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https://en.wikipedia.org/wiki/1975%E2%80%9376%20VfL%20Bochum%20season | The 1975–76 VfL Bochum season was the 38th season in club history.
Matches
Legend
Bundesliga
DFB-Pokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Sources
External links
1975–76 VfL Bochum season at Weltfussball.de
1975–76 VfL Bochum season at kicker.de
1975–76 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/Istv%C3%A1n%20Matetits | István Matetits (born 6 September 1993) is a Hungarian football player who plays for Kapuvári SE.
Club statistics
Updated to games played as of 2 June 2013.
References
External links
HLSZ
1993 births
Living people
People from Kapuvár
Hungarian men's footballers
Men's association football forwards
Győri ETO FC players
FC Ajka players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Hungarian expatriate men's footballers
Expatriate men's footballers in Austria
Hungarian expatriate sportspeople in Austria
Footballers from Győr-Moson-Sopron County |
https://en.wikipedia.org/wiki/Csan%C3%A1d%20Nov%C3%A1k | Csanád Novák (born 24 September 1994) is a Hungarian football player who plays for Nyíregyháza.
Club statistics
Updated to games played as of 28 April 2018.
References
MLSZ
HLSZ
1994 births
Living people
People from Tapolca
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Men's association football forwards
Győri ETO FC players
Kecskeméti TE players
Vasas SC players
Gyirmót FC Győr players
Mezőkövesdi SE footballers
Zalaegerszegi TE players
Szombathelyi Haladás footballers
Szolnoki MÁV FC footballers
Nyíregyháza Spartacus FC players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Footballers from Veszprém County |
https://en.wikipedia.org/wiki/Jouko%20V%C3%A4%C3%A4n%C3%A4nen | Jouko Antero Väänänen (born September 3, 1950 in Rovaniemi, Lapland) is a Finnish mathematical logician known for his contributions to set theory, model theory, logic and foundations of mathematics. He served as the vice-rector at the University of Helsinki, and a professor of mathematics at the University of Helsinki, as well as a professor of mathematical logic and foundations of mathematics at the University of Amsterdam. He completed his PhD at the University of Manchester under the supervision of Peter Aczel in 1977 with the PhD thesis entitled "Applications of set theory to generalized quantifiers". He was elected to the Finnish Academy of Science and Letters in 2002.
He served as a
member of the Senate of the University of Helsinki from 2004 to 2006 and the Treasurer of the European Mathematical Society from 2007 to 2014, as well as the Treasurer of the European Set Theory Society
since 2012.
Publications
Books
Dependence Logic, Cambridge University Press, 2007.
Models and Games, Cambridge University Press, 2011.
See also
Dependence logic
References
External links
Jouko Väänänen's home page
Jouko Väänänen in mathematics genealogy
1950 births
Living people
Finnish mathematicians
Academic staff of the University of Helsinki
Academic staff of the University of Amsterdam
Alumni of the University of Manchester
People from Rovaniemi |
https://en.wikipedia.org/wiki/J%C3%A1nos%20Nagy%20%28footballer%29 | János Nagy (born 7 August 1992) is a Hungarian striker player who plays for Romanian club Csíkszereda.
Club statistics
Updated to games played as of 27 June 2020.
Honours
Újpest
Hungarian Cup (1): 2013–14
External links
HLSZ
HLSZ
Living people
1992 births
Footballers from Szolnok
Hungarian men's footballers
Hungary men's under-21 international footballers
Men's association football midfielders
Újpest FC players
Szigetszentmiklósi TK footballers
BFC Siófok players
Kaposvári Rákóczi FC players
Kazincbarcikai SC footballers
FK Csíkszereda Miercurea Ciuc players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Nemzeti Bajnokság III players
Liga II players
21st-century Hungarian people
Hungarian expatriate men's footballers
Expatriate men's footballers in Romania
Hungarian expatriate sportspeople in Romania |
https://en.wikipedia.org/wiki/Iain%20M.%20Johnstone | Iain Murray Johnstone (born 1956) is an Australian born statistician who is the Marjorie Mhoon Fair Professor in Quantitative Science in the Department of Statistics at Stanford University.
Education
Johnstone was born in Melbourne in 1956. In 1977 he graduated in mathematics at the Australian National University, specializing in pure mathematics and statistics. Later he obtained an M.S. and a Ph.D. in statistics from Cornell University in 1981 under Lawrence D. Brown with the dissertation titled, Admissible Estimation of Poisson Means, Birth–Death Processes and Discrete Dirichlet Problems.
Research
In the 1990s, he was known for applications of wavelet methods for noise reduction in signal and image processing, and turned them in statistical decision theory. In the 2000s he turned to the theory of random matrices in multidimensional problems of statistics. In Biostatistics he cooperated with medical professionals in the application of statistical methods, particularly in cardiology and in prostate cancer.
Academic career
He joined the Department of Statistics, Stanford University after completion of his Ph.D. in 1981. He is the Marjorie Mhoon Fair Professor in Quantitative Science in the Department of Statistics at Stanford University.
Awards
He was a Guggenheim Fellow and Sloan Fellow. He was president of the Institute of Mathematical Statistics. He received the Guy Medal in Bronze 1995 and again in Silver 2010 from the Royal Statistical Society and the 1995 COPSS Presidents' Award. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. He is a member of the American Academy of Arts and Sciences and the National Academy of Sciences. He is a fellow of the American Statistical Association, the Institute for Mathematical Statistics and the American Association for the Advancement of Science.
References
External links
Home Page
1956 births
Living people
20th-century American mathematicians
21st-century Australian mathematicians
Stanford University Department of Statistics faculty
Cornell University alumni
Fellows of the American Academy of Arts and Sciences
Fellows of the American Statistical Association
Members of the United States National Academy of Sciences
Mathematical statisticians |
https://en.wikipedia.org/wiki/Ribbon%20category | In mathematics, a ribbon category, also called a tortile category, is a particular type of braided monoidal category.
Definition
A monoidal category is, loosely speaking, a category equipped with a notion resembling the tensor product (of vector spaces, say). That is, for any two objects , there is an object . The assignment is supposed to be functorial and needs to require a number of further properties such as a unit object 1 and an associativity isomorphism. Such a category is called braided if there are isomorphisms
A braided monoidal category is called a ribbon category if the category is left rigid and has a family of twists. The former means that for each object there is another object (called the left dual), , with maps
such that the compositions
equals the identity of , and similarly with . The twists are maps
,
such that
To be a ribbon category, the duals have to be thus compatible with the braiding and the twists.
Concrete Example
Consider the category of finite-dimensional vector spaces over . Suppose that is such a vector space, spanned by the basis vectors . We assign to the dual object spanned by the basis vectors . Then let us define
and its dual
(which largely amounts to assigning a given the dual ).
Then indeed we find that (for example)
and similarly for . Since this proof applies to any finite-dimensional vector space, we have shown that our structure over defines a (left) rigid monoidal category.
Then, we must define braids and twists in such a way that they are compatible. In this case, this largely makes one determined given the other on the reals. For example, if we take the trivial braiding
then , so our twist must obey . In other words it must operate elementwise across tensor products. But any object can be written in the form for some , , so our twists must also be trivial.
On the other hand, we can introduce any nonzero multiplicative factor into the above braiding rule without breaking isomorphism (at least in ). Let us for example take the braiding
Then . Since , then ; by induction, if is -dimensional, then .
Other Examples
The category of projective modules over a commutative ring. In this category, the monoidal structure is the tensor product, the dual object is the dual in the sense of (linear) algebra, which is again projective. The twists in this case are the identity maps.
A more sophisticated example of a ribbon category are finite-dimensional representations of a quantum group.
The name ribbon category is motivated by a graphical depiction of morphisms.
Variant
A strongly ribbon category is a ribbon category C equipped with a dagger structure such that the functor †: Cop → C coherently preserves the ribbon structure.
References
Monoidal categories
Dagger categories |
https://en.wikipedia.org/wiki/%C3%89tale%20homotopy%20type | In mathematics, especially in algebraic geometry, the étale homotopy type is an analogue of the homotopy type of topological spaces for algebraic varieties.
Roughly speaking, for a variety or scheme X, the idea is to consider étale coverings and to replace each connected component of U and the higher "intersections", i.e., fiber products, (n+1 copies of U, ) by a single point. This gives a simplicial set which captures some information related to X and the étale topology of it.
Slightly more precisely, it is in general necessary to work with étale hypercovers instead of the above simplicial scheme determined by a usual étale cover. Taking finer and finer hypercoverings (which is technically accomplished by working with the pro-object in simplicial sets determined by taking all hypercoverings), the resulting object is the étale homotopy type of X. Similarly to classical topology, it is able to recover much of the usual data related to the étale topology, in particular the étale fundamental group of the scheme and the étale cohomology of locally constant étale sheaves.
References
External links
http://ncatlab.org/nlab/show/étale+homotopy
Homotopy theory
Algebraic geometry |
https://en.wikipedia.org/wiki/Spectral%20expansion%20solution | In probability theory, the spectral expansion solution method is a technique for computing the stationary probability distribution of a continuous-time Markov chain whose state space is a semi-infinite lattice strip. For example, an M/M/c queue where service nodes can breakdown and be repaired has a two-dimensional state space where one dimension has a finite limit and the other is unbounded. The stationary distribution vector is expressed directly (not as a transform) in terms of eigenvalues and eigenvectors of a matrix polynomial.
References
Markov processes
Queueing theory |
https://en.wikipedia.org/wiki/Matrix%20geometric%20method | In probability theory, the matrix geometric method is a method for the analysis of quasi-birth–death processes, continuous-time Markov chain whose transition rate matrices with a repetitive block structure. The method was developed "largely by Marcel F. Neuts and his students starting around 1975."
Method description
The method requires a transition rate matrix with tridiagonal block structure as follows
where each of B00, B01, B10, A0, A1 and A2 are matrices. To compute the stationary distribution π writing π Q = 0 the balance equations are considered for sub-vectors πi
Observe that the relationship
holds where R is the Neut's rate matrix, which can be computed numerically. Using this we write
which can be solve to find π0 and π1 and therefore iteratively all the πi.
Computation of R
The matrix R can be computed using cyclic reduction or logarithmic reduction.
Matrix analytic method
The matrix analytic method is a more complicated version of the matrix geometric solution method used to analyse models with block M/G/1 matrices. Such models are harder because no relationship like πi = π1 Ri – 1 used above holds.
External links
Performance Modelling and Markov Chains (part 2) by William J. Stewart at 7th International School on Formal Methods for the Design of Computer, Communication and Software Systems: Performance Evaluation
References
Queueing theory |
https://en.wikipedia.org/wiki/Multiplicative%20sequence | In mathematics, a multiplicative sequence or m-sequence is a sequence of polynomials associated with a formal group structure. They have application in the cobordism ring in algebraic topology.
Definition
Let Kn be polynomials over a ring A in indeterminates p1, ... weighted so that pi has weight i (with p0 = 1) and all the terms in Kn have weight n (in particular Kn is a polynomial in p1, ..., pn). The sequence Kn is multiplicative if the map
is an endomorphism of the multiplicative monoid , where .
The power series
is the characteristic power series of the Kn. A multiplicative sequence is determined by its characteristic power series Q(z), and every power series with constant term 1 gives rise to a multiplicative sequence.
To recover a multiplicative sequence from a characteristic power series Q(z) we consider the coefficient of z j in the product
for any m > j. This is symmetric in the βi and homogeneous of weight j: so can be expressed as a polynomial Kj(p1, ..., pj) in the elementary symmetric functions p of the β. Then Kj defines a multiplicative sequence.
Examples
As an example, the sequence Kn = pn is multiplicative and has characteristic power series 1 + z.
Consider the power series
where Bk is the k-th Bernoulli number. The multiplicative sequence with Q as characteristic power series is denoted Lj(p1, ..., pj).
The multiplicative sequence with characteristic power series
is denoted Aj(p1,...,pj).
The multiplicative sequence with characteristic power series
is denoted Tj(p1,...,pj): these are the Todd polynomials.
Genus
The genus of a multiplicative sequence is a ring homomorphism, from the cobordism ring of smooth oriented compact manifolds to another ring, usually the ring of rational numbers.
For example, the Todd genus is associated to the Todd polynomials with characteristic power series .
References
Polynomials
Topological methods of algebraic geometry |
https://en.wikipedia.org/wiki/Paracompact%20uniform%20honeycombs | In geometry, uniform honeycombs in hyperbolic space are tessellations of convex uniform polyhedron cells. In 3-dimensional hyperbolic space there are 23 Coxeter group families of paracompact uniform honeycombs, generated as Wythoff constructions, and represented by ring permutations of the Coxeter diagrams for each family. These families can produce uniform honeycombs with infinite or unbounded facets or vertex figure, including ideal vertices at infinity, similar to the hyperbolic uniform tilings in 2-dimensions.
Regular paracompact honeycombs
Of the uniform paracompact H3 honeycombs, 11 are regular, meaning that their group of symmetries acts transitively on their flags. These have Schläfli symbol {3,3,6}, {6,3,3}, {3,4,4}, {4,4,3}, {3,6,3}, {4,3,6}, {6,3,4}, {4,4,4}, {5,3,6}, {6,3,5}, and {6,3,6}, and are shown below. Four have finite Ideal polyhedral cells: {3,3,6}, {4,3,6}, {3,4,4}, and {5,3,6}.
Coxeter groups of paracompact uniform honeycombs
This is a complete enumeration of the 151 unique Wythoffian paracompact uniform honeycombs generated from tetrahedral fundamental domains (rank 4 paracompact coxeter groups). The honeycombs are indexed here for cross-referencing duplicate forms, with brackets around the nonprimary constructions.
The alternations are listed, but are either repeats or don't generate uniform solutions. Single-hole alternations represent a mirror removal operation. If an end-node is removed, another simplex (tetrahedral) family is generated. If a hole has two branches, a Vinberg polytope is generated, although only Vinberg polytope with mirror symmetry are related to the simplex groups, and their uniform honeycombs have not been systematically explored. These nonsimplectic (pyramidal) Coxeter groups are not enumerated on this page, except as special cases of half groups of the tetrahedral ones. Six uniform honeycombs that arise here as alternations have been numbered 152 to 157, after the 151 Wythoffian forms not requiring alternation for their construction.
The complete list of nonsimplectic (non-tetrahedral) paracompact Coxeter groups was published by P. Tumarkin in 2003. The smallest paracompact form in H3 can be represented by or , or [∞,3,3,∞] which can be constructed by a mirror removal of paracompact hyperbolic group [3,4,4] as [3,4,1+,4] : = . The doubled fundamental domain changes from a tetrahedron into a quadrilateral pyramid. Another pyramid is or , constructed as [4,4,1+,4] = [∞,4,4,∞] : = .
Removing a mirror from some of the cyclic hyperbolic Coxeter graphs become bow-tie graphs: [(3,3,4,1+,4)] = [((3,∞,3)),((3,∞,3))] or , [(3,4,4,1+,4)] = [((4,∞,3)),((3,∞,4))] or , [(4,4,4,1+,4)] = [((4,∞,4)),((4,∞,4))] or . = , = , = .
Another nonsimplectic half groups is ↔ .
A radical nonsimplectic subgroup is ↔ , which can be doubled into a triangular prism domain as ↔ .
Linear graphs
[6,3,3] family
[6,3,4] family
There are 15 forms, generated by ring permutations of the Coxeter group: [6,3,4] o |
https://en.wikipedia.org/wiki/Parshin%27s%20conjecture | In mathematics, more specifically in algebraic geometry, Parshin's conjecture (also referred to as the Beilinson–Parshin conjecture) states that for any smooth projective variety X defined over a finite field, the higher algebraic K-groups vanish up to torsion:
It is named after Aleksei Nikolaevich Parshin and Alexander Beilinson.
Finite fields
The conjecture holds if by Quillen's computation of the K-groups of finite fields, showing in particular that they are finite groups.
Curves
The conjecture holds if by the proof of Corollary 3.2.3 of Harder.
Additionally, by Quillen's finite generation result (proving the Bass conjecture for the K-groups in this case) it follows that the K-groups are finite if .
References
Algebraic geometry
Algebraic K-theory
Conjectures |
https://en.wikipedia.org/wiki/Syria%20national%20football%20team%20records%20and%20statistics | The following is a list of the Syria national football team's competitive records and statistics. Their first international match was played on 19 April 1942 in Beirut against Lebanon, winning 2–1. The team they have played the most is Jordan, with a total of 40 matches played.
Individual records
Player records
Players in bold are still active with Syria.
Most capped players
Top goalscorers
Age records
Oldest player to make debut: Firas Al-Khatib, aged 36 years and 94 days vs , 5 September 2019
Youngest player to make debut: Abdelrazaq Al-Hussain, aged 17 years and 82 days vs , 07 Dec 2002
Oldest player to score: Firas Al-Khatib, aged 36 years and 94 days vs , 5 September 2019
Manager records
Team records
Wins
Largest win
13–0 vs Muscat and Oman on 6 September 1965
12–0 vs on 4 June 1997
12–0 vs on 30 April 2001
Largest home win
13–0 vs Muscat and Oman on 6 September 1965
Largest away win
12–0 vs on 4 June 1997
Largest win at the Asian Cup
2–1 vs on 9 January 2011
2–1 vs on 12 December 1996
Draws
Highest scoring draw
3–3 vs on 17 October 1998
3–3 vs on 18 May 2001
Highest scoring draw at the Asian Cup
1–1 vs on 1 December 1984
Defeats
Largest defeat
8–0 vs on 25 November 1949
8–0 vs on 16 October 1951
7–0 vs on 20 November 1949
Largest defeat at home
1–7 vs on 21 June 2004
Largest defeat away
8–0 vs on 25 November 1949
8–0 vs on 16 October 1951
Largest defeat at the Asian Cup
3–0 vs on 9 December 1996
3–0 vs on 4 December 1988
Attendance
Highest home attendance
50,000, vs , 30 March 1989
Highest away attendance
100,000, vs , 13 June 1997
World rankings
FIFA
Source: FIFA.com
Highest FIFA ranking 68th (July 2018)
Lowest FIFA ranking 152nd (September 2014, March 2015)
Elo
Source: Eloratings.net
Highest Elo ranking 53rd (October 1974)
Lowest Elo ranking 125th (September 1984)
Goal records
General
First goal Mudhafar Al-Aqqad vs on 1 August 1953
Most goals Firas Al-Khatib (2001–2019), 36 goals
. Highlighted names denote a player still playing or available for selection.
