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https://en.wikipedia.org/wiki/Shuffle%20algebra | In mathematics, a shuffle algebra is a Hopf algebra with a basis corresponding to words on some set, whose product is given by the shuffle product X ⧢ Y of two words X, Y: the sum of all ways of interlacing them. The interlacing is given by the riffle shuffle permutation.
The shuffle algebra on a finite set is the graded dual of the universal enveloping algebra of the free Lie algebra on the set.
Over the rational numbers, the shuffle algebra is isomorphic to the polynomial algebra in the Lyndon words.
The shuffle product occurs in generic settings in non-commutative algebras; this is because it is able to preserve the relative order of factors being multiplied together - the riffle shuffle permutation. This can be held in contrast to the divided power structure, which becomes appropriate when factors are commutative.
Shuffle product
The shuffle product of words of lengths m and n is a sum over the ways of interleaving the two words, as shown in the following examples:
ab ⧢ xy = abxy + axby + xaby + axyb + xayb + xyab
aaa ⧢ aa = 10aaaaa
It may be defined inductively by
u ⧢ ε = ε ⧢ u = u
ua ⧢ vb = (u ⧢ vb)a + (ua ⧢ v)b
where ε is the empty word, a and b are single elements, and u and v are arbitrary words.
The shuffle product was introduced by . The name "shuffle product" refers to the fact that the product can be thought of as a sum over all ways of riffle shuffling two words together: this is the riffle shuffle permutation. The product is commutative and associative.
The shuffle product of two words in some alphabet is often denoted by the shuffle product symbol ⧢ (Unicode character U+29E2 , derived from the Cyrillic letter sha).
Infiltration product
The closely related infiltration product was introduced by . It is defined inductively on words over an alphabet A by
fa ↑ ga = (f ↑ ga)a + (fa ↑ g)a + (f ↑ g)a
fa ↑ gb = (f ↑ gb)a + (fa ↑ g)b
For example:
ab ↑ ab = ab + 2aab + 2abb + 4 aabb + 2abab
ab ↑ ba = aba + bab + abab + 2abba + 2baab + baba
The infiltration product is also commutative and associative.
See also
Hopf algebra of permutations
Zinbiel algebra
References
External links
Shuffle product symbol
Combinatorics
Algebra |
https://en.wikipedia.org/wiki/Pansu%20derivative | In mathematics, the Pansu derivative is a derivative on a Carnot group, introduced by . A Carnot group admits a one-parameter family of dilations, . If and are Carnot groups, then the Pansu derivative of a function at a point is the function defined by
provided that this limit exists.
A key theorem in this area is the Pansu–Rademacher theorem, a generalization of Rademacher's theorem, which can be stated as follows: Lipschitz continuous functions between (measurable subsets of) Carnot groups are Pansu differentiable almost everywhere.
References
Lie groups |
https://en.wikipedia.org/wiki/Carnot%20group | In mathematics, a Carnot group is a simply connected nilpotent Lie group, together with a derivation of its Lie algebra such that the subspace with eigenvalue 1 generates the Lie algebra. The subbundle of the tangent bundle associated to this eigenspace is called horizontal. On a Carnot group, any norm on the horizontal subbundle gives rise to a Carnot–Carathéodory metric. Carnot–Carathéodory metrics have metric dilations; they are asymptotic cones (see Ultralimit) of finitely-generated nilpotent groups, and of nilpotent Lie groups, as well as tangent cones of sub-Riemannian manifolds.
Formal definition and basic properties
A Carnot (or stratified) group of step is a connected, simply connected, finite-dimensional Lie group whose Lie algebra admits a step- stratification. Namely, there exist nontrivial linear subspaces such that
, for , and .
Note that this definition implies the first stratum generates the whole Lie algebra .
The exponential map is a diffeomorphism from onto . Using these exponential coordinates, we can identify with , where and the operation is given by the Baker–Campbell–Hausdorff formula.
Sometimes it is more convenient to write an element as
with for .
The reason is that has an intrinsic dilation operation given by
.
Examples
The real Heisenberg group is a Carnot group which can be viewed as a flat model in Sub-Riemannian geometry as Euclidean space in Riemannian geometry. The Engel group is also a Carnot group.
History
Carnot groups were introduced, under that name, by and . However, the concept was introduced earlier by Gerald Folland (1975), under the name stratified group.
See also
Pansu derivative, a derivative on a Carnot group introduced by
References
Lie groups |
https://en.wikipedia.org/wiki/Max%E2%80%93min%20inequality | In mathematics, the max–min inequality is as follows:
For any function
When equality holds one says that , , and satisfies a strong max–min property (or a saddle-point property). The example function illustrates that the equality does not hold for every function.
A theorem giving conditions on , , and which guarantee the saddle point property is called a minimax theorem.
Proof
Define For all , we get for all by definition of the infimum being a lower bound. Next, for all , for all by definition of the supremum being an upper bound. Thus, for all and , making an upper bound on for any choice of . Because the supremum is the least upper bound, holds for all . From this inequality, we also see that is a lower bound on . By the greatest lower bound property of infimum, . Putting all the pieces together, we get
which proves the desired inequality.
References
See also
Minimax theorem
Mathematical optimization
Inequalities |
https://en.wikipedia.org/wiki/Strictly%20standardized%20mean%20difference | In statistics, the strictly standardized mean difference (SSMD) is a measure of effect size. It is the mean divided by the standard deviation of a difference between two random values each from one of two groups. It was initially proposed for quality control
and hit selection
in high-throughput screening (HTS) and has become a statistical parameter measuring effect sizes for the comparison of any two groups with random values.
Background
In high-throughput screening (HTS), quality control (QC) is critical. An important QC characteristic in a HTS assay is how much the positive controls, test compounds, and negative controls differ from one another. This QC characteristic can be evaluated using the comparison of two well types in HTS assays. Signal-to-noise ratio (S/N), signal-to-background ratio (S/B), and the Z-factor have been adopted to evaluate the quality of HTS assays through the comparison of two investigated types of wells. However, the S/B does not take into account any information on variability; and the S/N can capture the variability only in one group and hence cannot assess the quality of assay when the two groups have different variabilities.
Zhang JH et al. proposed the Z-factor. The advantage of the Z-factor over the S/N and S/B is that it takes into account the variabilities in both compared groups. As a result, the Z-factor has been broadly used as a QC metric in HTS assays. The absolute sign in the Z-factor makes it inconvenient to derive its statistical inference mathematically.
To derive a better interpretable parameter for measuring the differentiation between two groups, Zhang XHD
proposed SSMD to evaluate the differentiation between a positive control and a negative control in HTS assays. SSMD has a probabilistic basis due to its strong link with d+-probability (i.e., the probability that the difference between two groups is positive). To some extent, the d+-probability is equivalent to the well-established probabilistic index P(X > Y) which has been studied and applied in many areas.
Supported on its probabilistic basis, SSMD has been used for both quality control and hit selection in high-throughput screening.
Concept
Statistical parameter
As a statistical parameter, SSMD (denoted as ) is defined as the ratio of mean to standard deviation of the difference of two random values respectively from two groups. Assume that one group with random values has mean and variance and another group has mean and variance . The covariance between the two groups is Then, the SSMD for the comparison of these two groups is defined as
If the two groups are independent,
If the two independent groups have equal variances ,
In the situation where the two groups are correlated, a commonly used strategy to avoid the calculation of is first to obtain paired observations from the two groups and then to estimate SSMD based on the paired observations. Based on a paired difference with population mean and , SSMD is
Statistical e |
https://en.wikipedia.org/wiki/Jan%20J%C3%ADlek | Jan Jílek (born 5 June 1973) is a Czech football referee. He was a full international for FIFA from 2007 to 2010.
Career statistics
Statistics for Czech First League matches only.
References
External links
Jan Jílek on WorldReferee.com
Jan Jílek on rozhodci-cmfs.cz
Jan Jílek on weltfussball.de
1973 births
Living people
Czech football referees |
https://en.wikipedia.org/wiki/Convolution%20of%20probability%20distributions | The convolution/sum of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that corresponds to the addition of independent random variables and, by extension, to forming linear combinations of random variables. The operation here is a special case of convolution in the context of probability distributions.
Introduction
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively. Many well known distributions have simple convolutions: see List of convolutions of probability distributions
The general formula for the distribution of the sum of two independent integer-valued (and hence discrete) random variables is
For independent, continuous random variables with probability density functions (PDF) and cumulative distribution functions (CDF) respectively, we have that the CDF of the sum is:
If we start with random variables and , related by , and with no information about their possible independence, then:
However, if and are independent, then:
and this formula becomes the convolution of probability distributions:
Example derivation
There are several ways of deriving formulae for the convolution of probability distributions. Often the manipulation of integrals can be avoided by use of some type of generating function. Such methods can also be useful in deriving properties of the resulting distribution, such as moments, even if an explicit formula for the distribution itself cannot be derived.
One of the straightforward techniques is to use characteristic functions, which always exists and are unique to a given distribution.
Convolution of Bernoulli distributions
The convolution of two independent identically distributed Bernoulli random variables is a binomial random variable. That is, in a shorthand notation,
To show this let
and define
Also, let Z denote a generic binomial random variable:
Using probability mass functions
As are independent,
Here, we used the fact that for k>n in the last but three equality, and of Pascal's rule in the second last equality.
Using characteristic functions
The characteristic function of each and of is
where t is within some neighborhood of zero.
The expectation of the product is the product of the expectations since each is independent.
Since and have the same characteristic function, they must have the same distribution.
See also
List of convolutions of probability distributions
References
Theory of probability distributions |
https://en.wikipedia.org/wiki/Patrik%20Fla%C5%A1ar | Patrik Flašar (born April 4, 1987) is a Czech professional ice hockey defenceman. He played with HC Vítkovice in the Czech Extraliga during the 2010–11 Czech Extraliga season.
Career statistics
References
External links
1987 births
Czech ice hockey defencemen
HC Havířov players
HC Vrchlabí players
JKH GKS Jastrzębie players
LHK Jestřábi Prostějov players
Living people
MHK Kežmarok players
Stadion Hradec Králové players
TH Unia Oświęcim players
TMH Polonia Bytom players
Czech expatriate ice hockey players in Germany
Czech expatriate ice hockey players in Slovakia
Slovak expatriate sportspeople in Poland
Expatriate ice hockey players in Poland |
https://en.wikipedia.org/wiki/Tom%C3%A1%C5%A1%20Ficenc | Tomáš Ficenc (born December 28, 1977) is a Czech professional ice hockey defenceman. He played with HC Vítkovice in the Czech Extraliga during the 2010–11 Czech Extraliga season.
Career statistics
References
External links
Hokey.cz Tomáš Ficenc
1977 births
BK Havlíčkův Brod players
Czech ice hockey defencemen
HC Dukla Jihlava players
HC Slovan Ústečtí Lvi players
HC Vítkovice players
Living people
MsHK Žilina players
Ice hockey people from Jihlava
Czech expatriate ice hockey players in Slovakia |
https://en.wikipedia.org/wiki/Jakub%20Barto%C5%88 | Jakub Bartoň (born July 13, 1981) is a Czech former professional ice hockey defenceman. He played with HC Vítkovice in the Czech Extraliga during the 2010–11 Czech Extraliga season.
Career statistics
References
External links
1981 births
Living people
Basingstoke Bison players
Corsaires de Dunkerque players
Czech ice hockey defencemen
HC Havířov players
SK Horácká Slavia Třebíč players
HC Kometa Brno players
HC Oceláři Třinec players
HC Olomouc players
Orli Znojmo players
IHC Písek players
HC Slezan Opava players
Ice hockey people from Jihlava
Stadion Hradec Králové players
Hokej Šumperk 2003 players
HC Vítkovice players
Czech expatriate ice hockey people
Czech expatriate sportspeople in France
Czech expatriate sportspeople in England
Expatriate ice hockey players in England
Expatriate ice hockey players in France |
https://en.wikipedia.org/wiki/Lomax%20distribution | The Lomax distribution, conditionally also called the Pareto Type II distribution, is a heavy-tail probability distribution used in business, economics, actuarial science, queueing theory and Internet traffic modeling. It is named after K. S. Lomax. It is essentially a Pareto distribution that has been shifted so that its support begins at zero.
Characterization
Probability density function
The probability density function (pdf) for the Lomax distribution is given by
with shape parameter and scale parameter . The density can be rewritten in such a way that more clearly shows the relation to the Pareto Type I distribution. That is:
.
Non-central moments
The th non-central moment exists only if the shape parameter strictly exceeds , when the moment has the value
Related distributions
Relation to the Pareto distribution
The Lomax distribution is a Pareto Type I distribution shifted so that its support begins at zero. Specifically:
The Lomax distribution is a Pareto Type II distribution with xm=λ and μ=0:
Relation to the generalized Pareto distribution
The Lomax distribution is a special case of the generalized Pareto distribution. Specifically:
Relation to the beta prime distribution
The Lomax distribution with scale parameter λ = 1 is a special case of the beta prime distribution. If X has a Lomax distribution, then .
Relation to the F distribution
The Lomax distribution with shape parameter α = 1 and scale parameter λ = 1 has density , the same distribution as an F(2,2) distribution. This is the distribution of the ratio of two independent and identically distributed random variables with exponential distributions.
Relation to the q-exponential distribution
The Lomax distribution is a special case of the q-exponential distribution. The q-exponential extends this distribution to support on a bounded interval. The Lomax parameters are given by:
Relation to the (log-) logistic distribution
The logarithm of a Lomax(shape = 1.0, scale = λ)-distributed variable follows a logistic distribution with location log(λ) and scale 1.0.
This implies that a Lomax(shape = 1.0, scale = λ)-distribution equals a log-logistic distribution with shape β = 1.0 and scale α = log(λ).
Gamma-exponential (scale-) mixture connection
The Lomax distribution arises as a mixture of exponential distributions where the mixing distribution of the rate is a gamma distribution.
If λ|k,θ ~ Gamma(shape = k, scale = θ) and X|λ ~ Exponential(rate = λ) then the marginal distribution of X|k,θ is Lomax(shape = k, scale = 1/θ).
Since the rate parameter may equivalently be reparameterized to a scale parameter, the Lomax distribution constitutes a scale mixture of exponentials (with the exponential scale parameter following an inverse-gamma distribution).
See also
power law
compound probability distribution
hyperexponential distribution (finite mixture of exponentials)
normal-exponential-gamma distribution (a normal scale mixture with Lomax mixing distribution)
|
https://en.wikipedia.org/wiki/Algebraic%20cobordism | In mathematics, algebraic cobordism is an analogue of complex cobordism for smooth quasi-projective schemes over a field. It was introduced by .
An oriented cohomology theory on the category of smooth quasi-projective schemes Sm over a field k consists of a contravariant functor A* from Sm to commutative graded rings, together with push-forward maps f* whenever f:Y→X has relative dimension d for some d. These maps have to satisfy various conditions similar to those satisfied by complex cobordism. In particular they are "oriented", which means roughly that they behave well on vector bundles; this is closely related to the condition that a generalized cohomology theory has a complex orientation.
Over a field of characteristic 0, algebraic cobordism is the universal oriented cohomology theory for smooth varieties. In other words there is a unique morphism of oriented cohomology theories from algebraic cobordism to any other oriented cohomology theory.
and give surveys of algebraic cobordism.
The algebraic cobordism ring of generalized flag varieties has been computed by .
References
Algebraic geometry
Algebraic topology |
https://en.wikipedia.org/wiki/Ernst%20Peter%20Fischer | Ernst Peter Fischer (born 18 January 1947) in Wuppertal is a German Historian of Science and Publicist.
Life and work
Ernst Peter Fischer studied mathematics, physics, and biology and graduated from the California Institute of Technology in 1977. In 1987, he qualified as a university lecturer in the history of science, and taught as a professor at the University of Konstanz. Between 1989 and 1999 he was the publisher of the Mannheimer Forum. This position was previously held by Hoimar von Ditfurth.
During his free time, Fischer engaged in scientific journalism, as well as spending time as a mentor. He worked as a publisher for the Stiftung Forum für Verantwortung.
As a science publisher, Fisher wrote articles for several newspapers. Among them were GEO, Bild der Wissenschaft, Die Weltwoche and the Frankfurter Allgemeine Zeitung.
Awards
Fischer's published work has received multiple awards.
2002: Lorenz-Oken-Medaille
2003: Treviranus-Medaille
2003: Eduard-Rhein-Kulturpreis
2004: Medaille für Naturwissenschaftliche Publizistik der Deutschen Physikalischen Gesellschaft
2004: Sartorius-Preis der Akademie der Wissenschaften zu Göttingen
2011: Honorary member of the Naturforschende Gesellschaft zu Emden
Published works
Warum Spinat nur Popeye stark macht. Mythen und Legenden in der modernen Wissenschaft. Pantheon Verlag, München 2011, .
Information - eine kurze Geschichte in 5 Kapiteln. Verlagshaus Jacoby & Stuart 2010, .
Die Hintertreppe zum Quantensprung. Die Erforschung der kleinsten Teilchen der Natur von Max Planck bis Anton Zeilinger. Herbig Verlag, München 2010, .
Laser - Eine deutsche Erfolgsgeschichte von Einstein bis heute. Siedler-Verlag, München 2010, .
Die Charité: Ein Krankenhaus in Berlin - 1710 bis heute. Siedler-Verlag, München 2009, .
Die kosmische Hintertreppe: Die Erforschung des Himmels von Aristoteles bis Stephen Hawking. Nymphenburger Verlag, München 2009, .
Der kleine Darwin. Alles, was man über Evolution wissen sollte. Pantheon Verlag, München 2009, .
Das große Buch der Evolution. Fackelträger Verlag, Köln 2008, .
Einfach klug: 60 Ratschläge für ein gelingendes Leben. Nymphenburger Verlag, München 2009, .
Irren ist bequem: Wissenschaft quer gedacht. Kosmos Verlag, Stuttgart 2007, .
Der Physiker: Max Planck und das Zerfallen der Welt. Siedler Verlag, München 2007, .
