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https://en.wikipedia.org/wiki/List%20of%20F4%20polytopes | {{DISPLAYTITLE:List of F4 polytopes}}
In 4-dimensional geometry, there are 9 uniform 4-polytopes with F4 symmetry, and one chiral half symmetry, the snub 24-cell. There is one self-dual regular form, the 24-cell with 24 vertices.
Visualization
Each can be visualized as symmetric orthographic projections in Coxeter planes of the F4 Coxeter group, and other subgroups.
The 3D picture are drawn as Schlegel diagram projections, centered on the cell at pos. 3, with a consistent orientation, and the 5 cells at position 0 are shown solid.
Coordinates
Vertex coordinates for all 15 forms are given below, including dual configurations from the two regular 24-cells. (The dual configurations are named in bold.) Active rings in the first and second nodes generate points in the first column. Active rings in the third and fourth nodes generate the points in the second column. The sum of each of these points are then permutated by coordinate positions, and sign combinations. This generates all vertex coordinates. Edge lengths are 2.
The only exception is the snub 24-cell, which is generated by half of the coordinate permutations, only an even number of coordinate swaps. φ=(+1)/2.
References
J.H. Conway and M.J.T. Guy: Four-Dimensional Archimedean Polytopes, Proceedings of the Colloquium on Convexity at Copenhagen, page 38 und 39, 1965
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 26)
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
External links
Uniform, convex polytopes in four dimensions:, Marco Möller
4-polytopes |
https://en.wikipedia.org/wiki/H4%20polytope | {{DISPLAYTITLE:H4 polytope}}
In 4-dimensional geometry, there are 15 uniform polytopes with H4 symmetry. Two of these, the 120-cell and 600-cell, are regular.
Visualizations
Each can be visualized as symmetric orthographic projections in Coxeter planes of the H4 Coxeter group, and other subgroups.
The 3D picture are drawn as Schlegel diagram projections, centered on the cell at pos. 3, with a consistent orientation, and the 5 cells at position 0 are shown solid.
Coordinates
The coordinates of uniform polytopes from the H4 family are complicated. The regular ones can be expressed in terms of the golden ratio φ = (1 + )/2 and σ = (3 + 1)/2. Coxeter expressed them as 5-dimensional coordinates.<ref>Coxeter, Regular and Semi-Regular Polytopes II, Four-dimensional polytopes', p.296-298</ref>
References
J.H. Conway and M.J.T. Guy: Four-Dimensional Archimedean Polytopes, Proceedings of the Colloquium on Convexity at Copenhagen, page 38 und 39, 1965
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 26)
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs'', Ph.D. Dissertation, University of Toronto, 1966
Notes
External links
Uniform, convex polytopes in four dimensions:, Marco Möller
H4 uniform polytopes with coordinates: {5,3,3}, {3,3,5}, r{5,3,3},r{3,3,5}, t{3,3,5}, t{5,3,3}, rr{3,3,5}, rr{5,3,3}, tr{3,3,5}, tr{5,3,3}, 2t{5,3,3}, t03{5,3,3}, t013{3,3,5}, t013{5,3,3}, t0123{5,3,3}, grand antiprism
4-polytopes |
https://en.wikipedia.org/wiki/D4%20polytope | {{DISPLAYTITLE:D4 polytope}}
In 4-dimensional geometry, there are 7 uniform 4-polytopes with reflections of D4 symmetry, all are shared with higher symmetry constructions in the B4 or F4 symmetry families. there is also one half symmetry alternation, the snub 24-cell.
Visualizations
Each can be visualized as symmetric orthographic projections in Coxeter planes of the D4 Coxeter group, and other subgroups. The B4 coxeter planes are also displayed, while D4 polytopes only have half the symmetry. They can also be shown in perspective projections of Schlegel diagrams, centered on different cells.
Coordinates
The base point can generate the coordinates of the polytope by taking all coordinate permutations and sign combinations. The edges' length will be . Some polytopes have two possible generator points. Points are prefixed by Even to imply only an even count of sign permutations should be included.
References
J.H. Conway and M.J.T. Guy: Four-Dimensional Archimedean Polytopes, Proceedings of the Colloquium on Convexity at Copenhagen, page 38 und 39, 1965
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 26)
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
External links
Uniform, convex polytopes in four dimensions:, Marco Möller
4-polytopes |
https://en.wikipedia.org/wiki/Bangladesh%20National%20Film%20Award%20for%20Best%20Actress | Bangladesh National Film Award for Best Actress () is the highest award for film actresses in Bangladesh.
List of winners
Key
Records and statistics
Multiple wins
The following individuals received two or more Best Actress awards:
See also
Bangladesh National Film Award for Best Actor
Bangladesh National Film Award for Best Supporting Actor
Bangladesh National Film Award for Best Supporting Actress
Notes
References
Actress
National Film Awards (Bangladesh) |
https://en.wikipedia.org/wiki/Exposed%20point | In mathematics, an exposed point of a convex set is a point at which some continuous linear functional attains its strict maximum over . Such a functional is then said to expose . There can be many exposing functionals for . The set of exposed points of is usually denoted .
A stronger notion is that of strongly exposed point of which is an exposed point such that some exposing functional of attains its strong maximum over at , i.e. for each sequence we have the following implication: . The set of all strongly exposed points of is usually denoted .
There are two weaker notions, that of extreme point and that of support point of .
Mathematical analysis
Convex geometry
Functional analysis |
https://en.wikipedia.org/wiki/Birgit%20Speh | Birgit Speh (born 1949) is Goldwin Smith Professor of Mathematics at Cornell University. She is known for her work in Lie groups, including Speh representations (also known as Speh's representations).
Career
Speh received her Ph.D. from Massachusetts Institute of Technology in 1977. She was the first female mathematician to be given tenure by Cornell University, and the first to receive the title of Professor.
Awards and honors
In 2012, Speh became a fellow of the American Mathematical Society. She was selected to give the 2020 AWM-AMS Emmy Noether Lecture at the 2020 Joint Mathematics Meetings.
Selected publications
Speh, Birgit; Vogan, David A. Jr. Reducibility of generalized principal series representations. Acta Math. 145 (1980)
Speh, Birgit. Unitary representations of Gl(n,R) with nontrivial (g,K)-cohomology. Invent. Math. 71 (1983), no. 3, 443–465.
Speh, Birgit. The unitary dual of Gl(3,R) and Gl(4,R). Math. Ann. 258 (1981/82), no. 2, 113–133.
References
Living people
1949 births
American women mathematicians
20th-century American mathematicians
21st-century American mathematicians
Massachusetts Institute of Technology alumni
Cornell University faculty
Fellows of the American Mathematical Society
Group theorists
20th-century women mathematicians
21st-century women mathematicians
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/Quadric%20geometric%20algebra | Quadric geometric algebra (QGA) is a geometrical application of the geometric algebra. This algebra is also known as the Clifford algebra. QGA is a super-algebra over conformal geometric algebra (CGA) and spacetime algebra (STA), which can each be defined within sub-algebras of QGA.
CGA provides representations of spherical entities (points, spheres, planes, and lines) and a complete set of operations (translation, rotation, dilation, and intersection) that apply to them. QGA extends CGA to also include representations of some non-spherical entities: principal axes-aligned quadric surfaces and many of their degenerate forms such as planes, lines, and points.
General quadric surfaces are characterized by the implicit polynomial equation of degree 2
which can characterize quadric surfaces located at any center point and aligned along arbitrary axes. However, QGA includes vector entities that can represent only the principal axes-aligned quadric surfaces characterized by
This is still a very significant advancement over CGA.
A possible performance issue with using QGA is the increased computation required to use a 9D vector space, as compared to the smaller 5D vector space of CGA. A 5D CGA subspace can be used when only CGA entities are involved in computations.
In general, the operation of rotation does not work correctly on non-spherical QGA quadric surface entities. Rotation also does not work correctly on the QGA point entities. Attempting to rotate a QGA quadric surface may result in a different type of quadric surface, or a quadric surface that is rotated and distorted in an unexpected way. Attempting to rotate a QGA point may produce a value that projects as the expected rotated vector, but the produced value is generally not a correct embedding of the rotated vector. The failure of QGA points to rotate correctly also leads to the inability to use outermorphisms to rotate dual Geometric Outer Product Null Space (GOPNS) entities. To rotate a QGA point, it must be projected to a vector or converted to a CGA point for rotation operations, then the rotated result can be re-embedded or converted back into a QGA point. A quadric surface rotated by an arbitrary angle cannot be represented by any known QGA entity. Representation of general quadric surfaces with useful operations will require an algebra (that appears to be unknown at this time) that extends QGA.
Although rotation is generally unavailable in QGA, the transposition operation is a special-case modification of rotation by that works correctly on all QGA GIPNS entities. Transpositions allow QGA GIPNS entities to be reflected in the six diagonal planes , , and .
Entities for all principal axes-aligned quadric surfaces can be defined in QGA. These include ellipsoids, cylinders, cones, paraboloids, and hyperboloids in all of their various forms.
A powerful feature of QGA is the ability to compute the intersections of axes-aligned quadric surfaces. With few exceptions, the outer |
https://en.wikipedia.org/wiki/Tuval%20Foguel | Tuval Shmuel Foguel is Professor of Mathematics at Adelphi University in Garden City, New York. Tuval Foguel was born in 1959 in Berkeley, California to Hava and Shaul Foguel and he is a descendant of Saul Wahl. Through his mother Hava (née Sokolow), Professor Foguel is related to Nahum Sokolow. Professor Foguel received his B.S. in mathematics from York College, City University of New York in 1988 and his PhD in Mathematics under Michio Suzuki from the University of Illinois at Urbana–Champaign in 1992 with a focus on finite groups. He has introduced the term conjugate-permutable subgroup. In the past, Professor Foguel has also taught at the University of the West Indies, North Dakota State University, Auburn University Montgomery, and Western Carolina University.
Selected articles
Tuval Foguel, Josh Hiller (2020), A note on Abelian Partitionable groups, Communications in Algebra, 48, no.8, 3268-3274.
Tuval Foguel, Josh Hiller (2019), On Bruck's Prolongation and Contraction Maps, Quasigroups and Related Systems 27, 53-62.
Tuval Foguel, Nicholas Sizemore (2018), Partition Numbers of Finite Solvable Groups, Advances in Group Theory and Applications 6, 55-67.
Tuval Foguel and Josh Hiller (2016), A Note On Subloop Lattices. Results in Mathematics, 69, no.1, 11-21.
Tuval Foguel, Baojun Li (2015), On $\Pi$-property and $\Pi$-normality of subgroups of finite groups (II). Algebra and Logic, 54, No. 3, 211–225.
Risto Atanasov, Tuval Foguel (2014) Loops That Are Partitioned by Groups, Journal of Group Theory17, no. 5, 851–861.
Risto Atanasov, Tuval Foguel, Jeff Lawson (2013), Optimizing Capstone With Multiple Constraints PRIMUS 24, no.4, 392-402.
Tuval Foguel, Michael K. Kinyon, J.D. Phillips (2006), On twisted subgroups and Bol loops of odd order, Rocky Mountain Journal of Mathematics 36 no.1, 183-212.
Tuval Foguel, Luise-Charlotte Kappe (2005), On loops covered by subloops, Expositiones Mathematicae 23, 255 – 270.
Tuval Foguel, Abraham A. Ungar (2000), Involutory Decomposition of Groups into Twisted Subgroups and Subgroups, Journal of Group Theory 3, no. 1, 27-46.
Tuval Foguel (1997), Conjugate - Permutable Subgroups, Journal of Algebra, 191, 235 -239.
Tuval Foguel (1995), Finite Groups with a Special 2-Generator Property, Pacific Journal of Mathematics, 170, no. 2, 483-496
Tuval Foguel (1994), On Seminormal Subgroups, Journal of Algebra, 165, no. 3, 633-636.
N. Boston, W. Dabrowski, Tuval Foguel, P.J. Gies, D.A. Jackson, J. Leavitt, D.T. Ose (1993), The Proportion of Fixed-Point-Free Elements of a Transitive Permutation Group, Communications in *Algebra, 21, no. 9, 3259-3275.
Tuval Foguel (1992), Galois-Theoretical Groups, Journal of Algebra, 150, no. 2, 321-323.
See also
Conjugate-permutable subgroup
References
External links
Adelphi University – Faculty and Staff
1959 births
Living people
Adelphi University faculty
University of Illinois Urbana-Champaign alumni
American people of Israeli descent
Mathematicians from California
Mathematicians f |
https://en.wikipedia.org/wiki/Mark%20Ellingham | Mark Norman Ellingham is a professor of mathematics at Vanderbilt University whose research concerns graph theory. With Joseph D. Horton, he is the discoverer and namesake of the Ellingham–Horton graphs, two cubic 3-vertex-connected bipartite graphs that have no Hamiltonian cycle.
Ellingham earned his Ph.D. in 1986 from the University of Waterloo under the supervision of Lawrence Bruce Richmond. In 2012, he became one of the inaugural fellows of the American Mathematical Society.
References
20th-century American mathematicians
21st-century American mathematicians
Canadian mathematicians
Graph theorists
University of Waterloo alumni
Vanderbilt University faculty
Fellows of the American Mathematical Society
Living people
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Serre%27s%20criterion%20for%20normality | In algebra, Serre's criterion for normality, introduced by Jean-Pierre Serre, gives necessary and sufficient conditions for a commutative Noetherian ring A to be a normal ring. The criterion involves the following two conditions for A:
is a regular local ring for any prime ideal of height ≤ k.
for any prime ideal .
The statement is:
A is a reduced ring hold.
A is a normal ring hold.
A is a Cohen–Macaulay ring hold for all k.
Items 1, 3 trivially follow from the definitions. Item 2 is much deeper.
For an integral domain, the criterion is due to Krull. The general case is due to Serre.
Proof
Sufficiency
(After EGA IV2. Theorem 5.8.6.)
Suppose A satisfies S2 and R1. Then A in particular satisfies S1 and R0; hence, it is reduced. If are the minimal prime ideals of A, then the total ring of fractions K of A is the direct product of the residue fields : see total ring of fractions of a reduced ring. That means we can write where are idempotents in and such that . Now, if A is integrally closed in K, then each is integral over A and so is in A; consequently, A is a direct product of integrally closed domains Aei's and we are done. Thus, it is enough to show that A is integrally closed in K.
For this end, suppose
where all f, g, ai's are in A and g is moreover a non-zerodivisor. We want to show:
.
Now, the condition S2 says that is unmixed of height one; i.e., each associated primes of has height one. This is because if has height greater than one, then would contain a non zero divisor in . However, is associated to the zero ideal in so it can only contain zero divisors, see here. By the condition R1, the localization is integrally closed and so , where is the localization map, since the integral equation persists after localization. If is the primary decomposition, then, for any i, the radical of is an associated prime of and so ; the equality here is because is a -primary ideal. Hence, the assertion holds.
Necessity
Suppose A is a normal ring. For S2, let be an associated prime of for a non-zerodivisor f; we need to show it has height one. Replacing A by a localization, we can assume A is a local ring with maximal ideal . By definition, there is an element g in A such that and . Put y = g/f in the total ring of fractions. If , then is a faithful -module and is a finitely generated A-module; consequently, is integral over A and thus in A, a contradiction. Hence, or , which implies has height one (Krull's principal ideal theorem).
For R1, we argue in the same way: let be a prime ideal of height one. Localizing at we assume is a maximal ideal and the similar argument as above shows that is in fact principal. Thus, A is a regular local ring.
