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https://en.wikipedia.org/wiki/Raymondt%20Pimienta | Raymondt Pimienta (born 7 May 1982) is an Aruban football player. He played for Aruba national team in 2002, 2004, and 2008.
National team statistics
References
1982 births
Living people
Aruban men's footballers
Men's association football midfielders
SV Racing Club Aruba players
Aruba men's international footballers |
https://en.wikipedia.org/wiki/Mark%20Mackay%20%28footballer%29 | Mark Mackay (born September 25, 1978) is an Aruban football player. He has played for Aruba national team.
National team statistics
References
1978 births
Living people
Aruban men's footballers
Men's association football midfielders
SV Racing Club Aruba players
S.V. Transvaal players
SV Britannia players
Aruban Division di Honor players
SVB Eerste Divisie players
Expatriate men's footballers in Suriname
Aruba men's international footballers |
https://en.wikipedia.org/wiki/Gerald%20Zimmermann | Gerald Zimmermann (born January 16, 1973) is an Aruban football player. He has played for Aruba national team.
National team statistics
References
1973 births
Living people
Aruban men's footballers
Men's association football midfielders
SV Britannia players
SV Dakota players
Aruba men's international footballers |
https://en.wikipedia.org/wiki/Maurice%20Escalona | Maurice Escalona (born 27 January 1980) is an Aruban football player. He plays for the Aruba national team.
Statistics
National team statistics
International goals
References
1980 births
Living people
Aruban men's footballers
Aruba men's international footballers
Men's association football forwards
SV Racing Club Aruba players
SV Bubali players
SV Britannia players |
https://en.wikipedia.org/wiki/Juan%20Valdez%20%28footballer%29 | Juan Valdez (born November 24, 1983) is an Aruban football player. He has played for Aruba national team.
National team statistics
References
1983 births
Living people
Aruban men's footballers
Place of birth missing (living people)
Men's association football defenders
SV Britannia players
SV Racing Club Aruba players
SV Dakota players
Aruba men's international footballers |
https://en.wikipedia.org/wiki/Andy%20Figaroa | Andy Figaroa (born April 10, 1983) is an Aruban football player. He has appeared for the Aruba national team twice in 2004 and 2008.
National team statistics
References
1983 births
Living people
Aruban men's footballers
Men's association football defenders
SV Deportivo Nacional players
Aruba men's international footballers |
https://en.wikipedia.org/wiki/Theric%20Ruiz | Theric Ruiz (born September 18, 1984) is an Aruban football player. He played for the Aruba national team.
National team statistics
References
1984 births
Living people
Aruban men's footballers
SV Deportivo Nacional players
SV Britannia players
Aruban Division di Honor players
Men's association football defenders
Aruba men's international footballers |
https://en.wikipedia.org/wiki/Cayley%20process | Cayley process may refer to:
Cayley's omega process in invariant theory
Cayley–Dickson process for constructing nonassociative algebras |
https://en.wikipedia.org/wiki/Francis%20Dominic%20Murnaghan%20%28mathematician%29 | Francis Dominic Murnaghan (August 4, 1893 – March 24, 1976) was an Irish mathematician and former head of the mathematics department at Johns Hopkins University. His name is attached to developments in group theory and mathematics applied to continuum mechanics (Murnaghan and Birch–Murnaghan equations of state).
Biography
Frank Murnaghan was born in Omagh, County Tyrone, Ireland, seventh of the nine children of George Murnaghan, a Nationalist MP representing Mid Tyrone constituency. He graduated from Irish Christian Brothers secondary school in 1910, and University College Dublin with first-class honours BSc in Mathematical Sciences in 1913. Following an MSc in 1914, he was awarded a National University of Ireland (NUI) Travelling Studentship, which funded him to pursue his doctorate at Johns Hopkins University. In 1916, after just two years working under department chair Frank Morley's new PhD student Harry Bateman, he was awarded the Ph.D.
He then lectured at Rice University, and returned to Johns Hopkins University with the rank of associate professor at the young age of 25. In 1928 he was promoted to Professor and became only the fourth head of the Department of Mathematics (after J.J. Sylvester, Simon Newcomb and Frank Morley). After his retirement in 1949, he worked at the Instituto Tecnológico de Aeronáutica near São Paulo, Brasil, but returned to Baltimore in 1959. He continued working as a consultant for the Marine Engineering Laboratory; his last publication appeared in 1972.
Murnaghan was a member of US National Academy of Sciences, American Philosophical Society, Royal Irish Academy, and Brazilian Academy of Sciences. He wrote 15 books, some in English and some in Portuguese, and over 90 papers.
He was the father of Francis Dominic Murnaghan, Jr., former U.S. federal judge and uncle of Northern Irish barrister and politician Sheelagh Murnaghan.
Selected publications
See also
Acoustoelastic effect
Kronecker coefficient
Murnaghan–Nakayama rule
Murnaghan–Tait equation of state
References
External links
R.T. Cox, Francis Dominic Murnaghan (1893-1976), Year Book of the American Philosophical Society (1976), 109–114.
1893 births
1976 deaths
People from Omagh
20th-century Irish mathematicians
Group theorists
20th-century American mathematicians
Alumni of University College Dublin
Johns Hopkins University faculty
Irish emigrants to the United States
Members of the United States National Academy of Sciences
Members of the Royal Irish Academy
Fellows of the American Physical Society
Scientists from County Tyrone |
https://en.wikipedia.org/wiki/System%20T | In mathematics, System T can refer to:
A theory of arithmetic in all finite types used in Gödel's Dialectica interpretation
An axiom system of modal logic |
https://en.wikipedia.org/wiki/Samir%20Musayev | Samir Musayev (born 17 March 1979) is a retired Azerbaijani football player. He has played for Azerbaijan national team.
Career statistics
National team statistics
Honours
Individual
Azerbaijan Premier League Top Scorer (1): 2003–04
References
External links
1979 births
Living people
Azerbaijani men's footballers
Men's association football forwards
Azerbaijan men's international footballers |
https://en.wikipedia.org/wiki/Denis%20Maccan | Denis Maccan (born 19 May 1984) is an Italian footballer who plays as a forward, currently for Portogruaro.
Career statistics
Serie B : 13 caps, 1 goal
Serie C1 : 62 caps, 1 goal
Serie C2 : 68 caps, 26 goals
Total : 143 caps, 28 goals
References
External links
Career profile (from aic.it)
Living people
1984 births
Italian men's footballers
ASD Sangiovannese 1927 players
SS Arezzo players
Brescia Calcio players
FC Lumezzane players
Venezia FC players
AC Perugia Calcio players
Fidelis Andria 2018 players
Serie B players
Men's association football forwards
People from Pordenone
Footballers from Friuli Venezia Giulia |
https://en.wikipedia.org/wiki/Namig%20Hasanov | Namig Hasanov () (born 20 October 1979) is an Azerbaijani football player. He has played for Azerbaijan national team.
National team statistics
References
1979 births
Living people
Azerbaijani men's footballers
Men's association football midfielders
Azerbaijan men's international footballers |
https://en.wikipedia.org/wiki/Ruslan%20Musayev | Ruslan Musayev (born 11 May 1979) is a retired Azerbaijani football player who played for the Azerbaijan national team.
National team statistics
References
1979 births
Living people
Azerbaijani men's footballers
Azerbaijan men's international footballers
Azerbaijani expatriate men's footballers
Expatriate men's footballers in Estonia
Azerbaijan Premier League players
Meistriliiga players
Men's association football midfielders
FC Akhmat Grozny players
Pärnu JK Tervis players
FK Genclerbirliyi Sumqayit players
Azerbaijani expatriate sportspeople in Estonia
Expatriate men's footballers in Russia |
https://en.wikipedia.org/wiki/Gorenstein%E2%80%93Walter%20theorem | In mathematics, the Gorenstein–Walter theorem, proved by , states that if a finite group G has a dihedral Sylow 2-subgroup, and O(G) is the maximal normal subgroup of odd order, then G/O(G) is isomorphic to a 2-group, or the alternating group A7, or a subgroup of PΓL2(q) containing PSL2(q) for q an odd prime power. Note that A5 ≈ PSL2(4) ≈ PSL2(5) and A6 ≈ PSL2(9).
References
Theorems about finite groups |
https://en.wikipedia.org/wiki/Brauer%E2%80%93Fowler%20theorem | In mathematical finite group theory, the Brauer–Fowler theorem, proved by , states that if a group G has even order g > 2 then it has a proper subgroup of order greater than g1/3. The technique of the proof is to count involutions (elements of order 2) in G. Perhaps more important is another result that the authors derive from the same count of involutions, namely that
up to isomorphism there are only a finite number of finite simple groups with a given centralizer of an involution. This suggested that finite simple groups could be classified by studying their centralizers of involutions, and it led to the discovery of several sporadic groups. Later it motivated a part of the classification of finite simple groups.
References
Theorems about finite groups |
https://en.wikipedia.org/wiki/Brauer%20tree | In mathematics, in the theory of finite groups, a Brauer tree is a tree that encodes the characters of a block with cyclic defect group of a finite group. In fact, the trees encode the group algebra up to Morita equivalence. Such algebras coming from Brauer trees are called Brauer tree algebras.
described the possibilities for Brauer trees.
References
Finite groups |
https://en.wikipedia.org/wiki/National%20Aboriginal%20and%20Torres%20Strait%20Islander%20Social%20Survey | The National Aboriginal and Torres Strait Islander Social Survey (NATSISS) is a statistical survey administered by the Australian Bureau of Statistics which collects information on the social situation of Indigenous Australians (who are either Aboriginal Australians or Torres Strait Islanders), including on health, education, culture and labour force participation. The surveys are carried out every six years, starting in 2002. It succeeded the National Aboriginal and Torres Strait Islander Survey (NATSIS), the last survey of which was carried out in 1994.
The 2008 survey was carried out from August 2008 to April 2009 and involved about 13,300 Indigenous Australians.
References
Further reading
4714.0 – National Aboriginal and Torres Strait Islander Social Survey, 2002, Australian Bureau of Statistics, 23 June 2004, accessed 11 November 2010. Archived by WebCite on 11 November 2010.
4714.0 – National Aboriginal and Torres Strait Islander Social Survey, 2008, Australian Bureau of Statistics, 30 October 2009, accessed 11 November 2010. Archived by WebCite on 11 November 2010.
External links
National Aboriginal and Torres Strait Islander Social Survey, Australian Bureau of Statistics
Australian Bureau of Statistics
Indigenous Australian culture
Statistical data sets |
https://en.wikipedia.org/wiki/Cyclic%20surgery%20theorem | In three-dimensional topology, a branch of mathematics, the cyclic surgery theorem states that, for a compact, connected, orientable, irreducible three-manifold M whose boundary is a torus T, if M is not a Seifert-fibered space and r,s are slopes on T such that their Dehn fillings have cyclic fundamental group, then the distance between r and s (the minimal number of times that two simple closed curves in T representing r and s must intersect) is at most 1. Consequently, there are at most three Dehn fillings of M with cyclic fundamental group. The theorem appeared in a 1987 paper written by Marc Culler, Cameron Gordon, John Luecke and Peter Shalen.
References
Geometric topology
3-manifolds
Knot theory
Theorems in topology |
https://en.wikipedia.org/wiki/Zsolt%20Patvaros | Zsolt Patvaros (born 18 February 1993) is a Hungarian football player.
Club statistics
Updated to games played as of 19 May 2019.
References
HLSZ
1993 births
Living people
Footballers from Kecskemét
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Men's association football midfielders
Kecskeméti TE players
Zalaegerszegi TE players
Balmazújvárosi FC players
Nyíregyháza Spartacus FC players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/Baer%E2%80%93Suzuki%20theorem | In mathematical finite group theory, the Baer–Suzuki theorem, proved by and , states that if any two elements of a conjugacy class C of a finite group generate a nilpotent subgroup, then all elements of the conjugacy class C are contained in a nilpotent subgroup. gave a short elementary proof.
References
Theorems about finite groups |
https://en.wikipedia.org/wiki/Brauer%E2%80%93Suzuki%E2%80%93Wall%20theorem | In mathematics, the Brauer–Suzuki–Wall theorem, proved by , characterizes the one-dimensional unimodular projective groups over finite fields.
References
Theorems about finite groups |
https://en.wikipedia.org/wiki/Notifiable%20offence | A notifiable offence is any offence under United Kingdom law where the police must inform the Home Office, who use the report to compile crime statistics. The term Notifiable Offence is sometimes confused with recordable offence.
Reporting notifiable offences
There are strict rules regarding the recording of crime which is outlined in the National Crime Recording Standards and the Home Office Crime Counting Rules. An incident will be recorded as a crime (notifiable offence);
For offences against an identifiable victim if, on the balance of probability;
The circumstances as reported amount to a crime defined by law (the police will determine this, based on their knowledge of the law and counting rules and,
There is no credible evidence to the contrary.
For offences against the state (against society) the points to prove to evidence the offence must clearly be made out, before a crime is recorded. An offence is regarded as being "against the state" where there is no specific identifiable victim, an example being dangerous driving.
The following offences are generally categorised as notifiable offences;
violence, damage, firearms, public order
dishonesty, obscenity, drugs and sexual offences
data protection
the more serious road traffic offences
See also
Crime statistics in the United Kingdom
National Crime Recording Standards in England and Wales
Recordable offence
References
External links
The Home Office Counting Rules for Recorded Crime
Law enforcement
Law of the United Kingdom
Law enforcement in England and Wales
Crime statistics
Governance of policing in England
Governance of policing in Wales |
https://en.wikipedia.org/wiki/Class%20representative | Class representative may refer to:
in law, a lead plaintiff
in mathematics, A set of class representatives is a subset of X which contains exactly one element from each equivalence class
In Japan and Italy, the equivalent of a class president |
https://en.wikipedia.org/wiki/Trichotomy%20theorem | In group theory, the trichotomy theorem divides the finite simple groups of characteristic 2 type and rank at least 3 into three classes. It was proved by for rank 3 and by for rank at least 4. The three classes are groups of GF(2) type (classified by Timmesfeld and others), groups of "standard type" for some odd prime (classified by the Gilman–Griess theorem and work by several others), and groups of uniqueness type, where Aschbacher proved that there are no simple groups.
