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https://en.wikipedia.org/wiki/Greeks%20in%20Denmark | The Greeks in Denmark are a small community. , Statistics Denmark recorded 1,180 people of Greek origin living in Denmark, with 954 in Zealand, 177 in Jutland, 48 in Funen, and 1 in Bornholm.
History
Unskilled migrants began coming from Evros and Kastoria to Denmark in the 1960s; they worked primarily in the fur trade. Most of those initial migrants have returned to Greece as this sector became economically depressed. Political refugees fleeing the Greek military junta of 1967–1974 were numerically minor, but evoked a great deal of sympathy from the politically liberal Danish population. The number of Greek international students choosing Denmark as their destination showed an uptick after 1981, when Greece became a member of the European Economic Community.
Gender issues
Many migrants consist of Greek men in international marriages with Danish women. The number of Greek women married to Danish men is smaller. Either way, such relationships have an unusually high rate of divorce. Spouses typically return to Greece if they separate from their Danish partner.
See also
Denmark–Greece relations
Greek diaspora
Immigration to Denmark
References
Notes
Sources
Further reading
Diasporas in Denmark
Denmark
Denmark
Danish people of Greek descent |
https://en.wikipedia.org/wiki/Shota%20Kimura%20%28footballer%29 | is a former Japanese football player.
Kimura previously played for Ventforet Kofu in the J2 League.
Club statistics
References
External links
1988 births
Living people
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Ventforet Kofu players
Matsumoto Yamaga FC players
Kataller Toyama players
Iwate Grulla Morioka players
Men's association football forwards |
https://en.wikipedia.org/wiki/Joseph%20Kamp%C3%A9%20de%20F%C3%A9riet | Marie-Joseph Kampé de Fériet (Paris, 14 May 1893 – Villeneuve d'Ascq, 6 April 1982) was a French mathematician at Université Lille Nord de France from 1919 to 1969. Besides his works on mathematics and fluid mechanics, he directed the Institut de mécanique des fluides de Lille (ONERA Lille) and taught fluid dynamics and information theory at École centrale de Lille from 1930 to 1969.
He devised the Kampé de Fériet functions, which further generalize the generalized hypergeometric functions.
He was an Invited Speaker of the ICM in 1928 at Bologna, in 1932 at Zurich, and in 1954 at Amsterdam.
Works
J. Kampé de Fériet & P.E. Appell Fonctions hypergéometriques et hypersphériques (Paris, Gauthier-Villars, 1926)
J. Kampé de Fériet La fonction hypergéometrique (Paris, Gauthier-Villars, 1937)
References
External links
Biography at ONERA from Joseph Kampé de Fériet
University Biography
Kampé de Fériet 's Hypergeometric Function in MathWorld
1893 births
1982 deaths
Academic staff of the Lille University of Science and Technology
French mathematicians |
https://en.wikipedia.org/wiki/Vertex%20cycle%20cover | In mathematics, a vertex cycle cover (commonly called simply cycle cover) of a graph G is a set of cycles which are subgraphs of G and contain all vertices of G.
If the cycles of the cover have no vertices in common, the cover is called vertex-disjoint or sometimes simply disjoint cycle cover. This is sometimes known as exact vertex cycle cover. In this case the set of the cycles constitutes a spanning subgraph of G. A disjoint cycle cover of an undirected graph (if it exists) can be found in polynomial time by transforming the problem into a problem of finding a perfect matching in a larger graph.
If the cycles of the cover have no edges in common, the cover is called edge-disjoint or simply disjoint cycle cover.
Similar definitions exist for digraphs, in terms of directed cycles. Finding a vertex-disjoint cycle cover of a directed graph can also be performed in polynomial time by a similar reduction to perfect matching. However, adding the condition that each cycle should have length at least 3 makes the problem NP-hard.
Properties and applications
Permanent
The permanent of a (0,1)-matrix is equal to the number of vertex-disjoint cycle covers of a directed graph with this adjacency matrix. This fact is used in a simplified proof showing that computing the permanent is #P-complete.
Minimal disjoint cycle covers
The problems of finding a vertex disjoint and edge disjoint cycle covers with minimal number of cycles are NP-complete. The problems are not in complexity class APX. The variants for digraphs are not in APX either.
See also
Edge cycle cover, a collection of cycles covering all edges of G
References
NP-complete problems
Computational problems in graph theory |
https://en.wikipedia.org/wiki/Edge%20cycle%20cover | In mathematics, an edge cycle cover (sometimes called simply cycle cover) of a graph is a family of cycles which are subgraphs of G and contain all edges of G.
If the cycles of the cover have no vertices in common, the cover is called vertex-disjoint or sometimes simply disjoint cycle cover. In this case, the set of the cycles constitutes a spanning subgraph of G.
If the cycles of the cover have no edges in common, the cover is called edge-disjoint or simply disjoint cycle cover.
Properties and applications
Minimum-Weight Cycle Cover
For a weighted graph, the Minimum-Weight Cycle Cover Problem (MWCCP) is the problem to find a cycle cover with minimal sum of weights of edges in all cycles of the cover.
For bridgeless planar graphs the MWCCP can be solved in polynomial time.
Cycle k-cover
A cycle k-cover of a graph is a family of cycles which cover every edge of G exactly k times. It has been proven that every bridgeless graph has cycle k-cover for any integer even integer k≥4. For k=2, it is the well-known cycle double cover conjecture is an open problem in graph theory. The cycle double cover conjecture states that in every bridgeless graph, there exists a set of cycles that together cover every edge of the graph twice.
See also
Alspach's conjecture
Vertex cycle cover
References
Graph theory objects
Combinatorial optimization |
https://en.wikipedia.org/wiki/Takahiro%20Kuniyoshi | is a Japanese football player who last featured for Kataller Toyama.
Club career statistics
Updated to 23 February 2018.
References
External links
Profile at Kataller Toyama
1988 births
Living people
Association football people from Saitama Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Ventforet Kofu players
Sagan Tosu players
Kataller Toyama players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Ken%20Yorii | is a former Japanese football player.
Club statistics
References
External links
Guardian's Stats Centre
1984 births
Living people
Hannan University alumni
Association football people from Hiroshima Prefecture
Japanese men's footballers
J1 League players
J2 League players
Ventforet Kofu players
Matsumoto Yamaga FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Junya%20Kuno | is a former Japanese football player. He last played for Honda FC.
Club statistics
Updated to 2 February 2018.
References
External links
Profile at Fukushima United FC
1988 births
Living people
Association football people from Shizuoka Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Ventforet Kofu players
Fukushima United FC players
Honda FC players
Men's association football forwards |
https://en.wikipedia.org/wiki/Daisuke%20Kanzaki | is a former Japanese football player who last featured for Giravanz Kitakyushu.
Club statistics
Updated to 2 February 2018.
References
External links
Profile at Giravanz Kitakyushu
1985 births
Living people
University of Teacher Education Fukuoka alumni
Association football people from Ōita Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Ventforet Kofu players
V-Varen Nagasaki players
Giravanz Kitakyushu players
Men's association football midfielders
Sportspeople from Ōita (city) |
https://en.wikipedia.org/wiki/Atsushi%20Izawa | is a Japanese footballer who plays for Tochigi Uva FC.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Tokushima Vortis
1989 births
Living people
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
Ventforet Kofu players
Kataller Toyama players
Tokushima Vortis players
Tochigi City FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Valentine%20Mason%20Johnson | Valentine Mason Johnson (July 17, 1838 – October 19, 1909) was a professor of mathematics and the Superintendent of the West Florida Seminary during the American Civil War. Johnson was born in Spotsylvania County, Virginia and was an 1860 graduate of the Virginia Military Institute. Johnson died in Mountville, Virginia.
Johnson trained students at the West Florida Seminary who fought in the Battle of Natural Bridge and defeated Union forces attempting to capture Tallahassee, Florida. As a result of the battle, Tallahassee was the only Confederate capital east of the Mississippi River that did not fall to Union forces.
References
Presidents of Florida State University
Florida State University faculty
Virginia Military Institute alumni
People of Florida in the American Civil War
1838 births
1909 deaths |
https://en.wikipedia.org/wiki/Takuma%20Tsuda | is a former Japanese football player.
Club statistics
References
External links
1980 births
Living people
Teikyo University alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J1 League players
J2 League players
Ventforet Kofu players
Ehime FC players
Tochigi City FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Variance%20gamma%20process | In the theory of stochastic processes, a part of the mathematical theory of probability, the variance gamma process (VG), also known as Laplace motion, is a Lévy process determined by a random time change. The process has finite moments distinguishing it from many Lévy processes. There is no diffusion component in the VG process and it is thus a pure jump process. The increments are independent and follow a variance-gamma distribution, which is a generalization of the Laplace distribution.
There are several representations of the VG process that relate it to other processes. It can for example be written as a Brownian motion with drift subjected to a random time change which follows a gamma process (equivalently one finds in literature the notation ):
An alternative way of stating this is that the variance gamma process is a Brownian motion subordinated to a gamma subordinator.
Since the VG process is of finite variation it can be written as the difference of two independent gamma processes:
where
Alternatively it can be approximated by a compound Poisson process that leads to a representation with explicitly given (independent) jumps and their locations. This last characterization gives an understanding of the structure of the sample path with location and sizes of jumps.
On the early history of the variance-gamma process see Seneta (2000).
Moments
The mean of a variance gamma process is independent of and and is given by
The variance is given as
The 3rd central moment is
The 4th central moment is
Option pricing
The VG process can be advantageous to use when pricing options since it allows for a wider modeling of skewness and kurtosis than the Brownian motion does. As such the variance gamma model allows to consistently price options with different strikes and maturities using a single set of parameters. Madan and Seneta present a symmetric version of the variance gamma process. Madan, Carr and Chang extend the model to allow for an asymmetric form and present a formula to price European options under the variance gamma process.
Hirsa and Madan show how to price American options under variance gamma. Fiorani presents numerical solutions for European and American barrier options under variance gamma process. He also provides computer code to price vanilla and barrier European and American barrier options under variance gamma process.
Lemmens et al. construct bounds for arithmetic Asian options for several Lévy models including the variance gamma model.
Applications to credit risk modeling
The variance gamma process has been successfully applied in the modeling of credit risk in structural models. The pure jump nature of the process and the possibility to control skewness and kurtosis of the distribution allow the model to price correctly the risk of default of securities having a short maturity, something that is generally not possible with structural models in which the underlying assets follow a Brownian motion. Fiorani, |
https://en.wikipedia.org/wiki/Journal%20for%20Research%20in%20Mathematics%20Education | The Journal for Research in Mathematics Education is a peer-reviewed academic journal covering the field of mathematics education. The journal is published by the National Council of Teachers of Mathematics in five issues a year. The editor-in-chief is Patricio Herbst (University of Michigan).
Abstracting and indexing
The journal is abstracted and indexed in:
Current Contents/Social and Behavioral Sciences
DIALNET
EBSCO databases
Education Resources Information Center
Scopus
Social Sciences Citation Index
According to the Journal Citation Reports, the journal has a 2021 impact factor of 2.278.
See also
List of mathematics education journals
References
External links
English-language journals
Mathematics education journals
Academic journals established in 1970
5 times per year journals |
https://en.wikipedia.org/wiki/Journal%20of%20Mathematics%20Teacher%20Education | Journal of Mathematics Teacher Education is a peer-reviewed scientific journal within the field of mathematics education. The journal was founded by Thomas J. Cooney, and it first appeared in 1998. Published by Springer, the journal normally appears in 6 annual issues. The journal is paginated by volume.
According to the official description of the journal, it "is devoted to research that seeks to improve the education of mathematics teachers and develop teaching methods that better enable mathematics students to learn".
Associate editors
As of January 2013, the following served as associate editors for the journal:
Olive Chapman, Editor-in-Chief, University of Calgary, Canada
Gwendolyn Lloyd, Pennsylvania State University, USA
Joao Pedro da Ponte, University of Lisbon, Portugal
Despina Potari, University of Athens, Greece
Margaret Walshaw, Massay University, New Zealand
See also
List of scientific journals in mathematics education
External links
Journal web site
Online table of contents
Mathematics education
References/Endnotes
Academic journals established in 1998
Mathematics education journals |
https://en.wikipedia.org/wiki/Albin%20Gurklis | Albin J. Gurklis (March 16, 1918 – October 31, 2008) was a member of the Order of the Marians of the Immaculate Conception and a noted mathematics teacher at Marianapolis Preparatory School.
Early life
Albin J. Gurklis was born on March 16, 1918, to Dominick and Barbara Gurklis in a small home in Waterbury, Connecticut. When asked about his youth, Father Gurklis would reply that he "was small and not very good at math". Born into a Lithuanian family, he acquired his native tongue, speaking it along with American English.
College
Young Albin entered the novitiate and was ordained a priest at Marianapolis College, now Marianapolis Preparatory School on August 8, 1943. After being admitted to the order of the Marians of the Immaculate Conception, Father Gurklis completed his fourth year of theology at Marianapolis. He then proceeded to the Marian Hills Seminary in Clarendon Hills, Illinois, to complete his training. Father Gurklis, now with the title M.I.C., was admitted to Marquette University in Wisconsin to continue his studies in the area of mathematics attaining an M.S. in Mathematics in 1950 while completing a thesis paper on the Hexagramma Mysticum.