Max Planck - ein Porträt. Eine Vorlesung (auf DVD) von Ernst Peter Fischer über die Physik, das tragische Leben, sowie Religiosität und Philosophie von Max Planck. Rezension - Komplett Media GmbH, 2007, DVD: CD: .
Die Nachtseite der Wissenschaft. Vorlesung aus der Reihe "uni-auditorium", Audio CD, Komplett Media, Juni 2007, .
Schrödingers Katze auf dem Mandelbrotbaum: Durch die Hintertür zur Wissenschaft. Pantheon Verlag, München 2006, .
Brücken zum Kosmos: Wolfgang Pauli zwischen Kernphysik und Weltharmonie. Libelle Verlag, Lengwil (CH) 2005, .
Einstein trifft Picasso und geht mit ihm ins Kino oder: Die Erfindung der Moderne. Piper Ve |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20Cheltenham%20Town%20F.C.%20season | This page shows the progress of Cheltenham Town in the 2011–12 football season. They played their games in the fourth tier of English football, League Two.
League table
Squad statistics
Appearances and goals
|}
Top scorers
Disciplinary record
Results
Pre-season friendlies
League Two
FA Cup
League Cup
Football League Trophy
Transfers
Awards
References
Cheltenham Town F.C. seasons
Cheltenham Town |
https://en.wikipedia.org/wiki/Andr%C3%A9%E2%80%93Oort%20conjecture | In mathematics, the André–Oort conjecture is a problem in Diophantine geometry, a branch of number theory, that can be seen as a non-abelian analogue of the Manin–Mumford conjecture, which is now a theorem (proven in several different ways).
The conjecture concerns itself with a characterization of the Zariski closure of sets of special points in Shimura varieties.
A special case of the conjecture was stated by Yves André in 1989 and a more general statement (albeit with a restriction on the type of the Shimura variety) was conjectured by Frans Oort in 1995. The modern version is a natural generalization of these two conjectures.
Statement
The conjecture in its modern form is as follows. Each irreducible component of the Zariski closure of a set of special points in a Shimura variety is a special subvariety.
André's first version of the conjecture was just for one dimensional irreducible components, while Oort proposed that it should be true for irreducible components of arbitrary dimension in the moduli space of principally polarised Abelian varieties of dimension g.
It seems that André was motivated by applications to transcendence theory while Oort by the analogy with the Manin-Mumford
conjecture.
Partial results
Various results have been established towards the full conjecture by Ben Moonen, Yves André, Andrei Yafaev, Bas Edixhoven, Laurent Clozel, Bruno Klingler and Emmanuel Ullmo, among others. Some of these results were conditional upon the generalized Riemann hypothesis (GRH) being true.
In fact, the proof of the full conjecture under GRH was published by Bruno Klingler, Emmanuel Ullmo and Andrei Yafaev in 2014 in the Annals of Mathematics.
In 2006, Umberto Zannier and Jonathan Pila used techniques from o-minimal geometry and transcendental number theory to develop an approach to the Manin-Mumford-André-Oort type of problems.
In 2009, Jonathan Pila proved the André-Oort conjecture unconditionally for arbitrary products of modular curves, a result which earned him the 2011 Clay Research Award.
Bruno Klingler, Emmanuel Ullmo and Andrei Yafaev proved, in 2014, the functional transcendence result needed for the general Pila-Zannier approach and Emmanuel Ullmo has deduced from it a technical result needed for the induction step in the strategy. The remaining technical ingredient was the problem of bounding below the Galois degrees of special points.
For the case of the Siegel modular variety, this bound was deduced by Jacob Tsimerman in 2015 from the averaged Colmez conjecture and the Masser-Wustholtz isogeny estimates. The averaged Colmez conjecture was proved by Xinyi Yuan and Shou-Wu Zhang and independently by Andreatta, Goren, Howard and Madapusi-Pera.
In 2019-2020, Gal Biniyamini, Harry Schmidt and Andrei Yafaev, building on previous work and ideas of Harry Schmidt on torsion points in tori and abelian varieties and Gal Biniyamini's point counting results, have formulated a conjecture on bounds of heights of special points |
https://en.wikipedia.org/wiki/Petra%20Kvitov%C3%A1%20career%20statistics | This is a list of the main career statistics of Czech professional tennis player Petra Kvitová. To date, Kvitová has won 31 career singles titles including two Grand Slam singles titles at the Wimbledon Championships, one WTA Tour Championships singles title, nine WTA 1000 singles titles. She was also the Bronze medalist at the 2016 Rio Olympics, a runner-up at the 2015 WTA Finals and 2019 Australian Open, a semifinalist at the 2010 Wimbledon Championships, 2012 Australian Open, 2012 French Open and 2020 French Open, and a quarterfinalist at the 2011 Australian Open, 2012 Wimbledon Championships, 2013 Wimbledon Championships, 2015 US Open, 2017 US Open and 2020 Australian Open. Kvitová reached her career-high ranking of world No. 2 on 31 October 2011.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup, Hopman Cup, United Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 China Open.
Doubles
Current after the season 2016.
Mixed doubles
Grand Slam finals
Singles: 3 (2 titles, 1 runner-up)
Other significant finals
WTA Finals
Singles: 2 (1 title, 1 runner-up)
WTA Elite Trophy
Singles: 1 (1 title)
Olympic Games
Singles: 1 (bronze medal)
WTA 1000
Singles: 13 (9 titles, 4 runner-ups)
WTA career finals
Singles: 42 (31 titles, 11 runner-ups)
Team competition finals
Billie Jean King Cup: 6 (6 titles)
Hopman Cup: 1 (title)
ITF Circuit finals
Singles: 10 (7 titles, 3 runner-ups)
Junior finals
ITF Finals
Singles: 4 titles
Doubles: 4 (1 title, 3 runner-ups)
Fed Cup/Billie Jean King Cup
Singles: 40 (30–10)
Doubles: 1 (0–1)
WTA ranking
Current after the 2023 French Open.
WTA Tour career earnings
Current after the 2023 China Open.
Career Grand Slam statistics
Grand Slam tournament seedings
The tournaments won by Kvitová are in boldface, and advanced into finals by Kvitová are in italics.
Best Grand Slam results details
Grand Slam winners are in boldface, and runner–ups are in italics.
Record against other players
No. 1 wins
Record against top 10 players
She has a 64–71 () record against players who were, at the time the match was played, ranked in the top 10.
Double bagel matches (6–0, 6–0)
Longest winning streaks
14 match win streak (2011–2012)
14 match win streak (2018)
Notes
References
External links
Career Statistics
Tennis career statistics |
https://en.wikipedia.org/wiki/Radek%20Mat%C4%9Bjek | Radek Matějek (born 5 February 1973) is a Czech football referee. He has been a full international for FIFA since 2004.
Career statistics
Statistics for Gambrinus liga matches only.
References
External links
Radek Matějek on WorldReferee.com
Radek Matějek on weltfussball.de
1973 births
Living people
Czech football referees |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20Bury%20F.C.%20season | This page shows the progress of Bury F.C.'s season in 2011–12. They will play their games in the third tier of English football, Football League One.
League table
Squad statistics
Appearances and goals
|-
|colspan="14"|Players played for Bury this season who are no longer at the club:
|-
|colspan="14"|Players who played for Bury on loan and returned to their parent club:
|}
Top scorers
Disciplinary record
Results and fixtures
Pre-season friendlies
League One
FA Cup
League Cup
Football League Trophy
Transfers
Awards
References
Bury F.C. seasons
Bury |
https://en.wikipedia.org/wiki/Legal%20basis%20of%20official%20statistics%20in%20Switzerland | The legal basis of official statistics in Switzerland is the Swiss Federal Constitution. Article 65 of the Swiss Federal Constitution sets out the mandate and competencies of official statistics.
The legal bases of Swiss official statistics are set out in more detail in the Federal Statistics Act of 9 October 1992. The Federal Statistics Act formulates the tasks and organisation of federal statistics as well as basic principles relating to statistical data collection, publications and services. In particular, it outlines the principles of data protection.
Being the largest and oldest statistical survey, the census is governed by its own law (promulgated on 22 June 2007). This also applies to the simplified collection of data thanks to the harmonisation of population and other official personal registers, which is mentioned in Art. 65 of the Constitution.
Various ordinances add detail to the provisions in the above-named laws – concerning matters such as the organisation of federal statistics, the conduct of federal statistical surveys, fees for statistical services provided by administrative units of the Confederation, the Business and Enterprise Register and the Register of Buildings and Dwellings.
On the origin of the legal bases
On 23 July 1870, the Swiss Parliament approved a law on "Official Statistical Surveys in Switzerland", which was confined to organisational issues. This law resulted in the non-standardised and unsystematic development of statistics.
The Federal Statistics Act of 9 October 1992 replaced the 1870 law, laying a modern foundation for Swiss statistics. The salient innovations in the 1992 Act are: the coordination function of the Federal Statistical Office (FSO) in its capacity as the Confederation's central statistical unit, the establishment of a multi-year statistical programme for overall planning of Swiss statistics, and the institution of the Federal Statistics Commission as an advisory body to the Federal Council.
The new Federal Constitution of 18 April 1999 includes, for the first time, an article on statistics (Art. 65). Whereas in the old Federal Constitution the federal authorities were only given competence over specific statistical matters, under Art. 65 of the Federal Constitution of 1999, the federal authorities have general statistical competence: "The federal authorities shall obtain the necessary statistical data concerning the current status and changes in the population, the economy, society, education, research, spatial development and the environment in Switzerland". But statistical surveys by the cantons on their own territory are not excluded thereby – statistical competence is a parallel competence which allows parallel statistical activities by the federal authorities and the cantons under the coordination of the federal government.
From the Federal Statistics Act (BStatG)
General Provisions
Power to Commission Surveys and Participation
Organisation of Federal Statistics
Data Protect |
https://en.wikipedia.org/wiki/John%20Brownlee%20%28statistician%29 | John Brownlee (1868–1927) was a British physician and medical statistician who became the first director of the Statistics Department of the UK's Medical Research Committee.
Life
The son of a Church of Scotland minister, he studied at the University of Glasgow, obtaining degrees first in mathematics and natural philosophy and then in medicine. He became in 1900 physician-superintendent to the City of Glasgow Fever Hospital. In 1914 he became the founding director of the statistics department of the UK Medical Research Committee and held the post until his sudden death from bronchopneumonia in 1927.
Works
Brownlee was influenced by Karl Pearson's mathematical approach to statistics, and applied the Pearson family of distributions to epidemics. In the view of fellow epidemiologist and statistician Major Greenwood, Brownlee took these techniques further than any of his contemporaries. His studies included the epidemiology of phthisis and measles.
References
External links
University of Glasgow collection
1868 births
1927 deaths
20th-century Scottish medical doctors
British statisticians |
https://en.wikipedia.org/wiki/CSEM | Cesm or CSEM may refer to:
CSEM, School of Computer Science, Engineering and Mathematics, Flinders University
Child sexual exploitation material, an alternative name for child pornography.
Csém, a village in Hungary
Swiss Center for Electronics and Microtechnology, a Swiss research and development company
Controlled source electro-magnetic, an offshore geophysical technique |
https://en.wikipedia.org/wiki/Calgary%20Stampeders%20all-time%20records%20and%20statistics | The following is a select list of Calgary Stampeders all-time records and statistics current to the 2023 CFL season. Each category lists the top five players, where known, except for when the fifth place player is tied in which case all players with the same number are listed.
Service
Most Games Played
276 – Mark McLoughlin (1988–2003)
224 – Larry Robinson (1961–74)
223 – Jay McNeil (1994–2007)
216 – Jamie Crysdale (1993–2005)
214 – Alondra Johnson (1991–2003)
Most Seasons Played
16 – Mark McLoughlin (1988–2003)
14 – Larry Robinson (1961–74)
14 – Jay McNeil (1994–2007)
13 – Stu Laird (1984–96)
13 – Alondra Johnson (1991–2003)
13 – Jamie Crysdale (1993–2005)
Scoring
Most points – Career
2957 – Mark McLoughlin (1988–2003)
2129 – Rene Paredes (2011–19, 2021–23)
1275 – J.T. Hay (1979–88)
1030 – Larry Robinson (1961–75)
930 – Sandro DeAngelis (2005–09)
Most Points – Season
220 – Mark McLoughlin (1995)
220 – Mark McLoughlin (1996)
217 – Sandro DeAngelis (2008)
215 – Mark McLoughlin (1993)
214 – Sandro DeAngelis (2006)
Most Points – Game
30 – Earl Lunsford – versus Edmonton Eskimos, September 3, 1962
26 – Mark McLoughlin – versus Saskatchewan Roughriders, August 5, 1996
24 – Gene Filipski – at BC Lions, November 5, 1961
24 – Herm Harrison – at Winnipeg Blue Bombers, September 2, 1970
24 – Jon Cornish – versus Saskatchewan Roughriders, August 9, 2013
24 – Romar Morris – versus Edmonton Eskimos, September 8, 2018
24 – Reggie Begelton – versus Montreal Alouettes, August 17, 2019
24 – Tommy Stevens – versus Edmonton Eskimos, September 10, 2022
Most Touchdowns – Career
117 – Allen Pitts (1990–2000)
76 – Kelvin Anderson (1996–2002)
67 – Nik Lewis (2004–14)
62 – Tom Forzani (1973–83)
61 – Joffrey Reynolds (2004–11)
Most Touchdowns – Season
21 – Allen Pitts (1994)
19 – Tony Stewart (1994)
17 – Terry Evanshen (1967)
16 – Kelvin Anderson (1998)
15 – eight times, most recently Romby Bryant (2010)
Most Touchdowns – Game
5 – Earl Lunsford – versus Edmonton Eskimos, September 3, 1962
4 – Gene Filipski – at BC Lions, November 5, 1961
4 – Herm Harrison – at Winnipeg Blue Bombers, September 2, 1970
4 – Jon Cornish – versus Saskatchewan Roughriders, August 9, 2013
4 – Romar Morris – versus Edmonton Eskimos, September 8, 2018
4 – Reggie Begelton – versus Montreal Alouettes, August 17, 2019
4 – Tommy Stevens – versus Edmonton Eskimos, September 10, 2022
Most Rushing Touchdowns – Career
55 – Earl Lunsford (1956, 1959–63)
53 – Joffrey Reynolds (2004–11)
52 – Kelvin Anderson (1996–2002)
45 – James Sykes (1978–83)
44 – Jon Cornish (2007–15)
Most Rushing Touchdowns – Season
14 – Tony Stewart (1994)
13 – Earl Lunsford (1960)
13 – Lovell Coleman (1963)
13 – James Sykes (1978)
12 – Jon Cornish (2013)
Most Rushing Touchdowns – Game
5 – Earl Lunsford – versus Edmonton Eskimos, September 3, 1962
4 – Jon Cornish – versus Saskatchewan Roughriders, August 9, 2013
4 – Tommy Stevens – versus Edmonton Eskimos, September 10, 2022
3 – 17 times, most recently Jerome Messam – ve |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20Morecambe%20F.C.%20season | During the 2011–12 season, Morecambe F.C. competed in League Two.
League table
Squad statistics
Appearances and goals
|-
|colspan="14"|Players featured for Morecambe but left before the end of the season:
|-
|colspan="14"|Players featured for Morecambe on loan this season and returned to their parent club:
|}
Top scorers
Disciplinary record
Results
Pre-season friendlies
League Two
FA Cup
League Cup
Football League Trophy
Transfers
Awards
References
2011–12
2011–12 Football League Two by team |
https://en.wikipedia.org/wiki/Locally%20profinite%20group | In mathematics, a locally profinite group is a Hausdorff topological group in which every neighborhood of the identity element contains a compact open subgroup. Equivalently, a locally profinite group is a topological group that is Hausdorff, locally compact, and totally disconnected. Moreover, a locally profinite group is compact if and only if it is profinite; this explains the terminology. Basic examples of locally profinite groups are discrete groups and the p-adic Lie groups. Non-examples are real Lie groups, which have the no small subgroup property.
In a locally profinite group, a closed subgroup is locally profinite, and every compact subgroup is contained in an open compact subgroup.
Examples
Important examples of locally profinite groups come from algebraic number theory. Let F be a non-archimedean local field. Then both F and are locally profinite. More generally, the matrix ring and the general linear group are locally profinite. Another example of a locally profinite group is the absolute Weil group of a non-archimedean local field: this is in contrast to the fact that the absolute Galois group of such is profinite (in particular compact).
Representations of a locally profinite group
Let G be a locally profinite group. Then a group homomorphism is continuous if and only if it has open kernel.
Let be a complex representation of G. is said to be smooth if V is a union of where K runs over all open compact subgroups K. is said to be admissible if it is smooth and is finite-dimensional for any open compact subgroup K.
We now make a blanket assumption that is at most countable for all open compact subgroups K.
The dual space carries the action of G given by . In general, is not smooth. Thus, we set where is acting through and set . The smooth representation is then called the contragredient or smooth dual of .
The contravariant functor
from the category of smooth representations of G to itself is exact. Moreover, the following are equivalent.
is admissible.
is admissible.
The canonical G-module map is an isomorphism.
When is admissible, is irreducible if and only if is irreducible.
The countability assumption at the beginning is really necessary, for there exists a locally profinite group that admits an irreducible smooth representation such that is not irreducible.
Hecke algebra of a locally profinite group
Let be a unimodular locally profinite group such that is at most countable for all open compact subgroups K, and a left Haar measure on . Let denote the space of locally constant functions on with compact support. With the multiplicative structure given by
becomes not necessarily unital associative -algebra. It is called the Hecke algebra of G and is denoted by . The algebra plays an important role in the study of smooth representations of locally profinite groups. Indeed, one has the following: given a smooth representation of G, we define a new action on V:
Thus, we have the func |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20AFC%20Bournemouth%20season | The 2011–12 AFC Bournemouth season saw the club compete in League One, the FA Cup, the League Cup and the Football League Trophy. In the league the club finished in 11th place.