References
Theorems about finite groups |
https://en.wikipedia.org/wiki/Orchard-planting%20problem | In discrete geometry, the original orchard-planting problem (or the tree-planting problem) asks for the maximum number of 3-point lines attainable by a configuration of a specific number of points in the plane. There are also investigations into how many -point lines there can be. Hallard T. Croft and Paul Erdős proved
where is the number of points and is the number of -point lines.
Their construction contains some -point lines, where . One can also ask the question if these are not allowed.
Integer sequence
Define to be the maximum number of 3-point lines attainable with a configuration of points.
For an arbitrary number of points, was shown to be in 1974.
The first few values of are given in the following table .
Upper and lower bounds
Since no two lines may share two distinct points, a trivial upper-bound for the number of 3-point lines determined by points is
Using the fact that the number of 2-point lines is at least , this upper bound can be lowered to
Lower bounds for are given by constructions for sets of points with many 3-point lines. The earliest quadratic lower bound of was given by Sylvester, who placed points on the cubic curve . This was improved to in 1974 by , using a construction based on Weierstrass's elliptic functions. An elementary construction using hypocycloids was found by achieving the same lower bound.
In September 2013, Ben Green and Terence Tao published a paper in which they prove that for all point sets of sufficient size, , there are at most
3-point lines which matches the lower bound established by Burr, Grünbaum and Sloane. Thus, for sufficiently large , the exact value of is known.
This is slightly better than the bound that would directly follow from their tight lower bound of for the number of 2-point lines: proved in the same paper and solving a 1951 problem posed independently by Gabriel Andrew Dirac and Theodore Motzkin.
Orchard-planting problem has also been considered over finite fields. In this version of the problem, the points lie in a projective plane defined over a finite field..
Notes
References
.
.
.
.
External links
Discrete geometry
Euclidean plane geometry
Mathematical problems
Dot patterns |
https://en.wikipedia.org/wiki/ANOVA%20on%20ranks | In statistics, one purpose for the analysis of variance (ANOVA) is to analyze differences in means between groups. The test statistic, F, assumes independence of observations, homogeneous variances, and population normality. ANOVA on ranks is a statistic designed for situations when the normality assumption has been violated.
Logic of the F test on means
The F statistic is a ratio of a numerator to a denominator. Consider randomly selected subjects that are subsequently randomly assigned to groups A, B, and C. Under the truth of the null hypothesis, the variability (or sum of squares) of scores on some dependent variable will be the same within each group. When divided by the degrees of freedom (i.e., based on the number of subjects per group), the denominator of the F ratio is obtained.
Treat the mean for each group as a score, and compute the variability (again, the sum of squares) of those three scores. When divided by its degrees of freedom (i.e., based on the number of groups), the numerator of the F ratio is obtained.
Under the truth of the null hypothesis, the sampling distribution of the F ratio depends on the degrees of freedom for the numerator and the denominator.
Model a treatment applied to group A by increasing every score by X. (This model maintains the underlying assumption of homogeneous variances. In practice it is rare – if not impossible – for an increase of X in a group mean to occur via an increase of each member's score by X.) This will shift the distribution X units in the positive direction, but will not have any impact on the variability within the group. However, the variability between the three groups' mean scores will now increase. If the resulting F ratio raises the value to such an extent that it exceeds the threshold of what constitutes a rare event (called the Alpha level), the Anova F test is said to reject the null hypothesis of equal means between the three groups, in favor of the alternative hypothesis that at least one of the groups has a larger mean (which in this example, is group A).
Handling violation of population normality
Ranking is one of many procedures used to transform data that do not meet the assumptions of normality. Conover and Iman provided a review of the four main types of rank transformations (RT). One method replaces each original data value by its rank (from 1 for the smallest to N for the largest). This rank-based procedure has been recommended as being robust to non-normal errors, resistant to outliers, and highly efficient for many distributions. It may result in a known statistic (e.g., in the two independent samples layout ranking results in the Wilcoxon rank-sum / Mann–Whitney U test), and provides the desired robustness and increased statistical power that is sought. For example, Monte Carlo studies have shown that the rank transformation in the two independent samples t-test layout can be successfully extended to the one-way independent samples ANOVA, as well as the two in |
https://en.wikipedia.org/wiki/Strictly%20singular%20operator | In functional analysis, a branch of mathematics, a strictly singular operator is a bounded linear operator between normed spaces which is not bounded below on any infinite-dimensional subspace.
Definitions.
Let X and Y be normed linear spaces, and denote by B(X,Y) the space of bounded operators of the form . Let be any subset. We say that T is bounded below on whenever there is a constant such that for all , the inequality holds. If A=X, we say simply that T is bounded below.
Now suppose X and Y are Banach spaces, and let and denote the respective identity operators. An operator is called inessential whenever is a Fredholm operator for every . Equivalently, T is inessential if and only if is Fredholm for every . Denote by the set of all inessential operators in .
An operator is called strictly singular whenever it fails to be bounded below on any infinite-dimensional subspace of X. Denote by the set of all strictly singular operators in . We say that is finitely strictly singular whenever for each there exists such that for every subspace E of X satisfying , there is such that . Denote by the set of all finitely strictly singular operators in .
Let denote the closed unit ball in X. An operator is compact whenever is a relatively norm-compact subset of Y, and denote by the set of all such compact operators.
Properties.
Strictly singular operators can be viewed as a generalization of compact operators, as every compact operator is strictly singular. These two classes share some important properties. For example, if X is a Banach space and T is a strictly singular operator in B(X) then its spectrum satisfies the following properties: (i) the cardinality of is at most countable; (ii) (except possibly in the trivial case where X is finite-dimensional); (iii) zero is the only possible limit point of ; and (iv) every nonzero is an eigenvalue. This same "spectral theorem" consisting of (i)-(iv) is satisfied for inessential operators in B(X).
Classes , , , and all form norm-closed operator ideals. This means, whenever X and Y are Banach spaces, the component spaces , , , and are each closed subspaces (in the operator norm) of B(X,Y), such that the classes are invariant under composition with arbitrary bounded linear operators.
In general, we have , and each of the inclusions may or may not be strict, depending on the choices of X and Y.
Examples.
Every bounded linear map , for , , is strictly singular. Here, and are sequence spaces. Similarly, every bounded linear map and , for , is strictly singular. Here is the Banach space of sequences converging to zero. This is a corollary of Pitt's theorem, which states that such T, for q < p, are compact.
If then the formal identity operator is finitely strictly singular but not compact. If then there exist "Pelczynski operators" in which are uniformly bounded below on copies of , , and hence are strictly singular but not finitely strictly singu |
https://en.wikipedia.org/wiki/Thin%20group%20%28finite%20group%20theory%29 | In the mathematical classification of finite simple groups, a thin group is a finite group such that for every odd prime number p, the Sylow p-subgroups of the 2-local subgroups are cyclic. Informally, these are the groups that resemble rank 1 groups of Lie type over a finite field of characteristic 2.
defined thin groups and classified those of characteristic 2 type in which all 2-local subgroups are solvable.
The thin simple groups were classified by . The list of finite simple thin groups consists of:
The projective special linear groups PSL2(q) and PSL3(p) for p = 1 + 2a3b and PSL3(4)
The projective special unitary groups PSU3(p) for p =−1 + 2a3b and b = 0 or 1 and PSU3(2n)
The Suzuki groups Sz(2n)
The Tits group 2F4(2)'
The Steinberg group 3D4(2)
The Mathieu group M11
The Janko group J1
See also
Quasithin group
References
Finite groups |
https://en.wikipedia.org/wiki/List%20of%20places%20in%20Western%20Australia%20by%20population | Western Australia is the largest state of Australia, with an area of , and its fourth most populous, with a population of 2,660,026 as of the 2021 Australian census. Official population statistics are created by the Australian Bureau of Statistics, who have a census every five years. The most recent census for which data has been released is the 2021 census.
Urban centres by population
Urban centres are defined by the Australian Bureau of Statistics to be clusters with a population of 1,000 or higher of urban SA1's. SA1's are areas that subdivide all of Australia, and have a population between 200 and 800 people and an average population size of 400.
Local government areas by population
Western Australia is divided into local government areas, who maintain roads, provide waste collection services, parks, libraries among other things. They are classified as either Cities, Towns of Shires, depending on population.
Regions by population
Western Australia is made up of nine regions, as well as the Perth Metropolitan Region.
See also
Greater Perth
List of cities in Australia by population
List of places in New South Wales by population
List of places in the Northern Territory by population
List of places in Queensland by population
List of places in South Australia by population
List of places in Tasmania by population
List of places in Victoria by population
Local government areas of Western Australia
References
Western Australia
Places by population |
https://en.wikipedia.org/wiki/Jeffrey%20Yi-Lin%20Forrest | Yi Lin (; born 1959), also known as Jeffrey Forrest and Jeffrey Yi-Lin Forrest, is a professor of mathematics, systems science, economics, and finance at Pennsylvania State System of Higher Education (Slippery Rock campus) (SSHE) and at several major universities in China. Lin has been an active researcher in the field of systems science since mid-1980s and serves as the founder and president of the International Institute for General Systems Studies (IIGSS).
Biography
Yi Lin was born in Fuzhou, Fujian, People’s Republic of China, in 1959. He earned his BS degree in pure mathematics and an MS degree in general topology from Northwest University, Xi’an, respectively in 1982 and 1984. During 1985–1988, he pursued his PhD degree study under the supervision of Ben Fitzpatrick of Auburn University, Alabama, and earned his PhD degree in 1988. In 1990–1991, he did one year post-doctoral study in statistics under the guidance of Stephen Fienberg at Carnegie Mellon University, Pittsburgh.
From 1988 to 1992, Lin was an assistant professor, from 1992 to 2002, associate professor, from 2002 on, a professor in mathematics at SSHE (Slippery Rock campus). He was a visiting professor of the GMD Institute for Computer Architecture and Software Technology of the German National Research Center for Information Technology during the summer of 1997. Lin served as a guest professor at the Institute of Systems Engineering and Management Science, Henan Agricultural University, Zhengzhou, from 1997 to 2002; an adjunct professor at Hebei University of Economics and Trade since 1998, Shijiazhuang; visiting professor at Huazhong University of Science and Technology, Wuhan, from 2001 to 2004; honorary advisor of Chongqing Contemporary Research Institute of Systems Sciences, from 2004–2006; guest professor and a PhD program supervisor at College of Economics and Management, 2000–present, and executive president of the Institute for Grey Systems Studies, 2008–present, Nanjing University of Aeronautics and Astronautics; specially appointed professor at Department of Mathematics and Systems Science, National University of Defense Technology, Changsha, 2009–2011. Since 2009, Lin has served on the board of directors of the World Organization of Cybernetics and Systems.
Lin has lectured globally and organized various large scale projects involving scholars from over 80 countries and geographic regions representing over 50 different scientific disciplines. He was a founder of the International Institute for General Systems Studies (IIGSS), and has served as its president since its inception in 1993. Since 2008, Lin has been editor of the book series, entitled “Systems Evaluation, Prediction and Decision-Making,” published by the CRC Press of Taylor and Francis Group. In 1999, Lin was recognized with Norbert Wiener Award for the most outstanding paper in the 1998 volume of Kybernetes. In 2002, Lin’s joint work was selected by Literati Club as one highly commended paper for the ye |
https://en.wikipedia.org/wiki/Richard%20Bronson | Richard D. Bronson (born August 5, 1941) is an American professor emeritus of mathematics at Fairleigh Dickinson University where he served as Chair of the Department of Mathematics and Computer Science, Acting Dean of the College of Science and Engineering, Interim Provost of the Metropolitan Campus, Director of Government Affairs, and Senior Executive Assistant to the President. He served as an officer (2008-2011) of the International Association of University Presidents, where he was actively involved in the creation of the United Nations Academic Impact initiative and the World Innovative Summit in Education, held annually in Qatar. He is also the author of the political thriller Antispin.
Personal life
Richard D. Bronson was born in New York City on August 5, 1941. He attended Stevens Institute of Technology, where he earned his B.S., M.S., and Ph.D. in applied mathematics. He is married and has two children.
Writing
Bronson has written eleven books in mathematics, some in their third edition with many translated into multiple languages. He has published children’s poetry in magazines, including Highlights for Children. He was on the editorial staff of Simulation Magazine and SIAM News and the children’s magazine Kids Club. Antispin is his first novel.
Awards
In 1994, Richard Bronson was awarded the Distinguished College or University Teaching award by the New Jersey Section of Mathematical Association of America. He also received the Fairleigh Dickinson University Distinguished Faculty Award for Research & Scholarship, and the University College Outstanding Teacher Award.
Research
Bronson’s research interests are in mathematical modeling and computer simulation with a focus on macro-sociological theory. He has written extensively on the topic in articles for professional journals and a general-interest trade magazine.
Publications and presentations
Fiction
Antispin (e-book, published 2010; )
Non-fiction: books
Matrix Methods: An Introduction 3rd edition with Gabriel Costa (in production), Academic Press, New York. Second edition, 1991 (still in print). First edition 1970–1991.
Linear Algebra: An Introduction 2nd edition with Gabriel Costa, Academic Press, New York, 2007. First edition, 1995–2007.
Differential Equations 3rd edition with Gabriel Costa, Schaum's Outline Series, McGraw–Hill Book Company, New York, 2006. Second edition, 1993–2006; first edition under the title Modern Introductory Differential Equations, 1974–1993.
Differential Equations, Schaum’s Easy Outlines, McGraw–Hill Book Company, New York, 2003.
Operations Research 2nd edition, with G. Naadimuthu, Schaum's Outline Series, McGraw–Hill Book Company, New York, 1997. First edition, 1982–1997.
Matrix Operations, Schaum's Outline Series, McGraw–Hill Book Company, New York, 1989 (still in print).
Finite Mathematics with Calculus, with Gary Bronson, Brooks/Cole Publishing Co., CA, 2000–2003 (out of print).
Finite Mathematics, with Gary Bronson, West Publishing Co. |
https://en.wikipedia.org/wiki/Shearer%27s%20inequality | Shearer's inequality or also Shearer's lemma, in mathematics, is an inequality in information theory relating the entropy of a set of variables to the entropies of a collection of subsets. It is named for mathematician James B. Shearer.
Concretely, it states that if X1, ..., Xd are random variables and S1, ..., Sn are subsets of {1, 2, ..., d} such that every integer between 1 and d lies in at least r of these subsets, then
where is entropy and is the Cartesian product of random variables with indices j in .
