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https://en.wikipedia.org/wiki/2010%20Maria%20Sharapova%20tennis%20season | Results and statistics from Maria Sharapova's 2010 tennis season.
Yearly summary
Australian Open series
Sharapova began her season at the Australian Open, as the 14th seed. She was knocked out in the first round by compatriot Maria Kirilenko in three sets; this marked Sharapova's worst performance at a Major tournament since she lost in the first round of the 2003 French Open, and the first time she lost a match at the tournament since her heavy defeat in the 2007 final to Serena Williams (she did not participate in 2009 due to injury).
North American season
Rather than participate at the two Middle East Premier tournaments in Doha and Dubai, Sharapova decided to instead compete at the Cellular South Cup in Memphis, as a means of attempting to regain her confidence following her first round defeat in Australia. As the top seed in the tournament, Sharapova won the tournament without dropping a set, defeating Shenay Perry, Bethanie Mattek-Sands, Elena Baltacha, Petra Kvitová and Sofia Arvidsson on her way to capturing her 21st career title.
Sharapova's next tournament was Indian Wells. After receiving a bye in the first round, and defeating compatriot Vera Dushevina in the second, Sharapova was upset in the third round by Zheng Jie of China in three sets. Following the defeat, Sharapova then withdrew from Miami citing an elbow injury. This was the third year in a row in which Sharapova was forced to miss the North American hard-court season concluder.
Clay court season
After a few weeks off the tour, Sharapova returned at the Madrid Open in May, but, as it was at the Australian Open earlier in the year, her tournament would be another short affair, as she fell in the first round to Lucie Šafářová. Following the early exit in Madrid, Sharapova then entered the Internationaux de Strasbourg as a wildcard entry and the top seed, where she would win her second title for the year, by defeating Kristina Barrois in the final.
Sharapova then competed at the French Open as the 11th seed. After routine straight sets victories over Ksenia Pervak and Kirsten Flipkens in the first two rounds, Sharapova lost in the third round to four-times champion Justine Henin, however, she would become the first player since Svetlana Kuznetsova in 2005 to win a set against the Belgian at the French Open. Sharapova was also the last player to be beaten by the Belgian at the tournament; Henin's victory was her 23rd (and last) consecutive match victory at the tournament.
Grass court season
Following the French Open, Sharapova started her preparations for Wimbledon by reaching the final of the Aegon Classic in Birmingham, where she was beaten by top seed Li Na after serving seven double faults in the match.
Sharapova was seeded 16th at Wimbledon. She defeated Anastasia Pivovarova, Ioana Raluca Olaru and Barbora Záhlavová-Strýcová in the first three rounds, all in straight sets, to set up a fourth round showdown against defending champion Serena Williams, in what would |
https://en.wikipedia.org/wiki/List%20of%20polyhedral%20stellations | In the geometry of three dimensions, a stellation extends a polyhedron to form a new figure that is also a polyhedron. The following is a list of stellations of various polyhedra.
See also
List of Wenninger polyhedron models
The Fifty-Nine Icosahedra
Footnotes
References
Mathematics-related lists |
https://en.wikipedia.org/wiki/Hypertoric%20variety | In mathematics, a hypertoric variety or toric hyperkähler variety is a quaternionic analog of a toric variety constructed by applying the hyper-Kähler quotient construction of to a torus acting on a quaternionic vector space. gave a systematic description of hypertoric varieties.
References
Algebraic geometry |
https://en.wikipedia.org/wiki/International%20Symposium%20on%20Symbolic%20and%20Algebraic%20Computation | ISSAC, the International Symposium on Symbolic and Algebraic Computation, is an academic conference in the field of computer algebra. ISSAC has been organized annually since 1988, typically in July. The conference is regularly sponsored by the Association for Computing Machinery special interest group SIGSAM, and the proceedings since 1989 have been published by ACM. ISSAC is considered as being one of the most influential conferences for the publication of scientific computing research.
History
The first ISSAC took place in Rome on 4–8 July 1988. It succeeded a series of meetings held between 1966 and 1987 under the names SYMSAM, SYMSAC, EUROCAL, EUROSAM and EUROCAM.
ISSAC Awards
The Richard D. Jenks Memorial Prize for excellence in software engineering applied to computer algebra is awarded at ISSAC every other year since 2004.
The ISSAC Distinguished Paper Award is awarded at ISSAC since 2002 to authors that display excellence in areas that include, but are not limited to, algebraic computation, symbolic-numeric computation, and system design and implementation.
The ISSAC Distinguished Student Author Award is awarded at ISSAC since 2004 to authors if they were a student at the time their paper was submitted.
Conference topics
Typical topics include:
exact linear algebra;
polynomial system solving;
symbolic summation;
symbolic integration and computational differential algebra;
computational group theory;
symbolic-numeric algorithms;
the design and implementation of computer algebra systems;
applications of computer algebra.
See also
Journal of Symbolic Computation
References
External links
ISSAC web page
Bibliographic information about ISSAC at DBLP
Computer algebra
Theoretical computer science conferences
Recurring events established in 1988
Association for Computing Machinery conferences |
https://en.wikipedia.org/wiki/Adhesive%20category | In mathematics, an adhesive category is a category where pushouts of monomorphisms exist and work more or less as they do in the category of sets. An example of an adhesive category is the category of directed multigraphs, or quivers, and the theory of adhesive categories is important in the theory of graph rewriting.
More precisely, an adhesive category is one where any of the following equivalent conditions hold:
C has all pullbacks, it has pushouts along monomorphisms, and pushout squares of monomorphisms are also pullback squares and are stable under pullback.
C has all pullbacks, it has pushouts along monomorphisms, and the latter are also (bicategorical) pushouts in the bicategory of spans in C.
If C is small, we may equivalently say that C has all pullbacks, has pushouts along monomorphisms, and admits a full embedding into a Grothendieck topos preserving pullbacks and preserving pushouts of monomorphisms.
References
Steve Lack and Pawel Sobocinski, Adhesive categories, Basic Research in Computer Science series, BRICS RS-03-31, October 2003.
Richard Garner and Steve Lack, "On the axioms for adhesive and quasiadhesive categories", Theory and Applications of Categories, Vol. 27, 2012, No. 3, pp 27–46.
Steve Lack and Pawel Sobocinski, "Toposes are adhesive".
Steve Lack, "An embedding theorem for adhesive categories", Theory and Applications of Categories, Vol. 25, 2011, No. 7, pp 180–188.
External links
Category theory |
https://en.wikipedia.org/wiki/Symmetric%20probability%20distribution | In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function (for continuous probability distribution) or probability mass function (for discrete random variables) is reflected around a vertical line at some value of the random variable represented by the distribution. This vertical line is the line of symmetry of the distribution. Thus the probability of being any given distance on one side of the value about which symmetry occurs is the same as the probability of being the same distance on the other side of that value.
Formal definition
A probability distribution is said to be symmetric if and only if there exists a value such that
for all real numbers
where f is the probability density function if the distribution is continuous or the probability mass function if the distribution is discrete.
Multivariate distributions
The degree of symmetry, in the sense of mirror symmetry, can be evaluated quantitatively for multivariate distributions with the chiral index, which takes values in the interval [0;1], and which is null if and only if the distribution is mirror symmetric.
Thus, a d-variate distribution is defined to be mirror symmetric when its chiral index is null.
The distribution can be discrete or continuous, and the existence of a density is not required, but the inertia must be finite and non null.
In the univariate case, this index was proposed as a non parametric test of symmetry.
For continuous symmetric spherical, Mir M. Ali gave the following definition. Let denote the class of spherically symmetric distributions of the absolutely continuous type in the n-dimensional Euclidean space having joint density of the form inside a sphere with center at the origin with a prescribed radius which may be finite or infinite and zero elsewhere.
Properties
The median and the mean (if it exists) of a symmetric distribution both occur at the point about which the symmetry occurs.
If a symmetric distribution is unimodal, the mode coincides with the median and mean.
All odd central moments of a symmetric distribution equal zero (if they exist), because in the calculation of such moments the negative terms arising from negative deviations from exactly balance the positive terms arising from equal positive deviations from .
Every measure of skewness equals zero for a symmetric distribution.
Unimodal case
Partial list of examples
The following distributions are symmetric for all parametrizations. (Many other distributions are symmetric for a particular parametrization.)
References |
https://en.wikipedia.org/wiki/Set%20estimation | In statistics, a random vector x is classically represented by a probability density function.
In a set-membership approach or set estimation, x is represented by a set X to which x is assumed to belong. This means that the support of the probability distribution function of x is included inside X. On the one hand, representing random vectors by sets makes it possible to provide fewer assumptions on the random variables (such as independence) and dealing with nonlinearities is easier. On the other hand, a probability distribution function provides a more accurate information than a set enclosing its support.
Set-membership estimation
Set membership estimation (or set estimation for short) is an estimation approach which considers that measurements are represented by a set Y (most of the time a box of Rm, where m
is the number of measurements) of the measurement space. If p is the parameter vector and f is the model function, then the set of all feasible parameter vectors is
,
where P0 is the prior set for the parameters. Characterizing P corresponds to a set-inversion problem.
Resolution
When f is linear the feasible set P can be described by linear inequalities and can be approximated using linear programming techniques.
When f is nonlinear, the resolution can be performed using interval analysis. The feasible set P is then approximated by an inner and an outer subpavings. The main limitation of the method is its exponential complexity with respect to the number of parameters.
Example
Consider the following model
where p1 and p2 are the two parameters
to be estimated.
Assume that at times t1=−1, t2=1, t3=2,
the following interval measurements have been collected:
[y1]=[−4,−2],
[y2]=[4,9],
[y3]=[7,11],
as illustrated by Figure 1. The corresponding measurement set (here a box) is
.
The model function is defined by
The components of f are obtained using the model for each time measurement.
After solving the set inversion problem, we get the approximation depicted on Figure 2.
Red boxes are inside the feasible set P and blue boxes are outside P.
Recursive case
Set estimation can be used to estimate the state of a system described by state equations using a recursive implementation.
When the system is linear, the corresponding feasible set for the state vector can be described by polytopes or by ellipsoids
.
When the system is nonlinear, the set can be enclosed by subpavings.
Robust case
When outliers occur, the set estimation method generally returns an empty set. This is
due to the fact that the intersection between of sets of parameter vectors that are consistent
with the ith data bar is empty. To be robust with respect to outliers,
we generally characterize the set of parameter vectors that are consistent with
all data bars except q of them. This is possible using the notion of q-relaxed intersection.
See also
Set identification
References
Estimation theory |
https://en.wikipedia.org/wiki/Almost%20ring | In mathematics, almost modules and almost rings are certain objects interpolating between rings and their fields of fractions. They were introduced by in his study of p-adic Hodge theory.
Almost modules
Let V be a local integral domain with the maximal ideal m, and K a fraction field of V. The category of K-modules, K-Mod, may be obtained as a quotient of V-Mod by the Serre subcategory of torsion modules, i.e. those N such that any element n in N is annihilated by some nonzero element in the maximal ideal. If the category of torsion modules is replaced by a smaller subcategory, we obtain an intermediate step between V-modules and K-modules. Faltings proposed to use the subcategory of almost zero modules, i.e. N ∈ V-Mod such that any element n in N is annihilated by all elements of the maximal ideal.
For this idea to work, m and V must satisfy certain technical conditions. Let V be a ring (not necessarily local) and m ⊆ V an idempotent ideal, i.e. an ideal such that m2 = m. Assume also that m ⊗ m is a flat V-module. A module N over V is almost zero with respect to such m if for all ε ∈ m and n ∈ N we have εn = 0. Almost zero modules form a Serre subcategory of the category of V-modules. The category of almost V-modules, Va-Mod, is a localization of V-Mod along this subcategory.
The quotient functor V-Mod → Va-Mod is denoted by . The assumptions on m guarantee that is an exact functor which has both the right adjoint functor and the left adjoint functor . Moreover, is full and faithful. The category of almost modules is complete and cocomplete.
Almost rings
The tensor product of V-modules descends to a monoidal structure on Va-Mod. An almost module R ∈ Va-Mod with a map R ⊗ R → R satisfying natural conditions, similar to a definition of a ring, is called an almost V-algebra or an almost ring if the context is unambiguous. Many standard properties of algebras and morphisms between them carry to the "almost" world.
Example
In the original paper by Faltings, V was the integral closure of a discrete valuation ring in the algebraic closure of its quotient field, and m its maximal ideal. For example, let V be , i.e. a p-adic completion of . Take m to be the maximal ideal of this ring. Then the quotient V/m is an almost zero module, while V/p is a torsion, but not almost zero module since the class of p1/p2 in the quotient is not annihilated by p1/p2 considered as an element of m.
References
Commutative algebra |
https://en.wikipedia.org/wiki/NCAA%20Division%20I%20Men%27s%20Golf%20Tournament%20all-time%20individual%20records | The following is a list of National Collegiate Athletic Association (NCAA) Division I college golf individual statistics and records through the 2018 NCAA Division I Men's Golf Championship. The NCAA began sponsoring the national collegiate championship in 1939. Before that year the event was conducted by the National Intercollegiate Golf Association.
Individual national championships
Individual records
Most individual championships: 3
Ben Crenshaw, Texas (1971, 1972, 1973)
Phil Mickelson, Arizona State (1989, 1990, 1992)
Most consecutive individual championships: 3
Ben Crenshaw, Texas (1971–1973)
Lowest score (in relation to par), one round: 60 (−12)
Nick Dunlap, Alabama, (2023, second round, Hamptons Intercollegiate)
Lowest score (in relation to par), two rounds: 128 (−16)
Phil Mickelson, Arizona State (1992)
Lowest score (in relation to par), three rounds: 196 (−20)
Charles Howell III, Oklahoma State (2000)
Lowest score (in relation to par), four rounds: 265 (−23)
Charles Howell III, Oklahoma State (2000)
References
External links
NCAA Men's Golf
College golf in the United States
Golf records and rankings |
https://en.wikipedia.org/wiki/Stack-sortable%20permutation | In mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm whose internal storage is limited to a single stack data structure. The stack-sortable permutations are exactly the permutations that do not contain the permutation pattern 231; they are counted by the Catalan numbers, and may be placed in bijection with many other combinatorial objects with the same counting function including Dyck paths and binary trees.
Sorting with a stack
The problem of sorting an input sequence using a stack was first posed by , who gave the following linear time algorithm (closely related to algorithms for the later all nearest smaller values problem):
Initialize an empty stack
For each input value x:
While the stack is nonempty and x is larger than the top item on the stack, pop the stack to the output
Push x onto the stack
While the stack is nonempty, pop it to the output
Knuth observed that this algorithm correctly sorts some input sequences, and fails to sort others. For instance, the sequence 3,2,1 is correctly sorted: the three elements are all pushed onto the stack, and then popped in the order 1,2,3. However, the sequence 2,3,1 is not correctly sorted: the algorithm first pushes 2, and pops it when it sees the larger input value 3, causing 2 to be output before 1 rather than after it.
