball Association players by total career assists.
Statistics accurate as of January 16, 2023.
See also
List of Philippine Basketball Association players
References
External links
Philippine Basketball Association All-time Most Assists Leaders – PBA Online.net
Link Label
Assists, Career |
https://en.wikipedia.org/wiki/Variance%20%28disambiguation%29 | In probability theory and statistics, variance measures how far a set of numbers are spread out.
Variance may also refer to:
Variance (accounting), the difference between a budgeted, planned or standard cost and the actual amount incurred/sold
Variance Films, a film distribution company founded in 2008
Variance (land use), a deviation from the set of rules a municipality applies to land use and land development
Variance (album) (2009), third album by electronic musician Jega
Variance (magazine), an American online music magazine
See also
Covariance, probability theory and statistics
Covariance and contravariance (category theory)
Covariance and contravariance (computer science)
Genetic variance (disambiguation)
Invariance (physics) |
https://en.wikipedia.org/wiki/Saligrama%2C%20Mysore | {
"type": "FeatureCollection",
"features": [
{
"type": "Feature",
"properties": {},
"geometry": {
"type": "Point",
"coordinates": [
76.262853294611,
12.56015541614
]
}
}
]
}
Saligrama is a new sub-district of Mysore district, situated on the northern bank of the river Cauvery [Kaveri]. This place is esteemed as sacred by the Shri Vaishnavas on account of its having been the residence of Sri Ramanujacharya. It is the headquarters of Saligrama Taluk. It was established as a new taluk carving out of K.R.Nagar taluk with effect from 31.12.2020 and become ninth taluk of Mysore district of Karnataka, India.
A number of religious sites, famous old temples - including Sri Yoga Narasimha Swamy Temple, Sri Ramanuja Sripada Teertham, Sri Jyothirmaheswara Swamy Temple, Jain Basadis, and an Ashram are located in the town.
History
Swamy Ramanuja arrived in Karnataka where the local tribals received him in this place. The local people who were averse to Swamy Ramanuja conspired a plan to do away with him. Swamy Ramanuja learning their evil intentions ordered Mudaliandan Swamy to place his feet in the drinking water pond in that area now called Saligrama. At Saligrama, by partaking this Sripada theertham, the minds of the evildoers changed and they fell at Swamy Ramanuja lotus feet seeking forgiveness. Such was the greatness of our Mudaliandan Swamy.
When persecuted by the Chola king Kulottunga, Ramanujacharya is said to have fled the Chola country and first stayed at Vahnipushkarini (the place now known as 'Mirle') from where he moved on to Saligrama.
Etymology
Swamy Ramanuja named this place as "Saligramam" which is near Melkote. Even today this pond is maintained by the archakas who ensures that no intruder pollutes the pond by locking the gate. There is a small temple opposite to this pond in which Swamy Ramanuja's Thiruvadi chuvadugal are worshipped. There is also a deity of Swamy Ramanuja in Sesharoopa near the garbagriha.
Demographics
Population
According to census data released in 2011 by the Government of Karnataka, total area of Saligrama is spread across 1109.5 hectares with a total population of 11836 persons [Male - 5869 and Female - 5967] and 2976 households with an average of 4 persons per household.
Literacy
As per the report the total literacy rate is 71.93% [with Male - 77.33% and Female - 66.59%]. Comparing it with the previous census data, the total literacy rate has increased by 6% with 4% increase in the male and 7% increase in the female literacy rate.
Growth in population
Presently, there is a 0.5% increase in the total population of the village as it was about 12000 before 10 years. The rate of growth in female population has gone up by 2.9% and male population has decreased by -1.9%. So, the rate of population growth in female is 4.8% higher compared to their counterpart.
Sex ratio
According to the recent census, there are 1017 fem |
https://en.wikipedia.org/wiki/Constructible%20topology | In commutative algebra, the constructible topology on the spectrum of a commutative ring is a topology where each closed set is the image of in for some algebra B over A. An important feature of this construction is that the map is a closed map with respect to the constructible topology.