Hat-tricks
In major tournaments
AFC Asian Cup
Most goals in a single Asian Cup tournament Jamal Keshek (in 1980), 2 goalsNader Joukhadar (in 1996), 2 goals Abdelrazaq Al-Hussain (in 2011), 2 goals
Most goals in total at Asian Cup tournaments Walid Abu Al-Sel (in 1984, 1988), 2 goalsJamal Keshek (in 1980), 2 goalsNader Joukhadar (in 1996), 2 goals Abdelrazaq Al-Hussain (in 2011), 2 goals
Most goals in a single Asian Cup finals match A. Al-Hussain, 2 goals vs on 9 January 2011
First goal in an Asian Cup finals match Jamal Keshek, vs on 19 September 1980
Competition records
FIFA World Cup
*Denotes draws include knockout matches decided via penalty shoot-out.
AFC Asian Cup
*Denotes draws include knockout matches decided via penalty shoot-out.
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Olympic Games
*Denotes draws include knockout matches decided via penalty shoot-out.
WAFF Champion |
https://en.wikipedia.org/wiki/M/D/c%20queue | In queueing theory, a discipline within the mathematical theory of probability, an M/D/c queue represents the queue length in a system having c servers, where arrivals are determined by a Poisson process and job service times are fixed (deterministic). The model name is written in Kendall's notation. Agner Krarup Erlang first published on this model in 1909, starting the subject of queueing theory. The model is an extension of the M/D/1 queue which has only a single server.
Model definition
An M/D/c queue is a stochastic process whose state space is the set {0,1,2,3,...} where the value corresponds to the number of customers in the system, including any currently in service.
Arrivals occur at rate λ according to a Poisson process and move the process from state i to i + 1.
Service times are deterministic time D (serving at rate μ = 1/D).
c servers serve customers from the front of the queue, according to a first-come, first-served discipline. When the service is complete the customer leaves the queue and the number of customers in the system reduces by one.
The buffer is of infinite size, so there is no limit on the number of customers it can contain.
Waiting time distribution
Erlang showed that when ρ = (λ D)/c < 1, the waiting time distribution has distribution F(y) given by
Crommelin showed that, writing Pn for the stationary probability of a system with n or fewer customers,
References
Single queueing nodes |
https://en.wikipedia.org/wiki/Hermite%E2%80%93Minkowski%20theorem | In mathematics, especially in algebraic number theory, the Hermite–Minkowski theorem states that for any integer N there are only finitely many number fields, i.e., finite field extensions K of the rational numbers Q, such that the discriminant of K/Q is at most N. The theorem is named after Charles Hermite and Hermann Minkowski.
This theorem is a consequence of the estimate for the discriminant
where n is the degree of the field extension, together with Stirling's formula for n!. This inequality also shows that the discriminant of any number field strictly bigger than Q is not ±1, which in turn implies that Q has no unramified extensions.
References
Section III.2
Theorems in algebraic number theory |
https://en.wikipedia.org/wiki/Jannis%20Schliesing | Jannis Schliesing (born 5 January 1992) is a German football forward.
Statistics
References
External links
1992 births
Living people
Footballers from Münster
German men's footballers
Men's association football forwards
Rot-Weiß Oberhausen players
VfL Bochum II players
1. FC Bocholt players
3. Liga players |
https://en.wikipedia.org/wiki/Effect%20Model%20law | The Effect Model law states that a natural relationship exists for each individual between the frequency (observation) or the probability (prediction) of a morbid event without any treatment and the frequency or probability of the same event with a treatment . This relationship applies to a single individual, individuals within a population, or groups.
This law enables the prediction of the (absolute) benefit () of a treatment for a given patient. It has wide-reaching implications in R&D for new pharmaceutical products as well as personalized medicine.
The law was serendipitously discovered in the 1990s by Jean-Pierre Boissel. While studying the effectiveness of class-I antiarrhythmic drugs in the prevention of death after myocardial infarction, he stumbled upon a situation which contradicts one of the basic premises of meta-analysis theory, i.e. that the heterogeneity test was significant at the same time for the assumption “the relative risk () is a constant” and “ is a constant”.
Boissel formulated the hypothesis that the antiarrhythmic drugs efficacy was a function combining a beneficial effect () that is proportional to and a constant adverse effect (), independent of . The mathematical expression of this model is a linear equation with two parameters, the risk of lethal adverse event caused by treatment and the slope of the line which represents the true beneficial risk reduction. This equation gives the treatment net mortality reduction:
Illustration in the (Rc,Rt) plane
In 1987, L'Abbe, Detsky and O'Rourke recommended including a graphical representation of the various trials while designing a meta-analysis. For each trial, on the x-axis the frequency (risk) of the studied criterion in the control group should be represented, and on the y-axis, the risk in the treated group ( and ).
The shape of the resulting scatter plot illustrates some important aspects of the information concerning the effect of the treatment:
On an individual basis, the ability to measure and predict the absolute benefit of a treatment for a patient characterized by his or her idiosyncratic risk parameters (e.g., cholesterol level, systolic blood pressure, etc.);
Over a given population (e.g., French, Chinese, etc.), the ability to measure and predict health outcomes for a treatment available on the market or a drug candidate at any stage in the R&D process (from the target identification phase to clinical trials).
The law is expressed in two ways.
the function: or , equation in which is implicit.
the absolute benefit function : , equation in which and are implicit.
The forms above lead to as many values in the plane as there are patients, each one being represented by a dot which is more or less close to the neutrality frontier. The expression of the absolute benefit (i.e. the vertical distance to the neutrality frontier) has the advantage of leading directly to an individual prediction, making personalized medicine a practical reality. The |
https://en.wikipedia.org/wiki/Simplicial%20presheaf | In mathematics, more specifically in homotopy theory, a simplicial presheaf is a presheaf on a site (e.g., the category of topological spaces) taking values in simplicial sets (i.e., a contravariant functor from the site to the category of simplicial sets). Equivalently, a simplicial presheaf is a simplicial object in the category of presheaves on a site. The notion was introduced by A. Joyal in the 1970s. Similarly, a simplicial sheaf on a site is a simplicial object in the category of sheaves on the site.
Example: Consider the étale site of a scheme S. Each U in the site represents the presheaf . Thus, a simplicial scheme, a simplicial object in the site, represents a simplicial presheaf (in fact, often a simplicial sheaf).
Example: Let G be a presheaf of groupoids. Then taking nerves section-wise, one obtains a simplicial presheaf . For example, one might set . These types of examples appear in K-theory.
If is a local weak equivalence of simplicial presheaves, then the induced map is also a local weak equivalence.
Homotopy sheaves of a simplicial presheaf
Let F be a simplicial presheaf on a site. The homotopy sheaves of F is defined as follows. For any in the site and a 0-simplex s in F(X), set and . We then set to be the sheaf associated with the pre-sheaf .
Model structures
The category of simplicial presheaves on a site admits many different model structures.
Some of them are obtained by viewing simplicial presheaves as functors
The category of such functors is endowed with (at least) three model structures, namely the projective, the Reedy, and the injective model structure. The weak equivalences / fibrations in the first are maps
such that
is a weak equivalence / fibration of simplicial sets, for all U in the site S. The injective model structure is similar, but with weak equivalences and cofibrations instead.
Stack
A simplicial presheaf F on a site is called a stack if, for any X and any hypercovering H →X, the canonical map
is a weak equivalence as simplicial sets, where the right is the homotopy limit of
.
Any sheaf F on the site can be considered as a stack by viewing as a constant simplicial set; this way, the category of sheaves on the site is included as a subcategory to the homotopy category of simplicial presheaves on the site. The inclusion functor has a left adjoint and that is exactly .
If A is a sheaf of abelian group (on the same site), then we define by doing classifying space construction levelwise (the notion comes from the obstruction theory) and set . One can show (by induction): for any X in the site,
where the left denotes a sheaf cohomology and the right the homotopy class of maps.
See also
cubical set
N-group (category theory)
Notes
Further reading
Konrad Voelkel, Model structures on simplicial presheaves
References
B. Toën, Simplicial presheaves and derived algebraic geometry
External links
J.F. Jardine's homepage
Homotopy theory
Simplicial sets
Functors |
https://en.wikipedia.org/wiki/Chern%20Prize%20%28ICCM%29 | The Chern Prize in Mathematics was established in in honor of Professor Shiing-Shen Chern. The Chern Prize is presented every three years at the International Congress of Chinese Mathematicians to Chinese mathematicians and those of Chinese descent for "exceptional contributions to mathematical research or to public service activities in support of mathematics". Winners are selected by a committee of mathematicians to recognize the achievements of mathematicians of Chinese descent. In 2010, a special commemorative event was held in Beijing in addition to the normal award presentation to celebrate the centennial of Professor Chern's birth.
Past winners
See also
Morningside Medal
List of mathematics awards
References
Mathematics awards |
https://en.wikipedia.org/wiki/Morningside%20Medal | The Morningside Medal of Mathematics () is awarded to exceptional mathematicians of Chinese descent under the age of forty-five for their seminal achievements in mathematics and applied mathematics. The winners of the Morningside Medal of Mathematics are traditionally announced at the opening ceremony of the triennial International Congress of Chinese Mathematicians. Each Morningside Medalist receives a certificate, a medal, and cash award of US$25,000 for a gold medal, or US$10,000 for a silver medal.
Gold Medalists
Silver Medalists
See also
List of mathematics awards
References
Mathematics awards
Awards with age limits |
https://en.wikipedia.org/wiki/2013%E2%80%9314%20Queens%20Park%20Rangers%20F.C.%20season | The 2013–14 season was Queens Park Rangers's 125th professional season.
Players
As of 19 February 2014
First team squad
Loaned out
Transfers
In
Out
Loans in
Loans out
Season statistics
League table
l
Results summary
Results by matchday
Fixtures & results
Pre-season
Championship
Championship play-offs
Semi-final
Final
FA Cup
League Cup
Player statistics
Appearances, goals and discipline
Goalscorers
Clean sheets
References
Notes
Queens Park Rangers F.C. seasons
Queens Park Rangers |
https://en.wikipedia.org/wiki/Pull%20back%20%28disambiguation%29 | Pull back or pullback may refer to:
In mathematics
Pullback, a name given to two different mathematical processes
Pullback (cohomology), a term in topology
Pullback (differential geometry), a term in differential geometry
Pullback (category theory), a term in category theory
Pullback attractor, an aspect of a random dynamical system
Pullback bundle, the fiber bundle induced by a map of its base space
Other
Pull-back (finance), a term in financial trading
Pullback motor, a clockwork motor often used in toy cars
Euscirrhopterus poeyi, known as the pullback moth
Iijima Bishop Pullback, an opening in the game of shogi
The opposite of a pushback (migration) |
https://en.wikipedia.org/wiki/Henk%20Bos | Henk Bos may refer to:
Henk Bos (painter) (1901–1979), Dutch painter
Henk J. M. Bos (born 1940), Dutch historian of mathematics
Henk Bos (footballer) (born 1992), Dutch footballer
Henk Bos (speedway rider), see 2010 Individual Speedway European Championship |
https://en.wikipedia.org/wiki/2004%E2%80%9305%20FK%20Partizan%20season | The 2004–05 season was the 59th season in FK Partizan's existence. This article shows player statistics and all matches (official and friendly) that the club played during the 2004–05 season.
Players
Squad information
Transfers
In
Out
Loan in
Loan out
Friendlies
Competitions
First League of Serbia and Montenegro
Overview
League table
Serbia and Montenegro Cup
UEFA Cup
Second Qualifying Round
First round
Group E
Round of 32
Round of 16
See also
List of FK Partizan seasons
List of unbeaten football club seasons
References
External links
Official website
Partizanopedia 2004-2005 (in Serbian)
FK Partizan seasons
Partizan
Serbian football championship-winning seasons |
https://en.wikipedia.org/wiki/2005%E2%80%9306%20FK%20Partizan%20season | The 2005–06 season was the 60th season in FK Partizan's existence. This article shows player statistics and all matches (official and friendly) that the club played during the 2005–06 season.
Players
Squad information
Squad statistics
Transfers
In
Out
Loan in
Loan out
Competitions
Overview
Serbia and Montenegro SuperLiga
League table
Serbia and Montenegro Cup
UEFA Champions League
Second qualifying round
Third qualifying round
UEFA Cup
First round
See also
List of FK Partizan seasons
References
External links
Official website
Partizanopedia 2005-2006 (in Serbian)
FK Partizan seasons
Partizan |
https://en.wikipedia.org/wiki/Markov%E2%80%93Krein%20theorem | In probability theory, the Markov–Krein theorem gives the best upper and lower bounds on the expected values of certain functions of a random variable where only the first moments of the random variable are known. The result is named after Andrey Markov and Mark Krein.
The theorem can be used to bound average response times in the M/G/k queueing system.
References
Probability theorems |
https://en.wikipedia.org/wiki/2002%E2%80%9303%20FK%20Partizan%20season | The 2002–03 season was FK Partizan's 11th season in First League of Serbia and Montenegro. This article shows player statistics and all matches (official and friendly) that the club played during the 2002–03 season.
Players
Squad information
Squad statistics
Top scorers
Includes all competitive matches. The list is sorted by shirt number when total goals are equal.
Competitions
Overview
First League
Serbia and Montenegro Cup
Partizan will participate in the 1st Serbia and Montenegro Cup starting in 1/16 Round.
UEFA Champions League
Second Qualifying Round
Third Qualifying Round
UEFA Cup
First round
Second round
References
FK Partizan seasons
Partizan
Serbian football championship-winning seasons |
https://en.wikipedia.org/wiki/Decomposition%20method%20%28queueing%20theory%29 | In queueing theory, a discipline within the mathematical theory of probability, the decomposition method is an approximate method for the analysis of queueing networks where the network is broken into subsystems which are independently analyzed.
The individual queueing nodes are considered to be independent G/G/1 queues where arrivals are governed by a renewal process and both service time and arrival distributions are parametrised to match the first two moments of data.
References
Queueing theory |
https://en.wikipedia.org/wiki/Hironaka%27s%20example | In geometry, Hironaka's example is a non-Kähler complex manifold that is a deformation of Kähler manifolds found by . Hironaka's example can be used to show that several other plausible statements holding for smooth varieties of dimension at most 2 fail for smooth varieties of dimension at least 3.
Hironaka's example
Take two smooth curves C and D in a smooth projective 3-fold P, intersecting in two points c and d that are nodes for the reducible curve . For some applications these should be chosen so that there is a fixed-point-free automorphism exchanging the curves C and D and also exchanging the points c and d. Hironaka's example V is obtained by gluing two quasi-projective varieties and . Let be the variety obtained by blowing up along and then along the strict transform of , and let be the variety obtained by blowing up along D and then along the strict transform of C. Since these are isomorphic over , they can be glued, which results in a proper variety V. Then V has two smooth rational curves L and M lying over c and d such that is algebraically equivalent to 0, so V cannot be projective.
For an explicit example of this configuration, take t to be a point of order 2 in an elliptic curve E, take P to be , take C and D to be the sets of points of the form and , so that c and d are the points (0,0,0) and , and take the involution σ to be the one taking to .
A complete abstract variety that is not projective
Hironaka's variety is a smooth 3-dimensional complete variety but is not projective as it has a non-trivial curve algebraically equivalent to 0. Any 2-dimensional smooth complete variety is projective, so 3 is the smallest possible dimension for such an example. There are plenty of 2-dimensional complex manifolds that are not algebraic, such as Hopf surfaces (non Kähler) and non-algebraic tori (Kähler).
An effective cycle algebraically equivalent to 0
In a projective variety, a nonzero effective cycle has non-zero degree so cannot be algebraically equivalent to 0. In Hironaka's example the effective cycle consisting of the two exceptional curves is algebraically equivalent to 0.
A deformation of Kähler manifolds that is not a Kähler manifold
If one of the curves D in Hironaka's construction is allowed to vary in a family such that most curves of the family do not intersect D, then one obtains a family of manifolds such that most are projective but one is not. Over the complex numbers this gives a deformation of smooth Kähler (in fact projective) varieties that is not Kähler. This family is trivial in the smooth category, so in particular there are Kähler and non-Kähler smooth compact 3-dimensional complex manifolds that are diffeomorphic.
A smooth algebraic space that is not a scheme
Choose C and D so that P has an automorphism σ of order 2 acting freely on P and exchanging C and D, and also exchanging c and d. Then the quotient of V by the action of σ is a smooth 3-dimensional algebraic space with an irreducible c |
https://en.wikipedia.org/wiki/Classifying%20topos | In mathematics, a classifying topos for some sort of structure is a topos T such that there is a natural equivalence between geometric morphisms from a cocomplete topos E to T and the category of models for the structure in E.
Examples
The classifying topos for objects of a topos is the topos of presheaves over the opposite of the category of finite sets.
