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https://en.wikipedia.org/wiki/United%20States%20of%20America%20Mathematical%20Talent%20Search | The United States of America Mathematical Talent Search (USAMTS) is a mathematics competition open to all United States students in or below high school.
History
Professor George Berzsenyi initiated the contest in 1989 under the KöMaL model and under joint sponsorship of the Rose–Hulman Institute of Technology and the Consortium for Mathematics and its Applications.
As of 2021, the USAMTS is sponsored by the National Security Agency and administered by the Art of Problem Solving foundation. There were 718 participants in the 2004–2005 school year, with an average score of 49.25 out of 100.
Format
The competition is proof and research based. Students submit proofs within the round's timeframe (usually a month), and return solutions by mail or upload their solutions in a PDF file through the USAMTS website. During this time, students are free to use any mathematical resources that are available, so long as it is not the help of another person. Carefully written justifications are required for each problem.
Prior to academic year 2010–2011 the competition consisted of four rounds of five problems each, covering all non-calculus topics. Students were given approximately one month to solve the questions. Each question is scored out of five points; thus, a perfect score is .
In the academic year 2010–2011, the USAMTS briefly changed their format to two rounds of six problems each, and approximately six weeks are allotted for each round.
The current format consists of three problem sets, each five problems and lasting about a month each. Every question is still worth 5 points, making a perfect score .
Scoring
Every problem on the USAMTS is graded on a scale of 0 to 5, where a 0 is an answer that is highly flawed or incomplete and a 5 is a rigorous and well-written proof. As a result, possible scores over the three rounds range from 0 to 75. The solutions are graded every year by a volunteer group of university students and other people with professional mathematical experience. In addition to their scores, students receive detailed feedback on how they could improve their solutions if they attempt a problem but do not solve it.
Historic score distribution
Prizes
Prizes are given to all contestants who place within a certain range. These prizes include a shirt from AoPS, software, and one or two mathematical books of varying difficulty. Prizes are also awarded to students with outstanding solutions in individual rounds. Further, after the third round, given a high enough score, a student may qualify to take the AIME exam even without qualifying through the AMC 10 or 12 competitions.
References
External links
USAMTS website
Recent USAMTS Problems and Solutions and Older USAMTS Problems and Solutions
Mathematics competitions
Recurring events established in 1989 |
https://en.wikipedia.org/wiki/Poincar%C3%A9%20disk%20model | In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and straight lines are either circular arcs contained within the disk that are orthogonal to the unit circle or diameters of the unit circle.
The group of orientation preserving isometries of the disk model is given by the projective special unitary group , the quotient of the special unitary group SU(1,1) by its center .
Along with the Klein model and the Poincaré half-space model, it was proposed by Eugenio Beltrami who used these models to show that hyperbolic geometry was equiconsistent with Euclidean geometry. It is named after Henri Poincaré, because his rediscovery of this representation fourteen years later became better known than the original work of Beltrami.
The Poincaré ball model is the similar model for 3 or n-dimensional hyperbolic geometry in which the points of the geometry are in the n-dimensional unit ball.
History
The disk model was first described by Bernhard Riemann in an 1854 lecture (published 1868), which inspired an 1868 paper by Eugenio Beltrami. Henri Poincaré employed it in his 1882 treatment of hyperbolic, parabolic and elliptic functions, but it became widely known following Poincaré's presentation in his 1905 philosophical treatise, Science and Hypothesis. There he describes a world, now known as the Poincaré disk, in which space was Euclidean, but which appeared to its inhabitants to satisfy the axioms of hyperbolic geometry:"Suppose, for example, a world enclosed in a large sphere and subject to the following laws: The temperature is not uniform; it is greatest at their centre, and gradually decreases as we move towards the circumference of the sphere, where it is absolute zero. The law of this temperature is as follows: If be the radius of the sphere, and the distance of the point considered from the centre, the absolute temperature will be proportional to . Further, I shall suppose that in this world all bodies have the same co-efficient of dilatation, so that the linear dilatation of any body is proportional to its absolute temperature. Finally, I shall assume that a body transported from one point to another of different temperature is instantaneously in thermal equilibrium with its new environment. ...
If they construct a geometry, it will not be like ours, which is the study of the movements of our invariable solids; it will be the study of the changes of position which they will have thus distinguished, and will be 'non-Euclidean displacements,' and this will be non-Euclidean geometry. So that beings like ourselves, educated in such a world, will not have the same geometry as ours." (pp.65-68)Poincaré's disk was an important piece of evidence for the hypothesis that the choice of spatial geometry is conventional rather than factual, especially in the influential philosophical discussions of Rudolf Carnap and of Hans Reichenbach.
|
https://en.wikipedia.org/wiki/Gaston%20Gonnet | Gaston H. Gonnet is a Uruguayan Canadian computer scientist and entrepreneur. He is best known for his contributions to the Maple computer algebra system and the creation of a digital version of the Oxford English Dictionary.
Education and early life
Gonnet received his doctorate in computer science from the University of Waterloo in 1977. His thesis was entitled Interpolation and Interpolation-Hash Searching. His advisor was J. Alan George.
Career and research
In 1980 Gonnet co-founded the Symbolic Computation Group at the University of Waterloo. The work of SCG on a general-purpose computer algebra system later formed the core of the Maple system. In 1988, Gonnet co-founded (with Keith Geddes) the private company Waterloo Maple Inc., to sell Maple commercially. In the mid-1990s the company ran into trouble and a disagreement between his colleagues caused him to withdraw from chairman of the board and managerial involvement.
In 1984 Gonnet co-founded the New Oxford English Dictionary project at UW, which sought to create a searchable electronic version of the Oxford English Dictionary. The project was selected by the Oxford University Press as a partner for the computerisation leading to the publication of the second edition of the OED. The UW project's main contributions were in the parsing of the source text to enhance the tagging and on building a full text searching system based on PAT trees (a version of suffix array). This project later culminated in another successful commercial venture, the Open Text Corporation. Gonnet was founder and chairman of the Board of OTC until 1994.
Gonnet is a computer science professor at ETH Zurich in Zurich, Switzerland. In 1991, he began developing the Darwin programming language for biosciences, which would become the basis for OMA, a package and database for gene orthology prediction. He is chief scientist of two Canadian startups: CeeqIT and Porfiau.
Awards and honours
On June 9, 2011, Gonnet and Keith O. Geddes received the ACM Richard D. Jenks Memorial Prize for Excellence in Software Engineering Applied to Computer Algebra for the Maple Project.
On March 14, 2013, Gonnet was awarded a Dr. Honoris Causa by the Universidad de la República, engineering faculty from Uruguay.
See also
List of University of Waterloo people
References
Living people
Scientific computing researchers
Swiss computer scientists
University of Waterloo alumni
Uruguayan computer scientists
Uruguayan expatriates in Canada
Uruguayan expatriates in Switzerland
Uruguayan people of French descent
Place of birth missing (living people)
1948 births |
https://en.wikipedia.org/wiki/Cyclotomic%20field | In number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to , the field of rational numbers.
Cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with Fermat's Last Theorem. It was in the process of his deep investigations of the arithmetic of these fields (for prime ) – and more precisely, because of the failure of unique factorization in their rings of integers – that Ernst Kummer first introduced the concept of an ideal number and proved his celebrated congruences.
Definition
For , let ; this is a primitive th root of unity. Then the th cyclotomic field is the extension of generated by .
Properties
The th cyclotomic polynomial
is irreducible, so it is the minimal polynomial of over .
The conjugates of in are therefore the other primitive th roots of unity: for with .
The degree of is therefore , where is Euler's totient function.
The roots of are the powers of , so is the splitting field of (or of ) over .
Therefore is a Galois extension of .
The Galois group is naturally isomorphic to the multiplicative group , which consists of the invertible residues modulo , which are the residues with and . The isomorphism sends each to , where is an integer such that .
The ring of integers of is .
For , the discriminant of the extension is
In particular, is unramified above every prime not dividing .
If is a power of a prime , then is totally ramified above .
If is a prime not dividing , then the Frobenius element corresponds to the residue of in .
The group of roots of unity in has order or , according to whether is even or odd.
The unit group is a finitely generated abelian group of rank , for any , by the Dirichlet unit theorem. In particular, is finite only for }. The torsion subgroup of is the group of roots of unity in , which was described in the previous item. Cyclotomic units form an explicit finite-index subgroup of .
The Kronecker–Weber theorem states that every finite abelian extension of in is contained in for some . Equivalently, the union of all the cyclotomic fields is the maximal abelian extension of .
Relation with regular polygons
Gauss made early inroads in the theory of cyclotomic fields, in connection with the problem of constructing a regular -gon with a compass and straightedge. His surprising result that had escaped his predecessors was that a regular 17-gon could be so constructed. More generally, for any integer , the following are equivalent:
a regular -gon is constructible;
there is a sequence of fields, starting with and ending with , such that each is a quadratic extension of the previous field;
is a power of 2;
for some integers and Fermat primes . (A Fermat prime is an odd prime such that is a power of 2. The known Fermat primes are 3, 5, 17, 257, 65537, and it is likely that there are no others.)
Small examples
and : The equatio |
https://en.wikipedia.org/wiki/MuPAD | MuPAD is a computer algebra system (CAS). Originally developed by the MuPAD research group at the University of Paderborn, Germany, development was taken over by the company SciFace Software GmbH & Co. KG in cooperation with the MuPAD research group and partners from some other universities starting in 1997. MuPAD's graphics package was particularly successful, especially considering the era when it was developed.
Until autumn 2005, the version "MuPAD Light" was offered for free for research and education, but as a result of the closure of the home institute of the MuPAD research group, only the version "MuPAD Pro" became available for purchase.
The MuPAD kernel is bundled with Scientific Notebook and Scientific Workplace. Former versions of MuPAD Pro were bundled with SciLab. In MathCAD's version 14 release Mupad was adopted as the CAS engine.
In September 2008, SciFace was purchased by MathWorks and the MuPAD code was included in the Symbolic Math Toolbox add-on for MATLAB. On 28 September 2008, MuPAD was withdrawn from the market as a software product in its own right. However, it is still available in the Symbolic Math Toolbox in MATLAB and can also be used as a stand-alone program by the command mupad entered into the MATLAB terminal.
The MuPAD notebook feature has been removed in MATLAB R2020a. However, MATLAB's Symbolic Math Toolbox still uses the MuPAD language as part of its underlying computational engine. MATLAB Live Editor is the recommended environment for performing, documenting, and sharing symbolic math computations.
Functionality
MuPAD offers:
a computer algebra system to manipulate formulas symbolically
classic and verified numerical analysis in discretionary accuracy
program packages for linear algebra, differential equations, number theory, statistics, and functional programming
an interactive graphic system that supports animations and transparent areas in 3D
a programming language that supports object-oriented programming and functional programming
Often used commands are accessible via menus. MuPAD offers a notebook concept similar to word processing systems that allows the formulation of mathematical problems as well as graphics visualization and explanations in formatted text.
MuPad does not follow the NIST 4.37 definition for inverse hyperbolic cosine.
It is possible to extend MuPAD with C++-routines to accelerate calculations. Java code can also be embedded.
MuPAD's syntax was modeled on Pascal, and is similar to the one used in the Maple computer algebra system. An important difference between the two is that MuPAD provides support for object-oriented programming. This means that each object "carries with itself" the methods allowed to be used on it. For example, after defining
A := matrix( [[1,2],[3,4]] )
all of the following are valid expressions and give the expected result:
A+A, -A, 2*A, A*A, A^-1, exp( A ), A.A, A^0, 0*A
where A.A is the concatenated 2×4 matrix, while all others, including t |
https://en.wikipedia.org/wiki/Ernest%20Julius%20Wilczynski | Ernest Julius Wilczynski (November 13, 1876 – September 14, 1932) was an American mathematician considered the founder of projective differential geometry.
Born in Hamburg, Germany, Wilczynski's family emigrated to America and settled in Chicago, Illinois when he was very young. He attended public school in the US but went to college in Germany and received his PhD from the University of Berlin in 1897. He taught at the University of California until 1907, the University of Illinois from 1907 to 1910, and the University of Chicago from 1910 until illness forced his absence from the classroom in 1923. His doctoral students include Archibald Henderson, Ernest Preston Lane, Pauline Sperry, Ellis Stouffer, and Charles Thompson Sullivan.
Selected publications
Projective differential geometry of curves and ruled surfaces, Leipzig, Teubner 1906
Projective differential geometry of curved surfaces, Parts I–V, Transactions American Mathematical Society
vol. 8, 1907, Part I, pp. 223–260
vol. 9, 1908, Part II, pp. 79–120 ; Part III, pp. 293–315
vol. 10, 1909, Part IV, pp. 176–200 ; Part V, pp. 279–296
References
"Ernest Julius Wilczynski." Dictionary of American Biography. New York: Charles Scribner's Sons, 1936. Gale Biography In Context. Web. 14 Feb. 2011.
External links
Ernest P. Lane (1934), "Biographical Memoir of Ernest Julius Wilczynski 1876-1932", National Academy of Sciences of the US Biographical Memoirs Vol XVI (PDF)
Guide to the Ernest J. Wilczynski Papers 1892-1931 at the University of Chicago Special Collections Research Center
1876 births
1932 deaths
Humboldt University of Berlin alumni
University of California faculty
University of Illinois faculty
University of Chicago faculty
19th-century American mathematicians
20th-century American mathematicians
Differential geometers
Emigrants from the German Empire to the United States |
https://en.wikipedia.org/wiki/Giovanni%20Girolamo%20Saccheri | Giovanni Girolamo Saccheri (; 5 September 1667 – 25 October 1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He is considered the forerunner of non-Euclidean geometry.
Biography
The son of a lawyer, Saccheri was born in Sanremo, Genoa (now Italy) on September 5, 1667. From his youth he showed extreme precociousness and a spirit of inquiry. He entered the Jesuit novitiate in 1685. He studied philosophy and theology at the Jesuit College of Brera in Milan.
His mathematics teacher at the Brera college was Tommaso Ceva, who introduced him to his brother Giovanni. Ceva convinced Saccheri to devote himself to mathematical research and became the young man's mentor. Saccheri was in close scientific communion with both brothers. He used Ceva's ingenious methods in his first published work, 1693, solutions of six geometric problems proposed by the Sicilian mathematician Ruggero Ventimiglia (1670-1698).
Saccheri was ordained as a priest in March 1694. He taught philosophy at the University of Turin from 1694 to 1697 and philosophy, theology and mathematics at the University of Pavia from 1697 until his death. He published several works including Quaesita geometrica (1693), Logica demonstrativa (1697), and Neo-statica (1708). Saccheri died in Milan on 25 October 1733.
The Logica demonstrativa, reissued in Turin in 1701 and in Cologne in 1735, gives Saccheri the right to an eminent place in the history of modern logic. According to Thomas Heath “Mill’s account of the true distinction between real and nominal definitions was fully anticipated by Saccheri.”
Geometrical work
Saccheri is primarily known today for his last publication, in 1733 shortly before his death. Now considered an early exploration of non-Euclidean geometry, Euclides ab omni naevo vindicatus (Euclid Freed of Every Flaw) languished in obscurity until it was rediscovered by Eugenio Beltrami, in the mid-19th century.
The intent of Saccheri's work was ostensibly to establish the validity of Euclid by means of a reductio ad absurdum proof of any alternative to Euclid's parallel postulate. To do so, he assumed that the parallel postulate was false and attempted to derive a contradiction.
Since Euclid's postulate is equivalent to the statement that the sum of the internal angles of a triangle is 180°, he considered both the hypothesis that the angles add up to more or less than 180°.
The first led to the conclusion that straight lines are finite, contradicting Euclid's second postulate. So Saccheri correctly rejected it. However, the principle is now accepted as the basis of elliptic geometry, where both the second and fifth postulates are rejected.
The second possibility turned out to be harder to refute. In fact he was unable to derive a logical contradiction and instead derived many non-intuitive results; for example that triangles have a maximum finite area and that there is an absolute unit of length. He finally concluded that: "the hypothesis of the a |
https://en.wikipedia.org/wiki/Maschke%27s%20theorem | In mathematics, Maschke's theorem, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations of a finite group into irreducible pieces. Maschke's theorem allows one to make general conclusions about representations of a finite group G without actually computing them. It reduces the task of classifying all representations to a more manageable task of classifying irreducible representations, since when the theorem applies, any representation is a direct sum of irreducible pieces (constituents). Moreover, it follows from the Jordan–Hölder theorem that, while the decomposition into a direct sum of irreducible subrepresentations may not be unique, the irreducible pieces have well-defined multiplicities. In particular, a representation of a finite group over a field of characteristic zero is determined up to isomorphism by its character.