Squad statistics
Appearances and goals
|-
|colspan="14"|Players appeared for Bournemouth who have left the club:
|-
|colspan="14"|Players who played on loan for Bournemouth and returned to their parent club:
|}
Top scorers
Disciplinary record
Results
Pre-season friendlies
League One
Result round by round
League table
Results
FA Cup
League Cup
Football League Trophy
Transfers
Awards
References
AFC Bournemouth seasons
AFC Bournemouth |
https://en.wikipedia.org/wiki/Hopfian%20object | In the branch of mathematics called category theory, a hopfian object is an object A such that any epimorphism of A onto A is necessarily an automorphism. The dual notion is that of a cohopfian object, which is an object B such that every monomorphism from B into B is necessarily an automorphism. The two conditions have been studied in the categories of groups, rings, modules, and topological spaces.
The terms "hopfian" and "cohopfian" have arisen since the 1960s, and are said to be in honor of Heinz Hopf and his use of the concept of the hopfian group in his work on fundamental groups of surfaces.
Properties
Both conditions may be viewed as types of finiteness conditions in their category. For example, assuming Zermelo–Fraenkel set theory with the axiom of choice and working in the category of sets, the hopfian and cohopfian objects are precisely the finite sets. From this it is easy to see that all finite groups, finite modules and finite rings are hopfian and cohopfian in their categories.
Hopfian objects and cohopfian objects have an elementary interaction with projective objects and injective objects. The two results are:
An injective hopfian object is cohopfian.
A projective cohopfian object is hopfian.
The proof for the first statement is short: Let A be an injective hopfian object, and let f be an injective morphism from A to A. By injectivity, f factors through the identity map IA on A, yielding a morphism g such that gf=IA. As a result, g is a surjective morphism and hence an automorphism, and then f is necessarily the inverse automorphism to g. This proof can be dualized to prove the second statement.
Hopfian and cohopfian groups
Hopfian and cohopfian modules
Here are several basic results in the category of modules. It is especially important to remember that RR being hopfian or cohopfian as a module is different from R being hopfian or cohopfian as a ring.
A Noetherian module is hopfian, and an Artinian module is cohopfian.
The module RR is hopfian if and only if R is a directly finite ring. Symmetrically, these two are also equivalent to the module RR being hopfian.
In contrast with the above, the modules RR or RR can be cohopfian or not in any combination. An example of a ring cohopfian on one side but not the other side was given in . However, if either of these two modules is cohopfian, R is hopfian on both sides (since R is projective as a left or right module) and directly finite.
Hopfian and cohopfian rings
The situation in the category of rings is quite different from the category of modules. The morphisms in the category of rings with unity are required to preserve the identity, that is, to send 1 to 1.
If R satisfies the ascending chain condition on ideals, then R is hopfian. This can be proven by analogy with the fact for Noetherian modules. The counterpart idea for "cohopfian" does not exist however, since if f is a ring homomorphism from R into R preserving identity, and the image of f is not R |
https://en.wikipedia.org/wiki/Elizabeth%20East | Elizabeth East is a northern suburb of Adelaide, South Australia in the City of Playford.
Demographics
The by the Australian Bureau of Statistics counted 4,400 people in the suburb of Elizabeth East on census night. Of these, 2,196 (49.5%) were male and 2,239 (50.5%) were female.
The majority of residents 2,791 (63.1%) were Australian born, with 452 (10.2%) born in England.
The age distribution of Elizabeth East residents is similar to that of the greater Australian population. 67.9% of residents were aged 25 or over in 2016, compared to the Australian average of 68.8%; and 32.3% were younger than 25 years, compared to the Australian average of 31.5%.
References
Suburbs of Adelaide |
https://en.wikipedia.org/wiki/List%20of%20Major%20League%20Baseball%20career%20saves%20leaders | In baseball statistics, a relief pitcher is credited with a save (denoted by SV) who finishes a game for the winning team under certain prescribed circumstances. Most commonly a pitcher earns a save by entering in the ninth inning of a game in which his team is winning by three or fewer runs and finishing the game by pitching one inning without losing the lead.
Mariano Rivera is the all-time leader in saves with 652. Rivera and Trevor Hoffman are the only pitchers in MLB history to save more than 600 career games. Lee Smith, Francisco Rodríguez, John Franco, Billy Wagner, Kenley Jansen, and Craig Kimbrel are the only other pitchers to save more than 400 games in their careers.
Key
List
Stats updated as of the end of the 2023 season.
Notes
References
External links
Major League Baseball
Saves
Major League Baseball statistics |
https://en.wikipedia.org/wiki/Theil%E2%80%93Sen%20estimator | In non-parametric statistics, the Theil–Sen estimator is a method for robustly fitting a line to sample points in the plane (simple linear regression) by choosing the median of the slopes of all lines through pairs of points. It has also been called Sen's slope estimator, slope selection, the single median method, the Kendall robust line-fit method, and the Kendall–Theil robust line. It is named after Henri Theil and Pranab K. Sen, who published papers on this method in 1950 and 1968 respectively, and after Maurice Kendall because of its relation to the Kendall tau rank correlation coefficient.
Theil-Sen regression has several advantages over Ordinary least squares regression. It is insensitive to outliers. It can be used for significance tests even when residuals are not normally distributed. It can be significantly more accurate than non-robust simple linear regression (least squares) for skewed and heteroskedastic data, and competes well against least squares even for normally distributed data in terms of statistical power. It has been called "the most popular nonparametric technique for estimating a linear trend". There are fast algorithms for efficiently computing the parameters.
Definition
As defined by , the Theil–Sen estimator of a set of two-dimensional points is the median of the slopes determined by all pairs of sample points. extended this definition to handle the case in which two data points have the same coordinate. In Sen's definition, one takes the median of the slopes defined only from pairs of points having distinct coordinates.
Once the slope has been determined, one may determine a line from the sample points by setting the -intercept to be the median of the values . The fit line is then the line with coefficients and in slope–intercept form. As Sen observed, this choice of slope makes the Kendall tau rank correlation coefficient become approximately zero, when it is used to compare the values with their associated residuals . Intuitively, this suggests that how far the fit line passes above or below a data point is not correlated with whether that point is on the left or right side of the data set. The choice of does not affect the Kendall coefficient, but causes the median residual to become approximately zero; that is, the fit line passes above and below equal numbers of points.
A confidence interval for the slope estimate may be determined as the interval containing the middle 95% of the slopes of lines determined by pairs of points and may be estimated quickly by sampling pairs of points and determining the 95% interval of the sampled slopes. According to simulations, approximately 600 sample pairs are sufficient to determine an accurate confidence interval.
Variations
A variation of the Theil–Sen estimator, the repeated median regression of , determines for each sample point , the median of the slopes of lines through that point, and then determines the overall estimator as the median of these median |
https://en.wikipedia.org/wiki/Lafforgue%27s%20theorem | In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields, by giving a correspondence between automorphic forms on these groups and representations of Galois groups.
The Langlands conjectures were introduced by and describe a correspondence between representations of the Weil group of an algebraic function field and representations of algebraic groups over the function field, generalizing class field theory of function fields from abelian Galois groups to non-abelian Galois groups.
Langlands conjectures for GL1
The Langlands conjectures for GL1(K) follow from (and are essentially equivalent to) class field theory. More precisely the Artin map gives a map from the idele class group to the abelianization of the Weil group.
Automorphic representations of GLn(F)
The representations of GLn(F) appearing in the Langlands correspondence are automorphic representations.
Lafforgue's theorem for GLn(F)
Here F is a global field of some positive characteristic p, and ℓ is some prime not equal to p.
Lafforgue's theorem states that there is a bijection σ between:
Equivalence classes of cuspidal representations π of GLn(F), and
Equivalence classes of irreducible ℓ-adic representations σ(π) of dimension n of the absolute Galois group of F
that preserves the L-function at every place of F.
The proof of Lafforgue's theorem involves constructing a representation σ(π) of the absolute Galois group for each cuspidal representation π. The idea of doing this is to look in the ℓ-adic cohomology of the moduli stack of shtukas of rank n that have compatible level N structures for all N. The cohomology contains subquotients of the form
π⊗σ(π)⊗σ(π)∨
which can be used to construct σ(π) from π. A major problem is that the moduli stack is not of finite type, which means that there are formidable technical difficulties in studying its cohomology.
Applications
Lafforgue's theorem implies the Ramanujan–Petersson conjecture that if an automorphic form for GLn(F) has central character of finite order, then the corresponding Hecke eigenvalues at every unramified place have absolute value 1.
Lafforgue's theorem implies the conjecture of that an irreducible finite-dimensional l-adic representation of the absolute Galois group with determinant character of finite order is pure of weight 0.
See also
Local Langlands conjectures
References
Lafforgue, Laurent (2002), "Chtoucas de Drinfeld, formule des traces d'Arthur-Selberg et correspondance de Langlands." (Drinfeld shtukas, Arthur-Selberg trace formula and Langlands correspondence) Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), 383–400, Higher Ed. Press, Beijing, 2002.
Gérard Laumon (2002), "The work of Laurent Lafforgue", Proceedings of the ICM, Beijing 2002, vol. 1, 91–97,
G. Laumon (2000), "La correspondance de Langlands sur les corps de fonctions (d'après Laurent Lafforgue)" (The L |
https://en.wikipedia.org/wiki/Bernstein%E2%80%93Zelevinsky%20classification | In mathematics, the Bernstein–Zelevinsky classification, introduced by and , classifies the irreducible complex smooth representations of a general linear group over a local field in terms of cuspidal representations.
References
Representation theory |
https://en.wikipedia.org/wiki/Pranab%20K.%20Sen | Pranab Kumar Sen (born 7 November 1937 in Calcutta, India) is a statistician, a professor of statistics and the Cary C. Boshamer Professor of Biostatistics at the University of North Carolina at Chapel Hill.
Academic biography
Sen was the second of seven siblings; his father, a railway officer, died of leukemia when Sen was ten, and he was raised by his mother, the daughter of a physician. He began his undergraduate studies at Presidency College, Kolkata, initially intending to study medicine but shifting to statistics when it was discovered that he was too young for medical college. He received a B.S. from the University of Calcutta in 1955, an M.Sc. in 1957, and a Ph.D. in 1962; his doctoral advisor was Hari Kinkar Nandi. He taught for three years at the University of Calcutta and one more year at the University of California, Berkeley before joining the UNC faculty in 1965; although he has held visiting positions at other universities, he has remained at Chapel Hill for the rest of his career. He was the founding co-editor of two journals, Sequential Analysis and Statistics and Decisions, and was joint editor-in-chief of the Journal of Statistical Planning and Inference from 1980 to 1983.
Research and graduate advising
Sen is the author or co-author of multiple books on non-parametric statistics, the advisor of over 80 Ph.D. students, and the author of over 600 research publications. He is known for inventing the Hodges–Lehmann estimator independently of and contemporaneously with Hodges and Lehmann and for the Theil–Sen estimator, a form of robust regression that fits a line to two-dimensional sample points by choosing the slope of the fit line to be the median of the slopes of the lines through pairs of samples.
Awards and honors
Sen is a fellow of the Institute of Mathematical Statistics and of the American Statistical Association. He became the Cary C. Boshamer Professor in 1982. He was the Lukacs Distinguished Visiting Professor at Bowling Green State University in 1996–1997. In 2002, he won the Gottfried E. Noether Senior Scholar Award of the American Statistical Association, and he was the 2010 winner of the Wilks Memorial Award of the ASA "for outstanding contributions to statistical research, especially in nonparametric statistics and biostatistics; and for exceptional service in mentoring doctoral students." The Government of India awarded him the civilian honour of Padma Shri in 2011. In 2012, the University of Calcutta awarded him an honorary Doctor of Science degree.
In 2007, a festschrift was dedicated to him on the occasion of his 70th birthday.
References
1937 births
Living people
American statisticians
Indian statisticians
Presidency University, Kolkata alumni
University of Calcutta alumni
Academic staff of the University of Calcutta
University of California, Berkeley faculty
University of North Carolina at Chapel Hill faculty
Recipients of the Padma Shri in civil service
Fellows of the American Statistical Association
2 |
https://en.wikipedia.org/wiki/1943%20Croatian%20First%20League | Statistics of Croatian First League in the 1943 season.
First stage
City of Zagreb championship
City of Osijek championship
1 : HSK Gradjanski Osijek
2 : HSK Hajduk Osijek
City of Zemun championship
1 : HSK Zemun
City of Banja Luka championship
1 : HSK Hrvoje Banja Luka
2 : HBSK Banja Luka
City of Sarajevo championship
1 : SASK Sarajevo
2 : HSK Gjerzelez Sarajevo
Provincial Zagreb championship
1 : HRSK Zagorac Varazdin
Provincial Osijek championship
1 : HSK Bata Borovo
Provincial Sarajevo championship
1 : HSK Tomislav Zenica
Second stage
Group A
Group B
Group C
Group D
Play-offs
HASK Zagreb 4-0 ; 1-2 HSK Zemun
HSK Hajduk Osijek 0-4 ; 1-7 HŠK Građanski Zagreb
SASK Sarajevo 0-0 ; 0-3 HSK Concordia Zagreb
HSK Gradjanski Osijek 1-1 ; 1-4 HSK Licanin Zagreb
Final Stage
References
rsssf
Croatian First league seasons
Croatia
Croatia
1 |
https://en.wikipedia.org/wiki/1944%20Croatian%20First%20League | This article gives statistics of the Croatian First League in association football in the 1944 season.
First stage
City of Zagreb championship
Provincial Zagreb championship
1 : HSK Segesta Sisak
Zagreb play-offs
HSK Zeljeznicar Zagreb – HSK Segesta Sisak
City of Osijek championship
1 : HSK Gradjanski Osijek
2 : HSK Hajduk Osijek
3 : HSK Radnik Osijek
4 : HSK Olimpija Osijek
5 : HSK Graficar Osijek
6 : DSV Germania Osijek
Provincial Osijek championship
1 : HSK Borovo
2 : HSK Cibalia Vinkovci
3 : HSK Sparta Vukovar
Osijek play-offs
Round 1
HSK Gradjanski Osijek 7–0 ; ?-? HSK Sparta Vukovar
HSK Borovo 4–2 ; 0–1 HSK Cibalia Vinkovci
Round 2
HSK Hajduk Osijek 3–2 ; 0–2 HSK Radnik Osijek
HSK Borovo 2–1 ; ?-? HSK Gradjanski Osijek
Round 3
HSK Borovo 2–1 ; 0–0 HSK Radnik Osijek
City of Zemun championship
1 : HSK Dunav Zemun
2 : HSK Gradjanski Zemun
3 : SK Liet Zemun
4 : HSK Hajduk Zemun
Zemun play-offs
HSK Gradjanski Zemun – HSK Dunav Zemun
City of Banja Luka championship
1 : HBSK Banja Luka
2 : HSK Zvonimir Banja Luka
3 : HSK Hrvoje Banja Luka
City of Sarajevo
1 : SASK Sarajevo
2 : HSK Hajduk Sarajevo
3 : HSK Gjerzelez Sarajevo
Provincial Sarajevo
1 : HSK Tomislav Zenica
Sarajevo play-offs
Round 1
SASK Sarajevo – HSK Tomislav Zenica
HSK Gjerzelez Sarajevo – HSK Hajduk Sarajevo
Round 2
SASK Sarajevo – HSK Gjerzelez Sarajevo
Banja Luka / Sarajevo play-offs
SASK Sarajevo – HBSK Banja Luka
Second Stage
Group Zagreb
Group Provincial
Semifinals
HSK Gradjanski Zemun 0–2 ; 0–3 HSK Borovo
Finals
HSK Borovo 0–1 ; 0–3 SASK Sarajevo
Final
HASK Zagreb – SASK Sarajevo
References
rsssf
Croatian First league seasons
Croatia
Croatia
1 |
https://en.wikipedia.org/wiki/Fujita%20Sadasuke | , also known as Honda Teiken, was a Japanese mathematician in the Edo period. He is the author of Seiyō sampō (Essence of Mathematics) which was published in 1781.
Sadasuke was the father of Fujita Kagen (1765–1821), who is credited with publishing the first collection of sangaku problems.
Selected works
In a statistical overview derived from writings by and about Fujita Sadasuke, OCLC/WorldCat encompasses roughly 30 works in 30+ publications in 1 language and 30+ library holdings
, 1769
, 1781
, 1796
, 1807
See also
Sangaku, the custom of presenting mathematical problems, carved in wood tablets, to the public in Shinto shrines
Soroban, a Japanese abacus
Japanese mathematics
Notes
References
Fukagawa, Hidetoshi and Tony Rothman. (2008). Sacred Mathematics: Japanese Temple Geometry. Princeton: Princeton University Press. ; OCLC 181142099
Nussbaum, Louis-Frédéric and Käthe Roth. (2005). Japan encyclopedia. Cambridge: Harvard University Press. ; OCLC 58053128
David Eugene Smith and Yoshio Mikami. (1914). A History of Japanese Mathematics. Chicago: Open Court Publishing. OCLC 1515528 -- note alternate online, full-text copy at archive.org
18th-century Japanese mathematicians
19th-century Japanese mathematicians
Japanese writers of the Edo period
1734 births
1807 deaths |
https://en.wikipedia.org/wiki/1946%20Croatian%20First%20League | Statistics of Croatian First League in the 1946 season.