Notes
References
H. Matsumura, Commutative algebra, 1970.
Theorems in ring theory |
https://en.wikipedia.org/wiki/2nd%20Indie%20Soap%20Awards |
Awards
Winners are listed first and highlighted in boldface.
Statistics
References
External links
Indie Series Awards History and Archive of Past Winners
Indie Series Awards
2011 film awards |
https://en.wikipedia.org/wiki/Brendan%20Hassett | Brendan Edward Hassett is an American mathematician who works as a professor of mathematics at Brown University. His research interests include algebraic geometry and number theory.
Education and career
Hassett graduated from Yale College in 1992, and earned his doctorate in 1996 from Harvard University under the supervision of Joe Harris. After temporary positions at the Mittag-Leffler Institute, University of Chicago, and Chinese University of Hong Kong, he joined the Rice University faculty in 2000. He was promoted to full professor in 2006, chaired the department from 2009 to 2014, and was named as the Milton Brockett Porter Professor of Mathematics in 2013. In July 2015 he moved to Brown University. He is currently the Director of the Institute for Computational and Experimental Research in Mathematics.
Hassett has authored the textbook Introduction to Algebraic Geometry (Cambridge University Press, 2007).
In 2013, Hassett was named as a fellow of the American Mathematical Society "for contributions to higher-dimensional arithmetic geometry and birational geometry."
References
External links
Home page
Google scholar profile
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
Algebraic geometers
Number theorists
Yale University alumni
Harvard University alumni
Rice University faculty
Fellows of the American Mathematical Society
Brown University faculty |
https://en.wikipedia.org/wiki/Jonathan%20Danty | Jonathan Danty (born 7 October 1992) is a French professional rugby union player who plays as a centre for Top 14 club La Rochelle and the France national team.
Career statistics
List of international tries
Honours
France
1× Six Nations Championship: 2022
1× Grand Slam: 2022
Stade Français
1× Top 14: 2014–15
1× European Rugby Challenge Cup: 2016–17
La Rochelle
2× European Rugby Champions Cup: 2021–22, 2022–23
References
External links
France profile at FFR
Ligue Nationale De Rugby Profile
Living people
1992 births
French rugby union players
France international rugby union players
Rugby union centres
Rugby union players from Paris
Black French sportspeople
Stade Français Paris players
2023 Rugby World Cup players |
https://en.wikipedia.org/wiki/Toroidal%20embedding | In algebraic geometry, a toroidal embedding is an open embedding of algebraic varieties that locally looks like the embedding of the open torus into a toric variety. The notion was introduced by Mumford to prove the existence of semistable reductions of algebraic varieties over one-dimensional bases.
Definition
Let X be a normal variety over an algebraically closed field and a smooth open subset. Then is called a toroidal embedding if for every closed point x of X, there is an isomorphism of local -algebras:
for some affine toric variety with a torus T and a point t such that the above isomorphism takes the ideal of to that of .
Let X be a normal variety over a field k. An open embedding is said to a toroidal embedding if is a toroidal embedding.
Examples
Tits' buildings
See also
tropical compactification
References
Abramovich, D., Denef, J. & Karu, K.: Weak toroidalization over non-closed fields. manuscripta math. (2013) 142: 257.
External links
Toroidal embedding
Algebraic geometry |
https://en.wikipedia.org/wiki/Massimo%20Livi%20Bacci | Massimo Livi Bacci (November 9, 1936) is an Italian professor of Demography, School of Political Science “Cesare Alfieri,” University of Florence and Department of Statistics, Computing, Applications “Giuseppe Parenti”.
Early life and education
Livi Bacci was born in Florence. In 1960, he graduated from the Faculty of Political Science “Cesare Alfieri” of the University of Florence. In 1960-61 he studied at Brown University, supported by a Fulbright scholarship.
Academic career
In 1962 Livi Bacci began working in the University of Rome. In 1966 he became a full professor of demography in the Faculty of Economics, University of Florence. In 1984 he was a professor in demography in the Faculty of Political Science “Cesare Alfieri”, also the University of Florence.
Livi Bacci has spent periods teaching and conducting research about various aspects of demographics in the United States, Mexico, Brazil, and various European countries. His research has included studies on the effects of famine, disease, and culture on fertility rates and population changes. He has also studied methods of predicting future population growth.
Livi Bacci has written many books and articles about various topics related to population growth, decline, and migration. He is known for having developed the concept of "mortality crisis."
Livi Bacci was elected to the American Philosophical Society in 2004. As of 2015, he is a Professor Emeritus of the University of Florence.
Political career
Livi Bacci was elected to the Italian Senate twice from Toscana: April, 2006 and April 2008.
References
External links
Massimo Livi Bacci'', Personal page on the web site of Universita Degli Studi Firenze
1936 births
Living people
Brown University alumni
Academic staff of the University of Florence
Members of the American Philosophical Society |
https://en.wikipedia.org/wiki/Viral%20dynamics | Viral dynamics is a field of applied mathematics concerned with describing the progression of viral infections within a host organism. It employs a family of mathematical models that describe changes over time in the populations of cells targeted by the virus and the viral load. These equations may also track competition between different viral strains and the influence of immune responses. The original viral dynamics models were inspired by compartmental epidemic models (e.g. the SI model), with which they continue to share many common mathematical features, such as the concept of the basic reproductive ratio (R0). The major distinction between these fields is in the scale at which the models operate: while epidemiological models track the spread of infection between individuals within a population (i.e. "between host"), viral dynamics models track the spread of infection between cells within an individual (i.e. "within host"). Analyses employing viral dynamic models have been used extensively to study HIV, hepatitis B virus, and hepatitis C virus, among other infections
References
External links
Viral Dynamics Mathematical Modeling Training, Center for AIDS Research, University of Washington
Evolutionary dynamics
Evolutionary biology
Virology
Immunology
Applied mathematics
Mathematical modeling |
https://en.wikipedia.org/wiki/Kneser%E2%80%93Ney%20smoothing | Kneser–Ney smoothing, also known as Kneser-Essen-Ney smoothing, is a method primarily used to calculate the probability distribution of n-grams in a document based on their histories. It is widely considered the most effective method of smoothing due to its use of absolute discounting by subtracting a fixed value from the probability's lower order terms to omit n-grams with lower frequencies. This approach has been considered equally effective for both higher and lower order n-grams. The method was proposed in a 1994 paper by Reinhard Kneser, Ute Essen and .
A common example that illustrates the concept behind this method is the frequency of the bigram "San Francisco". If it appears several times in a training corpus, the frequency of the unigram "Francisco" will also be high. Relying on only the unigram frequency to predict the frequencies of n-grams leads to skewed results; however, Kneser–Ney smoothing corrects this by considering the frequency of the unigram in relation to possible words preceding it.
Method
Let be the number of occurrences of the word followed by the word in the corpus.
The equation for bigram probabilities is as follows:
Where the unigram probability depends on how likely it is to see the word in an unfamiliar context, which is estimated as the number of times it appears after any other word divided by the number of distinct pairs of consecutive words in the corpus:
Note that is a proper distribution, as the values defined in the above way are non-negative and sum to one.
The parameter is a constant which denotes the discount value subtracted from the count of each n-gram, usually between 0 and 1.
The value of the normalizing constant is calculated to make the sum of conditional probabilities over all equal to one.
Observe that (provided ) for each which occurs at least once in the context of in the corpus we discount the probability by exactly the same constant amount ,
so the total discount depends linearly on the number of unique words that can occur after .
This total discount is a budget we can spread over all proportionally to .
As the values of sum to one, we can simply define to be equal to this total discount:
This equation can be extended to n-grams. Let be the words before :
This model uses the concept of absolute-discounting interpolation which incorporates information from higher and lower order language models. The addition of the term for lower order n-grams adds more weight to the overall probability when the count for the higher order n-grams is zero. Similarly, the weight of the lower order model decreases when the count of the n-gram is non zero.
Modified Kneser–Ney smoothing
Modifications of this method also exist. Chen and Goodman's 1998 paper lists and benchmarks several such modifications. Computational efficiency and scaling to multi-core systems is the focus of Chen and Goodman’s 1998 modification. This approach is once used for Google Translate under a MapReduce implem |
https://en.wikipedia.org/wiki/Infinite%20skew%20polygon | In geometry, an infinite skew polygon or skew apeirogon is an infinite 2-polytope with vertices that are not all colinear. Infinite zig-zag skew polygons are 2-dimensional infinite skew polygons with vertices alternating between two parallel lines. Infinite helical polygons are 3-dimensional infinite skew polygons with vertices on the surface of a cylinder.
Regular infinite skew polygons exist in the Petrie polygons of the affine and hyperbolic Coxeter groups. They are constructed a single operator as the composite of all the reflections of the Coxeter group.
Regular zig-zag skew apeirogons in two dimensions
A regular zig-zag skew apeirogon has (2*∞), D∞d Frieze group symmetry.
Regular zig-zag skew apeirogons exist as Petrie polygons of the three regular tilings of the plane: {4,4}, {6,3}, and {3,6}. These regular zig-zag skew apeirogons have internal angles of 90°, 120°, and 60° respectively, from the regular polygons within the tilings:
Isotoxal skew apeirogons in two dimensions
An isotoxal apeirogon has one edge type, between two alternating vertex types. There's a degree of freedom in the internal angle, α. {∞α} is the dual polygon of an isogonal skew apeirogon.
Isogonal skew apeirogons in two dimensions
Isogonal zig-zag skew apeirogons in two dimensions
An isogonal skew apeirogon alternates two types of edges with various Frieze group symmetries. Distorted regular zig-zag skew apeirogons produce isogonal zig-zag skew apeirogons with translational symmetry:
Isogonal elongated skew apeirogons in two dimensions
Other isogonal skew apeirogons have alternate edges parallel to the Frieze direction. These isogonal elongated skew apeirogons have vertical mirror symmetry in the midpoints of the edges parallel to the Frieze direction:
Quasiregular elongated skew apeirogons in two dimensions
An isogonal elongated skew apeirogon has two different edge types; if both of its edge types have the same length: it can't be called regular because its two edge types are still different ("trans-edge" and "cis-edge"), but it can be called quasiregular.
Example quasiregular elongated skew apeirogons can be seen as truncated Petrie polygons in truncated regular tilings of the Euclidean plane:
Hyperbolic skew apeirogons
Infinite regular skew polygons are similarly found in the Euclidean plane and in the hyperbolic plane.
Hyperbolic infinite regular skew polygons also exist as Petrie polygons zig-zagging edge paths on all regular tilings of the hyperbolic plane. And again like in the Euclidean plane, hyperbolic infinite quasiregular skew polygons can be constructed as truncated Petrie polygons within the edges of all truncated regular tilings of the hyperbolic plane.
Infinite helical polygons in three dimensions
An infinite helical (skew) polygon can exist in three dimensions, where the vertices can be seen as limited to the surface of a cylinder. The sketch on the right is a 3D perspective view of such an infinite regular helical polygon.
This i |
https://en.wikipedia.org/wiki/Polyadic%20space | In mathematics, a polyadic space is a topological space that is the image under a continuous function of a topological power of an Alexandroff one-point compactification of a discrete space.
History
Polyadic spaces were first studied by S. Mrówka in 1970 as a generalisation of dyadic spaces. The theory was developed further by R. H. Marty, János Gerlits and Murray G. Bell, the latter of whom introduced the concept of the more general centred spaces.
Background
A subset K of a topological space X is said to be compact if every open cover of K contains a finite subcover. It is said to be locally compact at a point x ∈ X if x lies in the interior of some compact subset of X. X is a locally compact space if it is locally compact at every point in the space.
A proper subset A ⊂ X is said to be dense if the closure Ā = X. A space whose set has a countable, dense subset is called a separable space.
For a non-compact, locally compact Hausdorff topological space , we define the Alexandroff one-point compactification as the topological space with the set , denoted , where , with the topology defined as follows:
, for every compact subset .
Definition
Let be a discrete topological space, and let be an Alexandroff one-point compactification of . A Hausdorff space is polyadic if for some cardinal number , there exists a continuous surjective function , where is the product space obtained by multiplying with itself times.
Examples
Take the set of natural numbers with the discrete topology. Its Alexandroff one-point compactification is . Choose and define the homeomorphism with the mapping
It follows from the definition that the image space is polyadic and compact directly from the definition of compactness, without using Heine-Borel.
Every dyadic space (a compact space which is a continuous image of a Cantor set) is a polyadic space.
Let X be a separable, compact space. If X is a metrizable space, then it is polyadic (the converse is also true).
Properties
The cellularity of a space is
The tightness of a space is defined as follows: let , and . Define
Then
The topological weight of a polyadic space satisfies the equality .
Let be a polyadic space, and let . Then there exists a polyadic space such that and .
Polyadic spaces are the smallest class of topological spaces that contain metric compact spaces and are closed under products and continuous images. Every polyadic space of weight is a continuous image of .
A topological space has the Suslin property if there is no uncountable family of pairwise disjoint non-empty open subsets of . Suppose that has the Suslin property and is polyadic. Then is dyadic.
Let be the least number of discrete sets needed to cover , and let denote the least cardinality of a non-empty open set in . If is a polyadic space, then .
Ramsey's theorem
There is an analogue of Ramsey's theorem from combinatorics for polyadic spaces. For this, we describe the relationship between Boolea |
https://en.wikipedia.org/wiki/Functor%20represented%20by%20a%20scheme | In algebraic geometry, a functor represented by a scheme X is a set-valued contravariant functor on the category of schemes such that the value of the functor at each scheme S is (up to natural bijections) the set of all morphisms . The scheme X is then said to represent the functor and that classify geometric objects over S given by F.
The best known example is the Hilbert scheme of a scheme X (over some fixed base scheme), which, when it exists, represents a functor sending a scheme S to a flat family of closed subschemes of .
In some applications, it may not be possible to find a scheme that represents a given functor. This led to the notion of a stack, which is not quite a functor but can still be treated as if it were a geometric space. (A Hilbert scheme is a scheme, but not a stack because, very roughly speaking, deformation theory is simpler for closed schemes.)
Some moduli problems are solved by giving formal solutions (as opposed to polynomial algebraic solutions) and in that case, the resulting functor is represented by a formal scheme. Such a formal scheme is then said to be algebraizable if there is another scheme that can represent the same functor, up to some isomorphisms.
Motivation
The notion is an analog of a classifying space in algebraic topology. In algebraic topology, the basic fact is that each principal G-bundle over a space S is (up to natural isomorphisms) the pullback of a universal bundle along some map from S to . In other words, to give a principal G-bundle over a space S is the same as to give a map (called a classifying map) from a space S to the classifying space of G.
A similar phenomenon in algebraic geometry is given by a linear system: to give a morphism from a projective variety to a projective space is (up to base loci) to give a linear system on the projective variety.
Yoneda's lemma says that a scheme X determines and is determined by its points.
Functor of points
Let X be a scheme. Its functor of points is the functor
Hom(−,X) : (Affine schemes)op ⟶ Sets
sending an affine scheme Y to the set of scheme maps .
A scheme is determined up to isomorphism by its functor of points. This is a stronger version of the Yoneda lemma, which says that a X is determined by the map Hom(−,X):Schemesop → Sets.
Conversely, a functor F:(Affine schemes)op → Sets is the functor of points of some scheme if and only if F is a sheaf with respect to the Zariski topology on (Affine schemes), and F admits an open cover by affine schemes.