Formulations
Maschke's theorem addresses the question: when is a general (finite-dimensional) representation built from irreducible subrepresentations using the direct sum operation? This question (and its answer) are formulated differently for different perspectives on group representation theory.
Group-theoretic
Maschke's theorem is commonly formulated as a corollary to the following result:
Then the corollary is
The vector space of complex-valued class functions of a group has a natural -invariant inner product structure, described in the article Schur orthogonality relations. Maschke's theorem was originally proved for the case of representations over by constructing as the orthogonal complement of under this inner product.
Module-theoretic
One of the approaches to representations of finite groups is through module theory. Representations of a group are replaced by modules over its group algebra (to be precise, there is an isomorphism of categories between and , the category of representations of ). Irreducible representations correspond to simple modules. In the module-theoretic language, Maschke's theorem asks: is an arbitrary module semisimple? In this context, the theorem can be reformulated as follows:
The importance of this result stems from the well developed theory of semisimple rings, in particular, their classification as given by the Wedderburn–Artin theorem. When is the field of complex numbers, this shows that the algebra is a product of several copies of complex matrix algebras, one for each irreducible representation. If the field has characteristic zero, but is not algebraically closed, for example if is the field of real or rational numbers, then a somewhat more complicated statement holds: the group algebra is a product of matrix algebras over division rings over . The summands correspond to irreducible representations of over .
Category-theoretic
Reformulated in the language of semi-simple categories, Maschke's theorem states
Proofs
Group-theoretic
Let U be a subspace of V complement of W. Let be th |
https://en.wikipedia.org/wiki/Shreeram%20Shankar%20Abhyankar | Shreeram Shankar Abhyankar (22 July 1930 – 2 November 2012) was an Indian American mathematician known for his contributions to algebraic geometry. He, at the time of his death, held the Marshall Distinguished Professor of Mathematics Chair at Purdue University, and was also a professor of computer science and industrial engineering. He is known for Abhyankar's conjecture of finite group theory.
His latest research was in the area of computational and algorithmic algebraic geometry.
Career
Abhyankar was born in a Chitpavan Brahmin family in Ujjain, Madhya Pradesh, India. He earned his B.Sc. from Royal Institute of Science of University of Mumbai in 1951, his M.A. at Harvard University in 1952, and his Ph.D. at Harvard in 1955. His thesis, written under the direction of Oscar Zariski, was titled Local uniformization on algebraic surfaces over modular ground fields. Before going to Purdue, he was an associate professor of mathematics at Cornell University and Johns Hopkins University.
Abhyankar was appointed the Marshall Distinguished Professor of Mathematics at Purdue in 1967. His research topics include algebraic geometry (particularly resolution of singularities, a field in which he made significant progress over fields of finite characteristic), commutative algebra, local algebra, valuation theory, theory of functions of several complex variables, quantum electrodynamics, circuit theory, invariant theory, combinatorics, computer-aided design, and robotics. He popularized the Jacobian conjecture.
Death
Abhyankar died of a heart condition on 2 November 2012 at his residence near Purdue University.
Selected publications
Honours
Abhyankar has won numerous awards and honours.
Abhyankar received the Herbert Newby McCoy Award from Purdue University in 1973 .
Fellow of the Indian Academy of Sciences
Editorial board member of the Indian Journal of Pure and Applied Mathematics
Chauvenet Prize from the Mathematical Association of America (1978)
Honorary Doctorate Degree (Docteur Honoris Causa) by the University of Angers in France (29 October 1998)
Fellow of the American Mathematical Society (2012)
See also
Abhyankar's conjecture
Abhyankar's inequality
Abhyankar's lemma
Abhyankar–Moh theorem
References
External links
People from Ujjain
1930 births
Indian emigrants to the United States
20th-century Indian mathematicians
20th-century American mathematicians
21st-century American mathematicians
2012 deaths
American people of Marathi descent
Algebraic geometers
Purdue University faculty
Harvard Graduate School of Arts and Sciences alumni
Fellows of the American Mathematical Society
Fellows of the Indian Academy of Sciences
American academics of Indian descent |
https://en.wikipedia.org/wiki/99%20%28number%29 | 99 (ninety-nine) is the natural number following 98 and preceding 100.
In mathematics
99 is:
a composite number; a square-prime, of the form (p2, q). It is the 11th composite number of this form and the third of the form (32, q). It has an aliquot sum of 57, within an aliquot sequence of two composite numbers (99,57,23,1,0), to the Prime in the 23-aliquot tree.
a Kaprekar number
a lucky number
a palindromic number
the ninth repdigit
the sum of the cubes of three consecutive integers: 99 = 23 + 33 + 43
the sum of the sums of the divisors of the first 11 positive integers.
the highest two digit number in decimal.
In music
"99", a song by the band Toto on the Hydra album.
"99 Bottles of Beer", a counting song.
"99 Luftballons", a German-language song by the band Nena.
"99 Problems", a song by Jay-Z on The Black Album.
"99 Ways to Die", a song by Megadeth on the Hidden Treasures EP.
In other fields
The atomic number of einsteinium, an actinide.
".99" is frequently used as a price ender in pricing.
99, the jersey number of Wayne Gretzky, since permanently retired
References
External links
Integers |
https://en.wikipedia.org/wiki/List%20of%20Maidstone%20United%20F.C.%20records%20and%20statistics | This article details all-time records. For a season-by-season statistical breakdown see Maidstone United F.C. seasons
This list encompasses the records set by Maidstone United, their managers and their players.
Club records
Firsts
Only first team games considered.
First home match at Central Park, Sittingbourne: Maidstone United 11 Kingstonian XI (Friendly, 28 July 2001)
First home match at Bourne Park, Sittingbourne: Maidstone United 0–5 Gillingham (Friendly, 20 July 2002)
First home match at The Homelands, Ashford: Maidstone United 0–2 Accrington Stanley (Friendly, 11 July 2009)
First home match at the Gallagher Stadium, Maidstone: Maidstone United 0–5 Brighton & Hove Albion (Friendly, 14 July 2012)
First Kent County League match: Maidstone United 7–0 Scott Sports Reserves (Kent County League Division Four, August 1993)
First Kent League match: Tunbridge Wells 1–1 Maidstone United (Kent League Premier Division, 11 August 2001)
First Isthmian League match: Hastings United 0–2 Maidstone United (Isthmian League Division One South, 17 August 2006)
First National League match: Sutton United 0–2 Maidstone United (National League South, 8 August 2015)
First FA Cup match: Ramsgate 1–1 Maidstone United (24 August 2002)
First FA Trophy match: Maidstone United 2–0 Bury Town (7 October 2007)
First FA Vase match: Maidstone United 4–1 Carterton Town (9 September 2001)
First Kent Senior Cup match: Maidstone United 0–3 Folkestone Invicta (17 December 2003)
First Isthmian League Cup match: Maidstone United 0–3 Tonbridge Angels (12 September 2006)
First Kent Senior Trophy match: Maidstone United 0–1 Snodland (7 October 2000)
First Kent League Premier Division Cup match: Thamesmead Town 0–1 Maidstone United (24 November 2001)
Best league position and cup runs
League position: National League (division) - 14th (2016–17)
FA Cup: 2nd round (2014–15, 2017–18, 2018–19, 2019–20)
FA Trophy: 5th round (replay) (2020–21)
FA Vase: 3rd Round (replay) (2005–06)
Kent Senior Cup: Winners (2017–18, 2018–19)
Isthmian League Cup: Winners (2013–14)
Kent Senior Trophy: Winners (2002–03)
Kent League Premier Division Cup: Winners (2001–02, 2005–06)
Record Results
Only competitive first team games considered.
Victories
Overall: 12–1 vs Aylesford - (Kent County League Division 4, 26 March 1994)
National League: 1–4 vs Macclesfield Town, (16 September 2017)
National League South: 4–0 vs St Albans City, (28 September 2019)
Isthmian League Premier Division: 7–2 vs Hampton & Richmond Borough, (25 January 2014)
Isthmian League Division One South: 6–0 vs Corinthian-Casuals, (17 February 2007)
Kent League Premier Division: 9–0 vs Sporting Bengal United, (8 April 2006)
Kent County League: 12–1 vs Aylesford, (Division Four, 26 March 1994)
FA Cup: 10–0 vs Littlehampton Town, (1st qualifying round, 13 September 2014)
FA Trophy: 5–3 vs Abingdon United, (2nd qualifying round (replay), 7 November 2007)
FA Vase: 4–0
vs AFC Totton, (2nd qualifying round, 26 September 2004)
vs North Leigh, (1st r |
https://en.wikipedia.org/wiki/Survival%20function | The survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time.
The survival function is also known as the survivor function or reliability function.
The term reliability function is common in engineering while the term survival function is used in a broader range of applications, including human mortality. The survival function is the complementary cumulative distribution function of the lifetime. Sometimes complementary cumulative distribution functions are called survival functions in general.
Definition
Let the lifetime T be a continuous random variable with cumulative hazard function F(t) and hazard function f(t) on the interval [0,∞). Its survival function or reliability function is:
Examples of survival functions
The graphs below show examples of hypothetical survival functions. The x-axis is time. The y-axis is the proportion of subjects surviving. The graphs show the probability that a subject will survive beyond time t.
For example, for survival function 1, the probability of surviving longer than t = 2 months is 0.37. That is, 37% of subjects survive more than 2 months.
For survival function 2, the probability of surviving longer than t = 2 months is 0.97. That is, 97% of subjects survive more than 2 months.
Median survival may be determined from the survival function: The median survival is the point where the survival function intersects the value 0.5. For example, for survival function 2, 50% of the subjects survive 3.72 months. Median survival is thus 3.72 months.
In some cases, median survival cannot be determined from the graph. For example, for survival function 4, more than 50% of the subjects survive longer than the observation period of 10 months.
The survival function is one of several ways to describe and display survival data. Another useful way to display data is a graph showing the distribution of survival times of subjects. Olkin, page 426, gives the following example of survival data. The number of hours between successive failures of an air-conditioning system were recorded. The time between successive failures are 1, 3, 5, 7, 11, 11, 11, 12, 14, 14, 14, 16, 16, 20, 21, 23, 42, 47, 52, 62, 71, 71, 87, 90, 95, 120, 120, 225, 246, and 261 hours. The mean time between failures is 59.6. This mean value will be used shortly to fit a theoretical curve to the data. The figure below shows the distribution of the time between failures. The blue tick marks beneath the graph are the actual hours between successive failures.
The distribution of failure times is over-laid with a curve representing an exponential distribution. For this example, the exponential distribution approximates the distribution of failure times. The exponential curve is a theoretical distribution fitted to the actual failure times. This particular exponential curve is specified by the parameter lambda, λ= 1/(mean time between failures) = 1/59.6 = 0.0168. The di |
https://en.wikipedia.org/wiki/Riemann%20sphere | In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane: the complex plane plus one point at infinity. This extended plane represents the extended complex numbers, that is, the complex numbers plus a value for infinity. With the Riemann model, the point is near to very large numbers, just as the point is near to very small numbers.
The extended complex numbers are useful in complex analysis because they allow for division by zero in some circumstances, in a way that makes expressions such as well-behaved. For example, any rational function on the complex plane can be extended to a holomorphic function on the Riemann sphere, with the poles of the rational function mapping to infinity. More generally, any meromorphic function can be thought of as a holomorphic function whose codomain is the Riemann sphere.
In geometry, the Riemann sphere is the prototypical example of a Riemann surface, and is one of the simplest complex manifolds. In projective geometry, the sphere can be thought of as the complex projective line , the projective space of all complex lines in . As with any compact Riemann surface, the sphere may also be viewed as a projective algebraic curve, making it a fundamental example in algebraic geometry. It also finds utility in other disciplines that depend on analysis and geometry, such as the Bloch sphere of quantum mechanics and in other branches of physics.
The extended complex plane is also called the closed complex plane.
Extended complex numbers
The extended complex numbers consist of the complex numbers together with . The set of extended complex numbers may be written as , and is often denoted by adding some decoration to the letter , such as
The notation has also seen use, but as this notation is also used for the punctured plane , it can lead to ambiguity.
Geometrically, the set of extended complex numbers is referred to as the Riemann sphere (or extended complex plane).
Arithmetic operations
Addition of complex numbers may be extended by defining, for ,
for any complex number , and multiplication may be defined by
for all nonzero complex numbers , with . Note that and are left undefined. Unlike the complex numbers, the extended complex numbers do not form a field, since does not have an additive nor multiplicative inverse. Nonetheless, it is customary to define division on by
for all nonzero complex numbers with and . The quotients and are left undefined.
Rational functions
Any rational function (in other words, is the ratio of polynomial functions and of with complex coefficients, such that and have no common factor) can be extended to a continuous function on the Riemann sphere. Specifically, if is a complex number such that the denominator is zero but the numerator is nonzero, then can be defined as . Moreover, can be defined as the limit of as , which may be finite or infinite.
The set of complex rational functions—whose mathem |
https://en.wikipedia.org/wiki/Ken%20Ribet | Kenneth Alan Ribet (; born June 28, 1948) is an American mathematician working in algebraic number theory and algebraic geometry. He is known for the Herbrand–Ribet theorem and Ribet's theorem, which were key ingredients in the proof of Fermat's Last Theorem, as well as for his service as President of the American Mathematical Society from 2017 to 2019. He is currently a professor of mathematics at the University of California, Berkeley.
Early life and education
Kenneth Ribet was born in Brooklyn, New York to parents David Ribet and Pearl Ribet, both Jewish, on June 28, 1948. As a student at Far Rockaway High School, Ribet was on a competitive mathematics team, but his first field of study was chemistry.
Ribet earned his bachelor's degree and master's degree from Brown University in 1969. In 1973, Ribet received his Ph.D. from Harvard University under the supervision of John Tate.
Career
After receiving his doctoral degree, Ribet taught at Princeton University for three years before spending two years doing research in Paris. In 1978, Ribet joined the Department of Mathematics at the University of California, Berkeley, where he served three separate terms as supervisor of the department's graduate program, supervisor of the department's undergraduate program, and supervisor of the department's development.
Ribet has served as an editor for several mathematics journals, a book series editor for the Cambridge University Press, and a book series editor for Springer. He also served on the United States National Committee for Mathematics, representing the United States at the International Mathematical Union, and was the Chair of the Mathematics section of the National Academy of Sciences.
From February 1, 2017 to January 31, 2019, Ribet was President of the American Mathematical Society.
Research
Ribet's contributions in number theory and algebraic geometry were described by Benedict Gross and Barry Mazur as being "key to our understanding of the connections between the theory of modular forms and the ℓ-adic representations of the absolute Galois group of the field of rational numbers."
Ribet is credited with paving the way towards Andrew Wiles's proof of Fermat's Last Theorem. In 1986, Ribet proved that the epsilon conjecture formulated by Jean-Pierre Serre was true, and thereby proved that Fermat's Last Theorem would follow from the Taniyama–Shimura conjecture. Crucially it also followed that the full conjecture was not needed, but a special case, that of semistable elliptic curves, sufficed. An earlier theorem of Ribet's, the Herbrand–Ribet theorem, is the converse to Herbrand's theorem on the divisibility properties of Bernoulli numbers and is also related to Fermat's Last Theorem.
Awards and honors
Ribet received the Fermat Prize in 1989 jointly with Abbas Bahri. He was elected to the American Academy of Arts and Sciences in 1997 and the National Academy of Sciences in 2000. In 2012, he became a Fellow of the American Mathematical Soci |
https://en.wikipedia.org/wiki/Independent%20and%20identically%20distributed%20random%20variables | In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as i.i.d., iid, or IID. IID was first defined in statistics and finds application in different fields such as data mining and signal processing.
Introduction
Statistics commonly deals with random samples. A random sample can be thought of as a set of objects that are chosen randomly. More formally, it is "a sequence of independent, identically distributed (IID) random data points".
In other words, the terms random sample and IID are basically one and the same. In statistics, "random sample" is the typical terminology, but in probability it is more common to say "IID".
Identically distributed means that there are no overall trends–the distribution doesn't fluctuate and all items in the sample are taken from the same probability distribution.
Independent means that the sample items are all independent events. In other words, they are not connected to each other in any way; knowledge of the value of one variable gives no information about the value of the other and vice versa.
It is not necessary for IID variables to be uniformly distributed. Being IID merely requires that they all have the same distribution as each other, and are chosen independently from that distribution, regardless of how uniform or non-uniform their distribution may be.
Application
Independent and identically distributed random variables are often used as an assumption, which tends to simplify the underlying mathematics. In practical applications of statistical modeling, however, the assumption may or may not be realistic.
The i.i.d. assumption is also used in the central limit theorem, which states that the probability distribution of the sum (or average) of i.i.d. variables with finite variance approaches a normal distribution.