City of Zagreb preliminaries "A"
City of Zagreb preliminaries "B"
City of Zagreb championship
Zagreb Provincial championship
Borac Zagreb 0-1 ; 1-8 FD Dubrava Zagreb
City of Osijek championship
1 : FD Jedinstvo Osijek
2 : FD Udarnik Osijek
3 : FD Tipograf Osijek
4 : FD Sloga Osijek
5 : FD Bratstvo Osijek
Region of Banija championship
SFD Sloboda Sisak 8-1 ; 3-0 OFD Turkulin Petrinja
District of Karlovac championship
Udarnik Karlovac qualified to play-offs
District of Primorsko-goranska championship
FD Jedinstvo Susak qualified to play-offs
Also played FD Crikvenica, Omladinac Senj, Plavi Jadran Pag, NK Naprijed Hreljin
Region of Slavonia championship
Semifinals
Sloga Vinkovci 5-1 ; 1-5 ; 0-3 FD Proleter Belisce
SFD Naprijed Sisak 2-0 ; 1-0 FD Jedinstvo Osijek
Final
SFD Naprijed Sisak 2-0 ; 0-3 FD Proleter Belisce
District of Varazdin championship
District of Bjelovar championship
Bjelovar qualified to play-offs
Region of Dalmatia championship
Preliminary round
Zadar 1-0 ; 1-2 Sibenik
Final
RSD Split 0-2 ; 1-6 FD Hajduk Split
Play-offs
RSD Split 4-0 Dubrovnik
Sibenik 1-2; 0-4 RSD Split
Play-offs
Round 1
Bjelovar 1-5 ; 1-2 RSD Tekstilac Varazdin
Udarnik Karlovac 4-2 ; 1-3 FD Dubrava Zagreb
SFD Naprijed Sisak 2-1 ; 4-1 FD Amater Zagreb
FD Metalac Zagreb 8-0 ; 3-1 FD Jedinstvo Susak
Round 2
FD Dubrava Zagreb 3-2 ; 1-3 RSD Tekstilac Varazdin
FD Jedinstvo Susak 6-0 ; 2-4 SFD Naprijed Sisak
Additional play-off
Lokomotiva Zagreb 1-0 ; 3-0 FD Dubrava Zagreb
Final Stage
City of Rijeka championship
Rijeka/Istria Final
SD Kvarner Rijeka 1-2 ; 4-1 US Operaia Pula
References
rsssf
Croatian First league seasons
Croatia
Croatia
Croatia
Croatia
Football |
https://en.wikipedia.org/wiki/%CE%9810 | {{DISPLAYTITLE:θ10}}
In representation theory, a branch of mathematics, θ10 is a cuspidal unipotent complex irreducible representation of the symplectic group Sp4 over a finite, local, or global field.
introduced θ10 for the symplectic group Sp4(Fq) over a finite field Fq of order q, and showed that in this case it is
q(q – 1)2/2-dimensional. The subscript 10 in θ10 is a historical accident that has stuck: Srinivasan arbitrarily named some of the characters of Sp4(Fq) as θ1, θ2, ..., θ13, and the tenth one in her list happens to be the cuspidal unipotent character.
θ10 is the only cuspidal unipotent representation of Sp4(Fq). It is the simplest example of a cuspidal unipotent representation of a reductive group, and also the simplest example of a degenerate cuspidal representation (one without a Whittaker model).
General linear groups have no cuspidal unipotent representations and no degenerate cuspidal representations, so θ10 exhibits properties of general reductive groups that do not occur for general linear groups.
used the representations θ10 over local and global fields in their construction of counterexamples to the generalized Ramanujan conjecture for the symplectic group. described the representation θ10 of the Lie group Sp4(R) over the local field R in detail.
References
.
Representation theory
Automorphic forms |
https://en.wikipedia.org/wiki/Revista%20Colombiana%20de%20Estad%C3%ADstica | The Revista Colombiana de Estadística (English: Colombian Journal of Statistics) is a biannual peer-reviewed scientific journal on statistics published by the National University of Colombia. It covers research on statistics, including applications, statistics education, and the history of statistics.
History
The Revista Colombiana de Estadística was established in 1968. During the first years, the journal only published papers in Spanish but since 1985 it also publishes papers in English. The journal stopped publication between 1969 and 1979. In 1979, it was relaunched by Luis Thorin and since 1981 the publication has been continuous with two issues per year. Recently, since 2011 the Journal only publishes articles in English language.
Abstracting and indexing
The Revista Colombiana de Estadística is abstracted and indexed in Scopus, SciELO, Current Index to Statistics, Mathematical Reviews, Zentralblatt MATH, Redalyc, Latindex, and Publindex (category A1). According to the Journal Citation Reports, the journal has a 2014 impact factor of 0.179.
See also
Comparison of statistics journals
List of statistics journals
References
External links
Category A1 Publindex
Statistics journals
English-language journals
Biannual journals
Academic journals established in 1968
National University of Colombia academic journals |
https://en.wikipedia.org/wiki/Unipotent%20representation | In mathematics, a unipotent representation of a reductive group is a representation that has some similarities with unipotent conjugacy classes of groups.
Informally, Langlands philosophy suggests that there should be a correspondence between representations of a reductive group and conjugacy classes of a Langlands dual group, and the unipotent representations should be roughly the ones corresponding to unipotent classes in the dual group.
Unipotent representations are supposed to be the basic "building blocks" out of which one can construct all other representations in the following sense.
Unipotent representations should form a small (preferably finite) set of irreducible representations for each reductive group, such that all irreducible representations can be obtained from unipotent representations of possibly smaller groups by some sort of systematic process, such as (cohomological or parabolic) induction.
Finite fields
Over finite fields, the unipotent representations are those that occur in the decomposition of the Deligne–Lusztig characters R of the trivial representation 1 of a torus T . They were classified by .
Some examples of unipotent representations over finite fields are the trivial 1-dimensional representation, the Steinberg representation, and θ10.
Non-archimedean local fields
classified the unipotent characters over non-archimedean local fields.
Archimedean local fields
discusses several different possible definitions of unipotent representations of real Lie groups.
See also
Deligne–Lusztig theory
References
Representation theory |
https://en.wikipedia.org/wiki/Lee%20Sallows | Lee Cecil Fletcher Sallows (born April 30, 1944) is a British electronics engineer known for his contributions to recreational mathematics. He is particularly noted as the inventor of golygons, self-enumerating sentences, and geomagic squares.
Recreational mathematics
Sallows is an expert on the theory of magic squares and has invented several variations on them, including alphamagic squares and geomagic squares. The latter invention caught the attention of mathematician Peter Cameron who has said that he believes that "an even deeper structure may lie hidden beyond geomagic squares"
In "The lost theorem" published in 1997 he showed that every 3 × 3 magic square is associated with a unique parallelogram on the complex plane, a discovery that had escaped all previous researchers from ancient times down to the present day. In 2014 Sallows discovered a previously unnoticed result involving the medians of a triangle.
A golygon is a polygon containing only right angles, such that adjacent sides exhibit consecutive integer lengths. Golygons were invented and named by Sallows and introduced by A.K. Dewdney in the Computer Recreations column of the July 1990 issue of Scientific American.
In 2012 Sallows invented and named self-tiling tile sets—a new generalization of rep-tiles.
Personal life
Lee Sallows is the only son of Florence Eliza Fletcher and Leonard Gandy Sallows. He was born on 30 April 1944 at Brocket Hall in Hertfordshire, England, and grew up in the district of Upper Clapton in northeast London. Sallows attended Dame Alice Owen's School, then located at The Angel, Islington, but failed to settle in and was without diplomas when he left at age 17. Knowledge gained via interest in short-wave radio enabled him to find work as a technician within the electronics industry. In 1970 he moved to Nijmegen in the Netherlands, where until 2009, he worked as an electronic engineer at Radboud University. In 1975 Sallows met up with his Dutch partner Evert Lamfers, a cardiologist, with whom he has lived ever since.
Bibliography
2014 Sallows, Lee "More On Self-tiling Tile Sets", Mathematics Magazine, April 2014
2012 Sallows, Lee. "On Self-Tiling Tile Sets", Mathematics Magazine, December, 2012
2012 "Geometric Magic Squares: A Challenging New Twist Using Colored Shapes Instead of Numbers", Dover Publications,
1997 "The Lost Theorem", The Mathematical Intelligencer 1997 19; 4: 51–54.
1995 "The Impossible Problem", The Mathematical Intelligencer 1995 17; 1: 27–33.
1994 "Alphamagic Squares", In: The Lighter Side of Mathematics pp 305–39, Edited by R.K. Guy and R.E. Woodrow, pub. by The Mathematical Association of America, 1994,
1992
1991
1990 "A Curious New Result in Switching Theory", The Mathematical Intelligencer 1990; 12: 21–32.
1987 "In Quest of a Pangram", In: A Computer Science Reader, pp 200–20, Edited by EA Weiss, Springer-Verlag, New York,
1986 "Co-Descriptive Strings", (Lee Sallows & Victor L Eijkhout), Mathematical Gaze |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20Chesterfield%20F.C.%20season |
League table
Squad statistics
Appearances and goals
|-
|colspan="14"|Players played for Chesterfield but left before the end of the season:
|-
|colspan="14"|Players who played on loan for Chesterfield and returned to their parent club:
|}
Top scorers
Disciplinary record
Results
Pre-season friendlies
League One
FA Cup
League Cup
FL Trophy
Transfers
Awards
References
2011-12
2011–12 Football League One by team |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20Exeter%20City%20F.C.%20season |
League table
Statistics
Appearances and goals
|-
|colspan="14"|Players who left Exeter before the end of the season:
|-
|colspan="14"|Players who played on loan for Exeter and returned to their parent club:
|}
Top scorers
Disciplinary record
Results
Pre-season friendlies
League One
FA Cup
League Cup
FL Trophy
Transfers
Awards
References
2011–12
2011–12 Football League One by team |
https://en.wikipedia.org/wiki/Symplectic%20spinor%20bundle | In differential geometry, given a metaplectic structure on a -dimensional symplectic manifold the symplectic spinor bundle is the Hilbert space bundle associated to the metaplectic structure via the metaplectic representation. The metaplectic representation of the metaplectic group — the two-fold covering of the symplectic group — gives rise to an infinite rank vector bundle; this is the symplectic spinor construction due to Bertram Kostant.
A section of the symplectic spinor bundle is called a symplectic spinor field.
Formal definition
Let be a metaplectic structure on a symplectic manifold that is, an equivariant lift of the symplectic frame bundle with respect to the double covering
The symplectic spinor bundle is defined to be the Hilbert space bundle
associated to the metaplectic structure via the metaplectic representation also called the Segal–Shale–Weil representation of Here, the notation denotes the group of unitary operators acting on a Hilbert space
The Segal–Shale–Weil representation is an infinite dimensional unitary representation
of the metaplectic group on the space of all complex
valued square Lebesgue integrable square-integrable functions Because of the infinite dimension,
the Segal–Shale–Weil representation is not so easy to handle.
Notes
Further reading
Symplectic geometry
Structures on manifolds
Algebraic topology |
https://en.wikipedia.org/wiki/Felicia%20Chester | Felicia Chester (born March 24, 1988) is a basketball player who most recently played for the Chicago Sky of the Women's National Basketball Association.
DePaul statistics
Source
WNBA
Chester was selected in the second round of the 2011 WNBA draft (14th overall) by the Minnesota Lynx. She was then traded to Atlanta. She was waived before the season, but New York signed her on July 4, 2011.
References
External links
DePaul bio
Living people
1988 births
American women's basketball players
Basketball players from St. Louis
DePaul Blue Demons women's basketball players
Forwards (basketball)
Minnesota Lynx draft picks
New York Liberty players |
https://en.wikipedia.org/wiki/Vinberg%27s%20algorithm | In mathematics, Vinberg's algorithm is an algorithm, introduced by Ernest Borisovich Vinberg, for finding a fundamental domain of a hyperbolic reflection group.
used Vinberg's algorithm to describe the automorphism group of the 26-dimensional even unimodular Lorentzian lattice II25,1 in terms of the Leech lattice.
Description of the algorithm
Let be a hyperbolic reflection group. Choose any point ; we shall call it the basic (or initial) point. The fundamental domain of its stabilizer is a polyhedral cone in .
Let be the faces of this cone, and let be outer normal vectors to it. Consider the half-spaces
There exists a unique fundamental polyhedron of contained in and containing the point . Its faces containing are formed by faces of the cone . The other faces and the corresponding outward normals are constructed by induction. Namely, for we take a mirror such that the root orthogonal to it satisfies the conditions
(1) ;
(2) for all ;
(3) the distance is minimum subject to constraints (1) and (2).
References
Hyperbolic geometry
Reflection groups |
https://en.wikipedia.org/wiki/Dense%20submodule | In abstract algebra, specifically in module theory, a dense submodule of a module is a refinement of the notion of an essential submodule. If N is a dense submodule of M, it may alternatively be said that "N ⊆ M is a rational extension". Dense submodules are connected with rings of quotients in noncommutative ring theory. Most of the results appearing here were first established in , and .
It should be noticed that this terminology is different from the notion of a dense subset in general topology. No topology is needed to define a dense submodule, and a dense submodule may or may not be topologically dense in a module with topology.
Definition
This article modifies exposition appearing in and . Let R be a ring, and M be a right R module with submodule N. For an element y of M, define
Note that the expression y−1 is only formal since it is not meaningful to speak of the module-element y being invertible, but the notation helps to suggest that y⋅(y−1N) ⊆ N. The set y −1N is always a right ideal of R.
A submodule N of M is said to be a dense submodule if for all x and y in M with x ≠ 0, there exists an r in R such that xr ≠ {0} and yr is in N. In other words, using the introduced notation, the set
In this case, the relationship is denoted by
Another equivalent definition is homological in nature: N is dense in M if and only if
where E(M) is the injective hull of M.
Properties
It can be shown that N is an essential submodule of M if and only if for all y ≠ 0 in M, the set y⋅(y −1N) ≠ {0}. Clearly then, every dense submodule is an essential submodule.
If M is a nonsingular module, then N is dense in M if and only if it is essential in M.
A ring is a right nonsingular ring if and only if its essential right ideals are all dense right ideals.
If N and N' are dense submodules of M, then so is N ∩ N' .
If N is dense and N ⊆ K ⊆ M, then K is also dense.
If B is a dense right ideal in R, then so is y−1B for any y in R.
Examples
If x is a non-zerodivisor in the center of R, then xR is a dense right ideal of R.
If I is a two-sided ideal of R, I is dense as a right ideal if and only if the left annihilator of I is zero, that is, . In particular in commutative rings, the dense ideals are precisely the ideals which are faithful modules.
Applications
Rational hull of a module
Every right R module M has a maximal essential extension E(M) which is its injective hull. The analogous construction using a maximal dense extension results in the rational hull Ẽ(M) which is a submodule of E(M). When a module has no proper rational extension, so that Ẽ(M) = M, the module is said to be rationally complete. If R is right nonsingular, then of course Ẽ(M) = E(M).
The rational hull is readily identified within the injective hull. Let S=EndR(E(M)) be the endomorphism ring of the injective hull. Then an element x of the injective hull is in the rational hull if and only if x is sent to zero by all maps in S which are zero on M. In symbols,
|
https://en.wikipedia.org/wiki/Vladim%C3%ADr%20%C5%A0ver%C3%A1k | Vladimír Šverák (born 1959) is a Czech mathematician. Since 1990, he has been a professor at the University of Minnesota. Šverák made notable contributions to calculus of variations.
Šverák obtained his doctorate from the Charles University in Prague in 1986, under supervision of Jindřich Nečas. He worked on problems in the theory of non-linear elasticity. In 1992, he won an EMS Prize for producing a counterexample to a problem first posed by Charles B. Morrey, Jr. in 1950, whether rank-one convexity implies quasiconvexity. In 1994, Šverák was an Invited Speaker of the International Congress of Mathematicians in Zurich.
References
External links
Website at the University of Minnesota
1959 births
Living people
Czech mathematicians
Charles University alumni
University of Minnesota faculty |
https://en.wikipedia.org/wiki/Satake%20isomorphism | In mathematics, the Satake isomorphism, introduced by , identifies the Hecke algebra of a reductive group over a local field with a ring of invariants of the Weyl group. The geometric Satake equivalence is a geometric version of the Satake isomorphism, proved by .
Statement
Classical Satake isomorphism.
Let be a semisimple algebraic group, be a non-Archimedean local field and be its ring of integers. It's easy to see that is a grassmannian. For simplicity, we can think that and , for a prime number; in this case, is an infinite dimensional algebraic variety . One denotes the category of all compactly supported spherical functions on biinvariant under the action of as , the field of complex numbers, which is a Hecke algebra and can be also treated as a group scheme over . Let be the maximal torus of , be the Weyl group of . One can associate a cocharacter variety to . Let be the set of all cocharacters of , i.e. . The cocharacter variety is basically the group scheme created by adding the elements of as variables to , i.e. . There is a natural action of on the cocharacter variety , induced by the natural action of on . Then the Satake isomorphism is an algebra isomorphism from the category of spherical functions to the -invariant part of the aforementioned cocharacter variety. In formulas:
.
Geometric Satake isomorphism.
As Ginzburg said , "geometric" stands for sheaf theoretic. In order to obtain the geometric version of Satake isomorphism, one has to change the left part of the isomorphism, using Grothendieck group of the category of perverse sheaves on to replace the category of spherical functions; the replacement is de facto an algebra isomorphism over . One has also to replace the right hand side of the isomorphism by the Grothendieck group of finite dimensional complex representations of the Langlands dual of ; the replacement is also an algebra isomorphism over . Let denote the category of perverse sheaves on . Then, the geometric Satake isomorphism is
,
where the in stands for the Grothendieck group. This can be obviously simplified to
,
which is a fortiori an equivalence of Tannakian categories .
Notes
References
Representation theory |
https://en.wikipedia.org/wiki/Ichir%C5%8D%20Satake | (25 December 1927 – 10 October 2014) was a Japanese mathematician working on algebraic groups who introduced the Satake isomorphism and Satake diagrams. He was considered an iconic figure in the theory of linear algebraic groups and symmetric spaces.
Satake was born in Tokyo, Japan in 1927, and received his Ph.D. at the University of Tokyo in 1959 under the supervision of Shokichi Iyanaga. He was a professor at University of California, Berkeley from 1968 to 1983. After retirement he returned to Japan, where he spent time at Tohoku University and Chuo University. He died of respiratory failure on 10 October 2014.