Marianapolis years
After a brief period of ministry at Marian parishes across the US, Father Gurklis returned to his alma mater Marianapolis to teach his favorite subject: mathematics. Father Gurklis, affectionately known as "Father Gurks" or simply "Gurks" was a familiar sight on Marianapolis campus for the next 58 years. He taught Algebra I, Algebra II, Pre-Calculus, Geometry, and Calculus, and even held the position of department chair for several years. During those 58 years he taught over 2000 students and worked to make Marianapolis an environment which promoted "clear, rational thinking". He also served as Assistant Headmaster at Marianapolis as well as dorm prefect and house secretary. Father Gurklis had the ability to teach with his eyes partially closed in order to "see" the answer to the problem and by his early 70s was able to recite his lesson plans from memory, with the inclusion of blackboard examples. In January 2008, he retired at the age of 90 due to eye complications, bidding a solemn farewell to his educational career. However, Father Gurklis did not leave without a farewell party, which celebrated his accomplishments. During the ceremony, the faculty introduced the Father Gurklis Mathematics Award, intended to honor exemplary success in mathematics at Marianapolis.
Father Gurks was very proud of the achievements of his former students and certainly appreciated their visits after graduation. When asked one time about how he could remember so many former students, he replied “I never forget a student!”. Many Marinapolis graduates who have gone on to science and engineering careers credit Father Gurks with having given them the skills required to succeed in challenging college math courses.
Lithuanian community
Despite his work at Marianapolis, Father Gurklis was able to |
https://en.wikipedia.org/wiki/Continuous%20mapping%20theorem | In probability theory, the continuous mapping theorem states that continuous functions preserve limits even if their arguments are sequences of random variables. A continuous function, in Heine’s definition, is such a function that maps convergent sequences into convergent sequences: if xn → x then g(xn) → g(x). The continuous mapping theorem states that this will also be true if we replace the deterministic sequence {xn} with a sequence of random variables {Xn}, and replace the standard notion of convergence of real numbers “→” with one of the types of convergence of random variables.
This theorem was first proved by Henry Mann and Abraham Wald in 1943, and it is therefore sometimes called the Mann–Wald theorem. Meanwhile, Denis Sargan refers to it as the general transformation theorem.
Statement
Let {Xn}, X be random elements defined on a metric space S. Suppose a function (where S′ is another metric space) has the set of discontinuity points Dg such that . Then
where the superscripts, "d", "p", and "a.s." denote convergence in distribution, convergence in probability, and almost sure convergence respectively.
Proof
This proof has been adopted from
Spaces S and S′ are equipped with certain metrics. For simplicity we will denote both of these metrics using the |x − y| notation, even though the metrics may be arbitrary and not necessarily Euclidean.
Convergence in distribution
We will need a particular statement from the portmanteau theorem: that convergence in distribution is equivalent to
for every bounded continuous functional f.
So it suffices to prove that for every bounded continuous functional f. Note that is itself a bounded continuous functional. And so the claim follows from the statement above.
Convergence in probability
Fix an arbitrary ε > 0. Then for any δ > 0 consider the set Bδ defined as
This is the set of continuity points x of the function g(·) for which it is possible to find, within the δ-neighborhood of x, a point which maps outside the ε-neighborhood of g(x). By definition of continuity, this set shrinks as δ goes to zero, so that limδ → 0Bδ = ∅.
Now suppose that |g(X) − g(Xn)| > ε. This implies that at least one of the following is true: either |X−Xn| ≥ δ, or X ∈ Dg, or X∈Bδ. In terms of probabilities this can be written as
On the right-hand side, the first term converges to zero as n → ∞ for any fixed δ, by the definition of convergence in probability of the sequence {Xn}. The second term converges to zero as δ → 0, since the set Bδ shrinks to an empty set. And the last term is identically equal to zero by assumption of the theorem. Therefore, the conclusion is that
which means that g(Xn) converges to g(X) in probability.
Almost sure convergence
By definition of the continuity of the function g(·),
at each point X(ω) where g(·) is continuous. Therefore,
because the intersection of two almost sure events is almost sure.
By definition, we conclude that g(Xn) converges to g(X) almost surely.
|
https://en.wikipedia.org/wiki/Kota%20Fukatsu | is a Japanese football player who plays for FC Machida Zelvia.
Club statistics
1Includes J2/J3 Playoffs.
References
External links
Profile at FC Machida Zelvia
1984 births
Living people
People from Inzai
Association football people from Chiba Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Nagoya Grampus players
Mito HollyHock players
Kashiwa Reysol players
FC Gifu players
FC Machida Zelvia players
Tokyo Verdy players
Men's association football defenders |
https://en.wikipedia.org/wiki/Kan%20Kikuchi%20%28footballer%29 | is a former Japanese football player.
Club statistics
References
External links
1977 births
Living people
Asia University (Japan) alumni
Association football people from Tokyo Metropolis
Japanese men's footballers
Japanese expatriate men's footballers
J2 League players
Japan Football League players
FC Gifu players
Expatriate men's footballers in Indonesia
Japanese expatriate sportspeople in Indonesia
Liga 1 (Indonesia) players
Bontang F.C. players
Men's association football defenders
People from Nishitōkyō, Tokyo |
https://en.wikipedia.org/wiki/Ryuji%20Kitamura | is a Japanese former football player.
Club statistics
References
External links
1981 births
Living people
Aoyama Gakuin University alumni
People from Zushi, Kanagawa
Association football people from Kanagawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Nagoya Grampus players
FC Gifu players
Matsumoto Yamaga FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Collapse%20%28topology%29 | In topology, a branch of mathematics, a collapse reduces a simplicial complex (or more generally, a CW complex) to a homotopy-equivalent subcomplex. Collapses, like CW complexes themselves, were invented by J. H. C. Whitehead. Collapses find applications in computational homology.
Definition
Let be an abstract simplicial complex.
Suppose that are two simplices of such that the following two conditions are satisfied:
in particular
is a maximal face of and no other maximal face of contains
then is called a free face.
A simplicial collapse of is the removal of all simplices such that where is a free face. If additionally we have then this is called an elementary collapse.
A simplicial complex that has a sequence of collapses leading to a point is called collapsible. Every collapsible complex is contractible, but the converse is not true.
This definition can be extended to CW-complexes and is the basis for the concept of simple-homotopy equivalence.
Examples
Complexes that do not have a free face cannot be collapsible. Two such interesting examples are R. H. Bing's house with two rooms and Christopher Zeeman's dunce hat; they are contractible (homotopy equivalent to a point), but not collapsible.
Any n-dimensional PL manifold that is collapsible is in fact piecewise-linearly isomorphic to an n-ball.
See also
References
Algebraic topology
Properties of topological spaces |
https://en.wikipedia.org/wiki/Kazumasa%20Takagi | is a Japanese football player who plays for Kamatamare Sanuki.
Club statistics
Updated to 23 February 2020.
References
External links
Profile at Kamatamare Sanuki
1984 births
Living people
Association football people from Kagawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Sanfrecce Hiroshima players
Montedio Yamagata players
FC Gifu players
Tochigi SC players
Kamatamare Sanuki players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Shogo%20Shimada%20%28footballer%29 | is a former Japanese football player.
Club statistics
References
External links
1979 births
Living people
Osaka University of Commerce alumni
Association football people from Hyōgo Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Sagawa Shiga FC players
FC Gifu players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Masamichi%20Yamada | is a former Japanese football player.
Club statistics
References
External links
1981 births
Living people
Waseda University alumni
Japanese men's footballers
J2 League players
Japan Football League players
Kyoto Sanga FC players
Arte Takasaki players
FC Gifu players
Men's association football midfielders
Association football people from Kyoto |
https://en.wikipedia.org/wiki/Masato%20Katayama | is a former Japanese football player.
Club statistics
References
External links
1984 births
Living people
Kindai University alumni
Association football people from Osaka Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Matsumoto Yamaga FC players
FC Gifu players
Mito HollyHock players
Men's association football forwards |
https://en.wikipedia.org/wiki/Hiromi%20Kojima%20%28footballer%2C%20born%201989%29 | is a former Japanese football player.
Club statistics
References
External links
1989 births
Living people
Association football people from Gifu Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
FC Gifu players
FC Kariya players
Men's association football forwards |
https://en.wikipedia.org/wiki/Kazunori%20Kan | is a Japanese retired football player.
Club career
Tochigi SC
After nine seasons playing for Tochigi SC, Kan retired in December 2020.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Tochigi SC
1985 births
Living people
People from Imabari, Ehime
Kochi University alumni
Association football people from Ehime Prefecture
Japanese men's footballers
J2 League players
J3 League players
FC Gifu players
Tochigi SC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Satoshi%20Sato | is a former Japanese football player. He played for TDK and FC Gifu before retirement.
Club statistics
References
External links
1979 births
Living people
Association football people from Yamagata Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Blaublitz Akita players
FC Gifu players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Thomas%20Eder | Thomas Günther Eder (born 25 December 1980) is an Austrian football player currently playing for SV Grödig.
National team statistics
External links
1980 births
Living people
Austrian men's footballers
Austria men's international footballers
FC Red Bull Salzburg players
SV Ried players
FC Wacker Innsbruck (2002) players
Men's association football midfielders
Footballers from Salzburg |
https://en.wikipedia.org/wiki/Masatoshi%20Mizutani | is a former Japanese football player.
Club statistics
References
External links
1987 births
Living people
Association football people from Mie Prefecture
Japanese men's footballers
J2 League players
FC Gifu players
FC Kariya players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Ryoma%20Hashiuchi | is a former Japanese football player. His brother is Yuya Hashiuchi.
Club statistics
References
External links
1989 births
Living people
Association football people from Shiga Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
FC Gifu players
Reilac Shiga FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Y%C5%8Dsuke%20Mori | is a former Japanese football player.
Mori made one substitute's appearance in the 2009 Emperor's Cup for FC Gifu.
Club statistics
References
External links
1985 births
Living people
Nippon Bunri University alumni
Association football people from Kagoshima Prefecture
Japanese men's footballers
J2 League players
FC Gifu players
Men's association football defenders |
https://en.wikipedia.org/wiki/Nut%20Mountain | Nut Mountain is an unincorporated community in the Rural Municipality of Sasman No. 336, Saskatchewan, Canada. Listed as a designated place by Statistics Canada, the community had a population of 10 in the Canada 2016 Census.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Nut Mountain had a population of 5 living in 3 of its 4 total private dwellings, a change of from its 2016 population of 10. With a land area of , it had a population density of in 2021.
Nut Mountain
Nut Mountain is a large hill () in the east-central region of Saskatchewan. The mountain and several other nearby landmarks are named after the wild hazel nuts that grow abound in the countryside. The Assiniboine River has its headwaters near the Nut Hills. Ron Petrie, writer for the Regina Leader-Post, was raised near Nut Mountain.
See also
List of communities in Saskatchewan
References
Sasman No. 336, Saskatchewan
Designated places in Saskatchewan
Unincorporated communities in Saskatchewan
Hills of Saskatchewan
Division No. 10, Saskatchewan |
https://en.wikipedia.org/wiki/Medial%20rhombic%20triacontahedron | In geometry, the medial rhombic triacontahedron (or midly rhombic triacontahedron) is a nonconvex isohedral polyhedron. It is a stellation of the rhombic triacontahedron, and can also be called small stellated triacontahedron. Its dual is the dodecadodecahedron.
Its 24 vertices are all on the 12 axes with 5-fold symmetry (i.e. each corresponds to one of the 12 vertices of the icosahedron). This means that on each axis there is an inner and an outer vertex. The ratio of outer to inner vertex radius is , the golden ratio.
It has 30 intersecting rhombic faces, which correspond to the faces of the convex rhombic triacontahedron. The diagonals in the rhombs of the convex solid have a ratio of 1 to . The medial solid can be generated from the convex one by stretching the shorter diagonal from length 1 to . So the ratio of rhomb diagonals in the medial solid is 1 to .
This solid is to the compound of small stellated dodecahedron and great dodecahedron what the convex one is to the compound of dodecahedron and icosahedron:
The crossing edges in the dual compound are the diagonals of the rhombs.
The faces have two angles of , and two of . Its dihedral angles equal . Part of each rhomb lies inside the solid, hence is invisible in solid models.
Related hyperbolic tiling
It is topologically equivalent to a quotient space of the hyperbolic order-5 square tiling, by distorting the rhombi into squares. As such, it is topologically a regular polyhedron of index two:
Note that the order-5 square tiling is dual to the order-4 pentagonal tiling, and a quotient space of the order-4 pentagonal tiling is topologically equivalent to the dual of the medial rhombic triacontahedron, the dodecadodecahedron.
See also
Great rhombic triacontahedron
Great triambic icosahedron
References
External links
David I. McCooey: animation and measurements
Uniform polyhedra and duals
Dual uniform polyhedra |
https://en.wikipedia.org/wiki/Great%20rhombic%20triacontahedron | In geometry, the great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron. It is the dual of the great icosidodecahedron (U54). Like the convex rhombic triacontahedron it has 30 rhombic faces, 60 edges and 32 vertices (also 20 on 3-fold and 12 on 5-fold axes).
It can be constructed from the convex solid by expanding the faces by factor of , where is the golden ratio.
This solid is to the compound of great icosahedron and great stellated dodecahedron what the convex one is to the compound of dodecahedron and icosahedron:
The crossing edges in the dual compound are the diagonals of the rhombs.
What resembles an "excavated" rhombic triacontahedron (compare excavated dodecahedron and excavated icosahedron) can be seen within the middle of this compound. The rest of the polyhedron strikingly resembles a rhombic hexecontahedron.