Often the i.i.d. assumption arises in the context of sequences of random variables. Then "independent and identically distributed" implies that an element in the sequence is independent of the random variables that came before it. In this way, an i.i.d. sequence is different from a Markov sequence, where the probability distribution for the th random variable is a function of the previous random variable in the sequence (for a first order Markov sequence). An i.i.d. sequence does not imply the probabilities for all elements of the sample space or event space must be the same. For example, repeated throws of loaded dice will produce a sequence that is i.i.d., despite the outcomes being biased.
In signal processing and image processing the notion of transformation to i.i.d. implies two specifications, the "i.d." part and the "i." part:
i.d. – The signal level must be balanced on the time axis.
i. – The signal spectrum must be flattened, i.e. transformed by filtering (such as deconvol |
https://en.wikipedia.org/wiki/Ultraweak%20topology | In functional analysis, a branch of mathematics, the ultraweak topology, also called the weak-* topology, or weak-* operator topology or σ-weak topology, on the set B(H) of bounded operators on a Hilbert space is the weak-* topology obtained from the predual B*(H) of B(H), the trace class operators on H. In other words it is the weakest topology such that all elements of the predual are continuous (when considered as functions on B(H)).
Relation with the weak (operator) topology
The ultraweak topology is similar to the weak operator topology.
For example, on any norm-bounded set the weak operator and ultraweak topologies
are the same, and in particular the unit ball is compact in both topologies. The ultraweak topology is stronger than the weak operator topology.
One problem with the weak operator topology is that the dual of B(H) with the weak operator topology is "too small". The ultraweak topology fixes this problem: the dual is the full predual B*(H) of all trace class operators. In general the ultraweak topology is more useful than the weak operator topology, but it is more complicated to define, and the weak operator topology is often more apparently convenient.
The ultraweak topology can be obtained from the weak operator topology as follows.
If H1 is a separable infinite dimensional Hilbert space
then B(H) can be embedded in B(H⊗H1) by tensoring with the identity map on H1. Then the restriction of the weak operator topology on B(H⊗H1) is the ultraweak topology of B(H).
See also
Topologies on the set of operators on a Hilbert space
Ultrastrong topology
Weak operator topology
References
Topology of function spaces
Von Neumann algebras |
https://en.wikipedia.org/wiki/Simon%20Courcelles | Simon Courcelles (born June 10, 1986) is a former Canadian professional ice hockey centre who last played in the LNAH.
Career statistics
Regular season and playoffs
Notable awards and honours
Guy Carbonneau Trophy - QMJHL Best Defensive Forward (2004–05)
External links
1986 births
Lewiston Maineiacs players
Living people
Quebec Remparts players
Sherbrooke Saint-François players
Thetford Mines Isothermic players
Notre Dame Hounds players
Canadian ice hockey centres |
https://en.wikipedia.org/wiki/Denis%20Berger | Denis Berger (born 14 April 1983) is an Austrian footballer who plays for Türkspor Stuttgart.
Statistics
References
External links
1983 births
Living people
Austrian men's footballers
VfB Stuttgart II players
Sportfreunde Siegen players
KSV Hessen Kassel players
SV Ried players
SSV Jahn Regensburg players
Kickers Offenbach players
VfL Bochum players
FC Hansa Rostock players
SG Sonnenhof Großaspach players
Austrian Football Bundesliga players
2. Bundesliga players
3. Liga players
Men's association football midfielders
Austrian expatriate sportspeople in Germany
Expatriate men's footballers in Germany
Austrian expatriate men's footballers
Footballers from Vienna |
https://en.wikipedia.org/wiki/Tom%C3%A1%C5%A1%20Bokro%C5%A1 | Tomáš Bokroš (born 19 June 1989) is a Slovak professional ice hockey defenceman who currently playing for HK Dukla Trenčín of the Slovak Extraliga.
Career statistics
Regular season and playoffs
References
External links
1989 births
Living people
Slovak ice hockey defencemen
LHK Jestřábi Prostějov players
VHK Vsetín players
HKM Zvolen players
MsHK Žilina players
ŠHK 37 Piešťany players
HK Dukla Trenčín players
Södertälje SK players
HC Dynamo Pardubice players
HK Dukla Michalovce players
HK Poprad players
MHk 32 Liptovský Mikuláš players
Ice hockey people from Trenčín
Slovak expatriate ice hockey players in the Czech Republic
Slovak expatriate ice hockey players in Sweden |
https://en.wikipedia.org/wiki/Marek%20%C4%8Ealoga | Marek Ďaloga (born 10 March 1989) is a Slovak professional ice hockey defenceman for HC Kometa Brno of the Czech Extraliga (ELH).
Career statistics
Regular season and playoffs
International
References
External links
1989 births
Living people
Ice hockey people from Zvolen
Slovak ice hockey defencemen
Ice hockey players at the 2018 Winter Olympics
Ice hockey players at the 2022 Winter Olympics
Olympic ice hockey players for Slovakia
Medalists at the 2022 Winter Olympics
Olympic bronze medalists for Slovakia
Olympic medalists in ice hockey
HKM Zvolen players
HC 07 Detva players
HK Spišská Nová Ves players
HC Dynamo Pardubice players
HC Sparta Praha players
Ak Bars Kazan players
HC Slovan Bratislava players
HC Kunlun Red Star players
Mora IK players
Dinamo Riga players
HC Kometa Brno players
Slovak expatriate ice hockey players in the Czech Republic
Slovak expatriate ice hockey players in Sweden
Slovak expatriate sportspeople in China
Expatriate ice hockey players in China
Slovak expatriate sportspeople in Latvia
Expatriate ice hockey players in Latvia |
https://en.wikipedia.org/wiki/Peter%20Hra%C5%A1ko | Peter Hraško (born November 6, 1991) is a Slovak professional ice hockey defenceman who is currently playing for HKM Zvolen of the Slovak Extraliga.
Career statistics
Regular season and playoffs
International
Awards and honors
References
External links
1991 births
Living people
HC 07 Detva players
HC Slavia Praha players
HKM Zvolen players
Slovak ice hockey defencemen
Slovak expatriate ice hockey players in the Czech Republic
Expatriate ice hockey players in Kazakhstan
Slovak expatriate sportspeople in Kazakhstan |
https://en.wikipedia.org/wiki/Michal%20Jura%C5%A1ko | Michal Juraško (born April 21, 1984) is a Slovak professional ice hockey defenceman who is currently playing for HC Nové Zámky in the Slovak Extraliga.
Career statistics
External links
1984 births
Living people
HC 07 Detva players
HC Nové Zámky players
Slovak ice hockey defencemen
MsHK Žilina players
HKM Zvolen players
Ice hockey people from Zvolen
Újpesti TE (ice hockey) players
Expatriate ice hockey players in Hungary
Slovak expatriate ice hockey people
Slovak expatriate sportspeople in Hungary |
https://en.wikipedia.org/wiki/Jan%20Hran%C3%A1%C4%8D | Jan Hranáč (born October 26, 1969) is a Czech professional ice hockey defenceman who is currently playing for HKm Zvolen in the Slovak Extraliga.
Career statistics
External links
1969 births
Living people
Czech ice hockey defencemen
HC Lada Togliatti players
HC Litvínov players
HC Most players
HK Nitra players
HK 36 Skalica players
HKM Zvolen players
Orli Znojmo players
Rytíři Kladno players
Sportovní Klub Kadaň players
Czech expatriate ice hockey players in Slovakia
Czech expatriate ice hockey players in Russia |
https://en.wikipedia.org/wiki/Ji%C5%99%C3%AD%20Ku%C4%8Dn%C3%BD | Jiří Kučný is a Czech professional ice hockey defenceman who is currently playing for HKm Zvolen in the Slovak Extraliga.
Career statistics
External links
1983 births
Living people
Czech ice hockey defencemen
BK Mladá Boleslav players
HC Berounští Medvědi players
HC Oceláři Třinec players
HC Slavia Praha players
HC Slovan Bratislava players
HC Slovan Ústečtí Lvi players
HC Sparta Praha players
HKM Zvolen players
Motor České Budějovice players
MsHK Žilina players
Piráti Chomutov players
PSG Berani Zlín players
SK Horácká Slavia Třebíč players
Sportovní Klub Kadaň players
VHK Vsetín players
Czech expatriate ice hockey players in Slovakia |
https://en.wikipedia.org/wiki/Joe%20Smith%20%28footballer%2C%20born%201953%29 | Joe Smith (born 11 November 1953 in Glasgow) is a Scottish former footballer, who played for Aberdeen, Arbroath, Motherwell, Peterhead and Dunfermline.
Career statistics
Club
Appearances and goals by club, season and competition
References
External links
AFC Heritage profile
1953 births
Living people
Footballers from Glasgow
Men's association football midfielders
Scottish men's footballers
Aberdeen F.C. players
Arbroath F.C. players
Motherwell F.C. players
Peterhead F.C. players
Dunfermline Athletic F.C. players
Highland Football League players
Scottish Football League players
Scotland men's under-23 international footballers |
https://en.wikipedia.org/wiki/Paul%20Funk | Paul Georg Funk (14 April 1886, Vienna – 3 June 1969, Vienna) was an Austrian mathematician who introduced the Funk transform and who worked on the calculus of variations.
Biography
Born in Vienna in 1886, Paul Funk was the son of a deputy bank manager and went to high school in Baden and Gmunden. Then, studied mathematics in Tübingen, Vienna, and Göttingen, writing his PhD dissertation (Über Flächen mit lauter geschlossenen geodätischen Linien, 'On surfaces with many closed geodesic lines') under the supervision of David Hilbert.
He got his PhD in 1911 and spent the interwar years (1915-1939) in Prague as Professor of Mathematics at the . He became an associate professor in 1921 and a professor in 1927.
Suspended from his professorship in 1939 on account of his being Jewish, Funk was deported to the Theresienstadt concentration camp in 1944, where he spent the last months of the war. He was freed in 1945 and became professor at TU Wien.
He died in Vienna on 3 June, 1969. He was buried at Neustift Cemetery.
Major publications
References
Maximilian Pinl: Kollegen in dunkler Zeit. Jahresbericht DMV Bd.75, 1974, S.172.
External links
20th-century Austrian mathematicians
1886 births
1969 deaths
Variational analysts
Mathematicians from Austria-Hungary
Austrian Jews
Theresienstadt Ghetto survivors |
https://en.wikipedia.org/wiki/Daytona%20500%20history | This article documents historical records, statistics, and race recaps of the Daytona 500, held annually at Daytona International Speedway in Daytona Beach, Florida.
Pre-race history
The table below summarizes the pace cars, Grand Marshals, Honorary Starters, and performers of the national anthem at the Daytona 500. Since 2006, the pace car has been driven by a celebrity guest at the start of the race (mirroring the tradition used the Indy 500). During the race, however, a NASCAR official drives the pace car during caution periods. Since 2004, Brett Bodine has served as the official pace car driver. Previously, Robert "Buster" Auton and Elmo Langley were pace car drivers.
Race recaps
1959–1969
Lee Petty, patriarch of the racing family, won the 1959 Daytona 500 on February 22, 1959, defeating Johnny Beauchamp in a highly unusual manner. Petty and Beauchamp were lapping Joe Weatherly at the finish. Petty, Beauchamp, and Weatherly crossed the finish line three abreast with Weatherly on the outside, Beauchamp on the inside, and Petty in the middle. A photo finish in a race of that duration and speed seemed inconceivable and photo-finish cameras were not installed at the track. NASCAR initially declared Beauchamp the winner. After reviewing photographs and newsreels of the finish for three days, the call was reversed, and Petty was awarded the win. Petty received $19,050 for winning. Ken Marriott was scored as the last place driver having completed one lap and won $100.
In 1960, Robert "Junior" Johnson won, despite running a slower, year-old car in a field of 68 cars, most in Daytona 500 history through the present day. Johnson made use of the draft, then a little-understood phenomenon, to keep up with the leaders.
After three years of being the best driver never to win the Daytona 500, Glenn "Fireball" Roberts came to the 1962 edition race of the Daytona 500 on a hot roll, he won the American Challenge for winners of 1961 NASCAR events, the pole position for the Daytona 500, and the Twin-100-mile qualifier. He dominated the race, leading 144 of the 200 laps and finally won his first (and ultimately only) Daytona 500.
In 1963, it was DeWayne "Tiny" Lund who took the victory for the Wood Brothers, however the real drama began a couple weeks before the race when Lund helped pull 1961 winner Marvin Panch from a burning sportscar at a considerable risk to himself. As a result of his heroism, the Wood Brothers asked Lund to replace Panch in the Daytona 500 and Lund took the car to the winner's circle.
Driving a potent Plymouth with the new Hemi engine, Richard Petty led 184 of the 200 laps to win the 1964 Daytona 500 going away. Plymouths ran 1-2-3 at the finish. The triumph was Petty's first on a super-speedway.
The first rain-shortened Daytona 500 was the 1965 event. Leader Marvin Panch and Fred Lorenzen made contact on Lap 129, as rain began to fall; Panch spun out, and Lorenzen won when the race was finally called on Lap 133. The 1966 Day |
https://en.wikipedia.org/wiki/State%20Data%20Agency | The State Data Agency of Lithuania (), known as the Department of Statistics of Lithuania (), officially the Department of Statistics to the Government of the Republic of Lithuania, until 2023, is an institution in Lithuania which is responsible for collecting, processing, presenting and analysing statistics concerning the topics economy, society and environment, and governance regarding the state data. It is subordinate directly to the Government of Lithuania. Being a memember of the European Statistical System, the agency also supplies data to Eurostat.
A Director General, appointed by the Prime Minister, oversees its operations. Several commissions and working groups analyze its operations and suggest improvements. An advisory body, the Statistical Council, consists of representatives from the governmental bodies, NGOs, researchers, the media, and other interested parties; the council's makeup and operations are subject to governmental regulation.
History
The origins of statistics collection in Lithuania can be traced back to the 16th century, with the 1528 census of the Grand Duchy of Lithuania. An institution to collect statistics in the Republic of Lithuania was first established on 6 September 1919, as the General Department of Statistics. The first census of Lithuania was carried out in 1923. The institution in its current form was re-established on 18 April 1990 and codified by the Law on Statistics of the Republic of Lithuania. The institution became a member of the European Statistical System in 2004.
On 1 January 2023, the department was reorganized into an agency, as part of the Lithuanian Governance reform.
See also
Demographics of Lithuania
Eurostat
References
External links
https://www.stat.gov.lt Official website
https://osp.stat.gov.lt Official statistics portal
Statistics Lithuania - Lithuanian Statistical System. Government of Lithuania. Accessed 16 February 2011.
Statistical System of Lithuania. European Commission - Eurostat. Accessed 16 February 2011.
Government agencies of Lithuania
Lithuania
Statistical organizations |
https://en.wikipedia.org/wiki/1990%20S%C3%A3o%20Paulo%20FC%20season | The 1990 season was São Paulo's 61st season since club's existence.
Statistics
Scorers
Managers performance
Overall
{|class="wikitable"
|-
|Games played || 69 (33 Campeonato Paulista, 6 Copa do Brasil, 25 Campeonato Brasileiro, 5 Friendly match)
|-
|Games won || 28 (13 Campeonato Paulista, 3 Copa do Brasil, 10 Campeonato Brasileiro, 2 Friendly match)
|-
|Games drawn || 22 (10 Campeonato Paulista, 2 Copa do Brasil, 7 Campeonato Brasileiro, 3 Friendly match)
|-
|Games lost || 19 (10 Campeonato Paulista, 1 Copa do Brasil, 8 Campeonato Brasileiro, 0 Friendly match)
|-
|Goals scored || 76
|-
|Goals conceded || 50
|-
|Goal difference || +26
|-
|Best result || 6–1 (H) v Noroeste - Campeonato Paulista - 1990.06.19
|-
|Worst result || 0–2 (H) v Palmeiras - Campeonato Paulista - 1990.04.150–2 (A) v Criciúma - Copa do Brasil - 1990.08.02
|-
|Top scorer || Diego Aguirre (8)
|-
Friendlies
Copa Amistad
Copa Solidariedad de León
Official competitions
Campeonato Paulista
League table
Matches
Repechage stage
Matches
Record
Copa do Brasil
Round of 64
Round of 32
Eightfinals
Record
Campeonato Brasileiro
League table
Matches
Quarterfinals
Semifinals
Finals
Record
External links
official website
Brazilian football clubs 1990 season
1990 |
https://en.wikipedia.org/wiki/Carlos%20Mayor | Carlos Alberto Mayor (born 5 October 1965 in Buenos Aires, Argentina) is an Argentine former footballer who played as a defender.