Combinatorial version
Let be a family of subsets of [n] (possibly with repeats) with each included in at least members of . Let be another set of subsets of . Then
where the set of possible intersections of elements of with .
See also
Lovász local lemma
References
Information theory
Inequalities |
https://en.wikipedia.org/wiki/Eric%20Hays | Eric Hays is a former University of Montana basketball player who served as head basketball coach of at Hellgate High School in Missoula, Mont., for 25 years. He was a mathematics teacher there until his retirement in 2009.
Hays is best remembered for his outstanding performance at the 1975 NCAA tournament against the powerhouse UCLA Bruins in the Sweet 16. He scored a game-high 32 points on 13-of-16 shooting, grabbed seven rebounds and dished out six assists in the Grizzlies' 67–64 loss to the eventual national champions, who had six players that went on to play in the NBA.
Early life
Eric Hays was born July 4, 1952, in Junction City, Ore., a farming community roughly 15 miles from Eugene and 25 miles from Corvallis. Hays lived there for the first 18 years of his life and attended Junction City High School where he was a two-year starter on the basketball team as well as the football team's quarterback for one season before injuring the growth plate in his shoulder during his sophomore year. His high school consisted of 450 students throughout three grades.
Hays believed he would eventually raise a family in a similar community-oriented environment with a small school.
College career
Hays attended Washington State University in Pullman, Wash. Originally, he planned on being an accountant, but changed his aspirations toward coaching after observing one of his brother's high school games, in which he thought the coaching was "unfair" to the players. Hays then declared his major as math education and pursued his goals of becoming a high school teacher and basketball coach.
Hays also pursued basketball at WSU because the Cougars allowed players to "walk-on," meaning non-recruited students could try out for the team. Hays defied the odds and made the freshman team of 20. Before the season began, he rose to the position of "sixth man," the first player off the bench during games. By the fourth game that season, Hays was one of the starting five and never relinquished the role. The Junction City native ended the season second in both scoring and rebounding on a team that finished with an outstanding record of 20–2. Midway through his freshman year, Hays was awarded a full-ride scholarship by the university due to his excellence on the court.
To his surprise, he was cut by the new head coach after only two days of tryouts his sophomore year of 1971. Head coach Marv Harshman had abruptly left to coach the University of Washington in July of that year. Hays then followed Washington State's former assistant coach, the legendary Jud Heathcote, and transferred to the University of Montana in January 1972. He again made the team as a walk-on the following year.
Hays' high school dream was realized in his final year as a collegiate basketball player. He had always wanted to play at the Memorial Coliseum in Portland, Ore. At the twilight of his senior year, he was given the opportunity, and he didn't put it to waste. Entering the 1975 season, the Montana |
https://en.wikipedia.org/wiki/Cochran%E2%80%93Mantel%E2%80%93Haenszel%20statistics | In statistics, the Cochran–Mantel–Haenszel test (CMH) is a test used in the analysis of stratified or matched categorical data. It allows an investigator to test the association between a binary predictor or treatment and a binary outcome such as case or control status while taking into account the stratification. Unlike the McNemar test, which can only handle pairs, the CMH test handles arbitrary strata size. It is named after William G. Cochran, Nathan Mantel and William Haenszel. Extensions of this test to a categorical response and/or to several groups are commonly called Cochran–Mantel–Haenszel statistics. It is often used in observational studies where random assignment of subjects to different treatments cannot be controlled, but confounding covariates can be measured.
Definition
We consider a binary outcome variable such as case status (e.g. lung cancer) and a binary predictor such as treatment status (e.g. smoking). The observations are grouped in strata. The stratified data are summarized in a series of 2 × 2 contingency tables, one for each stratum. The i-th such contingency table is:
The common odds-ratio of the K contingency tables is defined as:
The null hypothesis is that there is no association between the treatment and the outcome. More precisely, the null hypothesis is and the alternative hypothesis is . The test statistic is:
It follows a distribution asymptotically with 1 df under the null hypothesis.
Subset stability
The standard odds- or risk ratio of all strata could be calculated, giving risk ratios , where is the number of strata. If the stratification were removed, there would be one aggregate risk ratio of the collapsed table; let this be .
One generally expects the risk of an event unconditional on the stratification to be bounded between the highest and lowest risk within the strata (or identically with odds ratios).
It is easy to construct examples where this is not the case, and is larger or smaller than all of for .
This is comparable but not identical to Simpson's paradox, and as with Simpson's paradox, it is difficult to interpret the statistic and decide policy based upon it.
Klemens
defines a statistic to be subset stable iff is bounded between and , and a well-behaved statistic as being infinitely differentiable and not dependent on the order of the strata.
Then the CMH statistic is the unique well-behaved statistic satisfying subset stability.
Related tests
The McNemar test can only handle pairs. The CMH test is a generalization of the McNemar test as their test statistics are identical when each stratum shows a pair.
Conditional logistic regression is more general than the CMH test as it can handle continuous variable and perform multivariate analysis. When the CMH test can be applied, the CMH test statistic and the score test statistic of the conditional logistic regression are identical.
Breslow–Day test for homogeneous association. The CMH test supposes that the effect of the treatment i |
https://en.wikipedia.org/wiki/Suzuki%20groups | In the area of modern algebra known as group theory, the Suzuki groups, denoted by Sz(22n+1), 2B2(22n+1), Suz(22n+1), or G(22n+1), form an infinite family of groups of Lie type found by , that are simple for n ≥ 1. These simple groups are the only finite non-abelian ones with orders not divisible by 3.
Constructions
Suzuki
originally constructed the Suzuki groups as subgroups of SL4(F22n+1) generated by certain explicit matrices.
Ree
Ree observed that the Suzuki groups were the fixed points of exceptional automorphisms of some symplectic groups of dimension 4, and used this to construct two further families of simple groups, called the Ree groups. In the lowest case the symplectic group B2(2)≈S6; its exceptional automorphism fixes the subgroup Sz(2) or 2B2(2), of order 20.
gave a detailed exposition of Ree's observation.
Tits
constructed the Suzuki groups as the symmetries of a certain ovoid in 3-dimensional projective space over a field of characteristic 2.
Wilson
constructed the Suzuki groups as the subgroup of the symplectic group in 4 dimensions preserving a certain product on pairs of orthogonal vectors.
Properties
Let q = 22n+1 and r = 2n, where n is a non-negative integer.
The Suzuki groups Sz(q) or 2B2(q) are simple for n≥1. The group Sz(2) is solvable and is the Frobenius group of order 20.
The Suzuki groups Sz(q) have orders q2(q2+1)(q−1). These groups have orders divisible by 5, but not by 3.
The Schur multiplier is trivial for n>1, Klein 4-group for n=1, i. e. Sz(8).
The outer automorphism group is cyclic of order 2n+1, given by automorphisms of the field of order q.
Suzuki group are Zassenhaus groups acting on sets of size (22n+1)2+1, and have 4-dimensional representations over the field with 22n+1 elements.
Suzuki groups are CN-groups: the centralizer of every non-trivial element is nilpotent.
Subgroups
When n is a positive integer, Sz(q) has at least 4 types of maximal subgroups.
The diagonal subgroup is cyclic, of order q – 1.
The lower triangular (Borel) subgroup and its conjugates, of order q2·(q-1). They are one-point stabilizers in a doubly transitive permutation representation of Sz(q).
The dihedral group Dq–1, normalizer of the diagonal subgroup, and conjugates.
Cq+2r+1:4
Cq–2r+1:4
Smaller Suzuki groups, when 2n+1 is composite.
Either q+2r+1 or q–2r+1 is divisible by 5, so that Sz(q) contains the Frobenius group C5:4.
Conjugacy classes
showed that the Suzuki group has q+3 conjugacy classes. Of these, q+1 are strongly real, and the other two are classes of elements of order 4.
q2+1 Sylow 2-subgroups of order q2, of index q–1 in their normalizers. 1 class of elements of order 2, 2 classes of elements of order 4.
q2(q2+1)/2 cyclic subgroups of order q–1, of index 2 in their normalizers. These account for (q–2)/2 conjugacy classes of non-trivial elements.
Cyclic subgroups of order q+2r+1, of index 4 in their normalizers. These account for (q+2r)/4 conjugacy classes of non-trivial elements.
Cy |
https://en.wikipedia.org/wiki/John%20Edwin%20Luecke | John Edwin Luecke is an American mathematician who works in topology and knot theory. He got his Ph.D. in 1985 from the University of Texas at Austin and is now a professor in the department of mathematics at that institution.
Work
Luecke specializes in knot theory and 3-manifolds. In a 1987 paper Luecke, Marc Culler, Cameron Gordon, and Peter Shalen proved the cyclic surgery theorem. In a 1989 paper Luecke and Cameron Gordon proved that knots are determined by their complements, a result now known as the Gordon–Luecke theorem.
Dr Luecke received a NSF Presidential Young Investigator Award in 1992 and Sloan Foundation fellow in 1994. In 2012 he became a fellow of the American Mathematical Society.
References
External links
John Edwin Luecke at the Mathematics Genealogy Project
Luecke's home page at the University of Texas at Austin
20th-century American mathematicians
21st-century American mathematicians
Topologists
University of Texas at Austin faculty
University of Texas at Austin College of Natural Sciences alumni
Fellows of the American Mathematical Society
Living people
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Jo%C3%A3o%20Carlos%20%28footballer%2C%20born%201988%29 | João Carlos Heidemann (born 6 April 1988), known as João Carlos, is a Brazilian footballer who plays as a goalkeeper for Cuiabá.
Career statistics
Honours
Atlético Goianiense
Campeonato Goiano: 2011
CSA
Campeonato Alagoano: 2019
Cuiabá
Campeonato Mato-Grossense: 2021, 2022, 2023
References
External links
1988 births
Living people
People from Paranavaí
Brazilian people of German descent
Brazilian men's footballers
Men's association football goalkeepers
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Club Athletico Paranaense players
Atlético Clube Goianiense players
Ipatinga Futebol Clube players
Fortaleza Esporte Clube players
Nacional Esporte Clube Ltda players
Boa Esporte Clube players
Associação Atlética Ponte Preta players
Centro Sportivo Alagoano players
Cuiabá Esporte Clube players
Footballers from Paraná (state) |
https://en.wikipedia.org/wiki/Kallman%E2%80%93Rota%20inequality | In mathematics, the Kallman–Rota inequality, introduced by , is a generalization of the Landau–Kolmogorov inequality to Banach spaces. It states that
if A is the infinitesimal generator of a one-parameter contraction semigroup then
References
.
Inequalities |
https://en.wikipedia.org/wiki/Walter%20theorem | In mathematics, the Walter theorem, proved by , describes the finite groups whose Sylow 2-subgroup is abelian. used Bender's method to give a simpler proof.
Statement
Walter's theorem states that if G is a finite group whose 2-sylow subgroups are abelian, then G/O(G) has a normal subgroup of odd index that is a product of groups each of which is a 2-group or one of the simple groups PSL2(q) for q = 2n or q = 3 or 5 mod 8, or the Janko group J1, or Ree groups 2G2(32n+1). (Here O(G) denotes the unique largest normal subgroup of G of
odd order.)
The original statement of Walter's theorem did not quite identify the Ree groups, but only stated that the corresponding groups have a similar subgroup structure as Ree groups. and later showed that they are all Ree groups, and gave a unified exposition of this result.
References
Theorems about finite groups |
https://en.wikipedia.org/wiki/Constrained%20Delaunay%20triangulation | In computational geometry, a constrained Delaunay triangulation is a generalization of the Delaunay triangulation that forces certain required segments into the triangulation as edges, unlike the Delaunay triangulation itself which is based purely on the position of a given set of vertices without regard to how they should be connected by edges. It can be computed efficiently and has applications in geographic information systems and in mesh generation.
Definition
The input to the constrained Delaunay triangulation problem is a planar straight-line graph, a set of points and non-crossing line segments in the plane.
The constrained Delaunay triangulation of this input is a triangulation of its convex hull, including all of the input segments as edges, and using only the vertices of the input. For every additional edge added to this input to make it into a triangulation, there should exist a circle through the endpoints of , such that any vertex interior to the circle is blocked from visibility from at least one endpoint of by a segment of the input. This generalizes the defining property of two-dimensional Delaunay triangulations of points, that each edge have a circle through its two endpoints containing no other vertices. A triangulation satisfying these properties always exists.
Jonathan Shewchuk has generalized this definition to constrained Delaunay triangulations of three-dimensional inputs, systems of points and non-crossing segments and triangles in three-dimensional space; however, not every input of this type has a constrained Delaunay triangulation according to his generalized definition.
Algorithms
Several algorithms for computing constrained Delaunay triangulations of planar straight-line graphs in time are known. The constrained Delaunay triangulation of a simple polygon can be constructed in linear time.
Applications
In topographic surveying, one constructs a triangulation from points shot in the field. If an edge of the triangulation crosses a river, the resulting surface does not accurately model the path of the river. So one draws break lines along rivers, edges of roads, mountain ridges, and the like. The break lines are used as constraints when constructing the triangulation.
Constrained Delaunay triangulation can also be used in Delaunay refinement methods for mesh generation, as a way to force the mesh to conform with the domain boundaries as it is being refined.
References
External links
Open Source implementation.
Geometry processing
Triangulation (geometry) |
https://en.wikipedia.org/wiki/Bussgang%20theorem | In mathematics, the Bussgang theorem is a theorem of stochastic analysis. The theorem states that the cross-correlation of a Gaussian signal before and after it has passed through a nonlinear operation are equal up to a constant. It was first published by Julian J. Bussgang in 1952 while he was at the Massachusetts Institute of Technology.
Statement
Let be a zero-mean stationary Gaussian random process and where is a nonlinear amplitude distortion.
If is the autocorrelation function of , then the cross-correlation function of and is
where is a constant that depends only on .
It can be further shown that
Derivation for One-bit Quantization
It is a property of the two-dimensional normal distribution that the joint density of and depends only on their covariance and is given explicitly by the expression
where and are standard Gaussian random variables with correlation .
Assume that , the correlation between and is,
.
Since
,
the correlation may be simplified as
.
The integral above is seen to depend only on the distortion characteristic and is independent of .
Remembering that , we observe that for a given distortion characteristic , the ratio is .
Therefore, the correlation can be rewritten in the form.The above equation is the mathematical expression of the stated "Bussgang‘s theorem".
If , or called one-bit quantization, then .
Arcsine law
If the two random variables are both distorted, i.e., , the correlation of and is . When , the expression becomes,where .