The rhombs have two angles of , and two of . Its dihedral angles equal . Part of each rhomb lies inside the solid, hence is invisible in solid models. The ratio between the lengths of the long and short diagonal of the rhombs equals the golden ratio .
References
External links
David I. McCooey: animation and measurements
Uniform polyhedra and duals
Dual uniform polyhedra |
https://en.wikipedia.org/wiki/Sidon%20sequence | In number theory, a Sidon sequence is a sequence of natural numbers in which all pairwise sums (for ) are different. Sidon sequences are also called Sidon sets; they are named after the Hungarian mathematician Simon Sidon, who introduced the concept in his investigations of Fourier series.
The main problem in the study of Sidon sequences, posed by Sidon, is to find the maximum number of elements that a Sidon sequence can contain, up to some bound . Despite a large body of research, the question has remained unsolved.
Early results
Paul Erdős and Pál Turán proved that, for every , the number of elements smaller than in a Sidon sequence is at most . Several years earlier, James Singer had constructed Sidon sequences with terms less than x. The bound was improved to in 1969 and to in 2023.
In 1994 Erdős offered 500 dollars for a proof or disproof of the bound .
Infinite Sidon sequences
Erdős also showed that, for any particular infinite Sidon sequence with denoting the number of its elements up to ,
That is, infinite Sidon sequences are thinner than the densest finite Sidon sequences.
For the other direction, Chowla and Mian observed that the greedy algorithm gives an infinite Sidon sequence with for every . Ajtai, Komlós, and Szemerédi improved this with a construction of a Sidon sequence with
The best lower bound to date was given by Imre Z. Ruzsa, who proved that a Sidon sequence with
exists. Erdős conjectured that an infinite Sidon set exists for which holds. He and Rényi showed the existence of a sequence with the conjectural density but satisfying only the weaker property that there is a constant such that for every natural number there are at most solutions of the equation . (To be a Sidon sequence would require that .)
Erdős further conjectured that there exists a nonconstant integer-coefficient polynomial whose values at the natural numbers form a Sidon sequence. Specifically, he asked if the set of fifth powers is a Sidon set. Ruzsa came close to this by showing that there is a real number with such that the range of the function is a Sidon sequence, where denotes the integer part. As is irrational, this function is not a polynomial. The statement that the set of fifth powers is a Sidon set is a special case of the later conjecture of Lander, Parkin and Selfridge.
Sidon sequences which are asymptotic bases
The existence of Sidon sequences that form an asymptotic basis of order (meaning that every sufficiently large natural number can be written as the sum of numbers from the sequence) has been proved for in 2010, in 2014, (the sum of four terms with one smaller than , for arbitrarily small positive ) in 2015 and in 2023 as a preprint, this later one was posed as a problem in a paper of Erdős, Sárközy and Sós in 1994.
Relationship to Golomb rulers
All finite Sidon sets are Golomb rulers, and vice versa.
To see this, suppose for a contradiction that is a Sidon set and not a Golomb ruler. Since |
https://en.wikipedia.org/wiki/H.%20J.%20Ryser | Herbert John Ryser (July 28, 1923 – July 12, 1985) was a professor of mathematics, widely regarded as one of the major figures in combinatorics in the 20th century. He is the namesake of the Bruck–Ryser–Chowla theorem, Ryser's formula for the computation of the permanent of a matrix, and Ryser's conjecture.
Early life
Ryser was born to the family of Fred G. and Edna (Huels) Ryser. He received the B.A. (1945), M.A. (1947), and Ph.D. (1948) from the University of Wisconsin. His doctoral thesis "Rational Vector Spaces" was supervised by Cornelius Joseph Everett, Jr. and Cyrus C. MacDuffee. (Ryser was Everett's only doctoral student.)
Career
After his Ph.D., Ryser spent a year at Princeton's Institute for Advanced Study, then joined the faculty of Ohio State University. In 1962 he took a professorship at Syracuse University, and in 1967 moved to Caltech. His doctoral students include Richard A. Brualdi, Clement W. H. Lam, and Marion Tinsley.
Ryser contributed to the theory of combinatorial designs, finite set systems, the permanent, combinatorial functions, and to many other topics in combinatorics. He served as editor of the journals Journal of Combinatorial Theory, Linear and Multilinear Algebra, and Journal of Algebra. Ryser's estate funded an endowment creating undergraduate mathematics scholarships at Caltech known as the H. J. Ryser Scholarships.
The Journal of Combinatorial Theory, Series A denoted two issues after Ryser's passing as the "Herbert J. Ryser Memorial Issue", parts 1 and 2.
Books
Combinatorial Mathematics (1963), #14 of the Carus Mathematical Monographs, published by the Mathematical Association of America. . Republished and translated into several languages.
Selected papers
References
1923 births
1985 deaths
20th-century American mathematicians
University of Wisconsin–Madison alumni
California Institute of Technology faculty
Ohio State University faculty
Combinatorialists |
https://en.wikipedia.org/wiki/Golden%20rhombus | In geometry, a golden rhombus is a rhombus whose diagonals are in the golden ratio:
Equivalently, it is the Varignon parallelogram formed from the edge midpoints of a golden rectangle.
Rhombi with this shape form the faces of several notable polyhedra.
The golden rhombus should be distinguished from the two rhombi of the Penrose tiling, which are both related in other ways to the golden ratio but have different shapes than the golden rhombus.
Angles
(See the characterizations and the basic properties of the general rhombus for angle properties.)
The internal supplementary angles of the golden rhombus are:
Acute angle: ;
by using the arctangent addition formula (see inverse trigonometric functions):
Obtuse angle:
which is also the dihedral angle of the dodecahedron.
Note: an "anecdotal" equality:
Edge and diagonals
By using the parallelogram law (see the basic properties of the general rhombus):
The edge length of the golden rhombus in terms of the diagonal length is:
Hence:
The diagonal lengths of the golden rhombus in terms of the edge length are:
Area
By using the area formula of the general rhombus in terms of its diagonal lengths and :
The area of the golden rhombus in terms of its diagonal length is:
By using the area formula of the general rhombus in terms of its edge length :
The area of the golden rhombus in terms of its edge length is:
Note: , hence:
As the faces of polyhedra
Several notable polyhedra have golden rhombi as their faces.
They include the two golden rhombohedra (with six faces each), the Bilinski dodecahedron (with 12 faces),
the rhombic icosahedron (with 20 faces),
the rhombic triacontahedron (with 30 faces), and
the nonconvex rhombic hexecontahedron (with 60 faces). The first five of these are the only convex polyhedra with golden rhomb faces, but there exist infinitely many nonconvex polyhedra having this shape for all of their faces.
See also
Golden triangle
References
Types of quadrilaterals
Golden ratio |
https://en.wikipedia.org/wiki/Great%20hexacronic%20icositetrahedron | In geometry, the great hexacronic icositetrahedron is the dual of the great cubicuboctahedron. Its faces are kites. Part of each kite lies inside the solid, hence is invisible in solid models.
Proportions
The kites have two angles of , one of and one of . The dihedral angle equals . The ratio between the lengths of the long and short edges is .
References
External links
Dual uniform polyhedra |
https://en.wikipedia.org/wiki/Noncentral%20distribution | Noncentral distributions are families of probability distributions that are related to other "central" families of distributions by means of a noncentrality parameter. Whereas the central distribution describes how a test statistic is distributed when the difference tested is null, noncentral distributions describe the distribution of a test statistic when the null is false (so the alternative hypothesis is true). This leads to their use in calculating statistical power.
If the noncentrality parameter of a distribution is zero, the distribution is identical to a distribution in the central family. For example, the Student's t-distribution is the central family of distributions for the noncentral t-distribution family.
Noncentrality parameters are used in the following distributions:
Noncentral t-distribution
Noncentral chi-squared distribution
Noncentral chi-distribution
Noncentral F-distribution
Noncentral beta distribution
In general, noncentrality parameters occur in distributions that are transformations of a normal distribution. The "central" versions are derived from normal distributions that have a mean of zero; the noncentral versions generalize to arbitrary means. For example, the standard (central) chi-squared distribution is the distribution of a sum of squared independent standard normal distributions, i.e., normal distributions with mean 0, variance 1. The noncentral chi-squared distribution generalizes this to normal distributions with arbitrary mean and variance.
Each of these distributions has a single noncentrality parameter. However, there are extended versions of these distributions which have two noncentrality parameters: the doubly noncentral beta distribution, the doubly noncentral F distribution and the doubly noncentral t distribution. These types of distributions occur for distributions that are defined as the quotient of two independent distributions. When both source distributions are central (either with a zero mean or a zero noncentrality parameter, depending on the type of distribution), the result is a central distribution. When one is noncentral, a (singly) noncentral distribution results, while if both are noncentral, the result is a doubly noncentral distribution. As an example, a t-distribution is defined (ignoring constant values) as the quotient of a normal distribution and the square root of an independent chi-squared distribution. Extending this definition to encompass a normal distribution with arbitrary mean produces a noncentral t-distribution, while further extending it to allow a noncentral chi-squared distribution in the denominator while produces a doubly noncentral t-distribution.
There are some "noncentral distributions" that are not usually formulated in terms of a "noncentrality parameter": see noncentral hypergeometric distributions, for example.
The noncentrality parameter of the t-distribution may be negative or positive while the noncentral parameters of the other three dis |
https://en.wikipedia.org/wiki/Great%20deltoidal%20icositetrahedron | In geometry, the great deltoidal icositetrahedron (or great sagittal disdodecahedron) is the dual of the nonconvex great rhombicuboctahedron. Its faces are darts. Part of each dart lies inside the solid, hence is invisible in solid models.
One of its halves can be rotated by 45 degrees to form the pseudo great deltoidal icositetrahedron, analogous to the pseudo-deltoidal icositetrahedron.
Proportions
Faces have three angles of and one of . Its dihedral angles equal . The ratio between the lengths of the long edges and the short ones equals .
References
External links
Dual uniform polyhedra |
https://en.wikipedia.org/wiki/Raoul%20Bricard | Raoul Bricard (23 March 1870 – 26 November 1943) was a French engineer and a mathematician. He is best known for his work in geometry, especially descriptive geometry and scissors congruence, and kinematics, especially mechanical linkages.
Biography
Bricard taught geometry at Ecole Centrale des Arts et Manufactures. In 1908 he became a professor of applied geometry at the National Conservatory of Arts and Crafts in Paris. In 1932 he received the Poncelet Prize in mathematics from the Paris Academy of Sciences for his work in geometry.
Work
In 1896 Bricard published a paper on Hilbert's third problem, even before the problem was stated by Hilbert. In it he proved that mirror symmetric polytopes are scissors congruent, and proved a weak version of Dehn's criterion.
In 1897 Bricard published an important investigation on flexible polyhedra. In it he classified all flexible octahedra, now known as Bricard octahedra. This work was the subject of Henri Lebesgue's lectures in 1938. Later Bricard discovered notable 6-bar linkages.
Bricard also gave one of the first geometric proofs of Morley's trisector theorem in 1922.
Books
Bricard authored six books, including a mathematics survey in Esperanto. He is listed in Encyclopedia of Esperanto.
Matematika terminaro kaj krestomatio (in Esperanto), Hachette, Paris, 1905
Géométrie descriptive, O. Doin et fils, 1911
Cinématique et mécanismes, A. Colin, 1921
Petit traité de perspective, Vuibert, 1924
Leçons de cinématique, Gauthier-Villars et cie., 1926
Le calcul vectoriel, A. Colin, 1929
Notes
References
Laurent R., Raoul Bricard, Professeur de Géométrie appliquée aux arts, in Fontanon C., Grelon A. (éds.), Les professeurs du Conservatoire national des arts et métiers, dictionnaire biographique, 1794-1955, INRP-CNAM, Paris 1994, vol. 1, pp. 286–291.
External links
19th-century French mathematicians
20th-century French mathematicians
20th-century French engineers
Geometers
1870 births
1943 deaths |
https://en.wikipedia.org/wiki/Ryota%20Miki | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Association football people from Osaka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Gamba Osaka players
Ehime FC players
Fagiano Okayama players
Men's association football forwards |
https://en.wikipedia.org/wiki/Lee%20Sang-yong | Lee Sang-Yong (born 9 January 1986) is a South Korean football player who is currently a free agent.
He has played for Chunnam Dragons in the K-League.
Club career statistics
References
1986 births
Living people
Men's association football defenders
South Korean men's footballers
Jeonnam Dragons players
K League 1 players
Footballers from Seoul |
https://en.wikipedia.org/wiki/Kim%20Jae-hyun%20%28footballer%29 | Kim Jae-hyeon (; born March 9, 1987) is a South Korean football player who plays for Gyeongju KHNP as a central defender. He changed his name from Kim Eung-jin () in 2015.
Club career statistics
External links
1987 births
Living people
Footballers from South Jeolla Province
Men's association football defenders
South Korean men's footballers
South Korea men's under-20 international footballers
Jeonnam Dragons players
Busan IPark players
Seoul E-Land FC players
K League 1 players
K League 2 players
Korea National League players |
https://en.wikipedia.org/wiki/Choi%20Kun-sik | Choi Kun-Sik (Hangul: 최근식; born 25 April 1981 in Gyeonggi-do) is a South Korean footballer. Position is forward.