Because this algorithm is a comparison sort, its success or failure does not depend on the numerical values of the input sequence, but only on their relative order; that is, an input may be described by the permutation needed to form that input from a sorted sequence of the same length. Knuth characterized the permutations that this algorithm correctly sorts as being exactly the permutations that do not contain the permutation pattern 231: three elements x, y, and z, appearing in the input in that respective order, with z < x < y. Moreover, he observed that, if the algorithm fails to sort an input, then that input cannot be sorted with a single stack.
As well as inspiring much subsequent work on sorting using more complicated systems of stacks and related data structures, Knuth's research kicked off the study of permutation patterns and of permutation classes defined by forbidden patterns.
Bijections and enumeration
The sequence of pushes and pops performed by Knuth's sorting algorithm as it sorts a stack-sortable permutation form a Dyck language: reinterpreting a push as a left parenthesis and a pop as a right parenthesis produces a string of balanced parentheses. Moreover, every Dyck string comes from a stack-sortable permutation in this way, and every two different stack-sortable permutations produce different Dyck strings. For this reason, the number of stack-sortable permutations of length n is the same as the number of Dyck strings of length 2n, the Catalan number
Stack-sortable permutations may also be translated directly to and from (unlabeled) binary trees, anot |
https://en.wikipedia.org/wiki/Isometry%20%28mathematics%29%20%28disambiguation%29 | {{safesubst:#invoke:RfD||INTDABLINK of redirects from incomplete disambiguation|month = October
|day = 14
|year = 2023
|time = 06:45
|timestamp = 20231014064523
|content=#REDIRECT Isometry (disambiguation)
}} |
https://en.wikipedia.org/wiki/Hasbullah%20Awang%20%28footballer%29 | Mohammed Hasbullah bin Awang (born 3 April 1983 in Terengganu) is a Malaysian footballer who plays and captain for Terengganu II in Malaysia Premier League as a defender.
Career statistics
References
External links
Hasbullah Awang Profile
1983 births
Living people
Malaysian men's footballers
Terengganu F.C. II players
Footballers from Terengganu
Malaysian people of Malay descent
Men's association football defenders |
https://en.wikipedia.org/wiki/B.%20L.%20S.%20Prakasa%20Rao | Bhagavatula Lakshmi Surya Prakasa Rao is an Indian statistician. He was born on 6 October 1942 in Porumamilla, Andhra Pradesh. He completed his B.A. (Honours) course in Mathematics from Andhra University in 1960 and moved to the Indian Statistical Institute, Kolkata, where he completed his M.Stat in Statistics in 1962. He graduated with a Ph.D in Statistics in 1966 from Michigan State University under Herman Rubin. He won the Shanti Swarup Bhatnagar Prize for Science and Technology in Mathematical Sciences in 1982 from the Government of India, the Outstanding Alumni award from the Michigan State University in 1996, and the National Award in memory of P V Sukhatme in 2008 from the Government of India. The Indian Society for Probability and Statistics awarded him the C R Rao Lifetime Achievement Award in 2022. He is an elected Fellow of the Institute of Mathematical Statistics (1983), Indian National Science Academy (1984), Indian Academy of Sciences (1992), and National Academy of Sciences (1993).
Academic life
He worked at the Indian Institute of Technology, Kanpur at the beginning of his career and later moved to Indian Statistical Institute, New Delhi. He was a Distinguished Scientist and Director of the Indian Statistical Institute, Kolkata from 1992 to 1995. He also held visiting professorships at the University of California, Berkeley, University of Illinois, University of Wisconsin, Purdue University, University of California, Davis and University of Iowa. He has held the Jawaharlal Nehru Chair Professorship (2006–08), Dr. Homi J. Bhabha Chair Professorship (2008–12) at the University of Hyderabad, and the Ramanujan Chair Professorship (2012–17) at CR Rao Advanced Institute of Mathematics, Statistics and Computer Science. Professor Prakasa Rao served as an INSA Senior Scientist at the CR Rao Advanced Institute of Mathematics, Statistics and Computer Science (CR Rao AIMSCS) from 2018 to 2023. He is currently an Emeritus Professor of the Indian Statistical Institute, and an INSA Honorary Scientist at the CR Rao AIMSCS.
Books
Among the books he has written are:
Associated Sequences, Demimartingales and Nonparametric Inference, Birkhauser, Springer, Basel (2012), ix +272 pp.
Statistical Inference for Fractional Diffusion Processes, John Wiley, Chichester (2010), xii +252 pp.
A First Course in Probability and Statistics, World Scientific, Singapore,(2009). Reprinted by Cambridge University Press India Private Limited, Delhi (2010), xii + 317pp.
Statistical Inference for Diffusion Type Processes, Arnold, London and Oxford University press, New York (1999), xvi+ 349pp.
Semimartingales and Their Statistical Inference, Chapman and Hall, London and CRC Press, Boca Raton, Florida (1999), xi+532 pp.
Identifiability in Stochastic Models: Characterization of Probability Distributions, Academic Press, Cambridge Mass. (1992). xiii + 253 pp.
Asymptotic Theory of Statistical Inference, Wiley, New York (1987). Reprinted by World Publishing Corporat |
https://en.wikipedia.org/wiki/Longest%20alternating%20subsequence | In combinatorial mathematics, probability, and computer science, in the longest alternating subsequence problem, one wants to find a subsequence of a given sequence in which the elements are in alternating order, and in which the sequence is as long as possible.
Formally, if is a sequence of distinct real numbers, then the subsequence is alternating<ref
name="Stanleybook"></ref> (or zigzag or down-up) if
Similarly, is reverse alternating (or up-down) if
Let denote the length (number of terms) of the longest alternating subsequence of . For example, if we consider some of the permutations of the integers 1,2,3,4,5, we have that
; because any sequence of 2 distinct digits are (by definition) alternating. (for example 1,2 or 1,4 or 3,5);
because 1,5,3,4 and 1,5,2,4 and 1,3,2,4 are all alternating, and there is no alternating subsequence with more elements;
because 5,3,4,1,2 is itself alternating.
Efficient algorithms
The longest alternating subsequence problem is solvable in time , where is the length of the original sequence.
Distributional results
If is a random permutation of the integers and , then it is possible to show<ref
name="widom"></ref><ref
name="stanley"></ref><ref
name="hr"></ref>
that
Moreover, as , the random variable , appropriately centered and scaled, converges to a standard normal distribution.
Online algorithms
The longest alternating subsequence problem has also been studied in the setting of online algorithms, in which the elements of are presented in an online fashion, and a decision maker needs to decide whether to include or exclude each element at the time it is first presented, without any knowledge of the elements that will be presented in the future,
and without the possibility of recalling on preceding observations.
Given a sequence of independent random variables with common continuous distribution , it is possible to construct a selection procedure that maximizes the expected number of alternating selections.
Such expected values can be tightly estimated, and it equals .
As , the optimal number of online alternating selections appropriately centered and scaled converges to a normal distribution.
See also
Alternating permutation
Permutation pattern and pattern avoidance
Counting local maxima and/or local minima in a given sequence
Turning point tests for testing statistical independence of observations
Number of alternating runs
Longest increasing subsequence
Longest common subsequence
References
Problems on strings
Permutations
Combinatorics
Dynamic programming |
https://en.wikipedia.org/wiki/Interval%20contractor | In mathematics, an interval contractor (or contractor for short) associated to a set is an operator which associates to a hyperrectangle in another box of such that the two following properties are always satisfied:
(contractance property)
(completeness property)
A contractor associated to a constraint (such as an equation or an inequality) is a
contractor associated to the set of all which satisfy the constraint.
Contractors make it possible to improve the efficiency of branch-and-bound algorithms classically used in interval analysis.
Properties of contractors
A contractor C is monotonic if we have
.
It is minimal if for all boxes [x], we have
,
where [A] is the interval hull of the set A, i.e., the smallest
box enclosing A.
The contractor C is thin if for all points x,
where {x} denotes the degenerated box enclosing x as a single point.
The contractor C is idempotent if for all boxes [x], we have
The contractor C is convergent if for all sequences [x](k) of boxes containing x, we have
Illustration
Figure 1 represents the set X painted grey and some boxes, some of them degenerated (i.e., they correspond to singletons). Figure 2 represents these boxes
after contraction. Note that no point of X has been removed by the contractor. The contractor
is minimal for the cyan box but is pessimistic for the green one. All degenerated blue boxes are contracted to
the empty box. The magenta box and the red box cannot be contracted.
Contractor algebra
Some operations can be performed on contractors to build more complex contractors.
The intersection, the union, the composition and the repetition are defined as follows.
Building contractors
There exist different ways to build contractors associated to equations and inequalities, say, f(x) in [y].
Most of them are based on interval arithmetic.
One of the most efficient and most simple is the forward/backward contractor (also called as HC4-revise).
The principle is to evaluate f(x) using interval arithmetic (this is the forward step).
The resulting interval is intersected with [y]. A backward evaluation of f(x) is then performed
in order to contract the intervals for the xi (this is the backward step). We now illustrate the principle on a simple example.
Consider the constraint
We can evaluate the function f(x) by introducing the two intermediate
variables a and b, as follows
The two previous constraints are called forward constraints. We get the backward constraints
by taking each forward constraint in the reverse order and isolating each variable on the right hand side. We get
The resulting forward/backward contractor
is obtained by evaluating the forward and the backward constraints using interval analysis.
References
Arithmetic
Computer arithmetic
Optimization algorithms and methods
Numerical analysis |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20SK%20Rapid%20Wien%20season | The 2011–12 SK Rapid Wien season is the 114th season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
References
Rapid Wien
2011-12 Rapid Wien Season |
https://en.wikipedia.org/wiki/2010%E2%80%9311%20SK%20Rapid%20Wien%20season | The 2010–11 SK Rapid Wien season is the 113th season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
Europa League
Qualification
Group stage
References
Rapid Wien
2010-11 Rapid Wien Season |
https://en.wikipedia.org/wiki/2009%E2%80%9310%20SK%20Rapid%20Wien%20season | The 2009–10 SK Rapid Wien season is the 112th season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
Europa League
Qualification
Group stage
References
2009-10 Rapid Wien Season
Austrian football clubs 2009–10 season |
https://en.wikipedia.org/wiki/Istanbul%20Center%20for%20Mathematical%20Sciences | The Istanbul Center for Mathematical Sciences (IMBM) is an independent center for mathematics situated in the South Campus of Boğaziçi University, Istanbul, in close proximity to the Mathematics Department. The center was initiated by several major universities in Istanbul and was formally inaugurated in 2006. The center aims to host and encourage the mathematical research and the interaction of researchers.
Background
IMBM is currently the only center for mathematics in Turkey. It was proposed by Betül Tanbay in 2003, then the chairwoman of the Mathematics Department of Boğaziçi University to its rector Sabih Tansal who immediately allocated a site. The center was opened in 2006 by the rectors of three leading universities in Istanbul, Boğaziçi University (state), Koç University (private) and Sabancı University (private). At that time, the three rectors were all mathematicians (Ayşe Soysal, Atilla Aşkar and Tosun Terzioğlu respectively) which made the contract easier. The universities provided academic and from time to time small amounts of financial support (an account of the history can be found in EMS Newsletter).
IMBM is administrated by a management committee, a scientific steering committee, and an international scientific advisory board. The scientific advisory board consists of the following mathematicians: David Mumford (Brown and Harvard Universities),
Victor Kac (MIT),
Selman Akbulut (Michigan State University),
Gilles Pisier (Paris 6 and Texas A&M ),
Edriss Titi (Weizmann Institute and University of California Irvine).
David Mumford agreed to join the Scientific Advisory Board during his visit to Turkey back in 2003. He has reported his personal observations in Notices of the AMS.
The opening seminar of IMBM was delivered by Dan Goldston, János Pintz and Cem Yalçın Yıldırım in 2006. Since then, the center has hosted many activities with distinguished participants.
Resources of IMBM come from endowment income, personal and institutional grants and collaboration agreements and gifts.
Buildings
There are two buildings of the center. Both have an excellent view of the Bosphorus strait. The buildings had been in very bad condition and were brought to life by the initiative of Betül Tanbay (Boğaziçi University Mathematics Department), the first codirector of IMBM. The first floor of the main building consists of three offices with a modest library and computers. A 40-person seminar room is on the second floor.
There are four bedrooms of the center, accommodating up to six people. Two bedrooms are located in the last floor of the main building. The other two are located in a self-contained one-storey house next to the main building, which has, besides, a kitchen and a living room.
References
External links
IMBM homepage
Boğaziçi University
Boğaziçi University Mathematics Department
Mathematical institutes |
https://en.wikipedia.org/wiki/2008%E2%80%9309%20SK%20Rapid%20Wien%20season | The 2008–09 SK Rapid Wien season is the 111th season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
Champions League qualification
References
2008-09 Rapid Wien Season
Rapid Wien season |
https://en.wikipedia.org/wiki/Lie-admissible%20algebra | In algebra, a Lie-admissible algebra, introduced by , is a (possibly non-associative) algebra that becomes a Lie algebra under the bracket [a, b] = ab − ba. Examples include associative algebras, Lie algebras, and Okubo algebras.
See also
Malcev-admissible algebra
Jordan-admissible algebra
References
Non-associative algebra |
https://en.wikipedia.org/wiki/Malcev-admissible%20algebra | In algebra, a Malcev-admissible algebra, introduced by , is a (possibly non-associative) algebra that becomes a Malcev algebra under the bracket [a, b] = ab − ba. Examples include alternative algebras, Malcev algebras and Lie-admissible algebras.
See also
Jordan-admissible algebra
References
Non-associative algebra |
https://en.wikipedia.org/wiki/Noncommutative%20Jordan%20algebra | In algebra, a noncommutative Jordan algebra is an algebra, usually over a field of characteristic not 2, such that the four operations of left and right multiplication by x and x2 all commute with each other. Examples include associative algebras and Jordan algebras.
Over fields of characteristic not 2, noncommutative Jordan algebras are the same as flexible Jordan-admissible algebras, where a Jordan-admissible algebra – introduced by and named after Pascual Jordan – is a (possibly non-associative) algebra that becomes a Jordan algebra under the product a ∘ b = ab + ba.
See also
Malcev-admissible algebra
Lie-admissible algebra
References
Non-associative algebra |
https://en.wikipedia.org/wiki/Admissible%20algebra | In mathematics, an admissible algebra is a (possibly non-associative) commutative algebra whose enveloping Lie algebra of derivations splits into the sum of an even and an odd part. Admissible algebras were introduced by .