Club statistics
Managerial statistics
References
External links
1965 births
Living people
Argentine men's footballers
Argentine expatriate men's footballers
Club de Gimnasia y Esgrima La Plata footballers
Argentinos Juniors footballers
Unión de Santa Fe footballers
Deportivo Español footballers
All Boys footballers
Deportes Iquique footballers
J1 League players
Japan Football League (1992–1998) players
Avispa Fukuoka players
Chilean Primera División players
Argentine Primera División players
Expatriate men's footballers in Chile
Expatriate men's footballers in Japan
Footballers at the 1988 Summer Olympics
Argentina men's international footballers
Argentine football managers
J2 League managers
Renofa Yamaguchi FC managers
Men's association football defenders
Olympic footballers for Argentina
Footballers from Buenos Aires |
https://en.wikipedia.org/wiki/Francisco%20Narcizio | Francisco Narcizio Abreu de Lima (born July 18, 1971) is a former Brazilian football player.
Club statistics
References
External links
1971 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Men's association football forwards
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
J1 League players
Ceará Sporting Club players
Yverdon-Sport FC players
Ferroviário Atlético Clube (CE) players
Botafogo de Futebol e Regatas players
Cerezo Osaka players
Esporte Clube Vitória players
Sport Club Internacional players
Rio Branco Esporte Clube players
Associação Atlética Ponte Preta players
Ituano FC players
Paraná Clube players
América Futebol Clube (MG) players
Avaí FC players |
https://en.wikipedia.org/wiki/Jos%C3%A9%20Luiz%20Drey | José Luiz Drey (born September 23, 1973), sometimes known as Zé Luiz, is a former Brazilian football player, coaching assistant, and manager.
Club statistics
References
External links
1973 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J1 League players
Shonan Bellmare players
Expatriate men's footballers in Japan
Men's association football defenders |
https://en.wikipedia.org/wiki/Wagner%20%28footballer%2C%20born%201966%29 | Antonio Wagner de Moraes (born June 2, 1966) is a former Brazilian football player.
Club statistics
References
External links
1966 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J1 League players
Japan Football League (1992–1998) players
Expatriate men's footballers in Japan
Shonan Bellmare players
Tokushima Vortis players
Kashiwa Reysol players
Men's association football forwards |
https://en.wikipedia.org/wiki/Raudnei | Raudnei Anversa Freire (born 18 July 1965) is a former Brazilian football player.
Club statistics
References
External links
sports.geocities.jp
1965 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Primeira Liga players
Segunda División players
J1 League players
Kyoto Sanga FC players
Clube Atlético Juventus players
FC Porto players
Deportivo de La Coruña players
C.F. Os Belenenses players
Gil Vicente F.C. players
Guarani FC players
CD Castellón footballers
Esporte Clube Bahia players
Esporte Clube Santo André players
América Futebol Clube (RN) players
Ituano FC players
Associação Desportiva São Caetano players
Paraná Clube players
Associação Atlética Portuguesa (Santos) players
Esporte Clube Juventude players
União São João Esporte Clube players
Expatriate men's footballers in Portugal
Expatriate men's footballers in Spain
Expatriate men's footballers in Japan
Men's association football forwards |
https://en.wikipedia.org/wiki/Denilson%20%28footballer%2C%20born%201972%29 | Denilson Antonio Paludo (born October 8, 1972) is a former Brazilian football player.
Club statistics
References
External links
1972 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J1 League players
Expatriate men's footballers in Japan
Yokohama Flügels players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Rodrigo%20Carbone | Rodrigo José Carbone (born March 17, 1974) is a former Brazilian football player.
Club statistics
References
External links
awx.jp
1974 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J1 League players
Kashima Antlers players
Expatriate men's footballers in Japan
Jeonnam Dragons players
K League 1 players
Expatriate men's footballers in Poland
Expatriate men's footballers in South Korea
Men's association football forwards |
https://en.wikipedia.org/wiki/Buz%20M.%20Walker | Buz M. Walker (August 20, 1863 – August 21, 1949) was a mathematics professor and the President of the Mississippi Agricultural and Mechanical College (now Mississippi State University) from 1925 to 1930. The Walker Engineering building at Mississippi State is named in his honor. He was an instructor at the school from 1883 to 1884, an assistant professor of mathematics from 1888 to 1927, dean of the engineering school from 1922 to 1925, and vice president of the university from 1913 to 1925. He was also involved with the school's athletics, a regular member of the Southern Intercollegiate Athletic Association, and its president around the time of World War I.
He graduated from Mississippi A&M with the class of 1883. From 1885 to 1887 Walker attended the University of Virginia and studied under professor William M. Thornton.
Mathematics
Buz M. Walker achieved worldwide distinction in 1906 with a University of Chicago dissertation "On the Resolution of the Higher Singularities of Algebraic Curves Into Ordinary Nodes", supervised by Oskar Bolza. Walker was an Invited Speaker of the ICM in 1936 in Oslo.
References
1863 births
1949 deaths
19th-century American mathematicians
Presidents of Mississippi State University
University of Chicago alumni
People from Oktibbeha County, Mississippi
20th-century American mathematicians |
https://en.wikipedia.org/wiki/The%20Soldier%27s%20Song%20%28novel%29 | The Soldier's Song is the debut novel from Alan Monaghan and the first in the Soldier's Song Trilogy.
Set during World War I, the novel follows the fortunes of Stephen Ryan, a gifted young maths scholar, as he enlists in the British army and leaves his native Ireland to fight in Europe. He finds his loyalties tested, however, when he returns from the front in 1916 to find Ireland in the midst of an uprising. The harsh realities of war combined with the strain of having to reflect on his own identity and allegiances take their toll as Stephen is pushed ever closer to his breaking point.
Reception
The novel was positively received upon its release and gained, for its author, a nomination at the 2010 Irish Book Awards for best newcomer. It has also been longlisted for the 2010/2011 Waverton Good Read Award.
References
External links
Pan Macmillan: The Soldier's Song
The Marsh Agency: The Soldier's Song
The View arts show reviews The Soldier's Song
Interview with author
Irish Times review
The Guardian review
2010 Irish novels
Novels set during World War I
Easter Rising
History of Ireland (1801–1923)
Novels set during the Irish War of Independence
2010 debut novels |
https://en.wikipedia.org/wiki/WWW%20Interactive%20Multipurpose%20Server | The WWW Interactive Multipurpose Server (WIMS) (sometimes referred to as WWW Interactive Mathematics Server) project is designed for supporting intensive mathematical exercises via the Internet or in a computer-equipped classroom with server-side interactivity, accessible at the address http://wims.unice.fr.
The system has the following main features:
A modular design allowing applications and software interfaces to be created and maintained independently from each other.
Features interfaces for software including MuPAD, PARI/GP, Gnuplot, POV-Ray, Co.
Dynamic rendering of mathematical formulas and animated graphics.
A structure of virtual classes, including mechanisms for automatic score gathering and processing.
The program is open source and freely available under the GNU General Public Licence, however each WIMS module has its own copyright policy, which may differ from that of the server program.
It is often cited and linked for its sophisticated "online calculator" tools capable of generating animated GIFs of parametric 2D or 3D graphs or allowing prime tests with very large numbers.
Author
Xiao Gang was a professor at University of Nice Sophia Antipolis. He was interested in solar energy and algebraic geometry. He was also the active site manager of the WIMS of the university he worked for. Xiao Gang died on June 27, 2014.
Xiao Gang taught himself during the Up to the Mountains and Down to the Countryside Movement. He obtained his master's degree from the University of Science and Technology of China. Xiao obtained his Ph.D. degree from University of Paris-Sud in 1984. Xiao Gang returned to China and became a lecturer at East China Normal University. He was promoted to professor in 1986, and was awarded the Shiing-Shen Chern Prize in Mathematics in 1991. In 1992, Xiao became a professor at University of Nice Sophia Antipolis.
External links
English WIMS at wims.unice.fr - The WIMS of the University of Nice Sophia Antipolis in France, the most popular WIMS for it was the first one and is hosted at the creator's university.
WIMS at wims.ac-nice.fr - The WIMS of the Académie de Nice - One of the few featuring a redesigned skin.
English WIMS help
List of WIMS Servers/Mirrors at wims.unice.fr
"WIMS A server for interactive mathematics on the internet" - Paper on WIMS by XIAO, Gang written in 1999
WIMS download page
Interface to the Direc exec WIMS module - This gives direct code access to many other WIMS modules (e.g. the POV-Ray renderer or a C compiler).
A list of frequent citers of unice.fr WIMS modules (some Wikipedia articles)
List of the online calculators available sorted by popularity.
WIMS EDU association site.
References
Servers (computing) |
https://en.wikipedia.org/wiki/Caryn%20Navy | Caryn Linda Navy (born July 5, 1953) is an American mathematician and computer scientist. Blind since childhood, she is chiefly known for her work in set-theoretic topology and Braille technology.
Early life
Navy was born in Brooklyn, New York in 1953. Born premature, she was diagnosed as totally blind from retinopathy of prematurity. Her family soon discovered that she could actually see from the corner of one eye, but at age 10 she lost all sight due to retinal detachment.
The next year, in sixth grade, Navy began learning to read and write Braille at school. She also learned the Nemeth Braille system for writing mathematics, which became her favorite subject. She enjoyed team math competitions, and at age 14 independently rediscovered Euclid's formula for even perfect numbers. She also learned Hebrew Braille in preparation for her bat mitzvah service. At age 16 Navy was hired for her first job, as a Dictaphone typist in New York City. She took a class to learn to travel the New York City Subway.
Education
Navy attended the Massachusetts Institute of Technology 1971–1975, majoring in mathematics. The only textbook she had
in Braille was her calculus book. All her other books were obtained as audiobooks from Recording for the Blind.
At MIT, her undergraduate advisor James Munkres introduced her to the subject of topology. Upon her graduation with a bachelor's degree in mathematics in 1975, she received the AMITA Senior Academic Award from the Association of MIT Alumnae. Early in her undergraduate career, Navy met David Holladay, an electrical engineering student. He looked up enough Braille to write her a note after their first meeting. They were married after graduation.
Navy attended graduate school at the University of Wisconsin–Madison, majoring in mathematics, with a minor in computer science. During her graduate education, she used an Optacon device to read textbooks that were not available in Braille or as audiobooks. She received her M.A. in 1977, and her Ph.D. in 1981 under the supervision of topologist Mary Ellen Rudin.
Mathematics
Navy's doctoral thesis, "Nonparacompactness in Para-Lindelöf Spaces", was important in the development of metrizability theory. The paper examines the properties of para-Lindelöf topological spaces, which are a generalization of both Lindelöf spaces and paracompact spaces. In a para-Lindelöf space, every open cover has a locally countable open refinement, that is, one such that each point of the space has a neighborhood that intersects only countably many elements of the refinement. The spaces constructed by Navy are counterexamples to the conjecture that all para-Lindelöf spaces are paracompact. Some of her spaces are even normal Moore spaces under suitable set-theoretic assumptions. Since every metrizable space is paracompact, these are counterexamples to the normal Moore space conjecture.
Stephen Watson called Navy's construction "a rather general one that permitted quite a lot of latitude" and said |
https://en.wikipedia.org/wiki/Single-entry%20single-exit | In mathematics graph theory, a single-entry single-exit (SESE) region in a given graph is an ordered edge pair.
For example, with the ordered edge pair, (a, b) of distinct control-flow edges a and b where:
a dominates b
b postdominates a
Every cycle containing a also contains b and vice versa.
where a node x is said to dominate node y in a directed graph if every path from start to y includes x. A node x is said to postdominate a node y if every path from y to end includes x.
So, a and b refer to the entry and exit edge, respectively.
The first condition ensures that every path from start into the region passes through the region’s entry edge, a.
The second condition ensures that every path from inside the region to end passes through the region’s exit edge, b.
The first two conditions are necessary but not enough to characterize SESE regions: since backedges do not alter the dominance or postdominance relationships, the first two conditions alone do not prohibit backedges entering or exiting the region.
The third condition encodes two constraints: every path from inside the region to a point 'above' a passed through b, and every path from a point 'below' b to a point inside the region passes through a.
References
Graph theory |
https://en.wikipedia.org/wiki/Fatality%20statistics%20in%20the%20Western%20Australian%20mining%20industry | Fatality statistics in the Western Australian mining industry captures the number of people killed in the industry in the Australian state of Western Australia. During the period 2000-2012 (inclusive), a total of 52 fatalities occurred. In 2006, the Chamber of Minerals and Energy of Western Australia commissioned a taxonomic study to analyse the 306 mining fatalities which occurred between 1970 and 2006. The Department of Mines and Petroleum, later renamed the Department of Mines, Industry Regulation and Safety, the governing authority for the industry in the state, has published statistics for fatalities in mining dating back to 1943 and intends to publish statistics dating back to 1886, though early records are not expected to be exhaustive.
Categorisation
The department lists the fatality statistics categorised by commodity, date, fiscal year, occupation, causes, report status and type of mining (underground or surface). Records up until 1967 are not categorised by commodity and instead appear as "not categorised" in the listing. Categorisation began in 1967 and almost all fatalities are categorised after 1968.
Omissions
The statistics do not include the 2000 Australia Beechcraft King Air crash, when a flight to the Gwalia Gold Mine, with seven Sons of Gwalia employees onboard failed to land, instead continuing on to Burketown, where it eventually crashed, having run out of fuel. The pilot and the plane's seven passengers were all killed.
Recent fatalities
The most recent fatalities in the Western Australian mining industry are:
12 June 2023: Kieren McDowall, an employee of AAA Asphalt Surfaces, was killed at Mineral Resources Ken's Bore site of its Onslow Iron project.
7 February 2023: Jody Byrne (51) was killed at BHP's Boodarie rail yard, near Port Hedland, having been struck by a locomotive.
13 October 2022: Gary Mitchell (59), a machine operator at Capricorn Metals' Karlawinda Gold Mine, was killed when his vehicle was crushed by a large dump truck.
11 October 2022: Airleg miner Terry Hogan (37) was killed by a rock fall near a vent rise in Gold Fields' Hamlet underground mine at St Ives, near Kambalda.
30 September 2021: David Armstrong (25), a shotfirer, was killed in a ground collapse during open pit mine blasting operations at Fortescue Metals Group’s Solomon iron ore hub.
17 September 2021: Scaffolder Eugene Tata (52) fell to his death from a conveyor walkway at CITIC Pacific Mining's Cape Preston project.
10 June 2021: Paul Tamati Ereka Martin died after becoming unconscious in Silver Lake Resources' Daisy Milano underground mine at Mount Monger.
9 December 2020: Paige Counsell (25), underground truck driver, was struck by a haul truck in the decline of the Big Bell Gold Mine, but died while being transported to a Perth hospital by the Royal Flying Doctor Service.
13 July 2020: Michael Johnson (38), bogger operator at Saracen Minerals' Dervish underground mine at Carosue Dam, died when his machine fell 25 metres down |
https://en.wikipedia.org/wiki/Duje%20Juri%C4%87 | Duje Jurić (born 1956 in Rupe, Croatia) is a Croatian contemporary artist and one of the key figures of the New Geometry movement of the 1980s. He lives and works in Zagreb, Croatia.
He was an associate of the Master Workshop of Ljubo Ivančić and Nikola Reiser (1982–1985). At the end of the 1980s he collaborated with Julije Knifer in making murals in Sète, a small town in southern France (1889 and 1990, Villa Saint-Claire). During the 1990s he supplemented his works with text and made artistic interventions upon various objects, either his own or objects belonging to others (such as doors, cabinets, suitcases, clothes, paint-brushes, etc.). In more recent years he has been involved with creating ambient, action and performance art. Jurić also works as an art restorer and in the period between 1977 and 1993 he was an associate member of the Croatian Conservation Institute. From 1984 to 1999 he worked as a freelance artist, followed by a position at the Museum of Contemporary Art, Zagreb (1999–2000). Following which, he has been teaching at the Academy of Fine Arts, University of Zagreb, first as an assistant professor, and now as a fully appointed professor in the Department of Painting.
He has had some sixty solo shows and over a hundred group exhibitions. He has also performed several actions and participated in a number of art projects, the highlight of which being his ambience art projects (light installations), and his theatre sets made for the Kugla Theatre project. He has received several awards, including the 2002 Croatian Association of Artists Award for Best Exhibition (for his exhibition in the Gliptoteka gallery, in the Croatian Academy of Sciences and Arts) and the 2002 Vladimir Nazor Award.
Notes and references
External links
Official Artist Blog
Croatian contemporary artists
Croatian artists
1956 births
Vladimir Nazor Award winners
Living people |
https://en.wikipedia.org/wiki/Thomas%20W.%20Hungerford | Thomas William Hungerford (March 21, 1936 – November 28, 2014) was an American mathematician who worked in algebra and mathematics education. He is the author or coauthor of several widely used and widely cited textbooks covering high-school to graduate-level mathematics. From 1963 until 1980 he taught at the University of Washington and then at Cleveland State University until 2003. From 2003–2014 he was at Saint Louis University. Hungerford had a special interest in promoting the use of technology to teach mathematics.