With respect to this topology, is a compact, Hausdorff, and totally disconnected topological space (i.e., a Stone space). In general, the constructible topology is a finer topology than the Zariski topology, and the two topologies coincide if and only if is a von Neumann regular ring, where is the nilradical of A.
Despite the terminology being similar, the constructible topology is not the same as the set of all constructible sets.
See also
Constructible set (topology)
References
Commutative algebra
Topology |
https://en.wikipedia.org/wiki/Kasper%20Degn | Kasper Degn is a Danish professional ice hockey player who participated at the 2010 IIHF World Championship as a member of the Denmark National men's ice hockey team.
Career statistics
References
1982 births
AaB Ishockey players
Aalborg Pirates players
Danish ice hockey forwards
Herning Blue Fox players
Living people
Nordsjælland Cobras players
SC Bietigheim-Bissingen players |
https://en.wikipedia.org/wiki/Chochana%20Boukhobza | Chochana Boukhobza ( , Sfax, March 2, 1959 – ) is an Israeli writer of Tunisian-Jewish descent. She was born in Sfax, Tunisia and emigrated to Israel at the age of 17. She studied mathematics in Israel.
She is the author of several novels, the first of which Un été à Jérusalem (A Summer in Jerusalem) won the Prix Mediterranée in 1986. Her second novel Le Cri was a finalist for the 1987 Prix Femina. She has also written several screenplays. In 2005, she co-directed a documentary Un billet aller-retour (A Return Ticket) (Barcelona-Paris Films Productions).
References
Israeli Jews
Israeli novelists
1959 births
Living people
People from Sfax
Tunisian emigrants to Israel
Israeli people of Tunisian-Jewish descent
Tunisian writers in French |
https://en.wikipedia.org/wiki/Triangular%20matrix%20ring | In algebra, a triangular matrix ring, also called a triangular ring, is a ring constructed from two rings and a bimodule.
Definition
If and are rings and is a -bimodule, then the triangular matrix ring consists of 2-by-2 matrices of the form , where and with ordinary matrix addition and matrix multiplication as its operations.
References
Ring theory |
https://en.wikipedia.org/wiki/Serhiy%20Tretyak%20%28footballer%2C%20born%201984%29 | Serhiy Tretyak (; born 28 November 1984) is a Ukrainian footballer.
He spent his career in the Ukrainian and Israeli football clubs.
Statistics
References
External links
1984 births
Living people
Footballers from Kyiv
Ukrainian men's footballers
Men's association football forwards
FC Borysfen Boryspil players
FC Borysfen-2 Boryspil players
FC Arsenal Kyiv players
FC Krasyliv players
FC Obolon Kyiv players
FC Obolon-2 Bucha players
FC Stal Alchevsk players
FC Volyn Lutsk players
FC Poltava players
FC CSKA Kyiv players
Maccabi Netanya F.C. players
Maccabi Yavne F.C. players
FC Merani Martvili players
FC Sioni Bolnisi players
FC Lyubomyr Stavyshche players
Ukrainian Premier League players
Ukrainian First League players
Israeli Premier League players
Erovnuli Liga players
Ukrainian expatriate men's footballers
Expatriate men's footballers in Israel
Ukrainian expatriate sportspeople in Israel
Expatriate men's footballers in Georgia (country)
Ukrainian expatriate sportspeople in Georgia (country) |
https://en.wikipedia.org/wiki/Koji%20Noda | is a Japanese footballer who currently plays for ReinMeer Aomori.
Career
On 9 January 2019, Noda signed with ReinMeer Aomori FC.
Career statistics
Updated to 23 February 2020.