Examples
Points as characters
Let X be a scheme over the base ring B. If x is a set-theoretic point of X, then the residue field of x is the residue field of the local ring (i.e., the quotient by the maximal ideal). For example, if X is an affine scheme Spec(A) and x is a prime ideal , then the residue field of x is the function field of the closed subscheme .
For simplicity, suppose . Then the inclusion of a set-theoretic point x into X corresponds to the ring homomorphism:
(wh |
https://en.wikipedia.org/wiki/Vittoria%20Bussi | Vittoria Bussi (born 19 March 1987) is an Italian professional racing cyclist. She holds a DPhil in pure mathematics from the University of Oxford for a 2014 thesis entitled Derived symplectic structures in generalized Donaldson–Thomas theory and categorification.
In September 2018, she set a new UCI Women's hour record, riding at the Aguascalientes Bicentenary Velodrome, Aguascalientes, Mexico, beating the previous record set by Evelyn Stevens in 2016 by 27 metres. It was Bussi's third attempt at the record, having fallen short of Stevens' performance in Aguascalientes in October 2017 by 404 metres and having abandoned a second attempt after 40 minutes the day before her record-breaking ride.
Later, on October 13, 2023, Bussi set another UCI Women's hour record, at the Velodromo Bicentenario in Mexico, with a 50.267km distance.
Major results
2020
3rd Mixed team relay, UEC European Road Championships
References
External links
1987 births
Living people
Italian female cyclists
Cyclists from Rome
Alumni of the University of Oxford
Sapienza University of Rome alumni
21st-century Italian women |
https://en.wikipedia.org/wiki/Household%20Finance%20and%20Consumption%20Survey%20%28Ireland%29 | The Household Finance and Consumption Survey (HFCS) is a statistical survey conducted by the Central Statistics Office (CSO) on behalf of the Central Bank of Ireland as part of the European Central Bank (ECB) Household Finance and Consumption Network (HFCN).
The HFCS is designed to collect household-level data on households’ finances and consumption, and is required by all Eurozone countries to facilitate comparable data analysis for the Euro area as a whole.
Household Finance and Consumption Survey 2013
The 2013 HFCS study was the first conducted in Ireland, carried out between March and September 2013 with 5,419 respondent households.
Results of the 2013 study were released in January 2015 by the Central Statistics Office.
Survey data is available on the CSO website in PDF format.
Methodology and scope
The 2013 study sample size consisted of 5,419 respondent households.
The survey collected a range of household information from the adults taking the survey, including the following household characteristics at micro level:
demographics
real and financial assets
liabilities
consumption and saving
income and employment
future pension entitlements, intergenerational transfers and gifts
attitudes to risk
Main uses and aims
The HFCS is designed to find out more about household finance and consumption in Ireland.
HFCS aims to collect information to help policy-makers respond to a variety of questions concerning:
Debt and financial pressures
Portfolio choice and demand for assets
Saving, liquidity constraints and the smoothing of consumption
Computational finance
External links
Central Statistics Office
Household Finance and Consumption Network (HFCN) (official) website
Central Bank of Ireland
References
Economy of the Republic of Ireland
Economic data
Panel data
Household income |
https://en.wikipedia.org/wiki/List%20of%20United%20States%20cities%20by%20crime%20rate | The following table of United States cities by crime rate is based on Federal Bureau of Investigation Uniform Crime Reports (UCR) statistics from 2019 for the 100 most populous cities in America that have reported data to the FBI UCR system.
The population numbers are based on U.S. Census estimates for the year end. The number of murders includes nonnegligent manslaughter. This list is based on the reporting. In most cases, the city and the reporting agency are identical. However, in some cases such as Charlotte, Honolulu, and Las Vegas, the reporting agency has more than one municipality.
Murder is the only statistic that all agencies are required to report. Consequently, some agencies do not report all the crimes. If components are missing the total is adjusted to 0.
Note about population
Often, one obtains very different results depending on whether crime rates are measured for the city jurisdiction or the metropolitan area.
Information is voluntarily submitted by each jurisdiction and some jurisdictions do not appear in the table because they either did not submit data or they did not meet deadlines.
The FBI website has this disclaimer on population estimates:
For the 2019 population estimates used in this table, the FBI computed individual rates of growth from one year to the next for every city/town and county using 2010 decennial population counts and 2011 through 2018 population estimates from the U.S. Census Bureau. Each agency’s rates of growth were averaged; that average was then applied and added to its 2018 Census population estimate to derive the agency’s 2019 population estimate.
It should also be mentioned that the FBI has recently switched its data reporting mechanism and currently some major metropolitan police departments (e.g. Baltimore) have not been included in the total.
Crime rates
Notes:
1 The figures are shown in this column for the offense of rape were reported using only the revised Uniform Crime Reporting (UCR) definition of rape. See the data declaration for further explanation.
2 The FBI does not publish arson data unless it receives it from either the agency or the state for all 12 months of the calendar year.
3 The population of the city of Mobile, Alabama, includes 55,819 inhabitants from the jurisdiction of the Mobile County Sheriff's Department.
4 Because of changes in the state/ or local agency's reporting practices, figures are not comparable to previous years' data.
5 The FBI determined that the agency's data were underreported. Consequently, those data are not included in this table.
6 Arson offenses are also reported by the Louisville Fire Department. Those figures are not included in this table.
7 Arson offenses are reported by the Toledo Fire Department; therefore, those figures are not included in this report.
8 This agency/state submits rape data classified according to the legacy UCR definition; therefore, the rape offense and violent crime total, which rape is a part of, is not inclu |
https://en.wikipedia.org/wiki/Mathematics%20and%20Plausible%20Reasoning | Mathematics and Plausible Reasoning is a two-volume book by the mathematician George Pólya describing various methods for being a good guesser of new mathematical results. In the Preface to Volume 1 of the book Pólya exhorts all interested students of mathematics thus: "Certainly, let us learn proving, but also let us learn guessing." P. R. Halmos reviewing the book summarised the central thesis of the book thus: ". . . a good guess is as important as a good proof."
Outline
Volume I: Induction and analogy in mathematics
Polya begins Volume I with a discussion on induction, not mathematical induction, but as a way of guessing new results. He shows how the chance observations of a few results of the form 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 3 + 7, etc., may prompt a sharp mind to formulate the conjecture that every even number greater than 4 can be represented as the sum of two odd prime numbers. This is the well known Goldbach's conjecture. The first problem in the first chapter is to guess the rule according to which the successive terms of the following sequence are chosen: 11, 31, 41, 61, 71, 101, 131, . . . In the next chapter the techniques of generalization, specialization and analogy are presented as possible strategies for plausible reasoning. In the remaining chapters, these ideas are illustrated by discussing the discovery of several results in various fields of mathematics like number theory, geometry, etc. and also in physical sciences.
Volume II: Patterns of Plausible Inference
This volume attempts to formulate certain patterns of plausible reasoning. The relation of these patterns with the calculus of probability are also investigated. Their relation to mathematical invention and instruction are also discussed. The following are
some of the patterns of plausible inference discussed by Polya.
Reviews
References
Mathematics books
Reasoning
Inference |
https://en.wikipedia.org/wiki/Alexander%20Buchstab | Aleksandr Adol'fovich Buchstab (October 4, 1905 – February 27, 1990; , variously transliterated as Bukhstab, Buhštab, or Bukhshtab) was a Soviet mathematician who worked in number theory and was "known for his work in sieve methods". He is the namesake of the Buchstab function, which he wrote about in 1937.
Buchstab was born in Stavropol; his father was a physician. He studied at the Rostov Polytechnic Institute and Rostov University before moving to the faculty of mechanics and mathematics at Moscow State University, where he earned a degree in 1928. He worked at the Moscow Higher Technical College from 1928 until 1930, and then from 1930 to 1939 at Azerbaijan University, where was the chair of algebra and function theory and then dean of physics and mathematics.
During this period, Buchstab also did graduate studies at Moscow State under the supervision of Aleksandr Khinchin. He defended his candidacy in 1939, and at that time was appointed to a professorship at the Moscow State Pedagogical University. During World War II he taught at the Azerbaijan State University and Dzerzhinskii Higher Naval Engineering College, returning to Moscow in 1943 and defending a doctorate from the Steklov Institute of Mathematics in 1944. He remained at the Moscow State Pedagogical University for the rest of his career, where his students included Gregory Freiman and Ilya Piatetski-Shapiro.
Selected publications
References
External links
Math-net.ru
1905 births
1990 deaths
Soviet mathematicians
Number theorists
Moscow State University alumni |
https://en.wikipedia.org/wiki/Bodil%20Branner | Bodil Branner (born 5 February 1943, in Aarhus) is a retired Danish mathematician, one of the founders of European Women in Mathematics and a former chair of the Danish Mathematical Society. Her research concerned holomorphic dynamics and the history of mathematics.
Education and career
Branner studied mathematics and physics at Aarhus University, where mathematician Svend Bundgaard was one of her mentors, and in 1967 earned a master's degree (the highest degree then available) under the supervision of Leif Kristensen. She had intended to travel to the U.S. for a doctorate, but her husband, a chemist, took an industry job in Copenhagen. Branner could not get a job as a high school teacher because she did not have a teaching qualification, but Bundgaard found her a position as a faculty assistant for Frederik Fabricius-Bjerre at the Technical University of Denmark. Despite this not beginning as an actual faculty position, she eventually earned tenure there in the 1970s. She was the first woman to chair the Danish Mathematical Society, from 1998 to 2002. She retired in 2008.
Recognition
A symposium in honor of Branner's 60th birthday was held in Holbæk in 2003, and published as a festschrift in 2006. In 2012, she became one of the inaugural fellows of the American Mathematical Society.
Selected publications
.
.
.
.
References
External links
Living people
20th-century Danish mathematicians
21st-century Danish mathematicians
Aarhus University alumni
Academic staff of the Technical University of Denmark
Fellows of the American Mathematical Society
1943 births
People from Aarhus
20th-century women mathematicians
21st-century women mathematicians |
https://en.wikipedia.org/wiki/Demographics%20of%20Kosovo | The Kosovo Agency of Statistics monitors various demographic features of the population of Kosovo, such as population density, ethnicity, education level, health of the populace, economic status, religious affiliations and other aspects of the population. Censuses, normally conducted at ten-year intervals, record the demographic characteristics of the population. According to the first census conducted after the 2008 declaration of independence in 2011, the permanent population of Kosovo had reached 1,810,366.
A 2011 demographic census shows that Albanians form the majority in Kosovo, with over 93% of the total population; significant minorities include Bosniaks (1.6%), Serbs (1.5%) and others. However, most Serbs boycotted the census and it therefore shows an inaccurate number of Serbs in Kosovo. After Albanians, Serbs form the largest ethnic community in Kosovo (6–7%). A 2023 CIA estimate put Kosovo's population at 1,964,327.
Kosovo has the youngest population in Europe. As of 2008, half of its roughly 2-million-strong population is under the age of 25, according to a recent report of the UN Development Programme, UNDP. According to the government data, it is estimated that more than 65 percent of the population are younger than 30.
History
2011 census
The final results of the 2011 census recorded Kosovo (excluding North Kosovo) as having 1,739,825 inhabitants. The European Centre for Minority Issues (ECMI) has called "for caution when referring to the 2011 census", due to the boycott by Serb-majority municipalities in North Kosovo and the large boycott by Serbs and Roma in southern Kosovo. The recorded total population was below most previous estimates. The census enjoyed considerable technical assistance from international agencies and appears to have been endorsed by Eurostat; it was, however, the first full census since 1981, and not one of an uninterrupted series. The results show that there were no people temporarily resident in hotels or refugee camps at the time of the census; that out of 312,711 conventional dwellings, 99,808 (over 30%) were unoccupied; and that three municipalities designed under the Ahtisaari Plan to have Serb majorities – Klokot, Novo Brdo, and Štrpce – in fact had ethnic Albanian majorities (although their municipal assemblies have Serb majorities).
Vital statistics
Source: Kosovo Agency of Statistics
Population estimates in the table below may be unreliable during the 1990s period. Besides, vital statistics do not fully include data from Serb-majority territories. Since 2011, in accordance with European statistical norms, live births and deaths record figures in Kosovo only (excluding foreign countries).
Current vital statistics
Marriages and divorces
Administrative divisions
Kosovo is administratively subdivided into seven districts, and 38 municipalities. With the current estimation on population, Kosovo ranks as the 150th largest country in the world based on how populous it is.
Ethnic groups
The |
https://en.wikipedia.org/wiki/Bernstein%E2%80%93Kushnirenko%20theorem | The Bernstein–Kushnirenko theorem (or Bernstein–Khovanskii–Kushnirenko (BKK) theorem), proven by David Bernstein and in 1975, is a theorem in algebra. It states that the number of non-zero complex solutions of a system of Laurent polynomial equations is equal to the mixed volume of the Newton polytopes of the polynomials , assuming that all non-zero coefficients of are generic. A more precise statement is as follows:
Statement
Let be a finite subset of Consider the subspace of the Laurent polynomial algebra consisting of Laurent polynomials whose exponents are in . That is:
where for each we have used the shorthand notation to denote the monomial
Now take finite subsets of , with the corresponding subspaces of Laurent polynomials, Consider a generic system of equations from these subspaces, that is:
where each is a generic element in the (finite dimensional vector space)
The Bernstein–Kushnirenko theorem states that the number of solutions of such a system is equal to
where denotes the Minkowski mixed volume and for each is the convex hull of the finite set of points . Clearly, is a convex lattice polytope; it can be interpreted as the Newton polytope of a generic element of the subspace .
In particular, if all the sets are the same, then the number of solutions of a generic system of Laurent polynomials from is equal to
where is the convex hull of and vol is the usual -dimensional Euclidean volume. Note that even though the volume of a lattice polytope is not necessarily an integer, it becomes an integer after multiplying by .
Trivia
Kushnirenko's name is also spelt Kouchnirenko. David Bernstein is a brother of Joseph Bernstein. Askold Khovanskii has found about 15 different proofs of this theorem.
References
See also
Bézout's theorem for another upper bound on the number of common zeros of polynomials in indeterminates.
Theorems in algebra
Theorems in geometry |
https://en.wikipedia.org/wiki/Harris%20Hancock | Harris Hancock (May 14, 1867 – March 19, 1944) was a mathematics professor at the University of Cincinnati who worked on algebraic number theory and related areas. He was the brother of the horse breeder Arthur B. Hancock.
Biography
Harris Hancock was born at his family's estate, Ellerslie, in Albemarle County, Virginia on May 14, 1867. He graduated from the University of Virginia's school of mathematics in 1886. He received an AB from Johns Hopkins University in 1888, an AM and PhD from the University of Berlin in 1894, and an ScD from the University of Paris in 1901.
He married Belle Lyman Clay on September 30, 1907, and they had two children.
Harris Hancock died at Ellerslie on March 19, 1944.
Publications
Articles
Books
Reprinted by Dover Publications, Inc., New York 1958
Reprinted by Dover Publications, Inc., New York 1958
Reprinted by Dover Publications, Inc., New York 1960
Reprinted by Dover Publications, Inc., New York 1964
Reprinted by Dover Publications, Inc., New York 1964, 2005
References
External links
Harris Hancock
1867 births
1944 deaths
Hancock family
20th-century American mathematicians
University of Cincinnati faculty
University of Paris alumni |
https://en.wikipedia.org/wiki/Lars%20Hesselholt | Lars Hesselholt (born September 25, 1966) is a Danish mathematician who works as a professor of mathematics at Nagoya University in Japan, as well as holding a temporary position as Niels Bohr Professor at the University of Copenhagen. His research interests include homotopy theory, algebraic K-theory, and arithmetic algebraic geometry.