The classifying topos for rings of a topos is the topos of presheaves over the opposite of the category of finitely presented rings.
The classifying topos for local rings of a topos is the topos of sheaves over the opposite of the category of finitely presented rings with the Zariski topology.
The classifying topos for linear orders with distinct largest and smallest elements of a topos is the topos of simplicial sets.
If G is a discrete group, the classifying topos for G-torsors over a topos is the topos BG of G-sets.
The classifying space of topological groups in homotopy theory.
References
External links
Topos theory |
https://en.wikipedia.org/wiki/Spherical%20basis | In pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions.
While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using polar and azimuthal angles and radial distance, the spherical basis are constructed from the standard basis and use complex numbers.
In three dimensions
A vector A in 3D Euclidean space can be expressed in the familiar Cartesian coordinate system in the standard basis ex, ey, ez, and coordinates Ax, Ay, Az:
or any other coordinate system with associated basis set of vectors. From this extend the scalars to allow multiplication by complex numbers, so that we are now working in rather than .
Basis definition
In the spherical bases denoted e+, e−, e0, and associated coordinates with respect to this basis, denoted A+, A−, A0, the vector A is:
where the spherical basis vectors can be defined in terms of the Cartesian basis using complex-valued coefficients in the xy plane:
in which denotes the imaginary unit, and one normal to the plane in the z direction:
The inverse relations are:
Commutator definition
While giving a basis in a 3-dimensional space is a valid definition for a spherical tensor, it only covers the case for when the rank is 1. For higher ranks, one may use either the commutator, or rotation definition of a spherical tensor. The commutator definition is given below, any operator that satisfies the following relations is a spherical tensor:
Rotation definition
Analogously to how the spherical harmonics transform under a rotation, a general spherical tensor transforms as follows, when the states transform under the unitary Wigner D-matrix , where is a (3×3 rotation) group element in SO(3). That is, these matrices represent the rotation group elements. With the help of its Lie algebra, one can show these two definitions are equivalent.
Coordinate vectors
For the spherical basis, the coordinates are complex-valued numbers A+, A0, A−, and can be found by substitution of () into (), or directly calculated from the inner product , ():
with inverse relations:
In general, for two vectors with complex coefficients in the same real-valued orthonormal basis ei, with the property ei·ej = δij, the inner product is:
where · is the usual dot product and the complex conjugate * must be used to keep the magnitude (or "norm") of the vector positive definite.
Properties (three dimensions)
Orthonormality
The spherical basis is an orthonormal basis, since the inner product , () of every pair vanishes meaning the basis vectors are all mutually orthogonal:
and each basis vector is a unit vector:
hence the need for the normalizing factors of .
Change of basis matrix
The defining relations () can be summarized by a tra |
https://en.wikipedia.org/wiki/Tensor%20operator | In pure and applied mathematics, quantum mechanics and computer graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. The coordinate-free generalization of a tensor operator is known as a representation operator.
The general notion of scalar, vector, and tensor operators
In quantum mechanics, physical observables that are scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor depends on how it is viewed by two observers whose coordinate frames are related to each other by a rotation. Alternatively, one may ask how, for a single observer, a physical quantity transforms if the state of the system is rotated. Consider, for example, a system consisting of a molecule of mass , traveling with a definite center of mass momentum, , in the direction. If we rotate the system by about the axis, the momentum will change to , which is in the direction. The center-of-mass kinetic energy of the molecule will, however, be unchanged at . The kinetic energy is a scalar and the momentum is a vector, and these two quantities must be represented by a scalar and a vector operator, respectively. By the latter in particular, we mean an operator whose expected values in the initial and the rotated states are and . The kinetic energy on the other hand must be represented by a scalar operator, whose expected value must be the same in the initial and the rotated states.
In the same way, tensor quantities must be represented by tensor operators. An example of a tensor quantity (of rank two) is the electrical quadrupole moment of the above molecule. Likewise, the octupole and hexadecapole moments would be tensors of rank three and four, respectively.
Other examples of scalar operators are the total energy operator (more commonly called the Hamiltonian), the potential energy, and the dipole-dipole interaction energy of two atoms. Examples of vector operators are the momentum, the position, the orbital angular momentum, , and the spin angular momentum, . (Fine print: Angular momentum is a vector as far as rotations are concerned, but unlike position or momentum it does not change sign under space inversion, and when one wishes to provide this information, it is said to be a pseudovector.)
Scalar, vector and tensor operators can also be formed by products of operators. For example, the scalar product of the two vector operators, and , is a scalar operator, which figures prominently in discussions of the spin–orbit interaction. Similarly, the quadrupole moment tensor of our example molecule has the nine components
Here, the indices and can independently take on the values 1, |
https://en.wikipedia.org/wiki/Crime%20in%20Cuba | Though the Cuban government does not release official crime statistics, Cuba is considered one of the safer countries in Latin America. Gun crime is virtually nonexistent, drug trafficking has been largely curtailed, and there is below-average crisis intervention from police. Murder rates are also below those of most Latin American countries, with an intentional homicide rate of 5.00/100,000 inhabitants (572 intentional homicides) in 2016, lower than any other country in the region.Cuba's historical, political, and economic evolution has greatly impacted the types and the prevalence of crime in the country. Indeed, the Cuban Revolution led by Fidel Castro ushered the beginning of the Communist Party's rule in Cuba, which remains the sole ruling party of Cuba to this day. Under the socialist system, the government has focused on crime prevention through efforts such as community policing, education, and social programs. The government has also focused on addressing the root causes of crime, such as poverty and inequality, and promoting social cohesion and solidarity among citizens.
At the same time, the authoritarian nature of the regime has allowed for the strict surveillance of its citizens, raising questions about civil liberties infringements in the government's attempts to reduce crime. The government has also used the strong presence of law enforcement agencies, such as the National Revolutionary Police (PNR), to maintain social order and prevent crime. The government's control over law enforcement agencies, including their structure, operations, and information dissemination, has resulted in limited availability of official crime statistics and concerns about the reliability of state-reported information. These factors make it challenging to accurately assess the crime situation in Cuba.
History
Cuba's history has been shaped by various political and social changes, including colonization, independence struggles, revolutions, and economic challenges. These factors have influenced the crime landscape in Cuba.
19th Century
During the colonial period, Cuba was a Spanish colony and experienced high levels of crime, including piracy, smuggling, and illegal slave trading.
For instance, despite Spain declaring the abolition of the slave trade in its colonies in 1811 through the Spanish Constitution of Cádiz, slavery persisted in Cuba for the remainder of the century. One of the main reasons for the persistence of slavery in Cuba was the island's thriving sugar industry, which heavily relied on enslaved labor. The increasing demand for labor in the sugarcane plantations led to an increase in the illegal slave trade as well, with plantation owners and traders importing enslaved people from Africa despite it being banned. Additionally, the Spanish government in Cuba did not actively enforce the ban on slavery, and there was widespread corruption among local officials who turned a blind eye to the illegal slave trade. The wealthy planters in Cuba |
https://en.wikipedia.org/wiki/Beilinson%20regulator | In mathematics, especially in algebraic geometry, the Beilinson regulator is the Chern class map from algebraic K-theory to Deligne cohomology:
Here, X is a complex smooth projective variety, for example. It is named after Alexander Beilinson. The Beilinson regulator features in Beilinson's conjecture on special values of L-functions.
The Dirichlet regulator map (used in the proof of Dirichlet's unit theorem) for the ring of integers of a number field F
is a particular case of the Beilinson regulator. (As usual, runs over all complex embeddings of F, where conjugate embeddings are considered equivalent.) Up to a factor 2, the Beilinson regulator is also generalization of the Borel regulator.
References
Algebraic geometry
Algebraic K-theory |
https://en.wikipedia.org/wiki/Asian%20Journal | Asian Journal may refer to
Asian Journal of Communication
Asian Journal of Distance Education
Asian Journal of International Law
Asian Journal of Mathematics
Asian Journal of Pentecostal Studies
Asian Journal of Public Affairs
Asian Journal of Pharmaceutics
Asian Journal of Social Psychology
Asian Journal of Transfusion Science
The Journal of Asian Studies
Asian Journal (newspaper), a Filipino-American newspaper |
https://en.wikipedia.org/wiki/Ingleton%27s%20inequality | In mathematics, Ingleton's inequality is an inequality that is satisfied by the rank function of any representable matroid. In this sense it is a necessary condition for representability of a matroid over a finite field. Let M be a matroid and let ρ be its rank function, Ingleton's inequality states that for any subsets X1, X2, X3 and X4 in the support of M, the inequality
ρ(X1)+ρ(X2)+ρ(X1∪X2∪X3)+ρ(X1∪X2∪X4)+ρ(X3∪X4) ≤ ρ(X1∪X2)+ρ(X1∪X3)+ρ(X1∪X4)+ρ(X2∪X3)+ρ(X2∪X4) is satisfied.
Aubrey William Ingleton, an English mathematician, wrote an important paper in 1969 in which he surveyed the representability problem in matroids. Although the article is mainly expository, in this paper Ingleton stated and proved Ingleton's inequality, which has found interesting applications in information theory, matroid theory, and network coding.
Importance of inequality
There are interesting connections between matroids, the entropy region and group theory. Some of those connections are revealed by Ingleton's Inequality.
Perhaps, the more interesting application of Ingleton's inequality concerns the computation of network coding capacities. Linear coding solutions are constrained by the inequality and it has an important consequence:
The region of achievable rates using linear network coding could be, in some cases, strictly smaller than the region of achievable rates using general network coding.
For definitions see, e.g.
Proof
Theorem (Ingleton's inequality): Let M be a representable matroid with rank function ρ and let X1, X2, X3 and X4 be subsets of the support set of M, denoted by the symbol E(M). Then:
ρ(X1)+ρ(X2)+ρ(X1∪X2∪X3)+ρ(X1∪X2∪X4)+ρ(X3∪X4) ≤ ρ(X1∪X2)+ρ(X1∪X3)+ρ(X1∪X4)+ρ(X2∪X3)+ρ(X2∪X4).
To prove the inequality we have to show the following result:
Proposition: Let V1,V2, V3 and V4 be subspaces of a vector space V, then
dim(V1∩V2∩V3) ≥ dim(V1∩V2) + dim(V3) − dim(V1+V3) − dim(V2+V3) + dim(V1+V2+V3)
dim(V1∩V2∩V3∩V4) ≥ dim(V1∩V2∩V3) + dim(V1∩V2∩V4) − dim(V1∩V2)
dim(V1∩V2∩V3∩V4) ≥ dim(V1∩V2) + dim(V3) + dim(V4) − dim(V1+V3) − dim(V2+V3) − dim(V1+V4) − dim(V2+V4) − dim(V1+V2+V3) + dim(V1+V2+V4)
dim (V1) + dim(V2) + dim(V1+V2+V3) + dim(V1+V2+V4) + dim(V3+V4) ≤ dim(V1+V2) + dim(V1+V3) + dim(V1+V4) + dim(V2+V3) + dim(V2+V4)
Where Vi+Vj represent the direct sum of the two subspaces.
Proof (proposition): We will use frequently the standard vector space identity:
dim(U) + dim(W) = dim(U+W) + dim(U∩W).
1. It is clear that (V1∩V2) + V3 ⊆ (V1+ V3) ∩ (V2+V3), then
2. It is clear that (V1∩V2∩V3) + (V1∩V2∩V4) ⊆ (V1∩V2), then
3. From (1) and (2) we have:
4. From (3) we have
If we add (dim(V1)+dim(V2)+dim(V3+V4)) at both sides of the last inequality, we get
Since the inequality dim(V1∩V2∩V3∩V4) ≤ dim(V3∩V4) holds, we have finished with the proof.♣
Proof (Ingleton's inequality): Suppose that M is a representable matroid and let A = [v1 v2 … vn] be a mat |
https://en.wikipedia.org/wiki/Spherinder | In four-dimensional geometry, the spherinder, or spherical cylinder or spherical prism, is a geometric object, defined as the Cartesian product of a 3-ball (or solid 2-sphere) of radius r1 and a line segment of length 2r2:
Like the duocylinder, it is also analogous to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment.
It can be seen in 3-dimensional space by stereographic projection as two concentric spheres, in a similar way that a tesseract (cubic prism) can be projected as two concentric cubes, and how a circular cylinder can be projected into 2-dimensional space as two concentric circles.
Relation to other shapes
In 3-space, a cylinder can be considered intermediate between a cube and a sphere. In 4-space there are three intermediate forms between the tesseract and the hypersphere. Altogether, they are the:
tesseract (1-ball × 1-ball × 1-ball × 1-ball), whose hypersurface is eight cubes connected at 24 squares
cubinder (2-ball × 1-ball × 1-ball)
spherinder (3-ball × 1-ball), whose hypersurface is two 3-balls and a tube-like cell connected at the respective bounding spheres of the 3-balls
duocylinder (2-ball × 2-ball)
glome (4-ball), whose hypersurface is a 3-sphere without any connecting boundaries.
These constructions correspond to the five partitions of 4, the number of dimensions.
If the two ends of a spherinder are connected together, or equivalently if a sphere is dragged around a circle perpendicular to its 3-space, it traces out a spheritorus. If the two ends of an uncapped spherinder are rolled inward, the resulting shape is a torisphere.
Spherindrical coordinate system
One can define a "spherindrical" coordinate system , consisting of spherical coordinates with an extra coordinate . This is analogous to how cylindrical coordinates are defined: and being polar coordinates with an elevation coordinate . Spherindrical coordinates can be converted to Cartesian coordinates using the formulas where is the radius, is the zenith angle, is the azimuthal angle, and is the height. Cartesian coordinates can be converted to spherindrical coordinates using the formulas The hypervolume element for spherindrical coordinates is which can be derived by computing the Jacobian.
Measurements
Hypervolume
Given a spherinder with a spherical base of radius and a height , the hypervolume of the spherinder is given by
Surface volume
The surface volume of a spherinder, like the surface area of a cylinder, is made up of three parts:
the volume of the top base:
the volume of the bottom base:
the volume of the lateral 3D surface: , which is the surface area of the spherical base times the height
Therefore, the total surface volume is
Proof
The above formulas for hypervolume and surface volume can be proven using integration. The hypervolume of an arbitrary 4D region is given by the quadruple integral
The hypervolume of the spherinder can be integrated over spherindrical coordinates.
Rela |
https://en.wikipedia.org/wiki/2013%E2%80%9314%20PFC%20CSKA%20Sofia%20season | The 2013–14 season was PFC CSKA Sofia's 66th consecutive season in A Group. This article shows player statistics and all matches (official and friendly) that the club will play during the 2013–14 season.
Players
Squad stats
Appearances for competitive matches only
|-
|colspan="14"|Players sold or loaned out after the start of the season:
|}
As of 17 May 2014
Top scorers
As of 17 May 2014
Disciplinary record
As of 17 May 2014
Players in/out
Summer transfers
In:
Out:
Winter transfers
In:
Out:
Pre-season and friendlies
Pre-season
On-season (autumn)
Mid-season
On-season (spring)
Competitions
A Group
First phase
Table
Results summary
Results by round
Fixtures and results
Championship group
Table
Results summary
Results by round
Fixtures and results
Bulgarian Cup
See also
PFC CSKA Sofia
References
External links
CSKA Official Site
CSKA Fan Page with up-to-date information
Bulgarian A Professional Football Group
UEFA Profile
PFC CSKA Sofia seasons
Cska Sofia |
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20%C3%89variste%20Galois | The following is a list of topics named after Évariste Galois (1811–1832), a French mathematician.
Mathematics
Galois closure
Galois cohomology
Galois connection
Galois correspondence
Galois/Counter Mode
Galois covering
Galois deformation
Galois descent
Galois extension
Galois field
Galois geometry
Galois group
Absolute Galois group
Galois LFSRs
Galois module
Galois representation
Galois ring
Galois theory
Differential Galois theory
Topological Galois theory
Inverse Galois problem
Other
Galois (crater)
Galois |
https://en.wikipedia.org/wiki/True%20length | In geometry, true length is any distance between points that is not foreshortened by the view type. In a three-dimensional Euclidean space, lines with true length are parallel to the projection plane. For example, in a top view of a pyramid, which is an orthographic projection, the base edges (which are parallel to the projection plane) have true length, whereas the remaining edges in this view are not true lengths. The same is true with an orthographic side view of a pyramid. If any face of a pyramid was parallel to the projection plane (for a particular view), all edges would demonstrate true length.
Examples of views in which all edges have true length are nets.
References
Further reading
Boundy, A.W. (2012) "Engineering Drawing." McGraw–Hill.
Simmons, C. H., Maguire, D. E., Phelps, N., & Knovel. (2009). "Manual of engineering drawing." Boston, Newnes.
Descriptive geometry
Length |
https://en.wikipedia.org/wiki/List%20of%20Kelantan%20FA%20records%20and%20statistics | Kelantan Football Association (Malay: Persatuan Bola Sepak Kelantan), is a professional football association based in Kota Bharu in the Malaysian state of Kelantan. The team had their first major success in the 2012 season when they won the League championship, Piala FA and Piala Malaysia. Domestically, Kelantan have won the Liga Super Championship on 2 occasions, most recently in the 2012 season, 2 Piala Malaysia, 2 Piala FA, 1 Piala Sumbangsih and 1 Liga Premier title. 2012 was their debut playing in the AFC Cup. They played well in the group stage to gain first place. However, the team lost in the quarter final to Erbil SC. Kelantan FA were the only team which won the Piala Emas Raja-Raja for the thirteen times.