Noticing that
,
and , ,
we can simplify the expression of asAlso, it is convenient to introduce the polar coordinate . It is thus found that
.
Integration gives，This is called "Arcsine law", which was first found by J. H. Van Vleck in 1943 and republished in 1966. The "Arcsine law" can also be proved in a simpler way by applying Price's Theorem.
The function can be approximated as when is small.
Price's Theorem
Given two jointly normal random variables and with joint probability function ,we form the meanof some function of . If as , then.Proof. The joint characteristic function of the random variables and is by definition the integral.From the two-dimensional inversion formula of Fourier transform, it follows that.Therefore, plugging the expression of into , and differentiating with respect to , we obtainAfter repeated integration by parts and using the condition at , we obtain the Price's theorem.
Proof of Arcsine law by Price's Theorem
If , then where is the Dirac delta function.
Substituting into Price's Theorem, we obtain,.When , . Thus,which is Van Vleck's well-known result of "Arcsine law".
Application
This theorem implies that a simplified correlator can be designed. Instead of having to multiply two signals, the cross-correlation problem reduces to the gating of one signal with another.
References
Further reading
E.W. Bai; V. Cerone; D. Regruto (2007) "Separable inputs for the identification of block-oriented |
https://en.wikipedia.org/wiki/Thompson%20order%20formula | In mathematical finite group theory, the Thompson order formula, introduced by John Griggs Thompson , gives a formula for the order of a finite group in terms of the centralizers of involutions, extending the results of .
Statement
If a finite group G has exactly two conjugacy classes of involutions with representatives t and z, then the Thompson order formula states
Here a(x) is the number of pairs (u,v) with u conjugate to t, v conjugate to z, and x in the subgroup generated by uv.
gives the following more complicated version of the Thompson order formula for the case when G has more than two conjugacy classes of involution.
where t and z are non-conjugate involutions, the sum is over a set of representatives x for the conjugacy classes of involutions, and a(x) is the number of ordered pairs of involutions u,v such that u is conjugate to t, v is conjugate to z, and x is the involution in the subgroup generated by tz.
Proof
The Thompson order formula can be rewritten as
where as before the sum is over a set of representatives x for the classes of involutions.
The left hand side is the number of pairs on involutions (u,v) with u conjugate to t, v conjugate to z. The right hand side counts these pairs in classes, depending the class of the involution in the cyclic group generated by uv. The key point is that uv has even order (as if it had odd order then u and v would be conjugate) and so the group it generates contains a unique involution x.
References
Finite groups |
https://en.wikipedia.org/wiki/Aschbacher%20block | In mathematical finite group theory, a block, sometimes called Aschbacher block, is a subgroup giving an obstruction to Thompson factorization and pushing up. Blocks were introduced by Michael Aschbacher.
Definition
A group L is called short if it has the following properties :
L has no subgroup of index 2
The generalized Fitting subgroup F*(L) is a 2-group O2(L)
The subgroup U = [O2(L), L] is an elementary abelian 2-group in the center of O2(L)
L/O2(L) is quasisimple or of order 3
L acts irreducibly on U/CU(L)
An example of a short group is the semidirect product of a quasisimple group with an irreducible module over the 2-element field F2
A block of a group G is a short subnormal subgroup.
References
Finite groups |
https://en.wikipedia.org/wiki/List%20of%20Wigan%20Athletic%20F.C.%20records%20and%20statistics | Wigan Athletic Football Club is a professional football team based in Wigan, Greater Manchester. The club was formed in 1932, and joined the Football League in 1978. Wigan Athletic currently compete in the third tier of English football, the EFL League One.
Club records
Matches
Firsts
First competitive match: Wigan Athletic 0–2 Port Vale Reserves, Cheshire League, 27 August 1932.
First FA Cup match: Wigan Athletic 1–1 Great Harwood, preliminary round, 16 September 1933.
First Northern Premier League match: Scarborough 0–2 Wigan Athletic, 10 August 1968.
First Football League match: Hereford United 0–0 Wigan Athletic, 19 August 1978.
Record results
Record win: 14–0 against Chorley (pre-season friendly) 1 August 2017
Record Football League win: 8–0 v Hull City, Championship, 14 July 2020.
Record Football League defeat: 1–9 v Tottenham Hotspur, Premier League, 2009.
Attendances
Highest attendance (Springfield Park): 27,526 v Hereford United, FA Cup, 1953.
Highest attendance (DW Stadium): 25,133 v Manchester United, Premier League, May 2008.
Player records
Appearances
Youngest player ever : Jensen Weir, aged 15 years, on 7 November 2017.
Oldest player ever: Dave Beasant, 43 years, 235 days, v Doncaster Rovers, 12 November 2002.
Most League appearances: Kevin Langley, 317, 1981–1986 & 1990–1994.
Most consecutive League appearances: Jimmy Bullard, 123, January 2003 to December 2005.
Goalscorers
Most goals in the League: 70, Andy Liddell, 1998–2004.
Most League goals scored in a season: 31, Graeme Jones, 1996–97.
Most goals in the Premiership: 24, Hugo Rodallega, 2009–2012.
Most goals at the DW Stadium: 41, Nathan Ellington, 2002–2005.
Transfer fees
Highest transfer fee paid: Charles N'Zogbia, £7 million, February 2009.
Highest transfer fee received: Antonio Valencia, £15 million, June 2009.
Progressive record fees paid
Progressive record fees received
Notes
A. Wigan paid Newcastle United £6 million for N'Zogbia, with Ryan Taylor (valued at £1 million) transferring to Newcastle in a part-exchange deal.
References
General
Specific
Records and Statistics
Wigan Athletic |
https://en.wikipedia.org/wiki/Thompson%20factorization | In mathematical finite group theory, a Thompson factorization, introduced by , is an expression of some finite groups as a product of two subgroups, usually normalizers or centralizers of p-subgroups for some prime p.
References
Finite groups |
https://en.wikipedia.org/wiki/Paulinho%20%28footballer%2C%20born%201984%29 | Paulo Cesar Elias, better known as Paulinho, (born 15 October 1984 in Guaranésia) is a Brazilian football player who plays as a left back. He plays for Novorizontino.
Career statistics
(Correct )
Contract
Atlético Paranaense
References
External links
1984 births
Living people
Brazilian men's footballers
Luverdense Esporte Clube players
Esporte Clube Novo Hamburgo players
Club Athletico Paranaense players
Atlético Clube Goianiense players
Avaí FC players
Paraná Clube players
Grêmio Novorizontino players
Clube de Regatas Brasil players
Cuiabá Esporte Clube players
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Campeonato Brasileiro Série D players
Men's association football defenders |
https://en.wikipedia.org/wiki/Thiago%20Santos%20%28footballer%2C%20born%201992%29 | Thiago de Jesus Santos, better known as Thiago Santos (Lagarto, April 14, 1992) is a Brazilian footballer.
Career statistics
(Correct )
Contract
Atlético Paranaense.
References
External links
wspsoccer
O Gol
1992 births
Living people
Brazilian men's footballers
Club Athletico Paranaense players
Ipatinga Futebol Clube players
Expatriate men's footballers in Thailand
Expatriate men's footballers in Cambodia
Men's association football forwards
Brazilian expatriate sportspeople in Cambodia
Footballers from Espírito Santo
People from Lagarto, Sergipe
Footballers from Sergipe
People from São Mateus, Espírito Santo |
https://en.wikipedia.org/wiki/Renan%20Foguinho | Renan Rodrigues da Silva, known as Renan Foguinho (born 9 October 1989) is a Brazilian footballer who plays as a defensive midfielder.
Career
Career statistics
(Correct )
Honours
Sul-americano: 2004
Jogos da Juventude: 2005–06
Taça BH: 2006
Campeonato Paranaense: 2009
Copa Tribuna de Futebol Junior: 2009
International
Brazil U-20
Torneio Hexagonal Internacional da Venezuela: 2009
References
External links
ogol.com
1989 births
Living people
Footballers from Londrina
Brazilian men's footballers
Brazil men's under-20 international footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Belarus
Expatriate men's footballers in Turkey
Campeonato Brasileiro Série A players
TFF First League players
Club Athletico Paranaense players
FC Dinamo Minsk players
Atlético Clube Goianiense players
Esporte Clube XV de Novembro (Piracicaba) players
Adanaspor footballers
Giresunspor footballers
Clube Náutico Capibaribe players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Edu%20Salles | Eduardo de Salles Oliveira, known as just Edu Salles, is a striker and most recently played in the Xerez Deportivo FC.
Career statistics
(Correct )
Contract
Atlético Paranaense.
References
External links
ogol.com
1990 births
Living people
Brazilian men's footballers
Club Athletico Paranaense players
Expatriate men's footballers in Thailand
Men's association football forwards
Footballers from Curitiba |
https://en.wikipedia.org/wiki/Bruno%20Furlan | Bruno de Oliveira Furlan (born 9 July 1992) is a Brazilian former footballer.
Career
He played for Dinamo Minsk on loan from Atlético Paranaense.
Career statistics
(Correct )
References
External links
ogol.com
1992 births
Living people
Brazilian men's footballers
Men's association football forwards
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Brazilian expatriate men's footballers
Expatriate men's footballers in Belarus
Club Athletico Paranaense players
FC Dinamo Minsk players
Clube Náutico Capibaribe players
Joinville Esporte Clube players
ABC Futebol Clube players
América Futebol Clube (RN) players
FC Vitebsk players
Footballers from Campo Grande |
https://en.wikipedia.org/wiki/Johan%20Teyler | Johannes or Johan Teyler (23 May 1648 – c.1709) was a Dutch Golden Age painter, engraver, mathematics teacher, and promoter of the technique in color printmaking now known as à la poupée.
Biography
Teyler was born at Nijmegen. His father was William Taylor, an English or Scottish mercenary, who changed his name to Teyler. Johan studied Latin at the Latin school of Nijmegen and Mathematics at the Kwartierlijke Academie, where he wrote a dissertation in favor of Descartes. After the death of his father, he studied in Leiden and afterwards acquired a post as Professor of Math and Philosophy in Nijmegen in 1670. He was a respected professor but was overlooked for promotion due to his Cartesian ideas. Through the mediation of his friend Gottfried Leibniz he attempted to acquire a professorship in Wolfenbüttel but gave up after discussions with Christiaan Huygens. The rest of his career was outside Academia. In 1676 he became Vestingbouwkundige fortification manager for Frederick William I, Elector of Brandenburg during the Scanian War. In 1678 he also became a tutor for the Elector's sons.
Later the same year he was dismissed and returned to Nijmegen to receive backpay which was still owed him there. With the extra funds he undertook a trip to Italy, Egypt, the Holy Land and Malta, and later sent his diary to the Elector. He later wrote a popular book on fortifications in 1688 called Architectura militaris (Rotterdam, 1688), and in the same year received a patent on a color printing process that involved using different colors of ink at the same time when printing plates. In 1695 he had a printing workshop in Rijswijk where he printed military-related works, but in 1697 he sold it and in 1698 undertook another trip to Berlin.
According to Houbraken he was a friend of Jacob de Heusch and a colleague in the Bentvueghels with the nickname Speculatie, who travelled with De Heusch to Berlin in 1698. They knew each other from their time in Rome as members of the Bentvueghel club, where Teyler also consorted with his former Math pupil from Nijmegen Jan van Call.
According to the RKD where he is registered as a painter, he returned from Italy in 1683 and remained in Nijmegen except for his trip to Berlin.
The Rijksmuseum has several hundred à la poupée prints by his workshop, many in multiple impressions, allowing the differences between each impression that are inevitable with the technique to be seen.
References
External resources
Verscheyde soorte van miniatuur. [n.p.] 1693.[n.p.] 1693. From the Lessing J. Rosenwald Collection at the Library of Congress
Color print from Admirandorum quadruplex spectaculum; delectum, pictum, et aeri in cisum, by Jan van Call
1648 births
1709 deaths
Dutch Golden Age painters
Dutch male painters
Members of the Bentvueghels
Artists from Nijmegen
17th-century Dutch mathematicians |
https://en.wikipedia.org/wiki/Quasisymmetric%20function | In algebra and in particular in algebraic combinatorics, a quasisymmetric function is any element in the ring of quasisymmetric functions which is in turn a subring of the formal power series ring with a countable number of variables. This ring generalizes the ring of symmetric functions. This ring can be realized as a specific limit of the rings of quasisymmetric polynomials in n variables, as n goes to infinity. This ring serves as universal structure in which relations between quasisymmetric polynomials can be expressed in a way independent of the number n of variables (but its elements are neither polynomials nor functions).
Definitions
The ring of quasisymmetric functions, denoted QSym, can be defined over any commutative ring R such as the integers.
Quasisymmetric
functions are power series of bounded degree in variables with coefficients in R, which are shift invariant in the sense that the coefficient of the monomial is equal to the coefficient of the monomial for any strictly increasing sequence of positive integers
indexing the variables and any positive integer sequence of exponents.
Much of the study of quasisymmetric functions is based on that of symmetric functions.
A quasisymmetric function in finitely many variables is a quasisymmetric polynomial.
Both symmetric and quasisymmetric polynomials may be characterized in terms of actions of the symmetric group
on a polynomial ring in variables .
One such action of permutes variables,
changing a polynomial by iteratively swapping pairs
of variables having consecutive indices.
Those polynomials unchanged by all such swaps
form the subring of symmetric polynomials.
A second action of conditionally permutes variables,
changing a polynomial
by swapping pairs of variables
except in monomials containing both variables.
Those polynomials unchanged by all such conditional swaps form
the subring of quasisymmetric polynomials. One quasisymmetric function in four variables is the polynomial
The simplest symmetric function containing these monomials is
Important bases
QSym is a graded R-algebra, decomposing as
where is the -span of all quasisymmetric functions that are homogeneous of degree . Two natural bases for are the monomial basis and the fundamental basis indexed by compositions of , denoted . The monomial basis consists of and all formal power series
The fundamental basis consists and all formal power series
where means we can obtain by adding together adjacent parts of , for example, (3,2,4,2) (3,1,1,1,2,1,2). Thus, when the ring is the ring of rational numbers, one has
Then one can define the algebra of symmetric functions as the subalgebra of QSym spanned by the monomial symmetric functions and all formal power series where the sum is over all compositions which rearrange to the partition . Moreover, we have . For example, and
Other important bases for quasisymmetric functions include the basis of quasisymmet |
https://en.wikipedia.org/wiki/L-balance%20theorem | In mathematical finite group theory, the L-balance theorem was proved by .