Hesselholt was born in Vejrumbro, a village in the Viborg Municipality of Denmark. He studied at Aarhus University, earning a bachelor's degree in 1988, a master's degree in 1992, and a Ph.D. in 1994; his dissertation, supervised by Ib Madsen, concerned K-theory. After postdoctoral studies at the Mittag-Leffler Institute, he joined the faculty of the Massachusetts Institute of Technology in 1994 as a C.L.E. Moore instructor, and stayed at MIT as an assistant and then associate professor, before moving to Nagoya in 2008. Hesselholt's wife is Japanese, and when he joined the Nagoya faculty he became the first westerner with a full professorship in mathematics in Japan. He is the managing editor of the Nagoya Mathematical Journal.
Hesselholt became a Sloan fellow in 1998, and was an invited speaker at the International Congress of Mathematicians in 2002. In 2012, he became one of the inaugural fellows of the American Mathematical Society, and a foreign member of the Royal Danish Academy of Sciences and Letters.
References
External links
Home page at Copenhagen
Home page at Nagoya
Google scholar profile
1966 births
Living people
Japanese mathematicians
Danish expatriates in Japan
20th-century Danish mathematicians
21st-century Danish mathematicians
Aarhus University alumni
Academic staff of Nagoya University
Academic staff of the University of Copenhagen
Fellows of the American Mathematical Society
Massachusetts Institute of Technology School of Science faculty |
https://en.wikipedia.org/wiki/J%C3%BCrgen%20P.%20Rabe | Jürgen P. Rabe is a German physicist and nanoscientist.
Life
Jürgen P. Rabe studied physics and mathematics at RWTH Aachen where in 1981 he obtained his diploma in physics, based on a thesis on semiconductor optics with Peter Grosse. 1984 he obtained his doctoral degree from the Department of Physics at the Technische Universität München, based on a biophysical thesis on model membranes, promoted by Erich Sackmann.
As a visiting scientist at the IBM Almaden Research Center in San José (1984–1986) he initiated the use of scanning tunneling microscopy for molecular monolayers, which he continued in Gerhard Wegner’s department at the Max Planck Institute for Polymer Research.
In 1992 he obtained his habilitation on this topic and became a professor for physical chemistry at Johannes Gutenberg-Universität in Mainz. Since 1994 Rabe is full professor for experimental physics with an emphasis on macromolecular and supramolecular systems at the Department of Physics at the Humboldt-Universität zu Berlin. Rabe is an elected scientific member of the Max Planck Society and external member of the Max Planck Institute of Colloids and Interfaces in Potsdam-Golm as well as founding director of the Integrative Research Institute for the Sciences IRIS Adlershof of Humboldt-Universität. He was visiting professor at the Materials Department of ETH Zürich and for the Department of Chemistry at Princeton University.
Jürgen P. Rabe is the brother of Klaus F. Rabe and cousin of Sophia Rabe-Hesketh and the economist Birgitta Rabe.
Research
Rabe became internationally known for his seminal scanning tunneling microscopy research on the structure, dynamics, and electronic properties of self-assembled molecular systems at solid-liquid interfaces. He developed concepts for a workbench to manipulate individual macromolecules and supramolecular systems, employing scanning probe microscopies, light, and molecularly modified graphite surfaces, which has been used to correlate structure and dynamics of molecular systems with mechanical, electronic, optical, and (bio)chemical properties from molecular to macromolecular lengths and time scales. It also led to the development of prototypical quasi 1- and 2- dimensional organic-inorganic hybrid systems, based on opto-electronically active molecular or graphene-based nanopores. In collaborative and interdisciplinary projects Rabe contributed to the development of advanced functional materials, including dendronized and conjugated polymers, multivalent biopolymer complexes, ultrathin films of conjugated molecules, supramolecular polymers and helical nanofilaments, nanographenes, and 2D materials as well as mixed 2D/3D heterostructures.
External links
For publications from Jürgen P. Rabe see "ResearcherID D-1032-2010" and "Google Scholar"
Curriculum Vitae Jürgen P. Rabe
References
21st-century German physicists
1955 births
20th-century German physicists
Living people
Max Planck Institute for Polymer Research alumni
Max P |
https://en.wikipedia.org/wiki/YoungJu%20Choie | YoungJu Choie (, born June 15, 1959) is a South Korean mathematician who works as a professor of mathematics at the Pohang University of Science and Technology (POSTECH). Her research interests include number theory and modular forms.
Education and career
Choie graduated from Ewha Womans University in 1982, and earned a doctorate in 1986 from Temple University under the supervision of Marvin Knopp. After temporary positions at Ohio State University and the University of Maryland, she became an assistant professor at University of Colorado in 1989, and moved to POSTECH as a full professor in 1990. Choie became a Fellow of the American Mathematical Society in 2013.
Mathematical work
Choie works on various aspects of Jacobi forms. Together with Winfried Kohnen, she has proved upper bounds on the first sign change of Fourier coefficients of cusp forms, generalizing the work of Siegel.
Selected works
Y. Choie, Y. Park and D. Zagier, Periods of modular forms on and Products of Jacobi Theta functions, Journal of the European Mathematical Society, Vol. 21, Issue 5, pp 1379–1410 (2019)
R. Bruggeman, Y. Choie and N. Diamantis, Holomorphic automorphic forms and cohomology, Memoirs of the American Mathematical Society, 253 (2018), no. 1212, vii+167 pp.
D. Bump and Y. Choie, “Schubert Eisenstein series”, American Journal of Mathematics Vol 136, No 6, Dec 2014, 1581-1608.
Y. Choie and W. Kohnen, “The first sign change of Fourier coefficients of cusp forms”, American Journal of Mathematics 131 (2009), no. 2, 517-543.
Y. Choie and D. Zagier, “Rational period functions for PSL(2, Z)”, Contemporary Mathematics, A tribute to Emil Grosswald: Number Theory and Related Analysis, 143, 89-108, 1993.
(Book) Y. Choie and MH. Lee, "Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms”, 318 pages, Springer Monographs in Mathematics on Springer Verlag 2019 (eBook )
(Book) M. Shi, Y. Choie, A. Sharma and P. Sole, “Codes and Modular forms”, World Scientific, (hardcover) | December 2019 Pages: 232
Service
Choie has been an editor of International Journal of Number Theory since 2004. In 2010–2011 she was editor-in-chief of the Bulletin of the Korean Mathematical Society. She became a president of the society of Korean Women in Mathematical Sciences in 2017.
Selective Public Service:
2020-2022: NCsoft, Non-executive director
2019-2020: The Presidential Advisory Council on Science and Technology, Deliberative Member, Republic of Korea.
2019-2020: University Councilor, Representative of Faculty at POSTECH, Pohang, Korea
2019-2020: Academic vice president of Korean Mathematical Society, Korea
2018-2021: Non-standing member of Board of Trustees, UNIST(Ulsan Institute of Science and Technology), Korea
2018-2020: Non-standing member of Board of Trustees, NRF(National Research Foundation), Korea
2018–2020, 2009-2013: Director of Pohang Mathematical Institute, POSTECH, Korea
2017.12-2019.11: Member, General review committee for academic r |
https://en.wikipedia.org/wiki/Stephanie%20Gandy | Stephanie Gandy (born May 10, 1982) is a former British – American female professional basketball player.
Michigan statistics
Source
External links
Profile at eurobasket.com
References
1982 births
Living people
Basketball players from Detroit
British women's basketball players
American women's basketball players
Small forwards
Power forwards (basketball)
21st-century American women |
https://en.wikipedia.org/wiki/With%20high%20probability | In mathematics, an event that occurs with high probability (often shortened to w.h.p. or WHP) is one whose probability depends on a certain number n and goes to 1 as n goes to infinity, i.e. the probability of the event occurring can be made as close to 1 as desired by making n big enough.
Applications
The term WHP is especially used in computer science, in the analysis of probabilistic algorithms. For example, consider a certain probabilistic algorithm on a graph with n nodes. If the probability that the algorithm returns the correct answer is , then when the number of nodes is very large, the algorithm is correct with a probability that is very near 1. This fact is expressed shortly by saying that the algorithm is correct WHP.
Some examples where this term is used are:
Miller–Rabin primality test: a probabilistic algorithm for testing whether a given number n is prime or composite. If n is composite, the test will detect n as composite WHP. There is a small chance that we are unlucky and the test will think that n is prime. But, the probability of error can be reduced indefinitely by running the test many times with different randomizations.
Freivalds' algorithm: a randomized algorithm for verifying matrix multiplication. It runs faster than deterministic algorithms WHP.
Treap: a randomized binary search tree. Its height is logarithmic WHP. Fusion tree is a related data structure.
Online codes: randomized codes which allow the user to recover the original message WHP.
BQP: a complexity class of problems for which there are polynomial-time quantum algorithms which are correct WHP.
Probably approximately correct learning: A process for machine-learning in which the learned function has low generalization-error WHP.
Gossip protocols: a communication protocol used in distributed systems to reliably deliver messages to the whole cluster using a constant amount of network resources on each node and ensuring no single point of failure.
See also
Randomized algorithm
Almost surely
References
Probability theory
Randomized algorithms |
https://en.wikipedia.org/wiki/List%20of%20R-7%20launches%20%282015%E2%80%932019%29 | This is a list of launches made by the R-7 Semyorka ICBM, and its derivatives between 2015 and 2019. All launches are orbital satellite launches, unless stated otherwise.
Launch statistics
Rocket configurations
Launch sites
Launch outcomes
Launch history
References |
https://en.wikipedia.org/wiki/Smooth%20maximum | In mathematics, a smooth maximum of an indexed family x1, ..., xn of numbers is a smooth approximation to the maximum function meaning a parametric family of functions such that for every , the function is smooth, and the family converges to the maximum function as . The concept of smooth minimum is similarly defined. In many cases, a single family approximates both: maximum as the parameter goes to positive infinity, minimum as the parameter goes to negative infinity; in symbols, as and as . The term can also be used loosely for a specific smooth function that behaves similarly to a maximum, without necessarily being part of a parametrized family.
Examples
Boltzmann operator
For large positive values of the parameter , the following formulation is a smooth, differentiable approximation of the maximum function. For negative values of the parameter that are large in absolute value, it approximates the minimum.
has the following properties:
as
is the arithmetic mean of its inputs
as
The gradient of is closely related to softmax and is given by
This makes the softmax function useful for optimization techniques that use gradient descent.
This operator is sometimes called the Boltzmann operator, after the Boltzmann distribution.
LogSumExp
Another smooth maximum is LogSumExp:
This can also be normalized if the are all non-negative, yielding a function with domain and range :
The term corrects for the fact that by canceling out all but one zero exponential, and if all are zero.
Mellowmax
The mellowmax operator is defined as follows:
It is a non-expansive operator. As , it acts like a maximum. As , it acts like an arithmetic mean. As , it acts like a minimum. This operator can be viewed as a particular instantiation of the quasi-arithmetic mean. It can also be derived from information theoretical principles as a way of regularizing policies with a cost function defined by KL divergence. The operator has previously been utilized in other areas, such as power engineering.
p-Norm
Another smooth maximum is the p-norm:
which converges to as .
An advantage of the p-norm is that it is a norm. As such it is scale invariant (homogeneous): , and it satisfies the triangle inequality.
Smooth maximum unit
The following binary operator is called the Smooth Maximum Unit (SMU):
where is a parameter. As , and thus .
See also
LogSumExp
Softmax function
Generalized mean
References
Mathematical notation
Basic concepts in set theory
https://www.johndcook.com/soft_maximum.pdf
M. Lange, D. Zühlke, O. Holz, and T. Villmann, "Applications of lp-norms and their smooth approximations for gradient based learning vector quantization," in Proc. ESANN, Apr. 2014, pp. 271-276.
(https://www.elen.ucl.ac.be/Proceedings/esann/esannpdf/es2014-153.pdf) |
https://en.wikipedia.org/wiki/Analytics%20%28ice%20hockey%29 | In ice hockey, analytics is the analysis of the characteristics of hockey players and teams through the use of statistics and other tools to gain a greater understanding of the effects of their performance. Three commonly used basic statistics in ice hockey analytics are "Corsi" and "Fenwick", both of which use shot attempts to approximate puck possession, and "PDO", which is often considered a measure of luck. However, new statistics are being created every year, with "RAPM", regularized adjusted plus-minus, and "xG", expected goals, being created very recently in regards to hockey even though they have been around in other sports before. RAPM tries to isolate a players play driving ability based on multiple factors, while xG tries to show how many goals a player should be expected to add to their team independent of shooting and goalie talent.
Hockey Hall of Fame coach Roger Nielson is credited as being an early pioneer of analytics and used measures of his own invention as early as his tenure with the Peterborough Petes in the late 1960s. In modern usage, analytics have traditionally been the domain of hockey bloggers and amateur statisticians. They have been increasingly adopted by National Hockey League (NHL) organizations themselves, and reached mainstream usage when the NHL partnered with SAP SE to create an "enhanced" statistical package that coincided with the launch of a new website featuring analytical statistics during the 2014–15 season.
Common statistics
Corsi
Corsi, called shot attempts (SAT) by the NHL, is the sum of shots on goal, missed shots and blocked shots. It is named after coach Jim Corsi, but was developed by an Edmonton Oilers blogger and fan who developed the statistic to better measure the workload of a goaltender during a game. However, today Corsi is used to approximate shot attempt differential for both teams and players, which can then be used to predict future goal differentials. If a team is losing in the goal differential halfway through the season, but possess a high Corsi, the team is creating more chances than their opponents which should result in the goal differential to get better as the team plays more games. Corsi is used to approximate puck possession – the length of time a player's team controls the puck – and is typically measured as either a ratio (like plus-minus) of shot attempts for less shot attempts against, or as a percentage. According to blogger Kent Wilson, most players will have a Corsi For percentage (CF%) between 40 and 60. A player or team ranked above 55% is often considered "elite".
Fenwick
Fenwick, called unblocked shot attempts (USAT) by the NHL, is a variant of Corsi that counts only shots on goal and missed shots; blocked shots, either for or against are not included. It is named after blogger Matt Fenwick and is viewed as having a stronger correlation to scoring chances. Fenwick is used to help judge team and player performances that strategically use shot blocking as part of |
https://en.wikipedia.org/wiki/D.%20Randy%20Garrison | Donn Randy Garrison (born 1945) is a Canadian professor emeritus at the University of Calgary who has published extensively on distance education.
Garrison is a holder of a B. Ed in Mathematics with a minor in Psychology. In 1972, he did his Master of Education in Computer Application in Education at the University of Calgary. He received an award for most outstanding achievement from the Sloan Consortium in 2009.
Research
The focus of Garrison's work has been on distance education, online and blended learning. He explored the relationship with teaching, learning and the communication process .
Garrison believed that at the start of the 21st century, online learning has focused on communication and collaboration.
By understanding the relationship among teaching presence, cognitive presence and social presence, educators will be able to better meet the needs of the learners.
Garrison believed that communication and collaboration between teacher and learner is essential in distance education.
Books
Garrison, D. R. (1989). Understanding distance education: A framework for the future. London: Routledge.