References
Non-associative algebra |
https://en.wikipedia.org/wiki/2007%E2%80%9308%20SK%20Rapid%20Wien%20season | The 2007–08 SK Rapid Wien season is the 110th season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Intertoto Cup
UEFA Cup
References
2007-08 Rapid Wien Season
Austrian football clubs 2007–08 season
Austrian football championship-winning seasons |
https://en.wikipedia.org/wiki/Gary%20Seitz | Gary Michael Seitz (born 1943) is an American mathematician, a Fellow of the American Mathematical Society and a College of Arts and Sciences Distinguished Professor Emeritus in Mathematics at the University of Oregon. He received his Ph.D. from the University of Oregon in 1968, where his adviser was Charles W. Curtis. Seitz specializes in the study of algebraic and finite groups. Seitz has been active in the effort to exploit the relationship between algebraic groups and the finite groups of Lie type, in order to study the structure and representations of groups in the latter class. Such information is important in its own right, but was also critical in the classification of the finite simple groups, a major achievement of 20th century mathematics. Seitz made contributions to the classification of finite simple groups, such as those containing standard subgroups of Lie type. Following the classification, he pioneered the study of the subgroup structure of simple algebraic groups, and as an application went a long way towards solving the maximal subgroup problem for finite groups. For this work he received the Creativity Award from the National Science Foundation in 1991.
Early life
He was born in Santa Monica, California, graduated from University High School in 1961. In high school he was a bowling champion with an average of 194 and a pool shark.
Education and career
Seitz received his B.A. and Masters at University of California, Berkeley. He went on to earn his Ph.D. at the University of Oregon in 1968. He joined the faculty of the University of Illinois at Chicago in 1968. In 1970, he moved to University of Oregon as assistant professor, where he became a full professor in 1977 and a CAS Distinguished Professor in 2000. In his tenure at University of Oregon he also served as the Department Head of Mathematics and Associate Dean for the sciences in the College of Arts and Sciences. He served as thesis advisor for ten PhD students of whom eight currently hold academic positions. He has been visiting professor at the Institute for Advanced Study, California Institute of Technology, Cambridge University, Institut des Hautes Etudes Scientifiques, Imperial College, Tel Aviv University, Utrecht University, Tokyo University, among other institutions. In 2004, about a dozen mathematicians gathered for an international conference at the University of Oregon to honor his work.
Books
The maximal subgroups of the classical algebraic groups, AMS Memoirs, 365, (1987), 1–286.
Maximal subgroups of exceptional algebraic groups, AMS Memoirs, 441, (1991), 1–197.
Finite and locally finite groups, NATO ASI Series, (with, B. Hartley, A. Borovik, R. Bryant), Kluwer publishing company, Vol. 471, 1995.
Reductive Subgroups of exceptional algebraic groups, AMS Memoirs, 580, (1996), 1–111. (with Martin Liebeck).
''Selected papers of E. B. Dynkin with commentary", American Mathematical Society, International Press (with, Onischik,Yushkevich), 2000
The maximal sub |
https://en.wikipedia.org/wiki/2006%E2%80%9307%20SK%20Rapid%20Wien%20season | The 2006–07 SK Rapid Wien season is the 109th season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
References
2006-07 Rapid Wien Season
Austrian football clubs 2006–07 season |
https://en.wikipedia.org/wiki/NCAA%20Division%20I%20Men%27s%20Golf%20Tournament%20all-time%20team%20records | The following is a list of National Collegiate Athletic Association (NCAA) Division I college golf team statistics and records through the 2018 NCAA Division I Men's Golf Championship. The NCAA began sponsoring the national collegiate championship in 1939. Before that year the event was conducted by the National Intercollegiate Golf Association.
Tournament match play records, since 2009
Team records
through 2017
Most consecutive team appearances, NCAA Regionals: 26
Oklahoma State (1989–2014)
Most consecutive team appearances, NCAA Championships: 65
Oklahoma State (1947–2011)
Best team score (in relation to par), two rounds: 553 (−23)
UNLV, 1998 (Chris Berry–138, Bill Lunde–138, Charley Hoffman–138, Jeremy Anderson–139, Scott Lander–143)
Best team score (in relation to par), three rounds: 824 (−16)
California, 2013 (Max Homa–201, Brandon Hagy–205, Michael Kim–212, Michael Weaver–214)
Best team score (in relation to par), four rounds: 1,116 (−36)
Oklahoma State, 2000 (Charles Howell III–265, Landry Mahan–281, Andres Hultman–288, Edward Loar–288, J. C. DeLeon–295)
Georgia Tech, 2000 (Matt Weibring–276, Carlton Forrester–282, Bryce Molder–282, Matt Kuchar–283, Troy Matteson–285)
Greatest margin of victory, strokes: 33
Wake Forest, 1975
References
External links
NCAA Men's Golf
College golf in the United States
Golf records and rankings |
https://en.wikipedia.org/wiki/2013%E2%80%9314%20Charlton%20Athletic%20F.C.%20season | During the 2013–14 English football season, Charlton Athletic competed in the Football League Championship for the second consecutive season.
Squad statistics
Appearances and goals
|}
Top scorers
Disciplinary record
Coaching staff
Until 11 March 2014
From 11 March 2014
Boardroom
Until 3 January 2014
From 3 January 2014
Season statistics
League table
Results summary
Results by round
Fixtures and results
Pre-season
Championship
League Cup
FA Cup
Transfers
In
Out
Loan In
Loan Out
References
Notes
Charlton Athletic F.C. seasons
Charlton Athletic F.C. |
https://en.wikipedia.org/wiki/D%C3%A1niel%20Kasza | Dániel Kasza (born 1 August 1994 in Eger) is a Hungarian football player who plays for Kelen SC.
Club statistics
External links
Profile
MLSZ
1994 births
Living people
Hungarian men's footballers
Men's association football midfielders
Footballers from Eger
Egri FC players
Rákospalotai EAC footballers
Cigánd SE players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/Jordan%20operator%20algebra | In mathematics, Jordan operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space. When the coefficients are real numbers, the algebras are called Jordan Banach algebras. The theory has been extensively developed only for the subclass of JB algebras. The axioms for these algebras were devised by . Those that can be realised concretely as subalgebras of self-adjoint operators on a real or complex Hilbert space with the operator Jordan product and the operator norm are called JC algebras. The axioms for complex Jordan operator algebras, first suggested by Irving Kaplansky in 1976, require an involution and are called JB* algebras or Jordan C* algebras. By analogy with the abstract characterisation of von Neumann algebras as C* algebras for which the underlying Banach space is the dual of another, there is a corresponding definition of JBW algebras. Those that can be realised using ultraweakly closed Jordan algebras of self-adjoint operators with the operator Jordan product are called JW algebras. The JBW algebras with trivial center, so-called JBW factors, are classified in terms of von Neumann factors: apart from the exceptional 27 dimensional Albert algebra and the spin factors, all other JBW factors are isomorphic either to the self-adjoint part of a von Neumann factor or to its fixed point algebra under a period two *-anti-automorphism. Jordan operator algebras have been applied in quantum mechanics and in complex geometry, where Koecher's description of bounded symmetric domains using Jordan algebras has been extended to infinite dimensions.
Definitions
JC algebra
A JC algebra is a real subspace of the space of self-adjoint operators on a real or complex Hilbert space, closed under the operator Jordan product a ∘ b = (ab + ba) and closed in the operator norm.
JC algebra
A JC algebra is a norm-closed self-adjoint subspace of the space of operators on a complex Hilbert space, closed under the operator Jordan product a ∘ b = (ab + ba) and closed in the operator norm.
Jordan operator algebra
A Jordan operator algebra is a norm-closed subspace of the space of operators on a complex Hilbert space, closed under the Jordan product a ∘ b = (ab + ba) and closed in the operator norm.
Jordan Banach algebra
A Jordan Banach algebra is a real Jordan algebra with a norm making it a Banach space and satisfying || a ∘ b || ≤ ||a||⋅||b||.
JB algebra
A JB algebra is a Jordan Banach algebra satisfying
JB* algebras
A JB* algebra or Jordan C* algebra is a complex Jordan algebra with an involution a ↦ a* and a norm making it a Banach space and satisfying
||a ∘ b || ≤ ||a||⋅||b||
||a*|| = ||a||
||{a,a*,a}|| = ||a||3 where the Jordan triple product is defined by {a,b,c} = (a ∘ b) ∘ c + (c ∘ b) ∘ a − (a ∘ c) ∘ b.
JW algebras
A JW algebra is a Jordan subalgebra of the Jordan algebra of self-adjoint operators on a complex Hilbert space that is closed in the weak operator topology.
JBW algebras
A JBW algebra is a J |
https://en.wikipedia.org/wiki/2005%E2%80%9306%20SK%20Rapid%20Wien%20season | The 2005–06 SK Rapid Wien season is the 108th season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
Champions League
Qualification rounds
Group stage
References
2005-06 Rapid Wien Season
Austrian football clubs 2005–06 season |
https://en.wikipedia.org/wiki/2013%E2%80%9314%20Barnsley%20F.C.%20season | The 2013–14 season was Barnsley's eighth consecutive season in the Championship since promotion in 2006.
Kit
|
|
Championship data
League table
Result summary
Result by round
Squad
Statistics
|-
|colspan="14"|Players who left the club during the season:
|}
Captains
As of 30 November 2013
Goalscorers
As of 3 May 2014
Disciplinary record
As of 3 May 2014
Suspensions served
As of 1 January 2014
Contracts
As of 30 June 2014
Transfers
As of 29 June 2014
In
Loans in
Out
Loans out
Fixtures & results
Pre-season
Championship
League Cup
FA Cup
Overall summary
Summary
As 3 May 2014
Score overview
As 3 May 2014
References
2013-14
2013–14 Football League Championship by team |
https://en.wikipedia.org/wiki/Homogeneous%20variety | In algebraic geometry, a homogeneous variety is an algebraic variety of the form G/P, G a linear algebraic group, P a parabolic subgroup. It is a smooth projective variety. If P is a Borel subgroup, it is usually called a flag variety.
See also
Homogeneous space
Symmetric space
Symmetric variety
Algebraic varieties |
https://en.wikipedia.org/wiki/Spherical%20variety | In algebraic geometry, given a reductive algebraic group G and a Borel subgroup B, a spherical variety is a G-variety with an open dense B-orbit. It is sometimes also assumed to be normal. Examples are flag varieties, symmetric spaces and (affine or projective) toric varieties.
There is also a notion of real spherical varieties.
A projective spherical variety is a Mori dream space.
Spherical embeddings are classified by so-called colored fans, a generalization of fans for toric varieties; this is known as Luna-Vust Theory.
In his seminal paper, developed a framework to classify complex spherical subgroups of reductive groups; he reduced the classification of spherical subgroups to wonderful subgroups. He further worked out the case of groups of type A and conjectured that combinatorial objects consisting of "homogeneous spherical data" classify spherical subgroups. This is known as the Luna Conjecture.
This classification is now complete according to Luna's program; see contributions of Bravi, Cupit-Foutou, Losev and Pezzini.
As conjectured by Knop, every "smooth" affine spherical variety is uniquely determined by its weight monoid.
This uniqueness result was proven by Losev.
has been developing a program to classify spherical varieties in arbitrary characteristic.
References
Paolo Bravi, Wonderful varieties of type E, Representation theory 11 (2007), 174–191.
Paolo Bravi and Stéphanie Cupit-Foutou, Classification of strict wonderful varieties, Annales de l'Institut Fourier (2010), Volume 60, Issue 2, 641–681.
Paolo Bravi and Guido Pezzini, Wonderful varieties of type D, Representation theory 9 (2005), pp. 578–637.
Paolo Bravi and Guido Pezzini, Wonderful subgroups of reductive groups and spherical systems, J. Algebra 409 (2014), 101–147.
Paolo Bravi and Guido Pezzini, The spherical systems of the wonderful reductive subgroups, J. Lie Theory 25 (2015), 105–123.
Paolo Bravi and Guido Pezzini, Primitive wonderful varieties, Arxiv 1106.3187.
Stéphanie Cupit-Foutou, Wonderful Varieties. a geometrical realization, Arxiv 0907.2852.
Michel Brion, "Introduction to actions of algebraic groups"
Algebraic geometry |
https://en.wikipedia.org/wiki/Iterated%20limit | In multivariable calculus, an iterated limit is a limit of a sequence or a limit of a function in the form
,
,
or other similar forms.
An iterated limit is only defined for an expression whose value depends on at least two variables. To evaluate such a limit, one takes the limiting process as one of the two variables approaches some number, getting an expression whose value depends only on the other variable, and then one takes the limit as the other variable approaches some number.
Types of iterated limits
This section introduces definitions of iterated limits in two variables. These may generalize easily to multiple variables.
Iterated limit of sequence
For each , let be a real double sequence. Then there are two forms of iterated limits, namely
.
For example, let
.
Then
, and
.
Iterated limit of function
Let . Then there are also two forms of iterated limits, namely
.
For example, let such that
.
Then
, and
.
The limit(s) for x and/or y can also be taken at infinity, i.e.,
.
Iterated limit of sequence of functions
For each , let be a sequence of functions. Then there are two forms of iterated limits, namely
.
For example, let such that
.
Then
, and
.
The limit in x can also be taken at infinity, i.e.,
.
Note that the limit in n is taken discretely, while the limit in x is taken continuously.
Comparison with other limits in multiple variables
This section introduces various definitions of limits in two variables. These may generalize easily to multiple variables.
Limit of sequence
For a double sequence , there is another definition of limit, which is commonly referred to as double limit, denote by
,
which means that for all , there exist such that implies .
The following theorem states the relationship between double limit and iterated limits.
Theorem 1. If exists and equals L, exists for each large m, and exists for each large n, then and also exist, and they equal L, i.e.,
.
Proof. By existence of for any , there exists such that implies .
Let each such that exists, there exists such that implies .
Both the above statements are true for and . Combining equations from the above two, for any there exists for all ,
,
which proves that . Similarly for , we prove: .
For example, let
.
Since , , and , we have
.
This theorem requires the single limits and to converge. This condition cannot be dropped. For example, consider
.
Then we may see that
,
but does not exist.
This is because does not exist in the first place.
Limit of function
For a two-variable function , there are two other types of limits. One is the ordinary limit, denoted by
,
which means that for all , there exist such that implies .
For this limit to exist, f(x, y) can be made as close to L as desired along every possible path approaching the point (a, b). In this definition, the point (a, b) is excluded from the paths. Therefore, the value of f at the point (a, b), even if it is defined, |
https://en.wikipedia.org/wiki/Nolan%20Wallach | Nolan Russell Wallach (born August 3, 1940) is a mathematician known for work in the representation theory of reductive algebraic groups. He is the author of the 2-volume treatise Real Reductive Groups.
Education and career
Wallach did his undergraduate studies at the University of Maryland, graduating in 1962. He earned his Ph.D. from Washington University in St. Louis in 1966, under the supervision of Jun-Ichi Hano.