Although they are often attributed to William Thurston, Satake was the first to introduce orbifold, which he did in the 1950s under the name of V-manifold. In , he gave the modern definition, along with the basic calculus of smooth functions and differential forms. He demonstrated that the de Rham theorem and Poincaré duality, along with their proofs, carry over to the orbifold setting. In , he demonstrated that the standard tensor calculus of bundles, connections, and curvature also carries over to orbifolds, along with the Chern-Gauss-Bonnet theorem and Shiing-Shen Chern's proof thereof.
Major publications
References
External links
FORMULA IN SIMPLE JORDAN ALGEBRAS ICHIRO SATAKE (Received May 7, 1984)
1927 births
2014 deaths
Deaths from respiratory failure
20th-century Japanese mathematicians
21st-century Japanese mathematicians
University of California, Berkeley faculty
University of Tokyo alumni
Academic staff of Tohoku University
Academic staff of Chuo University
University of Chicago faculty
Mathematicians from Tokyo
Group theorists
Topologists |
https://en.wikipedia.org/wiki/Victor%20Nicolas | Victor Edmond Nicolas (2 February 1906 – 16 July 1979) was a French sculptor.
Biography
Victor Nicolas was born in Brignoles, the son of Nicolas Bertin (1879–1918), professor of mathematics Mort pour la France, and Victorine Tardieu (1878–1965), teacher. He was the grandson of Fortuné Nicolas (1850–1920), judge of the canton court of Tavernes and mayor of Montmeyan from 1886 to 1892.
He was married to Josette Behar (1911–2011), sculptor, graduated from the École nationale supérieure des beaux-arts in Paris, with whom he had a son, Nicolas Vincent (1934–2009).
Educated at the college of Lorgues and then in high school of Toulon, where he received a scholarship from the artists society in Toulon.
Graduated from the École nationale supérieure des arts décoratifs in Paris. Student of Hector Lemaire, Camille Lefevre and Pierre Séguin. Eight medals won between 1924 and 1926.
Graduated from the École nationale supérieure des beaux-arts in Paris, sculpture section. Student of Jules Coutan, Paul Landowski and Auguste Carli between 1926 and 1930. Prize Roux of the Institut de France and prize Chenavard of the École nationale supérieure des beaux-arts. Elected chairman of the Fine Arts Section from the General Association of Students of Paris in 1928.
Three-time winner at the Salon des artistes français: honorable mention in 1929, bronze medal in 1933 and silver medal in 1934. Twice scholarship at the prestigious Prix de Rome of sculpture in 1930 and in 1933. Has worked in the studios of the sculptors Henri-Edouard Lombard and Naoum Aronson.
Set up his studio in Montmeyan, in the former chapel of the Holy Spirit, in 1930. Created many monuments in the departments of Var and Alpes-Maritimes. Also created various busts and work exhibited several times at the Henri Gaffié gallery of Nice.
Elected city councilor of Montmeyan and delegate for Senate election in 1935. Member of the National Front (French Resistance), designated mayor of Montmeyan in 1944, president of the Comité local de libération. Elected deputy mayor of Montmeyan in 1945 and designated deputy judge of the canton court of Tavernes in 1946.
Came to painting in 1953; his paintings and drawings are exhibited on several occasions in Artignosc-sur-Verdon and Draguignan between 1955 and 1957.
Appointed professor of drawing at the École des beaux-arts of Toulon in 1956 and taught there until the age of retirement in 1976. He died in a road accident in Montmeyan.
A posthumous exhibition of his paintings, drawings and sculptures is organised in Montmeyan in August and September 1981. The XXIVth Salon des imagiers of Toulon is dedicated to him from December 1981 to January 1982.
Work
Monument dedicated to Jean Aicard, jardin Alexandre 1er, Toulon, 1931 (the bronze bust was destroyed by the Germans during the occupation)
Tribute to the Unknown Soldier, plaster bas-relief, Prize Roux of the Institut de France, Paris, 1933
Fisherman pulling in his net, plaster statue, prize Chenavard of the |
https://en.wikipedia.org/wiki/Standardized%20mean%20of%20a%20contrast%20variable | In statistics, the standardized mean of a contrast variable (SMCV or SMC), is a parameter assessing effect size. The SMCV is defined as mean divided by the standard deviation of a contrast variable.
The SMCV was first proposed for one-way ANOVA cases
and was then extended to multi-factor ANOVA cases
.
Background
Consistent interpretations for the strength of group comparison, as represented by a contrast, are important.
When there are only two groups involved in a comparison, SMCV is the same as the strictly standardized mean difference (SSMD). SSMD belongs to a popular type of effect-size measure called "standardized mean differences" which includes Cohen's and Glass's
In ANOVA, a similar parameter for measuring the strength of group comparison is standardized effect size (SES). One issue with SES is that its values are incomparable for contrasts with different coefficients. SMCV does not have such an issue.
Concept
Suppose the random values in t groups represented by random variables have means and variances , respectively. A contrast variable is defined by
where the 's are a set of coefficients representing a comparison of interest and satisfy . The SMCV of contrast variable , denoted by , is defined as
where is the covariance of and . When are independent,
Classifying rule for the strength of group comparisons
The population value (denoted by ) of SMCV can be used to classify the strength of a comparison represented by a contrast variable, as shown in the following table. This classifying rule has a probabilistic basis due to the link between SMCV and c+-probability.
Statistical estimation and inference
The estimation and inference of SMCV presented below is for one-factor experiments. Estimation and inference of SMCV for multi-factor experiments has also been discussed.
The estimation of SMCV relies on how samples are obtained in a study. When the groups are correlated, it is usually difficult to estimate the covariance among groups. In such a case, a good strategy is to obtain matched or paired samples (or subjects) and to conduct contrast analysis based on the matched samples. A simple example of matched contrast analysis is the analysis of paired difference of drug effects after and before taking a drug in the same patients. By contrast, another strategy is to not match or pair the samples and to conduct contrast analysis based on the unmatched or unpaired samples. A simple example of unmatched contrast analysis is the comparison of efficacy between a new drug taken by some patients and a standard drug taken by other patients. Methods of estimation for SMCV and c+-probability in matched contrast analysis may differ from those used in unmatched contrast analysis.
Unmatched samples
Consider an independent sample of size ,
from the group . 's are independent. Let ,
and
When the groups have unequal variance, the maximal likelihood estimate (MLE) and method-of-moment estimate (MM) of SMCV () are, respe |
https://en.wikipedia.org/wiki/Survey%20data%20collection | With the application of probability sampling in the 1930s, surveys became a standard tool for empirical research in social sciences, marketing, and official statistics. The methods involved in survey data collection are any of a number of ways in which data can be collected for a statistical survey. These are methods that are used to collect information from a sample of individuals in a systematic way. First there was the change from traditional paper-and-pencil interviewing (PAPI) to computer-assisted interviewing (CAI). Now, face-to-face surveys (CAPI), telephone surveys (CATI), and mail surveys (CASI, CSAQ) are increasingly replaced by web surveys.
Modes of data collection
There are several ways of administering a survey. Within a survey, different methods can be used for different parts. For example, interviewer administration can be used for general topics but self-administration for sensitive topics. The choice between administration modes is influenced by several factors, including 1) costs, 2) coverage of the target population (including group-specific preferences for certain modes), 3) flexibility of asking questions, 4) respondents’ willingness to participate and 5) response accuracy. Different methods create mode effects that change how respondents answer. The most common modes of administration are listed under the following headings.
Mobile surveys
Mobile data collection or mobile surveys is an increasingly popular method of data collection. Over 50% of surveys today are opened on mobile devices. The survey, form, app or collection tool is on a mobile device such as a smart phone or a tablet. These devices offer innovative ways to gather data, and eliminate the laborious "data entry" (of paper form data into a computer), which delays data analysis and understanding. By eliminating paper, mobile data collection can also dramatically reduce costs: one World Bank study in Guatemala found a 71% decrease in cost while using mobile data collection, compared to the previous paper-based approach.
SMS surveys can reach any handset, in any language and in any country. As they are not dependent on internet access and the answers can be sent when its convenient, they are a suitable mobile survey data collection channel for many situations that require fast, high volume responses. As a result, SMS surveys can deliver 80% of responses in less than 2 hours and often at much lower cost compared to face-to-face surveys, due to the elimination of travel/personnel costs.
Apart from the high mobile phone penetration, further advantages are quicker response times and the possibility to reach previously hard-to-reach target groups. In this way, mobile technology allows marketers, researchers and employers to create real and meaningful mobile engagement in environments different from the traditional one in front of a desktop computer. However, even when using mobile devices to answer the web surveys, most respondents still answer from home.
Online su |
https://en.wikipedia.org/wiki/King%20effect | In statistics, economics, and econophysics, the king effect is the phenomenon in which the top one or two members of a ranked set show up as clear outliers. These top one or two members are unexpectedly large because they do not conform to the statistical distribution or rank-distribution which the remainder of the set obeys.
Distributions typically followed include the power-law distribution, that is a basis for the stretched exponential function, and parabolic fractal distribution.
The King effect has been observed in the distribution of:
French city sizes (where the point representing Paris is the "king", failing to conform to the stretched exponential), and similarly for other countries with a primate city, such as the United Kingdom (London), and the extreme case of Bangkok (see list of cities in Thailand).
Country populations (where only the points representing China and India fail to fit a stretched exponential).
Note, however, that the king effect is not limited to outliers with a positive evaluation attached to their rank: for rankings on an undesirable attribute, there may exist a pauper effect, with a similar detachment of extremely ranked data points from the reasonably distributed portion of the data set.
See also
Zipf's law
Didier Sornette
References
Statistical data sets
Economics effects |
https://en.wikipedia.org/wiki/Suicide%20in%20Switzerland | Switzerland had a standardised suicide rate of 10.7 per 100,000 (male 15.5, female 6.0) as of 2015.
The actual (non-standardised) rate was 12.5 (male 18.5, female 6.6) in 2014.
Statistics
The 2015 Swiss suicide rate of 10.7 (male 15.5, female 6.0) published by the World Health Organization is "age-standardised", attempting to control for differences in age structure for the purposes of international comparison.
The standardised Swiss suicide rate is similar to the rates of neighbouring France (12.7; male 19.0, female 5.9), Austria (11.7; male 18.5, female 5.3) and Germany (9.1; male 14.5, female 4.5). It is somewhat below the European average of 11.93, and close to the global average of 10.67.
The raw (non-standardised) Swiss suicide rate is somewhat higher; in 2014, 1,029 people committed non-assisted suicide (754 men, 275 women), for a rate of 12.5 per 100,000 (18.5 male, 6.6 female).
Not included are 742 assisted suicides (320 men, 422 women); most of the assisted suicides concerned elderly people suffering from a terminal disease.
The Swiss statistics of causes of death by years of potential life lost (YPLL) as of 2014 estimates suicides at 12,323 YPLL for men (12% of YPLL from all causes of death) and 4,750 YPLL for women (8% of YPLL from all causes of death). Standardised rates of YPLL per 100,000 people relative to the 2010 European standard population (Eurostat 2013) are 327.0 for men (29 hours per capita) and 128.6 (11 hours per capita) for women.
The suicide rate has declined steadily during the 1980s to 2000s, down from 25 in the mid 1980s. Since ca. 2010, the downward trend has stopped and there has been no further significant reduction in suicide rates.
The peak in the 1980s was preceded by a historically low rate of 17 in the 1960s.
The male-to-female gender ratio has been reduced from 6:1 in the late 19th century to about 2.5:1 today. In 1881, male suicide rate was at 42, close to 2.5 times the modern value, while female suicide rate was at 7, comparable to the modern value.
The Swiss cantons with the highest suicide rates for the period 2001–2010 were Appenzell Ausserrhoden for men (37) and canton of Schaffhausen for women (10); the canton with the lowest suicide rate was Italian-speaking Ticino (male 14, female 5), consistent with lower rates in southern Europe, but still notably higher than the rate in neighbouring Italy (at 5.4 as of 2015).
A statistic of suicide methods compiled for the period of 2001–2012 found that the preferred suicide method for men was by shooting (29.7%), followed by hanging (28.7%), poison (16.5%), jumping from a height (9.8%) and by train (7.9%). The statistics for women are markedly different, the most preferred method being poison (38.8%), and higher rates for jumping from a height (16.0%) and suicide by train (9.5%), but lower rates for hanging (18.5%) and shooting (3.0%).
Assisted suicide
In 2014, a total of 742 assisted suicides (320 men, 422 women) had been recorded, or 1.2% of de |
https://en.wikipedia.org/wiki/Petr%20Le%C5%A1ka | Petr Leška (born November 16, 1975) is a Czech professional ice hockey player. He played with HC Zlín in the Czech Extraliga during the 2010–11 Czech Extraliga season.
Career statistics
References
External links
1975 births
Czech ice hockey forwards
PSG Berani Zlín players
Living people
Sportspeople from Chomutov
Ice hockey people from the Ústí nad Labem Region
Södertälje SK players
Rögle BK players
Flint Generals (CoHL) players
HC Plzeň players
HC Sparta Praha players
Langley Thunder players
Surrey Eagles players
Czech expatriate ice hockey players in Canada
Czech expatriate ice hockey players in the United States
Czech expatriate ice hockey players in Sweden |
https://en.wikipedia.org/wiki/Automorphic%20L-function | In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic representation π of a reductive group G over a global field and a finite-dimensional complex representation r of the Langlands dual group LG of G, generalizing the Dirichlet L-series of a Dirichlet character and the Mellin transform of a modular form. They were introduced by .
and gave surveys of automorphic L-functions.
Properties
Automorphic -functions should have the following properties (which have been proved in some cases but are still conjectural in other cases).
The L-function should be a product over the places of of local functions.
Here the automorphic representation is a tensor product of the representations of local groups.
The L-function is expected to have an analytic continuation as a meromorphic function of all complex , and satisfy a functional equation
where the factor is a product of "local constants"
almost all of which are 1.
General linear groups
constructed the automorphic L-functions for general linear groups with r the standard representation (so-called standard L-functions) and verified analytic continuation and the functional equation, by using a generalization of the method in Tate's thesis. Ubiquitous in the Langlands Program are Rankin-Selberg products of representations of GL(m) and GL(n). The resulting Rankin-Selberg L-functions satisfy a number of analytic properties, their functional equation being first proved via the Langlands–Shahidi method.
In general, the Langlands functoriality conjectures imply that automorphic L-functions of a connected reductive group are equal to products of automorphic L-functions of general linear groups. A proof of Langlands functoriality would also lead towards a thorough understanding of the analytic properties of automorphic L-functions.
References
Automorphic forms
Zeta and L-functions
Langlands program |
https://en.wikipedia.org/wiki/Double%20centralizer%20theorem | In the branch of abstract algebra called ring theory, the double centralizer theorem can refer to any one of several similar results. These results concern the centralizer of a subring S of a ring R, denoted CR(S) in this article. It is always the case that CR(CR(S)) contains S, and a double centralizer theorem gives conditions on R and S that guarantee that CR(CR(S)) is equal to S.
Statements of the theorem
Motivation
The centralizer of a subring S of R is given by
Clearly CR(CR(S)) ⊇ S, but it is not always the case that one can say the two sets are equal. The double centralizer theorems give conditions under which one can conclude that equality occurs.
There is another special case of interest. Let M be a right R module and give M the natural left E-module structure, where E is End(M), the ring of endomorphisms of the abelian group M. Every map mr given by mr(x) = xr creates an additive endomorphism of M, that is, an element of E. The map r → mr is a ring homomorphism of R into the ring E, and we denote the image of R inside of E by RM. It can be checked that the kernel of this canonical map is the annihilator Ann(MR). Therefore, by an isomorphism theorem for rings, RM is isomorphic to the quotient ring R/Ann(MR). Clearly when M is a faithful module, R and RM are isomorphic rings.
So now E is a ring with RM as a subring, and CE(RM) may be formed. By definition one can check that CE(RM) = End(MR), the ring of R module endomorphisms of M. Thus if it occurs that CE(CE(RM)) = RM, this is the same thing as saying CE(End(MR)) = RM.
Central simple algebras
Perhaps the most common version is the version for central simple algebras, as it appears in :
Theorem: If A is a finite-dimensional central simple algebra over a field F and B is a simple subalgebra of A, then CA(CA(B)) = B, and moreover the dimensions satisfy
Artinian rings
The following generalized version for Artinian rings (which include finite-dimensional algebras) appears in . Given a simple R module UR, we will borrow notation from the above motivation section including RU and E=End(U). Additionally, we will write D=End(UR) for the subring of E consisting of R-homomorphisms. By Schur's lemma, D is a division ring.
Theorem: Let R be a right Artinian ring with a simple right module UR, and let RU, D and E be given as in the previous paragraph. Then
.
Remarks
In this version, the rings are chosen with the intent of proving the Jacobson density theorem. Notice that it only concludes that a particular subring has the centralizer property, in contrast to the central simple algebra version.
Since algebras are normally defined over commutative rings, and all the involved rings above may be noncommutative, it's clear that algebras are not necessarily involved.
If U is additionally a faithful module, so that R is a right primitive ring, then RU is ring isomorphic to R.
Polynomial identity rings
In , a version is given for polynomial identity rings. The notation Z(R) will be used to deno |
https://en.wikipedia.org/wiki/Selberg%27s%201/4%20conjecture | In mathematics, Selberg's conjecture, also known as Selberg's eigenvalue conjecture, conjectured by , states that the eigenvalues of the Laplace operator on Maass wave forms of congruence subgroups are at least 1/4. Selberg showed that the eigenvalues are at least 3/16. Subsequent works improved the bound, and the best bound currently known is 975/4096≈0.238..., due to .
The generalized Ramanujan conjecture for the general linear group implies Selberg's conjecture. More precisely, Selberg's conjecture is essentially the generalized Ramanujan conjecture for the group GL2 over the rationals at the infinite place, and says that the component at infinity of the corresponding representation is a principal series representation of GL2(R) (rather than a complementary series representation). The generalized Ramanujan conjecture in turn follows from the Langlands functoriality conjecture, and this has led to some progress on Selberg's conjecture.