Garrison, D. R. & Shale, D. (Eds.). (1990). Education at a distance: From issues to practice. Melbourne, Florida: Krieger.
Garrison, D. R. (Ed.) (1994). Research perspectives in adult education. Melbourne, Florida: Krieger.
Garrison, D. R., & Archer, W. (2000). A transactional perspective on teaching-learning: A framework for adult and higher education. Oxford, UK: Pergamon.
Garrison, D. R., & Anderson, T. (2003). E-Learning in the 21st century: A framework for research and practice. London: Routledge/Falmer.
Garrison, D. R., & Vaughan, N. (2008). Blended learning in higher education. San Francisco: Jossey-Bass.
Cleveland-Innes, M., & Garrison, D. R. (Eds.) (2010). An introduction to distance education: Understanding teaching and learning in a new era. London: Routledge.
Garrison, D. R. (2011). E-Learning in the 21st century: A framework for research and practice (2nd ed.). London: Routledge/Taylor and Francis.
Akyol, Z., & Garrison, D. R. (Eds.) (2013). Educational communities of inquiry: Theoretical framework, research and practice. Hershey, PA: IGI Global.
Vaughan, N. D., Cleveland-Innes, M., & Garrison, D. R. (2013). Teaching in blended learning environments: Creating and sustaining communities of inquiry. Athabasca, Athabasca University Press.
Garrison, D. R. (2016). Thinking Collaboratively: Learning in a Community of Inquiry. London: Routledge/Taylor and Francis.
Garrison, D. R. (2017). E-Learning in the 21st Century: A Community of Inquiry Framework for Research and Practice (3rd edition). London: Routledge/Taylor and Francis.
Cleveland-Innes, M., & Garrison, D. R. (Eds.) (2021). An introduction to distance education: Understanding teaching and learning in a new era (2nd edition). London: Routledge.
References
1945 births
Living people
Canadian cognitive scientists
Academic staff of the University of Calgary
University of Calgar |
https://en.wikipedia.org/wiki/Gail%20Smith%20%28journalist%29 | Gail Smith (born September 4, 1955) is a former Canadian television journalist and news anchor. From Trenton, Ontario, Smith received her bachelor's degree in mathematics and a master's degree in journalism from the University of Western Ontario.
Her broadcasting career started in 1978, first as a television news reporter for BCTV in Vancouver, British Columbia, and then as a producer and news anchor. Smith moved to Toronto, Ontario and joined CFTO in February 1982 as a television news reporter. Her career advancement at CFTO occurred at a time when the television news networks in Toronto competed to hire women as news anchors and attract larger audiences.
On September 4, 1982, Smith became the first female weekend news anchor at CFTO. After the television ratings for the weekend news program climbed 55 per cent, she became the station's first female late night news anchor on Night Beat News the following year. On August 20, 1984, she was paired with Tom Gibney to co-anchor the early evening news program, World Beat News, the station's top-ranked newscast at the time.
After a decade-long career in television news which included six years in Toronto, Smith resigned from CFTO. After an absence of nearly five years, Smith returned to television briefly as an afternoon news anchor for CKVR in Barrie, Ontario, on March 3, 1993.
References
Canadian television news anchors
Canadian television reporters and correspondents
Canadian women television journalists
1955 births
Living people
University of Western Ontario alumni
Carleton University alumni
People from Quinte West |
https://en.wikipedia.org/wiki/List%20of%20African-American%20women%20in%20STEM%20fields | The following is a list of notable African-American women who have made contributions to the fields of science, technology, engineering, and mathematics.
An excerpt from a 1998 issue of Black Issues in Higher Education by Juliane Malveaux reads: "There are other reasons to be concerned about the paucity of African American women in science, especially as scientific occupations are among the most pivotal and highly compensated in the occupational spectrum. Yet, both leaks in the pipeline and gender stereotyping contribute to the under-representation of African American women in the sciences.
Organizations like Dr. Shirley McBay's Quality Education for Minorities (QEM) have done significant work in creating a climate that encourages success in math, science, and engineering for minority students. Yet, efforts like this struggle for funding in an atmosphere that is hostile to affirmative action and to targeted educational opportunities. The evidence to support targeting, though, is in the gaps revealed by the data. Too many gaps reflect the relative absence of sisters in science.
Yet, women like Jemison, Jackson, and McBay offer stellar and motivational examples of what can be done in science careers. These sisters in science are true pioneers, women who make it possible for so many others to see work in science as an option for African American women."
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
V
W
Y
See also
List of Women in Technology International Hall of Fame inductees
STEM pipeline
National Society of Black Engineers
African American women in computer science
List of African-American women in medicine
Further reading
References
Lists of African-American people
Lists of women in STEM fields
Lists of American women
African-American women
African-American women engineers
African-American women scientists |
https://en.wikipedia.org/wiki/Double%20vector%20bundle | In mathematics, a double vector bundle is the combination of two compatible vector bundle structures, which contains in particular the tangent of a vector bundle and the double tangent bundle .
Definition and first consequences
A double vector bundle consists of , where
the side bundles and are vector bundles over the base ,
is a vector bundle on both side bundles and ,
the projection, the addition, the scalar multiplication and the zero map on E for both vector bundle structures are morphisms.
Double vector bundle morphism
A double vector bundle morphism consists of maps , , and such that is a bundle morphism from to , is a bundle morphism from to , is a bundle morphism from to and is a bundle morphism from to .
The 'flip of the double vector bundle is the double vector bundle .
Examples
If is a vector bundle over a differentiable manifold then is a double vector bundle when considering its secondary vector bundle structure.
If is a differentiable manifold, then its double tangent bundle is a double vector bundle.
References
Differential geometry
Topology
Differential topology |
https://en.wikipedia.org/wiki/Productive%20matrix | In linear algebra, a square nonnegative matrix of order is said to be productive, or to be a Leontief matrix, if there exists a nonnegative column matrix such as is a positive matrix.
History
The concept of productive matrix was developed by the economist Wassily Leontief (Nobel Prize in Economics in 1973) in order to model and analyze the relations between the different sectors of an economy. The interdependency linkages between the latter can be examined by the input-output model with empirical data.
Explicit definition
The matrix is productive if and only if and such as .
Here denotes the set of r×c matrices of real numbers, whereas and indicates a positive and a nonnegative matrix, respectively.
Properties
The following properties are proven e.g. in the textbook (Michel 1984).
Characterization
Theorem
A nonnegative matrix is productive if and only if is invertible with a nonnegative inverse, where denotes the identity matrix.
Proof
"If" :
Let be invertible with a nonnegative inverse,
Let be an arbitrary column matrix with .
Then the matrix is nonnegative since it is the product of two nonnegative matrices.
Moreover, .
Therefore is productive.
"Only if" :
Let be productive, let such that .
The proof proceeds by reductio ad absurdum.
First, assume for contradiction is singular.
The endomorphism canonically associated with can not be injective by singularity of the matrix.
Thus some non-zero column matrix exists such that .
The matrix has the same properties as , therefore we can choose as an element of the kernel with at least one positive entry.
Hence is nonnegative and reached with at least one value .
By definition of and of , we can infer that:
, using that by construction.
Thus , using that by definition of .
This contradicts and , hence is necessarily invertible.
Second, assume for contradiction is invertible but with at least one negative entry in its inverse.
Hence such that there is at least one negative entry in .
Then is positive and reached with at least one value .
By definition of and of , we can infer that:
, using that by construction
using that by definition of .
Thus , contradicting .
Therefore is necessarily nonnegative.
Transposition
Proposition
The transpose of a productive matrix is productive.
Proof
Let a productive matrix.
Then exists and is nonnegative.
Yet
Hence is invertible with a nonnegative inverse.
Therefore is productive.
Application
With a matrix approach of the input-output model, the consumption matrix is productive if it is economically viable and if the latter and the demand vector are nonnegative.
References
Mathematical economics
Linear algebra
Matrices
Matrix theory |
https://en.wikipedia.org/wiki/Bert%20Allum | Albert Edward Allum (15 October 1930 – 6 January 2018) was an English professional footballer who played in the Football League for Queens Park Rangers as an outside forward.
Career statistics
References
External links
English men's footballers
English Football League players
1950 births
Dover F.C. players
Queens Park Rangers F.C. players
People from Notting Hill
Footballers from the Royal Borough of Kensington and Chelsea
Southern Football League players
Men's association football outside forwards
Hereford United F.C. players
Brentford F.C. players
2018 deaths |
https://en.wikipedia.org/wiki/Celso%20Costa | Celso José da Costa (born April 7, 1949 in Congonhinhas) is a Brazilian mathematician working in differential geometry. His research activity has focused in the construction and classification of minimal surfaces embedded in three-dimensional Euclidean space. He is best known for his discovery of Costa's minimal surface, which was described in 1982.
He earned his Ph.D. from IMPA in 1982 under the supervision of Manfredo do Carmo.
References
External links
Academia Brasileira de Ciências – Celso José da Costa (in Portuguese)
Diário de Notícias - Celso da Costa, o matemático que nasceu como escritor aos 73 anos
1949 births
Living people
Differential geometers
Instituto Nacional de Matemática Pura e Aplicada alumni
20th-century Brazilian mathematicians |
https://en.wikipedia.org/wiki/Giovanni%20Parmigiani | Giovanni Parmigiani is a biostatistician. He is a professor of biostatistics at both the Dana–Farber Cancer Institute and the Harvard T.H. Chan School of Public Health, and is also associate director for population sciences at the Dana-Farber/Harvard Cancer Center. He is a fellow of the American Statistical Association. In 2009 he and his co-author Lurdes Inoue received a DeGroot Prize from the International Society for Bayesian Analysis for their book Decision Theory: Principles and Approaches.
References
Harvard T.H. Chan School of Public Health faculty
Biostatisticians
Living people
Italian statisticians
Fellows of the American Statistical Association
1959 births |
https://en.wikipedia.org/wiki/2015%20Cricket%20World%20Cup%20statistics | This is a list of statistics for the 2015 Cricket World Cup. Each list contains the top-five records except for the partnership records.
Team statistics
Highest team totals
Largest winning margin
By runs
By wickets
By balls remaining
Lowest team totals
This is a list of completed innings only, low totals in matches with reduced overs are omitted except when the team was all out. Successful run chases in the second innings are not counted.
Smallest winning margin
By runs
By wickets
By balls remaining
Individual statistics
Batting
Most runs
Highest scores
Most boundaries
Most ducks
Bowling
Most wickets
Best bowling figures
Most maidens
Most dot balls
Hat-tricks
Fielding
Most dismissals
This is a list of wicket-keepers with the most dismissals in the tournament.
Most catches
This is a list of the fielders who took the most catches in the tournament.
Other statistics
Highest partnerships
The following tables are lists of the highest partnerships for the tournament.
See also
2011 Cricket World Cup statistics
References
External links
Official 2015 World Cup site
Cricket World Cup at icc-cricket.com
Cricket World Cup statistics
statistics |
https://en.wikipedia.org/wiki/Kelsey%20Adrian | Kelsey Alexa Adrian (born October 5, 1989) is a Canadian female professional basketball player.
California and UC Santa Barbara statistics
Source
References
External links
Profile at usbasket.com
1989 births
Living people
People from Langley, British Columbia (city)
Canadian women's basketball players
Shooting guards
UC Santa Barbara Gauchos women's basketball players |
https://en.wikipedia.org/wiki/Elisabeth%20M.%20Werner | Elisabeth M. Werner is a mathematician who works as a professor of mathematics at Case Western Reserve University, as associate director of the Institute for Mathematics and its Applications, and as maître de conférences at the Lille University of Science and Technology. Her research interests include convex geometry, functional analysis, probability theory, and their applications.
Werner earned a diploma in mathematics from the University of Tübingen, in Germany, in 1985. She moved to France for her graduate studies, finishing her doctorate in 1989 at Pierre and Marie Curie University, under the supervision of Gilles Godefroy. On completing her doctorate she took a faculty position at Case, and two years later added her affiliation with Lille. At Case, she was promoted to full professor in 2002.
In 2012, she became one of the inaugural fellows of the American Mathematical Society.
References
External links
Home page
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
French mathematicians
20th-century German mathematicians
American women mathematicians
Mathematical analysts
University of Tübingen alumni
Pierre and Marie Curie University alumni
Academic staff of the Lille University of Science and Technology
Case Western Reserve University faculty
Fellows of the American Mathematical Society
20th-century women mathematicians
21st-century women mathematicians
21st-century American women |
https://en.wikipedia.org/wiki/Phihitshwane | Phietswana is a small village in the Barolong sub-district of the Southern District, Botswana. The population was 682 per the 2011 census.
References
Botswana Central Statistics Office
Villages in Botswana
Southern District (Botswana) |
https://en.wikipedia.org/wiki/Alexander%27s%20theorem | In mathematics Alexander's theorem states that every knot or link can be represented as a closed braid; that is, a braid in which the corresponding ends of the strings are connected in pairs. The theorem is named after James Waddell Alexander II, who published a proof in 1923.
Braids were first considered as a tool of knot theory by Alexander. His theorem gives a positive answer to the question Is it always possible to transform a given knot into a closed braid? A good construction example is found in Colin Adams's book.
However, the correspondence between knots and braids is clearly not one-to-one: a knot may have many braid representations. For example, conjugate braids yield equivalent knots. This leads to a second fundamental question: Which closed braids represent the same knot type?
This question is addressed in Markov's theorem, which gives ‘moves’ relating any two closed braids that represent the same knot.
References
Knot theory
Theorems in algebraic topology |
https://en.wikipedia.org/wiki/Ndulungu | Ndulungu is an administrative ward in the Iramba District of the Singida Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 11,390 people in the ward, from 10,380 in 2012.
References
Wards of Singida Region |
https://en.wikipedia.org/wiki/Magnetic%20gear | A magnetic gear resembles the traditional mechanical gear in geometry and function, using magnets instead of teeth. As two opposing magnets approach each other, they repel; when placed on two rings the magnets will act like teeth. As opposed to conventional hard contact backlash in a spur gear, where a gear may rotate freely until in contact with the next gear, the magnetic gear has a springy backlash. As a result magnetic gears are able to apply pressure no matter the relative angle. Although they provide a motion ratio as a traditional gear, such gears work without touching and are immune to wear of mating surfaces, have no noise, and may slip without damage.
A magnetically coupled gear can be used in a vacuum without lubrication, or operations involving hermetically sealed barriers. This can be an advantage in explosive or otherwise hazardous environments where leaks constitute a real danger.
Design
Magnetic gear systems typically use permanent magnets. They may also use electromagnets for specialized cases including changeable gear ratio. Magnetic gear coupling can be configured in several ways.
Parallel input and output axes, similar to spur gears, have magnetic attraction or repulsion between cogs, such as the north pole magnets on the driving gear attracting the south pole magnets of driven gear or north pole cogs on a driving gear tending to center between north pole cogs of the driven gear. The cogs may be inter meshed to improve coupling.
Another configuration is In-line axes that use "flux coupling". A stationary intermediate ferromagnetic cylinder allows a motion ratio due to the harmonic relationship between the number of poles input compared to output. There is no equivalent mechanical gear system, since the two rotating gears are physically isolated from each other and only interact magnetically.
In addition, there are "cycloidal drive" gears with a gear ratio similar to planetary drives, also called "epicyclic" or "eccentric" gears.