He became an instructor and then lecturer at the University of California, Berkeley. At Rutgers University he became in 1969 an assistant professor, in 1970 an associate professor, in 1972 a full professor, and in 1986 the Hermann Weyl Professor of Mathematics. In 1989 he became a professor at the University of California, San Diego, where he is now a professor emeritus. From 1997 to 2003 he was an associate editor of the Annals of Mathematics and from 1996 to 1998 an associate editor of the Bulletin of the American Mathematical Society.
Wallach was a Sloan Fellow from 1972 to 1974. In 1978 he was an Invited Speaker with talk The spectrum of compact quotients of semisimple Lie groups at the International Congress of Mathematicians in Helsinki. He was elected in 2004 a Fellow of the American Academy of Arts and Sciences and in 2012 a Fellow of the American Mathematical Society. His doctoral students include AMS Fellow Alvany Rocha. He has supervised more than 18 Ph.D. theses. Besides representation theory, Wallach has also published more than 150 papers in the fields of algebraic geometry, combinatorics, differential equations, harmonic analysis, number theory, quantum information theory, Riemannian geometry, and ring theory.
Selected publications
Articles
with Michel Cahen: Lorentzian symmetric spaces, Bull. Amer. Math. Soc., vol. 76, no. 3, 1970, pp. 585–591.
with M. do Carmo: Minimal immersions of spheres into spheres, Annals of Mathematics, vol. 93, 1971, pp. 43–62.
Compact homogeneous Riemannian manifolds with strictly positive curvature, Annals of Mathematics, vol. 96, 1972, pp. 277–295.
with S. Aloff: An infinite number of distinct 7-manifolds admitting positively curved Riemannian structures, Bull. Amer. Math. Soc., vol. 81, 1975, pp. 93–97
with D. DeGeorge: Limit formulas for multiplicities in L2(Γ\G), Annals of Mathematics, vol. 107, 1978, pp. 133–150.
with Roe Goodman: Classical and quantum mechanical systems of Toda lattice type, 3 Parts, Comm. Math. Phys., Part I, vol. 83, 1982, pp. 355–386, ; Part II, vol. 94, 1984, pp. 177–217, ; Part III, vol. 105, 1986, pp. 473–509,
with A. Rocha-Caridi: Characters of irreducible representations of the Lie algebra of vector fields on the circle, Invent. Math., vol. 72, 1983, pp. 57–75
with A. Rocha-Caridi: Highest weight modules over graded Lie algebras: resolutions, filtrations and character formulas, Transactions of the American Mathematical Society, vol. 277, 1983, pp. 133–162
with T. Enright, R. Howe: A classification of unitary highest weight modules, in: Re |
https://en.wikipedia.org/wiki/2004%E2%80%9305%20SK%20Rapid%20Wien%20season | The 2004–05 SK Rapid Wien season is the 107th season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
UEFA Cup
References
Notes
2004-05 Rapid Wien Season
Austrian football clubs 2004–05 season
Austrian football championship-winning seasons |
https://en.wikipedia.org/wiki/Andrea%20Malchiodi | Andrea Malchiodi (born September 30, 1972) is an Italian mathematician who is active in the fields of partial differential equations and calculus of variations, with several contributions to geometric analysis.
Scientific activity
Malchiodi received his Ph.D. in mathematics from the International School for Advanced Studies in 2000 under the supervision of Antonio Ambrosetti. He is a professor of mathematics at the Scuola Normale Superiore at Pisa. He was previously professor of mathematics at the International School for Advanced Studies and at the University of Warwick. Malchiodi has developed topological and analytical methods allowing to deal with a number of questions in geometric analysis, such as the Yamabe problem, the scalar curvature problem, problems coming from fourth order conformal geometry and concentration for singular perturbation problems. In particular, he proved some new intricate forms of improved Moser-Trudinger inequalities allowing to prove existence results for singular Liouville equations. Similar types of inequalities allow to prove existence results for Toda systems on surfaces. Malchiodi has been visiting professor in many universities and institutions, amongst which are Stanford University, The Institute for Advanced Study at Princeton, and ETH at Zurich. He belongs to the editorial board of several mathematical journals and is one of the managing editors of the journal Calculus of Variations & PDE.
Recognition
Malchiodi was awarded the Caccioppoli prize in 2006. In 2005 he was awarded, jointly with Antonio Ambrosetti, the Ferran Sunyer i Balaguer prize. Malchiodi was included in the list of invited speakers at the 2014 International Congress of Mathematicians in Seoul.
References
External links
Malchiodi's site at the Scuola Normale Superiore
Site of Caccioppoli Prize
1972 births
Living people
21st-century Italian mathematicians |
https://en.wikipedia.org/wiki/Giuseppe%20Mingione | Giuseppe Mingione (born 28 August 1972) is an Italian mathematician who is active in the fields of partial differential equations and calculus of variations.
Scientific activity
Mingione received his Ph.D. in mathematics from the University of Naples Federico II in 1999 having Nicola Fusco as advisor; he is professor of mathematics at the University of Parma. He has mainly worked on regularity aspects of the Calculus of Variations, solving a few longstanding questions about the Hausdorff dimension of the singular sets of minimisers of vectorial integral functionals and the boundary singularities of solutions to nonlinear elliptic systems. This connects to the work of authors as Almgren, De Giorgi, Morrey, Giusti, who proved theorems asserting regularity of solutions outside a singular set (i.e. a closed subset of null measure) both in geometric measure theory and for variational systems of partial differential equations. These are indeed called partial regularity results and one of the main issues is to establish whether the dimension of the singular set is strictly less than the ambient dimension. This question has found a positive answer for general integral functionals, thanks to the work of Kristensen and Mingione, who have also given explicit estimates for the dimension of the singular sets of minimisers. Subsequently, Mingione has worked on nonlinear potential theory obtaining potential estimates for solutions to nonlinear elliptic and parabolic equations. Such estimates allow to give a unified approach to the regularity theory of quasilinear, degenerate equations and relate to and upgrade previous work of Kilpeläinen, Malý, Trudinger, Wang.
Recognition
Mingione was awarded the Bartolozzi prize in 2005, the Stampacchia medal in 2006 and the Caccioppoli prize in 2010. In 2007 he was awarded an ERC grant. Mingione is listed as an ISI highly cited researcher and was invited to deliver the Nachdiplom Lectures in 2015 at ETH Zürich. He was invited speaker at the 2016 European Congress of Mathematics in Berlin. In 2017 he was appointed Commander of the Order of Merit of the Italian Republic by the President of the Italian Republic.
References
External links
Website
Site of Caccioppoli Prize
Site of European Research Council
1972 births
Living people
21st-century Italian mathematicians
PDE theorists
Functional analysts
Academic staff of the University of Parma
People from Caserta
Variational analysts
Mathematical analysts
European Research Council grantees
University of Naples Federico II alumni |
https://en.wikipedia.org/wiki/2003%E2%80%9304%20SK%20Rapid%20Wien%20season | The 2003–04 SK Rapid Wien season is the 106th season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
References
2003-04 Rapid Wien Season
Austrian football clubs 2003–04 season |
https://en.wikipedia.org/wiki/2002%E2%80%9303%20SK%20Rapid%20Wien%20season | The 2002–03 SK Rapid Wien season is the 105th season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
References
2002-03 Rapid Wien Season
Austrian football clubs 2002–03 season |
https://en.wikipedia.org/wiki/2001%E2%80%9302%20SK%20Rapid%20Wien%20season | The 2001–02 SK Rapid Wien season is the 104th season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
UEFA Cup
References
2001-02 Rapid Wien Season
Austrian football clubs 2001–02 season |
https://en.wikipedia.org/wiki/Ceiling%20effect | Ceiling effect might refer to:
Ceiling effect (pharmacology)
Ceiling effect (statistics)
See also
Ceiling (disambiguation) |
https://en.wikipedia.org/wiki/2000%E2%80%9301%20SK%20Rapid%20Wien%20season | The 2000–01 SK Rapid Wien season is the 103rd season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
UEFA Cup
References
2000-01 Rapid Wien Season
Austrian football clubs 2000–01 season |
https://en.wikipedia.org/wiki/1999%E2%80%932000%20SK%20Rapid%20Wien%20season | The 1999–2000 SK Rapid Wien season is the 102nd season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
Champions League qualification
UEFA Cup
References
1999-2000 Rapid Wien Season
Austrian football clubs 1999–2000 season |
https://en.wikipedia.org/wiki/1998%E2%80%9399%20SK%20Rapid%20Wien%20season | The 1998–99 SK Rapid Wien season is the 101st season in club history.
Squad statistics
Goal scorers
Fixtures and results
Bundesliga
League table
Cup
UEFA Cup
References
1998-99 Rapid Wien Season
Austrian football clubs 1998–99 season |
https://en.wikipedia.org/wiki/Diophantine%20quintuple | In number theory, a diophantine -tuple is a set of positive integers such that is a perfect square for any A set of positive rational numbers with the similar property that the product of any two is one less than a rational square is known as a rational diophantine -tuple.
Diophantine m-tuples
The first diophantine quadruple was found by Fermat: It was proved in 1969 by Baker and Davenport that a fifth positive integer cannot be added to this set.
However, Euler was able to extend this set by adding the rational number
The question of existence of (integer) diophantine quintuples was one of the oldest outstanding unsolved problems in number theory. In 2004 Andrej Dujella showed that at most a finite number of diophantine quintuples exist. In 2016 it was shown that no such quintuples exist by He, Togbé and Ziegler.
As Euler proved, every Diophantine pair can be extended to a Diophantine quadruple. The same is true for every Diophantine triple. In both of these types of extension, as for Fermat's quadruple, it is possible to add a fifth rational number rather than an integer.
The rational case
Diophantus himself found the rational diophantine quadruple More recently, Philip Gibbs found sets of six positive rationals with the property. It is not known whether any larger rational diophantine m-tuples exist or even if there is an upper bound, but it is known that no infinite set of rationals with the property exists.
References
External links
Andrej Dujella's pages on diophantine m-tuples
Diophantine equations |
https://en.wikipedia.org/wiki/Lung%20cancer%20susceptibility | Lung cancer susceptibility tests suggest the probability or susceptibility an individual may have of getting lung cancer. Lung cancer is a disease characterized by uncontrolled cell growth in the lung tissue. If left untreated, this growth can spread beyond the lungs in a process called metastasis, into nearby tissues or other parts of the body.
Lung cancer and genetics
Lung cancer is one of the most lethal and common forms of cancer worldwide. Pollution, smoking (active and passive), radiation (in the form of x-rays or gamma rays) and asbestos are risk factors for lung cancer. Symptoms may include persistent cough, chest pain, coughing up blood, fatigue, and swelling of the neck and face. There are different types of lung cancers, which can metastasize. Treatments include chemotherapy, surgery, and radiation. The treatment aimed at killing the cancer can also eliminate functioning lung cells (leukocytes).
Specific genetic factors can add to the risk of developing lung cancer. There are regions on chromosomes which are highly susceptible to mutation and, if present, increase the risk of developing lung cancer. These loci are the specific locations of a gene or a DNA sequence on a chromosome. Several loci are associated with an increased risk of developing lung cancer.
Approximately 26 different genes can mutate into one type of lung cancer, known as carcinoma. An example is the MAP pathway, which is inhibited by ME (a lung cancer treatment). The risk of developing lung cancer is higher for those with a family history of the disease. A second way the risk could go up is if the individual lives with a smoker.
Chromosomes involved
Many chromosomes are involved in the development of lung cancer, but those that greatly increase one's susceptibility to developing lung cancer are loci 15q25, 5p15, and 6p21. The locus 5p15 spans about 181 million base pairs on the short arm of chromosome 5, which is the largest chromosome. The locus 15q25 on chromosome 15 has genetic variants such as the CHRNA5-CHRNA3 locus, which also increases lung cancer susceptibility. Smoke is one of these risk factors: rs12914385, and rs8042374 are treated in cases where smoking is the known cause of lung cancer.
Gene expression, carcinogenic mechanisms, susceptibility chromosomes
Abnormal gene expression in chromosome loci, such as 5p15 and 15q25, is strongly linked with the risk for developing lung cancer. Gene expression, or the "turning on" of the gene, can directly affect the chromosome by changing the coding system. The process of lung cancer development transforms healthy cells into cancer cells, which can then metastasize to different parts of the body.
Susceptibility loci at chromosomes, disease markers and genes
In a large number of cases, the locus in chromosome region 15q25, which is strongly associated with lung cancer risk, was found to account for 14% (attributable risk) of lung cancer cases. Statistically similar risks were observed irrespective of smoking |
https://en.wikipedia.org/wiki/Quadratic%20Jordan%20algebra | In mathematics, quadratic Jordan algebras are a generalization of Jordan algebras introduced by . The fundamental identities of the quadratic representation of a linear Jordan algebra are used as axioms to define a quadratic Jordan algebra over a field of arbitrary characteristic. There is a uniform description of finite-dimensional simple quadratic Jordan algebras, independent of characteristic. If 2 is invertible in the field of coefficients, the theory of quadratic Jordan algebras reduces to that of linear Jordan algebras.
Definition
A quadratic Jordan algebra consists of a vector space A over a field K with a distinguished element 1 and a quadratic map of A into the K-endomorphisms of A, a ↦ Q(a), satisfying the conditions:
;
("fundamental identity");
("commutation identity"), where
Further, these properties are required to hold under any extension of scalars.
Elements
An element a is invertible if is invertible and there exists such that is the inverse of and : such b is unique and we say that b is the inverse of a. A Jordan division algebra is one in which every non-zero element is invertible.
Structure
Let B be a subspace of A. Define B to be a quadratic ideal or an inner ideal if the image of Q(b) is contained in B for all b in B; define B to be an outer ideal if B is mapped into itself by every Q(a) for all a in A. An ideal of A is a subspace which is both an inner and an outer ideal. A quadratic Jordan algebra is simple if it contains no non-trivial ideals.
For given b, the image of Q(b) is an inner ideal: we call this the principal inner ideal on b.
The centroid Γ of A is the subset of EndK(A) consisting of endomorphisms T which "commute" with Q in the sense that for all a
T Q(a) = Q(a) T;
Q(Ta) = Q(a) T2.
The centroid of a simple algebra is a field: A is central if its centroid is just K.
Examples
Quadratic Jordan algebra from an associative algebra
If A is a unital associative algebra over K with multiplication × then a quadratic map Q can be defined from A to EndK(A) by Q(a) : b ↦ a × b × a. This defines a quadratic Jordan algebra structure on A. A quadratic Jordan algebra is special if it is isomorphic to a subalgebra of such an algebra, otherwise exceptional.
Quadratic Jordan algebra from a quadratic form
Let A be a vector space over K with a quadratic form q and associated symmetric bilinear form q(x,y) = q(x+y) - q(x) - q(y). Let e be a "basepoint" of A, that is, an element with q(e) = 1. Define a linear functional T(y) = q(y,e) and a "reflection" y∗ = T(y)e - y. For each x we define Q(x) by
Q(x) : y ↦ q(x,y∗)x − q(x) y∗ .