Hungerford did his undergraduate work at the College of the Holy Cross and defended his Ph.D. thesis at the University of Chicago in 1963 (advised by Saunders Mac Lane). Throughout his career he wrote more than a dozen widely used mathematics textbooks, ranging from high school to graduate level.
Bibliography
Graduate
1974 Algebra (Graduate Texts in Mathematics #73). Springer Verlag.
Undergraduate
1997 Abstract Algebra: An Introduction, 2nd Edition. Cengage.
2005 Contemporary College Algebra and Trigonometry, 2nd Edition. Cengage.
2005 Contemporary College Algebra, 2nd Edition. Cengage.
2006 Contemporary Trigonometry. Cengage.
2009 Contemporary Precalculus, 5th Edition (with Douglas J. Shaw). Cengage.
2011 Mathematics with Applications, 10th Edition (with Margaret L. Lial and John P. Holcomb, Jr). Pearson.
2011 Finite Mathematics with Applications, 10th Edition (with Margaret L. Lial and John P. Holcomb, Jr). Pearson.
2013 Abstract Algebra: An Introduction, 3rd Edition, Cengage.
High school
2002 Precalculus: A Graphing Approach (with Irene Jovell and Betty Mayberry). Holt, Rinehart & Winston.
References
External links
Algebraists
20th-century American mathematicians
21st-century American mathematicians
College of the Holy Cross alumni
University of Chicago alumni
University of Washington faculty
Cleveland State University faculty
Saint Louis University faculty
Saint Louis University mathematicians
People from Oak Park, Illinois
1936 births
2014 deaths
Mathematicians from Illinois |
https://en.wikipedia.org/wiki/Fernando%20Nicolas%20Oliva | Fernando Nicolas Oliva (born September 26, 1971) is a former Argentine football player.
Club statistics
Honors
Shimizu S-Pulse
J.League Cup: 1996
Asian Cup Winners Cup: 2000
Emperor's Cup: 2001
Japanese Super Cup: 2001
References
External links
1971 births
Living people
Argentine men's footballers
J1 League players
Shimizu S-Pulse players
Talleres de Córdoba footballers
Argentine expatriate men's footballers
Expatriate men's footballers in Japan
Men's association football forwards
Footballers from Córdoba, Argentina |
https://en.wikipedia.org/wiki/2011%20Cricket%20World%20Cup%20statistics | This is a list of statistics for the 2011 Cricket World Cup. Each list contains at least the top five record
Team statistics
Highest team totals
Largest winning margin
By runs
By wickets
By balls remaining
Lowest team totals
This is a list of completed innings only, low totals in matches with reduced overs are omitted except when the team was all out. Successful run chases in the second innings are not counted.
Smallest winning margin
By runs
By wickets
By balls remaining
Individual statistics
Batting
Highest scores
Most runs
Most boundaries
Most ducks
Bowling
Most wickets
Best bowling figures
Most maidens
Hat-tricks
Fielding
Most dismissals
This is a list of wicket-keepers with the most dismissals in the tournament.
Most catches
This is a list of the outfielders who have taken the most catches in the tournament.
Other statistics
Highest partnerships
The following tables are lists of the highest partnerships for the tournament.
See also
Cricket World Cup statistics
References
External links
Official 2011 World Cup site
Statistics
Cricket World Cup statistics |
https://en.wikipedia.org/wiki/Effective%20topos | In mathematics, the effective topos introduced by captures the mathematical idea of effectivity within the category theoretical framework.
Definition
Preliminaries
Kleene realizability
The topos is based on the partial combinatory algebra given by Kleene's first algebra . In Kleene's notion of recursive realizability, any predicate is assigned realizing numbers, i.e. a subset of . The extremal propositions are and , realized by and . However in general, this process assigns more data to a proposition than just a binary truth value.
A formula with free variables will give rise to a map in the values of which is the subset of corresponding realizers.
Realizability topoi
is a prime example of a realizability topos. These are a class of elementary topoi with an intuitionistic internal logic and fulfilling a form of dependent choice. They are generally not Grothendieck topoi.
In particular, the effective topos is . Other realizability topos construction can be said to abstract away the some aspects played by here.
Description of Eff
The objects are pairs of sets together with a symmetric and transitive relation in , representing a form of equality predicate, but taking values in subsets of . One writes with just one argument to denote the so called existence predicate, expressing how an relates to itself. This may be empty and so the relation is not generally reflexive.
Arrows amount to equivalence classes of functional relations appropriately respecting the defined equalities.
The classifier amounts to . The pair (or, by abuse of notation, just that underlying powerset) may be denoted as .
An entailment relation on makes it into a Heyting pre-algebra.
Such a context allows to define the appropriate lattice-like logic structure, with logical operations given in terms of operations of the realizer sets, making use of pairs and computable functions.
The terminal object is a singleton with trivial existence predicate (). The finite product respect the equality appropriately.
The classifier's equality is given through equivalences in its lattice.
Properties
Relation to Sets
Some objects exhibit a rather trivial existence predicate depending only on the validity of the equality relation "" of sets, so that valid equality maps to the top set and rejected equality maps to . This gives rise to a full and faithful functor out of the category of sets, which has the finite limits preserving global sections functor as its left-adjoint.
This factors through a finite-limit preserving, full and faithful embedding -.
NNO
The topos has a natural numbers object with simply .
Sentences true about are exactly the recursively realized sentences of Heyting arithmetic .
Now arrows may be understood as the total recursive functions and this also holds internally for . The latter is the pair given by total recursive functions and a relation such that is the set of codes for . The latter is a subset of the naturals but not just a singlet |
https://en.wikipedia.org/wiki/Karoubi%20conjecture | In mathematics, the Karoubi conjecture is a conjecture by that the algebraic and topological K-theories coincide on C* algebras spatially tensored with the algebra of compact operators. It was proved by .
References
Operator algebras
K-theory
Theorems in algebraic topology |
https://en.wikipedia.org/wiki/Max%20Karoubi |
Max Karoubi () is a French mathematician, topologist, who works on K-theory, cyclic homology and noncommutative geometry and who founded the first European Congress of Mathematics.
In 1967, he received his Ph.D. in mathematics (Doctorat d'État) from the University of Paris, under the supervision of Henri Cartan and Alexander Grothendieck.
In 1973, he was nominated full professor at the University of Paris 7-Denis Diderot until 2007. He is now an emeritus professor there. In 2012 he became a fellow of the American Mathematical Society.
Karoubi has supervised 12 Ph.D. students, including Jean-Louis Loday and Christophe Soulé.
See also
Karoubi conjecture
Karoubi envelope
Publications
Notes
External links
Home page of Max Karoubi
20th-century French mathematicians
21st-century French mathematicians
Fellows of the American Mathematical Society
Living people
Academic staff of Paris Diderot University
University of Paris alumni
Topologists
1938 births
People from Tunis |
https://en.wikipedia.org/wiki/Measurable%20Riemann%20mapping%20theorem | In mathematics, the measurable Riemann mapping theorem is a theorem proved in 1960 by Lars Ahlfors and Lipman Bers in complex analysis and geometric function theory. Contrary to its name, it is not a direct generalization of the Riemann mapping theorem, but instead a result concerning quasiconformal mappings and solutions of the Beltrami equation. The result was prefigured by earlier results of Charles Morrey from 1938 on quasi-linear elliptic partial differential equations.
The theorem of Ahlfors and Bers states that if μ is a bounded measurable function on C with , then there is a
unique solution f of the Beltrami equation
for which f is a quasiconformal homeomorphism of C fixing the points 0, 1 and ∞. A similar result is true with C replaced by the unit disk D. Their proof used the Beurling transform, a singular integral operator.
References
Theorems in complex analysis
Bernhard Riemann |
https://en.wikipedia.org/wiki/Root%20of%20unity%20modulo%20n | In number theory, a kth root of unity modulo n for positive integers k, n ≥ 2, is a root of unity in the ring of integers modulo n; that is, a solution x to the equation (or congruence) . If k is the smallest such exponent for x, then x is called a primitive kth root of unity modulo n. See modular arithmetic for notation and terminology.
The roots of unity modulo are exactly the integers that are coprime with . In fact, these integers are roots of unity modulo by Euler's theorem, and the other integers cannot be roots of unity modulo , because they are zero divisors modulo .
A primitive root modulo , is a generator of the group of units of the ring of integers modulo . There exist primitive roots modulo if and only if where and are respectively the Carmichael function and Euler's totient function.
A root of unity modulo is a primitive th root of unity modulo for some divisor of and, conversely, there are primitive th roots of unity modulo if and only if is a divisor of
Roots of unity
Properties
If x is a kth root of unity modulo n, then x is a unit (invertible) whose inverse is . That is, x and n are coprime.
If x is a unit, then it is a (primitive) kth root of unity modulo n, where k is the multiplicative order of x modulo n.
If x is a kth root of unity and is not a zero divisor, then , because
Number of kth roots
For the lack of a widely accepted symbol, we denote the number of kth roots of unity modulo n by .
It satisfies a number of properties:
for
where λ denotes the Carmichael function and denotes Euler's totient function
is a multiplicative function
where the bar denotes divisibility
where denotes the least common multiple
For prime , . The precise mapping from to is not known. If it were known, then together with the previous law it would yield a way to evaluate quickly.
Examples
Let and . In this case, there are three cube roots of unity (1, 2, and 4). When however, there is only one cube root of unity, the unit 1 itself. This behavior is quite different from the field of complex numbers where every nonzero number has k kth roots.
Primitive roots of unity
Properties
The maximum possible radix exponent for primitive roots modulo is , where λ denotes the Carmichael function.
A radix exponent for a primitive root of unity is a divisor of .
Every divisor of yields a primitive th root of unity. One can obtain such a root by choosing a th primitive root of unity (that must exist by definition of λ), named and compute the power .
If x is a primitive kth root of unity and also a (not necessarily primitive) ℓth root of unity, then k is a divisor of ℓ. This is true, because Bézout's identity yields an integer linear combination of k and ℓ equal to . Since k is minimal, it must be and is a divisor of ℓ.
Number of primitive kth roots
For the lack of a widely accepted symbol, we denote the number of primitive kth roots of unity modulo n by .
It satisfies the following properties:
Con |
https://en.wikipedia.org/wiki/1989%20S%C3%A3o%20Paulo%20FC%20season | The 1989 season was São Paulo's 60th season since club's existence.
Statistics
Scorers
Managers performance
Overall
{|class="wikitable"
|-
|Games played || 52 (29 Campeonato Paulista, 19 Campeonato Brasileiro, 4 Friendly match)
|-
|Games won || 23 (14 Campeonato Paulista, 7 Campeonato Brasileiro, 2 Friendly match)
|-
|Games drawn || 22 (11 Campeonato Paulista, 9 Campeonato Brasileiro, 2 Friendly match)
|-
|Games lost || 7 (4 Campeonato Paulista, 3 Campeonato Brasileiro, 0 Friendly match)
|-
|Goals scored || 67
|-
|Goals conceded || 34
|-
|Goal difference || +33
|-
|Best result || 4–0 (A) v Juventus - Campeonato Paulista - 1989.04.19
|-
|Worst result || 1–4 (A) v Atlético Mineiro - Campeonato Brasileiro - 1989.09.20
|-
|Top scorer || Mário Tilico (12)
|-
Friendlies
Matches played with the B team
Torneo Hexagonal de Guadalajara
Official competitions
Campeonato Paulista
Matches
Second stage
Semifinals
Finals
Record
Campeonato Brasileiro
First stage
Matches
Second stage
Matches
Final
Record
External links
official website
References
Sao Paulo
São Paulo FC seasons |
https://en.wikipedia.org/wiki/Karol%20Mondek | Karol Mondek (born 2 June 1991) is a Slovak professional footballer who currently plays for ViOn Zlaté Moravce.
Career statistics
Honours
Raków Częstochowa
I liga: 2018–19
External links
References
1991 births
Living people
Slovak expatriate men's footballers
Slovak men's footballers
Men's association football midfielders
Slovak First Football League players
Eerste Divisie players
I liga players
Czech National Football League players
Czech First League players
AS Trenčín players
AGOVV players
FC Baník Ostrava players
Raków Częstochowa players
SFC Opava players
FC ViOn Zlaté Moravce players
Expatriate men's footballers in the Netherlands
Expatriate men's footballers in the Czech Republic
Expatriate men's footballers in Poland
Slovak expatriate sportspeople in the Netherlands
Slovak expatriate sportspeople in the Czech Republic
Slovak expatriate sportspeople in Poland
Sportspeople from Martin, Slovakia
Footballers from the Žilina Region |
https://en.wikipedia.org/wiki/Peter%20Valla | Peter Valla (born 20 March 1990 in Skalica) is a Slovak football defender who currently plays for PFK Piešťany, on loan from the Slovak Corgoň Liga club FK AS Trenčín.
Career statistics
External links
AS Trenčín profile
1990 births
Living people
Slovak men's footballers
Men's association football defenders
FK Senica players
AS Trenčín players
PFK Piešťany players
Slovak First Football League players
Sportspeople from Skalica
Footballers from the Trnava Region |
https://en.wikipedia.org/wiki/Vojtech%20Horv%C3%A1th | Vojtech Horváth (born 28 June 1984) is a Slovak football midfielder who currently plays for the Fortuna Liga club FC DAC 1904 Dunajská Streda.
Career statistics
External links
AS Trenčín profile
References
1984 births
Living people
Slovak men's footballers
Men's association football midfielders
FK Inter Bratislava players
FC Petržalka players
AS Trenčín players
Bruk-Bet Termalica Nieciecza players
FC DAC 1904 Dunajská Streda players
Slovak First Football League players
Slovak expatriate men's footballers
Slovak expatriate sportspeople in Poland
Expatriate men's footballers in Poland
Footballers from Dunajská Streda
FC ŠTK 1914 Šamorín players |
https://en.wikipedia.org/wiki/Martin%20%C5%A0evela | Martin Ševela (born 20 November 1975) is a Slovak former football manager and former player who played as a centre-back. Besides Slovakia, he has managed in Poland and Saudi Arabia.
Career statistics
Managerial statistics
As of 17 March 2023
Honours
Manager
AS Trenčín
Slovak First Football League: 2014–15, 2015–16
Slovak Cup: 2014–15, 2015–16
ŠK Slovan Bratislava
Slovak First Football League: 2018–19
Slovak Cup: 2017–18
Individual
Fortuna Liga Manager of the Season: 2015-16
External links
AS Trenčín profile
Fotbal.idnes.cz profile
References
1975 births
Living people
Slovak men's footballers
Men's association football defenders
Slovak First Football League players
FK Inter Bratislava players
FK Dubnica players
ŠK Slovan Bratislava players
AS Trenčín players
People from Senec District
Sportspeople from the Bratislava Region
1. FK Drnovice players
Slovak football managers
AS Trenčín managers
ŠK Slovan Bratislava managers
Zagłębie Lubin managers
Abha Club managers
Slovak First Football League managers
Ekstraklasa managers
Saudi Pro League managers
Slovak expatriate football managers
Slovak expatriate sportspeople in Poland
Slovak expatriate sportspeople in Saudi Arabia
Expatriate football managers in Poland
Expatriate football managers in Saudi Arabia |
https://en.wikipedia.org/wiki/The%20UTeach%20Institute | The UTeach Institute is a nonprofit organization created in 2006 in response to growing concerns about science, technology, engineering, and mathematics (STEM) education in the United States and interest in the secondary STEM teacher certification program, UTeach, started in 1997 at The University of Texas at Austin.
The UTeach Institute issued its first request for proposals to replicate UTeach in 2007. An initial cohort of 13 universities was selected to receive individual grants of up to $1.4 million each to replicate the program over a four-year implementation period from 2008 to 2012. A second cohort of 8 universities was selected for a 2010-2014 grant cycle, and a third cohort of universities is expected to begin implementation in Spring 2012. As of February 2011, excluding the original UTeach program at The University of Texas at Austin, 4,190 students currently were enrolled in UTeach programs at 21 universities across the country.
The UTeach Institute acts as the liaison between the original UTeach program at The University of Texas at Austin and individuals implementing the program on other university campuses. The Institute provides detailed technical assistance and support and hosts an annual conference in Austin, Texas focusing on issues of STEM teacher preparation, national and state STEM education policy, the UTeach program model, and UTeach replication. In addition to assisting the universities implementing UTeach, the UTeach Institute conducts ongoing evaluations of progress and fulfills reporting requirements to various funders.