Club statistics
External links
1981 births
Living people
Men's association football defenders
South Korean men's footballers
South Korean expatriate men's footballers
Daejeon Hana Citizen players
Changwon City FC players
Tochigi SC players
Roasso Kumamoto players
J2 League players
Korea National League players
K League 1 players
Expatriate men's footballers in Japan
South Korean expatriate sportspeople in Japan
Konkuk University alumni
Expatriate men's footballers in Thailand
Footballers from Gyeonggi Province |
https://en.wikipedia.org/wiki/Samuel%20Beatty%20%28mathematician%29 | Samuel Beatty (1881–1970) was dean of the Faculty of Mathematics at the University of Toronto, taking the position in 1934.
Early life
Beatty was born in 1881. In 1915, he graduated from the University of Toronto with a PhD and a dissertation entitled Extensions of Results Concerning the Derivatives of an Algebraic Function of a Complex Variable, with the help of his adviser, John Charles Fields. He was the first person to receive a PhD in mathematics from a Canadian university. In 1925 he was elected a Fellow of the Royal Society of Canada. In 1926, he published a problem in the American Mathematical Monthly, which formed the genesis for the Beatty sequence.
University of Toronto
Beatty was dean of the Faculty of Mathematics at the University of Toronto, taking the position in 1934. The famous mathematician Richard Brauer was recruited by Beatty in 1935. He invited Harold Scott MacDonald Coxeter to the University of Toronto with a position as an assistant professor, which Coxeter took; he remained in Toronto for the rest of his life. In June 1939, he was one of the founding members of the Committee of Teaching Staff. Beatty was appointed the 21st Chancellor of the University of Toronto in 1953, holding the position until 1959. He was associated with the university from 1911 to 1952, and a scholarship was established in his honor. He died in 1970.
In an era when extremely few women received PhDs in mathematics, Beatty supervised the mathematical PhDs of Mary Fisher and Muriel Kennett Wales.
Nobel Prize in Chemistry winner Walter Kohn, a student at the university while Beatty was a dean, expressed his appreciation in 1998 to the dean when accepting the prize for his development of the density functional theory. In 1942, when Kohn could not access the university's chemistry buildings during World War II because of his German nationality, Beatty had helped him to enroll in the Mathematics Department at the University.
Canadian Mathematical Society
Beatty was one of the founders of the Canadian Mathematical Congress and was elected to serve as the first president of the congress in 1945. Under his presidency, the Canadian Mathematical Congress began to promote mathematical development in Canada. Beatty served as the president of the Canadian Mathematical Congress until 1978 at which point the congress was renamed the Canadian Mathematical Society to avoid further confusion with the quadrennial mathematical congresses.
References
Overview of the Canadian Mathematical Society http://cms.math.ca/Docs/cms-eng.html
External links
Archival papers held by the University of Toronto Archives and Record Management Services.
1881 births
1970 deaths
Chancellors of the University of Toronto
Canadian university and college faculty deans
University of Toronto alumni
Canadian mathematicians
Fellows of the Royal Society of Canada
Presidents of the Canadian Mathematical Society |
https://en.wikipedia.org/wiki/Mean%20integrated%20squared%20error | In statistics, the mean integrated squared error (MISE) is used in density estimation. The MISE of an estimate of an unknown probability density is given by
where ƒ is the unknown density, ƒn is its estimate based on a sample of n independent and identically distributed random variables.
Here, E denotes the expected value with respect to that sample.
The MISE is also known as L2 risk function.
See also
Minimum distance estimation
Mean squared error
References
Estimation of densities
Nonparametric statistics
Point estimation performance |
https://en.wikipedia.org/wiki/Algebraic%20analysis | Algebraic analysis is an area of mathematics that deals with systems of linear partial differential equations by using sheaf theory and complex analysis to study properties and generalizations of functions such as hyperfunctions and microfunctions. Semantically, it is the application of algebraic operations on analytic quantities. As a research programme, it was started by the Japanese mathematician Mikio Sato in 1959. This can be seen as an algebraic geometrization of analysis. It derives its meaning from the fact that the differential operator is right-invertible in several function spaces.
It helps in the simplification of the proofs due to an algebraic description of the problem considered.
Microfunction
Let M be a real-analytic manifold of dimension n, and let X be its complexification. The sheaf of microlocal functions on M is given as
where
denotes the microlocalization functor,
is the relative orientation sheaf.
A microfunction can be used to define a Sato's hyperfunction. By definition, the sheaf of Sato's hyperfunctions on M is the restriction of the sheaf of microfunctions to M, in parallel to the fact the sheaf of real-analytic functions on M is the restriction of the sheaf of holomorphic functions on X to M.
See also
Hyperfunction
D-module
Microlocal analysis
Generalized function
Edge-of-the-wedge theorem
FBI transform
Localization of a ring
Vanishing cycle
Gauss–Manin connection
Differential algebra
Perverse sheaf
Mikio Sato
Masaki Kashiwara
Lars Hörmander
Citations
Sources
Further reading
Masaki Kashiwara and Algebraic Analysis
Foundations of algebraic analysis book review
Complex analysis
Fourier analysis
Generalized functions
Partial differential equations
Sheaf theory |
https://en.wikipedia.org/wiki/Stone%20functor | In mathematics, the Stone functor is a functor S: Topop → Bool, where Top is the category of topological spaces and Bool is the category of Boolean algebras and Boolean homomorphisms. It assigns to each topological space X the Boolean algebra S(X) of its clopen subsets, and to each morphism fop: X → Y in Topop (i.e., a continuous map f: Y → X) the homomorphism S(f): S(X) → S(Y) given by S(f)(Z) = f−1[Z].
See also
Stone's representation theorem for Boolean algebras
Pointless topology
References
Abstract and Concrete Categories. The Joy of Cats . Jiri Adámek, Horst Herrlich, George E. Strecker.
Peter T. Johnstone, Stone Spaces. (1982) Cambridge university Press
Functors
Boolean algebra
General topology |
https://en.wikipedia.org/wiki/Jakob%20Wilhelm%20Roux | Jakob Wilhelm Roux (13 April 1771, Jena - 22 August 1830, Heidelberg) was a German painter and draughtsman.
Roux was born to a Huguenot family. He studied mathematics for a time at the University of Jena. He later enrolled in the university of Christian Immanuel Oehme where his interests and classes turned to the arts. It was while studying there that he met the surgeon Justus Christian Loder, with whom he collaborated. Roux did a number of anatomical illustrations for Loder. Roux later primarily painted portraits.
He was first married in 1801 to Pauline Johanna Heyligenstädt, and they had two daughters and a son together. Two years after she died in 1823, Roux remarried to Charlotte Mariana Wippermann. They had two sons together. He died in Heidelberg in 1830.
References
External links
Karl Roux: Roux, Jacob. In: Allgemeine Deutsche Biographie (ADB). Band 29. Duncker & Humblot, Leipzig 1889, S. 409 f.
1771 births
1830 deaths
18th-century German painters
18th-century German male artists
German male painters
19th-century German painters
19th-century German male artists
German draughtsmen |
https://en.wikipedia.org/wiki/Delta-functor | In homological algebra, a δ-functor between two abelian categories A and B is a collection of functors from A to B together with a collection of morphisms that satisfy properties generalising those of derived functors. A universal δ-functor is a δ-functor satisfying a specific universal property related to extending morphisms beyond "degree 0". These notions were introduced by Alexander Grothendieck in his "Tohoku paper" to provide an appropriate setting for derived functors. In particular, derived functors are universal δ-functors.
The terms homological δ-functor and cohomological δ-functor are sometimes used to distinguish between the case where the morphisms "go down" (homological) and the case where they "go up" (cohomological). In particular, one of these modifiers is always implicit, although often left unstated.
Definition
Given two abelian categories A and B a covariant cohomological δ-functor between A and B is a family {Tn} of covariant additive functors Tn : A → B indexed by the non-negative integers, and for each short exact sequence
a family of morphisms
indexed by the non-negative integers satisfying the following two properties:
The second property expresses the functoriality of a δ-functor. The modifier "cohomological" indicates that the δn raise the index on the T. A covariant homological δ-functor between A and B is similarly defined (and generally uses subscripts), but with δn a morphism Tn(M '') → Tn-1(M). The notions of contravariant cohomological δ-functor between A and B and contravariant homological δ-functor between A and B can also be defined by "reversing the arrows" accordingly.
Morphisms of δ-functors
A morphism of δ-functors is a family of natural transformations that, for each short exact sequence, commute with the morphisms δ. For example, in the case of two covariant cohomological δ-functors denoted S and T, a morphism from S to T is a family Fn : Sn → Tn of natural transformations such that for every short exact sequence
the following diagram commutes:
Universal δ-functor
A universal δ-functor''' is characterized by the (universal) property that giving a morphism from it to any other δ-functor (between A and B) is equivalent to giving just F0. If S denotes a covariant cohomological δ-functor between A and B, then S is universal if given any other (covariant cohomological) δ-functor T (between A and B), and given any natural transformation
there is a unique sequence Fn indexed by the positive integers such that the family { F''n }n ≥ 0 is a morphism of δ-functors.
See also
Effaceable functor
Notes
References
Section XX.7 of
Section 2.1 of
Homological algebra |
https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Nagy%20theorem | The Erdős–Nagy theorem is a result in discrete geometry stating that a non-convex simple polygon can be made into a convex polygon by a finite sequence of flips. The flips are defined by taking a convex hull of a polygon and reflecting a pocket with respect to the boundary edge. The theorem is named after mathematicians Paul Erdős and Béla Szőkefalvi-Nagy.
Statement
A pocket of a non-convex simple polygon is a simple polygon bounded by a consecutive sequence of edges of the polygon together with a single edge of its convex hull that is not an edge of the polygon itself. Every convex hull edge that is not a polygon edge defines a pocket in this way. A flip of a pocket is obtained by reflecting the polygon edges that bound the pocket, across a reflection line containing the convex hull edge. Because the reflected pocket lies entirely within the reflected image of the convex hull, on the other side of this line, this operation cannot introduce any crossings, so the result of a flip is another simple polygon, with larger area.
In some cases, a single flip will cause a non-convex simple polygon to become convex. Once this happens, no more flips are possible.
The Erdős–Nagy theorem states that it is always possible to find a sequence of flips that produces a convex polygon in this way.
More strongly, for every simple polygon, every sequence of flips will eventually produce a convex polygon, in a finite number of steps.
There exist quadrilaterals that require an arbitrarily large (but finite) number of flips to be made convex. Therefore, it is not possible to bound the number of steps as a function of the number of sides of the polygon.
History
Paul Erdős conjectured the result in 1935 as a problem in the American Mathematical Monthly. In the version posed by Erdős, all pockets are to be flipped simultaneously; however, this may cause the polygon to become non-simple, as two pockets may flip on top of each other. In 1939, Szőkefalvi-Nagy pointed out this problem with Erdős's formulation, reformulated the problem in its now-standard form, and published a proof. Szőkefalvi-Nagy's proof had an incorrect case, which was pointed out in a 1995 survey of the problem by Branko Grünbaum; however, the proofs by Grünbaum and Godfried Toussaint are similarly incomplete. Additional proofs (some but not all correct) were provided in 1957 by two independent Russian mathematicians, Reshetnyak and Yusupov, in 1959, by Bing and Kazarinoff, and in 1993 by Wegner.
Demaine, Gassend, O'Rourke, and Toussaint survey this history and provide a corrected proof.
Variations
An alternative method of making non-convex polygons convex that has also been studied is to perform flipturns, 180-degree rotations of a pocket around the midpoint of its convex hull edge.
References
Branko Grünbaum, How to convexify a polygon, Geombinatorics, 5 (1995), 24–30.
Godfried Toussaint, The Erdős–Nagy Theorem and its Ramifications, Proc. 11th Canadian Conference on Computational Geometry ( |
https://en.wikipedia.org/wiki/Bogolyubov%20Prize | The Bogoliubov Prize is an international award offered by the Joint Institute for Nuclear Research (JINR) to scientists with outstanding contribution to theoretical physics and applied mathematics. The award is issued in the memory of the theoretical physicist and mathematician Nikolay Bogoliubov.
Laureates
1996 Anatoly Logunov (Russia) — for a generous contribution to quantum field theory.
1996 Chen Ning Yang (United States) — for a generous contribution to the elementary particle physics.
1999 Viktor Baryahtar (Ukraine) and Ilya Prigogine (Belgium) — for their significant achievements in theoretical physics.
2001–2002 Albert Tavchelidze (Georgia and Russia) and Yoichiro Nambu (USA) — for their contribution to the theory of color charge of quarks.
2006 Vladimir Kadyshevsky (JINR and Moscow State University, Russia).
2006–2008 Borys Paton and Dmitry Shirkov (JINR)
2014 Valery Rubakov and Marc Henneaux
2019 Dmitry Igorevich Kazakov and Đàm Thanh Sơn
See also
List of physics awards
References
JINR Awards
Physics awards
Physics education in Russia
Russian science and technology awards |
https://en.wikipedia.org/wiki/Land%20use%20statistics%20by%20country | This article includes the table with land use statistics by country. Countries are ranked by their total cultivated land area, which is the sum of the total arable land area and total area of permanent crops.
Arable land is defined as being cultivated for crops like wheat, maize, and rice, all of which are replanted after each harvest. Permanent cropland is defined as being cultivated for crops like citrus, coffee, and rubber, which are not replanted after each harvest; this also includes land under flowering shrubs, fruit trees, nut trees, and vines, but excludes land under trees grown for wood or timber. Other lands include any lands not arable nor under permanent crops; this includes permanent meadows and pastures, forests and woodlands, built-on areas, roads, barren land, and so on.