Then Q defines a quadratic Jordan algebra on A.
Quadratic Jordan algebra from a linear Jordan algebra
Let A be a unital Jordan algebra over a field K of characteristic not equal to 2. For a in A, let L denote the left multiplication map in the associative enveloping algebra
and define a K-endomorphism of A, called the quadratic representation, by
Then Q defines a quadratic |
https://en.wikipedia.org/wiki/1997%E2%80%9398%20SK%20Rapid%20Wien%20season | The 1997–98 SK Rapid Wien season is the 100th season in club history.
Squad statistics
Fixtures and results
Bundesliga
League table
Cup
UEFA Cup
References
1997-98 Rapid Wien Season
Austrian football clubs 1997–98 season |
https://en.wikipedia.org/wiki/Ironstone%20Plateau | The Ironstone Plateau (jabal hadid) is a region in the south and west of South Sudan.
Topology and rainfall
The land in the south and west of South Sudan slopes down to the northeast from the Nile-Congo Divide towards the Bahr el Ghazal swamps. The divide is formed by a plateau rising above sea level, with some peaks that rise to . Rainfall is higher on the plateau than in the lower clay floodplains.
The rainy season lasts from May until November. Annual rainfall is .
The plateau drains into the floodplain through rivers that cross an ironstone peneplain and then spread out into deltas and swamps.
The soils of the plateau have little capacity to hold water, so most of the run-off drains into the floodlands.
The many streams draining the plateau have formed steep and narrow valleys.
Soil and vegetation
The Ironstone Plateau takes its name from the hard red lateritic soil called ironstone that covers almost the entire area.
These soils are often thin and may be unsuitable for agriculture, except in the Green Belt in the extreme southwest of Western Equatoria and in a region around the Acholi Mountains in the Torit County of Eastern Equatoria.
The country north and east of the ironstone plateau is covered in clayish black cotton soil, mostly grasslands that are prone to flooding. The black cotton soil cracks when it is dry, but expands and becomes sticky in the rain, making travel difficult. The ironstone plateau has more trees and travel is easier.
The plateau and peneplain are mostly wooded.
People and economy
The people of the plateau generally speak Ubangian languages while the people of the floodplains are Nilotic.
The plateau population includes Zande in Western Equatoria and Bari speakers in Central Equatoria on either side of the Nile.
They raise some livestock and engage in rain-fed agriculture, growing cereals such as Sorghum and pearl millet, vegetables and cassava in mixed croppings.
Other crops are oil seeds, groundnuts, sesame, cowpeas and okra, and mangoes, citrus and melons.
The best soil for agriculture is beside the streams that drain the plateau.
The forests yield mahogany from the Raga region and plantation teak.
References
Citations
Sources
Agricultural regions
Regions of Africa
Geography of South Sudan |
https://en.wikipedia.org/wiki/Tour%20de%20France%20records%20and%20statistics | This is a list of records and statistics in the Tour de France, road cycling's premier competitive event.
One rider has been King of the Mountains, won the combination classification, combativity award, the points competition, and the Tour in the same year - Eddy Merckx in 1969, which was also the first year he participated. Had the young riders classification, which replaced the combination classification, existed at the time, Merckx would have won that jersey too.
The only rider to approach the feat of winning the green, polka dot and yellow jersey in the same Tour was Bernard Hinault in 1979, where he won the race and the points classification, but finished 2nd in the mountains competition. After Merckx in 1972 no other rider would win three distinctive jerseys in a single Tour until Tadej Pogačar in 2020, a feat he repeated the following year.
Twice the Tour was won by a racer who never wore the yellow jersey until the race was over. In 1947, Jean Robic overturned a three-minute deficit on a 257 km final stage into Paris. In 1968, Jan Janssen of the Netherlands secured his win in the individual time trial on the last day.
In addition to 1947 and 1968, in 1989 Greg LeMond overcame a +:50 deficit to Laurent Fignon on the last day of the race in Paris to win the race on the final day, however Lemond had worn the yellow jersey earlier in the race. This was the final time the last stage in Paris was held as an individual time trial.
The Tour has been won four times by a racer who led the general classification on the first stage and held the lead all the way to Paris. Maurice Garin did it during the Tour's first edition, 1903; he repeated the feat the next year, but the results were nullified in response to widespread cheating. Ottavio Bottecchia completed a GC start-to-finish sweep in 1924. In 1928, Nicolas Frantz also led the GC for the entire race, and the final podium was made up of three riders from his Alcyon–Dunlop team. Lastly, Belgian Romain Maes took the lead in the first stage of the 1935 tour, and never gave it away. Similarly, there have been four tours in which a racer has taken over the GC lead on the second stage and held the lead all the way to Paris. After dominating the ITT during Stage 1B of the 1961 Tour de France Jacques Anquetil held the Maillot Jaune from the first day all the way to Paris.
René Pottier, Roger Lapébie, Sylvère Maes, Fausto Coppi and Bradley Wiggins all won the Tour de France the last time they appeared in the race.
Appearances
Between 1920 and 1985, Jules Deloffre (1885 – 1963) was the record holder for the highest number of Tour de France participations, with 14, and was sole holder of this record until 1966 with the fourteenth and last participation of André Darrigade. The record for most the appearances as of 2021 is held by Sylvain Chavanel, with 18. George Hincapie had held the mark for the most consecutive finishes with sixteen, having completed every Tour de France that he participated in ex |
https://en.wikipedia.org/wiki/1996%E2%80%9397%20SK%20Rapid%20Wien%20season | The 1996–97 SK Rapid Wien season was the 99th season in club history.
Squad statistics
Fixtures and results
Bundesliga
League table
Cup
Austrian Supercup
Champions League
Qualification round
Group stage
References
1996-97 Rapid Wien Season
Austrian football clubs 1996–97 season |
https://en.wikipedia.org/wiki/1995%E2%80%9396%20SK%20Rapid%20Wien%20season | The 1995–96 SK Rapid Wien season was the 98th season in club history.
Squad statistics
Fixtures and results
Bundesliga
League table
Cup
Austrian Supercup
Cup Winners' Cup
References
1995-96 Rapid Wien Season
Austrian football clubs 1995–96 season
Austrian football championship-winning seasons |
https://en.wikipedia.org/wiki/1994%E2%80%9395%20SK%20Rapid%20Wien%20season | The 1994–95 SK Rapid Wien season is the 97th season in club history.
Squad statistics
Fixtures and results
Bundesliga
League table
Cup
References
1994-95 Rapid Wien Season
Austrian football clubs 1994–95 season |
https://en.wikipedia.org/wiki/Mich%C3%A8le%20Moons | Michèle Moons (born in 1951) is a Belgian scientist, leading researches on Celestial Mechanics for the department of mathematics of Facultés Universitaires Notre Dame de la Paix in Namur (Belgium).
She developed an analytical theory of the liberation of the moon in the early 1980s, that is widely used by several centers analyzing the moon's motion. She has also worked on the effects of resonant motion in the minor planet belt. For nearly ten years, she was assistant editor of the journal Celestial Mechanics and Dynamical Astronomy.
Her name has been given to the main-belt asteroid 7805 Moons, discovered in 1960 by Cornelis Johannes van Houten, Ingrid van Houten-Groeneveld and Tom Gehrels at Palomar Observatory.
References
External links
7805 Moons
1951 births
Living people
Belgian mathematicians
Belgian women scientists |
https://en.wikipedia.org/wiki/1993%E2%80%9394%20SK%20Rapid%20Wien%20season | The 1993–94 SK Rapid Wien season is the 96th season in club history.
Squad statistics
Fixtures and results
Bundesliga
League table
Cup
References
1993-94 Rapid Wien Season
Austrian football clubs 1993–94 season |
https://en.wikipedia.org/wiki/Weyl%27s%20theorem%20on%20complete%20reducibility | In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation theory of semisimple Lie algebras). Let be a semisimple Lie algebra over a field of characteristic zero. The theorem states that every finite-dimensional module over is semisimple as a module (i.e., a direct sum of simple modules.)
The enveloping algebra is semisimple
Weyl's theorem implies (in fact is equivalent to) that the enveloping algebra of a finite-dimensional representation is a semisimple ring in the following way.
Given a finite-dimensional Lie algebra representation , let be the associative subalgebra of the endomorphism algebra of V generated by . The ring A is called the enveloping algebra of . If is semisimple, then A is semisimple. (Proof: Since A is a finite-dimensional algebra, it is an Artinian ring; in particular, the Jacobson radical J is nilpotent. If V is simple, then implies that . In general, J kills each simple submodule of V; in particular, J kills V and so J is zero.) Conversely, if A is semisimple, then V is a semisimple A-module; i.e., semisimple as a -module. (Note that a module over a semisimple ring is semisimple since a module is a quotient of a free module and "semisimple" is preserved under the free and quotient constructions.)
Application: preservation of Jordan decomposition
Here is a typical application.
Proof: First we prove the special case of (i) and (ii) when is the inclusion; i.e., is a subalgebra of . Let be the Jordan decomposition of the endomorphism , where are semisimple and nilpotent endomorphisms in . Now, also has the Jordan decomposition, which can be shown (see Jordan–Chevalley decomposition#Lie algebras) to respect the above Jordan decomposition; i.e., are the semisimple and nilpotent parts of . Since are polynomials in then, we see . Thus, they are derivations of . Since is semisimple, we can find elements in such that and similarly for . Now, let A be the enveloping algebra of ; i.e., the subalgebra of the endomorphism algebra of V generated by . As noted above, A has zero Jacobson radical. Since , we see that is a nilpotent element in the center of A. But, in general, a central nilpotent belongs to the Jacobson radical; hence, and thus also . This proves the special case.
In general, is semisimple (resp. nilpotent) when is semisimple (resp. nilpotent). This immediately gives (i) and (ii).
Proofs
Analytic proof
Weyl's original proof (for complex semisimple Lie algebras) was analytic in nature: it famously used the unitarian trick. Specifically, one can show that every complex semisimple Lie algebra is the complexification of the Lie algebra of a simply connected compact Lie group . (If, for example, , then .) Given a representation of on a vector space one can first restrict to the Lie algebra of . Then, since is simply connected, there is an associated representation of . Integration over produce |
https://en.wikipedia.org/wiki/Whitehead%27s%20lemma%20%28Lie%20algebra%29 | In homological algebra, Whitehead's lemmas (named after J. H. C. Whitehead) represent a series of statements regarding representation theory of finite-dimensional, semisimple Lie algebras in characteristic zero. Historically, they are regarded as leading to the discovery of Lie algebra cohomology.
One usually makes the distinction between Whitehead's first and second lemma for the corresponding statements about first and second order cohomology, respectively, but there are similar statements pertaining to Lie algebra cohomology in arbitrary orders which are also attributed to Whitehead.
The first Whitehead lemma is an important step toward the proof of Weyl's theorem on complete reducibility.
Statements
Without mentioning cohomology groups, one can state Whitehead's first lemma as follows: Let be a finite-dimensional, semisimple Lie algebra over a field of characteristic zero, V a finite-dimensional module over it, and a linear map such that
.
Then there exists a vector such that for all .
In terms of Lie algebra cohomology, this is, by definition, equivalent to the fact that for every such representation. The proof uses a Casimir element (see the proof below).
Similarly, Whitehead's second lemma states that under the conditions of the first lemma, also .
Another related statement, which is also attributed to Whitehead, describes Lie algebra cohomology in arbitrary order: Given the same conditions as in the previous two statements, but further let be irreducible under the -action and let act nontrivially, so . Then for all .
Proof
As above, let be a finite-dimensional semisimple Lie algebra over a field of characteristic zero and a finite-dimensional representation (which is semisimple but the proof does not use that fact).
Let where is an ideal of . Then, since is semisimple, the trace form , relative to , is nondegenerate on . Let be a basis of and the dual basis with respect to this trace form. Then define the Casimir element by
which is an element of the universal enveloping algebra of . Via , it acts on V as a linear endomorphism (namely, .) The key property is that it commutes with in the sense for each element . Also,
Now, by Fitting's lemma, we have the vector space decomposition such that is a (well-defined) nilpotent endomorphism for and is an automorphism for . Since commutes with , each is a -submodule. Hence, it is enough to prove the lemma separately for and .
First, suppose is a nilpotent endomorphism. Then, by the early observation, ; that is, is a trivial representation. Since , the condition on implies that for each ; i.e., the zero vector satisfies the requirement.
Second, suppose is an automorphism. For notational simplicity, we will drop and write . Also let denote the trace form used earlier. Let , which is a vector in . Then
Now,
and, since , the second term of the expansion of is
Thus,
Since is invertible and commutes with , the vector has the required property.
No |
https://en.wikipedia.org/wiki/Linear%20Lie%20algebra | In algebra, a linear Lie algebra is a subalgebra of the Lie algebra consisting of endomorphisms of a vector space V. In other words, a linear Lie algebra is the image of a Lie algebra representation.
Any Lie algebra is a linear Lie algebra in the sense that there is always a faithful representation of (in fact, on a finite-dimensional vector space by Ado's theorem if is itself finite-dimensional.)
Let V be a finite-dimensional vector space over a field of characteristic zero and a subalgebra of . Then V is semisimple as a module over if and only if (i) it is a direct sum of the center and a semisimple ideal and (ii) the elements of the center are diagonalizable (over some extension field).
Notes
References
Lie algebras |
https://en.wikipedia.org/wiki/1992%E2%80%9393%20SK%20Rapid%20Wien%20season | The 1992–93 SK Rapid Wien season is the 95th season in club history.
Squad statistics
Fixtures and results
Bundesliga
Cup
UEFA Cup
References
1992-93 Rapid Wien Season
Austrian football clubs 1992–93 season |
https://en.wikipedia.org/wiki/1971%E2%80%9372%20VfL%20Bochum%20season | The 1971–72 VfL Bochum season was the 34th 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
1971–72 VfL Bochum season at Weltfussball.de
1971–72 VfL Bochum season at kicker.de
1971–72 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/List%20of%20career%20achievements%20by%20Babe%20Ruth | This page details statistics, records, and other achievements pertaining to Babe Ruth. At the time in which Babe Ruth played, some of baseball's modern awards did not exist. The Division Series and League Championship Series did not exist. The MLB All-Star Game did not exist until 1933, late in Ruth's career. At the time of his retirement, Ruth held many of baseball's most esteemed records, including the career records for home runs (714 — since broken), slugging percentage (0.690), runs batted in (2,213 — since broken), bases on balls (2,062 — since broken) and on-base plus slugging (1.164). At the time of his retirement, Ruth held many more records than are listed here.