UTeach has been a model for mathematics and science education programs at other institutions, and has been expanded to involve an additional forty-four universities in twenty-one states by 2019.
2008-2012 (cohort 1)
Florida State University
Louisiana State University
Northern Arizona University
Temple University
University of California, Berkeley
University of California, Irvine
University of Colorado Boulder
University of Florida
University of Houston
University of Kansas
University of North Texas
University of Texas, Dallas
Western Kentucky University
2010-2014 (cohort 2)
Cleveland State University
Middle Tennessee State University
University of Colorado Colorado Springs
University of Memphis
University of Tennessee, Chattanooga
University of Tennessee, Knoxville
University of Texas, Arlington
University of Texas at Tyler
2011-2015 (cohort 3)
Columbus State University
Southern Polytechnic State University
University of Massachusetts, Lowell
University of West Georgia
2012-2016 (cohort 4)
Boise State University
Florida Institute of Technology
Towson University
University of Arkansas at Fayetteville
University of Arkansas at Little Rock
University of Central Arkansas
University of Texas at Brownsville
University of Texas, Pan American
2013-2018 (cohort 5)
Drexel University
Florida International University
University of Maryland, College Park
Oklahoma State |
https://en.wikipedia.org/wiki/Aleksandar%20Trnini%C4%87 | Aleksandar Trninić (; born 27 March 1987) is a Serbian football defensive midfielder who plays for Radnički Beograd.
Career
In 2019, Trninić joined Al-Shabab in Kuwait.
Club statistics
References
External links
at mfkzemplin.sk
1987 births
Footballers from Belgrade
Living people
Serbian men's footballers
Men's association football defenders
SC Cham players
FK Rad players
FK Radnički Obrenovac players
FK Palilulac Beograd players
FK Čukarički players
FK Leotar players
MFK Zemplín Michalovce players
Debreceni VSC players
FK Vardar players
FK Radnički Niš players
Knattspyrnufélag Akureyrar players
Al-Shabab SC (Kuwait) players
FK Radnički Beograd players
Serbian SuperLiga players
Premier League of Bosnia and Herzegovina players
2. Liga (Slovakia) players
Serbian First League players
Nemzeti Bajnokság I players
Macedonian First Football League players
Úrvalsdeild karla (football) players
1. deild karla players
Kuwait Premier League players
Serbian expatriate men's footballers
Expatriate men's footballers in Switzerland
Serbian expatriate sportspeople in Switzerland
Expatriate men's footballers in Bosnia and Herzegovina
Serbian expatriate sportspeople in Bosnia and Herzegovina
Expatriate men's footballers in Slovakia
Serbian expatriate sportspeople in Slovakia
Expatriate men's footballers in Hungary
Serbian expatriate sportspeople in Hungary
Expatriate men's footballers in North Macedonia
Serbian expatriate sportspeople in North Macedonia
Expatriate men's footballers in Iceland
Serbian expatriate sportspeople in Iceland
Expatriate men's footballers in Kuwait
Serbian expatriate sportspeople in Kuwait |
https://en.wikipedia.org/wiki/Milos%20Raonic%20career%20statistics | This is a list of the main career statistics of tennis player Milos Raonic.
Grand Slam finals
Singles: 1 (1 runner-up)
Other significant finals
Masters 1000 finals
Singles: 4 (4 runner-ups)
ATP career finals
Singles: 23 (8 titles, 15 runner-ups)
Doubles: 1 (1 runner-up)
Singles performance timeline
Current through the 2023 Canadian Open.
ATP Challenger and ITF Futures finals
Singles: 8 (4–4)
Doubles: 9 (6–3)
Record against other players
Head-to-head against career-high top-20 players
The table below chronicles Raonic's head-to-head record against all players who have a career-high singles ranking of 20 or better. Active players are highlighted in bold.
|-bgcolor=efefef class=sortbottom
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|-
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|-
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|-
{{tennis hth opponent|hr=|w=2|l=2|o=' Dominic Thiem
|lm=}}
|-bgcolor=efefef class=sortbottom
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|-
|-bgcolor=efefef class=sortbottom
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|-
|-bgcolor=efefef class=sortbottom
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|-
|-bgcolor=efefef class=sortbottom
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|-
|-bgcolor=efefef class=sortbottom
|align=left colspan=10|Number 8 ranked players
|-
|-bgcolor=efefef class=sortbottom
|align=left colspan=10|Number 9 ranked players
|-
|-bgcolor=efefef class=sortbottom
|align=left colspan=10|Number 13 ranked players
|-
|-bgcolor=efefef class=sortbottom
|align=left colspan=10|Number 14 ranked players
|-
|-bgcolor=efefef class=sortbottom
|align=left colspan=10|Number 15 ranked players
|-
|-bgcolor=efefef class=sortbottom
|align=left colspan=10|Number 16 ranked players
|-
|-bgcolor=efefef class=sortbottom
|align=left colspan=10|Number 17 ranked players
|-
|-bgcolor=efefef class=sortbottom
|align=left colspan=10|Number 18 ranked players
|-
|-bgcolor=efefef class=sortbottom
|align=left colspan=10|Number 19 ranked players
|-
|-bgcolor=efefef class=sortbottom
|align=left colspan=10|Number 20 ranked players
|-
Wins over top-10 opponents
Raonic has a record against players who were, at the time the match was played, ranked in the top 10. He has registered top 10 victories in consecutive matches during four tournaments: 2012 Chennai Open, 2012 Japan Open, 2013 Thailand Open, and 2014 Paris Masters. He has also registered top 10 wins in consecutive matches once spanning two tournaments;he beat Fernando Verdasco in the final of the 2011 Pacific Coast Championships and again in the first match of the U.S. National Indoor Tennis Championships the following week.* Grand Slam seedings* National representation
Davis Cup (18–6)
Overall, Raonic has 18 match wins in 24 Davis Cup matches (16–5 in singles;2–1 in doubles). He is one of the most successful players in Canadian Davis Cup history, tied for the six most ma |
https://en.wikipedia.org/wiki/Claudinho%20%28footballer%2C%20born%201967%29 | Cláudio Batista dos Santos (born April 19, 1967) is a former Brazilian football player.
Club statistics
References
External links
1967 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J1 League players
Cerezo Osaka players
Men's association football forwards |
https://en.wikipedia.org/wiki/Marcelo%20Mabilia | Marcelo Mabilia, or simply Mabilia (born October 31, 1972, in Porto Alegre), is a Brazilian football manager and former forward.
Club statistics
Honours
Júbilo Iwata
J1 League: 1997
Juventude
Copa do Brasil: 1999
References
External links
1972 births
Living people
Footballers from Porto Alegre
Brazilian men's footballers
J1 League players
Campeonato Brasileiro Série A players
Expatriate men's footballers in Japan
Brazilian football managers
Brazilian expatriate men's footballers
Grêmio Foot-Ball Porto Alegrense players
Sport Club Internacional players
Mogi Mirim Esporte Clube players
Fluminense FC players
Ypiranga Futebol Clube players
Criciúma Esporte Clube players
Júbilo Iwata players
Esporte Clube Juventude players
Guarani FC players
Coritiba Foot Ball Club players
Figueirense FC players
Clube Náutico Capibaribe players
Mogi Mirim Esporte Clube managers
Associação Desportiva São Caetano managers
Esporte Clube Novo Hamburgo managers
Grêmio Foot-Ball Porto Alegrense managers
Esporte Clube Internacional de Lages managers
Tombense Futebol Clube managers
Men's association football forwards |
https://en.wikipedia.org/wiki/Johannes%20Hjelmslev | Johannes Trolle Hjelmslev (; 7 April 1873 – 16 February 1950) was a mathematician from Hørning, Denmark. Hjelmslev worked in geometry and history of geometry. He was the discoverer and eponym of the Hjelmslev transformation, a method for mapping an entire hyperbolic plane into a circle with a finite radius.
He was the father of Louis Hjelmslev.
Originally named Johannes Trolle Petersen, he changed his patronymic to the surname Hjelmslev to avoid confusion with Julius Petersen. Some of his results are known under his original name, including the Petersen–Morley theorem.
Publications
Johannes Hjelmslev, Grundprinciper for den infinitesimale Descriptivgeometri med Anvendelse paa Læren om variable Figurer. Afhandling for den philosophiske Doctorgrad, 1897
Johannes Hjelmslev, Deskriptivgeometri: Grundlag for Forelæsninger paa Polyteknisk Læreanstalt, Jul. Gjellerup 1904
Johannes Hjelmslev, Geometriske Eksperimenter, Jul. Gjellerup 1913
Johannes Hjelmslev, Darstellende Geometrie, Teubner 1914
Johannes Hjelmslev, Geometrische Experimente, Teubner 1915
Johannes Hjelmslev, Lærebog i Geometri til Brug ved den Polytekniske Læreanstalt, Jul. Gjellerup 1918
Johannes Hjelmslev, Die natürliche Geometrie- vier Vorträge, Hamburger Mathematische Einzelschriften 1923
Johannes Hjelmslev, Om et af den danske matematiker Georg Mohr udgivet skrift Euclides Danicus', udkommet i Amsterdam i 1672", Matematisk Tidsskrift B, 1928, pp 1-7
Johannes Hjelmslev, Grundlagen der projektiven Geometrie, 1929
Johannes Hjelmslev, Beiträge zur Lebensbeschreibung von Georg Mohr, Det Kongelige Danske Videnskabernes Selskab, Math.-Fys. Meddelelser, Bd.11, 1931, Nr.4
Johannes Hjelmslev, Grundlag for den projektive Geometri, Gyldendal 1943
See also
Hjelmslev's theorem
References
Gottwald, Ilgauds, Schlote Lexikon bedeutender Mathematiker, Leipzig 1990
External linksSalmonsens Konversationsleksikon, Salmonsens Konversationsleksikon'',
1873 births
1950 deaths
20th-century Danish mathematicians
Geometers
People from Skanderborg Municipality
Academic staff of the University of Copenhagen
Rectors of the University of Copenhagen
Members of the Royal Society of Sciences in Uppsala |
https://en.wikipedia.org/wiki/Periodic%20table%20of%20shapes | The periodic table of mathematical shapes is popular name given to a project to classify Fano varieties. The project was thought up by Professor Alessio Corti, from the Department of Mathematics at Imperial College London. It aims to categorise all three-, four- and five-dimensional shapes into a single table, analogous to the periodic table of chemical elements. It is meant to hold the equations that describe each shape and, through this, mathematicians and other scientists expect to develop a better understanding of the shapes’ geometric properties and relations.
The project has already won the Philip Leverhulme Prize—worth £70,000—from the Leverhulme Trust, and in 2019 a European Research Council grant.
While it is estimated that 500 million shapes can be defined algebraically in four dimensions, they may be decomposable (in the sense of the Minimal model program) into as few as a few thousand "building blocks".
See also
List of complex and algebraic surfaces
List of surfaces
Lists of shapes
List of mathematical shapes
List of two-dimensional geometric shapes
Fano variety
References
External links
Fano Varieties and Extremal Laurent Polynomials A collaborative research blog for the project.
'Periodic Table of Shapes' to Give a New Dimension to Math
Atoms ripple in the periodic table of shapes
Nature's building blocks brought to life
Databases of quantum periods for Fano manifolds by Tom Coates and Alexander M. Kasprzyk
Geometric shapes |
https://en.wikipedia.org/wiki/Stereotomy%20%28descriptive%20geometry%29 | Stereotomy (Greek: στερεός (stereós) "solid" and τομή (tomē) "cut ") is the art and science of cutting three-dimensional solids into particular shapes. Typically this involves materials such as stone or wood which is cut to be assembled into complex structures (wall, vault, arch, etc.). In practice, the engineer makes a drawing of the intended stonework, showing where the joints in the face are to be located, and the stone cutter then details each block and cuts it to fit exactly with the others.
In technical drawing stereotomy is sometimes referred to as descriptive geometry, and "is concerned with two-dimensional representations of three dimensional objects. Plane projections and perspective drawings of solid figures are used to describe and analyze their properties for engineering and manufacturing purposes. Attention is paid to the
properties of surfaces, including normal lines and tangent planes."
References
Descriptive geometry |
https://en.wikipedia.org/wiki/Joseph%20Lawson%20Hodges%20Jr. | Joseph Lawson Hodges Jr. (April 10, 1922 – March 1, 2000) was a statistician. He obtained a Ph.D. in 1949 at the University of California, Berkeley, and joined the statistics faculty there.
Born in 1922 in Shreveport, Louisiana, Hodges grew up in Phoenix, Arizona. He received his B.A. from the University of California in 1942. In the summer of 1944 he joined an Operations analysis group and after some training served in that capacity (together with his fellow budding statisticians Erich Leo Lehmann and George Nicholson) with the Twentieth Air Force on Harmon Air Force Base, Guam. After the war he continued this work for another year in Washington, D.C. There he met Theodora Jane Long, and they married in 1947. He then joined the new statistics program at Berkeley and remained there for the rest of his career.
Hodges is best known for his contributions to the field of statistics, including the Hodges–Lehmann estimator, the nearest neighbor rule (with Evelyn Fix) and Hodges’ estimator.
Bibliography
References
External links
1922 births
2000 deaths
American statisticians
University of California, Berkeley alumni
University of California, Berkeley College of Letters and Science faculty
20th-century American mathematicians
United States Army Air Forces personnel of World War II |
https://en.wikipedia.org/wiki/Jan%20de%20Leeuw | Jan de Leeuw (born December 19, 1945) is a Dutch statistician and psychometrician. He is distinguished professor emeritus of statistics and founding chair of the Department of Statistics, University of California, Los Angeles. In addition, he is the founding editor and former editor-in-chief of the Journal of Statistical Software, as well as the former editor-in-chief of the Journal of Multivariate Analysis and the Journal of Educational and Behavioral Statistics.
Education
Born in Voorburg, De Leeuw attended the Hogere Burgerschool in Voorburg and Alphen aan den Rijn from 1957 to 1963. He studied at Leiden University, where he received his propedeutic examination psychology summa cum laude in 1964; his candidate examination psychology summa cum laude in 1967; and his doctoral examination psychology summa cum laude in 1969. In 1973 he received his PhD cum laude with a thesis entitled "Canonical Analysis of Categorical Data" advised by John P. van de Geer. The thesis described an alternative organization of multivariate data analysis techniques, which formed the basis for the Gifi group in Leiden and the Gifi system more broadly.
Career and research
De Leeuw started his academic career as assistant professor in the Department of Data Theory in Leiden University in 1969. He was member of technical staff, Bell Labs, Murray Hill, New Jersey, in 1973–1974. Back in The Netherlands he was professor of data theory, Leiden University, from 1977 to 1987. In 1987 he moved to University of California, Los Angeles, where he became professor of psychology and mathematics, and director of the interdepartmental program in social statistics until 1998. From 1993 to 1998 he was also acting director of the interdivisional program in statistics. In 1998 to 2014 he became founding chair of the Department of Statistics at University of California, Los Angeles, where he was professor and distinguished professor from 1998 until 2014. After his retirement in July 2014 UCLA Statistics started a yearly De Leeuw Seminar series.
De Leeuw started as associate editor for Psychometrika (1982–1991); was advisory editor at Computational Statistics Quarterly (1983–1990);
associate editor for the Journal of Educational and Behavioral Statistics (1989–1991); editor for the Journal of Educational and Behavioral Statistics (1991–1997); editor for the Journal of Multivariate Analysis (1993–1997); and web editor for Institute of Mathematical Statistics (1996–1999). He is still member of the editorial board of the Journal of Classification (since 1984); member of the advisory board of Applied Stochastic Models and Data Analysis (since 1985); editor for Advanced Quantitative Techniques in the Social Sciences (since 1989) and editor for the Sage/SRM-Database of Social Research Methodology (since 1996). He was founding editor and editor-in-chief of the Journal of Statistical Software (1997–2015) and editor-in-chief for the Journal of Multivariate Analysis (1997–2015).
De Leeuw was el |
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20Euclid | This is a list of topics named after the Greek mathematician Euclid.