Percentage figures for arable land, permanent crops land and other lands are all taken from the CIA World Factbook as well as total land area figures (Note: the total area of a country is defined as the sum of total land area and total water area together.) All other figures, including total cultivated land area, are calculated on the basis of this mentioned dataset.
See also
Exclusive economic zone
Food and Agriculture Organization
References
External links
FAO – Country Profiles
Agricultural land
Lists by country |
https://en.wikipedia.org/wiki/Arthur%27s%20conjectures | In mathematics, the Arthur conjectures are some conjectures about automorphic representations of reductive groups over the adeles and unitary representations of reductive groups over local fields made by , motivated by the Arthur–Selberg trace formula.
Arthur's conjectures imply the generalized Ramanujan conjectures for cusp forms on general linear groups.
References
Automorphic forms
Representation theory
Conjectures |
https://en.wikipedia.org/wiki/First%20uncountable%20ordinal | In mathematics, the first uncountable ordinal, traditionally denoted by or sometimes by , is the smallest ordinal number that, considered as a set, is uncountable. It is the supremum (least upper bound) of all countable ordinals. When considered as a set, the elements of are the countable ordinals (including finite ordinals), of which there are uncountably many.
Like any ordinal number (in von Neumann's approach), is a well-ordered set, with set membership serving as the order relation. is a limit ordinal, i.e. there is no ordinal such that .
The cardinality of the set is the first uncountable cardinal number, (aleph-one). The ordinal is thus the initial ordinal of . Under the continuum hypothesis, the cardinality of is , the same as that of —the set of real numbers.
In most constructions, and are considered equal as sets. To generalize: if is an arbitrary ordinal, we define as the initial ordinal of the cardinal .
The existence of can be proven without the axiom of choice. For more, see Hartogs number.
Topological properties
Any ordinal number can be turned into a topological space by using the order topology. When viewed as a topological space, is often written as , to emphasize that it is the space consisting of all ordinals smaller than .
If the axiom of countable choice holds, every increasing ω-sequence of elements of converges to a limit in . The reason is that the union (i.e., supremum) of every countable set of countable ordinals is another countable ordinal.
The topological space is sequentially compact, but not compact. As a consequence, it is not metrizable. It is, however, countably compact and thus not Lindelöf (a countably compact space is compact if and only if it is Lindelöf). In terms of axioms of countability, is first-countable, but neither separable nor second-countable.
The space is compact and not first-countable. is used to define the long line and the Tychonoff plank—two important counterexamples in topology.
See also
Epsilon numbers (mathematics)
Large countable ordinal
Ordinal arithmetic
References
Bibliography
Thomas Jech, Set Theory, 3rd millennium ed., 2003, Springer Monographs in Mathematics, Springer, .
Lynn Arthur Steen and J. Arthur Seebach, Jr., Counterexamples in Topology. Springer-Verlag, New York, 1978. Reprinted by Dover Publications, New York, 1995. (Dover edition).
Ordinal numbers
Topological spaces |
https://en.wikipedia.org/wiki/Antiquarian%20science%20books | Antiquarian science books are original historical works (e.g., books or technical papers) concerning science, mathematics and sometimes engineering. These books are important primary references for the study of the history of science and technology, they can provide valuable insights into the historical development of the various fields of scientific inquiry (History of science, History of mathematics, etc.)
The landmark are significant first (or early) editions typically worth hundreds or thousands of dollars (prices may vary widely based on condition, etc.).
Reprints of these books are often available, for example from Great Books of the Western World, Dover Publications or Google Books.
Incunabula are extremely rare and valuable, but as the "scientific revolution" is only taken to have started around the 1540s, such works of Renaissance literature (including alchemy, Renaissance magic, etc.) are not usually included under the notion of "scientific" literature. Printed originals of the beginning scientific revolution thus date to the 1540s or later, notably beginning with the original publication of Copernican heliocentrism. Nicolaus Copernicus' De revolutionibus orbium coelestium of 1543 sold for more than US$2 million at auctions.
List of notable books
16th century
Tartaglia, Niccolò. Nova Scientia (A New Science). Venice, 1537. Ballistics.
Biringuccio, Vannoccio. De la pirotechnia. Venice, 1540. Metallurgy.
Fuchs, Leonhart. De Historia Stirpium Commentarii Insignes. Basel, 1542. Botany.
Copernicus, Nicolaus. De revolutionibus orbium coelestium. Wittenberg, 1543. Copernican heliocentrism.
Vesalius, Andreas. De humani corporis fabrica (On the Structure of the Human Body). Basel, 1543. Anatomy.
Cardano, Gerolamo. Artis magnae sive de regulis algebraicis (The Art of Solving Algebraic Equations). Nuremberg, 1545. Algebra.
Brunfels, Otto. Kreuterbüch, 1546. Botany.
Gessner, Conrad. Historia Animalium 1551-58. Zoology
Bock, Hieronymus. Kreutterbuch. Strasbourg, 1552. Botany.
Paracelsus. Theil der grossen Wundartzney. Frankfurt, 1556. Medicine.
Agricola, Georgius. De re metallica. Basel, 1561. Mineralogy.
Regiomontanus. De triangulis planis et sphaericis libri quinque. Basel, 1561. Trigonometry.
Bombelli, Rafael. Algebra. 1569/1572. Imaginary numbers.
Cesalpino, Andrea. De plantis libri XVI. 1583. Taxonomy.
Bruno, Giordano. De l'infinito, universo e mondi. 1584 Cosmology.
Stevin, Simon. De Thiende. 1585. Decimal numeral system.
Stevin, Simon. De Beghinselen der Weeghconst. 1586. Statics.
Brahe, Tycho. Astronomiae Instauratae Progymnasmata. 1588. Astronomy.
Viète, François. In artem analyticam isagoge (Introduction to the Analytical Art). Tours, 1591. Algebra.
Ruini, Carlo. Anatomia del Cavallo. Venice, 1598. Veterinary medicine.
17th century
Gilbert, William. De Magnete. London, 1600 Magnetism
Galilei, Galileo. Sidereus Nuncius (The Starry Messenger). Frankfurt, 1610. Astronomy
Napier, John. Mirifici Logarithmorum Canonis Descriptio, 1614. Lo |
https://en.wikipedia.org/wiki/Chiral%20polytope | In mathematics, there are two competing definitions for a chiral polytope. One is that it is a polytope that is chiral (or "enantiomorphic"), meaning that it does not have mirror symmetry. By this definition, a polytope that lacks any symmetry at all would be an example of a chiral polytope.
The other, competing definition of a chiral polytope is that it is a polytope that is as symmetric as possible without being mirror-symmetric, formalized in terms of the action of the symmetry group of the polytope on its flags. By this definition, even highly-symmetric and enantiomorphic polytopes such as the snub cube are not chiral. Much of the study of symmetric but chiral polytopes has been carried out in the framework of abstract polytopes, because of the paucity of geometric examples.
Polytopes without mirror symmetry
Many polytopes lack mirror symmetry, and in that sense form chiral polytopes.
The simplest example is a scalene triangle.
It is possible for polytopes to have a high degree of symmetry, but yet to lack mirror symmetry; a simple example is the disphenoid when its faces are not congruent to an isosceles triangle; an other example is the snub cube, which is vertex-transitive and chiral in this sense.
Symmetric chiral polytopes
Definition
The more technical definition of a chiral polytope is a polytope that has two orbits of flags under its group of symmetries, with
adjacent flags in different orbits. This implies that it must be vertex-transitive, edge-transitive, and face-transitive, as each vertex, edge, or face must be represented by flags in both orbits; however, it cannot be mirror-symmetric, as every mirror symmetry of the polytope would exchange some pair of adjacent flags.
For the purposes of this definition, the symmetry group of a polytope may be defined in either of two different ways: it can refer to the symmetries of a polytope as a geometric object (in which case the polytope is called geometrically chiral) or it can refer to the symmetries of the polytope as a combinatorial structure (an abstract polytope). Chirality is meaningful for either type of symmetry but the two definitions classify different polytopes as being chiral or nonchiral.
In three dimensions
In three dimensions, it is not possible for a geometrically chiral polytope to have finitely many finite faces. For instance, the snub cube is vertex-transitive, but its flags have more than two orbits, and it is neither edge-transitive nor face-transitive, so it is not symmetric enough to meet the formal definition of chirality. The quasiregular polyhedra and their duals, such as the cuboctahedron and the rhombic dodecahedron, provide another interesting type of near-miss: they have two orbits of flags, but are mirror-symmetric, and not every adjacent pair of flags belongs to different orbits. However, despite the nonexistence of finite chiral three-dimensional polyhedra, there exist infinite three-dimensional chiral skew polyhedra of types {4,6}, {6,4}, and { |
https://en.wikipedia.org/wiki/Ahmad%20Tijani | Əhməd Ticani (born 10 November 1987) is a Nigerian football striker who plays for Shusha in the Azerbaijan First Division.
Azerbaijan Career statistics
References
1987 births
Living people
Nigerian men's footballers
Expatriate men's footballers in Azerbaijan
Nigerian expatriate men's footballers
FC Baku players
Nigerian expatriate sportspeople in Azerbaijan
Men's association football forwards
Shusha FK players
People from Uyo |
https://en.wikipedia.org/wiki/Akihiro%20Sakata | is a Japanese footballer who plays for Fukushima United FC in J3 League.
Career statistics
Updated to 23 February 2018.
References
External links
Profile at Fukushima United FC
Profile at AC Nagano Parceiro
1984 births
Living people
Ritsumeikan University alumni
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Cerezo Osaka players
Shonan Bellmare players
Oita Trinita players
AC Nagano Parceiro players
Fukushima United FC players
Men's association football defenders
Association football people from Kyoto |
https://en.wikipedia.org/wiki/Kazuya%20Maeda%20%28footballer%2C%20born%201982%29 | is a former Japanese football player who last featured for Giravanz Kitakyushu.
Career statistics
Updated to 2 February 2018.
References
External links
1982 births
Living people
Osaka University of Health and Sport Sciences alumni
Association football people from Wakayama Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Cerezo Osaka players
Montedio Yamagata players
Giravanz Kitakyushu players
Men's association football defenders |
https://en.wikipedia.org/wiki/Kenjiro%20Ezoe | is a former Japanese football player.
Club statistics
References
External links
1982 births
Living people
Momoyama Gakuin University alumni
Association football people from Okayama Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Cerezo Osaka players
Kataller Toyama players
SP Kyoto FC players
Men's association football defenders
Universiade medalists in football
FISU World University Games gold medalists for Japan |
https://en.wikipedia.org/wiki/Noriyuki%20Sakemoto | is a Japanese football player who plays for Kagoshima United FC.
Club statistics
Updated to 23 February 2018.
References
External links
1984 births
Living people
Association football people from Wakayama Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Cerezo Osaka players
Cerezo Osaka U-23 players
Kagoshima United FC players
Men's association football midfielders
People from Gobō, Wakayama |
https://en.wikipedia.org/wiki/Ryuhei%20Niwa | is a Japanese football player who plays for SC Sagamihara.
Club statistics
Updated to 26 December 2017.
References
External links
Profile at JEF United Chiba
1986 births
Living people
Association football people from Kanagawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Vissel Kobe players
Cerezo Osaka players
Sagan Tosu players
JEF United Chiba players
Kagoshima United FC players
SC Sagamihara players
Men's association football defenders |
https://en.wikipedia.org/wiki/Karl%20Bopp | Karl Bopp (28 March 1877 – 5 December 1934) was a German historian of mathematics.
Biography
Bopp studied at the University of Strasbourg and the University of Heidelberg under Moritz Cantor. In 1906 he habilitated with a work about the conic sections of Grégoire de Saint-Vincent, and in 1915 he became professor extraordinarius in Heidelberg. As successor of Moritz Cantor he taught history of mathematics, political arithmetic, and Insurance. In 1933 he became ill and died in 1934.
Bopp's special field of interest were researches about Johann Heinrich Lambert. He edited Lambert's Monatsbuch, his letter exchanges with Leonhard Euler and Abraham Gotthelf Kästner, and his philosophical writings. Bopp wrote many historical papers, including two studies on the history of elliptic functions, and the re-publication of a paper by Nicolas Fatio de Duillier on the cause of gravitation. Under his supervision many dissertations were written by his students.
References
1877 births
1934 deaths
20th-century German historians
20th-century German mathematicians
German historians of mathematics
Heidelberg University alumni
Academic staff of Heidelberg University
German male non-fiction writers |
https://en.wikipedia.org/wiki/New%20Foundation | New Foundation may refer to:
The New Foundation (professional wrestling), a tag team consisting of Owen Hart and Jim Neidhart
New Foundations, an axiomatic set theory
New Foundation Association, a Korean independence movement during the Japanese colonial period
New Foundation Fellowship, a Christian Quaker ministry
the New Foundation development in the Church of England; see Historical development of Church of England dioceses |
https://en.wikipedia.org/wiki/Babenko%E2%80%93Beckner%20inequality | In mathematics, the Babenko–Beckner inequality (after and William E. Beckner) is a sharpened form of the Hausdorff–Young inequality having applications to uncertainty principles in the Fourier analysis of Lp spaces. The (q, p)-norm of the n-dimensional Fourier transform is defined to be
In 1961, Babenko found this norm for even integer values of q. Finally, in 1975, using Hermite functions as eigenfunctions of the Fourier transform, Beckner proved that the value of this norm for all is
Thus we have the Babenko–Beckner inequality that
To write this out explicitly, (in the case of one dimension,) if the Fourier transform is normalized so that
then we have
or more simply
Main ideas of proof
Throughout this sketch of a proof, let
(Except for q, we will more or less follow the notation of Beckner.)