Achievements
First batter to hit 30 home runs in one season (during the 1920 season)
First batter to hit 40 home runs in one season (during the 1920 season)
First batter to hit 50 home runs in a season (54 in 1920)
First batter to hit 60 homers in a season (60 in 1927)
First batter to hit 500 homers in a career (August 11, 1929)
2× All-Star (1933, 1934)
7× World Series champion (, , , , , , )
1923 AL MVP
12× AL home run champion (1918, 1919, 1920, 1921, 1923, 1924, 1926, 1927, 1928, 1929, 1930, 1931)
6× AL RBI champion (1919, 1920, 1921, 1923, 1926, 1928)
AL batting champion (1924)
AL ERA champion (1916)
Pitched a combined no-hitter on June 23, 1917
New York Yankees #3 retired
Major League Baseball All-Century Team
Major League Baseball All-Time Team
National Baseball Hall of Fame Class of 1936 (inaugural)
Ranked #1 on The Sporting News list of "Baseball's 100 Greatest Players" (1998)
Ranked #2 by ESPN SportsCenturys Top North American Athletes of the 20th Century(only next to Michael Jordan a basketball player)
Ranked #1 by The Baltimore Sun in 2012 as the Greatest Maryland Athlete of all time
Named the DHL Hometown Heroes greatest New York Yankee ever in 2006
All-time ranks
1st on all-time slugging % with 0.690
1st on all-time OPS with 1.164
1st on all-time OPS+ with 206
2nd on all-time on-base % list with .474
2nd on all-time At bats per home run list with 11.76
3rd on all-time RBI list with 2,213
3rd on all-time home run list with 714
3rd on all-time bases on balls list with 2,062
4th on all-time runs list with 2,174 (Tied with Hank Aaron)
7th on all-time total bases list with 5,793
9th on all-time batting average list with .342 (Tied with Dan Brothers)
Major league records
Regular seasonSlugging percentage, career: 0.690Slugging percentage, season: 0.847 (1920)
Broken by Barry Bonds, 0.863 (2001)On-base percentage, career: .474
Broken by Ted Williams in the 1946 season (finished career with .482)On-base plus slugging, career: 1.164On-base plus slugging, season: 1.379 (1920)
Broken by Barry Bonds, 1.381 (2002)Home runs, career: 714 (708 in AL, 6 in NL)
Broken by Hank Aaron on April 8, 1974Home runs, season: 60 (1927)
Broken by Roger Maris on October 1, 1961At bats per home run, career: 11.76
Broken by Mark McGwire in 1998 (finished career w |
https://en.wikipedia.org/wiki/Raymond%20J.%20Carroll | Raymond James Carroll is an American statistician, and Distinguished Professor of statistics, nutrition and toxicology at Texas A&M University. He is a recipient of 1988 COPSS Presidents' Award and 2002 R. A. Fisher Lectureship. He has made fundamental contributions to measurement error model, nonparametric and semiparametric modeling.
Biography
Carroll was born in Japan of military parents in 1949 and grew up in Washington, D.C., Germany and Wichita Falls, Texas. He graduated with a B.A. from University of Texas at Austin in 1971 and a Ph.D. in statistics from Purdue University in 1974 under the supervision of Shanti S. Gupta. He was on the faculty at the University of North Carolina at Chapel Hill from 1974 to 1987. He also had visiting positions at the University of Heidelberg, the University of Wisconsin, and the National Heart, Lung, and Blood Institute. Carroll has been a full professor of statistics, nutrition and toxicology at Texas A&M University since 1987, was head of the Department of Statistics from 1987 to 1990, and was named a Distinguished Professor in 1997. He has visiting appointments at the Australian National University, the Humboldt University in Berlin and the National Cancer Institute. He was the founding director of the Texas A&M Center for Statistical Bioinformatics, and has been the director of Texas A&M Institute for Applied Mathematics and Computational Science since 2010. He holds an honorary doctorate from the Institut de Statistique, Université Catholique de Louvain in Belgium.
Carroll's many areas of research include measurement error model, nonparametric and semiparametric regression, inverse problem, functional data analysis, case-control studies, among others. His work has a broad variety of application fields, including radiation and nutritional epidemiology, molecular biology, genomics and many others. He has authored or coauthored four books, over 300 refereed papers and has given over 300 invited talks. He has supervised and mentored more than 30 Ph.D. students and can claim more than 90 descendants in his mathematical genealogy.
He received the COPSS Presidents' Award in 1988 and gave the Fisher Lecture at the 2002 Joint Statistical Meetings. He was the first statistician given a Method to Extend Research in Time (MERIT) Award from the National Cancer Institute. He served as editor of Biometrics and Journal of the American Statistical Association (Theory and Methods), and chair of ASA's Section on Nonparametric Statistics. A conference on "Statistical Methods for Complex Data" was held on the Texas A&M University campus in honor of Carroll in 2009. In the same year, the Raymond J. Carroll Young Investigator Award was established to honor Carroll for his fundamental contributions in many areas of statistical methodology and practice. The award is given bi-annually on odd numbered years to a statistician who has made important contributions to the area of statistics, with the recipients being Samuel Kou an |
https://en.wikipedia.org/wiki/Wailadmi%20Passah | Wailadmi Passah (born 22 February 1988 in Jowai in Meghalaya) is an Indian football player. He is currently playing for Shillong Lajong F.C. in the I-League in India as a defender.
Career statistics
Club
References
Wailadmi Passah at goal.com
Indian men's footballers
1988 births
Living people
People from West Jaintia Hills district
Shillong Lajong FC players
I-League players
Footballers from Meghalaya
Men's association football defenders |
https://en.wikipedia.org/wiki/Chhakchhuak%20Lallawmzuala | Chhakchhuak Lallawmzuala (born 8 April 1990 in Mizoram) is an Indian footballer who plays as a defender for Aizawl in the I-League.
Career statistics
Club
References
External links
Profile at Goal.com
1990 births
Living people
I-League players
Men's association football defenders
Indian men's footballers
Shillong Lajong FC players
Footballers from Mizoram
Royal Wahingdoh FC players
Aizawl FC players |
https://en.wikipedia.org/wiki/Yang%20Sang-moon | Yang Sang-moon (born March 24, 1961) is a retired South Korean professional baseball pitcher who played for the Lotte Giants and Pacific Dolphins.
References
External links
Career statistics and player information from Korea Baseball Organization
1961 births
Living people
Baseball announcers
Lotte Giants managers
LG Twins managers
Lotte Giants coaches
LG Twins coaches
Pacific Dolphins players
Chungbo Pintos players
Lotte Giants players
South Korean baseball managers
South Korean baseball coaches
South Korean baseball players
KBO League pitchers
Korea University alumni
Busan High School alumni
Baseball players from Busan
South Korean Buddhists |
https://en.wikipedia.org/wiki/1972%E2%80%9373%20VfL%20Bochum%20season | The 1972–73 VfL Bochum season was the 35th season in club history.
Matches
Legend
Bundesliga
DFB-Pokal
DFB-Ligapokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
Sources
External links
1972–73 VfL Bochum season at Weltfussball.de
1972–73 VfL Bochum season at kicker.de
1972–73 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/Rajendra%20Bhatia | Rajendra Bhatia (born 1952) is an Indian mathematician, author, and educator. He is currently a professor of mathematics at Ashoka University located in Sonipat, Haryana ,India.
Education
He studied at the University of Delhi, where he completed his BSc degree in physics and MSc degree in mathematics, and moved to the Indian Statistical Institute, Kolkata, where he completed his Ph.D. in 1982 under the probabilist K. R. Parthasarathy.
Research
Bhatia's research interests include matrix inequalities, calculus of matrix functions, means of matrices, and connections between harmonic analysis, geometry and matrix analysis.
He is one of the eponyms of the Bhatia–Davis inequality.
Academic life
Rajendra Bhatia founded the series Texts and Readings in Mathematics in 1992 and the series Culture and History of Mathematics on the history of Indian mathematics. He has served on the editorial boards of several major international journals such as Linear Algebra and Its Applications, and the SIAM Journal on Matrix Analysis and Applications.
Awards
Bhatia was awarded the INSA Medal for Young Scientists in 1982. He won the Shanti Swarup Bhatnagar Prize for Science and Technology in Mathematical Science in 1995. In 2017 he was awarded the Hans Schneider Prize in Linear Algebra.
Books
See also
Bhatia–Davis inequality
References
External links
A Brief History of Fourier Series by Prof. Rajendra Bhatia
1952 births
Living people
20th-century Indian mathematicians
21st-century Indian mathematicians
Indian Statistical Institute alumni
Academic staff of the Indian Statistical Institute
Fellows of the Indian National Science Academy
Fellows of the Indian Academy of Sciences
Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science |
https://en.wikipedia.org/wiki/First%20stellation%20of%20the%20rhombic%20dodecahedron | In geometry, the first stellation of the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon.
It is a stellation of the rhombic dodecahedron and has the same outer shell and the same visual appearance as two other shapes: a solid, Escher's solid, with 48 triangular faces, and a polyhedral compound of three flattened octahedra with 24 overlapping triangular faces.
Escher's solid can tessellate space to form the stellated rhombic dodecahedral honeycomb.
Stellation, solid, and compound
The first stellation of the rhombic dodecahedron has 12 faces, each of which is a non-convex hexagon. It is a stellation of the rhombic dodecahedron, meaning that each of its faces lies in the same plane as one of the rhombus faces of the rhombic dodecahedron, with each face containing the rhombus in the same plane, and that it has the same symmetries as the rhombic dodecahedron. It is the first stellation, meaning that no other self-intersecting polyhedron with the same face planes and the same symmetries has smaller faces. Extending the faces outwards even farther in the same planes leads to two more stellations, if the faces are required to be simple polygons.
For polyhedra formed only using faces in the same 12 planes and with the same symmetries, but with the faces allowed to become non-simple or with multiple faces in a single plane, additional possibilities arise.
In particular, removing the inner rhombus from each hexagonal face of the stellation leaves four triangles, and the resulting system of 48 triangles forms a different non-convex polyhedron without self-intersections that forms the boundary of a solid shape, sometimes called Escher's solid. This shape appears in M. C. Escher's works Waterfall and in a study for Stars (although Stars itself features a different shape, the compound of three octahedra). As the stellation and the solid have the same visual appearance, it is not possible to determine which of the two Escher intended to depict in Waterfall. In Study for Stars, Escher depicts the polyhedron in a skeletal form, and includes edges that are part of the skeletal form of Escher's solid but are not part of the stellation. (In the stellation, these line segments are formed by crossings of faces rather than edges.) However, an alternative interpretation for the same skeletal form is that it depicts a third shape with a similar appearance, the polyhedral compound of three flattened octahedra with 24 overlapping triangular faces.
The 48 triangular faces of the solid are isosceles; if the longest edge of these triangles is length then the other two are , the surface area of the solid is and the volume of the solid is .
Vertices, edges, and faces
The vertices of the first stellation of the rhombic dodecahedron include the 12 vertices of the cuboctahedron, together with eight additional vertices (the degree-3 vertices of the rhombic dodecahedron). Escher's solid has six additional vertices, at |
https://en.wikipedia.org/wiki/Camillo%20De%20Lellis | Camillo De Lellis (born 11 June 1976) is an Italian mathematician who is active in the fields of calculus of variations, hyperbolic systems of conservation laws, geometric measure theory and fluid dynamics. He is a permanent faculty member in the School of Mathematics at the Institute for Advanced Study. He is also one of the two managing editors of Inventiones Mathematicae.
Biography
Prior joining the faculty of the Institute for Advanced Study, De Lellis was a professor of mathematics at the University of Zurich from 2004 to 2018. Before this, he was a postdoctoral researcher at ETH Zurich and at the Max Planck Institute for Mathematics in the Sciences. He received his PhD in mathematics from the Scuola Normale Superiore at Pisa, under the guidance of Luigi Ambrosio in 2002.
Scientific activity
De Lellis has given a number of remarkable contributions in different fields related to partial differential equations. In geometric measure theory he has been interested in the study of regularity and singularities of minimising hypersurfaces, pursuing a program aimed at disclosing new aspects of the theory started by Almgren in his "Big regularity paper".
There Almgren proved his famous regularity theorem asserting that the singular set of an m-dimensional mass-minimizing surface has dimension at most m − 2. De Lellis has also worked on various aspects of the theory of hyperbolic systems of conservation laws and of incompressible fluid dynamics. In particular, together with László Székelyhidi Jr., he has introduced the use of convex integration methods and differential inclusions to analyse non-uniqueness issues for weak solutions to the Euler equation.
Recognition
De Lellis has been awarded the Stampacchia Medal in 2009, the Fermat Prize in 2013 and the Caccioppoli Prize in 2014. He has been invited speaker at the International Congress of Mathematicians in 2010 and plenary speaker at the European Congress of Mathematics in 2012. In 2012 he has also been awarded a European Research Council grant. In 2020 he has been awarded the Bôcher Memorial Prize. In 2021 he became a member of the German Academy of Sciences Leopoldina. He has also been included in the list of invited plenary speakers of the 2022 International Congress of Mathematicians, in Saint Petersburg. In 2022 he was awarded the Maryam Mirzakhani Prize in Mathematics from the NAS.
References
External links
Site at the University of Zurich
Site of the European Congress of Mathematics in 2012
Site of the European Research Council
1976 births
Living people
21st-century Italian mathematicians
Variational analysts
European Research Council grantees
Academic staff of the University of Zurich
Institute for Advanced Study faculty
Members of the German National Academy of Sciences Leopoldina |
https://en.wikipedia.org/wiki/1973%E2%80%9374%20VfL%20Bochum%20season | The 1973–74 VfL Bochum season was the 36th season in club history.
Matches
Legend
Bundesliga
DFB-Pokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
References
External links
1973–74 VfL Bochum season at Weltfussball.de
1973–74 VfL Bochum season at kicker.de
1973–74 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/The%20Big%20Bang%20Fair | The Big Bang UK Young Scientists and Engineers Fair, founded 2009, is the United Kingdom’s largest celebration of STEM (science, technology, engineering and maths) for young people, and is one of the largest youth events in the UK. The fair takes place annually in June. It is led by EngineeringUK in partnership with over 200 organisations across government, industry, education and the wider science and engineering community.
The Big Bang programme exists to bring science and engineering to life for young people. The Big Bang celebrates and raises the profile of young people’s achievements in science and engineering and encourages more young people to take part in science, technology, engineering and maths initiatives with support from their parents and teachers.
Big Bang at School events take place across the UK to enable young people to discover close to home the exciting and rewarding science and engineering careers that their science and maths subjects can lead to.
In 2012, the Big Bang Fair was hosted in the National Exhibition Centre in Birmingham. An all-girls team of pupils from a state school in the Highlands- Alness Academy were awarded the prestigious title of UK Young Engineers of the Year for their work on health and safety prototypes to be used in Haiti, which had recently suffered major earthquake damage alongside an outbreak of cholera. The six girls were Josie Tolliday, Emma Roddick, Cassie Armstrong, Meg Beattie, Holly Henderson and Kayleigh MacDonald.