References
External links
Automorphic forms
Conjectures |
https://en.wikipedia.org/wiki/Dual-flashlight%20plot | In statistics, a dual-flashlight plot is a type of scatter-plot in which the standardized mean of a contrast variable (SMCV) is plotted against the mean of a contrast variable representing a comparison of interest
. The commonly used dual-flashlight plot is for the difference between two groups in high-throughput experiments such as microarrays and high-throughput screening studies, in which we plot the SSMD versus average log fold-change on the y- and x-axes, respectively, for all genes or compounds (such as siRNAs or small molecules) investigated in an experiment.
As a whole, the points in a dual-flashlight plot look like the beams of a flashlight with two heads, hence the name dual-flashlight plot.
With the dual-flashlight plot, we can see how the genes or compounds are distributed into each category in effect sizes, as shown in the figure. Meanwhile, we can also see the average fold-change for each gene or compound. The dual-flashlight plot is similar to the volcano plot. In a volcano plot, the p-value (or q-value), instead of SMCV or SSMD, is plotted against average fold-change
. The advantage of using SMCV over p-value (or q-value) is that, if there exist any non-zero true effects for a gene or compound, the estimated SMCV goes to its population value whereas the p-value (or q-value) for testing no mean difference (or zero contrast mean) goes to zero when the sample size increases
. Hence, the value of SMCV is comparable whereas the value of p-value or q-value is not comparable in experiments with different sample size, especially when many investigated genes or compounds do not have exactly zero effects. The dual-flashlight plot bears the same advantage that the SMCV has, as compared to the volcano plot.
See also
Effect size
SSMD
SMCV
Contrast variable
ANOVA
Volcano plot (statistics)
Further reading
Zhang XHD (2011) "Optimal High-Throughput Screening: Practical Experimental Design and Data Analysis for Genome-scale RNAi Research, Cambridge University Press"
References
Bioinformatics
Statistical charts and diagrams |
https://en.wikipedia.org/wiki/Donaldson%E2%80%93Thomas%20theory | In mathematics, specifically algebraic geometry, Donaldson–Thomas theory is the theory of Donaldson–Thomas invariants. Given a compact moduli space of sheaves on a Calabi–Yau threefold, its Donaldson–Thomas invariant is the virtual number of its points, i.e., the integral of the cohomology class 1 against the virtual fundamental class. The Donaldson–Thomas invariant is a holomorphic analogue of the Casson invariant. The invariants were introduced by . Donaldson–Thomas invariants have close connections to Gromov–Witten invariants of algebraic three-folds and the theory of stable pairs due to Rahul Pandharipande and Thomas.
Donaldson–Thomas theory is physically motivated by certain BPS states that occur in string and gauge theorypg 5. This is due to the fact the invariants depend on a stability condition on the derived category of the moduli spaces being studied. Essentially, these stability conditions correspond to points in the Kahler moduli space of a Calabi-Yau manifold, as considered in mirror symmetry, and the resulting subcategory is the category of BPS states for the corresponding SCFT.
Definition and examples
The basic idea of Gromov–Witten invariants is to probe the geometry of a space by studying pseudoholomorphic maps from Riemann surfaces to a smooth target. The moduli stack of all such maps admits a virtual fundamental class, and intersection theory on this stack yields numerical invariants that can often contain enumerative information. In similar spirit, the approach of Donaldson–Thomas theory is to study curves in an algebraic three-fold by their equations. More accurately, by studying ideal sheaves on a space. This moduli space also admits a virtual fundamental class and yields certain numerical invariants that are enumerative.
Whereas in Gromov–Witten theory, maps are allowed to be multiple covers and collapsed components of the domain curve, Donaldson–Thomas theory allows for nilpotent information contained in the sheaves, however, these are integer valued invariants. There are deep conjectures due to Davesh Maulik, Andrei Okounkov, Nikita Nekrasov and Rahul Pandharipande, proved in increasing generality, that Gromov–Witten and Donaldson–Thomas theories of algebraic three-folds are actually equivalent. More concretely, their generating functions are equal after an appropriate change of variables. For Calabi–Yau threefolds, the Donaldson–Thomas invariants can be formulated as weighted Euler characteristic on the moduli space. There have also been recent connections between these invariants, the motivic Hall algebra, and the ring of functions on the quantum torus.
The moduli space of lines on the quintic threefold is a discrete set of 2875 points. The virtual number of points is the actual number of points, and hence the Donaldson–Thomas invariant of this moduli space is the integer 2875.
Similarly, the Donaldson–Thomas invariant of the moduli space of conics on the quintic is 609250.
Definition
For a Calabi-Yau thre |
https://en.wikipedia.org/wiki/Base%20change%20lifting | In mathematics, base change lifting is a method of constructing new automorphic forms from old ones, that corresponds in Langlands philosophy to the operation of restricting a representation of a Galois group to a subgroup.
The Doi–Naganuma lifting from 1967 was a precursor of the base change lifting. Base change lifting was introduced by for Hilbert modular forms of cyclic totally real fields of prime degree, by comparing the trace of twisted Hecke operators on Hilbert modular forms with the trace of Hecke operators on ordinary modular forms. gave a representation theoretic interpretation of Saito's results and used this to generalize them. extended the base change lifting to more general automorphic forms and showed how to use the base change lifting for GL2 to prove the Artin conjecture for tetrahedral and some octahedral 2-dimensional representations of the Galois group.
, and gave expositions of the base change lifting for GL2 and its applications to the Artin conjecture.
Properties
If E/F is a finite cyclic Galois extension of global fields, then the base change lifting of gives a map from automorphic forms for GLn(F) to automorphic forms for GLn(E) = ResE/FGLn(F). This base change lifting is the special case of Langlands functoriality, corresponding (roughly) to the diagonal embedding of the Langlands dual GLn(C) of GLn to the Langlands dual GLn(C)×...×GLn(C) of ResE/FGLn.
References
Langlands program |
https://en.wikipedia.org/wiki/Curt%20Meyer | Curt Meyer (19 November 1919 – 18 April 2011) was a German mathematician. He made notable contributions to number theory.
A native of Bremerhaven, Meyer obtained his doctorate from the Humboldt University of Berlin in 1950, under supervision of Helmut Hasse. In 1966 he became professor of mathematics at the University of Cologne, a position he held until 1985.
Among his most important results is an alternative solution to the class number 1 problem, building on the original Stark–Heegner theorem.
Books by Meyer
References
External links
1919 births
2011 deaths
20th-century German mathematicians
21st-century German mathematicians
Humboldt University of Berlin alumni
Academic staff of the University of Cologne |
https://en.wikipedia.org/wiki/Christopher%20Deninger | Christopher Deninger (born 8 April 1958) is a German mathematician at the University of Münster. Deninger's research focuses on arithmetic geometry, including applications to L-functions.
Career
Deninger obtained his doctorate from the University of Cologne in 1982, under the supervision of Curt Meyer. In 1992 he shared a Gottfried Wilhelm Leibniz Prize with Michael Rapoport, Peter Schneider and Thomas Zink. In 1998 he was a plenary speaker at the International Congress of Mathematicians in 1998 in Berlin. In 2012 he became a fellow of the American Mathematical Society.
Mathematical work
Artin–Verdier duality
In a series of papers between 1984 and 1987, Deninger studied extensions of Artin–Verdier duality. Broadly speaking, Artin–Verdier duality, a consequence of class field theory, is an arithmetic analogue of Poincaré duality, a duality for sheaf cohomology on a compact manifold. In this parallel, the (spectrum of the) ring of integers in a number field corresponds to a 3-manifold. Following work of Mazur, Deninger (1984) extended Artin–Verdier duality to function fields. Deninger then extended these results in various directions, such as non-torsion sheaves (1986), arithmetic surfaces (1987), as well as higher-dimensional local fields (with Wingberg, 1986). The appearance of Bloch's motivic complexes considered in the latter papers influenced work of several authors including , who identified Bloch's complexes to be the dualizing complexes over higher-dimensional schemes.
Special values of L-functions
Another group of Deninger's papers studies L-functions and their special values. A classical example of an L-function is the Riemann zeta function ζ(s), for which formulas such as
ζ(2) = π2 / 6
are known since Euler. In a landmark paper, had proposed a set of far-reaching conjectures describing the special values of L-functions, i.e., the values of L-functions at integers. In very rough terms, Beilinson's conjectures assert that for a smooth projective algebraic variety X over Q, motivic cohomology of X should be closely related to Deligne cohomology of X. In addition, the relation between these two cohomology theories should explain, according to Beilinson's conjecture, the pole orders and the values of
L(hn(X), s)
at integers s. Bloch and Beilinson proved essential parts of this conjecture for h1(X) in the case where X is an elliptic curve with complex multiplication and s=2. In 1988, Deninger & Wingberg gave an exposition of that result. In 1989 and 1990, Deninger extended this result to certain elliptic curves considered by Shimura, at all s≥2. Deninger & Nart (1995) expressed the height pairing, a key ingredient of Beilinson's conjecture, as a natural pairing of Ext-groups in a certain category of motives. In 1995, Deninger studied Massey products in Deligne cohomology and conjectured therefrom a formula for the special value for the L-function of an elliptic curve at s=3, which was subsequently confirmed by . As of 2018, Beilinson's |
https://en.wikipedia.org/wiki/Annette%20Huber-Klawitter | Annette Huber-Klawitter (née Huber, born 23 May 1967) is a German mathematician at the University of Freiburg. Her research interests includes algebraic geometry, in particular the Bloch–Kato conjectures.
A native of Frankfurt am Main, Huber-Klawitter began her academic career at the Goethe University Frankfurt. She obtained her doctorate from the University of Münster in 1994, under the supervision of Christopher Deninger. In 1996 Huber-Klawitter won an EMS Prize. She was an invited speaker at the 2002 International Congress of Mathematicians in Beijing. In 2012 she became a fellow of the American Mathematical Society.
References
External links
Website at the University of Freiburg
1967 births
Living people
20th-century German mathematicians
University of Münster alumni
Academic staff of Leipzig University
Academic staff of the University of Freiburg
Fellows of the American Mathematical Society
Women mathematicians
21st-century German mathematicians |
https://en.wikipedia.org/wiki/Dmitry%20Kramkov | Dmitry Olegovich Kramkov () is a Russian mathematician at Carnegie Mellon University. His research field are statistics and financial mathematics.
Kramkov obtained his doctorate from Steklov Institute of Mathematics in 1992, under supervision of Albert Shiryaev. In 1996 he was awarded an EMS Prize for his work in filtered statistical experiments.
Kramkov's optional decomposition theorem is named after him.
References
20th-century births
Living people
Moscow Institute of Physics and Technology alumni
Russian mathematicians
Carnegie Mellon University faculty
Soviet mathematicians
Year of birth missing (living people)
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Euler%E2%80%93Rodrigues%20formula | In mathematics and mechanics, the Euler–Rodrigues formula describes the rotation of a vector in three dimensions. It is based on Rodrigues' rotation formula, but uses a different parametrization.
The rotation is described by four Euler parameters due to Leonhard Euler. The Rodrigues formula (named after Olinde Rodrigues), a method of calculating the position of a rotated point, is used in some software applications, such as flight simulators and computer games.
Definition
A rotation about the origin is represented by four real numbers, , , , such that
When the rotation is applied, a point at position rotates to its new position
Vector formulation
The parameter may be called the scalar parameter and the vector parameter. In standard vector notation, the Rodrigues rotation formula takes the compact form
Symmetry
The parameters and describe the same rotation. Apart from this symmetry, every set of four parameters describes a unique rotation in three-dimensional space.
Composition of rotations
The composition of two rotations is itself a rotation. Let and be the Euler parameters of two rotations. The parameters for the compound rotation (rotation 2 after rotation 1) are as follows:
It is straightforward, though tedious, to check that . (This is essentially Euler's four-square identity, also used by Rodrigues.)
Rotation angle and rotation axis
Any central rotation in three dimensions is uniquely determined by its axis of rotation (represented by a unit vector ) and the rotation angle . The Euler parameters for this rotation are calculated as follows:
Note that if is increased by a full rotation of 360 degrees, the arguments of sine and cosine only increase by 180 degrees. The resulting parameters are the opposite of the original values, ; they represent the same rotation.
In particular, the identity transformation (null rotation, ) corresponds to parameter values . Rotations of 180 degrees about any axis result in .
Connection with quaternions
The Euler parameters can be viewed as the coefficients of a quaternion; the scalar parameter is the real part, the vector parameters , , are the imaginary parts.
Thus we have the quaternion
which is a quaternion of unit length (or versor) since
Most importantly, the above equations for composition of rotations are precisely the equations for multiplication of quaternions. In other words, the group of unit quaternions with multiplication, modulo the negative sign, is isomorphic to the group of rotations with composition.
Connection with SU(2) spin matrices
The Lie group SU(2) can be used to represent three-dimensional rotations in complex matrices. The SU(2)-matrix corresponding to a rotation, in terms of its Euler parameters, is
Alternatively, this can be written as the sum
where the are the Pauli spin matrices. Thus, the Euler parameters are the real and imaginary coordinates in an SU(2) matrix corresponding to an element of the spin group Spin(3), which maps by a double cove |
https://en.wikipedia.org/wiki/Sphere%E2%80%93cylinder%20intersection | In the theory of analytic geometry for real three-dimensional space, the curve formed from the intersection between a sphere and a cylinder can be a circle, a point, the empty set, or a special type of curve.
For the analysis of this situation, assume (without loss of generality) that the axis of the cylinder coincides with the z-axis; points on the cylinder (with radius ) satisfy
We also assume that the sphere, with radius is centered at a point on the positive x-axis, at point . Its points satisfy
The intersection is the collection of points satisfying both equations.
Trivial cases
Sphere lies entirely within cylinder
If , the sphere lies entirely in the interior of the cylinder. The intersection is the empty set.
Sphere touches cylinder in one point
If the sphere is smaller than the cylinder () and , the sphere lies in the interior of
the cylinder except for one point. The intersection is the single point .
Sphere centered on cylinder axis
If the center of the sphere lies on the axis of the cylinder, . In that case, the intersection consists of
two circles of radius . These circles lie in the planes
If , the intersection is a single circle in the plane .
Non-trivial cases
Subtracting the two equations given above gives
Since is a quadratic function of , the projection of the intersection onto the xz-plane is the section of an orthogonal parabola; it is only a section due to the fact that .
The vertex of the parabola lies at point , where
Intersection consists of two closed curves
If , the condition cuts the parabola into two segments. In this case, the intersection of sphere and cylinder consists of two closed curves, which are mirror images of each other.
Their projection in the xy-plane are circles of radius .
Each part of the intersection can be parametrized by an angle :
The curves contain the following extreme points:
Intersection is a single closed curve
If , the intersection of sphere and cylinder consists of a single closed curve.
It can be described by the same parameter equation as in the previous section, but the angle
must be restricted to , where .
The curve contains the following extreme points:
Limiting case
In the case , the cylinder and sphere are tangential to each other at point .
The intersection resembles a figure eight: it is a closed curve which intersects itself. The above parametrization becomes
where now goes through two full revolutions.
In the special case , the intersection is known as Viviani's curve. Its parameter representation is
The volume of the intersection of the two bodies, sometimes called Viviani's volume, is
See also
Viviani's curve
References
Analytic geometry
Spherical geometry
Spherical curves
Geometric intersection |
https://en.wikipedia.org/wiki/List%20of%20the%20busiest%20airports%20in%20Poland | This is a list of the busiest airports in Poland.
At a glance
2023 (statistics from January to September)
2022
2021
2020
2019
2018
2017
2016
Notes:
: Olsztyn-Mazury Airport commenced operation on 20 January 2016.
2015
Notes:
: Radom Airport became operational on 29 May 2014. However, it didn't commence operation until 1 September 2015.
See also
List of airports in Poland
List of the busiest airports in Europe
References
Po |
https://en.wikipedia.org/wiki/List%20of%20the%20busiest%20airports%20in%20Croatia | The following are lists of busiest airports in Croatia.
In graph
By passenger traffic
References
External links
CCAA 2009–2010 statistics
CCAA 2010–2011 statistics
CCAA 2011–2012 statistics
CCAA 2014–2015 statistics
2020 passenger traffic stats at the Croatian Bureau of Statistics website (11 February 2021)
Croatia
Busiest
Airports, busiest
Croatia
Airports, busiest |
https://en.wikipedia.org/wiki/Nichols%20algebra | In algebra, the Nichols algebra of a braided vector space (with the braiding often induced by a finite group) is a braided Hopf algebra which is denoted by and named after the mathematician Warren Nichols. It takes the role of quantum Borel part of a pointed Hopf algebra such as a quantum groups and their well known finite-dimensional truncations. Nichols algebras can immediately be used to write down new such quantum groups by using the Radford biproduct.
The classification of all such Nichols algebras and even all associated quantum groups (see Application) has been progressing rapidly, although still much is open: The case of an abelian group was solved in 2005, but otherwise this phenomenon seems to be very rare, with a handful examples known and powerful negation criteria established (see below). See also this List of finite-dimensional Nichols algebras.
The finite-dimensional theory is greatly governed by a theory of root systems and Dynkin diagrams, strikingly similar to those of semisimple Lie algebras. A comprehensive introduction is found in the lecture of Heckenberger.
Definition
Consider a Yetter–Drinfeld module V in the Yetter–Drinfeld category . This is especially a braided vectorspace, see Braided monoidal category.
The tensor algebra of a Yetter–Drinfeld module is always a Braided Hopf algebra. The coproduct and counit of is defined in such a way that the elements of are primitive, that is
for all
The Nichols algebra can be uniquely defined by several equivalent characterizations, some of which focus on the Hopf algebra structure and some are more combinatorial. Regardless, determining the Nichols algebra explicitly (even decide if it's finite-dimensional) can be very difficult and is open in several concrete instances (see below).
Definition I: Combinatorical formula
Let be a braided vector space, this means there is an action of the braid group on for any , where the transposition acts as . Clearly there is a homomorphism to the symmetric group but neither does this admit a section, nor does the action on in general factorize over this.