The two-point lemma
Let be the discrete measure with weight at the points Then the operator
maps to with norm 1; that is,
or more explicitly,
for any complex a, b. (See Beckner's paper for the proof of his "two-point lemma".)
A sequence of Bernoulli trials
The measure that was introduced above is actually a fair Bernoulli trial with mean 0 and variance 1. Consider the sum of a sequence of n such Bernoulli trials, independent and normalized so that the standard deviation remains 1. We obtain the measure which is the n-fold convolution of with itself. The next step is to extend the operator C defined on the two-point space above to an operator defined on the (n + 1)-point space of with respect to the elementary symmetric polynomials.
Convergence to standard normal distribution
The sequence converges weakly to the standard normal probability distribution with respect to functions of polynomial growth. In the limit, the extension of the operator C above in terms of the elementary symmetric polynomials with respect to the measure is expressed as an operator T in terms of the Hermite polynomials with respect to the standard normal distribution. These Hermite functions are the eigenfunctions of the Fourier transform, and the (q, p)-norm of the Fourier transform is obtained as a result after some renormalization.
See also
Entropic uncertainty
References
Inequalities |
https://en.wikipedia.org/wiki/Well-behaved%20statistic | Although the term well-behaved statistic often seems to be used in the scientific literature in somewhat the same way as is well-behaved in mathematics (that is, to mean "non-pathological") it can also be assigned precise mathematical meaning, and in more than one way. In the former case, the meaning of this term will vary from context to context. In the latter case, the mathematical conditions can be used to derive classes of combinations of distributions with statistics which are well-behaved in each sense.
First Definition: The variance of a well-behaved statistical estimator is finite and one condition on its mean is that it is differentiable in the parameter being estimated.
Second Definition: The statistic is monotonic, well-defined, and locally sufficient.
Conditions for a Well-Behaved Statistic: First Definition
More formally the conditions can be expressed in this way. is a statistic for that is a function of the sample, . For to be well-behaved we require:
: Condition 1
differentiable in , and the derivative satisfies:
: Condition 2
Conditions for a Well-Behaved Statistic: Second Definition
In order to derive the distribution law of the parameter T, compatible with , the statistic must obey some technical properties. Namely, a statistic s is said to be well-behaved if it satisfies the following three statements:
monotonicity. A uniformly monotone relation exists between s and ? for any fixed seed – so as to have a unique solution of (1);
well-defined. On each observed s the statistic is well defined for every value of ?, i.e. any sample specification such that has a probability density different from 0 – so as to avoid considering a non-surjective mapping from to , i.e. associating via to a sample a ? that could not generate the sample itself;
local sufficiency. constitutes a true T sample for the observed s, so that the same probability distribution can be attributed to each sampled value. Now, is a solution of (1) with the seed . Since the seeds are equally distributed, the sole caveat comes from their independence or, conversely from their dependence on ? itself. This check can be restricted to seeds involved by s, i.e. this drawback can be avoided by requiring that the distribution of is independent of ?. An easy way to check this property is by mapping seed specifications into s specifications. The mapping of course depends on ?, but the distribution of will not depend on ?, if the above seed independence holds – a condition that looks like a local sufficiency of the statistic S.
The remainder of the present article is mainly concerned with the context of data mining procedures applied to statistical inference and, in particular, to the group of computationally intensive procedure that have been called algorithmic inference.
Algorithmic inference
In algorithmic inference, the property of a statistic that is of most relevance is the pivoting step which allows to transference of probability-considerati |
https://en.wikipedia.org/wiki/Twisting%20properties | Twisting properties in general terms are associated with the properties of samples that identify with statistics that are suitable for exchange.
Description
Starting with a sample observed from a random variable X having a given distribution law with a non-set parameter, a parametric inference problem consists of computing suitable values – call them estimates – of this parameter precisely on the basis of the sample. An estimate is suitable if replacing it with the unknown parameter does not cause major damage in next computations. In algorithmic inference, suitability of an estimate reads in terms of compatibility with the observed sample.
In turn, parameter compatibility is a probability measure that we derive from the probability distribution of the random variable to which the parameter refers. In this way we identify a random parameter Θ compatible with an observed sample.
Given a sampling mechanism , the rationale of this operation lies in using the Z seed distribution law to determine both the X distribution law for the given θ, and the Θ distribution law given an X sample. Hence, we may derive the latter distribution directly from the former if we are able to relate domains of the sample space to subsets of Θ support. In more abstract terms, we speak about twisting properties of samples with properties of parameters and identify the former with statistics that are suitable for this exchange, so denoting a well behavior w.r.t. the unknown parameters. The operational goal is to write the analytic expression of the cumulative distribution function , in light of the observed value s of a statistic S, as a function of the S distribution law when the X parameter is exactly θ.
Method
Given a sampling mechanism for the random variable X, we model to be equal to . Focusing on a relevant statistic for the parameter θ, the master equation reads
When s is a well-behaved statistic w.r.t the parameter, we are sure that a monotone relation exists for each between s and θ. We are also assured that Θ, as a function of for given s, is a random variable since the master equation provides solutions that are feasible and independent of other (hidden) parameters.
The direction of the monotony determines for any a relation between events of the type or vice versa , where is computed by the master equation with . In the case that s assumes discrete values the first relation changes into where is the size of the s discretization grain, idem with the opposite monotony trend. Resuming these relations on all seeds, for s continuous we have either
or
For s discrete we have an interval where lies, because of .
The whole logical contrivance is called a twisting argument. A procedure implementing it is as follows.
Algorithm
Remark
The rationale behind twisting arguments does not change when parameters are vectors, though some complication arises from the management of joint inequalities. Instead, the difficulty of dealing with a v |
https://en.wikipedia.org/wiki/Bootstrapping%20populations | Bootstrapping populations in statistics and mathematics starts with a sample observed from a random variable.
When X has a given distribution law with a set of non fixed parameters, we denote with a vector , a parametric inference problem consists of computing suitable values – call them estimates – of these parameters precisely on the basis of the sample. An estimate is suitable if replacing it with the unknown parameter does not cause major damage in next computations. In Algorithmic inference, suitability of an estimate reads in terms of compatibility with the observed sample.
In this framework, resampling methods are aimed at generating a set of candidate values to replace the unknown parameters that we read as compatible replicas of them. They represent a population of specifications of a random vector compatible with an observed sample, where the compatibility of its values has the properties of a probability distribution. By plugging parameters into the expression of the questioned distribution law, we bootstrap entire populations of random variables compatible with the observed sample.
The rationale of the algorithms computing the replicas, which we denote population bootstrap procedures, is to identify a set of statistics exhibiting specific properties, denoting a well behavior, w.r.t. the unknown parameters. The statistics are expressed as functions of the observed values , by definition. The may be expressed as a function of the unknown parameters and a random seed specification through the sampling mechanism , in turn. Then, by plugging the second expression in the former, we obtain expressions as functions of seeds and parameters – the master equations – that we invert to find values of the latter as a function of: i) the statistics, whose values in turn are fixed at the observed ones; and ii) the seeds, which are random according to their own distribution. Hence from a set of seed samples we obtain a set of parameter replicas.
Method
Given a of a random variable X and a sampling mechanism for X, the realization x is given by , with . Focusing on well-behaved statistics,
{|
|-
|
|-
|
|-
|
|}
for their parameters, the master equations read
{| width=100%
|-
|
|-
| width=90% |
| width=10% align="center" | (1)
|-
|
|}
For each sample seed a vector of parameters is obtained from the solution of the above system with fixed to the observed values.
Having computed a huge set of compatible vectors, say N, the empirical marginal distribution of is obtained by:
{| width=100%
|-
| width=90% |
| width=10% align="center" | (2)
|}
where is the j-th component of the generic solution of (1) and where is the indicator function of in the interval
Some indeterminacies remain if X is discrete and this we will be considered shortly.
The whole procedure may be summed up in the form of the following Algorithm, where the index of denotes the parameter vector from which the statistics vector is derived |
https://en.wikipedia.org/wiki/Complexity%20index | In modern computer science and statistics, the complexity index of a function denotes the level of informational content, which in turn affects the difficulty of learning the function from examples. This is different from computational complexity, which is the difficulty to compute a function. Complexity indices characterize the entire class of functions to which the one we are interested in belongs. Focusing on Boolean functions, the detail of a class of Boolean functions c essentially denotes how deeply the class is articulated.
Technical definition
To identify this index we must first define a sentry function of .
Let us focus for a moment on a single function c, call it a concept defined on a set of elements that we may figure as points in a Euclidean space. In this framework, the above function associates to c a set of points that, since are defined to be external to the concept, prevent it from expanding into another function of . We may dually define these points in terms of sentinelling a given concept c from being fully enclosed (invaded) by another concept within the class. Therefore, we call these points either sentinels or sentry points; they are assigned by the sentry function to each concept of in such a way that:
the sentry points are external to the concept c to be sentineled and internal to at least one other including it,
each concept including c has at least one of the sentry points of c either in the gap between c and , or outside and distinct from the sentry points of , and
they constitute a minimal set with these properties.
The technical definition coming from is rooted in the inclusion of an augmented concept made up of c plus its sentry points by another in the same class.
Definition of sentry function
For a concept class on a space , a sentry function is a total function satisfying the following conditions:
Sentinels are outside the sentineled concept ( for all ).
Sentinels are inside the invading concept (Having introduced the sets , an invading concept is such that and . Denoting the set of concepts invading c, we must have that if , then ).
is a minimal set with the above properties (No exists satisfying (1) and (2) and having the property that for every ).
Sentinels are honest guardians. It may be that but so that . This however must be a consequence of the fact that all points of are involved in really sentineling c against other concepts in and not just in avoiding inclusion of by . Thus if we remove remains unchanged (Whenever and are such that and , then the restriction of to is a sentry function on this set).
is the frontier of c upon .
With reference to the picture on the right, is a candidate frontier of against . All points are in the gap between a and . They avoid inclusion of in , provided that these points are not used by the latter for sentineling itself against other concepts. Vice versa we expect that uses and as its own sentinels, uses and and use |
https://en.wikipedia.org/wiki/Luigi%20Bodio | Luigi Bodio (born 12 October 1840 in Milan–2 November 1920 in Rome) was an Italian economist and statistician, among the founders of Italian Statistics. He was the first General Secretary of the International Statistical Institute (ISI) and among the first Presidents of ISI.
Biography
Bodio graduated in 1861 at University of Pisa as a doctor of law, and afterward traveled abroad with government scholarship to complete his postgraduate education in economics and statistics. In 1864 he became Professor in National Economics in Livorno, and in 1867 also in Milan. From 1868 to 1872 Bodio was Professor in Economics and Economic Geography at University of Venice. In 1872, after the death of Pietro Maestri, he was President of the Italian Royal Statistical Office (founded by Maestri) in Rome. Since 1876 Bodio was an editor, together with Cesare Correnti and Paolo Boselli, of the "Archivio di statistica". In the same year, he conducted the first official surveys on Italian migration. In 1882 Bodio became a member of the Accademia Nazionale dei Lincei.
In 1885 was a founding member and General Secretary of the International Statistical Institute up to 1905. In 1909 he was elected President of the International Statistical Institute and remained in charge until his death in 1920. In 1900 Bodio was elected National Senator, and he was General Commissioner of Migration (1901–04), an Inter-ministerial Body created to address and protect the Italian migration abroad. In 1996, the International Cooperation Centre for Statistics (ICstat) was dedicated to Luigi Bodio in recognition of his dedication and promotion of the statistical cooperation.
Writings
"Statistique internationale des caisses d'épargne", 1876
"Saggio sul commercio esterno terrestre e marittimo del regno d'Italia", 1865
"Dei documenti statistici del regno d'Italia", 1867
"Dei rapporti della statistica coll' economia politica e colle altre scienze affini", 1869
"Del patrimonio delle entrate e delle spese della pubblica beneficenza in Italia", 1889
References
External links
ICstat - International Cooperation Center for Statistics "Luigi Bodio"
International Statistical Institute
Presidents of the International Statistical Institute
Elected Members of the International Statistical Institute
1840 births
1920 deaths
Italian statisticians
Academic staff of the University of Milan
Scientists from Milan |
https://en.wikipedia.org/wiki/Simple-homotopy%20equivalence | In mathematics, particularly the area of topology, a simple-homotopy equivalence is a refinement of the concept of homotopy equivalence. Two CW-complexes are simple-homotopy equivalent if they are related by a sequence of collapses and expansions (inverses of collapses), and a homotopy equivalence is a simple homotopy equivalence if it is homotopic to such a map.
The obstruction to a homotopy equivalence being a simple homotopy equivalence is the Whitehead torsion,
A homotopy theory that studies simple-homotopy types is called simple homotopy theory.
See also
Discrete Morse theory
References
Homotopy theory
Equivalence (mathematics) |
https://en.wikipedia.org/wiki/Renato%20Michell%20Gonz%C3%A1lez | Renato Michell González Castellanos (born October 4, 1988) is a Mexican footballer who currently plays as a midfielder.