Kelantan team became a symbol of unity of the people of Kelantan. It can be seen during the match when various background Kelantan fans come to the stadium to support their team. Kelantan team revival began when Annuar Musa took over the president post during 2009 season. Since then, Kelantan team has become among the respected team in the Malaysian football.
Honours
Domestic
League
Division 1/ Liga Super
Winners (2): 2011, 2012
Runners-up : 2010
Division 2/ Liga Premier
Winners : 2000
Division 3/ Liga FAM
Winners (3): 1953*, 1954, 2005 (* shared)
Runners-up : 1963, 1971, 1972
Cups
Piala Malaysia
Winners (2): 2010, 2012
Runners-up : 1955, 1970, 2009, 2013
Piala FA
Winners (2): 2012, 2013
Runners-up : 2009, 2011, 2015
Piala Sumbangsih
Winners : 2011
Runners-up : 2012, 2013
Asian
AFC Cup: 3 appearances
2012: Quarter-finals (lost 2–6 on aggregate to Arbil)
2013: Round of 16 (lost 0–2 to Kitchee)
2014: Group stage (4th position)
Treble
"Treble Winner" (Liga Super, Piala FA and Piala Malaysia): 1
2012
U21 Team
Piala Presiden
Winners (7): 1985, 1995, 2005, 2011, 2013, 2015, 2016
Runners-up : 1988, 2003, 2006–07
U19 Team
Piala Belia
Winners (2): 2008, 2014
Runners-up : 2013
Record of success
League history
1998–2000: Liga Perdana 2 (2)
2001–2003: Liga Perdana 1 (1)
2004: Liga Premier (2)
2005: Liga FAM (3)
2006–2008: Liga Premier (2)
2009–: Liga Super (1)
League records
Remarks:
Player records
(2008–present)
Appearances
Most appearances in total (League & Cup) – 356 Mohd Badhri Mohd Radzi (2008–)
Most League appearances – 219 Mohd Badhri Mohd Radzi (2008–)
Goalscoring
Leading Goalscorer (League & Cup) – 95 Mohd Badhri Mohd Radzi (2008–)
Leading Goalscorer (League only) – 55 Mohd Badhri Mohd Radzi (2008–)
Leading Goalscorer (Piala FA) –
Leading Goalscorer (Piala Malaysia) – 22 Indra Putra Mahayuddin (2009–2010, 2012–2013, 2016–)
Leading Goalscorer (AFC Cup) – 7 Mohammed Ghaddar (2012), Mohd Badhri Mohd Radzi (2012–2014)
Top goalscorer by years
Team records
(2009–present)
Matches
Record wins
Record League win: 6–0 v FELDA United, Liga Super, 9 April 2011, 6–0 v Perak, Liga Super, 7 July 2012
Record Piala FA win: 5–1 v PDRM, Second Round 1st leg, 21 February 2009, 1–5 v Selangor, Semi-Fina |
https://en.wikipedia.org/wiki/1959%20Soviet%20census | The 1959 Soviet census conducted in January 1959 was the first post-World War II census held in the Soviet Union.
Background
For a decade after World War II, there were no new population statistics released by the Soviet Union, and a proposal for a new Soviet census for 1949 was rejected by Soviet leader Joseph Stalin. During this time, most Western experts estimated that the population of the Soviet Union was between 215 and 220 million people, but in June 1956 (after Stalin's death), the Soviet government announced that the country's population at that point was only 200,200,000.
Results
The new census announced the Soviet Union's population to be 208,826,650, an increase of almost forty million from the results of the last (disputed) census from 1939. A majority of this population increase was due to the Soviet territorial expansion of the 1939–1945 time period, rather than due to natural population growth. The deficit of men to women in the total Soviet population massively increased between 1939 and 1959, in large part due to World War II. The Soviet Union acquired some additional territories (after its 1939 census) in 1939–1945 in what is now Ukraine, Belarus, Moldova, the Baltic republics, Karelia, Tuva, and Kaliningrad Oblast. The Soviet Union was just 33% urban in 1939, but urbanized rapidly to become almost half (48%) urban in 1959.
The 1959 Soviet Union census reported populations in 126 nationality (ethnic group) categories, in comparison to only 97 categories in the 1939 census. Ethnic Russians still made up a majority of the Soviet population in 1959, but their percentage was smaller than in 1939 (again, partly due to the acquisition of mainly non-Russian territories in 1939–1945). Despite the acquisition of additional territories between these censuses, the Soviet Jewish population in 1959 (almost 2.3 million) was only about 75% of what it was in 1939, at least in large part due to the Holocaust. The populations of the Baltic Soviet Socialist Republics (which were heavily affected by World War II) did not change much between 1939 and 1959, with Lithuania actually experiencing a population decline during this time period. During the same time, the population of the Russian SFSR (which was heavily affected by World War II) increased by less than ten percent. The population increase in Ukraine and Byelorussia between 1939 and 1959 was completely or almost completely due to the Soviet territorial expansions of 1939–1940. Without these territorial expansions, Ukraine's population would have only barely increased and Belarus's population would have actually decreased between 1939 and 1959. The Central Asian and Caucasian Soviet Socialist Republics experienced large population increases between 1939 and 1959 despite the fact that they did not acquire any new territories during this time period.
This census is also noteworthy as being the first census to classify Brest Region population as Byelorussians.
City ranking
Moscow - 5,045 |
https://en.wikipedia.org/wiki/Projection%20plane | A projection plane, or plane of projection, is a type of view in which graphical projections from an object intersect. Projection planes are used often in descriptive geometry and graphical representation. A picture plane in perspective drawing is a type of projection plane.
With perspective drawing, the lines of sight, or projection lines, between an object and a picture plane return to a vanishing point and are not parallel. With parallel projection the lines of sight from the object to the projection plane are parallel.
See also
Image plane
Picture plane
References
Graphical projections
Planes (geometry) |
https://en.wikipedia.org/wiki/OdaTV | OdaTV (also known as Odatv.com, Odatv or odaTV), an online news portal based in Turkey, was founded in 2007. It is one of the most followed news portals in Turkey and according to the Alexa statistics, it is the 119th most visited website in the country.
The portal was founded by Soner Yalçın and Cüneyt Özdemir. Özdemir soon left after a difference of opinion. OdaTV was described in 2012 by the Committee to Protect Journalists as a portal which is "harshly critical of the government". In the early 2011, Odatv case was initiated as part of the Ergenekon trials, with OdaTV accused of being the "media arm" of the Ergenekon organization. Twelve of its journalists were under indictment in connection with the case, which Reporters without Borders has called "absurd". The court acquitted all journalists in April 2017 after the prosecutors failed to provide enough evidence.
On 2019, OdaTV writer Nihat Genç left the newspaper to found his own newspaper Veryansın TV.
Ergenekon Trials
In February 2011, OdaTV's offices were raided and some of its staff were arrested (including the founder Soner Yalçın and executive editor Barış Pehlivan as well as news co-ordinator Doğan Yurdakul, journalist Barış Terkoğlu) and accused of links with the Ergenekon organization. Odatv columnists Muhammet Sait Çakır, Coşkun Musluk and Müyesser Uğur were also charged.
Digital documents linking to the Ergenekon conspiracy are the basis of the case against Barış Terkoğlu, Ahmet Şık, Nedim Şener and the other detainees in the OdaTV case. Examinations of the documents conducted by computer experts at Boğaziçi University, Yıldız Technical University, Middle East Technical University, and the American data processing company DataDevastation have refuted the validity of the documents, concluding that outside sources targeted the journalists' computers. Rare and malicious computer viruses, including Autorun-BJ and Win32:Malware-gen, allowed the placement of the documents to go unnoticed by the defendants. Another judicial report prepared by the governmental agency TÜBİTAK also confirmed the infection by malicious viruses but could not confirm or reject any outside intervention.
Digital forensics company Arsenal Consulting examined the OdaTV evidence and found that while the malware on Barış Pehlivan's OdaTV computer was much more interesting than known prior to Arsenal’s involvement (e.g. the Ahtapot remote access trojan never seen before “in the wild”), it was not responsible for delivery of the incriminating documents. The “Anchors in Relative Time” analysis technique was used to reveal a series of local (physical access) and remote (across the Internet) attacks against his computer. The final two local attacks (on the evenings of February 9 and 11, 2011) resulted in delivery of the incriminating documents to his computer, just prior to its seizure by the Turkish National Police. Arsenal’s work has been covered by Motherboard and a detailed case study is under ongoing developmen |
https://en.wikipedia.org/wiki/Yemen%20national%20football%20team%20records%20and%20statistics | This is a list of Yemen national football team's all kinds of competitive records.
Individual records
Player records
Manager records
Team records
Competition records
World Cup record
AFC Asian Cup record
All qualifications
Asian Games record
Football at the Asian Games has been an under-23 tournament since 2002.
Arabian Gulf Cup record
Arab Cup record
Pan Arab Games record
WAFF Championship
Palestine Cup of Nations
Head-to-head record
The list shown below shows the Yemen national football team all-time international record against opposing nations.
^ Include
External links
FIFA.com
World Football Elo Ratings: Yemen
record
National association football team records and statistics |
https://en.wikipedia.org/wiki/Lori%20A.%20Clarke | Lori A. Clarke is an American computer scientist noted for her research on software engineering.
Biography
Clarke received a B.A. in Mathematics from the University of Rochester in 1969. She received a Ph.D in Computer Science from the University of Colorado in 1976.
She then joined the Department of Computer Science at the University of Massachusetts Amherst as an assistant professor in 1976. While there she was promoted to associate professor in 1981 and to professor in 1986. In 2011, she became the chair of the School of Computer Science. In 2015 she became an emeritus professor.
She was a board member for SIGSOFT from 1985 to 2001, including the chair from 1993 to 1997. She was a board member of CRA from 1999 to 2009. She is also noted for her leadership in broadening participation in computing. She has been a member of the CRA-W Board since 2001 and was the co-chair of CRA-W from 2005 to 2008.
Awards
In the year 1998 she was named an ACM Fellow.
Her other notable awards include:
IEEE Fellow in 2011 for contributions to software testing and verification.
ACM SIGSOFT Outstanding Research Award, 2011
ACM SIGSOFT Distinguished Service Award, 2002
References
External links
University of Massachusetts Amherst: Lori A. Clarke, Department of Computer Science
Living people
American computer scientists
American women computer scientists
University of Massachusetts Amherst faculty
Fellows of the Association for Computing Machinery
Fellow Members of the IEEE
Year of birth missing (living people)
21st-century American women |
https://en.wikipedia.org/wiki/Leon%20J.%20Osterweil | Leon Joel Osterweil is an American computer scientist noted for his research on software engineering.
Biography
Osterweil received a B. A. in mathematics from Princeton University in 1965. He received a M.A. in mathematics in 1970 and a Ph.D in mathematics in 1971 from the University of Maryland.
He then joined the Department of Computer Science at the University of Colorado Boulder as an assistant professor in 1971. While there he was promoted to associate professor in 1977 and to professor in 1982, he was chair of the department from 1981 to 1986. In 1988, he became a professor at the University of California at Irvine and he was department chair from 1989 to 1992. In 1993, he became a professor of Computer Science at the University of Massachusetts Amherst.
Awards
In the year 1998, he was named an ACM Fellow.
His other notable awards include:
ACM SIGSOFT Outstanding Research Award, 2003
ICSE's Most Influential Paper Award, 1997
ACM SIGSOFT Influential Educator Award, 2010
References
External links
University of Massachusetts Amherst: Leon J. Osterweil, Department of Computer Science
American computer scientists
University of Massachusetts Amherst faculty
Fellows of the Association for Computing Machinery
Living people
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/N-topological%20space | In mathematics, an N-topological space is a set equipped with N arbitrary topologies. If τ1, τ2, ..., τN are N topologies defined on a nonempty set X, then the N-topological space is denoted by (X,τ1,τ2,...,τN).
For N = 1, the structure is simply a topological space.
For N = 2, the structure becomes a bitopological space introduced by J. C. Kelly.
Example
Let X = {x1, x2, ...., xn} be any finite set. Suppose Ar = {x1, x2, ..., xr}. Then the collection τ1 = {φ, A1, A2, ..., An = X} will be a topology on X. If τ1, τ2, ..., τm be m such topologies (chain topologies) defined on X, then the structure (X, τ1, τ2, ..., τm) is an ''m''-topological space.
References
Mathematical terminology
Topology |
https://en.wikipedia.org/wiki/Fabry%20gap%20theorem | In mathematics, the Fabry gap theorem is a result about the analytic continuation of complex power series whose non-zero terms are of orders that have a certain "gap" between them. Such a power series is "badly behaved" in the sense that it cannot be extended to be an analytic function anywhere on the boundary of its disc of convergence.
The theorem may be deduced from the first main theorem of Turán's method.
Statement of the theorem
Let 0 < p1 < p2 < ... be a sequence of integers such that the sequence pn/n diverges to ∞. Let (αj)j∈N be a sequence of complex numbers such that the power series
has radius of convergence 1. Then the unit circle is a natural boundary for the series f.
Converse
A converse to the theorem was established by George Pólya. If lim inf pn/n is finite then there exists a power series with exponent sequence pn, radius of convergence equal to 1, but for which the unit circle is not a natural boundary.
See also
Gap theorem (disambiguation)
Lacunary function
Ostrowski–Hadamard gap theorem
References
Mathematical series
Theorems in complex analysis |
https://en.wikipedia.org/wiki/Tur%C3%A1n%27s%20method | In mathematics, Turán's method provides lower bounds for exponential sums and complex power sums. The method has been applied to problems in equidistribution.
The method applies to sums of the form
where the b and z are complex numbers and ν runs over a range of integers. There are two main results, depending on the size of the complex numbers z.
Turán's first theorem
The first result applies to sums sν where for all n. For any range of ν of length N, say ν = M + 1, ..., M + N, there is some ν with |sν| at least c(M, N)|s0| where
The sum here may be replaced by the weaker but simpler .
We may deduce the Fabry gap theorem from this result.
Turán's second theorem
The second result applies to sums sν where for all n. Assume that the z are ordered in decreasing absolute value and scaled so that |z1| = 1. Then there is some ν with
See also
Turán's theorem in graph theory
References
Exponentials
Analytic number theory |
https://en.wikipedia.org/wiki/Van%20der%20Corput%27s%20method | In mathematics, van der Corput's method generates estimates for exponential sums. The method applies two processes, the van der Corput processes A and B which relate the sums into simpler sums which are easier to estimate.
The processes apply to exponential sums of the form
where f is a sufficiently smooth function and e(x) denotes exp(2πix).
Process A
To apply process A, write the first difference fh(x) for f(x+h)−f(x).
Assume there is H ≤ b−a such that
Then
Process B
Process B transforms the sum involving f into one involving a function g defined in terms of the derivative of f. Suppose that f is monotone increasing with f'(a) = α, f'(b) = β. Then f' is invertible on [α,β] with inverse u say. Further suppose f'' ≥ λ > 0. Write
We have
Applying Process B again to the sum involving g returns to the sum over f and so yields no further information.
Exponent pairs
The method of exponent pairs gives a class of estimates for functions with a particular smoothness property. Fix parameters N,R,T,s,δ. We consider functions f defined on an interval [N,2N] which are R times continuously differentiable, satisfying
uniformly on [a,b] for 0 ≤ r < R.
We say that a pair of real numbers (k,l) with 0 ≤ k ≤ 1/2 ≤ l ≤ 1 is an exponent pair if for each σ > 0 there exists δ and R depending on k,l,σ such that
uniformly in f.
By Process A we find that if (k,l) is an exponent pair then so is .
By Process B we find that so is .
A trivial bound shows that (0,1) is an exponent pair.
The set of exponents pairs is convex.
It is known that if (k,l) is an exponent pair then the Riemann zeta function on the critical line satisfies
where .
The exponent pair conjecture' states that for all ε > 0, the pair (ε,1/2+ε) is an exponent pair. This conjecture implies the Lindelöf hypothesis.
References
Exponentials
Analytic number theory |
https://en.wikipedia.org/wiki/Merlin%20%28assembler%29 | Merlin is a MOS Technology 6502 macro assembler developed by mathematics professor Glen Bredon for the Apple II under DOS 3.3. It was published commercially by Southwestern Data Systems, later known as Roger Wagner Publishing. Merlin continued to be updated as successors to the 6502 became available: first the 65C02 and later the 65816 and 65802. A ProDOS version was made available as Merlin Pro (this package also included the DOS 3.3 version). The 8-bit version of Merlin was later renamed Merlin 8, and a 16-bit version, dubbed Merlin 16, was released for the Apple IIGS. Versions for the Commodore 64 and Commodore 128 were released as Merlin 64 and Merlin 128 respectively.
Merlin includes an integrated source code editor (initially a line editor; later versions include a full-screen editor) and also a disassembler, called Sourceror. A related utility, Sourceror.FP, can generate a commented disassembly of the Apple II's Applesoft BASIC, the source code for which had never been released by Apple, from the customer's own ROM.
Reception
Ahoy! called Merlin 64 "an excellent little assembler with many value added features. For ease of use, I couldn't imagine how it could be better ... an outstanding value".
Legacy
On August 24, 2000, what would have been the author's 68th birthday, his widow released all of his Apple II software and source code (e.g. DOS.MASTER) as public domain software.
In January, 2015 a Windows edition of Merlin titled "Merlin 32" was released by Brutal Deluxe.
References
Apple II software
Assemblers
Commodore 64 software
Commodore 128 software
Public-domain software with source code |
https://en.wikipedia.org/wiki/Andreas%20Kittou | Andreas Kittou (; born 9 September 1990 in Paralimni) is a Cypriot football goalkeeper who plays for Ayia Napa.