Consider nevertheless a set-theoretic section sending transposition to transposition and arbitrary elements via any reduced expression. This is not a group homomorphism, but Matsumoto's theorem (group theory) tells us that the action of any on is well-defined independently of the choice of a reduced expression. Finally the Nichols algebra is then
This definition was later (but independently) given by Woronowicz. It has the disadvantage of being rarely useful in algebraic proofs but it represents an intuition in its own right and it has the didactical advantage of being very explicit and independent of the notation of a Hopf algebra.
Definition II: Prescribed primitives
The Nichols algebra is the unique Hopf algebra in the braided category generated by the given , such that are the only primitive elements.
This is the original definition due to Nichols and it makes |
https://en.wikipedia.org/wiki/Alvis%E2%80%93Curtis%20duality | In mathematics, the Alvis–Curtis duality is a duality operation on the characters of a reductive group over a finite field, introduced by and studied by his student . introduced a similar duality operation for Lie algebras.
Alvis–Curtis duality has order 2 and is an isometry on generalized characters.
discusses Alvis–Curtis duality in detail.
Definition
The dual ζ* of a character ζ of a finite group G with a split BN-pair is defined to be
Here the sum is over all subsets J of the set R of simple roots of the Coxeter system of G. The character ζ is the truncation of ζ to the parabolic subgroup PJ of the subset J, given by restricting ζ to PJ and then taking the space of invariants of the unipotent radical of PJ, and ζ is the induced representation of G. (The operation of truncation is the adjoint functor of parabolic induction.)
Examples
The dual of the trivial character 1 is the Steinberg character.
showed that the dual of a Deligne–Lusztig character R is εGεTR.
The dual of a cuspidal character χ is (–1)|Δ|χ, where Δ is the set of simple roots.
The dual of the Gelfand–Graev character is the character taking value |ZF|ql on the regular unipotent elements and vanishing elsewhere.
References
Representation theory
Duality theories |
https://en.wikipedia.org/wiki/Charles%20W.%20Curtis | Charles Whittlesey Curtis (born October 13, 1926) is a mathematician and historian of mathematics, known for his work in finite group theory and representation theory. He is a retired professor of mathematics at the University of Oregon.
Research
Curtis introduced Curtis duality, a duality operation on the characters of a reductive group over a finite field. His book with Irving Reiner, , was the standard text on representation theory for many years.
Biography
Curtis received a bachelor's degree from Bowdoin College in 1948, and his Ph.D. from Yale University in 1951, under the supervision of Nathan Jacobson. He taught at the University of Wisconsin–Madison from 1954 to 1963. Subsequently, he moved to the University of Oregon, where he is an emeritus professor.
While at Yale, on June 17, 1950 in Cheshire, Connecticut, Curtis married his wife Elizabeth, a kindergarten teacher and childcare provider. At the time of their 50th anniversary in 2000, they had three grandchildren.
In 2012 he became a fellow of the American Mathematical Society.
Publications
.
References
External links
Pictures of C. W. Curtis from Oberwolfach
20th-century American mathematicians
Group theorists
American historians of mathematics
Institute for Advanced Study visiting scholars
Bowdoin College alumni
Yale University alumni
University of Oregon faculty
University of Wisconsin–Madison faculty
Fellows of the American Mathematical Society
1926 births
Living people
21st-century American mathematicians |
https://en.wikipedia.org/wiki/Lester%20R.%20Rice-Wray | Lester R. Rice-Wray was a professor of mathematics at the University of Denver who later was elected to the City Council in Los Angeles, California, and was the first councilman there to face a recall election under the 1925 city charter.
Biography
Rice-Wray was born in Missouri and educated in both public and private schools. He was a licensed teacher at the age of 16. At the outbreak of World War I, he worked in Washington, D.C., to "straighten out the inefficiencies of the American Express Railway Company in the District of Columbia, which was a center of supply distribution." He moved to Los Angeles in 1920 and became president of the Greater Slauson-Avenue Improvement Association.
He was married. His first wife died at the age of 53 on January 28, 1929. His second wife, Nellie, obtained a divorce in November 1935 on the grounds that her husband struck her and refused to support her properly and that he was abusive and drank to excess.
City Council
Elections
Rice-Wray defeated 6th District Council Member Edward E. Moore in 1927 with the backing of Mayor George E. Cryer and political boss Kent Parrot, but was quickly enveloped in controversy over his support of a massive Slauson Avenue storm drain project. Petitioners for a recall election charged him with ignoring the wishes of his constituents opposed to the project, which affected some 30,000 property owners and for which they would be taxed. The area was later described as 50 million square feet "bounded by Slauson Avenue, extending into the city of Inglewood and Van Ness avenue to Gramercy Place." In the resulting August 1928 election, Rice-Wray was recalled from office by a vote of 10,168 to 5,872. James G. McAllister was elected to succeed him. He was the first City Council member to face a recall election under the 1925 City Charter.
Afterward, a new electoral possibility opened for Rice-Wray, the transfer of the 11th District from Downtown to the coast region, including Venice and Palms." There was no incumbent, so Rice-Wray ran for the vacancy in 1929, but he was soundly defeated in the final by J.C. Barthel, 11,410 votes to 6,647.
Council activity
While in the council, Rice-Wray was fined $25 () by Superior Judge Leonard Wilson for having sent the judge a letter urging quick action on a lawsuit involving the removal of sanitariums from the Mar Vista area. He apologized to the judge for his zealousness, but Wilson nevertheless held the council member in contempt and imposed the fine.
References
Access to the Los Angeles Times links requires the use of a library card.
Los Angeles City Council members
University of Denver faculty
Recalled American politicians
20th-century American mathematicians |
https://en.wikipedia.org/wiki/Murray%20R.%20Spiegel | Murray Ralph Spiegel (1923-1991) was an author of textbooks on mathematics, including titles in a collection of Schaum's Outlines.
Spiegel was a native of Brooklyn and a graduate of New Utrecht High School. He received his bachelor's degree in mathematics and physics from Brooklyn College in 1943. He earned a master's degree in 1947 and doctorate in 1949, both in mathematics and both at Cornell University.
He was a teaching fellow at Harvard University in 1943–1945, a consultant with Monsanto Chemical Company in the summer of 1946, and a teaching fellow at Cornell University from 1946 to 1949. He was a consultant in geophysics for Beers & Heroy in 1950, and a consultant in aerodynamics for Wright Air Development Center from 1950 to 1954. Spiegel joined the faculty of Rensselaer Polytechnic Institute in 1949 as an assistant professor. He became an associate professor in 1954 and a full professor in 1957. He was assigned to the faculty Rensselaer Polytechnic Institute of Hartford, CT, when that branch was organized in 1955, where he served as chair of the mathematics department. His PhD dissertation, supervised by Marc Kac, was titled On the Random Vibrations of Harmonically Bound Particles in a Viscous Medium.
Works
Schaum's Outline of College Algebra (First Edition: 1956) [Most Recent Edition: 2018]
Schaum's Outline of College Physics
Schaum's Outline of Statistics (FE: 1961) [MRE: 2018]
Schaum's Outline of Advanced Calculus (1963) [2010]
Schaum's Outline of Complex Variables (1964) [2009]
Schaum's Outline of Laplace Transforms (1965)
Schaum's Mathematical Handbook of Formulas and Tables (1968) [2008]
Schaum's Outline of Vector Analysis [And An Introduction to Tensor Analysis] (1968) [2009]
Schaum's Outline of Real Variables (1969)
Schaum's Outline of Advanced Mathematics for Engineers and Scientists (1971) [2009]
Schaum's Outline of Finite Differences and Difference Equations (1971)
Schaum's Outline of Fourier Analysis with Applications to Boundary-Value Problems (1974)
Schaum's Outline of Probability and Statistics (1975) [2013]
Schaum's Outline of Theoretical Mechanics (1967)
Applied Differential Equations (1963) [1980]
References
External links
20th-century American mathematicians
21st-century American mathematicians
Rensselaer Polytechnic Institute faculty
1923 births
1991 deaths
Brooklyn College alumni |
https://en.wikipedia.org/wiki/Voorhoeve%20index | In mathematics, the Voorhoeve index is a non-negative real number associated with certain functions on the complex numbers, named after Marc Voorhoeve. It may be used to extend Rolle's theorem from real functions to complex functions, taking the role that for real functions is played by the number of zeros of the function in an interval.
Definition
The Voorhoeve index of a complex-valued function f that is analytic in a complex neighbourhood of the real interval = [a, b] is given by
(Different authors use different normalization factors.)
Rolle's theorem
Rolle's theorem states that if is a continuously differentiable real-valued function on the real line, and , where , then its derivative has a zero strictly between and . Or, more generally, if denotes the number of zeros of the continuously differentiable function on the interval , then
Now one has the analogue of Rolle's theorem:
This leads to bounds on the number of zeros of an analytic function in a complex region.
References
Calculus
Complex analysis |
https://en.wikipedia.org/wiki/Moore%20determinant | In mathematics, Moore determinant, named after Eliakim Hastings Moore, may refer to
The determinant of a Moore matrix over a finite field
The Moore determinant of a Hermitian matrix over a quaternion algebra |
https://en.wikipedia.org/wiki/Moore%20determinant%20of%20a%20Hermitian%20matrix | In mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by .
See also
Dieudonné determinant
References
Matrices |
https://en.wikipedia.org/wiki/List%20of%20D.C.%20United%20records%20and%20statistics | D.C. United is an American professional soccer club based in Washington, D.C.. The club was founded in 1995 as an inaugural Major League Soccer franchise, and began play in 1996. The club currently plays in MLS.
This list encompasses the major honors won by D.C. United, records set by the franchise, their head coaches and their players, and details the club's North American performances. The player records section includes details of the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by United players on the international stage. Attendance records at Robert F. Kennedy Memorial Stadium, the club's home stadium since 1995, are also included in the list.
Honors
D.C. United has won honors both domestically and in CONCACAF competitions. The team has won the MLS Cup and the MLS Supporters' Shield four times, the most championships and premierships, respectively, of any Major League Soccer franchise. Additionally, in domestic play, United has won two U.S. Open Cup titles. United is one of only two MLS sides to win a CONCACAF competition, winning the CONCACAF Champions' Cup in 1998. The last major title the club won was the Open Cup in 2013. In terms of league play, their last league premiership was in 2007, and their last league championship was in 2004.
Continental
CONCACAF Champions' Cup
Winners (1): 1998
CONCACAF Giants Cup
Runners-up (1): 2001
Domestic
MLS Cup
Winners (4): 1996, 1997, 1999, 2004
Runners-up (1): 1998
MLS Supporters' Shield
Winners (4): 1997, 1999, 2006, 2007
Runners-up (1): 1998
Cups
U.S. Open Cup
Winners (3): 1996, 2008, 2013
Runners-up (2): 1997, 2009
Player records
Appearances
Competitive, professional matches only, appearances as substitutes in brackets.
Goalscorers
MLS Cup Playoffs
Jaime Moreno (12)
Raúl Díaz Arce (8)
Roy Lassiter (7)
Tony Sanneh (6)
Alecko Eskandarian (4)
Marco Etcheverry (3)
Christian Gomez (3)
Ben Olsen (2)
Roy Wegerle (2)
Richie Williams (2)
Steve Rammel (2)
US Open Cup
Jaime Moreno (13)
Abdul Thompson Conten (5)
Raúl Díaz Arce (5)
Christian Gomez (4)
Eddie Pope (4)
Chris Albright (4)
Thabiso Khumalo (4)
Jamil Walker (3)
Branko Boskovic (3)
Luciano Emilio (3)
Fred (3)
Santino Quaranta (3)
CONCACAF Champions League & Continental competitions
Luciano Emilio (9)
Christian Gomez (8)
Roy Lassiter (7)
Jaime Moreno (6)
AJ Wood (3)
Eddie Pope (2)
Fred (2)
Rod Dyachenko (2)
Francis Doe (2)
Marco Etcheverry (2)
Chris Pontius (2)
Player award winners
MLS MVP
Most Valuable Player:
Marco Etcheverry (1998),
Christian Gomez (2006),
Luciano Emilio (2007),
Dwayne De Rosario (2011)
MLS Golden Boot
Golden Boot:
Jaime Moreno (1997),
Luciano Emilio (2007),
Dwayne De Rosario (2011)
MLS Best XI
The MLS Best XI is an acknowledgment of the best eleven players in the league in a given season for Major League Soccer.
5 times:
Jaime Moreno: (1997), (1999), (2004), (2005), (2006)
4 times: |
https://en.wikipedia.org/wiki/Basic%20affine%20jump%20diffusion | In mathematics probability theory, a basic affine jump diffusion (basic AJD) is a stochastic process Z of the form
where is a standard Brownian motion, and is an independent compound Poisson process with constant jump intensity and independent exponentially distributed jumps with mean . For the process to be well defined, it is necessary that and . A basic AJD is a special case of an affine process and of a jump diffusion. On the other hand, the Cox–Ingersoll–Ross (CIR) process is a special case of a basic AJD.
Basic AJDs are attractive for modeling default times in credit risk applications, since both the moment generating function
and the characteristic function
are known in closed form.
The characteristic function allows one to calculate the density of an integrated basic AJD
by Fourier inversion, which can be done efficiently using the FFT.
References
Stochastic processes |
https://en.wikipedia.org/wiki/Friedrich%20Franz | Friedrich Franz, , (1 December 1783 – 4 December 1860) was a professor of physics and applied mathematics at the Faculty of Philosophy of University of Olomouc, who greatly influenced his student Gregor Johann Mendel, later known as "The Father of Genetics".
Biography
Friedrich Franz graduated in 1831 the University of Prague as Doctor of Philosophy and Liberal Arts. Before he came in 1842 to Olomouc, he taught physics at a philosophical institute (type of grammar school) in Brno (Brünn).
Franz was the first lecturer on the daguerreotype process in Moravia. He started experimenting already in 1839, the same year that Louis Daguerre developed this method of taking photographs.
He also arranged exhibitions. The fact that this photographic process took roots in Moravia is attributable to him. Franz is believed to be the author of photography of "Corpus Christi" taken in Brno on 10 June 1841, which is the first reportage photography in the Czech lands and one of the first photographies worldwide. He is also believed to be the author of the first portrait photos in the Czech lands. In 1841 he made photo portraits of Brno Bishop František Antonín Gindl.
In Olomouc, Gregor Johann Mendel was one of the most favourite Franz's students. Franz immediately recognized his great talent, and they soon became good friends. They debated a number of topics, such as the origin of the solar system and of life as such, the development of Goethe's philosophy and the purpose of human life. Franz also provided the newest scientific literature to Mendel and recommended him to enter the St Thomas's Abbey, where Mendel later defined his famous laws of inheritance.
In 1844 Franz became the dean of the Faculty of Philosophy. After the Austrian government dissolved the Olomouc Faculty of Philosophy following the students' and professors' participation on 1848 revolution, Franz became briefly the rector of the University in 1852, before he left and became a director of a grammar school in Salzburg, while later he was a Premonstratensian prelate in Nová Říše (Neureisch).
See also
Johann Karl Nestler
References
1783 births
1860 deaths
People from Vysoké Veselí
German Bohemian people
Austrian geneticists
Austrian photographers
19th-century Austrian Roman Catholic priests
Academic staff of Palacký University Olomouc
Premonstratensians |
https://en.wikipedia.org/wiki/Nemmers%20Prize | Nemmers Prize may refer to:
Nemmers Prize in Mathematics
Nemmers Prize in Economics
Nemmers Prize in Music Composition
Nemmers Prize in Medical Science
Nemmers Prize in Earth Sciences |
https://en.wikipedia.org/wiki/James%20J.%20Andrews%20%28mathematician%29 | James J. Andrews (March 18, 1930 – July 28, 1998) was an American mathematician, a professor of mathematics at Florida State University who specialized in knot theory, topology, and group theory.
Andrews was born March 18, 1930, in Seneca Falls, New York. He did his undergraduate studies at Hofstra College, and earned his doctorate in 1957 from the University of Georgia under the supervision of M. K. Fort, Jr. He worked at Oak Ridge National Laboratory, the University of Georgia, and the University of Washington before joining the FSU faculty in 1961. Andrews was a visiting scholar at the Institute for Advanced Study in 1963-64. From 1965-67, he looked into cryptology research at the Institute for Defense Analysis, Naval Postgraduate School, Monterey, California. He retired in 1994, and died July 28, 1998, in Tallahassee, Florida.
Andrews is known with Morton L. Curtis for the Andrews–Curtis conjecture concerning Nielsen transformations of balanced group presentations. Andrews and Curtis formulated the conjecture in a 1965 paper; it remains open.
References
1930 births
1998 deaths
American humanists
20th-century American mathematicians
Group theorists
Topologists
Hofstra University alumni
University of Georgia alumni
University of Georgia faculty
University of Washington faculty
Florida State University faculty
Institute for Advanced Study visiting scholars
People from Seneca Falls, New York
Mathematicians from New York (state) |
https://en.wikipedia.org/wiki/Morton%20L.%20Curtis | Morton Landers Curtis (November 11, 1921 – February 4, 1989) was an American mathematician, an expert on group theory and the W. L. Moody, Jr. Professor of Mathematics at Rice University.
Born in Texas, Curtis earned a bachelor's degree in 1948 from Texas A&I University, and received his Ph.D. in 1951 from the University of Michigan under the supervision of Raymond Louis Wilder. Subsequently, he taught mathematics at Florida State University before moving to Rice. At Rice, he was the Ph.D. advisor of well-known mathematician John Morgan.
Curtis is, with James J. Andrews, the namesake of the Andrews–Curtis conjecture concerning Nielsen transformations of balanced group presentations. Andrews and Curtis formulated the conjecture in a 1965 paper; it remains open. Together with Gustav A. Hedlund and Roger Lyndon, he proved the Curtis–Hedlund–Lyndon theorem characterizing cellular automata as being defined by continuous equivariant functions on a shift space.
Curtis was the author of two books, Matrix Groups (Springer-Verlag, 1979), and Abstract Linear Algebra (Springer-Verlag, 1990).