External links
Career statistics at BDFA
Living people
1988 births
Club América footballers
Venados F.C. players
Footballers from Mexico City
Global F.C. players
Mexican expatriate men's footballers
Mexican men's footballers
Expatriate men's footballers in the Philippines
Men's association football midfielders |
https://en.wikipedia.org/wiki/Geometric%20combinatorics | Geometric combinatorics is a branch of mathematics in general and combinatorics in particular. It includes a number of subareas such as polyhedral combinatorics (the study of faces of convex polyhedra), convex geometry (the study of convex sets, in particular combinatorics of their intersections), and discrete geometry, which in turn has many applications to computational geometry. Other important areas include metric geometry of polyhedra, such as the Cauchy theorem on rigidity of convex polytopes. The study of regular polytopes, Archimedean solids, and kissing numbers is also a part of geometric combinatorics. Special polytopes are also considered, such as the permutohedron, associahedron and Birkhoff polytope.
See also
Topological combinatorics
References
What is geometric combinatorics?, Ezra Miller and Vic Reiner, 2004
Topics in Geometric Combinatorics
Geometric Combinatorics, Edited by: Ezra Miller and Victor Reiner
Combinatorics
Discrete geometry |
https://en.wikipedia.org/wiki/Schur%27s%20property | In mathematics, Schur's property, named after Issai Schur, is the property of normed spaces that is satisfied precisely if weak convergence of sequences entails convergence in norm.
Motivation
When we are working in a normed space X and we have a sequence that converges weakly to , then a natural question arises. Does the sequence converge in perhaps a more desirable manner? That is, does the sequence converge to in norm? A canonical example of this property, and commonly used to illustrate the Schur property, is the sequence space.
Definition
Suppose that we have a normed space (X, ||·||), an arbitrary member of X, and an arbitrary sequence in the space. We say that X has Schur's property if converging weakly to implies that . In other words, the weak and strong topologies share the same convergent sequences. Note however that weak and strong topologies are always distinct in infinite-dimensional space.
Examples
The space ℓ1 of sequences whose series is absolutely convergent has the Schur property.
Name
This property was named after the early 20th century mathematician Issai Schur who showed that ℓ1 had the above property in his 1921 paper.
See also
Radon-Riesz property for a similar property of normed spaces
Schur's theorem
Notes
References
Functional analysis |
https://en.wikipedia.org/wiki/Takahito%20Chiba | is a former Japanese football player.
Club statistics
References
External links
1984 births
Living people
Association football people from Hokkaido
Japanese men's footballers
J1 League players
J2 League players
Cerezo Osaka players
Hokkaido Consadole Sapporo players
ReinMeer Aomori players
Men's association football defenders |
https://en.wikipedia.org/wiki/Noboru%20Nakayama | is a former Japanese football player.
He is now a coach for Cerezo Osaka youth academy.
Club statistics
References
External links
1987 births
Living people
Association football people from Osaka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Cerezo Osaka players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Kenta%20Tanno | is a Japanese professional footballer who plays as a goalkeeper for club Iwate Grulla Morioka.
Club career statistics
.
Reserves performance
Honours
Club
J1 League: 2021
Emperor's Cup: 2020
Japanese Super Cup: 2021
References
External links
1986 births
Living people
Association football people from Miyagi Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Cerezo Osaka players
Cerezo Osaka U-23 players
V-Varen Nagasaki players
Oita Trinita players
Kawasaki Frontale players
Iwate Grulla Morioka players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Kento%20Shiratani | is a former Japanese football player.
Club statistics
National team statistics
Appearances in major competitions
References
External links
1989 births
Living people
Association football people from Kyoto Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Cerezo Osaka players
Mito HollyHock players
Fagiano Okayama players
Roasso Kumamoto players
FC Machida Zelvia players
Men's association football forwards |
https://en.wikipedia.org/wiki/Koji%20Onishi | is a former Japanese football player.
He moved to Kamatamare Sanuki on a loan deal in May 2010. He announced his retirement from the game in December 2010.
Club statistics
References
External links
1988 births
Living people
Association football people from Tokushima Prefecture
Japanese men's footballers
J2 League players
Tokushima Vortis players
Kamatamare Sanuki players
Men's association football forwards |
https://en.wikipedia.org/wiki/Sampling%20probability | In statistics, in the theory relating to sampling from finite populations, the sampling probability (also known as inclusion probability) of an element or member of the population, is its probability of becoming part of the sample during the drawing of a single sample. For example, in simple random sampling the probability of a particular unit to be selected into the sample is
where is the sample size and is the population size.
Each element of the population may have a different probability of being included in the sample. The inclusion probability is also termed the "first-order inclusion probability" to distinguish it from the "second-order inclusion probability", i.e. the probability of including a pair of elements. Generally, the first-order inclusion probability of the ith element of the population is denoted by the symbol πi and the second-order inclusion probability that a pair consisting of the ith and jth element of the population that is sampled is included in a sample during the drawing of a single sample is denoted by πij.
See also
Sampling bias
Sampling design
Sampling frame
References
Sampling (statistics) |
https://en.wikipedia.org/wiki/Grunwald%E2%80%93Wang%20theorem | In algebraic number theory, the Grunwald–Wang theorem is a local-global principle stating that—except in some precisely defined cases—an element x in a number field K is an nth power in K if it is an nth power in the completion for all but finitely many primes of K. For example, a rational number is a square of a rational number if it is a square of a p-adic number for almost all primes p. The Grunwald–Wang theorem is an example of a local-global principle.
It was introduced by , but there was a mistake in this original version that was found and corrected by . The theorem considered by Grunwald and Wang was more general than the one stated above as they discussed the existence of cyclic extensions with certain local properties, and the statement about nth powers is a consequence of this.
History
, a student of Helmut Hasse, gave an incorrect proof of the erroneous statement that an element in a number field is an nth power if it is an nth power locally almost everywhere. gave another incorrect proof of this incorrect statement. However discovered the following counter-example: 16 is a p-adic 8th power for all odd primes p, but is not a rational or 2-adic 8th power. In his doctoral thesis written under Emil Artin, Wang gave and proved the correct formulation of Grunwald's assertion, by describing the rare cases when it fails. This result is what is now known as the Grunwald–Wang theorem. The history of Wang's counterexample is discussed by
Wang's counter-example
Grunwald's original claim that an element that is an nth power almost everywhere locally is an nth power globally can fail in two distinct ways: the element can be an nth power almost everywhere locally but not everywhere locally, or it can be an nth power everywhere locally but not globally.
An element that is an nth power almost everywhere locally but not everywhere locally
The element 16 in the rationals is an 8th power at all places except 2, but is not an 8th power in the 2-adic numbers.
It is clear that 16 is not a 2-adic 8th power, and hence not a rational 8th power, since the 2-adic valuation of 16 is 4 which is not divisible by 8.
Generally, 16 is an 8th power in a field K if and only if the polynomial has a root in K. Write
Thus, 16 is an 8th power in K if and only if 2, −2 or −1 is a square in K. Let p be any odd prime. It follows from the multiplicativity of the Legendre symbol that 2, −2 or −1 is a square modulo p. Hence, by Hensel's lemma, 2, −2 or −1 is a square in .
An element that is an nth power everywhere locally but not globally
16 is not an 8th power in although it is an 8th power locally everywhere (i.e. in for all p). This follows from the above and the equality .
A consequence of Wang's counter-example
Wang's counterexample has the following interesting consequence showing that one cannot always find a cyclic Galois extension of a given degree of a number field in which finitely many given prime places split in a specified way:
There exist |
https://en.wikipedia.org/wiki/Daniel%20Kane | Daniel Kane may refer to:
Daniel Kane (mathematician) (born 1986), American assistant professor in mathematics
Daniel Kane (linguist), Australian linguist, an expert in Jurchen and Khitan languages
Dan Kane, American investigative journalist
See also
Daniel Cane, businessman |
https://en.wikipedia.org/wiki/Lothar%20Woelk | Lothar Woelk (born 3 August 1954) is a German former professional footballer who played as a Defender, making 420 appearances in the Bundesliga.
Career statistics
Honours
DFB-Pokal finalist: 1987–88
References
External links
1954 births
Living people
People from Recklinghausen
German men's footballers
West German men's footballers
Footballers from Münster (region)
Men's association football defenders
Bundesliga players
VfL Bochum players
MSV Duisburg players |
https://en.wikipedia.org/wiki/History%20of%20science%20and%20technology%20in%20Mexico | The history of science and technology in Mexico spans many years.
Indigenous Mesoamerican civilizations developed mathematics, astronomy, and calendrics, and solved technological problems of water management for agriculture and flood control in Central Mexico.
Following the Spanish conquest in 1521, New Spain (colonial Mexico) was brought into the European sphere of science and technology. The Royal and Pontifical University of Mexico, established in 1551, was a hub of intellectual and religious development in colonial Mexico for over a century. During the Spanish American Enlightenment in Mexico, the colony made considerable progress in science, but following the war of independence and political instability in the early nineteenth century, progress stalled.
During the late 19th century under the regime of Porfirio Díaz, the process of industrialization began in Mexico. Following the Mexican Revolution, a ten-year civil war, Mexico made significant progress in science and technology. During the 20th century, new universities, such as the National Polytechnical Institute, Monterrey Institute of Technology and research institutes, such as those at the National Autonomous University of Mexico, were established in Mexico.
According to the World Bank, Mexico is Latin America's largest exporter of high-technology goods (High-technology exports are manufactured goods that involve high R&D intensity, such as in aerospace, computers, pharmaceuticals, scientific instruments, and electrical machinery) with $40.7 billion worth of high-technology goods exports in 2012. Mexican high-technology exports accounted for 17% of all manufactured goods in the country in 2012 according to the World Bank.
Indigenous Civilizations
The Olmec, a Pre-Columbian civilization living in the tropical lowlands of south-central Mexico, calendar system required an advanced understanding of mathematics. The Olmec number system was based on 20 instead of decimal and used three symbols- a dot for one, a bar for five, and a shell-like symbol for zero. The concept of zero is one of the Olmecs' greatest achievements. It permitted numbers to be written by position and allowed for complex calculations. Although the invention of zero is often attributed to the Mayans, it was originally conceived by the Olmecs.
To predict planting and harvesting times, early peoples studied the movements of the sun, stars, and planets. They used this information to make calendars. The Aztecs created two calendars- one for farming, and one for religion. The farming calendar let them know when to plant and to harvest crops. An Aztec calendar stone dug up in Mexico City in 1790 includes information about the months of the year and pictures of the sun god at the center.
Colonial Era
After the Viceroyalty of New Spain was founded, the Spanish brought the scientific culture that dominated Spain to the Viceroyalty of New Spain.
The Franciscan order founded the first school of higher learning in the Ameri |
https://en.wikipedia.org/wiki/Institut%20de%20Math%C3%A9matiques%20de%20Toulouse | Institut de Mathématiques de Toulouse (Toulouse Mathematics Institute; IMT) is a research laboratory of the mathematics community of the Toulouse area in France. It is partially supported by the French public research agency CNRS as unit UMR 5129. In 2020 the research in IMT is organized into six main teams, with some overlap:
Analyse,
Dynamique et géométrie complexe,
Équations aux dérivées partielles,
Géométrie topologie algèbre,
Probabilités,
Statistiques et optimisation.
IMT is one of the largest French research centres in mathematics, and its scientific activities cover almost all domains of mathematics. It had approximately 200 permanent researchers and 100 PhD students in 2020, belonging to various institutions of the University of Toulouse and CNRS.
The main buildings of IMT are located on the Paul Sabatier University campus.
IMT is in charge of the Fermat Prize and of the publication Annales de la Faculté des Sciences de Toulouse.
External links
Institut de Mathématiques de Toulouse
Geographic location with Wikimapia
IMT scientific production on HAL
Mathematical institutes
French National Centre for Scientific Research |
https://en.wikipedia.org/wiki/Ethnic%20groups%20in%20Senegal | There are various ethnic groups in Senegal, The Wolof according to CIA statistics are the majority ethnic group in Senegal. Many subgroups of those can be further distinguished, based on religion, location and language. According to one 2005 estimate, there are at least twenty distinguishable groups of largely varying size.
Major groups
The largest group is the Wolof, representing 43.3% of the population of the country. They live predominantly in the west, having descended from the kingdoms of Cayor, Waalo and Jolof that once existed in that area. Their population is focused in large urban centres. Most are Muslim, being either Mouride or Tijānī. The Lebou people of Cap-Vert and Petite Côte are considered a subgroup of the Wolof. however they represent less than 1% of its population. The prevalence of the Wolof both linguistically and politically has continued to increase throughout the years; this tendency has been called the "wolofisation" of Senegal.
The Fula, those who speak the Fula language, are the second most populous group, representing 23.8% of the country's population. This figure includes the Toucouleurs, but according to surveys, this subgroup is sometimes considered separate from the Fula. They were Islamized very early. The territory inhabited by the Fula is larger than that of the Wolof, however many areas are sparsely populated, such as Ferlo, Kolda, the Senegal River Valley, and Badiar. Traditionally nomadic, the vast majority has become sedentary, although there is a current rural exodus. Since Ahmed Sékou Touré became president of Guinea, many Guinean Fula have immigrated to Senegal, particularly from Fouta Djallon.