The letter L stands for the layer of a group, and "balance" refers to the property discussed below.
Statement
The L-balance theorem of Gorenstein and Walter states that if X is a finite group and T a 2-subgroup of X then
Here L2′(X) stands for the 2-layer of a group X, which is the product of all the 2-components of the group, the minimal subnormal subgroups of X mapping onto components of X/O(X).
A consequence is that if a and b are commuting involutions of a group G then
This is the property called L-balance.
More generally similar results are true if the prime 2 is replaced by a prime p, and in this case the condition is called Lp-balance, but the proof of this requires the classification of finite simple groups (more precisely the Schreier conjecture).
References
Theorems about finite groups |
https://en.wikipedia.org/wiki/Disc%20theorem | In the area of mathematics known as differential topology, the disc theorem of states that two embeddings of a closed k-disc into a connected n-manifold are ambient isotopic provided that if k = n the two embeddings are equioriented.
The disc theorem implies that the connected sum of smooth oriented manifolds is well defined.
A different although related and similar named result is the disc embedding theorem proved by Freedman in 1982.
References
Sources
Differential topology
Theorems in differential topology |
https://en.wikipedia.org/wiki/Separation%20%28statistics%29 | In statistics, separation is a phenomenon associated with models for dichotomous or categorical outcomes, including logistic and probit regression. Separation occurs if the predictor (or a linear combination of some subset of the predictors) is associated with only one outcome value when the predictor range is split at a certain value.
The phenomenon
For example, if the predictor X is continuous, and the outcome y = 1 for all observed x > 2. If the outcome values are (seemingly) perfectly determined by the predictor (e.g., y = 0 when x ≤ 2) then the condition "complete separation" is said to occur. If instead there is some overlap (e.g., y = 0 when x < 2, but y has observed values of 0 and 1 when x = 2) then "quasi-complete separation" occurs. A 2 × 2 table with an empty (zero) cell is an example of quasi-complete separation.
The problem
This observed form of the data is important because it sometimes causes problems with the estimation of regression coefficients. For example, maximum likelihood (ML) estimation relies on maximization of the likelihood function, where e.g. in case of a logistic regression with completely separated data the maximum appears at the parameter space's margin, leading to "infinite" estimates, and, along with that, to problems with providing sensible standard errors. Statistical software will often output an arbitrarily large parameter estimate with a very large standard error.
Possible remedies
An approach to "fix" problems with ML estimation is the use of regularization (or "continuity corrections").
In particular, in case of a logistic regression problem, the use of exact logistic regression or Firth logistic regression, a bias-reduction method based on a penalized likelihood, may be an option.
Alternatively, one may avoid the problems associated with likelihood maximization by switching to a Bayesian approach to inference. Within a Bayesian framework, the pathologies arising from likelihood maximization are avoided by the use of integration rather than maximization, as well as by the use of sensible prior probability distributions.
References
Further reading
External links
Logistic regression using Firth's bias reduction: a solution to the problem of separation in logistic regression
Logistic regression |
https://en.wikipedia.org/wiki/Characteristic%202%20type | In finite group theory, a branch of mathematics, a group is said to be of characteristic 2 type or even type or of even characteristic if it resembles a group of Lie type over a field of characteristic 2.
In the classification of finite simple groups, there is a major division between group of characteristic 2 type, where involutions resemble unipotent elements, and other groups, where involutions resemble semisimple elements.
Groups of characteristic 2 type and rank at least 3 are classified by the trichotomy theorem.
Definitions
A group is said to be of even characteristic if
for all maximal 2-local subgroups M that contain a Sylow 2-subgroup of G.
If this condition holds for all maximal 2-local subgroups M then G is said to be of characteristic 2 type.
use a modified version of this called even type.
References
Finite groups |
https://en.wikipedia.org/wiki/Julio%20C%C3%A9sar%20%28footballer%2C%20born%201990%29 | Julio César da Silva Rodríguez (born 23 January 1990), the Julio César, is a Brazilian footballer who plays as a forward for Ironi Tiberias.
Career
Played in the Palmeiras.
Career statistics
(Correct )
Contract
Palmeiras.
References
External links
palmeiras.com.br
1990 births
Living people
Brazilian men's footballers
Sociedade Esportiva Palmeiras players
Oeste Futebol Clube players
Camboriú Futebol Clube players
Esporte Clube São Bento players
Marília Atlético Clube players
Independente Futebol Clube players
Associação Desportiva São Caetano players
Desportivo Brasil players
Hapoel Nof HaGalil F.C. players
Hapoel Ashkelon F.C. players
Hapoel Iksal F.C. players
Maccabi Bnei Reineh F.C. players
Ironi Tiberias F.C. players
Liga Leumit players
Brazilian expatriate men's footballers
Expatriate men's footballers in Israel
Brazilian expatriate sportspeople in Israel
Men's association football forwards |
https://en.wikipedia.org/wiki/Kervaire%20manifold | In mathematics, specifically in differential topology, a Kervaire manifold is a piecewise-linear manifold of dimension constructed by by plumbing together the tangent bundles of two -spheres, and then gluing a ball to the result. In 10 dimensions this gives a piecewise-linear manifold with no smooth structure.
See also
Exotic sphere
References
Differential topology
Manifolds |
https://en.wikipedia.org/wiki/Certainty%20effect | The certainty effect is the psychological effect resulting from the reduction of probability from certain to probable . It is an idea introduced in prospect theory.
Normally a reduction in the probability of winning a reward (e.g., a reduction from 80% to 20% in the chance of winning a reward) creates a psychological effect such as displeasure to individuals, which leads to the perception of loss from the original probability thus favoring a risk-averse decision. However, the same reduction results in a larger psychological effect when it is done from certainty than from uncertainty.
Example
illustrated the certainty effect by the following examples.
First, consider this example:
Which of the following options do you prefer?
A. a sure gain of $30
B. 80% chance to win $45 and 20% chance to win nothing
In this case, 78% of participants chose option A while only 22% chose option B. This demonstrates the typical risk-aversion phenomenon in prospect theory and framing effect because the expected value of option B ($45x0.8=$36) exceeds that of A by 20%.
Now, consider this problem:
Which of the following options do you prefer?
C. 25% chance to win $30 and 75% chance to win nothing
D. 20% chance to win $45 and 80% chance to win nothing
In this case, 42% of participants chose option C while 58% chose option D.
As before, the expected value of the first option ($30x0.25=$7.50) was 20% lower than that of option D ($45x0.2=9) however, when neither option was certain, risk-taking increased.
See also
Pseudocertainty effect
Framing effect
Prospect theory
Allais paradox
Bibliography
Papers
General references
Risk
Cognitive biases
Prospect theory |
https://en.wikipedia.org/wiki/Dempwolff%20group | In mathematical finite group theory, the Dempwolff group is a finite group of order 319979520 = 215·32·5·7·31, that is the unique nonsplit extension of by its natural module of order . The uniqueness of such a nonsplit extension was shown by , and the existence by , who showed using some computer calculations of that the Dempwolff group is contained in the compact Lie group as the subgroup fixing a certain lattice in the Lie algebra of , and is also contained in the Thompson sporadic group (the full automorphism group of this lattice) as a maximal subgroup.
showed that any extension of by its natural module splits if , and showed that it also splits if is not 3, 4, or 5, and in each of these three cases there is just one non-split extension. These three nonsplit extensions can be constructed as follows:
The nonsplit extension is a maximal subgroup of the Chevalley group .
The nonsplit extension is a maximal subgroup of the sporadic Conway group Co3.
The nonsplit extension is a maximal subgroup of the Thompson sporadic group Th.
References
External links
Dempwolff group at the atlas of groups.
Finite groups |
https://en.wikipedia.org/wiki/Paulinho%20%28footballer%2C%20born%20January%201993%29 | Paulo Modesto da Silva Júnior (born 7 January 1993), commonly known as Paulinho, is a Brazilian footballer who plays for Atlético Mineiro as a defensive midfielder.
Career statistics
(Correct )
See also
Football in Brazil
List of football clubs in Brazil
References
External links
Atlético Mineiro profile
1993 births
Living people
Footballers from Belo Horizonte
Brazilian men's footballers
Men's association football midfielders
Campeonato Brasileiro Série A players
Clube Atlético Mineiro players |
https://en.wikipedia.org/wiki/Felipe%20Cordeiro | Felipe Cordeiro de Araujo is a Brazilian professional footballer who plays as a right back for Botafogo-PB.
Career
On 24 August 2009, he joined Copa Sul-Americana.
Career statistics
Honours
'Confiança
Campeonato Sergipano: 2017
References
External links
Galo Digital
goal
ogol.com
100 anos Galo
1991 births
Living people
Brazilian men's footballers
Men's association football fullbacks
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série C players
Campeonato Brasileiro Série D players
Clube Atlético Mineiro players
Tupi Football Club players
Associação Atlética Caldense players
Anápolis Futebol Clube players
Red Bull Bragantino II players
Esporte Clube Santo André players
Madureira Esporte Clube players
Grêmio Novorizontino players
Guarani Esporte Clube (MG) managers
Agremiação Sportiva Arapiraquense players
Associação Desportiva Confiança players
Brazilian football managers
Footballers from Paraíba |
https://en.wikipedia.org/wiki/Aleks%20%28footballer%29 | Aleksander Douglas de Faria, better known as Aleks or Aleksander (born February 20, 1991) is a Brazilian goalkeeper.
Career
Career statistics
(Correct )
Honours
National team
South American Youth Championship: 2011
FIFA U-20 World Cup: 2011
Contract
Avaí
References
External links
Avaí
1991 births
Footballers from Curitiba
Living people
Brazilian men's footballers
Brazil men's under-20 international footballers
Brazil men's youth international footballers
Men's association football goalkeepers
Grêmio Foot-Ball Porto Alegrense players
Avaí FC players
Clube Recreativo e Atlético Catalano players
Mirassol Futebol Clube players
Clube Atlético Tricordiano players
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série C players |
https://en.wikipedia.org/wiki/Clayton%20%28footballer%2C%20born%201989%29 | Clayton Nascimento Meireles (born April 12, 1989 in Cantagalo, Rio de Janeiro), better known as Clayton, is a Brazilian footballer who plays as a centre back for Barra-SC.
Career statistics
(Statistics )
Honours
Hawaii
Campeonato Catarinense: 2010
Guarani from Palhoça
Campeonato Catarinense Série B: 2012
Brusque
Campeonato Catarinense Série B: 2015
References
1989 births
Living people
Brazilian men's footballers
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série D players
Avaí FC players
Associação Atlética Iguaçu players
Marília Atlético Clube players
Sociedade Esportiva, Recreativa e Cultural Guarani players
Brusque Futebol Clube players
Vila Nova Futebol Clube players
Clube Náutico Marcílio Dias players
América Futebol Clube (RN) players
Men's association football central defenders
People from Cantagalo, Rio de Janeiro
Footballers from Rio de Janeiro (state) |
https://en.wikipedia.org/wiki/Gabriel%20Valongo | Gabriel Valongo da Silva better known as Gabriel (Camaçari, June 30, 1987) is a Brazilian footballer who plays as a center back for Luverdense.
Career statistics
(Correct )
Honours
Avaí
Campeonato Catarinense: 2010
Contract
a three-year contract with Atlético Paranaense.
a one-year loan deal with Guarani. (June 2011 to May 2012)
References
External links
soccerway
Avaí
1987 births
Living people
Brazilian men's footballers
Avaí FC players
Club Athletico Paranaense players
Guarani FC players
Associação Desportiva São Caetano players
Men's association football central defenders
Footballers from Bahia |
https://en.wikipedia.org/wiki/The%20Classical%20Groups | The Classical Groups: Their Invariants and Representations is a mathematics book by , which describes classical invariant theory in terms of representation theory. It is largely responsible for the revival of interest in invariant theory, which had been almost killed off by David Hilbert's solution of its main problems in the 1890s.
gave an informal talk about the topic of his book. There was a second edition in 1946.
Contents
Chapter I defines invariants and other basic ideas and describes the relation to Felix Klein's Erlangen program in geometry.
Chapter II describes the invariants of the special and general linear group of a vector space V on the polynomials over a sum of copies of V and its dual. It uses the Capelli identity to find an explicit set of generators for the invariants.
Chapter III studies the group ring of a finite group and its decomposition into a sum of matrix algebras.
Chapter IV discusses Schur–Weyl duality between representations of the symmetric and general linear groups.
Chapters V and VI extend the discussion of invariants of the general linear group in chapter II to the orthogonal and symplectic groups, showing that the ring of invariants is generated by the obvious ones.
Chapter VII describes the Weyl character formula for the characters of representations of the classical groups.
Chapter VIII on invariant theory proves Hilbert's theorem that invariants of the special linear group are finitely generated.
Chapter IX and X give some supplements to the previous chapters.
References
Invariant theory
Representation theory
Mathematics books |
https://en.wikipedia.org/wiki/Propositional%20proof%20system | In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for proving classical propositional tautologies.
Mathematical definition
Formally a pps is a polynomial-time function P whose range is the set of all propositional tautologies (denoted TAUT). If A is a formula, then any x such that P(x) = A is called a P-proof of A. The condition defining pps can be broken up as follows:
Completeness: every propositional tautology has a P-proof,
Soundness: if a propositional formula has a P-proof then it is a tautology,
Efficiency: P runs in polynomial time.
In general, a proof system for a language L is a polynomial-time function whose range is L. Thus, a propositional proof system is a proof system for TAUT.
Sometimes the following alternative definition is considered: a pps is given as a proof-verification algorithm P(A,x) with two inputs. If P accepts the pair (A,x) we say that x is a P-proof of A. P is required to run in polynomial time, and moreover, it must hold that A has a P-proof if and only if it is a tautology.
If P1 is a pps according to the first definition, then P2 defined by P2(A,x) if and only if P1(x) = A is a pps according to the second definition. Conversely, if P2 is a pps according to the second definition, then P1 defined by
(P1 takes pairs as input) is a pps according to the first definition, where is a fixed tautology.
Algorithmic interpretation
One can view the second definition as a non-deterministic algorithm for solving membership in TAUT. This means that proving a superpolynomial proof size lower-bound for pps would rule out existence of a certain class of polynomial-time algorithms based on that pps.