References
1989 deaths
Group theorists
Institute for Advanced Study visiting scholars
University of Michigan alumni
Florida State University faculty
Rice University faculty
Place of birth missing
Texas A&M University–Kingsville alumni
1921 births
20th-century American mathematicians
Mathematicians from Texas |
https://en.wikipedia.org/wiki/Doi%E2%80%93Naganuma%20lifting | In mathematics, the Doi–Naganuma lifting is a map from elliptic modular forms to Hilbert modular forms of a real quadratic field, introduced by and .
It was a precursor of the base change lifting.
It is named for Japanese mathematicians Kōji Doi (土井公二） and Hidehisa Naganuma (長沼英久).
See also
Saito–Kurokawa lift, a similar lift to Siegel modular forms
References
Modular forms |
https://en.wikipedia.org/wiki/1908%E2%80%9309%20SEGAS%20Championship | Statistics of SEGAS Championship in the 1908–09 season.
Overview
Peiraikos Syndesmos won the championship.
Reported Final Table
1.Peiraikos Syndesmos Pireas
2.Goudi F.C Athens
3.Podosferikos Omilos Athinon (P.O.A)
4.Ethnikos G.S. Athens
References
Panhellenic Championship seasons
Greece
1908–09 in Greek football |
https://en.wikipedia.org/wiki/1909%E2%80%9310%20SEGAS%20Championship | Statistics of SEGAS Championship in the 1909–10 season.
Overview
Goudi Athens won the championship.
References
Panhellenic Championship seasons
Greece
1909–10 in Greek football |
https://en.wikipedia.org/wiki/1910%E2%80%9311%20SEGAS%20Championship | Statistics of SEGAS Championship in the 1910–11 season.
Overview
Podosferikos Omilos Athinon won the championship.
References
Panhellenic Championship seasons
Greece
1910–11 in Greek football |
https://en.wikipedia.org/wiki/1911%E2%80%9312%20SEGAS%20Championship | Statistics of SEGAS Championship in the 1911–12 season.
Overview
Goudi Athens won the championship.
References
Panhellenic Championship seasons
Greece
1911–12 in Greek football |
https://en.wikipedia.org/wiki/1921%E2%80%9322%20FCA%20Championship | Statistics of Football Clubs Association Championship in the 1921–22 season. Only the Athens-Piraeus championship was held.
Athens-Piraeus Football Clubs Association
*Withdrawal.
External Links
1921-22 championship
Panhellenic Championship seasons
1921 in association football
1922 in association football
1921–22 in Greek football |
https://en.wikipedia.org/wiki/1923%E2%80%9324%20FCA%20Championship | Statistics of Football Clubs Association Championship in the 1923–24 season.
Athens Football Clubs Association
*Known results only.
The match took place on 8 June 1924 at Leoforos Alexandras Stadium.
|+Final Round
|}
Apollon Athens won the championship.
Athens-Piraeus Football Clubs Association
Macedonia Football Clubs Association
External links
Rsssf 1923–24 championship
Panhellenic Championship seasons
1923 in association football
1924 in association football
1923–24 in Greek football |
https://en.wikipedia.org/wiki/1924%E2%80%9325%20FCA%20Championship | Statistics of Football Clubs Association Championship in the 1924–25 season.
Athens Football Clubs Association
Group A
Group B
Athens Final Round
|+Semi-finals
|}
|+Final
|}
Panathinaikos won the championship.
Piraeus Football Clubs Association
Group A
Group B
Piraeus Final Round
|+Semi-finals
|}
The final took place on 17 May 1925 at Leoforos Alexandras Stadium.
|+Final
|}
Olympiacos won the championship.
External links
Rsssf 1924–25 championship
Panhellenic Championship seasons
1924–25 in Greek football
1924–25 domestic association football leagues |
https://en.wikipedia.org/wiki/1925%E2%80%9326%20FCA%20Championship | Statistics of Football Clubs Association Championship for the 1925–26 season.
Athens Football Clubs Association
Piraeus Football Clubs Association
Macedonia Football Clubs Association
References
External links
Rsssf 1925–26 championship
Panhellenic Championship seasons
1925–26 in Greek football
1925–26 domestic association football leagues |
https://en.wikipedia.org/wiki/1926%E2%80%9327%20FCA%20Championship | Statistics of Football Clubs Association Championship in the 1926–27 season.
Athens Football Clubs Association
Qualification round
Final round
Both matches took place at Leoforos Alexandras Stadium, on 5 and 27 June 1927, respectively:
|+Championship play-offs
|}
Panathinaikos won the Athenian championship.
Piraeus Football Clubs Association
|+Championship play-off
|}
|+Replay
|}
Olympiacos won the Piraeus' championship.
*Initially, the match was scheduled to take place on 12 June 1927 at Panathinaikos' stadium, but due to the fact that Panathinaikos wanted the postponed match with AEK Athens for the Athenian championship final, the match between Olympiacos and Ethnikos was held at Panellinios' stadium. After an episodic game, Olympiakos prevailed 4–2. However, due to the fact that the fight after the episodes was delayed to end, the Piraeus' association set for a rematch initially on 10 July and then its next decision was to postpone it to September. Finally the match was decided to take place on 17 July 1927 at Panathinaikos' stadium, where Olympiakos won by 1–0.
Macedonia Football Clubs Association
References
External links
Rsssf 1926–27 championship
Panhellenic Championship seasons
Greece
1926–27 in Greek football |
https://en.wikipedia.org/wiki/Andrei%20Zelevinsky | Andrei Vladlenovich Zelevinsky (; 30 January 1953 – 10 April 2013) was a Russian-American mathematician who made important contributions to algebra, combinatorics, and representation theory, among other areas.
Biography
Zelevinsky graduated in 1969 from the Moscow Mathematical School No. 2.
After winning a silver medal as a member of the USSR team at the International Mathematical Olympiad he was admitted without examination to the mathematics department of Moscow State University
where he obtained his PhD in 1978 under the mentorship of Joseph Bernstein,
Alexandre Kirillov and Israel Gelfand.
He worked in the mathematical laboratory of Vladimir Keilis-Borok at the Institute of Earth Science (1977–85), and at the Council for Cybernetics of the Soviet Academy of Sciences (1985–90). In the early 1980s, at a great personal risk, he taught at the Jewish People's University, an unofficial organization offering first-class mathematics education to talented students denied admission to Moscow State University's math department.
In 1990–91, Zelevinsky was a visiting professor at Cornell University, and from 1991 until his death was on faculty at Northeastern University, Boston.
With his wife, Galina, he had a son and a daughter; he also had several grandchildren.
Zelevinsky is a relative of the physicists Vladimir Zelevinsky and Tanya Zelevinsky.
Research
Zelevinsky's most notable achievement is the discovery (with Sergey Fomin) of cluster algebras.
His other contributions include:
Bernstein–Zelevinsky classification of representations of p-adic groups;
introduction (jointly with Israel Gelfand and Mikhail Kapranov) of A-systems of hypergeometric equations (also known as GKZ-systems) and development of the theory of hyperdeterminants;
generalization of the Littlewood–Richardson rule and Robinson–Schensted correspondence using the combinatorics of "pictures";
work (jointly with Arkady Berenstein and Sergey Fomin) on total positivity;
work (with Sergey Fomin) on the Laurent phenomenon, including its applications to Somos sequences.
Awards and recognition
Invited lecture at the International Congress of Mathematicians (Berlin, 1998)
Humboldt Research Award (2004)
Fellow (2012) of the American Mathematical Society
University Distinguished Professorship (2013) at Northeastern University
Steele Prize for Seminal Contribution to Research (2018)
References
External links
Home page of Andrei Zelevinsky (including CV)
Conference in memory of Andrei Zelevinsky
Publications of Andrei Zelevinsky (in Russian)
Publications of Andrei Zelevinsky (in English)
Research Focus: Andrei Zelevinsky's Cluster Algebras
Live journal run by Andrei Zelevinsky from 2007 to 2013
20th-century American mathematicians
21st-century American mathematicians
Russian mathematicians
Northeastern University faculty
Fellows of the American Mathematical Society
1953 births
2013 deaths
International Mathematical Olympiad participants
Soviet mathematicians
Combinatorialists |
https://en.wikipedia.org/wiki/Bill%20Tilden%20career%20statistics | This is a list of the main career statistics of American former tennis player Bill Tilden (1893–1953) whose amateur and professional career spanned three decades from the early 1910s to the mid 1940s.
Major titles
Performance timeline
Bill Tilden joined professional tennis in 1931 and was unable to compete in the amateur Grand Slam tournaments from that year onward.
Grand Slam tournaments
Pro Slam
ILTF Majors
Career titles
Amateur era
According to Bud Collins, as an amateur (1912–1930) Tilden won 138 of 192 tournaments, lost 28 finals and had a 907–62 match record, a 93.60% winning percentage. Only known titles are detailed here.
Professional era
Davis Cup
Tilden won 34 out of 41 Davis Cup matches; 25 of his 30 singles matches and 9 out of 11 doubles. He was a member of the victorious United States Davis Cup teams in 1920, 1921, 1922, 1923, 1924, 1925 and 1926.
Professional tours
Records
Winning streak of Grand Slam events: 8 titles (1920–1926). Including 6 U.S. titles and 2 Wimbledon titles.
Winning streak in single matches at Grand Slam events: 51 (1920–1926)
Second best match winning % in Grand Slam events: 89.76%, with a record of 114–13 (1916–1930). Notice that Björn Borg has a winning percentage of 89.81% with a record of 141–16 (1974–1981) in a span time of about the half of Tilden. This highlights the longevity of Tilden's career.
Winning streak in single matches at U.S. Championships: 42 (1920–1926)
Most single titles at U.S. Championships: 7 (1920–1925, 1929)
Most single finals at U.S. Championships: 10 (1918–1925, 1927, 1929)
Won single + doubles + mixed doubles titles at same U.S. Championships event (1922, 1923)
Winning streak in single matches: 98 (1924–1925)
Best match winning % in one season: 98.73%, with a record of 78–1 (1925)
Most appearances in final of Davis Cup: 11 with a record of 21–7 in singles (1920–1930)
Career match performance year on year
References
General sources
World Tennis Magazines.
Bud Collins, The Bud Collins History of Tennis, 2008.
Joe McCauley, The History of Professional Tennis, London 2001.
Tilden, Bill |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20FK%20Partizan%20season | The 2011–12 season is FK Partizan's 6th season in Serbian SuperLiga. This article shows player statistics and all matches (official and friendly) that the club have and will play during the 2011–12 season.
Players
Squad information
Squad statistics
Top scorers
Includes all competitive matches. The list is sorted by shirt number when total goals are equal.
Transfers
In
Out
Competitions
Overview
Serbian SuperLiga
League table
Matches
Serbian Cup
UEFA Champions League
Qualifying rounds
By finishing 1st in the 2010–11 Serbian SuperLiga, Partizan qualified for the Champions League. They will start in the second qualifying round.
UEFA Europa League
Play-off round
Friendlies
Sponsors
See also
List of FK Partizan seasons
References
External links
Official website
Partizanopedia 2011-12 (in Serbian)
FK Partizan seasons
Partizan
Partizan
Serbian football championship-winning seasons |
https://en.wikipedia.org/wiki/Football%20records%20and%20statistics%20in%20Brazil | This page details football records in Brazil.
Highest Single-Match Attendances
Most matches with attendance of more than 100,000, ranked by club.
Flamengo = 117
Vasco = 72
Fluminense = 59
Botafogo = 43
Corinthians = 23
Santos = 20
Atlético = 19
São Paulo = 17
Cruzeiro = 15
Palmeiras = 13
National team
Overall
These records include state leagues and achievements conquered by expatriate Brazilian footballers.
Clubs
Most state leagues titles: 57, ABC
Most state league consecutive titles: 10, ABC (1932–1941), América Mineiro (1916–1925)
Most goals scored: 12,691 (up to 2021), Santos
Most consecutive matches without a victory: 62, Atlético Mogi
Record win: Botafogo 24–0 Mangueira, Campeonato Carioca (30 May 1909)
Record win in 21st century: Ulbra 21–0 Shallon, Campeonato Rondoniense (14 May 2006)
Record away win: Cáceres 0–14 Sorriso, Campeonato Matogrossense (21 March 2010)
Most goals with both teams scoring: 24, Náutico 21–3 Flamengo Recife, Campeonato Pernambucano (1 July 1945)
Individual
Most goals scored: Pelé, 1,279 goals
Most hat-tricks: Pelé, 96
Most goals scored in a single match: Dadá Maravilha, 10 goals (Sport Recife 14–0 Santo Amaro, 1976)
Most free kick goals scored: Zico, 101 goals
Most decorated player: Dani Alves, 43 titles
Most appearances: Fábio, 1,256+ matches
Most matches by one club: Rogério Ceni, 1,237 matches for São Paulo
Most matches as a captain by a club: Rogério Ceni, 978 matches for São Paulo
Goalkeeper with most goals scored: Rogério Ceni, 131 goals
Goalkeeper with most consecutive minutes without conceding a goal: Mazaropi, 1,816 minutes without a goal
Oldest player appearance: Pedro Ribeiro Lima (Perilima), 66 years (2014 Campeonato Paraibano Second Division)
Oldest goalscorer: Pedro Ribeiro Lima (Perilima), 58 years (Campinense 5–1 Perilima, 2007)
Fastest goal: Fred, 3,17 sec (2003)
Campeonato Brasileiro
Records in this section refer to (Level 1) i.e. Taça Brasil from its founding in 1959 through to 1968, the Torneio Roberto Gomes Pedrosa from its founding in 1967 through to 1970, and the Campeonato Brasileiro Série A or Brasileirão from 1971 to the present. Some records relating to team performances are divided into records in the round-robin era (from 2003 to the present) and the championships before it.
Titles
Most Brazilian national titles: 11
Palmeiras (1960, 1967 (TB), 1967 (R), 1969, 1972, 1973, 1993, 1994, 2016, 2018, 2022)
Most consecutive Brazilian national titles: 5:
Santos (1961, 1962, 1963, 1964, 1965)
Top-flight Appearances
Most appearances: 63
Grêmio
Santos
Most appearances (Taça Brasil era): 9
Grêmio
Most appearances (Campeonato Brasileiro era): 53
Flamengo
Most consecutive seasons in top-flight: 56
Cruzeiro (1966–2019)
Flamengo (1968–2023)
Fewest appearances in top-flight (Taça Brasil era): 1, joint record:
Auto Esporte (PB) (1959)
Ferroviário (MA) (1959)
Hercílio Luz (1959)
Manufatora (1959)
Estrela do Mar (PB) (1960)
Paula Ramos (1960)
Comercial (PR) (1962 |
https://en.wikipedia.org/wiki/List%20of%20Santos%20FC%20records%20and%20statistics | Santos FC is a football club based in Santos, that competes in the Campeonato Paulista, São Paulo's state league, and the Campeonato Brasileiro Série A or Brasileirão, Brazil's national league. The club was founded in 1912 by the initiative of three sports enthusiasts from Santos by the names of Raimundo Marques, Mário Ferraz de Campos, and Argemiro de Souza Júnior, and played its first friendly match on 23 June 1912. Initially Santos played against other local clubs in the city and state championships, but in 1959 the club became one of the founding members of the Taça Brasil, Brazil's first truly national league. As of 2022, Santos is one of only three clubs never to have been relegated from the top level of Brazilian football, the others being São Paulo and Flamengo.
Santos has amassed various records since the foundation. Regionally, domestically, and continentally, they have set several records in winning various official and unofficial competitions. On 20 January 1998, Santos became the first in the history of football to reach the milestone of 10,000 goals, scored by Jorginho. It is one of Brazil's richest football club in terms of revenue, with an annual revenue of $45.1m (€31.5m), and one of the most valuable clubs, worth over $86.7m (€60.6m) in 2011. The Santista club is the most successful club in Brazilian football in terms of overall trophies, having won nine national, six continental and three international titles. In 1962, Santos became the first club in the world to win the continental treble consisting of the Paulista, Taça Brasil, and the Copa Libertadores. That same year, it also became the first football club ever to win four out of four competitions in a single year, thus completing the quadruple, comprising the aforementioned treble and the Intercontinental Cup.
Santos has employed several famous players, with eleven FIFA World Cup, six Copa América and one FIFA Confederations Cup winners among the previous and current Santos players. Arnaldo Patusca was the first Santista player to participate with the national team during the 1916 Copa América. Araken Patusca was the first player from the club to participate with Brazil at a World Cup in 1930. The first Peixe to participate with the national team at the Confederations Cup was Léo at the 2001 FIFA Confederations Cup. Pelé, often ranked as the greatest player of all time, was voted South American footballer of the year in 1973, won the FIFA World Cup Best Young Player award in 1958 and FIFA World Cup Golden Ball in 1970. Pepe is often considered one of the greatest wingers of all time, and is the player who won the most Brasileirãos, with seven titles in total. He has also won the most Campeonato Paulistas, with 13 titles in total, and is the only player to spend his entire player career with Santos. Coutinho, considered one of the greatest forwards in the sport, was the top scorer during Santos' victorious campaign during the 1962 Copa Libertadores and scored Santos' 5000 |
https://en.wikipedia.org/wiki/Ian%20Burns | Ian Burns (19 April 1939 – 6 December 2015) was a Scottish professional football right-half who played for Aberdeen and Brechin City.
Career statistics
Club
Appearances and goals by club, season and competition
References
External links
AFC Heritage profile
1939 births
2015 deaths
Scottish men's footballers
Footballers from Aberdeen
Men's association football wing halves
Aberdeen F.C. players
Brechin City F.C. players
Scottish Football League players
Banks O' Dee F.C. players
Date of birth missing |
https://en.wikipedia.org/wiki/Annam%C3%A1ria%20Kir%C3%A1ly | Annamária Király (born 29 August 1985) is a retired Hungarian team handball goalkeeper.
Achievements
EHF Cup:
Semifinalist: 2006
References
External links
Career statistics on Worldhandball.com
1985 births
Living people
Sportspeople from Debrecen
Hungarian female handball players |
Subsets and Splits
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