References
External links
Profile at Zweigen Kanazawa
Koji Noda – Urawa Red Diamonds official profile
Koji Noda – Yahoo! Japan sports profile
1986 births
Living people
Hannan University alumni
Association football people from Fukuoka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Urawa Red Diamonds players
Fagiano Okayama players
V-Varen Nagasaki players
Ventforet Kofu players
Zweigen Kanazawa players
ReinMeer Aomori players
Men's association football defenders |
https://en.wikipedia.org/wiki/Martin%20Bland | John Martin Bland (born 6 March 1947), known as Martin Bland, is a British statistician. He has been professor of health statistics at the University of York since 2003. Bland is known for his work on medical measurement, particularly methodology for method comparison studies such as the Bland–Altman plot.
Bland was born in Stockport and obtained a BSc, MSc and diploma from Imperial College, London, followed by a PhD in epidemiology from the University of London. Between 1976 and 2003 he worked at St. George's Hospital Medical School, University of London.
Books
References
External links
Personal home page at the University of York
British statisticians
Living people
1947 births
Academics of the University of York
Alumni of Imperial College London
People from Stockport |
https://en.wikipedia.org/wiki/Marcum%20Q-function | In statistics, the generalized Marcum Q-function of order is defined as
where and and is the modified Bessel function of first kind of order . If , the integral converges for any . The Marcum Q-function occurs as a complementary cumulative distribution function for noncentral chi, noncentral chi-squared, and Rice distributions. In engineering, this function appears in the study of radar systems, communication systems, queueing system, and signal processing. This function was first studied for , and hence named after, by Jess Marcum for pulsed radars.
Properties
Finite integral representation
The generalized Marcum Q-function can alternatively be defined as a finite integral as
However, it is preferable to have an integral representation of the Marcum Q-function such that (i) the limits of the integral are independent of the arguments of the function, (ii) and that the limits are finite, (iii) and that the integrand is a Gaussian function of these arguments. For positive integral value of , such a representation is given by the trigonometric integral
where
and the ratio is a constant.
For any real , such finite trigonometric integral is given by
where is as defined before, , and the additional correction term is given by
For integer values of , the correction term tend to vanish.
Monotonicity and log-concavity
The generalized Marcum Q-function is strictly increasing in and for all and , and is strictly decreasing in for all and
The function is log-concave on for all
The function is strictly log-concave on for all and , which implies that the generalized Marcum Q-function satisfies the new-is-better-than-used property.
The function is log-concave on for all
Series representation
The generalized Marcum Q function of order can be represented using incomplete Gamma function as
where is the lower incomplete Gamma function. This is usually called the canonical representation of the -th order generalized Marcum Q-function.
The generalized Marcum Q function of order can also be represented using generalized Laguerre polynomials as
where is the generalized Laguerre polynomial of degree and of order .
The generalized Marcum Q-function of order can also be represented as Neumann series expansions
where the summations are in increments of one. Note that when assumes an integer value, we have .
For non-negative half-integer values , we have a closed form expression for the generalized Marcum Q-function as
where is the complementary error function. Since Bessel functions with half-integer parameter have finite sum expansions as
where is non-negative integer, we can exactly represent the generalized Marcum Q-function with half-integer parameter. More precisely, we have
for non-negative integers , where is the Gaussian Q-function. Alternatively, we can also more compactly express the Bessel functions with half-integer as sum of hyperbolic sine and cosine functions:
where , , and |
https://en.wikipedia.org/wiki/Henry%20Mann | Henry Berthold Mann (27 October 1905, Vienna – 1 February 2000, Tucson) was a professor of mathematics and statistics at the Ohio State University. Mann proved the Schnirelmann-Landau conjecture in number theory, and as a result earned the 1946 Cole Prize. He and his student developed the ("Mann-Whitney") U-statistic of nonparametric statistics. Mann published the first mathematical book on the design of experiments: .
Early life of a number theorist
Born in Vienna, Austria-Hungary, to a Jewish family, Mann earned his Ph.D. degree in mathematics in 1935 from the University of Vienna under the supervision of Philipp Furtwängler. Mann immigrated to the United States in 1938, and lived in New York, supporting himself by tutoring students.