Magnetic gears advantages:
Leak proof mechanical coupling
Shear / overload proof mechanical coupling
Wear is limited to bearings, not mating contact surfaces of gears
Interchangeable ratios either electronically or mechanically in minutes not hours.
The magnetic gear is a magnetic coupling device that renders a mechanical ratio between two magnetically-coupled devices such that:
They have a ratio of rotation or translational movement between input and output which may be unity in the case of a pure magnetic coupling or one of many gear ratios in a magnetic gearbox.
They have a torque or traction limiting factor based on the magnetic coupling force.
They have no physical contact between the main driving and driven elements.
A magnetic gear is composed of magnets of the type permanent, electromagnetic or otherwise magnetically induced fields. It consists of two or more elements that are usually rotating but can be linear or curve linear in nature.
The classical gear is defined as a rati |
https://en.wikipedia.org/wiki/List%20of%20Djurg%C3%A5rdens%20IF%20Hockey%20players | This is a list of Djurgårdens IF Hockey players. Fredrik Bremberg has the record of most points during the Elitserien/SHL regular season with 501.
Goaltenders
Statistics are complete to the end of the 2014–15 SHL season.
Skaters
Statistics are complete to the end of the 2014–15 SHL season.
References
http://www.hockeydb.com/ihdb/stats/display_players.php?tmi=5508
https://web.archive.org/web/20141113111348/http://www.difhockey.se/klubb/historia/trojnummer
http://historical.stats.swehockey.se
Djurgardens IF Hockey |
https://en.wikipedia.org/wiki/Abortion%20in%20Belize | Abortion in Belize is restricted by criminal law, but permitted under certain conditions.
Statistics
As of 2017, the most recent statistics available regarding abortion in Belize are from 1996. During that year, 2,603 abortions were reported, along with 6,678 live births. 5% of hospitalizations were due to abortion during that year, making it the fourth highest cause of hospitalization.
Due to legal restrictions against abortion, as well as its significant financial cost, illegal abortions are common in Belize, especially for low-income women. In 1998, an estimated one in seven maternal deaths in Belize were due to unsafe, illegal abortions.
Legal status
Abortion in Belize is governed by sections 108–110 of the Criminal Code (enacted December 1980). Abortion is considered a criminal offense except when performed by a registered medical practitioner under certain conditions. The sentence for performing an illegal abortion in Belize is life imprisonment.
Abortion is permitted under the following circumstances:
To protect the life of the mother
To protect the physical or mental health of the mother or any existing children of her family
If there is substantial risk that the child will be severely handicapped
In addition, the law states that "account may be taken of the pregnant woman's actual or reasonably foreseeable environment", suggesting that abortions can be performed on socioeconomic grounds. Belize does not provide an explicit exception for pregnancies that are the result of rape or incest.
See Also
Reproductive rights in Latin America
References
Belize
Health in Belize
Belize |
https://en.wikipedia.org/wiki/Barber%20v%20Somerset%20CC | Barber v Somerset CC [2004] UKHL 13 is a UK labour law case, concerning wrongful dismissal.
Facts
Heard along with the Hatton case, Mr Barber was a maths teacher at East Bridgwater Community School (previously Sydenham Comprehensive School) who had to take on more work given funding cuts, and was working between 61 and 70 hours a week. He was head of department but then had to become the ‘Mathematical Area of Experience Co-ordinator’. He took off three weeks, and returned. The employer was unsympathetic. His work worsened and then Mr Barber had a mental collapse in November 1996, and took early retirement at 52 in March 1997.
First Instance awarded £101,000 in general and special damages.
Judgment
Lord Hope and Lord Rodger gave short opinions. Lord Walker held that Mr Barber should receive £72,547 for the employer's breach of duty by failing to take steps to ensure his health was sound following his three-week break. The school managers should have reassessed Mr Barber's workload for the sake of his health.
Lord Bingham, Lord Steyn concurred with Lord Walker.
References
United Kingdom labour case law
House of Lords cases
2004 in United Kingdom case law
Somerset County Council |
https://en.wikipedia.org/wiki/2009%20Maldivian%20Second%20Division%20Football%20Tournament | Statistics of Second Division Football Tournament in the 2009 season.
Stadiums
Matches were played at 2 venues; Henveiru Football Ground and Maafannu Turf Ground.
Teams
Twelve teams compete in the league – top 2 teams qualify to play in the 2010 Dhivehi league play-off and bottom 2 teams will be relegated to Third division.
League table
Source: Haveeru Sports(C) Champion; (P) Promoted; (R) Relegated.
Results
Awards
Notes
Vyansa gained promotion to the 2010 Dhivehi League after winning second in the 2010 Dhivehi league play-off.
References
Maldivian Second Division Football Tournament seasons
Maldives
Maldives
2 |
https://en.wikipedia.org/wiki/2010%20Maldivian%20Second%20Division%20Football%20Tournament | Statistics of Second Division Football Tournament in the 2010 season.
Stadiums
Group stage were played at Maafannu Turd Ground. League round was held at Gaumee Football Dhan'du.
Teams
9 teams are competition in the 2010 Second Division Football Tournament. These teams were divided into 2 groups (5 teams in group A, 4 in group B).
Group A
Club Eagles
Club Gaamagu
Police Club
Sports Club Mecano
United Victory
Group B
Dhivehi Sifainge Club
Hurriyya Sports Club
L.T. Sports Club
Red Line Club
Group stage
From each group, the top three teams will be advanced for the league round.
Police Club, Club Eagles and United Victory advanced to the league round from Group A. L.T. Sports Club, Dhivehi Sifainge Club and Red Line Club advanced from Group B.
League round
The top three teams from each group is qualified to this round. This round will be played between the 6 teams, where they will be engaged in a round-robin tournament within itself. The highest ranked team will be declared as champions. Second placed team will be qualified to play in the 2011 Dhivehi league play-off with the champion team.
Dhivehi Sifainge Club won topped the league round, while Club Eagles finished at second. Due to the Football Association of Maldives rules, Dhivehi Sifainge Club is not eligible to play in any play-offs for the first division. Therefore, the play-offs were held with only 3 teams.
Awards
Notes
Club Eagles gained promotion to the 2011 Dhivehi League after winning second in the 2011 Dhivehi league play-off.
References
Maldivian Second Division Football Tournament seasons
Maldives
Maldives
2 |
https://en.wikipedia.org/wiki/2011%20Maldivian%20Second%20Division%20Football%20Tournament | Statistics of Second Division Football Tournament in the 2011 season.
Teams
9 teams are competition in the 2011 Second Division Football Tournament, and these teams were divided into 2 groups (5 teams in group A, 4 in group B).
Group A
Club Gaamagu
Club Riverside
Red Line Club
L.T. Sports Club
Hurriyya Sports Club
Group B
J.J. Sports Club
Sports Club Mecano
United Victory
Thoddoo FC
Group stage round
From each group, the top three teams will be advanced for the league round.
Group A
Hurriyya Sports Club, Club Riverside and Red Line Club advanced to the league round as the top three teams of the group.
Group B
United Victory, J.J. Sports Club and Sports Club Mecano advanced to the league round as the top three teams of the group.
Relegation
Team with the worst record among the knocked-out teams from the group stage is relegated to the third division. Thoddoo FC relegated to third division without getting a single point from the group stage.
League round
The top three teams from each group is qualified to this round. As a total of six teams will be playing in this round of the tournament, the team with the highest number of points will be declared as champions. The champion and runner-up team will also play in the Playoff for 2012 Dhivehi League.
Awards
References
External links
Second Division 2011 at RSSSF
Maldivian Second Division Football Tournament seasons
Maldives
Maldives
2 |
https://en.wikipedia.org/wiki/Pavle%20Papi%C4%87 | Pavle Papić (1919, Antofagasta – 2005, Zagreb) was a Croatian mathematician.
Papić graduated mathematics from the University of Zagreb where in 1953 he received his doctorate degree in mathematics under the supervision of Đuro Kurepa. From 1966 until 1968 he was a dean of Faculty of Natural Sciences and Mathematics at the University of Zagreb, from 1968 until 1974 a director of Institute of Mathematics in Zagreb. Since 1977 he was a corresponding member of the Yugoslav Academy of Arts and Sciences and since 1994 a corresponding member of the Croatian Academy of Arts and Sciences.
His interests were in set theory and general topology. He found necessary and sufficient conditions for metrizability and orderability of pseudometric and ultrametric spaces.
References
1919 births
2005 deaths
Croatian mathematicians
Faculty of Science, University of Zagreb alumni
Yugoslav mathematicians |
https://en.wikipedia.org/wiki/Wallis%20Professor%20of%20Mathematics | The Wallis Professorship of Mathematics is a chair in the Mathematical Institute of the University of Oxford. It was established in 1969 in honour of John Wallis, who was Savilian Professor of Geometry at Oxford from 1649 to 1703.
List of Wallis Professors of Mathematics
1969 to 1985: John Kingman
1985 to 1997: Simon Donaldson
1999 to 2022: Terence Lyons
2022 to date: Massimiliano Gubinelli
See also
List of professorships at the University of Oxford
References
Mathematics education in the United Kingdom
Professorships at the University of Oxford
St Anne's College, Oxford
Professorships in mathematics
1969 establishments in England |
https://en.wikipedia.org/wiki/1959%20Djurg%C3%A5rdens%20IF%20season | The 1959 season was Djurgårdens IF's 59th in existence, their 15th season in Allsvenskan and their 10th consecutive season in the league. They were competing in Allsvenskan.
Player statistics
Appearances for competitive matches only.
|}
Goals
Total
Competitions
Overall
Allsvenskan
League table
Matches
Nordic Cup
The tournament continued into the 1960 season.
Round of 16
Quarter-finals
References
http://www.fotbollsweden.se
Djurgårdens IF Fotboll seasons
Djurgarden
Swedish football championship-winning seasons |
https://en.wikipedia.org/wiki/1954%E2%80%9355%20Djurg%C3%A5rdens%20IF%20season | The 1954–55 season was Djurgårdens IF's 55th in existence, their 11th season in Allsvenskan and their sixth consecutive season in the league. They were competing in Allsvenskan.
Player statistics
Appearances for competitive matches only.
|}
Goals
Total
Competitions
Overall
Allsvenskan
League table
References
http://www.fotbollsweden.se
Djurgårdens IF Fotboll seasons
Djurgarden
Swedish football championship-winning seasons |
https://en.wikipedia.org/wiki/William%20A.%20Veech | William A. Veech was the Edgar O. Lovett Professor of Mathematics at Rice University until his death. His research concerned dynamical systems; he is particularly known for his work on interval exchange transformations, and is the namesake of the Veech surface. He died unexpectedly on August 30, 2016 in Houston, Texas.
Education
Veech graduated from Dartmouth College in 1960, and earned his Ph.D. in 1963 from Princeton University under the supervision of Salomon Bochner.
Contributions
An interval exchange transformation is a dynamical system defined from a partition of the unit interval into finitely many smaller intervals, and a permutation on those intervals. Veech and Howard Masur independently discovered that, for almost every partition and every irreducible permutation, these systems are uniquely ergodic, and also made contributions to the theory of weak mixing for these systems. The Rauzy–Veech–Zorich induction map, a function from and to the space of interval exchange transformations is named in part after Veech: Rauzy defined the map, Veech constructed an infinite invariant measure for it, and Zorich strengthened Veech's result by making the measure finite.
The Veech surface and the related Veech group are named after Veech, as is the Veech dichotomy according to which geodesic flow on the Veech surface is either periodic or ergodic.
Veech played a role in the Nobel-prize-winning discovery of buckminsterfullerene in 1985 by a team of Rice University chemists including Richard Smalley. At that time, Veech was chair of the Rice mathematics department, and was asked by Smalley to identify the shape that the chemists had determined for this molecule. Veech answered, "I could explain this to you in a number of ways, but what you've got there, boys, is a soccer ball."
Veech is the author of A Second Course in Complex Analysis (W. A. Benjamin, 1967; Dover, 2008, ).
Awards and honors
In 2012, Veech became one of the inaugural fellows of the American Mathematical Society.
References
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
Mathematical analysts
Dartmouth College alumni
Rice University faculty
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Jacques%20Hurtubise%20%28mathematician%29 | Jacques Claude Hurtubise FRSC (born March 12, 1957) is a Canadian mathematician who works as a professor of mathematics and chair of the mathematics department at McGill University. His research interests include moduli spaces, integrable systems, and Riemann surfaces. Among other contributions, he is known for proving the Atiyah–Jones conjecture.
After undergraduate studies at the Université de Montréal, Hurtubise became a Rhodes Scholar at the University of Oxford for 1978–1981, and earned a DPhil from Oxford in 1982, supervised by Nigel Hitchin, with a dissertation concerning links between algebraic geometry and differential geometry. Following his DPhil, he taught at the Université du Québec à Montréal until 1988, when he moved to McGill. He has also been director of the Centre de Recherches Mathématiques.
Hurtubise won the Coxeter–James Prize of the Canadian Mathematical Society in 1993, and was an AMS Centennial Fellow for 1993–1994. In 2004 he became a fellow of the Royal Society of Canada, and in 2012, he became one of the inaugural fellows of the American Mathematical Society.
In 2018 the Canadian Mathematical Society listed him in their inaugural class of fellows.
In 2022 he has been the recipient of the 2022 David Borwein Distinguished Career Award by the Canadian Mathematical Society (CMS), "for his exceptional, continued, and broad contributions to mathematics".
References
1957 births
Living people
20th-century Canadian mathematicians
21st-century Canadian mathematicians
Université de Montréal alumni
Alumni of the University of Oxford
Academic staff of the Université du Québec à Montréal
Academic staff of McGill University
Canadian Rhodes Scholars
Fellows of the Royal Society of Canada
Fellows of the American Mathematical Society
Fellows of the Canadian Mathematical Society
Presidents of the Canadian Mathematical Society |
https://en.wikipedia.org/wiki/STEM%20pipeline | The STEM (Science, Technology, Engineering, and Mathematics) pipeline is a critical infrastructure for fostering the development of future scientists, engineers, and problem solvers. It's the educational and career pathway that guides individuals from early childhood through to advanced research and innovation in STEM-related fields.
Description
The "pipeline" metaphor is based on the idea that having sufficient graduates requires both having sufficient input of students at the beginning of their studies, and retaining these students through completion of their academic program. The STEM pipeline is a key component of workplace diversity and of workforce development that ensures sufficient qualified candidates are available to fill scientific and technical positions.
The STEM pipeline was promoted in the United States from the 1970s onwards, as “the push for STEM (science, technology, engineering, and mathematics) education appears to have grown from a concern for the low number of future professionals to fill STEM jobs and careers and economic and educational competitiveness.”
Today, this metaphor is commonly used to describe retention problems in STEM fields, called “leaks” in the pipeline. For example, the White House reported in 2012 that 80% of minority groups and women who enroll in a STEM field switch to a non-STEM field or drop out during their undergraduate education. These leaks often vary by field, gender, ethnic and racial identity, socioeconomic background, and other factors, drawing attention to structural inequities involved in STEM education and careers.
Current efforts
The STEM pipeline concept is a useful tool for programs aiming at increasing the total number of graduates, and is especially important in efforts to increase the number of underrepresented minorities and women in STEM fields. Using STEM methodology, educational policymakers can examine the quantity and retention of students at all stages of the K–12 educational process and beyond, and devise programs and interventions to improve educational processes and outcomes. STEM programs focus on increasing social and academic supports for students. STEM programs may also focus on bringing students together with professionals in their field, to provide mentoring, role models and learning opportunities in industry.