The third group is the Serer, who represent 14.7% of the national population. Serer pre-colonial kingdoms included : the Kingdom of Sine, Kingdom of Saloum, Biffeche and previously the Kingdom of Baol (ruled by the Joof family). Serer medieval history is characterized by resisting Islamization from the 11th century (during the Almoravids' advance) to the 19th century (the Marabout wars of Senegambia), resulting in the Battle of Fandane-Thiouthioune, commonly known as the Battle of Somb. The Serer anti-French movement during the colonial era resulted in the Battle of Logandème. The Serer people includes, but not limited to : the Saafi, Ndut, Laalaa, Niominka, Palor, etc. Many of these speak the Cangin languages.
The Jola represent 5% of the country's population, and mostly live in Ziguinchor where they primarily make their living from rice cultivation and fishing. Traditionally animist, they have historically resisted the spread of both Islam and Christianity in the country. While much of the Jola population now adheres to either Islam or Christianity, many mix these religions with animist beliefs. The Jola hold their ethnic distinctiveness as of great importance.
Other groups also live in the Ziguinchor Region. While these groups lead lifestyles that are very similar to the Jola, they speak different languages |
https://en.wikipedia.org/wiki/Combinatorics%20on%20words | Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages. The subject looks at letters or symbols, and the sequences they form. Combinatorics on words affects various areas of mathematical study, including algebra and computer science. There have been a wide range of contributions to the field. Some of the first work was on square-free words by Axel Thue in the early 1900s. He and colleagues observed patterns within words and tried to explain them. As time went on, combinatorics on words became useful in the study of algorithms and coding. It led to developments in abstract algebra and answering open questions.
Definition
Combinatorics is an area of discrete mathematics. Discrete mathematics is the study of countable structures. These objects have a definite beginning and end. The study of enumerable objects is the opposite of disciplines such as analysis, where calculus and infinite structures are studied. Combinatorics studies how to count these objects using various representations. Combinatorics on words is a recent development in this field that focuses on the study of words and formal languages. A formal language is any set of symbols and combinations of symbols that people use to communicate information.
Some terminology relevant to the study of words should first be explained. First and foremost, a word is basically a sequence of symbols, or letters, in a finite set. One of these sets is known by the general public as the alphabet. For example, the word "encyclopedia" is a sequence of symbols in the English alphabet, a finite set of twenty-six letters. Since a word can be described as a sequence, other basic mathematical descriptions can be applied. The alphabet is a set, so as one would expect, the empty set is a subset. In other words, there exists a unique word of length zero. The length of the word is defined by the number of symbols that make up the sequence, and is denoted by |w|. Again looking at the example "encyclopedia", |w| = 12, since encyclopedia has twelve letters. The idea of factoring of large numbers can be applied to words, where a factor of a word is a block of consecutive symbols. Thus, "cyclop" is a factor of "encyclopedia".
In addition to examining sequences in themselves, another area to consider of combinatorics on words is how they can be represented visually. In mathematics various structures are used to encode data. A common structure used in combinatorics is the tree structure. A tree structure is a graph where the vertices are connected by one line, called a path or edge. Trees may not contain cycles, and may or may not be complete. It is possible to encode a word, since a word is constructed by symbols, and encode the data by using a tree. This gives a visual representation of the object.
Major contributions
The first books on combinatorics on words that summarize the origins of the subj |
https://en.wikipedia.org/wiki/Relationships%20among%20probability%20distributions | In probability theory and statistics, there are several relationships among probability distributions. These relations can be categorized in the following groups:
One distribution is a special case of another with a broader parameter space
Transforms (function of a random variable);
Combinations (function of several variables);
Approximation (limit) relationships;
Compound relationships (useful for Bayesian inference);
Duality;
Conjugate priors.
Special case of distribution parametrization
A binomial distribution with parameters n = 1 and p is a Bernoulli distribution with parameter p.
A negative binomial distribution with parameters n = 1 and p is a geometric distribution with parameter p.
A gamma distribution with shape parameter α = 1 and rate parameter β is an exponential distribution with rate parameter β.
A gamma distribution with shape parameter α = v/2 and rate parameter β = 1/2 is a chi-squared distribution with ν degrees of freedom.
A chi-squared distribution with 2 degrees of freedom (k = 2) is an exponential distribution with a mean value of 2 (rate λ = 1/2 .)
A Weibull distribution with shape parameter k = 1 and rate parameter β is an exponential distribution with rate parameter β.
A beta distribution with shape parameters α = β = 1 is a continuous uniform distribution over the real numbers 0 to 1.
A beta-binomial distribution with parameter n and shape parameters α = β = 1 is a discrete uniform distribution over the integers 0 to n.
A Student's t-distribution with one degree of freedom (v = 1) is a Cauchy distribution with location parameter x = 0 and scale parameter γ = 1.
A Burr distribution with parameters c = 1 and k (and scale λ) is a Lomax distribution with shape k (and scale λ.)
Transform of a variable
Multiple of a random variable
Multiplying the variable by any positive real constant yields a scaling of the original distribution.
Some are self-replicating, meaning that the scaling yields the same family of distributions, albeit with a different parameter:
normal distribution, gamma distribution, Cauchy distribution, exponential distribution, Erlang distribution, Weibull distribution, logistic distribution, error distribution, power-law distribution, Rayleigh distribution.
Example:
If X is a gamma random variable with shape and rate parameters (α, β), then Y = aX is a gamma random variable with parameters (α,β/a).
If X is a gamma random variable with shape and scale parameters (k, θ), then Y = aX is a gamma random variable with parameters (k,aθ).
Linear function of a random variable
The affine transform ax + b yields a relocation and scaling of the original distribution. The following are self-replicating:
Normal distribution, Cauchy distribution, Logistic distribution, Error distribution, Power distribution, Rayleigh distribution.
Example:
If Z is a normal random variable with parameters (μ = m, σ2 = s2), then X = aZ + b is a normal random variable with parameters (μ = am + b, σ2 = a2s2).
R |
https://en.wikipedia.org/wiki/Annales%20de%20la%20Facult%C3%A9%20des%20Sciences%20de%20Toulouse | The Annales de la Faculté des Sciences de Toulouse is a peer-reviewed scientific journal covering all fields of mathematics. Articles are written in English or French. It is published by the Institut de Mathématiques de Toulouse and edited with the help of the Centre de diffusion de revues académiques mathématiques. The editor-in-chief is Vincent Guedj (Université Paul Sabatier). The journal is abstracted and indexed in Zentralblatt MATH.
History
The journal was established in 1887 by Marie Henri Andoyer, Benjamin Baillaud, G. Berson, T. Chauvin, E. Cosserat, A. Destrem, C. Fabre, A. Legoux, Paul Sabatier, and Thomas Joannes Stieltjes. Originally, the journal was multidisciplinary; the present version corresponds to the original "Mathematics" section.
References
External links
Online archive
Print:
Online:
Mathematics journals
Publications established in 1887
1887 establishments in France
Multilingual journals |
https://en.wikipedia.org/wiki/Kentoku%20Noborio | is a former Japanese football player.
Club statistics
References
External links
1983 births
Living people
Fukuoka University alumni
Association football people from Kagoshima Prefecture
Japanese men's footballers
J1 League players
J2 League players
Kyoto Sanga FC players
Tokushima Vortis players
Giravanz Kitakyushu players
Men's association football defenders |
https://en.wikipedia.org/wiki/Takuya%20Muguruma | is a former Japanese football player.
Club statistics
References
External links
1984 births
Living people
Association football people from Kyoto Prefecture
Japanese men's footballers
J1 League players
J2 League players
Kyoto Sanga FC players
Albirex Niigata players
Tokushima Vortis players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Shogo%20Nishikawa | is a Japanese retired football player.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Tochigi SC
1983 births
Living people
Hiroshima Shudo University alumni
Japanese men's footballers
J1 League players
J2 League players
Sanfrecce Hiroshima players
Tokushima Vortis players
Montedio Yamagata players
Yokohama FC players
Tochigi SC players
FC Ryukyu players
Men's association football defenders
Association football people from Hiroshima |
https://en.wikipedia.org/wiki/Sociedad%20Mexicana%20de%20Geograf%C3%ADa%20y%20Estad%C3%ADstica | Sociedad Mexicana de Geografía y Estadística (Mexican Society for Geography and Statistics) is a national organization founded on 18 April 1833 to promote the mapping and boundary demarcation of the newly independent Mexican state. The aim of its founders was to aid a number of governmental agencies and through the efforts of liberal head of state, Valentín Gómez Farías. It was the first geographical society in the Americas and the fourth in the world.
From the beginning, the scope of projects was very broad, covering not only the physiography of the territory but also its natural resources and their potential for development. Also included in their study was the nature of the population, its size, age distribution, ethnic and linguistic makeup. One of the first publications was in 1850, the work of geographer , followed by an atlas of the republic, started in 1841 and completed in 1850, but not published for several years due to lack of funds.
Among the achievements of the Society were:
Initiatives within the Mexican government to issue laws providing a process for determining the official names of cities and towns.
Promoted legislation for the care of forests and conservation of archaeological monuments as a national priority.
Produced a report on the metric system, which allowed Mexico to be among the first countries in Latin America to adopt it.
Proposed the laying out of a telegraph system for Mexico City.
Sponsoring the publication of the Boletín de la Sociedad Mexicana de Geografía y Estadística (Bulletin of the Society) for the dissemination of all the reports and data that the Society accumulated.
Currently the Society contributes to the research, analysis and understanding of the major problems of Mexico through its 55 specialized academies and local societies involved in the various Mexican states. This includes close ties with Instituto Nacional de Estadística y Geografía (INEGI), and working with the various Mexican universities as well as with major U.S. institutions.
Notable presidents
1839-1846, 1848-1850, and 1853 Juan Nepomuceno Almonte
1861 Miguel Lerdo de Tejada
1881-1889 Ignacio Manuel Altamirano
1934, 1944, and 1946 Jesús Silva Herzog
1959 Isidro Fabela
References
Peña, Sergio de la and Wilkie, James W. (1994) La Estadística Económica en México: Los Orígenes (Economic Statistics in Mexico: The Origins) Siglo Veintiuno Editores, Universidad Autónoma Metropolitana-Azcapotzalco, Mexico City,
Dunbar, Gary S. (1988) ""The Compass Follows the Flag": The French Scientific Mission to Mexico, 1864-1867" Annals of the Association of American Geographers 78(2): pp. 229–240, especially 233-234
External links
Blog de la Sociedad Mexicana de Geografía y Estadística.
Official website of the Sociedad Mexicana de Geografía y Estadística, in Spanish
List of presidents of the Sociedad Mexicana de Geografía y Estadística, in Spanish
Geographic societies
Scientific organizations based in Mexico
Organizations established |
https://en.wikipedia.org/wiki/Hwang%20Jin-sung | Hwang Jin-sung (黄镇晟，born May 5, 1984) is a South Korean footballer. He has played for Gangwon FC.
Club statistics
Honors
Club
Pohang Steelers
K-League Champion : 2007
Korean FA Cup (1): 2008
K-League Cup (1): 2009
AFC Champions League (1): 2009
FORTIS Hong Kong New Years cup(1):2010
2012 K League Best XI
References
External links
Profile at ThePlayersAgent
1984 births
Living people
Men's association football midfielders
South Korean men's footballers
South Korean expatriate men's footballers
South Korean expatriate sportspeople in Belgium
Expatriate men's footballers in Belgium
Pohang Steelers players
Royale Union Tubize-Braine players
Kyoto Sanga FC players
Fagiano Okayama players
Seongnam FC players
Gangwon FC players
K League 1 players
J2 League players
Footballers from Seoul |
https://en.wikipedia.org/wiki/Park%20Yun-hwa | Park Yun-Hwa (; born 13 June 1978) is a South Korean football midfielder.
His previous club is FC Seoul, Gwangju Sangmu (military service), Daegu FC and Gyeongnam FC.
Club career statistics
External links
1986 births
Living people
Men's association football midfielders
South Korean men's footballers
FC Seoul players
Gimcheon Sangmu FC players
Daegu FC players
Pohang Steelers players
Gyeongnam FC players
K League 1 players
People from Wonju
Footballers from Gangwon Province, South Korea |
https://en.wikipedia.org/wiki/Yoo%20Chang-hyun | Yoo Chang-hyun (born May 14, 1985) is a South Korea football player who plays for Seongnam FC.
Club career statistics
References
1985 births
Living people
South Korean men's footballers
Men's association football forwards
Pohang Steelers players
Gimcheon Sangmu FC players
Jeonbuk Hyundai Motors players
Seongnam FC players
Seoul E-Land FC players
K League 1 players
K League 2 players
Footballers from Gyeonggi Province |
https://en.wikipedia.org/wiki/Lee%20Gwang-jae%20%28footballer%29 | Lee Gwang-jae (hangul: 이광재, born January 1, 1980) is a retired South Korean footballer.
Club career statistics
External links
1980 births
Living people
Footballers from Seoul
South Korean men's footballers
Men's association football forwards
Gimcheon Sangmu FC players
Jeonnam Dragons players
Pohang Steelers players
Jeonbuk Hyundai Motors players
Daegu FC players
Yanbian Funde F.C. players
Goyang Zaicro FC players
China League One players
K League 1 players
K League 2 players
South Korean expatriate men's footballers
Expatriate men's footballers in China
South Korean expatriate sportspeople in China
Expatriate men's footballers in Thailand
South Korean expatriate sportspeople in Thailand |
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