Club statistics
References
External links
Cyprus Football Association Profile
1990 births
Living people
Cypriot men's footballers
Enosis Neon Paralimni FC players
Ayia Napa FC players
Anorthosis Famagusta FC players
AEL Limassol players
Cypriot First Division players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Linear%20function%20%28calculus%29 | In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane.
The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change in the input.
Linear functions are related to linear equations.
Properties
A linear function is a polynomial function in which the variable has degree at most one:
.
Such a function is called linear because its graph, the set of all points in the Cartesian plane, is a line. The coefficient a is called the slope of the function and of the line (see below).
If the slope is , this is a constant function defining a horizontal line, which some authors exclude from the class of linear functions. With this definition, the degree of a linear polynomial would be exactly one, and its graph would be a line that is neither vertical nor horizontal. However, in this article, is required, so constant functions will be considered linear.
If then the linear function is said to be homogeneous. Such function defines a line that passes through the origin of the coordinate system, that is, the point . In advanced mathematics texts, the term linear function often denotes specifically homogeneous linear functions, while the term affine function is used for the general case, which includes .
The natural domain of a linear function , the set of allowed input values for , is the entire set of real numbers, One can also consider such functions with in an arbitrary field, taking the coefficients in that field.
The graph is a non-vertical line having exactly one intersection with the -axis, its -intercept point The -intercept value is also called the initial value of If the graph is a non-horizontal line having exactly one intersection with the -axis, the -intercept point The -intercept value the solution of the equation is also called the root or zero of
Slope
The slope of a nonvertical line is a number that measures how steeply the line is slanted (rise-over-run). If the line is the graph of the linear function , this slope is given by the constant .
The slope measures the constant rate of change of per unit change in x: whenever the input is increased by one unit, the output changes by units: , and more generally for any number . If the slope is positive, , then the function is increasing; if , then is decreasing
In calculus, the derivative of a general function measures its rate of change. A linear function has a constant rate of change equal to its slope , so its derivative is the constant function .
The fundamental idea of differential calculus is that any smooth function (not necessarily linear) can be closely approximated near a given point by a unique linear function. The derivative is the slope of this linear function, and the approximation is: for . The graph of the linear approximation |
https://en.wikipedia.org/wiki/Henrik%20Madsen | Henrik Nyholm Madsen (born 25 February 1983) is a retired Danish footballer. He previously played at FC Vestsjælland.
References
External links
Official Danish Superliga player statistics at danskfodbold.com
Living people
1983 births
Danish men's footballers
Denmark men's youth international footballers
Danish 1st Division players
HB Køge players
Aarhus Gymnastikforening players
Næstved Boldklub players
FC Vestsjælland players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Point%20groups%20in%20four%20dimensions | In geometry, a point group in four dimensions is an isometry group in four dimensions that leaves the origin fixed, or correspondingly, an isometry group of a 3-sphere.
History on four-dimensional groups
1889 Édouard Goursat, Sur les substitutions orthogonales et les divisions régulières de l'espace, Annales Scientifiques de l'École Normale Supérieure, Sér. 3, 6, (pp. 9–102, pp. 80–81 tetrahedra), Goursat tetrahedron
1951, A. C. Hurley, Finite rotation groups and crystal classes in four dimensions, Proceedings of the Cambridge Philosophical Society, vol. 47, issue 04, p. 650
1962 A. L. MacKay Bravais Lattices in Four-dimensional Space
1964 Patrick du Val, Homographies, quaternions and rotations, quaternion-based 4D point groups
1975 Jan Mozrzymas, Andrzej Solecki, R4 point groups, Reports on Mathematical Physics, Volume 7, Issue 3, p. 363-394
1978 H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space.
1982 N. P. Warner, The symmetry groups of the regular tessellations of S2 and S3
1985 E. J. W. Whittaker, An atlas of hyperstereograms of the four-dimensional crystal classes
1985 H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, Coxeter notation for 4D point groups
2003 John Conway and Smith, On Quaternions and Octonions, Completed quaternion-based 4D point groups
2018 N. W. Johnson Geometries and Transformations, Chapter 11,12,13, Full polychoric groups, p. 249, duoprismatic groups p. 269
Isometries of 4D point symmetry
There are four basic isometries of 4-dimensional point symmetry: reflection symmetry, rotational symmetry, rotoreflection, and double rotation.
Notation for groups
Point groups in this article are given in Coxeter notation, which are based on Coxeter groups, with markups for extended groups and subgroups. Coxeter notation has a direct correspondence the Coxeter diagram like [3,3,3], [4,3,3], [31,1,1], [3,4,3], [5,3,3], and [p,2,q]. These groups bound the 3-sphere into identical hyperspherical tetrahedral domains. The number of domains is the order of the group. The number of mirrors for an irreducible group is nh/2, where h is the Coxeter group's Coxeter number, n is the dimension (4).
For cross-referencing, also given here are quaternion based notations by Patrick du Val (1964) and John Conway (2003). Conway's notation allows the order of the group to be computed as a product of elements with chiral polyhedral group orders: (T=12, O=24, I=60). In Conway's notation, a (±) prefix implies central inversion, and a suffix (.2) implies mirror symmetry. Similarly Du Val's notation has an asterisk (*) superscript for mirror symmetry.
Involution groups
There are five involutional groups: no symmetry [ ]+, reflection symmetry [ ], 2-fold rotational symmetry [2]+, 2-fold rotoreflection [2+,2+], and central point symmetry [2+,2+,2+] as a 2-fold double rotation.
Rank 4 Coxeter groups
A polychoric group is one of five symmetry groups of the 4-dimensiona |
https://en.wikipedia.org/wiki/Poincar%C3%A9%20separation%20theorem | In mathematics, the Poincaré separation theorem, also known as the Cauchy interlacing theorem, gives some upper and lower bounds of eigenvalues of a real symmetric matrix B'AB that can be considered as the orthogonal projection of a larger real symmetric matrix A onto a linear subspace spanned by the columns of B. The theorem is named after Henri Poincaré.
More specifically, let A be an n × n real symmetric matrix and B an n × r semi-orthogonal matrix such that B'B = Ir. Denote by , i = 1, 2, ..., n and , i = 1, 2, ..., r the eigenvalues of A and B'AB, respectively (in descending order). We have
Proof
An algebraic proof, based on the variational interpretation of eigenvalues, has been published in Magnus' Matrix Differential Calculus with Applications in Statistics and Econometrics. From the geometric point of view, B'AB can be considered as the orthogonal projection of A onto the linear subspace spanned by B, so the above results follow immediately.
References
Inequalities
Matrix theory |
https://en.wikipedia.org/wiki/Negative%20hypergeometric%20distribution | In probability theory and statistics, the negative hypergeometric distribution describes probabilities for when sampling from a finite population without replacement in which each sample can be classified into two mutually exclusive categories like Pass/Fail or Employed/Unemployed. As random selections are made from the population, each subsequent draw decreases the population causing the probability of success to change with each draw. Unlike the standard hypergeometric distribution, which describes the number of successes in a fixed sample size, in the negative hypergeometric distribution, samples are drawn until failures have been found, and the distribution describes the probability of finding successes in such a sample. In other words, the negative hypergeometric distribution describes the likelihood of successes in a sample with exactly failures.
Definition
There are elements, of which are defined as "successes" and the rest are "failures".
Elements are drawn one after the other, without replacements, until failures are encountered. Then, the drawing stops and the number of successes is counted. The negative hypergeometric distribution, is the discrete distribution of this .
The negative hypergeometric distribution is a special case of the beta-binomial distribution with parameters and both being integers (and ).
The outcome requires that we observe successes in draws and the bit must be a failure. The probability of the former can be found by the direct application of the hypergeometric distribution and the probability of the latter is simply the number of failures remaining divided by the size of the remaining population . The probability of having exactly successes up to the failure (i.e. the drawing stops as soon as the sample includes the predefined number of failures) is then the product of these two probabilities:
Therefore, a random variable follows the negative hypergeometric distribution if its probability mass function (pmf) is given by
where
is the population size,
is the number of success states in the population,
is the number of failures,
is the number of observed successes,
is a binomial coefficient
By design the probabilities sum up to 1. However, in case we want show it explicitly we have:
where we have used that,
which can be derived using the binomial identity, , and the Chu–Vandermonde identity, , which holds for any complex-values and and any non-negative integer .
Expectation
When counting the number of successes before failures, the expected number of successes is and can be derived as follows.
where we have used the relationship , that we derived above to show that the negative hypergeometric distribution was properly normalized.
Variance
The variance can be derived by the following calculation.
Then the variance is
Related distributions
If the drawing stops after a constant number of draws (regardless of the number of failures), then the number of successes ha |
https://en.wikipedia.org/wiki/List%20of%20polygons | In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain. These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners.
The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον (polygōnon/polugōnon), noun use of neuter of πολύγωνος (polygōnos/polugōnos, the masculine adjective), meaning "many-angled". Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well.
Greek numbers
Polygons are primarily named by prefixes from Ancient Greek numbers.
Systematic polygon names
To construct the name of a polygon with more than 20 and fewer than 100 edges, combine the prefixes as follows. The "kai" connector is not included by some authors.
Extending the system up to 999 is expressed with these prefixes; the names over 99 no longer correspond to how they are actually expressed in Greek.
List of n-gons by Greek numerical prefixes
See also
Platonic solid
Dice
List of polygons, polyhedra and polytopes
Circle
Ellipses
Shapes
References
NAMING POLYGONS
Benjamin Franklin Finkel, A Mathematical Solution Book Containing Systematic Solutions to Many of the Most Difficult Problems, 1888
Polygons |
https://en.wikipedia.org/wiki/Mava | MAVA may refer to:
MAVA-Renault, a Greek company
Men Against Violence and Abuse, an Indian organisation
Multiple abstract variance analysis, a technique in statistics
Mava () may refer to the following villages in Iran:
Mava, Chenaran, in Razavi Khorasan Province
Mava, Nishapur, in Razavi Khorasan Province
Mava, Hamadan
Mava, Kermanshah (disambiguation)
Mava, Khuzestan (disambiguation)
People with the name
Mava Lee Thomas (1929–2013), American baseball player
See also
Mawa (disambiguation)
MEWA (disambiguation)
Mewa or Khoa, a milk product of India |
https://en.wikipedia.org/wiki/Spin%20matrix | The term spin matrix refers to a number of matrices, which are related to Spin (physics).
Quantum mechanics and pure mathematics
Pauli matrices, also called the "Pauli spin matrices".
Generalizations of Pauli matrices
Gamma matrices, which can be represented in terms of the Pauli matrices.
Higher-dimensional gamma matrices
See also
In pure mathematics and physics:
Wigner D-matrix, represent spins and rotations of quantum states and tensor operators.
Higher spin alternating sign matrix
Spin group
Spin (physics)#Higher spins |
https://en.wikipedia.org/wiki/Multisymplectic%20integrator | In mathematics, a multisymplectic integrator is a numerical method for the solution of a certain class of partial differential equations, that are said to be multisymplectic. Multisymplectic integrators are geometric integrators, meaning that they preserve the geometry of the problems; in particular, the numerical method preserves energy and momentum in some sense, similar to the partial differential equation itself. Examples of multisymplectic integrators include the Euler box scheme and the Preissman box scheme.
Multisymplectic equations
A partial differential equation (PDE) is said to be a multisymplectic equation if it can be written in the form
where is the unknown, and are (constant) skew-symmetric matrices and denotes the gradient of . This is a natural generalization of , the form of a Hamiltonian ODE.
Examples of multisymplectic PDEs include the nonlinear Klein–Gordon equation , or more generally the nonlinear wave equation , and the KdV equation .
Define the 2-forms and by
where denotes the dot product. The differential equation preserves symplecticity in the sense that
Taking the dot product of the PDE with yields the local conservation law for energy:
The local conservation law for momentum is derived similarly:
The Euler box scheme
A multisymplectic integrator is a numerical method for solving multisymplectic PDEs whose numerical solution conserves a discrete form of symplecticity. One example is the Euler box scheme, which is derived by applying the symplectic Euler method to each independent variable.
The Euler box scheme uses a splitting of the skewsymmetric matrices and of the form:
For instance, one can take and to be the upper triangular part of and , respectively.
Now introduce a uniform grid and let denote the approximation to where and are the grid spacing in the time- and space-direction. Then the Euler box scheme is
where the finite difference operators are defined by
The Euler box scheme is a first-order method, which satisfies the discrete conservation law
Preissman box scheme
Another multisymplectic integrator is the Preissman box scheme, which was introduced by Preissman in the context of hyperbolic PDEs. It is also known as the centred cell scheme. The Preissman box scheme can be derived by applying the Implicit midpoint rule, which is a symplectic integrator, to each of the independent variables. This leads to the scheme
where the finite difference operators and are defined as above and the values at the half-integers are defined by
The Preissman box scheme is a second-order multisymplectic integrator which satisfies the discrete conservation law
Notes
References
.
.
.
.
.
.
Numerical differential equations |
https://en.wikipedia.org/wiki/Bayu%20Pradana | Bayu Pradana Andriatmoko (born 19 April 1991) is an Indonesian professional footballer who plays as a defensive midfielder for Liga 1 club Barito Putera.
Career statistics
Club
International
Honours
International
Indonesia
AFF Championship runner-up: 2016
Individual
Liga 1 Best XI: 2017
Indonesia Soccer Championship A Best XI: 2016
References
External links
Bayu Pradana at Liga Indonesia
Indonesian men's footballers
People from Salatiga
Living people
1991 births
Persis Solo players
Persipasi Bekasi players
Kalteng Putra F.C. players
Persiba Balikpapan players
PS Mitra Kukar players
PS Barito Putera players
Indonesian Premier Division players
Indonesian Premier League players
Liga 1 (Indonesia) players
Indonesia men's youth international footballers
Indonesia men's international footballers
Men's association football midfielders
Footballers from Central Java |
https://en.wikipedia.org/wiki/Inder%20Bir%20Singh%20Passi | Inder Bir Singh Passi (20 August 1939 – 2 October 2021) was an Indian mathematician who specialised in algebra.
IBS Passi was the former dean of university instructions (DUI) and professor emeritus of the department of mathematics at Panjab University. He was awarded in 1983 the Shanti Swarup Bhatnagar Prize for Science and Technology, the highest science award in India, in the mathematical sciences category. Passi was a noted group-theorist in India, had made significant contribution to certain aspects of theory of groups specially to the study of group rings. His results on the dimension subgroups, augmentation powers in group rings, and related problems have received wide recognition. His 1979 monograph summarizing the state of the subject is a basic reference source.
References
External links
Indian National Science Academy database
1939 births
2021 deaths
Presidents of the Indian Mathematical Society
20th-century Indian mathematicians
Indian group theorists
Panjab University
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/International%20Conference%20on%20Computational%20Intelligence%20Methods%20for%20Bioinformatics%20and%20Biostatistics | The International Conference on Computational Intelligence Methods for Bioinformatics and Biostatistics (CIBB) is a yearly scientific conference focused on machine learning and computational intelligence applied to bioinformatics and biostatistics.
Organization and history
The CIBB conferences are typically organized by members of the IEEE Computational Intelligence Society (IEEE CIS) and the International Neural Network Society (INNS), among others. Their main themes are machine learning, data mining, and computational intelligence algorithms applied to biological and biostatistical problems.
The CIBB conference was originally started by Francesco Masulli (Università di Genova), Antonina Starita (Università di Pisa), and Roberto Tagliaferri (Università di Salerno) as a special session within other international conferences held in Italy: the 14th Italian Workshop on Neural Networks (2004), the 6th International Workshop on Fuzzy Logic and Applications (2005), the 7th International Fuzzy Logic and Intelligent Technologies in Nuclear Science Conference on Applied Artificial Intelligence (2006), and the 7th International Workshop on Fuzzy Logic and Applications (2007). Because of the broad participation of researchers to the CIBB special session at the latter meeting, which included twenty-six submitted papers, the CIBB steering committee decided to turn CIBB into an autonomous conference starting with the 2008 edition in Vietri sul Mare, Italy.
During their first editions, the CIBB conferences were organized and attended mainly by Italian researchers at various academic locations throughout Italy. As international audience and importance of the conference grew, following editions moved outside Italy. The 2012 CIBB conference was held for the first time outside Europe, in Houston, Texas.
Format
The conference is a single track meeting that includes invited talks as well as oral and poster presentations of refereed papers. It usually lasts three days in September, and traditionally includes some special sessions about the application of computational intelligence to specific aspects of biology (for example, the "Special session on machine learning in health informatics and biological systems" at CIBB 2018,) and occasionally some tutorials.
At the 2011 conference edition in Gargnano, the scientific committee gave a young researcher best paper award.
Publications
Proceedings of the conferences are published as a book series by Springer Science+Business Media, whereas selected papers are published in journals such as BMC Bioinformatics.
References
External links
CIBB conference series on WikiCfp.com
Artificial intelligence conferences
Computer science conferences
Bioinformatics |
https://en.wikipedia.org/wiki/Uniformly%20smooth%20space | In mathematics, a uniformly smooth space is a normed vector space satisfying the property that for every there exists such that if with and then
The modulus of smoothness of a normed space X is the function ρX defined for every by the formula
The triangle inequality yields that . The normed space X is uniformly smooth if and only if tends to 0 as t tends to 0.
Properties
Every uniformly smooth Banach space is reflexive.
A Banach space is uniformly smooth if and only if its continuous dual is uniformly convex (and vice versa, via reflexivity). The moduli of convexity and smoothness are linked by
and the maximal convex function majorated by the modulus of convexity δX is given by
Furthermore,
A Banach space is uniformly smooth if and only if the limit
exists uniformly for all (where denotes the unit sphere of ).