Maintaining a healthy and diverse STEM pipeline has been a concern in several developed countries, such as the United Kingdom, the United States, and Germany.
United States
In the United States, although efforts to increase the number of women and African Americans in STEM fields have been ongoing, as recently as 2010 the results have been evaluated as "poor". In 2014, one report declared that "traditionally underrepresented groups remain underrepresented", while another article commented, "You can go through your entire scholarly trajectory in computer science without seeing one face of color", where "of color" refers to African Americans.
STEM pipeline |
https://en.wikipedia.org/wiki/Bhargava%20cube | In mathematics, in number theory, a Bhargava cube (also called Bhargava's cube) is a configuration consisting of eight integers placed at the eight corners of a cube. This configuration was extensively used by Manjul Bhargava, a Canadian-American Fields Medal winning mathematician, to study the composition laws of binary quadratic forms and other such forms. To each pair of opposite faces of a Bhargava cube one can associate an integer binary quadratic form thus getting three binary quadratic forms corresponding to the three pairs of opposite faces of the Bhargava cube. These three quadratic forms all have the same discriminant and Manjul Bhargava proved that their composition in the sense of Gauss is the identity element in the associated group of equivalence classes of primitive binary quadratic forms. (This formulation of Gauss composition was likely first due to Dedekind.) Using this property as the starting point for a theory of composition of binary quadratic forms Manjul Bhargava went on to define fourteen different composition laws using a cube.
Integer binary quadratic forms
An expression of the form , where a, b and c are fixed integers and x and y are variable integers, is called an integer binary quadratic form. The discriminant of the form is defined as
The form is said to be primitive if the coefficients a, b, c are relatively prime. Two forms
are said to be equivalent if there exists a transformation
with integer coefficients satisfying which transforms to . This relation is indeed an equivalence relation in the set of integer binary quadratic forms and it preserves discriminants and primitivity.
Gauss composition of integer binary quadratic forms
Let and be two primitive binary quadratic forms having the same discriminant and let the corresponding equivalence classes of forms be and . One can find integers such that
The class is uniquely determined by the classes [Q(x, y)] and [Q′(x, y)] and is called the composite of the classes and . This is indicated by writing
The set of equivalence classes of primitive binary quadratic forms having a given discriminant D is a group under the composition law described above. The identity element of the group is the class determined by the following form:
The inverse of the class is the class .
Quadratic forms associated with the Bhargava cube
Let (M, N) be the pair of 2 × 2 matrices associated with a pair of opposite sides of a Bhargava cube; the matrices are formed in such a way that their rows and columns correspond to the edges of the corresponding faces. The integer binary quadratic form associated with this pair of faces is defined as
The quadratic form is also defined as
However, the former definition will be assumed in the sequel.
The three forms
Let the cube be formed by the integers a, b, c, d, e, f, g, h. The pairs of matrices associated with opposite edges are denoted by (M1, N1), (M2, N2), and (M3, N3). The first rows of M1, M2 and M3 are respect |
https://en.wikipedia.org/wiki/Marie%20Machacek | Marie E. Machacek is an astrophysicist conducting research in the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. She earned a BA in physics and mathematics from Coe College, in 1969; an MS in physics from the University of Michigan, in 1970; and a PhD in physics from the University of Iowa, in 1973. Her current research explores interacting galaxies and the evolution of galaxies in galaxy groups and clusters. She is also the current coordinator for the SAO Astronomy Intern Program.
Machacek was co-author of a Center for Astrophysics Harvard & Smithsonian study concerning galaxy NGC 5195 presented in January 2016 at the 227th meeting of the American Astronomical Society (AAS).
Machacek was an Alumni Fellow at the University of Michigan 1974-77. She was on the physics faculty of Northeastern University, 1979-2002. In 2003-2004 she was a Fellow of the Radcliffe Institute for Advanced Study at Harvard University.
References
Living people
Year of birth missing (living people)
American astrophysicists
American women physicists
21st-century American women |
https://en.wikipedia.org/wiki/Curtis%20Huttenhower | Curtis Huttenhower is a Professor of Computational Biology and Bioinformatics in the Department of Biostatistics, School of Public Health, Harvard University.
Education
Huttenhower gained his BS from the Rose-Hulman Institute of Technology in 2000, where he majored in computer science, chemistry and mathematics. He then spent two years as a software developer for Microsoft, working on the Microsoft Natural Language Development Platform. Huttenhower gained his MS in computational linguistics from Carnegie Mellon University in 2003, where he studied with Dannie Durand and Eric Nyberg. In 2003, Huttenhower moved to Princeton University where he was awarded a PhD in 2008 for research in genomics supervised by Olga Troyanskaya. His PhD thesis was titled Analysis of large genomic data collections.
Research
Huttenhower joined the Harvard T.H. Chan School of Public Health in 2009 as an assistant professor of computational biology and bioinformatics, becoming an associate professor in 2013. Huttenhower's lab worked extensively with the NIH Human Microbiome Project (HMP) to identify and characterise the microorganisms found in association with both healthy and diseased humans. As of 2015, he co-leads one of the follow-up 'HMP2' Centers for Characterizing the Gut Microbial Ecosystem in Inflammatory Bowel Disease.
Awards and honors
Huttenhower received an NSF CAREER award in 2010 for his research on microbial communities and was awarded a Presidential Early Career Award for Scientists and Engineers in 2012. In 2015, Huttenhower was awarded the Overton Prize from the International Society for Computational Biology. His PhD supervisor Olga Troyanskaya had been awarded the same prize in 2011. Huttenhower is also a member of the editorial boards for the academic journals Genome Biology, Microbiome and BMC Bioinformatics.
References
Living people
Overton Prize winners
1981 births
21st-century American biologists
Recipients of the Presidential Early Career Award for Scientists and Engineers
Computational biologists
American bioinformaticians |
https://en.wikipedia.org/wiki/Lucy%20R.%20Wyatt | Lucy R. Wyatt is an English mathematician and a professor in the School of Mathematics and Statistics at the University of Sheffield, Yorkshire. She is a member of the Environmental Dynamics research group in the School of Mathematics.
Education
Wyatt obtained a BSc in mathematics from the University of Manchester in 1972. In 1973 she was awarded an M.Sc. in fluid mechanics from the University of Bristol,
and in 1976 she obtained her PhD in physical oceanography from the University of Southampton.
In 1981 she began working on the oceanographic applications of HF radar as a research assistant at the University of Birmingham, and in 1987 she joined the Department of Applied Mathematics, the University of Sheffield. Wyatt's research interests include high-frequency radar oceanography and ocean surface waves. She has been an associate editor of the IEEE Journal of Oceanic Engineering.
Publications
Limits to the Inversion of HF Radar Backscatter for Ocean Wave Measurement
HF radar data quality requirements for wave measurement
Radio frequency interference cancellation for sea-state remote sensing by high-frequency radar
HF Radar data availability and measurement accuracy in Liverpool Bay before and after the construction of Rhyl-Flats wind farm
External grants
The measurement of the directional wavenumber frequency spectrum with HF radar (NERC)
Applications of computational geometry to the analysis of directional ocean wave spectra measured by HF radar (EPSRC)
A non-linear inversion for HF radar wave measurement (OCE 62) (EPSRC)
OSCR antenna beam measurement (NERC)
References
External links
Living people
21st-century English mathematicians
British oceanographers
Academics of the University of Sheffield
Alumni of the University of Manchester
Alumni of the University of Bristol
Alumni of the University of Southampton
21st-century women mathematicians
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Dot%20product%20representation%20of%20a%20graph | A dot product representation of a simple graph is a method of representing a graph using vector spaces and the dot product from linear algebra. Every graph has a dot product representation.
Definition
Let G be a graph with vertex set V. Let F be a field, and f a function from V to Fk such that xy is an edge of G if and only if f(x)·f(y) ≥ t. This is the dot product representation of G. The number t is called the dot product threshold, and the smallest possible value of k is called the dot product dimension.
Properties
A threshold graph is a dot product graph with positive t and dot product dimension 1.
Every interval graph has dot product dimension at most 2.
Every planar graph has dot product dimension at most 4.
See also
Adjacency matrix
References
External links
Graph theory |
https://en.wikipedia.org/wiki/Artin%E2%80%93Tate%20lemma | In algebra, the Artin–Tate lemma, named after Emil Artin and John Tate, states:
Let A be a commutative Noetherian ring and commutative algebras over A. If C is of finite type over A and if C is finite over B, then B is of finite type over A.
(Here, "of finite type" means "finitely generated algebra" and "finite" means "finitely generated module".) The lemma was introduced by E. Artin and J. Tate in 1951 to give a proof of Hilbert's Nullstellensatz.
The lemma is similar to the Eakin–Nagata theorem, which says: if C is finite over B and C is a Noetherian ring, then B is a Noetherian ring.
Proof
The following proof can be found in Atiyah–MacDonald. Let generate as an -algebra and let generate as a -module. Then we can write
with . Then is finite over the -algebra generated by the . Using that and hence is Noetherian, also is finite over . Since is a finitely generated -algebra, also is a finitely generated -algebra.
Noetherian necessary
Without the assumption that A is Noetherian, the statement of the Artin–Tate lemma is no longer true. Indeed, for any non-Noetherian ring A we can define an A-algebra structure on by declaring . Then for any ideal which is not finitely generated, is not of finite type over A, but all conditions as in the lemma are satisfied.
References
External links
http://commalg.subwiki.org/wiki/Artin-Tate_lemma
Theorems about algebras
Lemmas in algebra
Commutative algebra |
https://en.wikipedia.org/wiki/Regular%20skew%20apeirohedron | In geometry, a regular skew apeirohedron is an infinite regular skew polyhedron, with either skew regular faces or skew regular vertex figures.
History
According to Coxeter, in 1926 John Flinders Petrie generalized the concept of regular skew polygons (nonplanar polygons) to finite regular skew polyhedra in 4-dimensions, and infinite regular skew apeirohedra in 3-dimensions (described here).
Coxeter identified 3 forms, with planar faces and skew vertex figures, two are complements of each other. They are all named with a modified Schläfli symbol {l,m|n}, where there are l-gonal faces, m faces around each vertex, with holes identified as n-gonal missing faces.
Coxeter offered a modified Schläfli symbol {l,m|n} for these figures, with {l,m} implying the vertex figure, m l-gons around a vertex, and n-gonal holes. Their vertex figures are skew polygons, zig-zagging between two planes.
The regular skew polyhedra, represented by {l,m|n}, follow this equation:
2 sin(/l) · sin(/m) = cos(/n)
Regular skew apeirohedra of Euclidean 3-space
The three Euclidean solutions in 3-space are {4,6|4}, {6,4|4}, and {6,6|3}. John Conway named them mucube, muoctahedron, and mutetrahedron respectively for multiple cube, octahedron, and tetrahedron.
Mucube: {4,6|4}: 6 squares about each vertex (related to cubic honeycomb, constructed by cubic cells, removing two opposite faces from each, and linking sets of six together around a faceless cube.)
Muoctahedron: {6,4|4}: 4 hexagons about each vertex (related to bitruncated cubic honeycomb, constructed by truncated octahedron with their square faces removed and linking hole pairs of holes together.)
Mutetrahedron: {6,6|3}: 6 hexagons about each vertex (related to quarter cubic honeycomb, constructed by truncated tetrahedron cells, removing triangle faces, and linking sets of four around a faceless tetrahedron.)
Coxeter gives these regular skew apeirohedra {2q,2r|p} with extended chiral symmetry [[(p,q,p,r)]+] which he says is isomorphic to his abstract group (2q,2r|2,p). The related honeycomb has the extended symmetry [[(p,q,p,r)]].
Regular skew apeirohedra in hyperbolic 3-space
In 1967, C. W. L. Garner identified 31 hyperbolic skew apeirohedra with regular skew polygon vertex figures, found in a similar search to the 3 above from Euclidean space.
These represent 14 compact and 17 paracompact regular skew polyhedra in hyperbolic space, constructed from the symmetry of a subset of linear and cyclic Coxeter groups graphs of the form [[(p,q,p,r)]], These define regular skew polyhedra {2q,2r|p} and dual {2r,2q|p}. For the special case of linear graph groups r = 2, this represents the Coxeter group [p,q,p]. It generates regular skews {2q,4|p} and {4,2q|p}. All of these exist as a subset of faces of the convex uniform honeycombs in hyperbolic space.
The skew apeirohedron shares the same antiprism vertex figure with the honeycomb, but only the zig-zag edge faces of the vertex figure are realized, while the other faces mak |
https://en.wikipedia.org/wiki/Chance%20of%20Rain | Chance of Rain may refer to:
Probability of precipitation
Chance of Rain (Laurel Halo album), 2013
Chance of Rain (Stefanie Heinzmann album), 2015 |
https://en.wikipedia.org/wiki/Bernd%20Siebert | Bernd Siebert (born 5 March 1964 in Berlin-Wilmersdorf) is a German mathematician who researches in algebraic geometry.
Life
Siebert studied mathematics starting 1984 at the University of Erlangen. In 1986, he changed to the University of Bonn and in 1987 to the University of Göttingen where he finished his Diplom in 1989 under the supervision of Hans Grauert with distinction. He became Grauert's PhD student and assistant in Göttingen. He received his PhD in 1992 (Faserzykelräume, geometrische Plattifikation und meromorphe Äquivalenzrelationen). A stay at the Courant Institute followed in 1993–94 after which we went to Bochum. In 1997–98 he spent some time at the MIT as a visiting scholar before completing his habilitation in Bochum in 1998 (Gromov–Witten invariants for general symplectic manifolds). As a DFG-Heisenberg Fellow, he went to the Universität Paris VI/Universität Paris VII from 2000 to 2002. From there, he was called to a professorship at the Albert-Ludwigs-Universität Freiburg in 2002. He moved on to the Universität Hamburg in 2008, and in 2011, he became the head of the Graduiertenkolleg Mathematics Inspired by String Theory and QFT. In 2018, Siebert joined the faculty of the University of Texas at Austin as a professor of mathematics and holds the Sid W. Richardson Foundation Regents Chair in Mathematics #4.
In his research, Bernd Siebert contributed substantially to the theory of Gromov–Witten invariants. Around 2002 by his insights in logarithmic geometry, he entered into an ongoing joint research program with Mark Gross. This generated a sequence of relevant papers that relate to Mirror Symmetry and tropical geometry.
In 2014, jointly with Mark Gross, he became an invited speaker at the International Congress of Mathematics in Seoul for the section complex geometry (Local mirror symmetry in the tropics). Both of them were awarded the Clay Research Award in 2016.
Papers
References
External links
Homepage
Mathematische Genealogie
1964 births
Living people
21st-century German politicians
Courant Institute of Mathematical Sciences alumni
20th-century German mathematicians
People from Wilmersdorf
University of Bonn alumni
University of Erlangen-Nuremberg alumni
21st-century German mathematicians |
https://en.wikipedia.org/wiki/1914%20Ottoman%20census | The 1914 Ottoman census was collected and published as the Memalik-i Osmaniyyenin 1330 Senesi Nütus Istatistiki. These statistics were prepared by using the figures from the 1905–06 census of the Ottoman Empire and reflecting births and deaths registered in six years from last. The register states that birth and mortality rate used on "nomads" such as the nomadic Nestorians.