As an example, exponential proof size lower-bounds in resolution for the pigeon hole principle imply that any algorithm based on resolution cannot decide TAUT or SAT efficiently and will fail on pigeon hole principle tautologies. This is significant because the class of algorithms based on resolution includes most of current propositional proof search algorithms and modern industrial SAT solvers.
History
Historically, Frege's propositional calculus was the first propositional proof system. The general definition of a propositional proof system is due to Stephen Cook and Robert A. Reckhow (1979).
Relation with computational complexity theory
Propositional proof system can be compared using the notion of p-simulation. A propositional proof system P p-simulates Q (written as P ≤pQ) when there is a polynomial-time function F such that P(F(x)) = Q(x) for every x. That is, given a Q-proof x, we can find in polynomial time a P-proof of the same tautology. If P ≤pQ and Q ≤pP, the proof systems P and Q are p-equivalent. There is also a weaker notion of simulation: a pps P simulates or weakly p-simulates a pps Q if there is a polynomial p such that for every Q-proof x of a tautology A, there is a P-proof y of A such that the lengt |
https://en.wikipedia.org/wiki/1991%E2%80%9392%20Saudi%20First%20Division | Statistics of the 1991–92 Saudi First Division.
External links
Saudi Arabia Football Federation
Saudi League Statistics
Al Jazirah 6 May 1992 issue 7160
Saudi First Division League seasons
Saud
2 |
https://en.wikipedia.org/wiki/2007%E2%80%9308%20PFC%20CSKA%20Sofia%20season | The 2007–08 season was PFC CSKA Sofia's 60th consecutive season in A Group. This article shows player statistics and all matches (official and friendly) that the club have and will play during the 2007–08 season.
Players
Squad information
Appearances for competitive matches only
|-
|colspan="14"|Players sold or loaned out after the start of the season:
|}
As of game played start of season
Players in/out
Summer transfers
In:
Out:
Winter transfers
In:
Out:
Pre-season and friendlies
Pre-season
On-season (autumn)
Mid-season
On-season (spring)
Competitions
A Group
Table
Results summary
Results by round
Fixtures and results
Bulgarian Cup
UEFA Cup
Second qualifying round
First round
See also
List of unbeaten football club seasons
External links
Official Site
PFC CSKA Sofia seasons
Cska Sofia
Bulgarian football championship-winning seasons |
https://en.wikipedia.org/wiki/Diogo%20Orlando | Orlando Diogo de Oliveira, commonly known as Diogo Orlando (born December 4, 1983), is a Brazilian footballer who plays for Sampaio Corrêa as a defensive midfielder.
Career statistics
(Correct )
Honours
Volta Redonda
Campeonato Carioca Série B: 2004
Vitória
Campeonato Capixaba: 2006
Jaguaré
Copa Espírito Santo: 2007
Avaí
Campeonato Catarinense: 2012
Ceará
Campeonato Cearense: 2013
Santo André
Campeonato Paulista Série A2: 2016
References
External links
Central Brasileirão
1983 births
Living people
Footballers from Volta Redonda
Brazilian men's footballers
Men's association football midfielders
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série D players
Volta Redonda FC players
Associação Jaguaré Esporte Clube players
Vitória Futebol Clube (ES) players
Americano FC players
Mirassol Futebol Clube players
Associação Desportiva São Caetano players
Avaí FC players
Ceará Sporting Club players
Esporte Clube Santo André players
Associação Portuguesa de Desportos players
Gostaresh Foulad F.C. players
Associação Olímpica de Itabaiana players
Sampaio Corrêa Futebol Clube players
União Recreativa dos Trabalhadores players |
https://en.wikipedia.org/wiki/List%20of%20Malm%C3%B6%20FF%20records%20and%20statistics | Malmö Fotbollförening, also known simply as Malmö FF, is a Swedish professional association football club based in Malmö. The club is affiliated with Skånes Fotbollförbund (the Scanian Football Association), and plays its home games at Stadion. Formed on 24 February 1910, Malmö FF is the most successful club in Sweden in terms of trophies won. The club have won the most Swedish championship titles of any club with twenty, a record twenty-three league titles, and a record fourteen national cup titles. The team competes in Allsvenskan as of the 2018 season, the club's 18th consecutive season in the top flight, and their 83rd overall. The main rivals of the club are Helsingborgs IF, IFK Göteborg and, historically, IFK Malmö.
This list encompasses the major honours won by Malmö FF and records set by the club, their managers and their players. 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 Malmö FF players on the international stage. The club's attendance records, at Stadion, their home since 2009, Malmö Stadion, their home between 1958 and 2008, and Malmö IP, their home between 1910 and 1958, are also included in the list.
The club currently holds the record for the most Swedish championships with 20, the most Allsvenskan titles with 23 and Svenska Cupen triumphs with 14. The club's record appearance maker is Krister Kristensson, who made 348 league appearances between 1963 and 1978, and the club's record goalscorer is Hans Håkansson, who scored 163 goals in 192 league games between 1927 and 1938.
All statistics accurate as of match played 6 November 2016.
Honors
Malmö FF's first trophy was the Division 2 Sydsvenska Serien, which they won in the 1920–21 season. Their first national senior honour came first in 1944, when they won the 1943–44 Allsvenskan title. The club also won Svenska Cupen for the first time the same year. In terms of the number of trophies won, the 1970s was Malmö FF's most successful decade, during which time they won five league titles and four cup titles.
The club currently holds the record for most Swedish championships with 22, most Allsvenskan titles with 25, most Svenska Cupen titles with 15, and the record for the most Svenska Cupen final appearances with eighteen. They also became the first and, as of 2017, the only Swedish club to reach the final of the European Cup (present day UEFA Champions League) in 1979. Malmö FF is also the only Nordic club to have been represented at the Intercontinental Cup (succeeded by FIFA Club World Cup) in which they competed for the 1979 title. Their most recent major trophy came in October 2016, when they won their most recent Allsvenskan title.
Domestic
Swedish Champions
Winners (22): 1943–44, 1948–49, 1949–50, 1950–51, 1952–53, 1965, 1967, 1970, 1971, 1974, 1975, 1977, 1986, 1988, 2004, 2010, 2013, 2014, 2016, 2017, 2020, 2021
League
Allsv |
https://en.wikipedia.org/wiki/List%20of%20places%20in%20Tasmania%20by%20population | This is a list of places in the Australian state of Tasmania by population.
Urban centres are defined by the Australian Bureau of Statistics as being a population cluster of 1,000 or more people.
See also
Demographics of Australia
List of cities in Australia
List of places in New South Wales by population
List of places in the Northern Territory by population
List of cities in Queensland by population
List of places in South Australia by population
List of places in Victoria by population
List of places in Western Australia by population
Notes and references
Tasmania
Tasmania by population
Cities by population |
https://en.wikipedia.org/wiki/Residue%20at%20infinity | In complex analysis, a branch of mathematics, the residue at infinity is a residue of a holomorphic function on an annulus having an infinite external radius. The infinity is a point added to the local space in order to render it compact (in this case it is a one-point compactification). This space denoted is isomorphic to the Riemann sphere. One can use the residue at infinity to calculate some integrals.
Definition
Given a holomorphic function f on an annulus (centered at 0, with inner radius and infinite outer radius), the residue at infinity of the function f can be defined in terms of the usual residue as follows:
Thus, one can transfer the study of at infinity to the study of at the origin.
Note that , we have
Motivation
One might first guess that the definition of the residue of at infinity should just be the residue of at . However, the reason that we consider instead is that one does not take residues of functions, but of differential forms, i.e. the residue of at infinity is the residue of at .
See also
Riemann sphere
Algebraic variety
Residue theorem
References
Murray R. Spiegel, Variables complexes, Schaum,
Henri Cartan, Théorie élémentaire des fonctions analytiques d'une ou plusieurs variables complexes, Hermann, 1961
Mark J. Ablowitz & Athanassios S. Fokas, Complex Variables: Introduction and Applications (Second Edition), 2003, , P211-212.
Complex analysis |
https://en.wikipedia.org/wiki/Bayes%20classifier | In statistical classification, the Bayes classifier minimizes the probability of misclassification.
Definition
Suppose a pair takes values in , where is the class label of . Assume that the conditional distribution of X, given that the label Y takes the value r is given by
for
where "" means "is distributed as", and where denotes a probability distribution.
A classifier is a rule that assigns to an observation X=x a guess or estimate of what the unobserved label Y=r actually was. In theoretical terms, a classifier is a measurable function , with the interpretation that C classifies the point x to the class C(x). The probability of misclassification, or risk, of a classifier C is defined as
The Bayes classifier is
In practice, as in most of statistics, the difficulties and subtleties are associated with modeling the probability distributions effectively—in this case, . The Bayes classifier is a useful benchmark in statistical classification.
The excess risk of a general classifier (possibly depending on some training data) is defined as
Thus this non-negative quantity is important for assessing the performance of different classification techniques. A classifier is said to be consistent if the excess risk converges to zero as the size of the training data set tends to infinity.
Considering the components of to be mutually independent, we get the naive bayes classifier, where
Proof of Optimality
Proof that the Bayes classifier is optimal and Bayes error rate is minimal proceeds as follows.
Define the variables: Risk , Bayes risk , all possible classes to which the points can be classified . Let the posterior probability of a point belonging to class 1 be . Define the classifier as
Then we have the following results:
(a) , i.e. is a Bayes classifier,
(b) For any classifier , the excess risk satisfies
(c)
Proof of (a): For any classifier , we have
(due to Fubini's theorem)
Notice that is minimised by taking ,
Therefore the minimum possible risk is the Bayes risk, .
Proof of (b):
Proof of (c):
The general case that the Bayes classifier minimises classification error when each element can belong to either of n categories proceeds by towering expectations as follows.
This is minimised by simultaneously minimizing all the terms of the expectation using the classifier
for each observation x.
See also
Naive Bayes classifier
References
Bayesian statistics
Statistical classification |
https://en.wikipedia.org/wiki/Symmetric%20product | Symmetric product may refer to:
The product operation of a symmetric algebra
The symmetric product of tensors
The symmetric product of an algebraic curve
The Symmetric product (topology), or infinite symmetric product of a space X in algebraic topology |
https://en.wikipedia.org/wiki/D6%20polytope | {{DISPLAYTITLE:D6 polytope}}
In 6-dimensional geometry, there are 47 uniform polytopes with D6 symmetry, of which 16 are unique and 31 are shared with the B6 symmetry. There are two regular forms, the 6-orthoplex, and 6-demicube with 12 and 32 vertices respectively.
They can be visualized as symmetric orthographic projections in Coxeter planes of the D6 Coxeter group, and other subgroups.
Graphs
Symmetric orthographic projections of these 16 polytopes can be made in the D6, D5, D4, D3, A5, A3, Coxeter planes. Ak has [k+1] symmetry, Dk has [2(k-1)] symmetry. B6 is also included although only half of its [12] symmetry exists in these polytopes.
These 16 polytopes are each shown in these 7 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
Notes
6-polytopes |
https://en.wikipedia.org/wiki/D7%20polytope | {{DISPLAYTITLE:D7 polytope}}
In 7-dimensional geometry, there are 95 uniform polytopes with D7 symmetry; 32 are unique, and 63 are shared with the B7 symmetry. There are two regular forms, the 7-orthoplex, and 7-demicube with 14 and 64 vertices respectively.
They can be visualized as symmetric orthographic projections in Coxeter planes of the D6 Coxeter group, and other subgroups.
Graphs
Symmetric orthographic projections of these 32 polytopes can be made in the D7, D6, D5, D4, D3, A5, A3, Coxeter planes. Ak has [k+1] symmetry, Dk has [2(k-1)] symmetry. B7 is also included although only half of its [14] symmetry exists in these polytopes.
These 32 polytopes are each shown in these 8 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
Notes
7-polytopes |
https://en.wikipedia.org/wiki/D8%20polytope | {{DISPLAYTITLE:D8 polytope}}
In 8-dimensional geometry, there are 191 uniform polytopes with D8 symmetry, 64 are unique, and 127 are shared with the B8 symmetry. There are two regular forms, the 8-orthoplex, and 8-demicube with 16 and 128 vertices respectively.
They can be visualized as symmetric orthographic projections in Coxeter planes of the D8 Coxeter group, and other subgroups.
Graphs
Symmetric orthographic projections of these 64 polytopes can be made in the D8, D7, D6, D5, D4, D3, A5, A3, Coxeter planes. Ak has [k+1] symmetry, Dk has [2(k-1)] symmetry. B8 is also included although only half of its [16] symmetry exists in these polytopes.
These 64 polytopes are each shown in these 10 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.
References
8-polytopes |
https://en.wikipedia.org/wiki/Anu%C5%A1ka%20Ferligoj | Anuška Ferligoj is a Slovenian mathematician, born August 19, 1947, in Ljubljana, Slovenia, whose specialty is statistics and network analysis. Her specific interests include multivariate analysis (theory and application in social sciences, medicine, etc.), cluster analysis (constraints, multi-criteria clustering), social network analysis (blockmodeling, reliability and validity of network measurement), methodological research of public opinion, analysis of scientific networks. She is Fellow of the European Academy of Sociology.
She is a professor emeritus (2020) at the University of Ljubljana, Slovenia, and has been employed by the Faculty of Social Sciences since 1972. In 2003–2005, she was the dean of the Faculty of Social Sciences. In 1992–2012, she was the head of the Centre for Methodology and Informatics at the Institute of Social Sciences (currently – its associate member). In 2002–2013, she headed the graduate program on statistics, and in 2012–2020 the master program on applied statistics. Since 2017, she is an academic supervisor of the International Laboratory for Applied Network Research of National Research University Higher School of Economics in Moscow, Russia.
She is an elected member of the European Academy of Sociology and International Statistical Institute, and has been a member of boards of the International Network for Social Network Analysis, International Federation of Classification Societies, and International Sociological Association. She was an editor of the journal Advances in Methodology and Statistics (Metodološki zvezki) in 1987 – 2012. She has been a member of the editorial boards of several scientific journals, including Methodology, Statistics in Transition, Bulletin of Sociological Methodology, Structure and Dynamics: eJournal of Anthropology and Related Sciences, Journal of Classification, Journal of Mathematical Sociology, and Social Networks.