The all-girl team have continued to excel in their extra-curricular activities. Cassie Armstrong is now an elected Member of Scottish Youth Parliament; Emma Roddick went on to become Donald Dewar Debater of the Year; Kayleigh MacDonald has been successful in dance competition Rock Challenge.
Criticism
The Big Bang Fair has been criticised by NGOs such as the Campaign Against the Arms Trade and Friends of the Earth due to the heavy involvement of arms manufacturers and fossil fuel companies at the event. The event has been described as being a PR stunt rather than being a genuine attempt to educate children and get them involved in STEM in future. Furthermore it has also been criticised for presenting a "distorted view of the value of science" in reference to the involvement of arms manufacturers and oil companies.
References
External links
Annual events in the United Kingdom
Engineering education in the United Kingdom
Science events in the United Kingdom
Science exhibitions
Science festivals
Youth science |
https://en.wikipedia.org/wiki/Affine%20bundle | In mathematics, an affine bundle is a fiber bundle whose typical fiber, fibers, trivialization morphisms and transition functions are affine.
Formal definition
Let be a vector bundle with a typical fiber a vector space . An affine bundle modelled on a vector bundle is a fiber bundle whose typical fiber is an affine space modelled on so that the following conditions hold:
(i) Every fiber of is an affine space modelled over the corresponding fibers of a vector bundle .
(ii) There is an affine bundle atlas of whose local trivializations morphisms and transition functions are affine isomorphisms.
Dealing with affine bundles, one uses only affine bundle coordinates possessing affine transition functions
There are the bundle morphisms
where are linear bundle coordinates on a vector bundle , possessing linear transition functions .
Properties
An affine bundle has a global section, but in contrast with vector bundles, there is no canonical global section of an affine bundle. Let be an affine bundle modelled on a vector bundle . Every global section of an affine bundle yields the bundle morphisms
In particular, every vector bundle has a natural structure of an affine bundle due to these morphisms where is the canonical zero-valued section of . For instance, the tangent bundle of a manifold naturally is an affine bundle.
An affine bundle is a fiber bundle with a general affine structure group of affine transformations of its typical fiber of dimension . This structure group always is reducible to a general linear group , i.e., an affine bundle admits an atlas with linear transition functions.
By a morphism of affine bundles is meant a bundle morphism whose restriction to each fiber of is an affine map. Every affine bundle morphism of an affine bundle modelled on a vector bundle to an affine bundle modelled on a vector bundle yields a unique linear bundle morphism
called the linear derivative of .
See also
Fiber bundle
Fibered manifold
Vector bundle
Affine space
Notes
References
S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Vols. 1 & 2, Wiley-Interscience, 1996, .
Sardanashvily, G., Advanced Differential Geometry for Theoreticians. Fiber bundles, jet manifolds and Lagrangian theory, Lambert Academic Publishing, 2013, ; .
Differential geometry
Fiber bundles |
https://en.wikipedia.org/wiki/KNBS%20%28disambiguation%29 | KNBS may refer to:
KNBS, a radio station in Bowling Green, Missouri formerly known as KPVR
King's Norton Boys' School
Kenya National Bureau of Statistics
KNBS (TV), a TV station in Walla Walla, Washington in 1960 |
https://en.wikipedia.org/wiki/Volterra%20lattice | In mathematics, the Volterra lattice, also known as the discrete KdV equation, the Kac–van Moerbeke lattice, and the Langmuir lattice, is a system of ordinary differential equations with variables indexed by some of the points of a 1-dimensional lattice. It was introduced by and and is named after Vito Volterra. The Volterra lattice is a special case of the generalized Lotka–Volterra equation describing predator–prey interactions, for a sequence of species with each species preying on the next in the sequence. The Volterra lattice also behaves like a discrete version of the KdV equation. The Volterra lattice is an integrable system, and is related to the Toda lattice. It is also used as a model for Langmuir waves in plasmas.
Definition
The Volterra lattice is the set of ordinary differential equations for functions an:
where n is an integer. Usually one adds boundary conditions: for example, the functions an could be periodic: an = an+N for some N, or could vanish for n ≤ 0 and n ≥ N.
The Volterra lattice was originally stated in terms of the variables Rn = –log an in which case the equations are
References
Integrable systems |
https://en.wikipedia.org/wiki/National%20Institute%20of%20Statistics%20%28Tunisia%29 | The National Institute of Statistics (officially in (INS); or in ) is Tunisia's statistics agency. Its head office is in Tunis.
Regions
The INS divides Tunisia into 6 regions.
North East
Tunis
Nabuel
Ben Arous
Ariana
Bizerte
Menouba
Zaghouan
North West
Siliana
Kef
Béja
Jendouba
Central West
Sidi Bouzid
Kasserine
Kairouan
Central East
Sfax
Sousse
Monastir
Mahdia
South West
Tozeur
Gafsa
Kebili
South East
Tataouine
Medenine
Gabès
References
External links
Institute of Statistics (Direct frame)
Tunisia
Government of Tunisia |
https://en.wikipedia.org/wiki/National%20Institute%20of%20Statistics%20%28Cameroon%29 | The National Institute of Statistics (, INS) is an agency of the government of Cameroon. Its head office is in the centre of Yaoundé, in front of the Immeuble rose.
References
External links
National Institute of Statistics
Cameroon
Government of Cameroon |
https://en.wikipedia.org/wiki/Mutation%20%28Jordan%20algebra%29 | In mathematics, a mutation, also called a homotope, of a unital Jordan algebra is a new Jordan algebra defined by a given element of the Jordan algebra. The mutation has a unit if and only if the given element is invertible, in which case the mutation is called a proper mutation or an isotope. Mutations were first introduced by Max Koecher in his Jordan algebraic approach to Hermitian symmetric spaces and bounded symmetric domains of tube type. Their functorial properties allow an explicit construction of the corresponding Hermitian symmetric space of compact type as a compactification of a finite-dimensional complex semisimple Jordan algebra. The automorphism group of the compactification becomes a complex subgroup, the complexification of its maximal compact subgroup. Both groups act transitively on the compactification. The theory has been extended to cover all Hermitian symmetric spaces using the theory of Jordan pairs or Jordan triple systems. Koecher obtained the results in the more general case directly from the Jordan algebra case using the fact that only Jordan pairs associated with period two automorphisms of Jordan algebras are required.
Definitions
Let A be a unital Jordan algebra over a field k of characteristic ≠ 2. For a in A define the Jordan multiplication operator on A by
and the quadratic representation Q(a) by
It satisfies
the fundamental identity
the commutation or homotopy identity
where
In particular if a or b is invertible then
It follows that A with the operations Q and R and the identity element defines a quadratic Jordan algebra, where a quadratic Jordan algebra consists of a vector space A with a distinguished element 1 and a quadratic map of A into endomorphisms of A, a ↦ Q(a), satisfying the conditions:
("fundamental identity")
("commutation or homotopy identity"), where
The Jordan triple product is defined by
so that
There are also the formulas
For y in A the mutation Ay is defined to the vector space A with multiplication
If Q(y) is invertible, the mutual is called a proper mutation or isotope.
Quadratic Jordan algebras
Let A be a quadratic Jordan algebra over a field k of characteristic ≠ 2. Following , a linear Jordan algebra structure can be associated with A such that, if L(a) is Jordan multiplication, then the quadratic structure is given by Q(a) = 2L(a)2 − L(a2).
Firstly the axiom Q(a)R(b,a) = R(a,b)Q(a) can be strengthened to
Indeed, applied to c, the first two terms give
Switching b and c then gives
Now let
Replacing b by a and a by 1 in the identity above gives
In particular
The Jordan product is given by
so that
The formula above shows that 1 is an identity. Defining a2 by a∘a = Q(a)1, the only remaining condition to be verified is the Jordan identity
In the fundamental identity
Replace a by a + t1, set b = 1 and compare the coefficients of t2 on both sides:
Setting b = 1 in the second axiom gives
and therefore L(a) must commute with L(a2).
Inverses
Let A be a |
https://en.wikipedia.org/wiki/1991%E2%80%9392%20SK%20Rapid%20Wien%20season | The 1991–92 SK Rapid Wien season was the 94th season in club history.
Squad statistics
Fixtures and results
Bundesliga
Cup
References
1991-92 Rapid Wien Season
Rapid |
https://en.wikipedia.org/wiki/1990%E2%80%9391%20SK%20Rapid%20Wien%20season | The 1990–91 SK Rapid Wien season was the 93rd season in club history.
Squad statistics
Fixtures and results
League
Cup
UEFA Cup
References
1990-91 Rapid Wien Season
Rapid |
https://en.wikipedia.org/wiki/Bal%C3%A1zs%20Szab%C3%B3%20%28footballer%29 | Balázs Szabó (born 28 October 1995) is a Hungarian football player who plays for Kazincbarcika.
Club statistics
Updated to games played as of 19 May 2019.
Honours
Diósgyőr
Hungarian League Cup (1): 2013–14
References
Balázs Szabó at HLSZ
1995 births
People from Kazincbarcika
Living people
Hungarian men's footballers
Men's association football midfielders
Diósgyőri VTK players
Soproni VSE players
BFC Siófok players
Balmazújvárosi FC players
Szolnoki MÁV FC footballers
Kazincbarcikai SC footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Nemzeti Bajnokság III players
Footballers from Borsod-Abaúj-Zemplén County |
https://en.wikipedia.org/wiki/AKNS%20system | In mathematics, the AKNS system is an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, Alan C. Newell, and Harvey Segur from their publication in Studies in Applied Mathematics: .
Definition
The AKNS system is a pair of two partial differential equations for two complex-valued functions p and q of 2 variables t and x:
If p and q are complex conjugates this reduces to the nonlinear Schrödinger equation.
Huygens' principle applied to the Dirac operator gives rise to the AKNS hierarchy.
Applications to General Relativity
In 2021, the dynamics of three-dimensional (extremal) black holes on General Relativity with negative cosmological constant were showed equivalent to two independent copies of the AKNS system. This duality was addressed through the imposition of suitable boundary conditions to the Chern-Simons action. In this scheme, the involution of conserved charges of the AKNS system yields an infinite-dimensional commuting asymptotic symmetry algebra of gravitational charges.
See also
Huygens principle
References
Integrable systems |
https://en.wikipedia.org/wiki/R.%20L.%20Hudson | Robin Lyth Hudson (4 May 1940 – 12 January 2021) was a British mathematician notable for his contribution to quantum probability.
Education and career
Hudson received his Ph.D. from the University of Oxford in 1966 under John T. Lewis with a thesis entitled Generalised Translation-Invariant Mechanics. He was appointed assistant lecturer at the University of Nottingham in 1964, promoted to a chair in 1985 and served as head of department from 1987 to 1990. He spent sabbatical semesters in Heidelberg (1978), Austin, Texas (1983), and Colorado Boulder (1996). After taking early retirement in 1997, he held part-time research posts at Nottingham Trent University (1997–2005), the Slovak Academy
of Sciences (1997–2000) and Loughborough University (2005–21), and a visiting professorship at the University of Łódź (2002) which awarded him an honorary doctorate in 2013.
Hudson was a mathematical physicist who was one of the pioneers of quantum probability. An early result, now known as Hudson's theorem in quantum optics, shows that the pure quantum states with positive Wigner quasiprobability distribution are the Gaussian ones. Together with PhD students, Hudson established one of the first quantum central limit theorems, proved an early quantum de Finetti theorem, and introduced quantum Brownian motion as a non-commuting pair of families of unbounded operators, using the formalism of quantum field theory. He collaborated with K. R. Parthasarathy first at the University of Manchester, and later at University of Nottingham and at Loughborough University, on their seminal work in quantum stochastic calculus.
In later papers he developed a theory of quantum stochastic double product integrals and their application to the quantum Yang–Baxter equation, the quantisation of Lie bialgebras and quantum Lévy area.
Selected works
References
External links
Mathematical genealogy project page on Robin Lyth Hudson
Hudson ancestry
1940 births
Living people
20th-century British mathematicians
21st-century British mathematicians
Probability theorists
Alumni of the University of Oxford
Academics of the University of Nottingham |
https://en.wikipedia.org/wiki/1989%E2%80%9390%20SK%20Rapid%20Wien%20season | The 1989–90 SK Rapid Wien season was the 92nd season in club history.
Squad
Squad and statistics
Squad statistics
Fixtures and results
League
Cup
UEFA Cup
References
1989-90 Rapid Wien Season
Rapid |
https://en.wikipedia.org/wiki/Kim%20Jin-wook | Kim Jin-wook (born August 5, 1960) is the former manager of the Doosan Bears and KT Wiz of the KBO League.
References
External links
Career statistics and player information from Korea Baseball Organization
KT Wiz managers
Doosan Bears managers
Doosan Bears coaches
Ssangbangwool Raiders players
Doosan Bears players
South Korean baseball managers
South Korean baseball coaches
South Korean baseball players
KBO League pitchers
People from Yeongcheon
1961 births
Living people
Sportspeople from North Gyeongsang Province |
https://en.wikipedia.org/wiki/Connection%20%28fibred%20manifold%29 | In differential geometry, a fibered manifold is surjective submersion of smooth manifolds . Locally trivial fibered manifolds are fiber bundles. Therefore, a notion of connection on fibered manifolds provides a general framework of a connection on fiber bundles.
Formal definition
Let be a fibered manifold. A generalized connection on is a section , where is the jet manifold of .
Connection as a horizontal splitting
With the above manifold there is the following canonical short exact sequence of vector bundles over :
where and are the tangent bundles of , respectively, is the vertical tangent bundle of , and is the pullback bundle of onto .
A connection on a fibered manifold is defined as a linear bundle morphism
over which splits the exact sequence . A connection always exists.
Sometimes, this connection is called the Ehresmann connection because it yields the horizontal distribution
of and its horizontal decomposition .
At the same time, by an Ehresmann connection also is meant the following construction. Any connection on a fibered manifold yields a horizontal lift of a vector field on onto , but need not defines the similar lift of a path in into . Let
be two smooth paths in and , respectively. Then is called the horizontal lift of if
A connection is said to be the Ehresmann connection if, for each path in , there exists its horizontal lift through any point . A fibered manifold is a fiber bundle if and only if it admits such an Ehresmann connection.
Connection as a tangent-valued form
Given a fibered manifold , let it be endowed with an atlas of fibered coordinates , and let be a connection on . It yields uniquely the horizontal tangent-valued one-form
on which projects onto the canonical tangent-valued form (tautological one-form or solder form)
on , and vice versa. With this form, the horizontal splitting reads
In particular, the connection in yields the horizontal lift of any vector field on to a projectable vector field
on .
Connection as a vertical-valued form
The horizontal splitting of the exact sequence defines the corresponding splitting of the dual exact sequence
where and are the cotangent bundles of , respectively, and is the dual bundle to , called the vertical cotangent bundle. This splitting is given by the vertical-valued form
which also represents a connection on a fibered manifold.