Mathematics
Number theory
Euclidean algorithm
Extended Euclidean algorithm
Euclidean division
Euclid–Euler theorem
Euclid number
Euclid's lemma
Euclid's orchard
Euclid–Mullin sequence
Euclid's theorem
Algebra
Euclidean domain
Euclidean field
Geometry
Euclidean group
Euclidean geometry
Non-Euclidean geometry
Euclid's formula
Euclidean distance
Euclidean distance matrix
Euclidean space
Pseudo-Euclidean space
Euclidean vector
Euclidean relation
Euclidean topology
Euclid's fifth postulate
Other
Euclid's Elements
Euclid's Optics
Euclid (spacecraft)
Euclid, Ohio
Euclid, Minnesota
Euclidean rhythm a term coined by Godfried Toussaint in his 2005 paper "The Euclidean Algorithm Generates Traditional Musical Rhythms"
Euclid (computer program)
Euclid (programming language)
Euclid, a supercomputer built by the fictional character Maximillian Cohen in the 1998 film π
Euclid Creek
Euclid Avenue, a street in Manassas, Virginia
Euclid Avenue, a street in Arlington Heights, Illinois
Euclid Avenue, a street in Miami Beach, Florida
Euclid Avenue, a street in Des Moines, Iowa
Euclid St, a street in Orange County, California
Euclid Avenue, a street in Toronto, Ontario
Euclid, an object designation within the SCP Foundation stories, denoting an anomaly that is difficult, but fairly straightforward to contain.
Mount Euclid in New Zealand's Paparoa Range was named after him in 1970 by the Department of Scientific and Industrial Research.
Euclidate
References
Euclid |
https://en.wikipedia.org/wiki/Transactions%20of%20the%20Kansas%20Academy%20of%20Science | Transactions of the Kansas Academy of Science is a biannual peer-reviewed academic journal published by the Kansas Academy of Science. The journal covers biological and physical sciences, mathematics and computer science, history, culture, and philosophy of science, and science education. The journal is abstracted and indexed in The Zoological Record and BIOSIS Previews.
References
External links
Multidisciplinary scientific journals
Publications established in 1872
English-language journals
Biannual journals
1872 establishments in Kansas
Academic journals published by learned and professional societies |
https://en.wikipedia.org/wiki/No%20small%20subgroup | In mathematics, especially in topology, a topological group is said to have no small subgroup if there exists a neighborhood of the identity that contains no nontrivial subgroup of An abbreviation '"NSS"' is sometimes used. A basic example of a topological group with no small subgroup is the general linear group over the complex numbers.
A locally compact, separable metric, locally connected group with no small subgroup is a Lie group. (cf. Hilbert's fifth problem.)
See also
References
M. Goto, H., Yamabe, On some properties of locally compact groups with no small group
Group theory
05
Lie groups
Topological groups |
https://en.wikipedia.org/wiki/Peter%20Tr%C5%A1ka | Peter Trška (born 1 June 1992) is a Slovak professional ice hockey defenceman who currently plays for Selber Wölfe of the Deutsche Eishockey Liga 2 (DEL2).
Career statistics
Regular season and playoffs
International
References
External links
1992 births
Living people
People from Dubnica nad Váhom
Ice hockey people from the Trenčín Region
Slovak ice hockey defencemen
VHK Vsetín players
HC Slovan Bratislava players
HK 36 Skalica players
BK Mladá Boleslav players
HC Benátky nad Jizerou players
HC Kometa Brno players
HC Vítkovice players
PSG Berani Zlín players
Fischtown Pinguins players
Slovak expatriate ice hockey players in Germany
Slovak expatriate ice hockey players in the Czech Republic |
https://en.wikipedia.org/wiki/Miroslav%20Preisinger | Miroslav Preisinger (born 3 February 1991) is a Slovak professional ice hockey player who currently playing for HC Slovan Bratislava of the Slovak Extraliga.
Career statistics
Regular season and playoffs
International
Awards and honors
References
External links
1991 births
Living people
HC '05 Banská Bystrica players
HC Plzeň players
Sarnia Sting players
HK 36 Skalica players
Slovak ice hockey centres
HK Poprad players
HKM Zvolen players
HC Slovan Bratislava players
Ice hockey people from Bratislava
Slovak expatriate ice hockey players in Canada
Slovak expatriate ice hockey players in the Czech Republic |
https://en.wikipedia.org/wiki/Lyryx%20Learning | Lyryx Learning (Lyryx) is an educational software company offering open educational resources (OERs) paired with online homework & exams for undergraduate introductory courses in Mathematics & Statistics and Business & Economics.
History
In 1997, Claude Laflamme and Keith Nicholson, Professors in the Department of Mathematics and Statistics at the University of Calgary, began work on the design of online tools to support student learning in their classes. Laflamme and Nicholson developed and implemented a formative assessment system which provided immediate, substantive feedback to students based on their work.
In 2000, Laflamme and Nicholson, together with two software developers, Bruce Bauslaugh and Richard Cannings, formed Lyryx Learning Inc., to offer this platform in a number of quantitative disciplines. By 2010, Lyryx supported approximately 100,000 students and 2,000 instructors per year in Canada.
After several years of developing formative online assessment for content from various publishers, including McGraw-Hill Ryerson in Canada and Flat World Knowledge in the US, Lyryx became a fully independent publisher supporting OERs in 2013, with the launch of Lyryx with Open Texts.
Lyryx with Open Texts
To support the use of OERs in undergraduate introductory courses in Mathematics & Statistics and Business & Economics, Lyryx moved to a social enterprise business model: Funding from the online homework supports both the development and maintenance of OERs as well as contributions to the community. In addition, Lyryx also offers an option of free access to their online homework from an institution's computer labs.
Lyryx with Open Texts includes:
Adapted Open Texts: Open textbooks which can be distributed at no cost, and editorial services to adapt the open textbooks for each specific course. All textbooks are licensed under a Creative Commons license.
Formative Online Assessment: Algorithmically generated homework and exam questions are automatically graded, and individualized feedback is also provided to the student.
Course Supplements: A wide variety of materials to support the instructor including slides, solutions manuals, and test banks. For select products, Lyryx offers source codes in an editable format in LaTeX.
User Support: In-house support for both instructors and students, 365 days/year.
List of Textbooks
Accounting
Introduction to Financial Accounting
Introduction to Financial Accounting: US GAAP
Intermediate Financial Accounting Volume I
Intermediate Financial Accounting Volume II
Economics
Principles of Microeconomics
Principles of Macroeconomics
Principles of Economics
Mathematics
Calculus: Early Transcendentals
Linear Algebra with Applications
A First Course in Linear Algebra
Business Mathematics
Business Math: A Step-by-Step Handbook
Repositories
In addition to lyryx.com, Lyryx Learning open textbooks are also listed in the following repositories:
Merlot
OER Commons
BCcampus
Manitoba Open Textboo |
https://en.wikipedia.org/wiki/1983%E2%80%9384%20Yemeni%20League | Statistics of the Yemeni League for the 1983–84 season.
Results
North Yemen
South Yemen
References
Yemeni League seasons
1984 in Yemeni sport
1983 in Yemeni sport |
https://en.wikipedia.org/wiki/Lambda-connectedness | In applied mathematics, lambda-connectedness (or λ-connectedness) deals with partial connectivity for a discrete space.
Assume that a function on a discrete space (usually a graph) is given. A degree of connectivity (connectedness) will be defined to measure the connectedness of the space with respect to the function. It was invented to create a new method for image segmentation. The method has expanded to handle other problems related to uncertainty for incomplete information analysis.
For a digital image and a certain value of , two pixels are called -connected if there is a path linking those two pixels and the connectedness of this path is at least . -connectedness is an equivalence relation.
Background
Connectedness is a basic measure in many areas of mathematical science and social sciences. In graph theory, two vertices are said to be connected if there is a path between them. In topology, two points are connected if there is a continuous function that could move from one point to another continuously. In management science, for example, in an institution, two individuals are connected if one person is under the supervision of the other. Such connected relations only describe either full connection or no connection. lambda-connectedness is introduced to measure incomplete or fuzzy relations between two vertices, points, human beings, etc.
In fact, partial relations have been studied in other aspects. Random graph theory allows one to assign a probability to each edge of a graph. This method assumes, in most cases, each edge has the same probability. On the other hand, Bayesian networks are often used for inference and analysis when relationships between each pair of states/events, denoted by vertices, are known. These relationships are usually represented by conditional probabilities among these vertices and are usually obtained from outside of the system.
-connectedness is based on graph theory; however, graph theory only deals with vertices and edges with or without weights. In order to define a partial, incomplete, or fuzzy connectedness, one needs to assign a function on the vertex in the graph. Such a function is called a potential function. It can be used to represent the intensity of an image, the surface of a XY-domain, or the utility function of a management or economic network.
Basic concepts
A generalized definition of -connectedness can be described as follows: a simple system , where is called a potential function of . If is an image, then is a 2D or 2D grid space and is an intensity function. For a color image, one can use to represent .
Neighbor connectivity will be first defined on a pair of adjacent points. Then one can define the general connectedness for any two points.
Assume is used to measure the neighbor-connectivity of x,y where x and y are adjacent.
In graph G = (V, E), a finite sequence is called a path, if .
The path-connectivity of a path
is defined as
Finally, the degree of conne |
https://en.wikipedia.org/wiki/Daniel%20%28footballer%2C%20born%201970%29 | Daniel Conceicao Silva (born October 10, 1970) is a former Brazilian football player.
Club statistics
References
External links
kyotosangadc
1970 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J1 League players
Kyoto Sanga FC players
Vissel Kobe players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Pseudospectral%20knotting%20method | In applied mathematics, the pseudospectral knotting method is a generalization and enhancement of a standard pseudospectral method for optimal control. The concept was introduced by I. Michael Ross and F. Fahroo in 2004, and forms part of the collection of the Ross–Fahroo pseudospectral methods.
Definition
According to Ross and Fahroo a pseudospectral (PS) knot is a double Lobatto point; i.e. two boundary points on top of one another. At this point, information (such as discontinuities, jumps, dimension changes etc.) is exchanged between two standard PS methods. This information exchange is used to solve some of the most difficult problems in optimal control known as hybrid optimal control problems.
In a hybrid optimal control problem, an optimal control problem is intertwined with a graph problem. A standard pseudospectral optimal control method is incapable of solving such problems; however, through the use of pseudospectral knots, the information of the graph can be encoded at the double Lobatto points thereby allowing a hybrid optimal control problem to be discretized and solved using powerful software such as DIDO.
Applications
PS knots have found applications in aerospace problems such as the ascent guidance of a launch vehicles, and advancing the Aldrin Cycler through the use of solar sails.
PS knots have also been used for anti-aliasing of PS optimal control solutions and for capturing critical information in switches in solving bang-bang-type optimal control problems.
Software
The PS knotting method was first implemented in the MATLAB optimal control software package, DIDO.
See also
Legendre pseudospectral method
Chebyshev pseudospectral method
Ross–Fahroo lemma
Ross' π lemma
Ross–Fahroo pseudospectral methods
References
Optimal control
Numerical analysis
Control theory |
https://en.wikipedia.org/wiki/List%20of%20integrals%20of%20Gaussian%20functions | In the expressions in this article,
is the standard normal probability density function,
is the corresponding cumulative distribution function (where erf is the error function), and
is Owen's T function.
Owen has an extensive list of Gaussian-type integrals; only a subset is given below.
Indefinite integrals
In the previous two integrals, is the double factorial: for even it is equal to the product of all even numbers from 2 to , and for odd it is the product of all odd numbers from 1 to ; additionally it is assumed that .
Definite integrals
References
Gaussian functions
Gaussian function |
https://en.wikipedia.org/wiki/Lee%20Jong-min%20%28footballer%2C%20born%201987%29 | Lee Jong-Min (; 21 May 1987) is a South Korean footballer
Club statistics
References
External links
1987 births
Living people
Men's association football defenders
South Korean men's footballers
South Korean expatriate men's footballers
J1 League players
J2 League players
Japan Football League players
Montedio Yamagata players
Tochigi SC players
Avispa Fukuoka players
Matsumoto Yamaga FC players
Expatriate men's footballers in Japan
South Korean expatriate sportspeople in Japan
Footballers from Gyeonggi Province |
https://en.wikipedia.org/wiki/Kentaro%20Shigematsu | is a Japanese football player who currently plays for Kamatamare Sanuki.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Kamatamare Sanuki
Profile at Machida Zelvia
1991 births
Living people
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
J3 League players
FC Tokyo players
Avispa Fukuoka players
Ventforet Kofu players
Ehime FC players
Tochigi SC players
FC Machida Zelvia players
Kamatamare Sanuki players
Men's association football forwards |
https://en.wikipedia.org/wiki/PhysMath%20School%2C%20Yerevan | Officially the Physics and Mathematics Specialized School named after Artashes Shahinyan under the Yerevan State University, colloquially known as PhysMath School, is a state-owned high school located in Yerevan, Armenia. It is currently among the leading educational complexes in Yerevan. The school has a branch in Stepanakert; the capital of the unrecognized state of Artsakh.
Overview
The PhysMath School was founded in 1965 in affiliation with the Yerevan State University and through the efforts of professor Artashes Shahinyan. Following the death of Shahinyan in 1978, the school was named after him.
The school is known for its role in preparing physics and mathematics teachers. It was ranked 1st in Armenia for the 2013-14 educational year.
The current headmaster of the school is Armen Sargsyan, serving since 2002.
References
External links
Official website
Education in Yerevan
Schools in Armenia
Schools in the Soviet Union
1965 establishments in the Soviet Union |
https://en.wikipedia.org/wiki/Permocalculus | Permocalculus is a genus of red algae known from Permian to Cretaceous strata. Closely aligned to Gymnocodium, it is placed in the Gymnocodiaceae.
References
Fossil algae
Red algae genera
Permian first appearances
Cretaceous extinctions
Enigmatic red algae taxa |
https://en.wikipedia.org/wiki/Principle%20of%20permanence | In the history of mathematics, the principle of permanence, or law of the permanence of equivalent forms, was the idea that algebraic operations like addition and multiplication should behave consistently in every number system, especially when developing extensions to established number systems.
Before the advent of modern mathematics and its emphasis on the axiomatic method, the principle of permanence was considered an important tool in mathematical arguments. In modern mathematics, arguments have instead been supplanted by rigorous proofs built upon axioms, and the principle is instead used as a heuristic for discovering new algebraic structures. Additionally, the principle has been formalized into a class of theorems called transfer principles, which state that all statements of some language that are true for some structure are true for another structure.
History
The principle was described by George Peacock in his book A Treatise of Algebra (emphasis in original):
132. Let us again recur to this principle or law of the permanence of equivalent forms, and consider it when stated in the form of a direct and converse proportion.
"Whatever form is Algebraically equivalent to another, when expressed in general symbols, must be true, whatever those symbols denote."
Conversely, if we discover an equivalent form in Arithmetical Algebra or any other subordinate science, when the symbols are general in form though specific in their nature, the same must be an equivalent form, when the symbols are general in their nature as well as in their form.
The principle was later revised by Hermann Hankel and adopted by Giuseppe Peano, Ernst Mach, Hermann Schubert, Alfred Pringsheim, and others.
Around the same time period as A Treatise of Algebra, Augustin-Louis Cauchy published Cours d'Analyse, which used the term "generality of algebra" to describe (and criticize) a method of argument used by 18th century mathematicians like Euler and Lagrange that was similar to the Principle of Permanence.
Applications
One of the main uses of the principle of permanence is to show that a functional equation that holds for the real numbers also holds for the complex numbers.
As an example, the equation hold for all real numbers s, t. By the principle of permanence for functions of two variables, this suggests that it holds for all complex numbers as well.
For a counter example, consider the following properties
commutativity of addition: for all ,
left-cancellative property of addition: if , then , for all .
Both properties hold for all natural, integer, rational, real, and complex numbers.
However, when, following Georg Cantor, natural numbers are extended beyond infinity, no systems are known that satisfy both properties simultaneously.
In ordinal arithmetic, addition is left-cancellative, but no longer commutative. For example, .
In cardinal arithmetic, addition is commutative, but no longer left-cancellative, since whenever or is infinite. For exam |
https://en.wikipedia.org/wiki/Adam%20Lap%C5%A1ansk%C3%BD | Adam Lapšanský (born 10 April 1990) is a Slovak professional ice hockey player who currently playing for HC Nové Zámky of the Slovak Extraliga.
Career statistics
Regular season and playoffs
International
Awards and honours
References
External links
Living people
HK Poprad players
MHK Kežmarok players
HC Sparta Praha players
Piráti Chomutov players
HC Litvínov players
HC Stadion Litoměřice players
HC Slovan Ústečtí Lvi players
HC Košice players
Indy Fuel players
Ravensburg Towerstars players
HC Karlovy Vary players
HK Dukla Trenčín players
Bratislava Capitals players
Slovak ice hockey forwards
1990 births
Sportspeople from Spišská Nová Ves
Ice hockey people from the Košice Region
HK Dukla Michalovce players
HC Nové Zámky players
Slovak expatriate ice hockey players in the Czech Republic
Slovak expatriate ice hockey players in Germany |
https://en.wikipedia.org/wiki/Mat%C3%BA%C5%A1%20Palo%C4%8Dko | Matúš Paločko (born 23 December 1990) is a Slovak professional ice hockey player currently playing for HK Dukla Michalovce of the Slovak Extraliga.