She was a Fulbright scholar in 1990—1991 and visiting professor at the University of Pittsburgh (1996) and at the University of Vienna (2009/10). She was awarded the title of Ambassador of Science of the Republic of Slovenia in 1997. The book Generalized Blockmodeling received Harrison White Outstanding Book Award given by Mathematical Sociology Section at the American Sociological Association. Jointly with Vladimir Batagelj, she received Simmel award from the International Network for Social Network Analysis and was a keynote speaker at the XXVI Sunbelt Social Networks Conference in 2007.
Early life and education
Anuška Ferligoj obtained her B.S. in mathematics and physics in 1971, and her M.S. in operational research in 1979 from the University of Ljubljana. In 1983 she obtained her Ph.D. in information science from the same university under the supervision of Professor Branislav Ivanović.
Since 1972, she was employed as assistant, assistant professor, associate professor and finally from 1994 as full professor at the Faculty of Social Sciences.
Research and c |
https://en.wikipedia.org/wiki/George%20Rettger | George Edward Rettger (July 29, 1868 – June 5, 1921) was a 19th-century Major League Baseball pitcher.
External links
Baseball Reference – major league statistics
19th-century baseball players
Major League Baseball pitchers
St. Louis Browns (AA) players
Cleveland Spiders players
Cincinnati Reds players
Baseball players from Ohio
1868 births
1921 deaths
Evansville Hoosiers players
Minneapolis Millers (baseball) players
Atlanta Windjammers players
Milwaukee Brewers (minor league) players
Toledo White Stockings players
Milwaukee Creams players
Columbus Senators players
Kansas City Blues (baseball) players |
https://en.wikipedia.org/wiki/Zuse%20Institute%20Berlin | The Zuse Institute Berlin (abbreviated ZIB, or Konrad-Zuse-Zentrum für Informationstechnik Berlin) is a research institute for applied mathematics and computer science on the campus of Freie Universität Berlin in Dahlem, Berlin, Germany.
The ZIB was founded by law as a statutory establishment and as a non-university research institute of the State of Berlin in 1984. In close interdisciplinary cooperation with the Berlin universities and scientific institutions Zuse Institute implements research and development in the field of information technology with a particular focus on application-oriented algorithmic mathematics and practical computer science. ZIB also provides high-performance computer capacity as an accompanying service as part of the Network of high performance computers in Northern Germany (Norddeutscher Verbund von Hoch- und Höchstleistungsrechnern (HLRN)).
Konrad Zuse, born in Berlin in 1910, is the namesake of the ZIB.
SCIP (optimization software)
SCIP (Solving Constraint Integer Programs) is a mixed integer programming solver and a framework for branch and cut and branch and price, developed primarily at Zuse Institute Berlin. Unlike most commercial solvers, SCIP gives the user low-level control of and information about the solving process. Run as a standalone solver, it is one of the fastest non-commercial solvers for mixed integer programs.
SCIP is implemented as C callable library.
For user plugins, C++ wrapper classes are provided.
The solver for the LP relaxations is not a native component of SCIP, an open LP interface is provided instead.
Currently supported LP solvers are CLP, CPLEX, MOSEK, SoPlex, and Xpress.
SCIP can be run on Linux, Mac, Sun, and Windows operating systems.
Prior versions of SCIP were distributed under a source-available license that allowed free academic use. Starting from version 8.0.3 the full suite was released under the Apache 2.0 license.
Features
The design of SCIP is based on the notion of constraints. It supports about 20 constraint types for mixed-integer linear programming, mixed-integer nonlinear programming, mixed-integer all-quadratic programming and Pseudo-Boolean optimization. It can also solve Steiner Trees and multi-objective optimization problems.
Interfaces
There are several native interface libraries available for SCIP. SCIP can be accessed through the modeling system of GAMS. Interfaces to MATLAB and AMPL are available within the standard distribution. There are also currently externalized interfaces for Python, Java, Julia, and Rust.
References
Further reading
.
External links
Homepage Zuse Institute Berlin
Research institutes in Berlin
Scientific organisations based in Germany
Supercomputer sites |
https://en.wikipedia.org/wiki/2010%20Mongolian%20Premier%20League | Statistics of Mongolian Premier League in the 2010 season.
Overview
Khangarid won the championship.
League standings
Group A standings
Group B standings
Play-offs
Semi-finals
Third place
Final
References
FIFA.com
Mongolia Premier League seasons
Mongolia
Mongolia
football |
https://en.wikipedia.org/wiki/Equichordal%20point%20problem | In Euclidean plane geometry, the equichordal point problem is the question whether a closed planar convex body can have two equichordal points. The problem was originally posed in 1916 by Fujiwara and in 1917 by Wilhelm Blaschke, Hermann Rothe, and Roland Weitzenböck. A generalization of this problem statement was answered in the negative in 1997 by Marek R. Rychlik.
Problem statement
An equichordal curve is a closed planar curve for which a point in the plane exists such that all chords passing through this point are equal in length. Such a point is called an equichordal point. It is easy to construct equichordal curves with a single equichordal point, particularly when the curves are symmetric; the simplest construction is a circle.
It has long only been conjectured that no convex equichordal curve with two equichordal points can exist. More generally, it was asked whether there exists a Jordan curve with two equichordal points and , such that the curve
would be star-shaped with respect to each of the two points.
Excentricity (or eccentricity)
Many results on equichordal curves refer to their excentricity. It turns out that the smaller the excentricity, the harder it is to disprove the existence of curves with two equichordal points. It can be shown rigorously that a small excentricity means that the curve must be close to the circle.
Let be the hypothetical convex curve with two equichordal points and . Let be the common length of all chords of the curve passing through or . Then excentricity is the ratio
where is the distance between the points and .
The history of the problem
The problem has been extensively studied, with significant papers published over eight decades preceding its solution:
In 1916 Fujiwara proved that no convex curves with three equichordal points exist.
In 1917 Blaschke, Rothe and Weitzenböck formulated the problem again.
In 1923 Süss showed certain symmetries and uniqueness of the curve, if it existed.
In 1953 G. A. Dirac showed some explicit bounds on the curve, if it existed.
In 1958 Wirsing showed that the curve, if it exists, must be an analytic curve. In this deep paper, he correctly identified the problem as perturbation problem beyond all orders.
In 1966 Ehrhart proved that there are no equichordal curves with excentricities > 0.5.
In 1988 Michelacci proved that there are no equichordal curves with excentricities > 0.33. The proof is mildly computer-assisted.
In 1992 Schäfke and Volkmer showed that there is at most a finite number of values of excentricity for which the curve may exist. They outlined a feasible strategy for a computer-assisted proof. Their method consists of obtaining extremely accurate approximations to the hypothetical curve.
In 1996 Rychlik fully solved the problem.
Rychlik's proof
Marek Rychlik's proof was published in the hard to read article.
There is also an easy to read, freely available on-line, research announcement article, but it only hints at the idea |
https://en.wikipedia.org/wiki/Perturbation%20problem%20beyond%20all%20orders | In mathematics, perturbation theory works typically by expanding unknown quantity in a power series in a small parameter. However, in a perturbation problem beyond all orders, all coefficients of the perturbation expansion vanish and the difference between the function and the constant function 0 cannot be detected by a power series.
A simple example is understood by an attempt at trying to expand in a Taylor series in about 0. All terms in a naïve Taylor expansion are identically zero. This is because the function possesses an essential singularity at in the complex -plane, and therefore the function is most appropriately modeled by a Laurent series -- a Taylor series has a zero radius of convergence. Thus, if a physical problem possesses a solution of this nature, possibly in addition to an analytic part that may be modeled by a power series, the perturbative analysis fails to recover the singular part. Terms of nature similar to are considered to be "beyond all orders" of the standard perturbative power series.
See also
Asymptotic expansion
References
J P Boyd, "The Devil's Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series", https://link.springer.com/article/10.1023/A:1006145903624
C. M. Bender and S. A. Orszag, "Advanced Mathematical Methods for Scientists and Engineers", https://link.springer.com/book/10.1007%2F978-1-4757-3069-2
C. M. Bender, Lectures on Mathematical Physics, https://www.perimeterinstitute.ca/video-library/collection/11/12-psi-mathematical-physics
Perturbation theory
Asymptotic analysis |
https://en.wikipedia.org/wiki/Convex%20curve | In geometry, a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going back to Archimedes. Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions. Important subclasses of convex curves include the closed convex curves (the boundaries of bounded convex sets), the smooth curves that are convex, and the strictly convex curves, which have the additional property that each supporting line passes through a unique point of the curve.
Bounded convex curves have a well-defined length, which can be obtained by approximating them with polygons, or from the average length of their projections onto a line. The maximum number of grid points that can belong to a single curve is controlled by its length. The points at which a convex curve has a unique supporting line are dense within the curve, and the distance of these lines from the origin defines a continuous support function. A smooth simple closed curve is convex if and only if its curvature has a consistent sign, which happens if and only if its total curvature equals its total absolute curvature.
Definitions
Archimedes, in his On the Sphere and Cylinder, defines convex arcs as the plane curves that lie on one side of the line through their two endpoints, and for which all chords touch the same side of the curve. This may have been the first formal definition of any notion of convexity, although convex polygons and convex polyhedra were already long known before Archimedes. For the next two millennia, there was little study of convexity: its in-depth investigation began again only in the 19th century, when Augustin-Louis Cauchy and others began using mathematical analysis instead of algebraic methods to put calculus on a more rigorous footing.
Many other equivalent definitions for the convex curves are possible, as detailed below. Convex curves have also been defined by their supporting lines, by the sets they form boundaries of, and by their intersections with lines. In order to distinguish closed convex curves from curves that are not closed, the closed convex curves have sometimes also been called convex loops, and convex curves that are not closed have also been called convex arcs.
Background concepts
A plane curve is the image of any continuous function from an interval to the Euclidean plane. Intuitively, it is a set of points that could be traced out by a moving point. More specifically, smooth curves generally at least require that the function from the interval to the plane be continuously differentiable, and in some contexts are defined to require higher derivatives. The function parameterizing a smooth curve is often assumed to be regular, meaning that its derivative stays away from zero; intuitively, the moving point never slows to a halt or reverses direction. Each interior point of a smooth curve has a tangent line. If, in additi |
https://en.wikipedia.org/wiki/Quadratic%20pair | In mathematical finite group theory, a quadratic pair for the odd prime p, introduced by , is a finite group G together with a quadratic module, a faithful representation M on a vector space over the finite field with p elements such that G is generated by elements with minimal polynomial (x − 1)2. Thompson classified the quadratic pairs for p ≥ 5. classified the quadratic pairs for p = 3. With a few exceptions, especially for p = 3, groups with a quadratic pair for the prime p tend to be more or less groups of Lie type in characteristic p.
See also
p-stable group
References
Finite groups |
https://en.wikipedia.org/wiki/Barsotti%E2%80%93Tate%20group | In algebraic geometry, Barsotti–Tate groups or p-divisible groups are similar to the points of order a power of p on an abelian variety in characteristic p. They were introduced by under the name equidimensional hyperdomain and by under the name p-divisible groups, and named Barsotti–Tate groups by .
Definition
defined a p-divisible group of height h (over a scheme S) to be an inductive system of groups Gn for n≥0, such that Gn is a finite group scheme over S of order phn and such that Gn is (identified with) the group of elements of order divisible by pn in Gn+1.
More generally, defined a Barsotti–Tate group G over a scheme S to be an fppf sheaf of commutative groups over S that is p-divisible, p-torsion,
such that the points G(1) of order p of G are (represented by) a finite locally free scheme.
The group G(1) has rank ph for some locally constant function h on S, called the rank or height of the group G. The subgroup G(n) of points of order pn is a scheme of rank pnh, and G is the direct limit of these subgroups.
Example
Take Gn to be the cyclic group of order pn (or rather the group scheme corresponding to it). This is a p-divisible group of height 1.
Take Gn to be the group scheme of pnth roots of 1. This is a p-divisible group of height 1.
Take Gn to be the subgroup scheme of elements of order pn of an abelian variety. This is a p-divisible group of height 2d where d is the dimension of the Abelian variety.
References
Algebraic groups |
https://en.wikipedia.org/wiki/Uniqueness%20theorem | In mathematics, a uniqueness theorem, also called a unicity theorem, is a theorem asserting the uniqueness of an object satisfying certain conditions, or the equivalence of all objects satisfying the said conditions. Examples of uniqueness theorems include:
Alexandrov's uniqueness theorem of three-dimensional polyhedra
Black hole uniqueness theorem
Cauchy–Kowalevski theorem is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems.
Cauchy–Kowalevski–Kashiwara theorem is a wide generalization of the Cauchy–Kowalevski theorem for systems of linear partial differential equations with analytic coefficients.
Division theorem, the uniqueness of quotient and remainder under Euclidean division.
Fundamental theorem of arithmetic, the uniqueness of prime factorization.
Holmgren's uniqueness theorem for linear partial differential equations with real analytic coefficients.
Picard–Lindelöf theorem, the uniqueness of solutions to first-order differential equations.
Thompson uniqueness theorem in finite group theory
Uniqueness theorem for Poisson's equation
Electromagnetism uniqueness theorem for the solution of Maxwell's equation
Uniqueness case in finite group theory
The word unique is sometimes replaced by essentially unique, whenever one wants to stress that the uniqueness is only referred to the underlying structure, whereas the form may vary in all ways that do not affect the mathematical content.
A uniqueness theorem (or its proof) is, at least within the mathematics of differential equations, often combined with an existence theorem (or its proof) to a combined existence and uniqueness theorem (e.g., existence and uniqueness of solution to first-order differential equations with boundary condition).
See also
Existence theorem
Rigidity (mathematics)
Uniqueness quantification
References
Mathematical terminology |
https://en.wikipedia.org/wiki/Federal%20Statistics%20Committee%20%28Switzerland%29 | The Swiss Federal Statistics Committee (FStatC) is an advisory body for the Federal Council, the Federal Statistical Office and other statistics producers of the Confederation. It includes high-ranking representatives from the cantons and municipalities, from the economy, social partners, the scientific world, the Swiss National Bank as well as from the federal administration. The committee was established with the nomination of its members by the Federal Council on 10 November 1993. Its legal basis is the Federal Statistical Act of 9 October 1992 and the Ordinance of 30 June 1993 on the Conduct of Federal Statistical Surveys.
The Federal Statistics Committee reports to the Federal Department of Home Affairs. The presidency is held by a representative from the scientific world and the Committee usually convenes three times a year.