When , the Lp-spaces are uniformly smooth (and uniformly convex).
Enflo proved
that the class of Banach spaces that admit an equivalent uniformly convex norm coincides with the class of super-reflexive Banach spaces, introduced by Robert C. James.
As a space is super-reflexive if and only if its dual is super-reflexive, it follows that the class of Banach spaces that admit an equivalent uniformly convex norm coincides with the class of spaces that admit an equivalent uniformly smooth norm. The Pisier renorming theorem
states that a super-reflexive space X admits an equivalent uniformly smooth norm for which the modulus of smoothness ρX satisfies, for some constant C and some
It follows that every super-reflexive space Y admits an equivalent uniformly convex norm for which the modulus of convexity satisfies, for some constant and some positive real q
If a normed space admits two equivalent norms, one uniformly convex and one uniformly smooth, the Asplund averaging technique produces another equivalent norm that is both uniformly convex and uniformly smooth.
See also
Uniformly convex space
Notes
References
.
Banach spaces
Convex analysis |
https://en.wikipedia.org/wiki/2013%E2%80%9314%20FK%20Borac%20Banja%20Luka%20season | The 2013–14 season is FK Borac 4th season in Premier League of Bosnia and Herzegovina. This article shows player statistics and all matches (official and friendly) that the club have and will play during the 2013–14 season.
Players
Squad statistics
Top scorers
Includes all competitive matches. The list is sorted by shirt number when total goals are equal.
Transfers
In
Out
For recent transfers, see List of Bosnian football transfers summer 2013 and List of Bosnian football transfers winter 2013-14
Tournaments
Premier League of Bosnia and Herzegovina
League table
Results and positions by round
Matches
Republika Srpska Cup
Bosnia and Herzegovina Football Cup
Borac Banja Luka will participate in the 10th Bosnia and Herzegovina Football Cup starting in the Round of 32.
Friendlies
Borac Banja Luka
FK Borac Banja Luka seasons |
https://en.wikipedia.org/wiki/Hermite%20distribution | In probability theory and statistics, the Hermite distribution, named after Charles Hermite, is a discrete probability distribution used to model count data with more than one parameter. This distribution is flexible in terms of its ability to allow a moderate over-dispersion in the data.
The authors Kemp and Kemp have called it "Hermite distribution" from the fact its probability function and the moment generating function can be expressed in terms of the coefficients of (modified) Hermite polynomials.
History
The distribution first appeared in the paper Applications of Mathematics to Medical Problems, by Anderson Gray McKendrick in 1926. In this work the author explains several mathematical methods that can be applied to medical research. In one of this methods he considered the bivariate Poisson distribution and showed that the distribution of the sum of two correlated Poisson variables follow a distribution that later would be known as Hermite distribution.
As a practical application, McKendrick considered the distribution of counts of bacteria in leucocytes. Using the method of moments he fitted the data with the Hermite distribution and found the model more satisfactory than fitting it with a Poisson distribution.
The distribution was formally introduced and published by C. D. Kemp and Adrienne W. Kemp in 1965 in their work Some Properties of ‘Hermite’ Distribution. The work is focused on the properties of this distribution for instance a necessary condition on the parameters and their maximum likelihood estimators (MLE), the analysis of the probability generating function (PGF) and how it can be expressed in terms of the coefficients of (modified) Hermite polynomials. An example they have used in this publication is the distribution of counts of bacteria in leucocytes that used McKendrick but Kemp and Kemp estimate the model using the maximum likelihood method.
Hermite distribution is a special case of discrete compound Poisson distribution with only two parameters.
The same authors published in 1966 the paper An alternative Derivation of the Hermite Distribution. In this work established that the Hermite distribution can be obtained formally by combining a Poisson distribution with a normal distribution.
In 1971, Y. C. Patel did a comparative study of various estimation procedures for the Hermite distribution in his doctoral thesis. It included maximum likelihood, moment estimators, mean and zero frequency estimators and the method of even points.
In 1974, Gupta and Jain did a research on a generalized form of Hermite distribution.
Definition
Probability mass function
Let X1 and X2 be two independent Poisson variables with parameters a1 and a2. The probability distribution of the random variable Y = X1 + 2X2 is the Hermite distribution with parameters a1 and a2 and probability mass function is given by
where
n = 0, 1, 2, ...
a1, a2 ≥ 0.
(n − 2j)! and j! are the factorials of (n − 2j) and j, respectively.
is the i |
https://en.wikipedia.org/wiki/Surender%20Kumar%20Malik | Surender Kumar Malik (8 September 1942 – 7 July 2001) was an Indian mathematician who specialised in applied mathematics, especially in nonlinear phenomena.
He was awarded in 1983 the Shanti Swarup Bhatnagar Prize for Science and Technology, the highest science award in India, in the mathematical sciences category.
Malik did pioneering work on nonlinear dispersive waves in self-gravitating media, electrohydrodynamics and magnetohydrodynamics. In particular his theory on nonlinear breakup of a self-gravitating column has thrown some light on the phenomenon of condensation in astronomical bodies. His work on nonlinear self-focussing in magnetic fluids is expected to have industrial applications.
References
External links
Indian National Science Academy database
"Homage paid to Dr S.K. Malik". Chandigarh Tribune. Retrieved February 17, 2017.
1942 births
2001 deaths
Indian mathematicians
Delhi University alumni
Panjab University alumni
Applied mathematicians
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/Rajagopalan%20Parthasarathy | Rajagopalan Parthasarathy is an Indian mathematician who specialised in representation theory of Lie groups and algebras.
He was awarded in 1985 the Shanti Swarup Bhatnagar Prize for Science and Technology, the highest science award in India, in the mathematical sciences category.
Prof. Parthasarathy is an expert in representation theory of semisimple Lie groups. His initial work was on the realization of the so-called discrete series of representations of a semisimple Lie group in the space of Dirac Spinors. He made considerable progress in many central problems in representation theory. His work on the resolution of the Blattner's conjecture and the question of unitarisability of certain highest weight modules are significant contributions to this area in mathematics.
References
External links
Indian National Science Academy database
1945 births
Living people
20th-century Indian mathematicians
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/Tarlok%20Nath%20Shorey | Tarlok Nath Shorey is an Indian mathematician who specialises in theory of numbers. He is currently a distinguished professor in the department of mathematics at IIT Bombay. Previously, he worked at TIFR.
He was awarded in 1987 the Shanti Swarup Bhatnagar Prize for Science and Technology, the highest science award in India, in the mathematical sciences category. Shorey has done significant work on transcendental number theory, in particular best estimates for linear forms in logarithms of algebraic numbers.
He has obtained some new applications of Baker’s method to Diophantine equations and Ramanujan’s T-function.
Shorey's contribution to irreducibility of Laguerre polynomials is extensive.
Selected publications
T. N. Shorey, On gaps between numbers with a large prime factor, II Acta Arith. 25(1973/74).
T. N. Shorey and R. Tijdeman, On the greatest prime factor of an arithmetical progression, A tribute to Paul Erdős, Cambridge Univ. Press, Cambridge, 1990.
T. N. Shorey and R. Tijdeman, On the greatest prime factor of an arithmetical progression. II, Acta Arith. 53 (1990).
T. N. Shorey and R. Tijdeman, On the greatest prime factors of an arithmetical progression. III, Approximations diophantiennes et nombres transcendents (Luminy, 1990), 275{280, de Gruyter, Berlin, 1992.
T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Univ. Press, Cambridge, 1986.
References
External links
Indian National Science Academy database
1945 births
Living people
Indian number theorists
20th-century Indian mathematicians
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/Zeev%20Rudnick | Zeev Rudnick or Ze'ev Rudnick (born 1961 in Haifa, Israel) is a mathematician, specializing in number theory and in mathematical physics, notably quantum chaos. Rudnick is a professor at the School of Mathematical Sciences and the Cissie and Aaron Beare Chair in Number Theory at Tel Aviv University.
Education
Rudnick received his PhD from Yale University in 1990 under the supervision of Ilya Piatetski-Shapiro and Roger Evans Howe.
Career
Rudnick joined Tel Aviv University in 1995, after working as an assistant professor at Princeton and Stanford. In 2003–4 Rudnick was a Leverhulme visiting professor at the University of Bristol and in 2008–2010 and 2015–2016 he was a member of the Institute for Advanced Study at Princeton.
In 2012, Rudnick was inducted as a fellow of the American Mathematical Society.
Research
Rudnick has been studying different aspects of quantum chaos and number theory. He has contributed to one of the discoveries concerning the Riemann zeta function, namely, that the Riemann zeros appear to display the same statistics as those which are believed to be present in energy levels of quantum chaotic systems and described by random matrix theory. Together with Peter Sarnak, he has formulated the Quantum Unique Ergodicity conjectures for eigenfunctions on negatively curved manifolds, and has investigated the question arising from Quantum Chaos in other arithmetic models such as the Quantum Cat map (with Par Kurlberg) and the flat torus (with CP Hughes and with Jean Bourgain). Another interest is the interface between function field arithmetic and corresponding problems in number fields.
Education
Ph.D., 1990, Yale University.
M.Sc., 1985, The Hebrew University, Jerusalem.
B.Sc., 1984, Bar-Ilan University, Ramat Gan.
Awards and fellowships
ERC Advanced Grants, 1.7 million euro, 2013–2018., 2019–2024.
Fellow of the American Mathematical Society, 2012–.
Annales Henri Poincaré Distinguished Paper Award for the year, 2011.
Erdős Prize of the Israel Mathematical Union, 2001.
Alon Fellow, 1995.
Sloan Foundation Doctoral Dissertation Fellowship, 1989–1990.
Selected works
Z. Rudnick, P. Sarnak, The behaviour of eigenstates of arithmetic hyperbolic manifolds, Comm. in Math. Physics 161, 195–213 (1994).
W. Luo, Z. Rudnick and P. Sarnak, On Selberg's eigenvalue conjecture, Geom. and Func. Analysis 5 (1995), 387–401.
Z. Rudnick and P. Sarnak, Zeros of principal L-functions and random matrix theory, Duke Mathematical Journal 81 (1996), 269–322 (special volume in honor of J. Nash).
P. Kurlberg and Z. Rudnick, Hecke theory and equidistribution for the quantization of linear maps of the torus, Duke Mathematical Journal 103 (2000), 47–78.
Z. Rudnick and K. Soundararajan, Lower bounds for moments of L-functions, Proc. of the National Academy of Sciences of the USA, 102 (19), (May 10, 2005), 6837–6838.
Z. Rudnick, What is Quantum Chaos?, Notices of the AMS, 55 number 1 (2008), 32–34.
J. Bourgain and Z. Rudnick, Restriction of toral eige |
https://en.wikipedia.org/wiki/Dudley%20Weldon%20Woodard | Dudley Weldon Woodard (October 3, 1881 – July 1, 1965) was a Galveston-born American mathematician and professor, and the second African-American to earn a PhD in mathematics; the first was Woodard's mentor Elbert Frank Cox, who earned a PhD from Cornell in 1925).
He received his B.A. degree from Wilberforce University in Ohio (1903), his B.S. degree (1906) and M.Sc. degree (1907) at the University of Chicago. He taught collegiate mathematics in Tuskegee for many years, until finally he earned his PhD at the University of Pennsylvania (1928). His doctoral thesis was entitled, On Two-Dimensional Analysis Situs with Special Reference to the Jordan Curve Theorem, and was advised by John R. Kline.
During his lifetime, he published three papers. The second of these, The Characterization of the Closed N-Cell in Fundamenta Mathematicae, 13 (1929), is, according to Scott Williams, Professor of Mathematics at the State University of New York-Buffalo, the first paper published in an accredited mathematics journal by an African American. He also published a study for the Committee of twelve for the advancement of the interests of the Negro race on Jackson, Mississippi in 1909, a textbook, Practical Arithmetic (1911), and an article on geometry teaching at Tuskegee in 1913.
Woodard was a respected mathematician, professor and mentor to his students at Howard University in Washington DC, where he established the masters program in mathematics. One of his best known students was William Waldron Schieffelin Claytor, who later took his PhD at the University of Pennsylvania (1933), also under Woodard's former advisor, John R. Kline.
Woodard retired in 1947, after having become chairman of the mathematics department. He died on July 1, 1965, at his home in Cleveland, Ohio, aged 83.
References
1881 births
1965 deaths
20th-century American mathematicians
African-American mathematicians
20th-century African-American academics
20th-century American academics
Howard University faculty
Wilberforce University alumni
University of Chicago alumni
University of Pennsylvania School of Arts and Sciences alumni
People from Galveston, Texas
20th-century African-American scientists |
https://en.wikipedia.org/wiki/Central%20Organization%20for%20Statistics | The Central Organization of Statistics & Information Technology (COSIT) or the Central Organization for Statistics (COS, ) is the Government of Iraq's statistics agency. It has its headquarters in Hay Al-Elwiya, Baghdad.
References
External links
Central Organization for Statistics
Central Organization for Statistics
Government agencies of Iraq
Iraq |
https://en.wikipedia.org/wiki/Neithalath%20Mohan%20Kumar | Neithalath Mohan Kumar (N. Mohan Kumar) (born 12 May 1951) is an Indian mathematician who specializes in commutative algebra and algebraic geometry. Kumar is a full professor at Washington University in St. Louis.
In 1994, he was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology, the highest science award in India in the mathematical sciences category. Kumar has made profound and original contributions to commutative algebra and algebraic geometry. He is well known for his contribution settling the Eisenbud-Evans conjecture proposed by David Eisenbud. His work on rational double points on rational surfaces has also been acclaimed.
References
Algebraic geometers
1951 births
Living people
University of Mumbai alumni
Washington University in St. Louis faculty
Washington University in St. Louis mathematicians
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/National%20Death%20Index | National Death Index (NDI) is a United States resource available to researchers from the US National Center for Health Statistics to obtain death status (regular NDI) or cause of death (NDI Plus) for deaths of citizens occurring within the US.
The fees for routine NDI searches consist of a $350.00 service charge plus $0.15 per user record for each year of death searched. For example, 1,000 records searched against 10 years would cost $350 + ($0.15 x 1,000 x 10) or $1,850. Fees for the NDI Plus service are slightly higher ($0.21) per record.
NDI is similar to Social Security Death Master File in terms of providing death status and date of death. However, NDI Plus service offers further information on cause of death.
The index was initially approved during Dorothy P. Rice's tenure as director.
In 2011, the National Death Index was linked to the General Social Survey, allowing for the analysis of societal attitudes and demographics, and their relationship to death.
References
External links
About the National Death Index
Centers for Disease Control and Prevention |
https://en.wikipedia.org/wiki/V.%20S.%20Sunder | Professor Vaikalathur Shankar Sunder (born 6 April 1952) is an Indian mathematician who specialises in subfactors, operator algebras and functional analysis in general.
In 1996, he was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology, the highest science award in India, in the mathematical sciences category.
Sunder is one of the first Indian operator algebraists. In addition to publishing about sixty papers, he has written six books including at least three monographs at the graduate level or higher on von Neumann algebras. One of the books was co-authored with Vaughan Jones, an operator algebraist, who has received the Fields Medal.
References
External links
Indian National Science Academy database
V.S. Sunder
1952 births
Living people
20th-century Indian mathematicians
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science
IIT Madras alumni
Indiana University alumni
Academic staff of the Indian Statistical Institute |
https://en.wikipedia.org/wiki/2013%E2%80%9314%20FK%20Vojvodina%20season | The 2013–14 season was FK Vojvodina's 8th season in Serbian SuperLiga. This article shows player statistics and all matches (official and friendly) that the club played during the 2013–14 season.
Players
Squad information
Squad statistics
Matches
Serbian SuperLiga
Serbian Cup
UEFA Europa League
External links
Official website
FK Vojvodina seasons
Vojvodina
Vojvodina |
https://en.wikipedia.org/wiki/List%20of%20Crystal%20Palace%20F.C.%20records%20and%20statistics | This article lists the records set by Crystal Palace F.C., their managers and players, including honours won by the club and details of their performance in European competition. The player records section itemises the club's leading goalscorers and those who have made the most appearances in first-team competitions. It also records notable achievements by Palace players on the international stage, and the highest transfer fees paid and received by the club.