In additive number theory, Mann proved the Schnirelmann–Landau conjecture on the asymptotic density of sumsets in 1942. By doing so he established Mann's theorem and earned the 1946 Cole Prize.
Statistics
In 1942 the Carnegie Foundation awarded Mann a fellowship to learn statistics while assisting the operations research group of Harold Hotelling at Columbia University. His group also supported Abraham Wald, and Wald and Mann collaborated on several papers. In statistics, Mann is known for the ("Mann–Whitney") U-statistic and its associated hypothesis test for nonparametric statistics. Collaborating with Wald, Mann developed the Mann–Wald theorem of asymptotic statistics and econometrics.
Mann wrote the first mathematical book on the design of experiments , whose principles allowed later statisticians to design and to analyze customized experiments. Like contemporary "self-help" and "how to" books, the earlier books gave easy-to-follow examples but little theory beyond exhortations to follow three principles of Ronald A. Fisher—to "replicate", to "establish control" (for example with blocking), and to "randomize" (assignment of treatments to units). Earlier books provided useful examples of designed experiments along with the design's analysis of variance, but no basis for constructing new designs for new problems, according to .
According to Denis Conniffe:
Later life
In 1946 Mann returned to Ohio State University, where he served as a professor mathematics until his retirement in 1964. Mann then became a professor at the U.S. Army's Mathematics Research Center at the University of Wisconsin–Madison 1964–1971. Mann was professor at the University of Arizona from 1971 to 1975. His doctoral students include George Marsaglia and William Yslas Vélez.
Publications
References
American statisticians
Number theorists
Additive combinatorialists
Group theorists
20th-century American mathematicians
University of Arizona faculty
Ohio State University faculty
University of Wisconsin–Madison faculty
Academics from Columbus, Ohio
Jewish emigrants from Austria after the Anschluss to the United States
1905 births
2000 deaths
Econometricians
20th-century American economists
Mathematical statisticians
University of Vienna |
https://en.wikipedia.org/wiki/1996%20S%C3%A3o%20Paulo%20FC%20season | The 1996 season was São Paulo's 67th season since club's existence.
Statistics
Scorers
Overall
{|class="wikitable"
|-
|Games played || 69 (30 Campeonato Paulista, 2 Copa Masters CONMEBOL, 3 Copa do Brasil, 2 Copa de Oro, 23 Campeonato Brasileiro, 2 Supercopa Libertadores, 7 Friendly match)
|-
|Games won || 35 (16 Campeonato Paulista, 2 Copa Masters CONMEBOL, 2 Copa do Brasil, 1 Copa de Oro, 9 Campeonato Brasileiro, 1 Supercopa Libertadores, 4 Friendly match)
|-
|Games drawn || 19 (7 Campeonato Paulista, 0 Copa Masters CONMEBOL, 1 Copa do Brasil, 0 Copa de Oro, 8 Campeonato Brasileiro, 0 Supercopa Libertadores, 3 Friendly match)
|-
|Games lost || 15 (7 Campeonato Paulista, 0 Copa Masters CONMEBOL, 0 Copa do Brasil, 1 Copa de Oro, 6 Campeonato Brasileiro, 1 Supercopa Libertadores, 0 Friendly match)
|-
|Goals scored || 130
|-
|Goals conceded || 85
|-
|Goal difference || +45
|-
|Best result || 7–3 (H) v Botafogo - Copa Masters CONMEBOL - 1996.02.08
|-
|Worst result || 0–5 (H) v Corinthians - Campeonato Paulista - 1996.03.10
|-
|Most appearances ||
|-
|Top scorer || Valdir Bigode (31)
|-
Friendlies
Copa dos Campeões Mundiais
Official competitions
Campeonato Paulista
First round
Matches
Second round
Matches
Final standings
Record
Copa Masters CONMEBOL
Record
Copa do Brasil
Round of 32
Eightfinals
Record
Copa de Oro
Record
Campeonato Brasileiro
First stage
Matches
Record
Supercopa Sudamericana
Record
External links
official website
São Paulo
São Paulo FC seasons |
https://en.wikipedia.org/wiki/Meixner%E2%80%93Pollaczek%20polynomials | In mathematics, the Meixner–Pollaczek polynomials are a family of orthogonal polynomials P(x,φ) introduced by , which up to elementary changes of variables are the same as the Pollaczek polynomials P(x,a,b) rediscovered by in the case λ=1/2, and later generalized by him.