Duties and responsibilities of the Federal Statistical Committee
Central to the Federal Statistical Committee's work is the accompaniment and monitoring of the multi-annual programme for federal statistics. Amongst other things this also includes the preparation of an annual report to the Federal Council on the current situation and new developments in federal statistics.
The Federal Statistical Committee is also responsible for the adoption of recommendations and guidelines developed by the FSO as well as the appraisal of propositions on the introduction, abolition or modification of the most important statistics and on major transdisciplinary projects.
Furthermore, the Federal Statistical Committee is also responsible for encouraging the collaboration and coordination of official statistics producers as well as assessing policy on the dissemination of statistical information.
On a more general note, the role of the Federal Statistical Committee is to ensure that official statistics meet the requirements of a democratic society and to help predict what demands will be made upon statistical information in the future.
Statistical multi-annual programme
In collaboration with the other statistical bodies of the Confederation and in consultation with the interested parties for each legislative period, the Federal Statistical Office produces a multi-annual programme of statistical activities at federal level. The multi-annual programme finds its legal basis in the Federal Statistical Act and aims to ensure transparent and comprehensive planning of federal statistics. It provides information on the most important federal statistics work, the current financial and human resources outlay of the Confederation, and planned cooperation with partners abroad. In addition, it enables Parliament to monitor the statistical work planned in relation to its political goals and to comment on this.
Footnotes
External links
Federal Statistical Office's internet site
Admin.ch, Federal Department of Home Affairs, Federal Statistical Committee (French)
FSO, The multi-annual programme for federal statistics
Statistical organiza |
https://en.wikipedia.org/wiki/Renatinho%20%28footballer%2C%20born%20May%201988%29 | Renato Costa Silva, the Renatinho born in Goiânia is a Brazilian footballer, who is currently playing for Plácido de Castro.
Career
Played in the Inhumas and Atlético Goianiense.
Career statistics
(Correct )
Contract
Atlético Goianiense.
See also
Football in Brazil
List of football clubs in Brazil
References
External links
ogol
soccerway
1988 births
Living people
Brazilian men's footballers
Footballers from Goiânia
Men's association football defenders
Atlético Clube Goianiense players |
https://en.wikipedia.org/wiki/Rank%203%20permutation%20group | In mathematical finite group theory, a rank 3 permutation group acts transitively on a set such that the stabilizer of a point has 3 orbits. The study of these groups was started by . Several of the sporadic simple groups were discovered as rank 3 permutation groups.
Classification
The primitive rank 3 permutation groups are all in one of the following classes:
classified the ones such that where the socle T of T0 is simple, and T0 is a 2-transitive group of degree .
classified the ones with a regular elementary abelian normal subgroup
classified the ones whose socle is a simple alternating group
classified the ones whose socle is a simple classical group
classified the ones whose socle is a simple exceptional or sporadic group.
Examples
If G is any 4-transitive group acting on a set S, then its action on pairs of elements of S is a rank 3 permutation group. In particular most of the alternating groups, symmetric groups, and Mathieu groups have 4-transitive actions, and so can be made into rank 3 permutation groups.
The projective general linear group acting on lines in a projective space of dimension at least 3 is a rank-3 permutation group.
Several 3-transposition groups are rank-3 permutation groups (in the action on transpositions).
It is common for the point-stabilizer of a rank-3 permutation group acting on one of the orbits to be a rank-3 permutation group. This gives several "chains" of rank-3 permutation groups, such as the Suzuki chain and the chain ending with the Fischer groups.
Some unusual rank-3 permutation groups (many from ) are listed below.
For each row in the table below, in the grid in the column marked "size", the number to the left of the equal sign is the degree of the permutation group for the permutation group mentioned in the row. In the grid, the sum to the right of the equal sign shows the lengths of the three orbits of the stabilizer of a point of the permutation group. For example, the expression 15 = 1+6+8 in the first row of the table under the heading means that the permutation group for the first row has degree 15, and the lengths of three orbits of the stabilizer of a point of the permutation group are 1, 6 and 8 respectively.
Notes
References
Finite groups |
https://en.wikipedia.org/wiki/Ushiki%27s%20theorem | In mathematics, particularly in the study of functions of several complex variables, Ushiki's theorem, named after S. Ushiki, states that certain well-behaved functions cannot have certain kinds of well-behaved invariant manifolds.
The theorem
A biholomorphic mapping cannot have a 1-dimensional compact smooth invariant manifold. In particular, such a map cannot have a homoclinic connection or heteroclinic connection.
Commentary
Invariant manifolds typically appear as solutions of certain asymptotic problems in dynamical systems. The most common is the stable manifold or its kin, the unstable manifold.
The publication
Ushiki's theorem was published in 1980. The theorem appeared in print again several years later, in a certain Russian journal, by an author apparently unaware of Ushiki's work.
An application
The standard map cannot have a homoclinic or heteroclinic connection. The practical consequence is that one cannot show the existence of a Smale's horseshoe in this system by a perturbation method, starting from a homoclinic or heteroclinic connection. Nevertheless, one can show that Smale's horseshoe exists in the standard map for many parameter values, based on crude rigorous numerical calculations.
See also
Melnikov distance
Equichordal point problem
References
Dynamical systems
Theorems in complex analysis
Several complex variables |
https://en.wikipedia.org/wiki/Invariant%20manifold | In dynamical systems, a branch of mathematics, an invariant manifold is a topological manifold that is invariant under the action of the dynamical system. Examples include the slow manifold, center manifold, stable manifold, unstable manifold, subcenter manifold and inertial manifold.
Typically, although by no means always, invariant manifolds are constructed as a 'perturbation' of an invariant subspace about an equilibrium.
In dissipative systems, an invariant manifold based upon the gravest, longest lasting modes forms an effective low-dimensional, reduced, model of the dynamics.
Definition
Consider the differential equation
with flow being the solution of the differential equation with .
A set is called an invariant set for the differential equation if, for each , the solution , defined on its maximal interval of existence, has its image in . Alternatively, the orbit
passing through each lies in . In addition, is called an invariant manifold if is a manifold.
Examples
Simple 2D dynamical system
For any fixed parameter , consider the variables governed by the pair of coupled differential equations
The origin is an equilibrium. This system has two invariant manifolds of interest through the origin.
The vertical line is invariant as when the -equation becomes which ensures remains zero. This invariant manifold, , is a stable manifold of the origin (when ) as all initial conditions lead to solutions asymptotically approaching the origin.
The parabola is invariant for all parameter . One can see this invariance by considering the time derivative and finding it is zero on as required for an invariant manifold. For this parabola is the unstable manifold of the origin. For this parabola is a center manifold, more precisely a slow manifold, of the origin.
For there is only an invariant stable manifold about the origin, the stable manifold including all .
Invariant manifolds in non-autonomous dynamical systems
A differential equation
represents a non-autonomous dynamical system, whose solutions are of the form with . In the extended phase space of such a system, any initial surface generates an invariant manifold
A fundamental question is then how one can locate, out of this large family of invariant manifolds, the ones that have the highest influence on the overall system dynamics. These most influential invariant manifolds in the extended phase space of a non-autonomous dynamical systems are known as Lagrangian Coherent Structures.
See also
Hyperbolic set
Lagrangian coherent structure
Spectral submanifold
References
Dynamical systems |
https://en.wikipedia.org/wiki/Homoclinic%20connection | In dynamical systems, a branch of mathematics, a homoclinic connection is a structure formed by the stable manifold and unstable manifold of a fixed point.
Definition for maps
Let be a map defined on a manifold , with a fixed point .
Let and be the stable manifold and the unstable manifold
of the fixed point , respectively. Let be a connected invariant manifold such that
Then is called a homoclinic connection.
Heteroclinic connection
It is a similar notion, but it refers to two fixed points, and . The condition satisfied by
is replaced with:
This notion is not symmetric with respect to and .
Homoclinic and heteroclinic intersections
When the invariant manifolds and , possibly with , intersect but there is no homoclinic/heteroclinic connection, a different structure is formed by the two manifolds, sometimes referred to as the homoclinic/heteroclinic tangle. The figure has a conceptual drawing illustrating their complicated structure. The theoretical result supporting the drawing is the lambda-lemma. Homoclinic tangles are always accompanied by a Smale horseshoe.
Definition for continuous flows
For continuous flows, the definition is essentially the same.
Comments
There is some variation in the definition across various publications;
Historically, the first case considered was that of a continuous flow on the plane, induced by an ordinary differential equation. In this case, a homoclinic connection is a single trajectory that converges to the fixed point both forwards and backwards in time. A pendulum in the absence of friction is an example of a mechanical system that does have a homoclinic connection. When the pendulum is released from the top position (the point of highest potential energy), with infinitesimally small velocity, the pendulum will return to the same position. Upon return, it will have exactly the same velocity. The time it will take to return will increase to as the initial velocity goes to zero. One of the demonstrations in the pendulum article exhibits this behavior.
Significance
When a dynamical system is perturbed, a homoclinic connection splits. It becomes a disconnected invariant set. Near it, there will be a chaotic set called Smale's horseshoe. Thus, the existence of a homoclinic connection can potentially lead to chaos. For example, when a pendulum is placed in a box, and the box is subjected to small horizontal oscillations, the pendulum may exhibit chaotic behavior.
See also
Homoclinic orbit
Heteroclinic orbit
Dynamical systems |
https://en.wikipedia.org/wiki/Marquinhos%20%28footballer%2C%20born%201992%29 | Marcos Vinícius Bento, the Marquinhos (born 1 April 1992 in Franca) is a midfielder who plays in the Palmeiras B.
Career
Played in the Cruzeiro.
Career statistics
(Correct )
Contract
Cruzeiro.
References
External links
ogol
soccerway
1992 births
Living people
Brazilian men's footballers
Cruzeiro Esporte Clube players
Villa Nova Atlético Clube players
Men's association football midfielders
Footballers from São Paulo (state) |
https://en.wikipedia.org/wiki/State%20Statistics%20Committee | The State Statistics Committee of Azerbaijan Republic () is a governmental agency within the Cabinet of Azerbaijan in charge of collection, processing and disseminating statistical data on the economy, demographics and other sectors of activity in Azerbaijan Republic. The agency is headed by Arif Valiyev.
History
The statistics offices were initially created and operated in Shamakhi from 1846 through 1859, in Baku from 1859 and in Ganja from 1867 after their incorporation into Russian governorates. Until 1917, statistical data was given in 20 to 27 tables and contained information on population, labor, job markets, number of factories and plants, agricultural data, prices on commodities, military data, etc.
With the establishment of the Azerbaijan Democratic Republic, the authorities tried to create a centralized office for statistical data collection but succeeded only in establishment of separate statistics offices within various ministries such as within State Property Ministry on November 15, 1918, and within the Department of Land of the Ministry of Agriculture in July 1919.
After establishment of Soviet rule on July 8, 1920 Nariman Narimanov created an interim collegium of statistics within the Azerbaijan Revolutionary Committee. From 1924 forward, regional statistical bodies were created in each region.
In 1928, a new statute was approved by the Council of People's Commissars of Azerbaijan SSR for creation of Central Statistics Department. In 1948, the Central Statistics Department was transferred to the Cabinet of Ministers of Azerbaijan.
In 1987, the Central Statistics Department was transformed into State Statistics Committee of Azerbaijan SSR and its statute was approved by the Council of Ministers of March 1988.
On February 18, 1994 President of independent Azerbaijan, Heydar Aliyev signed the Law on Statistics establishing the State Statistics Committee of Azerbaijan Republic.
Structure
The committee is headed by its chairman. It consists of the Central Administration, State Statistics Committee of Nakhichevan AR, Baku City Statistics Department, 81 raion statistics offices, Main Accounting Office and Department for Scientific Research and Projection of Statistical Data.
The State Statistical Committee of the Republic of Azerbaijan ensures the activity of the statistical information system on the basis of the single methodology in the social and economic spheres in the country. The State Statistical Committee of Azerbaijan is an independent central economic body regulating the statistical and registration activity and operating in the system of the central executive bodies.
The committee carries out its activities on the basis of the comprehensive and objective study of socioeconomic processes taking place in the country, provides the information on the socioeconomic state of the country and is responsible for the implementation of the policy, aiming at the increase of the role of statistical information through respecting the |
https://en.wikipedia.org/wiki/Thompson%20uniqueness%20theorem | In mathematical finite group theory, Thompson's original uniqueness theorem states that in a minimal simple finite group of odd order there is a unique maximal subgroup containing a given elementary abelian subgroup of rank 3. gave a shorter proof of the uniqueness theorem.
References
Theorems about finite groups
Uniqueness theorems |
https://en.wikipedia.org/wiki/Arif%20Valiyev | Arif Valiyev Mikayil oglu () was an Azerbaijani politician who served as the Chairman of the State Statistics Committee of Azerbaijan Republic.
Early life
Valiyev was born on June 28, 1943, in Hasansu village of Agstafa District, Azerbaijan. In 1971, he graduated from the Azerbaijan State Economic University.
Political career
In May 1993, Valiyev was appointed the Chairman of the State Statistics Committee of Azerbaijan Republic, the post which he has held to this day.
He was married and has two sons.
He died in Baku in 2014 after a long illness.
See also
Cabinet of Azerbaijan
References
1943 births
2014 deaths
People from Aghstafa District
Government ministers of Azerbaijan
Burials at II Alley of Honor |
https://en.wikipedia.org/wiki/Mitchell%20order | In mathematical set theory, the Mitchell order is a well-founded preorder on the set of normal measures on a measurable cardinal κ. It is named for William Mitchell. We say that M ◅ N (this is a strict order) if M is in the ultrapower model defined by N. Intuitively, this means that M is a weaker measure than N (note, for example, that κ will still be measurable in the ultrapower for N, since M is a measure on it).
In fact, the Mitchell order can be defined on the set (or proper class, as the case may be) of extenders for κ; but if it is so defined it may fail to be transitive, or even well-founded, provided κ has sufficiently strong large cardinal properties. Well-foundedness fails specifically for rank-into-rank extenders; but Itay Neeman showed in 2004 that it holds for all weaker types of extender.
The Mitchell rank of a measure is the order type of its predecessors under ◅; since ◅ is well-founded this is always an ordinal. Using the method of coherent sequences, for any rank Mitchell constructed an inner model for a measurable cardinal of rank .
A cardinal that has measures of Mitchell rank α for each α < β is said to be β-measurable.
References
Measures (set theory)
Large cardinals |
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