Treating a connection as a vertical-valued form, one comes to the following important construction. Given a fibered manifold , let be a morphism and the pullback bundle of by . Then any connection on induces the pullback connection
on .
Connection as a jet bundle section
Let be the jet manifold of sections of a fibered manifold , with coordinates . Due to the canonical imbedding
any connection on a fibered manifold is represented by a global section
of the jet bundle , and vice versa. It is an affine bundle modelled on a vector bundle
There are the fol |
https://en.wikipedia.org/wiki/Minimum%20rank%20of%20a%20graph | In mathematics, the minimum rank is a graph parameter for a graph G. It was motivated by the Colin de Verdière graph invariant.
Definition
The adjacency matrix of an undirected graph is a symmetric matrix whose rows and columns both correspond to the vertices of the graph. Its elements are all 0 or 1, and the element in row i and column j is nonzero whenever vertex i is adjacent to vertex j in the graph. More generally, a generalized adjacency matrix is any symmetric matrix of real numbers with the same pattern of nonzeros off the diagonal (the diagonal elements may be any real numbers). The minimum rank of is defined as the smallest rank of any generalized adjacency matrix of the graph; it is denoted by .
Properties
Here are some elementary properties.
The minimum rank of a graph is always at most equal to n − 1, where n is the number of vertices in the graph.
For every induced subgraph H of a given graph G, the minimum rank of H is at most equal to the minimum rank of G.
If a graph is disconnected, then its minimum rank is the sum of the minimum ranks of its connected components.
The minimum rank is a graph invariant: isomorphic graphs necessarily have the same minimum rank.
Characterization of known graph families
Several families of graphs may be characterized in terms of their minimum ranks.
For , the complete graph Kn on n vertices has minimum rank one. The only graphs that are connected and have minimum rank one are the complete graphs.
A path graph Pn on n vertices has minimum rank n − 1. The only n-vertex graphs with minimum rank n − 1 are the path graphs.
A cycle graph Cn on n vertices has minimum rank n − 2.
Let be a 2-connected graph. Then if and only if is a linear 2-tree.
A graph has if and only if the complement of is of the form for appropriate nonnegative integers with for all .
Notes
References
.
Algebraic graph theory
Graph invariants |
https://en.wikipedia.org/wiki/Image%20geometry%20correction | Image Geometry Correction (often referred to as Image Warping) is the process of digitally manipulating image data such that the image’s projection precisely matches a specific projection surface or shape. Image geometry correction compensates for the distortion created by off-axis projector or screen placement or non-flat screen surface, by applying a pre-compensating inverse distortion to that image in the digital domain.
Usually, Image geometry correction is applied such that equal areas of projection surface are perceived by the viewer map to equal areas in the source image. It can also be used to apply a special effect distortion. The term “Image” Geometry Correction, implying a static image, is slightly misleading. Image geometry correction applies to static or dynamic images (i.e. moving video).
Overview
Image geometry correction is generally implemented in 2 different ways:
Graphics processing
Signal processing
Both techniques involve the real time execution of a spatial transformation from the input image to the output image, and both techniques require powerful hardware. The spatial transformation must be pre-defined for a particular desired geometric, and may be calculated by several different methods (more to follow).
In Graphics Processing, the spatial transformation consists of a polygon mesh (usually triangles). The transformation is executed by texture mapping from the rectilinear mesh of the input image to the transformed shape of the destination image. Each polygon on the input image is thus applied to an equivalent (but transformed in shape and location) polygon in the output image.
Graphics Processing based Image Geometry Correction, may be performed with inexpensive PC-based graphics controllers. The sophisticated software that uses the texture mapping hardware of a graphics controller is not standard, and is available only through vendors of specialty software (i.e. Mersive Technologies and Scalable Display Technologies).
Graphics Processing based image geometry correction is very effective for content that originates in the PC. Its major drawback is that it is tied to the graphics controller platform, and cannot process signals that originate outside the graphics controller.
In Signal Processing based image geometry correction, the spatial transformation consists of spatially defined 2-dimensional image re-sampling or scaling filter. The scaling operation is performed with different scaling ratios in different parts of the image, according to the defined transformation. Special care must be taken in the design of the scaling filter to ensure that spatial frequencies remain balanced in all areas of the image, and that the Nyquist criterion is met in all areas of the image.
Signal Processing based image geometry correction is implemented by specially designed hardware in the projection system (i.e. IDT, Silicon Optix or GEO Semiconductor), or in stand-alone Video Signal Processors (i.e. Flexible Pictu |
https://en.wikipedia.org/wiki/2013%E2%80%9314%20Fleetwood%20Town%20F.C.%20season | The 2013–14 season was Fleetwood Town's second-consecutive season in Football League Two.
League Two Data
League table
Result Summary
Result by round
Kit
|
Squad
Statistics
|}
Goalscorers
Disciplinary record
Contracts
Transfers
In
Loan In
Out
Loans out
Fixtures and results
Pre-season
League Two
Football League Cup
FA Cup
Johnstone's Paint Trophy
Overall summary
Summary
Score overview
References
2013-14
2013–14 Football League Two by team |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20First%20Vienna%20FC%20season | The 2011–12 First Vienna FC season was the third consecutive season in the second highest professional division in Austria after the promotion in 2009.
Squad
Squad and statistics
|-
! colspan="12" style="background:#dcdcdc; text-align:center;"| Goalkeepers
|-
! colspan="12" style="background:#dcdcdc; text-align:center;"| Defenders
|-
! colspan="12" style="background:#dcdcdc; text-align:center;"| Midfielders
|-
! colspan="12" style="background:#dcdcdc; text-align:center;"| Forwards
|}
References
Vienna
First Vienna FC seasons |
https://en.wikipedia.org/wiki/Interval%20propagation | In numerical mathematics, interval propagation or interval constraint propagation is the problem of contracting interval domains associated to variables of R without removing any value that is consistent with a set of constraints (i.e., equations or inequalities). It can be used to propagate uncertainties in the situation where errors are represented by intervals. Interval propagation considers an estimation problem as a constraint satisfaction problem.
Atomic contractors
A contractor associated to an equation involving the variables x1,...,xn is an operator which contracts the intervals [x1],..., [xn] (that are supposed to enclose the xi's) without removing any value for the variables that is consistent with the equation.
A contractor is said to be atomic if it is not built as a composition of other contractors. The main theory that is used to build atomic contractors are based on interval analysis.
Example. Consider for instance the equation
which involves the three variables x1,x2 and x3.
The associated contractor is given by the following statements
For instance, if
the contractor performs the following calculus
For other constraints, a specific algorithm for implementing the atomic contractor should be written. An illustration is the atomic contractor associated to the equation
is provided by Figures 1 and 2.
Decomposition
For more complex constraints, a decomposition into atomic constraints (i.e., constraints for which an atomic contractor exists) should be performed. Consider for instance the constraint
could be decomposed into
The interval domains that should be associated to the new intermediate variables are
Propagation
The principle of the interval propagation is to call all available atomic contractors until no more contraction could be observed.
As a result of the Knaster-Tarski theorem, the procedure always converges to intervals which enclose all feasible values for the variables. A formalization of the interval propagation can be made thanks to the contractor algebra. Interval propagation converges quickly to the result and can deal with problems involving several hundred of variables.
Example
Consider the electronic circuit of Figure 3.
Assume that from different measurements, we know that
From the circuit, we have the following equations
After performing the interval propagation, we get
References
Algebra of random variables
Numerical analysis
Statistical approximations |
https://en.wikipedia.org/wiki/Ternar | Ternar may refer to:
Tomislav Ternar, a Slovenian tennis player
in mathematics, a triple system
See also
Ternary (disambiguation) |
https://en.wikipedia.org/wiki/Petkov%C5%A1ek%27s%20algorithm | Petkovšek's algorithm (also Hyper) is a computer algebra algorithm that computes a basis of hypergeometric terms solution of its input linear recurrence equation with polynomial coefficients. Equivalently, it computes a first order right factor of linear difference operators with polynomial coefficients. This algorithm was developed by Marko Petkovšek in his PhD-thesis 1992. The algorithm is implemented in all the major computer algebra systems.
Gosper-Petkovšek representation
Let be a field of characteristic zero. A nonzero sequence is called hypergeometric if the ratio of two consecutive terms is rational, i.e. . The Petkovšek algorithm uses as key concept that this rational function has a specific representation, namely the Gosper-Petkovšek normal form. Let be a nonzero rational function. Then there exist monic polynomials and such that
and
for every nonnegative integer ,
and
.
This representation of is called Gosper-Petkovšek normal form. These polynomials can be computed explicitly. This construction of the representation is an essential part of Gosper's algorithm. Petkovšek added the conditions 2. and 3. of this representation which makes this normal form unique.
Algorithm
Using the Gosper-Petkovšek representation one can transform the original recurrence equation into a recurrence equation for a polynomial sequence . The other polynomials can be taken as the monic factors of the first coefficient polynomial resp. the last coefficient polynomial shifted . Then has to fulfill a certain algebraic equation. Taking all the possible finitely many triples and computing the corresponding polynomial solution of the transformed recurrence equation gives a hypergeometric solution if one exists.
In the following pseudocode the degree of a polynomial is denoted by and the coefficient of is denoted by .
algorithm petkovsek is
input: Linear recurrence equation .
output: A hypergeometric solution if there are any hypergeometric solutions.
for each monic divisor of do
for each monic divisor of do
for each do
for each root of do
Find non-zero polynomial solution of
if such a non-zero solution exists then
return a non-zero solution of
If one does not end if a solution is found it is possible to combine all hypergeometric solutions to get a general hypergeometric solution of the recurrence equation, i.e. a generating set for the kernel of the recurrence equation in the linear span of hypergeometric sequences.
Petkovšek also showed how the inhomogeneous problem can be solved. He considered the case where the right-hand side of the recurrence equation is a sum of hypergeometric sequences. After grouping together certain hypergeometric sequences of the right-hand side, for each of those groups a certain recurrence equation is solved for a rational solution. These rational solutions can be |
https://en.wikipedia.org/wiki/Yurii%20Reshetnyak | Yurii Grigorievich Reshetnyak (, 26 September 1929 – 17 December 2021) was a Soviet and Russian mathematician and academician.
He worked in geometry and the theory of functions of a real variable. He was known for his work in the Reshetnyak gluing theorem. Reshetnyak received the 2000 Lobachevsky Prize from the Russian Academy of Sciences.
Reshetnyak died on 17 December 2021, at the age of 92.
Selected publications
with A. D. Aleksandrov:
References
1929 births
2021 deaths
Mathematicians from Saint Petersburg
Soviet mathematicians |
https://en.wikipedia.org/wiki/Jan%20Hogendijk | Jan Pieter Hogendijk (born 21 July 1955) is a Dutch mathematician and historian of science. Since 2005, he is professor of history of mathematics at the University of Utrecht.
Hogendijk became a member of the Royal Netherlands Academy of Arts and Sciences in 2010.
Hogendijk has contributed to the study of Greek mathematics and mathematics in medieval Islam; he provides a list of Sources on his website (below).
In 2012, he was awarded the inaugural Otto Neugebauer Prize for History of Mathematics, by the European Mathematical Society, "for having illuminated how Greek mathematics was absorbed in the medieval Arabic world, how mathematics developed in medieval Islam, and how it was eventually transmitted to Europe."
A bibliography of Hogendijk's publications is included in his website.
Selected works
1994: "B.L. van der Waerden's detective work in ancient and medieval mathematical astronomy", Nieuw Archief voor Wiskunde Vierde Serie 12(3): 145–58.
2008: "The Introduction to Geometry by Qusta ibn Luqa: translation and commentary", Suhayl 8: 163–221.
References
External links
Personal website
1955 births
Living people
20th-century Dutch historians
20th-century Dutch mathematicians
21st-century Dutch mathematicians
Utrecht University alumni
Academic staff of Heidelberg University
Academic staff of Utrecht University
Members of the Royal Netherlands Academy of Arts and Sciences
People from Leeuwarden
21st-century Dutch historians |
https://en.wikipedia.org/wiki/Poverty%20in%20North%20Korea | Poverty in North Korea is extensive, though reliable statistics are hard to come by due to lack of reliable research, pervasive censorship and extensive media manipulation in North Korea.
Poverty in North Korea has been widely repeated by Western media sources with the majority referring to the famine that affected the country in the mid-1990s. A 2006 report suggests that North Korea requires an estimated 5.3m tonnes of grain per year while harvesting only an estimated 4.5m tonnes, and thus relies on foreign aid to overcome the deficit. Starvation continues to be a systemic problem. In 2021, there were reports of widespread starvation in North Korea.
North Korea has a command economy, which is common among communist nations. The government has complete control over all monetary exchanges, causing the economy to remain stagnant due to a lack of competition between businesses. Poverty in North Korea has also been attributed to poor governance by the totalitarian regime. It is estimated that 60% of the total population of North Korea live below the poverty line in 2020.
See also
Media coverage of North Korea
Jangmadang
Economy of North Korea#Crisis and famine
References
Further reading |
https://en.wikipedia.org/wiki/Beck%E2%80%93Fiala%20theorem | In mathematics, the Beck–Fiala theorem is a major theorem in discrepancy theory due to József Beck and Tibor Fiala. Discrepancy is concerned with coloring elements of a ground set such that each set in a certain set system is as balanced as possible, i.e., has approximately the same number of elements of each color. The Beck–Fiala theorem is concerned with the case where each element doesn't appear many times across all sets. The theorem guarantees that if each element appears at most times, then the elements can be colored so that the imbalance is at most .
Statement
Formally, given a universe
and a collection of subsets
such that for each ,
then one can find an assignment
such that
Proof sketch
The proof is based on a simple linear-algebraic argument. Start with for all elements and call all variables active in the beginning.
Consider only sets with . Since each element appears at most times in a set, there are less than such sets. Now, enforce linear constraints for them. Since it is a non-trivial linear subspace of with fewer constraints than variables, there is a non-zero solution. Normalize this solution, and at least one of the values is either . Set this value and inactivate this variable. Now, ignore the sets with less than active variables. And repeat the same procedure enforcing the linear constraints that the sum of active variables of each remaining set is still the same. By the same counting argument, there is a non-trivial solution, so one can take linear combinations of this with the original one until some element becomes . Repeat until all variables are set.
Once a set is ignored, the sum of the values of its variables is zero and there are at most unset variables. The change in those can increase to at most .
References
Discrepancy theory |
https://en.wikipedia.org/wiki/2013%E2%80%9314%20FK%20%C5%BDeljezni%C4%8Dar%20season |
2013–14 statistics
Squad information
Total squad cost: €5.775.000
Disciplinary record
Includes all competitive matches. The list is sorted by position, and then shirt number.
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Out
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