Honours and achievements
Leagues
English first tier (currently the Premier League)
Highest finish: 3rd place, 1990–91
English second tier (currently the EFL Championship)
Champions (2): 1978–79, 1993–94
Runners-up (1): 1968–69
Play-off winners (4) (record): 1988–89, 1996–97, 2003–04, 2012–13
Play-off runners-up (1): 1995–96
English third tier (currently EFL League One)
Champions (1): 1920–21
Runners-up (4): 1928–29 (South), 1930–31 (South), 1938–39 (South), 1963–64
English fourth tier (currently EFL League Two)
Runners-up (1): 1960–61
Cups
FA Cup
Runners-up (2): 1989–90, 2015–16
Full Members Cup
Winners (1): 1990–91
Wartime
Football League South
Champions (1): 1940–41
Football League South 'D' Division
Champions (1): 1939–40
Regional
Southern Football League Division One
Runners-up (1): 1913–14
Southern Football League Division Two
Champions (1): 1905–06
United League
Champions (1): 1906–07
Runners-up (1): 1905–06
Southern Professional Floodlit Cup
Runners-up (1): 1958–59
London Challenge Cup
Winners (3): 1912–13, 1913–14, 1920–21
Runners-up (6): 1919–20, 1921–22, 1922–23, 1931–32, 1937–38, 1946–47
Surrey Senior Cup
Winners (3): 1996–97, 2000–01, 2001–02
Kent Senior Shield
Winners (1): 1911–12
Runners-up (1): 1912–13
Player records
Appearances
Youngest first-team player: John Bostock, 15 years, 287 days, v Watford, 29 October 2007
Oldest first-team player: Jack Little, 41 years, 68 days v Gillingham (away), 3 April 1926
First substitute: Keith Smith, v Leyton Orient, 28 August 1965
Most appearances
Competitive and professional matches only
Goalscorers
Most goals in a season: 54, Peter Simpson, 1930–31
Most league goals in a season: 46, Peter Simpson, 1930–31
Most league goals in a top-flight season: 21, Andy Johnson, 2004–05
Most goals in a competitive match: 6, Peter Simpson, v Exeter City, Football League Division Three South, 4 October 1930
Most goals in an FA Cup match: 4, Peter Simpson, v Newark Town, 13 December 1930
Most goals in a League Cup match: 3
Mark Bright, v Southend United, 25 September 1990
Ian Wright, v Southend United, 25 September 1990
Dwight Gayle, v Walsall, 26 August 2014
Dwight Gayle, v Charlton Athletic, 23 September 2015
Fastest recorded goal: 6 seconds, Keith Smith v Derby County (away), 12 December 1964
Most hat-tricks, all competitions: 20, Peter Simpson
Oldest player to score a goal: Kevin Phillips, 39 years 306 days, v Watford, 27 May 2013
Quickest hat-trick in a League match: Kevin Phillips, 8 minutes, 37 seconds v |
https://en.wikipedia.org/wiki/Outcome%20%28probability%29 | In probability theory, an outcome is a possible result of an experiment or trial. Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). All of the possible outcomes of an experiment form the elements of a sample space.
For the experiment where we flip a coin twice, the four possible outcomes that make up our sample space are (H, T), (T, H), (T, T) and (H, H), where "H" represents a "heads", and "T" represents a "tails". Outcomes should not be confused with events, which are (or informally, "groups") of outcomes. For comparison, we could define an event to occur when "at least one 'heads'" is flipped in the experiment - that is, when the outcome contains at least one 'heads'. This event would contain all outcomes in the sample space except the element (T, T).
Sets of outcomes: events
Since individual outcomes may be of little practical interest, or because there may be prohibitively (even infinitely) many of them, outcomes are grouped into sets of outcomes that satisfy some condition, which are called "events." The collection of all such events is a sigma-algebra.
An event containing exactly one outcome is called an elementary event. The event that contains all possible outcomes of an experiment is its sample space. A single outcome can be a part of many different events.
Typically, when the sample space is finite, any subset of the sample space is an event (that is, all elements of the power set of the sample space are defined as events). However, this approach does not work well in cases where the sample space is uncountably infinite (most notably when the outcome must be some real number). So, when defining a probability space it is possible, and often necessary, to exclude certain subsets of the sample space from being events.
Probability of an outcome
Outcomes may occur with probabilities that are between zero and one (inclusively). In a discrete probability distribution whose sample space is finite, each outcome is assigned a particular probability. In contrast, in a continuous distribution, individual outcomes all have zero probability, and non-zero probabilities can only be assigned to ranges of outcomes.
Some "mixed" distributions contain both stretches of continuous outcomes and some discrete outcomes; the discrete outcomes in such distributions can be called atoms and can have non-zero probabilities.
Under the measure-theoretic definition of a probability space, the probability of an outcome need not even be defined. In particular, the set of events on which probability is defined may be some σ-algebra on and not necessarily the full power set.
Equally likely outcomes
In some sample spaces, it is reasonable to estimate or assume that all outcomes in the space are equally likely (that they occur with equal probability). For example, when tossing an ordinary coin, one typically assumes that the outcomes "head" and |
https://en.wikipedia.org/wiki/Subhashis%20Nag | Subhashis Nag (14 August 1955 – 22 December 1998) was an Indian mathematician who specialised in complex analytic geometry, particularly Teichmüller theory, and its relations to string theory.
He won the Shanti Swarup Bhatnagar Prize for Science and Technology in 1998, the highest science award in India, in the mathematical sciences category. However, he died on 22 December 1998, before the actual award ceremony was held.
Books authored
References
1955 births
1998 deaths
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/Goldberg%20polyhedron | In mathematics, and more specifically in polyhedral combinatorics, a Goldberg polyhedron is a convex polyhedron made from hexagons and pentagons. They were first described in 1937 by Michael Goldberg (1902–1990). They are defined by three properties: each face is either a pentagon or hexagon, exactly three faces meet at each vertex, and they have rotational icosahedral symmetry. They are not necessarily mirror-symmetric; e.g. and are enantiomorphs of each other. A Goldberg polyhedron is a dual polyhedron of a geodesic sphere.
A consequence of Euler's polyhedron formula is that a Goldberg polyhedron always has exactly twelve pentagonal faces. Icosahedral symmetry ensures that the pentagons are always regular and that there are always 12 of them. If the vertices are not constrained to a sphere, the polyhedron can be constructed with planar equilateral (but not in general equiangular) faces.
Simple examples of Goldberg polyhedra include the dodecahedron and truncated icosahedron. Other forms can be described by taking a chess knight move from one pentagon to the next: first take steps in one direction, then turn 60° to the left and take steps. Such a polyhedron is denoted A dodecahedron is and a truncated icosahedron is
A similar technique can be applied to construct polyhedra with tetrahedral symmetry and octahedral symmetry. These polyhedra will have triangles or squares rather than pentagons. These variations are given Roman numeral subscripts denoting the number of sides on the non-hexagon faces: and
Elements
The number of vertices, edges, and faces of GP(m,n) can be computed from m and n, with T = m2 + mn + n2 = (m + n)2 − mn, depending on one of three symmetry systems:
The number of non-hexagonal faces can be determined using the Euler characteristic, as demonstrated here.
Construction
Most Goldberg polyhedra can be constructed using Conway polyhedron notation starting with (T)etrahedron, (C)ube, and (D)odecahedron seeds. The chamfer operator, c, replaces all edges by hexagons, transforming GP(m,n) to GP(2m,2n), with a T multiplier of 4. The truncated kis operator, y = tk, generates GP(3,0), transforming GP(m,n) to GP(3m,3n), with a T multiplier of 9.
For class 2 forms, the dual kis operator, z = dk, transforms GP(a,0) into GP(a,a), with a T multiplier of 3. For class 3 forms, the whirl operator, w, generates GP(2,1), with a T multiplier of 7. A clockwise and counterclockwise whirl generator, w = wrw generates GP(7,0) in class 1. In general, a whirl can transform a GP(a,b) into GP(a + 3b,2ab) for a > b and the same chiral direction. If chiral directions are reversed, GP(a,b) becomes GP(2a + 3b,a − 2b) if a ≥ 2b, and GP(3a + b,2b − a) if a < 2b.
Examples
See also
Capsid
Geodesic sphere
Fullerene#Other buckyballs
Conway polyhedron notation
Goldberg–Coxeter construction
Notes
References
Joseph D. Clinton, Clinton’s Equal Central Angle Conjecture
External links
Dual Geodesic Icosahedra
Goldberg variations: New shapes fo |
https://en.wikipedia.org/wiki/T.%20R.%20Ramadas | Trivandrum Ramakrishnan "T. R." Ramadas (born 30 March 1955) is an Indian mathematician who specializes in algebraic and differential geometry, and mathematical physics. He was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 1998, the highest science award in India, in the mathematical sciences category.
He studied engineering in IIT Kanpur then joined TIFR as a graduate student in physics finally changing to mathematics after his interactions with M S Narasimhan.
He is currently a professor at Chennai Mathematical Institute, Chennai, Tamil Nadu.
Selected publications
"The "Harder-Narasimhan Trace" and Unitarity of the KZ/Hitchin Connection: genus 0", Ann. of Math. 169, 1–39 (2009).
(With V.B. Mehta) "Moduli of vector bundles, Frobenius splitting, and invariant theory", Ann. of Math. 144, 269–313 (1996).
"Factorisation of generalised theta functions II", Topology 35, 641–654 (1996).
(With M.S. Narasimhan) "Factorisation of generalised theta functions I", Invent. Math. 114, 565–624 (1993).
(With I.M. Singer and J. Weitsman) "Some comments on Chern Simons gauge theory", Commun. Math. Phys. 126, 409–420 (1989).
(With P.K. Mitter) "The two-dimensional O(N) nonlinear =E5 model: renormalisation and effective actions", Commun. Math. Phys. 122, 575–596 (1989).
(With M.S. Narasimhan) "Geometry of SU(2) gauge fields", Commun. Math. Phys. 67, 121–136 (1979).
References
1955 births
Living people
Scientists from Thiruvananthapuram
Algebraists
Mathematical physicists
20th-century Indian mathematicians
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/New%20Zealand%20men%27s%20national%20football%20team%20results%20%281922%E2%80%931969%29 | This page details the match results and statistics of the New Zealand men's national football team from its first match in 1922 until the second match against Israel in 1969.
Key
Key to matches
Att. = Match attendance
(H) = Home ground
(A) = Away ground
(N) = Neutral ground
Key to record by opponent
Pld = Games played
W = Games won
D = Games drawn
L = Games lost
GF = Goals for
GA = Goals against
A-International results
New Zealand's score is shown first in each case.
Best/worst results
Streaks
Most wins in a row
7, 31 August 1958–4 June 1962
6, 30 September 1951–16 September 1952
Most matches without a loss
9, 30 September 1951–14 August 1954
Most losses in a row
16, 23 July 1927–19 September 1951
Most matches without a win
16, 23 July 1927–19 September 1951
Results by opposition
Results by year
See also
New Zealand national football team
New Zealand at the FIFA World Cup
New Zealand at the FIFA Confederations Cup
New Zealand at the OFC Nations Cup
References
1922–69 |
https://en.wikipedia.org/wiki/T.%20N.%20Venkataramana | Tyakal Nanjundiah Venkataramana (born 1958) is an Indian mathematician who specialises in algebraic groups and automorphic forms.
He was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 2001, the highest science award in India, in the mathematical sciences category. Venkataramana's first major work was the extension of G. A. Margulis's work on arithmeticity of higher rank lattices to the case of groups in positive characteristics. He also has contributions to non-vanishing theorems on cohomology of arithmetic groups, to Lefschetz type theorems on restriction of cohomology on locally symmetric spaces and to arithmeticity of monodromy groups.
Other awards/honours
Young Scientist Award (1990)
Birla Award (2000)
ICTP Prize (2000)
Fellow, Indian Academy of Sciences, Bangalore
Fellow, Indian National Science Academy, 2004
Fellow of the American Mathematical Society, 2012
Speaker at the ARbeitstagung, 1999
Invited Speaker at the ICM, 2010, Hyderabad
References
1958 births
20th-century Indian mathematicians
Indian group theorists
Academic staff of Tata Institute of Fundamental Research
Fellows of the Indian National Science Academy
Fellows of the Indian Academy of Sciences
Fellows of the American Mathematical Society
University of Mumbai alumni
Living people
Scientists from Bangalore
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/2013%E2%80%9314%20Red%20Star%20Belgrade%20season | This article shows player statistics and all results & fixtures (official and friendly) that the club have played (and will play) during the 2013–14 season. In season 2013–14 Red Star will be competing in Serbian SuperLiga, Serbian Cup and UEFA Europa League.
Previous season positions
Club
Club management
{| class="toccolours" style="border:#f00 solid 1px; background:#fff; font-size:88%;"
|+ style="background:#f00; color:#fff; font-size:120%;"| Current management
|
President: Dragan Džajić
Vice-president: Nebojša Čović
Vice-president: Slaviša Kokeza
Vice-president: Ivica Tončev
Sport director: Zoran Stojadinović
General secretary: Miodrag Zečević
Deputy general secretary: Stefan Pantović
Marketing director: Goran Broćić
Coaching staff
Grounds
Kit
Players
Current squad
Foreign players
Abiola Dauda
Ifeanyi Onyilo
Nejc Pečnik
Omega Roberts
Miguel Araujo
Players with dual citizenship
Abiola Dauda
Boban Bajković
Filip Kasalica
Marko Vešović
Vukan Savićević
Transfers
In
Total spending: Undisclosed (~ €1,500,000)
Loan return and promoted
Out
Total income: Undisclosed (~ €4,960,000)
Loan out
Overall transfer activity
Spending
Undisclosed (~ €1,500,000)
Income
Undisclosed (~ €4,960,000)
Net expenditure
Undisclosed (~ €3,460,000)
Non-competitive
Preseason
Uhrencup
Competitions
Overall
UEFA Europa League
Second qualifying round
Third qualifying round
Serbian Cup
Red Star will participate in the 8th Serbian Cup starting in First Round.
Matches
Serbian SuperLiga
The 2013–14 season is Red Star's 8th season in Serbian SuperLiga.
Matches
Results and positions by round
League table
Statistics
Squad statistics
Goalscorers
Includes all competitive matches. The list is sorted by shirt number when total goals are equal.
Clean sheets
Includes all competitive matches. The list is sorted by shirt number when total clean sheets are equal.
Captains
References
Red Star Belgrade seasons
Red Star Belgrade season
Serbian football championship-winning seasons |
https://en.wikipedia.org/wiki/K-SVD | In applied mathematics, k-SVD is a dictionary learning algorithm for creating a dictionary for sparse representations, via a singular value decomposition approach. k-SVD is a generalization of the k-means clustering method, and it works by iteratively alternating between sparse coding the input data based on the current dictionary, and updating the atoms in the dictionary to better fit the data. It is structurally related to the expectation maximization (EM) algorithm. k-SVD can be found widely in use in applications such as image processing, audio processing, biology, and document analysis.
k-SVD algorithm
k-SVD is a kind of generalization of k-means, as follows.
The k-means clustering can be also regarded as a method of sparse representation. That is, finding the best possible codebook to represent the data samples by nearest neighbor, by solving
which is nearly equivalent to
which is k-means that allows "weights".
The letter F denotes the Frobenius norm. The sparse representation term enforces k-means algorithm to use only one atom (column) in dictionary . To relax this constraint, the target of the k-SVD algorithm is to represent signal as a linear combination of atoms in .
The k-SVD algorithm follows the construction flow of the k-means algorithm. However, in contrast to k-means, in order to achieve a linear combination of atoms in , the sparsity term of the constraint is relaxed so that the number of nonzero entries of each column can be more than 1, but less than a number .
So, the objective function becomes
or in another objective form
In the k-SVD algorithm, the is first fixed and the best coefficient matrix is found. As finding the truly optimal is hard, we use an approximation pursuit method. Any algorithm such as OMP, the orthogonal matching pursuit can be used for the calculation of the coefficients, as long as it can supply a solution with a fixed and predetermined number of nonzero entries .
After the sparse coding task, the next is to search for a better dictionary . However, finding the whole dictionary all at a time is impossible, so the process is to update only one column of the dictionary each time, while fixing . The update of the -th column is done by rewriting the penalty term as
where denotes the k-th row of X.
By decomposing the multiplication into sum of rank 1 matrices, we can assume the other terms are assumed fixed, and the -th remains unknown. After this step, we can solve the minimization problem by approximate the term with a matrix using singular value decomposition, then update with it. However, the new solution of vector is very likely to be filled, because the sparsity constraint is not enforced.
To cure this problem, define as
which points to examples that use atom (also the entries of that is nonzero). Then, define as a matrix of size , with ones on the entries and zeros otherwise. When multiplying , this shrinks the row vector by discarding the zero entries. Simil |
https://en.wikipedia.org/wiki/Ueli%20Aebi | Ueli Aebi is a Swiss structural biologist and co-founder of the Maurice E. Müller Institute for Structural Biology at the Biozentrum University of Basel.
Life
Aebi studied physics, mathematics, and molecular biology at the Universities of Bern and Basel from 1967 to 1974, graduating in 1977 in biophysics at the University of Basel. After establishing his academic career in the United States (University of California, Los Angeles, Johns Hopkins University School of Medicine), in 1986 he returned to the Biozentrum as professor of structural biology. He was co-founder of the Maurice E. Müller Institute for Structural Biology and its director from 1986 until reaching emeritus status in 2011.
Work
Aebi is recognized as a pioneer in integrative structural biology as well as mechano- and nanobiology. His work focused on the elucidation of the structure, function and assembly of the cyto- and nucleoskeleton and the nuclear pore complex (NPC), as well as the amyloid fibrils that are a hallmark of Alzheimer's disease. He studied the architecture of diverse supramolecular assemblies using a combination of light, electron and atomic force microscopy, X-ray crystallography, and protein engineering. Among others, Aebi determined the 3-dimensional structure of the NPC by cryo-electron tomography.
Awards and honors
1993 Elected Member of the European Molecular Biology Organization
1999 Elected Member of the Academia Europaea
2007 Dr. honoris causa (h.c.) from the 1st Medical Faculty, Charles University, Prague, Czech Republic
2011 Carl Zeiss Lecture Award of the German Society for Cell Biology
2011 Distinguished Scientist Award of the Microscopy Society of America
References
External links
Webpage Biozentrum, Emeriti
Living people
Scientists from Bern
University of Bern alumni
Johns Hopkins School of Medicine alumni
Members of the European Molecular Biology Organization
Members of Academia Europaea
Biozentrum University of Basel
University of Basel alumni
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Bogdan%20Mili%C4%8Di%C4%87 | Bogdan Miličić (Serbian Cyrillic: Богдан Миличић; born January 6, 1989) is a Serbian football player who plays for FK Jedinstvo Putevi Užice.