They are defined by
Examples
The first few Meixner–Pollaczek polynomials are
Properties
Orthogonality
The Meixner–Pollaczek polynomials Pm(λ)(x;φ) are orthogonal on the real line with respect to the weight function
and the orthogonality relation is given by
Recurrence relation
The sequence of Meixner–Pollaczek polynomials satisfies the recurrence relation
Rodrigues formula
The Meixner–Pollaczek polynomials are given by the Rodrigues-like formula
where w(x;λ,φ) is the weight function given above.
Generating function
The Meixner–Pollaczek polynomials have the generating function
See also
Sieved Pollaczek polynomials
References
Orthogonal polynomials |
https://en.wikipedia.org/wiki/Parabolic%20geometry%20%28differential%20geometry%29 | In differential geometry and the study of Lie groups, a parabolic geometry is a homogeneous space G/P which is the quotient of a semisimple Lie group G by a parabolic subgroup P. More generally, the curved analogs of a parabolic geometry in this sense is also called a parabolic geometry: any geometry that is modeled on such a space by means of a Cartan connection.
Examples
The projective space Pn is an example. It is the homogeneous space PGL(n+1)/H where H is the isotropy group of a line. In this geometrical space, the notion of a straight line is meaningful, but there is no preferred ("affine") parameter along the lines. The curved analog of projective space is a manifold in which the notion of a geodesic makes sense, but for which there are no preferred parametrizations on those geodesics. A projective connection is the relevant Cartan connection that gives a means for describing a projective geometry by gluing copies of the projective space to the tangent spaces of the base manifold. Broadly speaking, projective geometry refers to the study of manifolds with this kind of connection.
Another example is the conformal sphere. Topologically, it is the n-sphere, but there is no notion of length defined on it, just of angle between curves. Equivalently, this geometry is described as an equivalence class of Riemannian metrics on the sphere (called a conformal class). The group of transformations that preserve angles on the sphere is the Lorentz group O(n+1,1), and so Sn = O(n+1,1)/P. Conformal geometry is, more broadly, the study of manifolds with a conformal equivalence class of Riemannian metrics, i.e., manifolds modeled on the conformal sphere. Here the associated Cartan connection is the conformal connection.
Other examples include:
CR geometry, the study of manifolds modeled on a real hyperquadric , where is the stabilizer of an isotropic line (see CR manifold)
contact projective geometry, the study of manifolds modeled on where is that subgroup of the symplectic group stabilizing the line generated by the first standard basis vector in
References
Slovak, J. Parabolic Geometries, Research Lecture Notes, Part of DrSc-dissertation, Masaryk University, 1997, 70pp, IGA Preprint 97/11 (University of Adelaide)
Differential geometry
Homogeneous spaces |
https://en.wikipedia.org/wiki/Zone%202%20of%20Milan | The Zone 2 of Milan (in Italian: Zona 2 di Milano) is one of the 9 administrative zones of Milan, Italy. In the "sunburst" geometry of the zones of Milan, Zone 2 is the slice that connects the centre to the periphery in the north-east direction.
Overview
The history and development of Zone 2 have been largely influenced by its location on important routes leading from Milan to major nearby settlements such as Monza as well as towards Venice and other main cities of the Italian North-East.
The Naviglio Martesana canal, which traverses most of Zone 2, has been a prominent transportation means in the development of the Milanese area; between the 19th and 20th century, this role has been taken on by the railway system, which again was largely based in what is now Zone 2. The Milano Centrale railway station, the most important railway station in Milan and one of the most important railway nodes in Italy, is located in the eponymous district of Zone 2.