Career statistics
Regular season and playoffs
References
External links
Living people
Slovak ice hockey forwards
1990 births
HK Poprad players
HC Prešov players
HC Stadion Litoměřice players
HK Spišská Nová Ves players
MHk 32 Liptovský Mikuláš players
HK Dukla Michalovce players
Ice hockey people from Poprad
Slovak expatriate ice hockey players in the Czech Republic |
https://en.wikipedia.org/wiki/Michael%20Vandas | Michael Vandas (born 2 February 1991) is a Slovak professional ice hockey player who currently playing for HK Spišská Nová Ves of the Slovak Extraliga.
Career statistics
Regular season and playoffs
International
References
External links
Living people
Slovak ice hockey forwards
1991 births
HK Poprad players
HC Vítkovice players
HC Litvínov players
HKM Zvolen players
HC Slovan Bratislava players
HK Spišská Nová Ves players
Ice hockey people from Poprad
Slovak expatriate ice hockey players in the Czech Republic
Slovak expatriate ice hockey players in the United States |
https://en.wikipedia.org/wiki/Samuel%20Tak%C3%A1%C4%8D | Samuel Takáč (born 3 December 1991) is a Slovak professional ice hockey player for HC Slovan Bratislava of the Slovak Extraliga.
Career statistics
Regular season and playoffs
Bold indicates led league
International
Awards and honors
References
External links
1991 births
Living people
Slovak ice hockey centres
Ice hockey people from Poprad
HK Poprad players
HK Dukla Michalovce players
Rapaces de Gap players
LHC Les Lions players
HC Slovan Bratislava players
Ice hockey players at the 2022 Winter Olympics
Olympic ice hockey players for Slovakia
Medalists at the 2022 Winter Olympics
Olympic bronze medalists for Slovakia
Olympic medalists in ice hockey
Expatriate ice hockey players in France
Slovak expatriate ice hockey people
Slovak expatriate sportspeople in France |
https://en.wikipedia.org/wiki/Tom%C3%A1%C5%A1%20Troliga | Tomáš Troliga (born 24 April 1984) is a Slovak professional ice hockey player who played with HK SKP Poprad in the Slovak Extraliga during the 2010–11 season.
Career statistics
Regular season and playoffs
International
External links
Living people
HK Poprad players
Slovak ice hockey forwards
Sportspeople from Prešov
Ice hockey people from the Prešov Region
St. Louis Blues draft picks
1984 births
Slovak expatriate ice hockey players in Canada
Slovak expatriate ice hockey players in the United States
Slovak expatriate ice hockey players in the Czech Republic |
https://en.wikipedia.org/wiki/Jaroslav%20Kas%C3%ADk | Jaroslav Kasík is a Czech professional ice hockey defenceman who played with HK SKP Poprad in the Slovak Extraliga during the 2010–11 season.
Career statistics
External links
Living people
1983 births
BK Mladá Boleslav players
HC Berounští Medvědi players
HC Kobra Praha players
HC Oceláři Třinec players
HC Slovan Ústečtí Lvi players
HC Sparta Praha players
HC Vítkovice players
HK Poprad players
Motor České Budějovice players
Piráti Chomutov players
Czech ice hockey defencemen
Ice hockey people from Prague
Czech expatriate ice hockey players in Slovakia |
https://en.wikipedia.org/wiki/%C4%BDubom%C3%ADr%20Malina | Ľubomír Malina (born August 15, 1991) is a Slovak professional ice hockey defenceman who currently plays professionally in Slovakia for HK Spišská Nová Ves of the Slovak Extraliga.
Career statistics
Regular season and playoffs
References
External links
1991 births
Living people
Slovak ice hockey defencemen
People from Kežmarok
Ice hockey people from the Prešov Region
HK Poprad players
HK Spišská Nová Ves players
HC ZUBR Přerov players
AZ Havířov players
MsHK Žilina players
Slovak expatriate ice hockey players in the Czech Republic |
https://en.wikipedia.org/wiki/Tom%C3%A1%C5%A1%20N%C3%A1da%C5%A1di | Tomáš Nádašdi (born May 14, 1980) is a Slovak former professional ice hockey defenceman.
Career statistics
Regular season and playoffs
External links
Living people
HK Poprad players
HC Košice players
Rytíři Kladno players
Slovak ice hockey defencemen
1980 births
Sportspeople from Spišská Nová Ves
Ice hockey people from the Košice Region
Slovak expatriate ice hockey players in the Czech Republic
Expatriate ice hockey players in Denmark
Slovak expatriate sportspeople in Denmark |
https://en.wikipedia.org/wiki/Minhyong%20Kim | Minhyong Kim is a South Korean mathematician who specialises in arithmetic geometry and anabelian geometry.
Biography
Kim received his PhD at Yale University in 1990 under the supervision of Serge Lang and Barry Mazur, going on to work in a number of universities, including M.I.T., Columbia, Arizona, Purdue, the Korea Institute for Advanced Study, UCL (University College London) and the University of Oxford. He is currently the Christopher Zeeman Professor of Algebra, Geometry, and Public Understanding of Mathematics at University of Warwick.
Research
Kim has made contributions to the application of arithmetic homotopy theory to the study of Diophantine problems, especially to finiteness theorems of the Faltings–Siegel type.
His work was featured in 2017 in the Quanta Magazine, where he described his work as being inspired by physics.
Awards
In 2012, Minhyong Kim received the Ho-Am Prize for Science, with the Ho-Am committee citing him as "one of the leading researchers in the area of arithmetic algebraic geometry".
Education
1982 - 1985 B.S. Department of Mathematics, Seoul National University
1985 - 1990 Ph.D. Department of Mathematics, Yale University
Work
1990 – 1993 C. L. E. Moore Instructor, Massachusetts Institute of Technology
1993 – 1996 J.F. Ritt Assistant Professor, Columbia University
1995 – 2007 Assistant Professor, Associate Professor, and Professor, University of Arizona
2001 – 2002 Professor, Korea Institute for Advanced Study
2005 – 2007 Professor, Purdue University
2007 – 2011 Chair of Pure Mathematics, University College London
2010 – 2013 Yun San Chair Professor, Pohang University of Science and Technology
2011 – 2020 Professor of Number Theory and Fellow of Merton College, University of Oxford
2013 – Present Invited Chair Professor, Seoul National University
2020 - Present Christopher Zeeman Professor of Algebra, Geometry, and Public Understanding of Mathematics, University of Warwick
Grants and awards
1991 - 1993 NSF grant DMS-9106444
1997 - 2001 NSF grant DMS-9701489 : 'Effective Diophantine Geometry over Function Fields'.
1998 - 2002 NSF Group Infrastructure Grant : 'Southwestern Center for Arithmetic Geometry', Co-PI with six other researchers from the University of Arizona, UTexas Austin, USC, and the University of New Mexico.
2003 - 2006 NSF Infrastructure grant : 'Southwestern Center for Arithmetic Geometry', Co-PI with nine other researchers from the University of Arizona, UTexas Austin, USC, UC Berkeley, and the University of New Mexico.
2005 - 2008 NSF grant DMS-0500504 : 'Motivic fundamental groups, multiple polylogarithms, and Diophantine geometry'.
2006 - 2008 Japan Society for the Promotion of Science, Core-to-Core program 'New Developments of Arithmetic Geometry, Motive, Galois Theory, and Their Practical Applications,' Foreign member
2008 EPSRC grant, 46437, for workshop 'Non-commutative constructions in arithmetic and geometry'
2009 EPSRC grant, EP/G024979/1, 3- |
https://en.wikipedia.org/wiki/Ending%20lamination%20theorem | In hyperbolic geometry, the ending lamination theorem, originally conjectured by , states that hyperbolic 3-manifolds with finitely generated fundamental groups are determined by their topology together with certain "end invariants", which are geodesic laminations on some surfaces in the boundary of the manifold.
The ending lamination theorem is a generalization of the Mostow rigidity theorem to hyperbolic manifolds of infinite volume. When the manifold is compact or of finite volume, the Mostow rigidity theorem states that the fundamental group determines the manifold. When the volume is infinite the fundamental group is not enough to determine the manifold: one also needs to know the hyperbolic structure on the surfaces at the "ends" of the manifold, and also the ending laminations on these surfaces.
and proved the ending lamination conjecture for Kleinian surface groups. In view of the Tameness theorem this implies the ending lamination conjecture for all finitely generated Kleinian groups, from which the general case of ELT follows.
Ending laminations
Ending laminations were introduced by .
Suppose that a hyperbolic 3-manifold has a geometrically tame end of the form S×[0,1) for some compact surface S without boundary, so that S can be thought of as the "points at infinity" of the end. The ending lamination of this end is (roughly) a lamination on the surface S, in other words a closed subset of S that is written as the disjoint union of geodesics of S. It is characterized by the following property. Suppose that there is a sequence of closed geodesics on S whose lifts tends to infinity in the end. Then the limit of these simple geodesics is the ending lamination.
References
Hyperbolic geometry
3-manifolds
Kleinian groups |
https://en.wikipedia.org/wiki/Albert%20Tom%C3%A0s | Albert Tomàs Sobrepera (born December 19, 1970) is a former Spanish football player.
Club statistics
References
External links
odn.ne.jp
1970 births
Living people
Spanish men's footballers
Spanish expatriate men's footballers
J1 League players
La Liga players
Segunda División players
Segunda División B players
FC Barcelona players
FC Barcelona C players
FC Barcelona Atlètic players
UE Lleida players
Albacete Balompié players
CD Toledo players
Levante UD footballers
Gimnàstic de Tarragona footballers
CE Sabadell FC footballers
Vissel Kobe players
Spanish expatriate sportspeople in Japan
Expatriate men's footballers in Japan
Men's association football defenders
Catalonia men's international footballers
Footballers from Barcelona |
https://en.wikipedia.org/wiki/Bui%C3%BA%20%28footballer%2C%20born%201980%29 | Aldieres Joaquim dos Santos Neto (born 5 May 1980), known as Buiú, is a former Brazilian football player.
Club statistics
References
External links
odn.ne.jp
1980 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J1 League players
Kashiwa Reysol players
Campeonato Paranaense players
Mirassol Futebol Clube players
Coritiba Foot Ball Club players
Expatriate men's footballers in Japan
Brazilian expatriate sportspeople in Japan
Men's association football midfielders
People from Monte Aprazível
Footballers from São Paulo (state) |
https://en.wikipedia.org/wiki/Marc%C3%A3o%20%28footballer%2C%20born%201965%29 | Marco Antônio de Almeida Ferreira, sometimes known as Marcão (born December 20, 1965), is a Brazilian former football player.
Club statistics
References
External links
odn.ne.jp
1965 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J1 League players
Kashiwa Reysol players
Expatriate men's footballers in Japan
Men's association football defenders |
https://en.wikipedia.org/wiki/Fabinho%20%28footballer%2C%20born%201974%29 | Fabio Augusto Justino (born June 16, 1974), known as Fabinho, is a former Brazilian football player.
Club statistics
References
External links
geocities.jp
1974 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J1 League players
Shimizu S-Pulse players
Vissel Kobe players
Men's association football forwards |
https://en.wikipedia.org/wiki/Edwin%20Ifeanyi | Edwin Ifeanyi (born April 28, 1972) is a former Cameroonian football player.
Club statistics
National team statistics
References
External links
1972 births
Living people
Cameroonian men's footballers
Cameroonian expatriate men's footballers
J1 League players
J2 League players
Japan Football League (1992–1998) players
FC Tokyo players
Tokyo Verdy players
Omiya Ardija players
Oita Trinita players
Montedio Yamagata players
Expatriate men's footballers in Japan
Men's association football midfielders
Cameroon men's international footballers |
https://en.wikipedia.org/wiki/Lutz%20Sch%C3%BClbe | Lutz Schülbe (born 9 November 1961) is a German former footballer.
Career statistics
Notes
References
External links
1961 births
Living people
German men's footballers
East German men's footballers
Dynamo Dresden players
Hallescher FC players
DDR-Oberliga players
Men's association football forwards |
https://en.wikipedia.org/wiki/Sum%20of%20squares | In mathematics, statistics and elsewhere, sums of squares occur in a number of contexts:
Statistics
For partitioning of variance, see Partition of sums of squares
For the "sum of squared deviations", see Least squares
For the "sum of squared differences", see Mean squared error
For the "sum of squared error", see Residual sum of squares
For the "sum of squares due to lack of fit", see Lack-of-fit sum of squares
For sums of squares relating to model predictions, see Explained sum of squares
For sums of squares relating to observations, see Total sum of squares
For sums of squared deviations, see Squared deviations from the mean
For modelling involving sums of squares, see Analysis of variance
For modelling involving the multivariate generalisation of sums of squares, see Multivariate analysis of variance
Number theory
For the sum of squares of consecutive integers, see Square pyramidal number
For representing an integer as a sum of squares of 4 integers, see Lagrange's four-square theorem
Legendre's three-square theorem states which numbers can be expressed as the sum of three squares
Jacobi's four-square theorem gives the number of ways that a number can be represented as the sum of four squares.
For the number of representations of a positive integer as a sum of squares of k integers, see Sum of squares function.
Fermat's theorem on sums of two squares says which primes are sums of two squares.
The sum of two squares theorem generalizes Fermat's theorem to specify which composite numbers are the sums of two squares.
Pythagorean triples are sets of three integers such that the sum of the squares of the first two equals the square of the third.
A Pythagorean prime is a prime that is the sum of two squares; Fermat's theorem on sums of two squares states which primes are Pythagorean primes.
Pythagorean triangles with integer altitude from the hypotenuse have the sum of squares of inverses of the integer legs equal to the square of the inverse of the integer altitude from the hypotenuse.
Pythagorean quadruples are sets of four integers such that the sum of the squares of the first three equals the square of the fourth.
The Basel problem, solved by Euler in terms of , asked for an exact expression for the sum of the squares of the reciprocals of all positive integers.
Rational trigonometry's triple-quad rule and triple-spread rule contain sums of squares, similar to Heron's formula.
Squaring the square is a combinatorial problem of dividing a two-dimensional square with integer side length into smaller such squares.
Algebra and algebraic geometry
For representing a polynomial as the sum of squares of polynomials, see Polynomial SOS.
For computational optimization, see Sum-of-squares optimization.
For representing a multivariate polynomial that takes only non-negative values over the reals as a sum of squares of rational functions, see Hilbert's seventeenth problem.
The Brahmagupta–Fibonacci identity says the set of all s |
https://en.wikipedia.org/wiki/Arun%20Sundararajan | Arun Sundararajan (Tamil: அருண் சுந்தர்ராஜன்) (born in the United Kingdom) is the NEC Faculty Fellow, Professor of Technology, Operations, and Statistics and a Doctoral Coordinator at the Stern School of Business, New York University. For 2010–12, he is the Distinguished Academic Fellow at the Center for IT and the Networked Economy, Indian School of Business. Sundararajan is an expert on the economics of digital goods and network effects. He also conducts research about network science and the socioeconomic transformation of India.
Life and work
Arun Sundararajan graduated from the Indian Institute of Technology Madras in 1993 with a BTech in electrical engineering. He subsequently attended the University of Rochester where he received an M. Phil in operations research and a PhD in business administration. After he earned his doctorate, he joined the faculty at New York University, where his work focuses on the transformation of business and society by information technologies, and the Indian economy.
Sundararajan's scholarly research analyzes what makes the economics of IT products and industries unique. He asserts that there are three technological invariants—digitization, exponential growth, and modularity—that have characterized and distinguished information technologies since the 1960s, and that these invariants lead to the ubiquity of information goods, digital piracy and network effects in IT industries. His research papers illustrate how these distinctive economics of information technologies warrant new pricing strategies, careful digital rights management, and a deeper understanding of network structure and dynamics.
Sundararajan periodically writes and speaks about transformation through information technologies and business with a frequent focus on privacy and on India.
He has been elected to the editorial boards of the prestigious journals Management Science and Information Systems Research (where he is currently a Senior Editor). He co-founded the NYU Summer Workshop on the Economics of Information Technology and the Workshop on Information in Networks. He received a 2010 Google-WPP Marketing Research Award, the Best Paper award at the 2008 INFORMS Conference on Information Systems and Technology, and the Best Overall Paper award at the 2004 International Conference on Information Systems.
See also
Digital rights management
Network effects
Price discrimination
Sharing economy
Bibliography
Patent:
Book:
References
External links
Arun Sundararajan's personal web page
NYU Stern Faculty Page
Center for IT and the Networked Economy, Indian School of Business
Living people
New York University Stern School of Business faculty
University of Rochester alumni
21st-century American economists
Information systems researchers
Indian emigrants to the United States
Scientists from Chennai
Year of birth missing (living people)
IIT Madras alumni |
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