Statistics
External links
stats at Srbijafudbal
Bogdan Miličić Stats at Utakmica.rs
Living people
1989 births
Footballers from Užice
Serbian men's footballers
Serbian expatriate men's footballers
FK Sloboda Užice players
FK Borac Čačak players
FK Zlatibor Čajetina players
Shirak SC players
Serbian SuperLiga players
Serbian First League players
Armenian Premier League players
Men's association football defenders
Serbian expatriate sportspeople in Armenia
Expatriate men's footballers in Armenia |
https://en.wikipedia.org/wiki/Ignatov%27s%20theorem | In probability and mathematical statistics, Ignatov's theorem is a basic result on the distribution of record values of a stochastic process.
Statement
Let X1, X2, ... be an infinite sequence of independent and identically distributed random variables. The initial rank of the nth term of this sequence is the value r such that for exactly r values of i less than or equal to n. Let denote the stochastic process consisting of the terms Xi having initial rank k; that is, Yk,j is the jth term of the stochastic process that achieves initial rank k. The sequence Yk is called the sequence of kth partial records. Ignatov's theorem states that the sequences Y1, Y2, Y3, ... are independent and identically distributed.
Note
The theorem is named after Tzvetan Ignatov a Bulgarian professor in probability and mathematical statistics at Sofia University. Due to it and his general contributions to mathematics, Prof. Ignatov was granted a Doctor Honoris Causa degree in 2013 from Sofia University. The recognition is given on extremely rare occasions and only to scholars with internationally landmark results.
References
Ilan Adler and Sheldon M. Ross, "Distribution of the Time of the First k-Record", Probability in the Engineering and Informational Sciences, Volume 11, Issue 3, July 1997, pp. 273–278
Ron Engelen, Paul Tommassen and Wim Vervaat, "Ignatov's Theorem: A New and Short Proof", Journal of Applied Probability, Vol. 25, A Celebration of Applied Probability (1988), pp. 229–236
Ignatov, Z., "Ein von der Variationsreihe erzeugter Poissonscher Punktprozess", Annuaire Univ. Sofia Fac. Math. Mech. 71, 1977, pp. 79–94
Ignatov, Z., "Point processes generated by order statistics and their applications". In: P. Bartfai and J. Tomko, eds., Point Processes and Queueing Problems, Keszthely (Hungary). Coll. Mat. Soc. 5. Janos Bolyai 24, 1978, pp. 109–116
Samuels, S., "All at once proof of Ignatov's theorem", Contemp. Math. 125, 1992, pp. 231–237
Yi-Ching Yao, "On Independence of k-Record Processes: Ignatov's Theorem Revisited", The Annals of Applied Probability, Vol. 7, No. 3 (Aug., 1997), pp. 815–821
Doctor Honoris Causa degree, 2013, in English
Doctor Honoris Causa degree, 2013, in Bulgarian
Theorems regarding stochastic processes |
https://en.wikipedia.org/wiki/2013%20FIFA%20Confederations%20Cup%20statistics | These are the statistics for the 2013 FIFA Confederations Cup, an eight-team tournament running from 15 June 2013 through 30 June 2013. The tournament took place in Brazil.
Goalscorers
5 goals
Fernando Torres
Fred
4 goals
Neymar
Abel Hernández
3 goals
Javier Hernández
Nnamdi Oduamadi
David Villa
Edinson Cavani
Luis Suárez
2 goals
Jô
Paulinho
Mario Balotelli
Shinji Okazaki
Jordi Alba
David Silva
1 goal
Dante
Davide Astori
Giorgio Chiellini
Daniele De Rossi
Alessandro Diamanti
Emanuele Giaccherini
Sebastian Giovinco
Andrea Pirlo
Keisuke Honda
Shinji Kagawa
Elderson Echiéjilé
Mikel John Obi
Juan Mata
Pedro
Roberto Soldado
Jonathan Tehau
Diego Forlán
Nicolás Lodeiro
Diego Lugano
Diego Pérez
Own goal
Atsuto Uchida (for Italy)
Jonathan Tehau (for Nigeria)
Nicolas Vallar (for Nigeria)
Source: FIFA
Assists
3 assists
Walter Gargano
Neymar
2 assists
Oscar
Yasuhito Endō
Brown Ideye
Ahmed Musa
David Villa
Nicolás Lodeiro
1 assist
Twenty-six players
Source: FIFA
Scoring
Man of the Match
Overall statistics
Bold numbers indicate the maximum values in each column.
Stadiums
References
External links
2013 FIFA Confederations Cup at FIFA.com
Statistics |
https://en.wikipedia.org/wiki/Sundaram%20Thangavelu | S. Thangavelu (Sundaram Thangavelu) (born 1957) is an Indian mathematician who specialised in harmonic analysis. He is a professor in the Department of Mathematics of Indian Institute of Science, Bangalore.
After obtaining an MSc degree from Madras University in 1980, Thangavelu moved to Princeton University and obtained the PhD degree in 1987 from there under the supervision of Elias Stein. He returned to India and worked at Tata Institute of Fundamental Research until 1993 when he moved to Indian Statistical Institute, Bangalore. In 2005, he shifted to Indian Institute of Science and continues there as Professor in the Department of Mathematics.
He was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 2002, the highest science award in India, in the mathematical sciences category.
Thangavelu has made significant contributions to the field of harmonic analysis on Euclidean spaces, Heisenberg groups and symmetric spaces, and also authored three monographs in these areas.
Monographs
Lectures on Hermite & Laguerre Expansions Mathematical Notes, 42. Princeton University Press, Princeton, New Jersey, 1993.
Harmonic Analysis on the Heisenberg Group, Progress in Mathematics, 159. Birkhäuser Boston, Inc., Boston, Massachusetts, 1998.
An Introduction to the Uncertainty Principle: Hardy's Theorem on Lie Groups, Progress in Mathematics, 217. Birkhäuser Boston, Inc., Boston, Massachusetts, 2004.
Other awards/honours
Fellow of the Indian Academy of Sciences, Bangalore
B.M. Birla Science Prize in Mathematics for the year 1996
Fellow of the Indian National Science Academy, New Delhi
References
1957 births
Living people
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/Vasudevan%20Srinivas | Vasudevan Srinivas (born 6 June 1958) is an Indian mathematician working in algebraic geometry. He is a Distinguished Professor in the School of Mathematics Tata Institute of Fundamental Research, Mumbai. Srinivas is an elected Fellow of the Third World Academy of Sciences, American Mathematical Society, Indian National Science Academy, and the Indian Academy of Sciences.
Srinivas received the BSc degree from Bangalore University and did his MS (1978) and PhD (1982) degrees at the University of Chicago. Spencer Bloch was his research supervisor. He began his academic career at the Tata Institute of Fundamental Research, Mumbai in 1983.
Career
Mathematical contributions
Srinivas works in the field of algebraic geometry; his particular subfields of interest include the areas of algebraic cycles, K-theory, commutative algebra and positive characteristic methods. He is well-known for the Bloch-Srinivas method of diagonal decomposition to study algebraic cycles. He has also made outstanding contributions to the study of algebraic cycles on singular varieties, an area of which he is essentially an originator. Among some of his other contributions are the resolution of the Zariski problem for linear systems (in collaboration with Steven Dale Cutkosky), the characterization of the projecive space among homogeneous spaces (in collaboration with Kapil Paranjape) and the characterization of rational singularities (in collaboration with Vikram Mehta).
Srinivas's book on "Algebraic K-theory" which grew out of his lectures on the topic at TIFR in 1986-87 is now a standard reference for the subject for beginning researchers in the area.
Service
Srinivas has played an important role in the promotion of mathematics through various scientific bodies, in both advisory and administrative capacities. He served on the International Mathematical Union Executive Committee from 2011 to 2018. He serves on the editorial boards of several mathematics journals. He is presently the Chairman of the National Board for Higher Mathematics, India.
Awards and distinctions
He was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 2003, the highest science award in India, in the mathematical sciences category.
In 2010, he was an invited speaker at the International Congress of Mathematicians held at Hyderabad.
Other awards/honours
Indian National Science Academy Medal for Young Scientists, 1987
B.M. Birla Science Prize in Mathematics for the year 1995
Fellow of the Indian National Science Academy, New Delhi
TWAS Prize (2008)
Fellow of the American Mathematical Society, 2012
Humboldt Research Award, 2013
DFG Mercator Fellowship 2020-2024
References
1958 births
Living people
20th-century Indian mathematicians
Bangalore University alumni
University of Chicago alumni
Academic staff of Tata Institute of Fundamental Research
Fellows of the American Mathematical Society
TWAS laureates
Recipients of the Shanti Swarup Bhatnagar Award in Mathematica |
https://en.wikipedia.org/wiki/Arup%20Bose | Arup Bose (born 1 April 1959) is an Indian statistician. He is a Professor of Theoretical Statistics and Mathematics, in Indian Statistical Institute, Kolkata.
Arup Bose obtained his B.Stat, M.Stat and Ph.D (Statistics) degrees from the Indian Statistical Institute, Kolkata where G. Jogesh Babu was his PhD supervisor. He then joined Purdue University, USA, as an Assistant Professor. After four years at Purdue, he returned to India in 1991 and joined the Indian Statistical Institute, Kolkata as an Associate Professor and was promoted to full Professorship in 1995.
Most notable areas of his research include, sequential analysis, statistical estimation in diffusion processes, the law of large numbers and central limit theorems, resampling methods, censored data problems, M-estimation, U-statistics, time series, asymptotic properties of estimators and so on.
He is a member of Bernoulli Society for Mathematical Statistics and Probability, Netherlands, life member of Calcutta Statistical Association and a life member of Indian Mathematical Society.
He was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 2004, the highest science award in India, in the mathematical sciences category.
He was an invited speaker in International Congress of Mathematicians 2010, Hyderabad on the topic of "Probability and Statistics."
Other awards/honours
Elected Fellow of Institute of Mathematical Statistics, USA, 2002
National Award in Statistics in honour of Prof C. R. Rao for the year 2002–03
Young Researcher Award, International Indian Statistical Association USA 2004
Fellow of the Indian Academy of Sciences, Bangalore (2006)
Fellow of the Indian National Science Academy, New Delhi (2007)
Fellow of the National Academy of Sciences, Allahabad (2009)
J. C. Bose Fellow, DST Govt. of India 2009–2013, 2013–2018
Bernoulli Society Council Member, 2015–2019
References
20th-century Indian mathematicians
1959 births
Indian statisticians
Indian Statistical Institute alumni
Academic staff of the Indian Statistical Institute
Purdue University faculty
Fellows of the Indian National Science Academy
Fellows of the Indian Academy of Sciences
Fellows of The National Academy of Sciences, India
Living people
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science
21st-century Bengalis
Bengali mathematicians
Bengali Hindus
Scientists from Kolkata |
https://en.wikipedia.org/wiki/Probal%20Chaudhuri | Probal Chaudhuri (born 1963) is an Indian statistician. He is a professor of theoretical statistics and mathematics in the Indian Statistical Institute, Kolkata.
Chaudhuri obtained his BStat and MStat degrees from the Indian Statistical Institute, Kolkata, and PhD from University of California, Berkeley. He then joined University of Wisconsin, Madison as an assistant professor in 1988. After two years he returned to India in 1990 and joined the Indian Statistical Institute, Kolkata, as a lecturer. He was promoted to full professorship in 1997. Some of the widely used statistical techniques and concepts that he has invented and developed include: local polynomial nonparametric quantile regression, a geometric notion of quantiles for multivariate data, adaptive transformation and re-transformation technique for the construction of affine invariant distribution-free tests and robust estimates from multivariate data and the scale-space approach in function estimation and smoothing.
He was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 2005, the highest science award in India, in the mathematical sciences category.
He was an invited speaker in International Congress of Mathematicians 2010, Hyderabad on the topic of "Probability and Statistics."
Other awards/honours
BM Birla Science Award (2001)
C. R. Rao National Award in Statistics (2005)
Fellow of Indian Academy of Sciences, Bangalore
Fellow of National Academy of Sciences (India), Allahabad
References
1963 births
Living people
20th-century Indian mathematicians
Fellows of the Indian National Science Academy
Academic staff of the Indian Statistical Institute
Indian Statistical Institute alumni
University of California, Berkeley alumni
University of Wisconsin–Madison faculty
Indian statisticians
Probability theorists
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science
Scientists from West Bengal |
https://en.wikipedia.org/wiki/Kapil%20Hari%20Paranjape | Kapil Hari Paranjape is an Indian mathematician specializing in algebraic geometry. He is a Professor of Mathematics at the Indian Institute of Science Education and Research, Mohali.
Biography
He was born in Mumbai, Maharashtra near the Kabootar Khana in Dadar but grew up in New Delhi. He completed his schooling from Sardar Patel Vidyalaya in 1977. He then joined Indian Institute of Technology Kanpur where he pursued a five-years integrated Master’s programme in Mathematics and graduated in 1982. He was awarded the General Proficiency Prize for Mathematics from IIT Kanpur (1982).
He joined School of Mathematics, Tata Institute of Fundamental Research as was awarded his PhD in Mathematics in 1992.
Paranjape is also involved in the promotion of Linux and GNU and writes a blog Mast Kalandar.
Career
He worked as a Reader at TIFR from 1993-1998. During this he also held various visiting positions at
University of Chicago, University of Paris-Sud and University of Warwick. He was appointed as Professor at the Theoretical Statistics and Mathematics Unit of the Indian Statistical Institute, Bangalore. He moved to Institute of Mathematical Sciences, Chennai in 1996. Between 2001 and 2009 he has held visiting positions at California Institute of Technology. Since 2009 he is a professor of Mathematics at Indian Institute of Science Education and Research, Mohali. He was Clark Way Harrison Visiting Professor in Washington University in 2019.
Awards and honors
He was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 2005, the highest science award in India, in the mathematical sciences category. His citation read "Dr Paranjape has made outstanding contributions in the field of algebraic geometry, especially the theory of algebraic cycles. He has made highly significant contributions in connecting Hodge Theory to the study of Chow Groups. He has also established deep relations between Calabi-Yau varieties and modular forms.". He is also a recipient of various other honors, among them are
Fellowship of Indian Academy of Sciences Bangalore, 1997
Fellowship of National Academy of Sciences Allahabad, 1999
Associate of the ICTP, Trieste, 1999-2001
B. M. Birla award for young scientists, 1999
DST Swarnajayanti Grant, 2001
NBHM National Lecturer, India, 2004-2005
Debian Developer, 2007
Fellowship of Indian National Science Academy, New Delhi, 2009
J C Bose National Fellowship, 2010
Fellowship of The World Academy of Sciences (TWAS), 2019
References
External links
People from Sahibzada Ajit Singh Nagar district
Fellows of the Indian National Science Academy
20th-century Indian mathematicians
IIT Kanpur alumni
21st-century Indian mathematicians
TWAS fellows
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/2013%E2%80%9314%20F.C.%20Copenhagen%20season | This article shows statistics of individual players for the football club F.C. Copenhagen. It also lists all matches that F.C. Copenhagen played in the 2013–14 season.
Players
Squad information
This section show the squad as currently, considering all players who are confirmedly moved in and out (see section Players in / out).
Squad stats
Players in / out
In
Out
Club
Coaching staff
Kit
|
|
|
|
Other information
Competitions
Overall
Danish Superliga
Classification
Results summary
Results by round
UEFA Champions League
Group B
Results summary
Matches
Competitive
References
External links
F.C. Copenhagen official website
2013-14
Danish football clubs 2013–14 season
2013–14 UEFA Champions League participants seasons |
https://en.wikipedia.org/wiki/Carr%E2%80%93Madan%20formula | In financial mathematics, the Carr–Madan formula of Peter Carr and Dilip B. Madan shows that the analytical solution of the European option price can be obtained once the explicit form of the characteristic function of , where is the price of the underlying asset at time , is available. This analytical solution is in the form of the Fourier transform, which then allows for the fast Fourier transform to be employed to numerically compute option values and Greeks in an efficient manner.
References
Further reading
.
Mathematical finance
Special functions
Financial models
Options_(finance)
Fourier analysis |
https://en.wikipedia.org/wiki/Integer-valued%20function | In mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member of its domain.
The floor and ceiling functions are examples of integer-valued functions of a real variable, but on real numbers and, generally, on (non-disconnected) topological spaces integer-valued functions are not especially useful. Any such function on a connected space either has discontinuities or is constant. On the other hand, on discrete and other totally disconnected spaces integer-valued functions have roughly the same importance as real-valued functions have on non-discrete spaces.
Any function with natural, or non-negative integer values is a partial case of an integer-valued function.
Examples
Integer-valued functions defined on the domain of all real numbers include the floor and ceiling functions, the Dirichlet function, the sign function and the Heaviside step function (except possibly at 0).
Integer-valued functions defined on the domain of non-negative real numbers include the integer square root function and the prime-counting function.
Algebraic properties
On an arbitrary set , integer-valued functions form a ring with pointwise operations of addition and multiplication, and also an algebra over the ring of integers. Since the latter is an ordered ring, the functions form a partially ordered ring:
Uses
Graph theory and algebra
Integer-valued functions are ubiquitous in graph theory. They also have similar uses in geometric group theory, where length function represents the concept of norm, and word metric represents the concept of metric.
Integer-valued polynomials are important in ring theory.
Mathematical logic and computability theory
In mathematical logic, such concepts as primitive recursive functions and μ-recursive functions represent integer-valued functions of several natural variables or, in other words, functions on . Gödel numbering, defined on well-formed formulae of some formal language, is a natural-valued function.
Computability theory is essentially based on natural numbers and natural (or integer) functions on them.
Number theory
In number theory, many arithmetic functions are integer-valued.
Computer science
In computer programming, many functions return values of integer type due to simplicity of implementation.
See also
Integer-valued polynomial
Semi-continuity
Rank (disambiguation)#Mathematics
Grade (disambiguation)#In mathematics
Types of functions |
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