Especially as a consequence of the development of the railway system, in the early 20th century the Milanese north-east quickly changed from a rural area to a mostly industrial city outskirt, experiencing, at the same time, a dramatic increase in population. In the mid-20th century, as factories were gradually dismantled as a consequence of the expansion of the city centre, Zone 2 changed again, this time into a mostly residential and tertiary area. The recent evolution of Zone 2 is also strongly influenced by the high concentration of extra-European immigrants, the highest in Milan, which has led to the development of distinctively multi-ethnic neighbourhoods such as that of Viale Padova (in the Loreto district).
The complex history of Zone 2 is witnessed by its diverse landscape, which includes such contrasting elements as modern skyscraper-punctuated districts, old-fashioned popular Milanese neighbourhoods, luxury villas on the banks of the Naviglio Martesana, restored "cascine" (country houses), abandoned factories, and modern high-income residential areas.
Subdivision
The main quartieri (districts) of Zone 2 are Adriano, Crescenzago, Gorla, Greco, Loreto, Maggiolina (also known as Villaggio dei Giornalisti), Mandello, Mirabello, Ponte Seveso, Porta Nuova, Precotto, Stazione Centrale, Nolo and Turro.
Many of these districts were independent comuni up until the first decades of the 20th century, before being annexed to Milan. This is reflected, amongst other things, in the fact that many of them are evidently structured as small towns rather than as typical metropolitan areas.
Notable places
Corso Buenos Aires, major shopping street
Milano Centrale railway station, Milan's most important railway station
Naviglio Martesana, canal connecting Milan to the river Adda
References
External links
Zone 2 of Milan (municipal website)
Zones of Milan |
https://en.wikipedia.org/wiki/Globe%20Derby%20Park%2C%20South%20Australia | Globe Derby Park is a suburb of Adelaide, South Australia. It is located in the City of Salisbury.
Demographics
The 2006 Census by the Australian Bureau of Statistics counted 314 persons in Globe Derby Park on census night. Of these, 49.0% were male and 51.0% were female.
The majority of residents (87.3%) are of Australian birth, with another common census response being England (5.4%).
The age distribution of Globe Derby Park residents is skewed towards an older population compared to the greater Australian population. 79.6% of residents were over 25 years in 2006, compared to the Australian average of 66.5%; and 20.4% were younger than 25 years, compared to the Australian average of 33.5%.
By census night 2011, the population had increased to 359 people.
Attractions
The suburb is most notable for the Globe Derby Park harness racing venue after which it was named. The suburb was created in 1998, renaming the southern part of the suburb of Bolivar.
Parks
The Little Para River is on the suburb's northern boundary, with a sealed cycling and walking trail that passes under Port Wakefield Road. The Whites Road Wetland is in Globe Derby Park adjacent to the river and path.
Dry Creek is on the southern boundary of Globe Derby Park. The Little Para Trail loops round the western side of the suburb and joins the Dry Creek linear trail.
Transport
The suburb is serviced by the following main roads:
Port Wakefield Road, part of the National Highway.
See also
List of Adelaide suburbs
References
External links
City of Salisbury
Local Government Association of SA – City of Salisbury
2006 ABS Census Data by Location
Suburbs of Adelaide |
https://en.wikipedia.org/wiki/Lusin%27s%20separation%20theorem | In descriptive set theory and mathematical logic, Lusin's separation theorem states that if A and B are disjoint analytic subsets of Polish space, then there is a Borel set C in the space such that A ⊆ C and B ∩ C = ∅. It is named after Nikolai Luzin, who proved it in 1927.
The theorem can be generalized to show that for each sequence (An) of disjoint analytic sets there is a sequence (Bn) of disjoint Borel sets such that An ⊆ Bn for each n.
An immediate consequence is Suslin's theorem, which states that if a set and its complement are both analytic, then the set is Borel.
Notes
References
( for the European edition)
.
Descriptive set theory
Theorems in the foundations of mathematics
Theorems in topology |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.