The 1914 census list reflected major changes in the territorial boundaries and administrative division of the Ottoman state. The population statistics and 1914 Ottoman general election were major population sources. The empire's total population was provided as 18,520,015. The grand total for 1914 showed a "net gain" of 1,131,454 from the 1905-06 Ottoman census survey. The data reflects the loss of territory and population in Europe due to Balkan Wars, as the total net gain figure would be 3,496,068.
The census underestimated non-Muslim populations. For example, in Diyarbekir the Armenian population was reported at 73,226 in the 1914 Ottoman census, but in September 1915 Mehmed Reshid announced that he had deported 120,000 Armenians from the province.
Census data
As a result of the substantial territorial losses in Europe suffered during the Balkan Wars, the total population of the empire fell to 18,520,016, of whom an even larger percentage than before, 15,044,846, was counted as Muslim, with 1,729,738 as Greek Orthodox, 1,161,169 as Armenian Gregorian, 187,073 as Jewish, 68,838 as Armenian Catholic, 65,844 as Protestant, and 62,468 as Greek Catholic. No separate figures were given for Franks.
The capital, Constantinople (Istanbul) was an important location due to expulsions from Balkan Wars. According to the 1914 census, its population increased slightly, to 909,978, excluding Franks, with 560,434 Muslims, 205,375 Greek Orthodox, 72,963 Armenian Gregorian, 52,126 Jews, 9,918 Armenian Catholics, 2,905 Roman Catholics, 1,213 Protestants, and 387 Greek Catholics.
1 Sanjak
Notes
References
Bibliography
Demographics of the Ottoman Empire
1914 in the Ottoman Empire
1914 censuses |
https://en.wikipedia.org/wiki/Sesquialtera | Sesquialtera ('one and a half') may refer to:
Sesquialterum in mathematics, the ratio 3:2, a superparticular ratio
Sesquialtera or the equivalent Greek term hemiola, three in the time of two as variously used in music theory:
Sesquialtera commonly describes a tempo proportion in mensural notation
Hemiola is more common for the temporary substitution of a 2+2+2 musical meter for 3+3
Sesquialtera (organ stop), combining mutation ranks at 2' and 1', i.e. both 3:2 and 5:4 pitch ratios
Sesquialtera (moth), a genus of moth in the family Geometridae |
https://en.wikipedia.org/wiki/Antoni%20Malet | Antoni Malet (born 23 February 1950) is a Catalan historian of mathematics. He is a professor of history of science at Pompeu Fabra University, Barcelona. His research interests are mostly in the history of mathematics and optics in the sixteenth and seventeenth centuries.
Malet earned his Ph.D. in 1989 from Princeton University as a student of Charles Gillispie, with the thesis Studies on James Gregorie (1638–1675).
Selected publications
"From Indivisibles to Infinitesimals. Studies on Seventeenth-Century Mathematizations of Infinitely Small Quantities". Barcelona 1996.
"Ferran Sunyer i Balaguer (1912–1967)". Barcelona 1995.
with J. Paradís: "Els orígens i l’ensenyament de l’àlgebra simbòlica" (in Catalan). Barcelona 1984.
"James Gregorie on Tangents and the “Taylor” Rule of Series Expansions". Archive for History of Exact Sciences, Volume 46, 1993, 97–137.
"Mil años de matematicas en Iberia". In: A. Duran (Herausgeber): El legado de las matematicas. Universität Sevilla 2000, S. 193–224.
"Kepler and the Telescope". Annals of Science, 60, 2003, 107–36.
"Isaac Barrow on the Mathematization of Nature: Theological Voluntarism and the Rise of Geometrical Optics". Journal of the History of Ideas, 58, 1997, 265–287.
"Gregorie, Descartes, Kepler, and the Law of Refraction". Archives Internationales d'Histoire des Sciences, 40, 1990, 278–304.
References
External links
Homepage
Historians of mathematics
Academic staff of Pompeu Fabra University
Living people
1950 births
Princeton University alumni |
https://en.wikipedia.org/wiki/Niccol%C3%B2%20Guicciardini | Niccolò Guicciardini Corsi Salviati (born 28 May 1957 in Firenze) is an Italian historian of mathematics. He is a professor at the University of Milan, and is known for his studies on the works of Isaac Newton.
Guicciardini obtained his Ph.D. from Middlesex Polytechnic in 1987 under the supervision of Ivor Grattan-Guinness.
In 2011 he was awarded the Fernando Gil International Prize for the Philosophy of Science.
Selected publications
The development of Newtonian calculus in Britain, 1700-1800, Cambridge University Press, 1989 (paperback 2003).
Reading the Principia: the debate on Newton's mathematical methods for natural philosophy from 1687 to 1736, Cambridge University Press, 1999 (paperback 2003).
Isaac Newton on mathematical certainty and method, MIT Press, 2009 (paperback 2011).
References
External links
Homepage
Italian historians of mathematics
1957 births
Living people
Academic staff of the University of Bergamo
Newton scholars
University of Milan alumni |
https://en.wikipedia.org/wiki/Lie%20algebra%20extension | In the theory of Lie groups, Lie algebras and their representation theory, a Lie algebra extension is an enlargement of a given Lie algebra by another Lie algebra . Extensions arise in several ways. There is the trivial extension obtained by taking a direct sum of two Lie algebras. Other types are the split extension and the central extension. Extensions may arise naturally, for instance, when forming a Lie algebra from projective group representations. Such a Lie algebra will contain central charges.
Starting with a polynomial loop algebra over finite-dimensional simple Lie algebra and performing two extensions, a central extension and an extension by a derivation, one obtains a Lie algebra which is isomorphic with an untwisted affine Kac–Moody algebra. Using the centrally extended loop algebra one may construct a current algebra in two spacetime dimensions. The Virasoro algebra is the universal central extension of the Witt algebra.
Central extensions are needed in physics, because the symmetry group of a quantized system usually is a central extension of the classical symmetry group, and in the same way the corresponding symmetry Lie algebra of the quantum system is, in general, a central extension of the classical symmetry algebra. Kac–Moody algebras have been conjectured to be symmetry groups of a unified superstring theory. The centrally extended Lie algebras play a dominant role in quantum field theory, particularly in conformal field theory, string theory and in M-theory.
A large portion towards the end is devoted to background material for applications of Lie algebra extensions, both in mathematics and in physics, in areas where they are actually useful. A parenthetical link, (background material), is provided where it might be beneficial.
History
Due to the Lie correspondence, the theory, and consequently the history of Lie algebra extensions, is tightly linked to the theory and history of group extensions. A systematic study of group extensions was performed by the Austrian mathematician Otto Schreier in 1923 in his PhD thesis and later published. The problem posed for his thesis by Otto Hölder was "given two groups and , find all groups having a normal subgroup isomorphic to such that the factor group is isomorphic to ".
Lie algebra extensions are most interesting and useful for infinite-dimensional Lie algebras. In 1967, Victor Kac and Robert Moody independently generalized the notion of classical Lie algebras, resulting in a new theory of infinite-dimensional Lie algebras, now called Kac–Moody algebras. They generalize the finite-dimensional simple Lie algebras and can often concretely be constructed as extensions.
Notation and proofs
Notational abuse to be found below includes for the exponential map given an argument, writing for the element in a direct product ( is the identity in ), and analogously for Lie algebra direct sums (where also and are used interchangeably). Likewise for semidirect products and sem |
https://en.wikipedia.org/wiki/Arlene%20Stamp | Arlene Stamp (born 1938) is a Canadian conceptual artist and educator who lives and works in Calgary, Alberta.
Career
Born in London, Ontario, Stamp initially studied mathematics, graduating in 1960 from the University of Western Ontario. This background influenced her study of art, first at the Alberta College of Art and Design (1974-1976) and then at the University of Calgary (1979-1980). She is noted for her "mathematical-abstract paintings" and works based on "complex mathematical formulas and recursive pattern theories". She has completed an artistic series on the work of Gladys Johnston, the colour red, and the grid patterns of floor tiles, among other concepts. Her work has been exhibited across Canada and she has worked collaboratively with other artists on installations and site-specific pieces. In 2013, Nickle Galleries in Calgary held a retrospective of Stamp's 30-year practice with an exhibition of paintings, drawings and installations.
A teacher at art schools across the country, Stamp has also held studio residencies at the Emma Lake Artists' Workshops (1977) and the Banff Centre for continuing education (1979). She was inducted into the Royal Canadian Academy of Arts in 2007.
References
1938 births
Living people
Artists from London, Ontario
Canadian conceptual artists
Women conceptual artists
21st-century Canadian women artists
Members of the Royal Canadian Academy of Arts
Canadian abstract artists |
https://en.wikipedia.org/wiki/Laurent%20Saloff-Coste | Laurent Saloff-Coste (born 1958) is a French mathematician whose research is in Analysis, Probability theory, and Geometric group theory.
Saloff-Coste received his "doctorat de 3eme cycle" in 1983 at the Pierre and Marie Curie University, Paris VI. He completed his "Doctorat d'Etat" in 1989 under Nicholas Varopoulos. In the 1990s, he worked as "Directeur de Recherche" (CNRS) at Paul Sabatier University in Toulouse. Since 1998, he is a professor of Mathematics at Cornell University in Ithaca, New York, where he was chair from 2009 to 2015.
Saloff-Coste works in the areas of analysis and probability theory, including problems involving geometry and partial differential equations. In particular, he has studied the behavior of diffusion processes on manifolds and their fundamental solutions, in connection to the geometry of the underlying spaces. He also studies random walks on groups and how their behavior reflects the algebraic structure of the underlying group. He has developed quantitative estimates for the convergence of finite Markov chains and corresponding stochastic algorithms.
He received the Rollo Davidson Prize in 1994, and is a fellow of the American Mathematical Society and of the Institute of Mathematical Statistics. In 2011 he was elected to the American Academy of Arts and Sciences.
Selected publications
Aspects of Sobolev Type Inequalities, London Mathematical Society Lecture Notes, Band 289, Cambridge University Press, 2002.
Random walks on finite groups, in Harry Kesten (publisher) Probability on Discrete Structures, Encyclopaedia Math. Sciences, Band 110, Springer Verlag, 2004, S. 263–346.
with Persi Diaconis Comparison theorems for random walks on finite groups, Annals of Probability, Band 21, 1993, S. 2131–2156
Lectures on finite Markov chains, in Lectures on Probability Theory and Statistics, Lecture Notes in Mathematics, Band 1665, 1997, S. 301-413
with Nicholas Varopoulos, T. Coulhon Analysis and geometry on groups, Cambridge Tracts in Mathematics, Band 100, Cambridge University Press 1992
with Dominique Bakry, Michel Ledoux Markov Semigroups at Saint Flour, Series Probability at Saint Flour, Springer Verlag 2012
External links
Website
References
Cornell University faculty
1958 births
Living people |
https://en.wikipedia.org/wiki/Ruel%20Vance%20Churchill | Ruel Vance Churchill (12 December 1899, Akron, Indiana – 31 October 1987, Ann Arbor, Michigan) was an American mathematician known for writing three widely used textbooks on applied mathematics.
In 1922 Churchill received his undergraduate degree from the University of Chicago. In 1929 he received his PhD from the University of Michigan under George Rainich with thesis On the Geometry of the Riemann Tensor. He spent his entire career as a member of the U. of Michigan mathematics faculty and retired in 1965 as professor emeritus. His doctoral students include Earl D. Rainville.
Books
Complex Variables and Applications, McGraw-Hill, 1st edition 1948, 2nd edition 1960, The 3rd (1974) and later editions were co-authored with James Ward Brown
Fourier Series and Boundary Value Problems, McGraw-Hill, 1941, 2nd edition 1963
Modern Operational Mathematics in Engineering, McGraw-Hill, 1944
Operational Mathematics, McGraw-Hill, 1958, 2nd edition of the 1944 book but with a new title, 3rd edition 1972
Selected articles
with R. C. F. Bartels:
with C. L. Dolph:
References
External links
1899 births
1987 deaths
20th-century American mathematicians
University of Chicago alumni
University of Michigan alumni
University of Michigan faculty
People from Indiana
American textbook writers |
https://en.wikipedia.org/wiki/Ayron%20del%20Valle | Ayron del Valle Rodríguez (born January 27, 1989) is a Colombian professional footballer who plays as a forward for Malaysia Super League club Selangor.
Career Statistics
References
1989 births
Living people
Men's association football forwards
Colombian men's footballers
Independiente Medellín footballers
Real Cartagena footballers
Atlético Huila footballers
Once Caldas footballers
Deportivo Pasto footballers
Deportes Tolima footballers
Alianza Petrolera F.C. players
América de Cali footballers
Millonarios F.C. players
Querétaro F.C. footballers
FC Juárez footballers
Categoría Primera A players
Categoría Primera B players
Liga MX players
People from Bolívar Department |
https://en.wikipedia.org/wiki/Carlos%20Matheus | Carlos Matheus Silva Santos (born May 1, 1984 in Aracaju) is a Brazilian mathematician working in dynamical systems, analysis and geometry. He currently works at the CNRS, in Paris.
He earned his Ph.D. from the Instituto de Matemática Pura e Aplicada (IMPA) in 2004 under the supervision of Marcelo Viana, at the age of 19.
Selected publications
with G. Forni, and A. Zorich: "Square-tiled cyclic covers", Journal of Modern Dynamics, vol. 5, no. 2, pp. 285–318 (2011).
with A. Avila, and J.-C. Yoccoz: "SL(2,R)-invariant probability measures on the moduli spaces of translation surfaces are regular", Geometric and Functional Analysis, vol. 23, no. 6, pp. 1705–1729 (2013).
with M. Möller, and J.-C. Yoccoz: "A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces", ''Inventiones mathematicae (2014).
Further reading
Época – Os segredos das ilhas de excelência (by Carlos Rydlewski, in Portuguese)
References
External links
Matheus' home-page at the IMPA
Matheus' personal blog "Disquisitiones Mathematicae"
Brazilian mathematicians
1984 births
Living people
People from Aracaju
Dynamical systems theorists
Mathematical analysts
Geometers
Instituto Nacional de Matemática Pura e Aplicada alumni
Brazilian expatriate academics |
https://en.wikipedia.org/wiki/Boris%20Khesin | Boris Aronovich Khesin (in Russian: Борис Аронович Хесин, born in 1964) is a Russian and Canadian mathematician working on infinite-dimensional Lie groups, Poisson geometry and hydrodynamics. He is a professor at the University of Toronto.
Khesin obtained his Ph.D. from Moscow State University in 1990 under the supervision of Vladimir Arnold (Thesis: Normal forms and versal deformations of evolution differential equations).
In 1997 he was awarded the Aisenstadt Prize.
Boris Khesin specializes in instructing high-level calculus, including trigonometric functions, inverse function theorem, differentiation, integration, and fundamental theorem of calculus.
References
Russian mathematicians
1964 births
Living people
Moscow State University alumni
Soviet mathematicians
Canadian mathematicians |
https://en.wikipedia.org/wiki/Neville%20theta%20functions | In mathematics, the Neville theta functions, named after Eric Harold Neville, are defined as follows:
where: K(m) is the complete elliptic integral of the first kind, , and is the elliptic nome.
Note that the functions θp(z,m) are sometimes defined in terms of the nome q(m) and written θp(z,q) (e.g. NIST). The functions may also be written in terms of the τ parameter θp(z|τ) where .
Relationship to other functions
The Neville theta functions may be expressed in terms of the Jacobi theta functions
where .
The Neville theta functions are related to the Jacobi elliptic functions. If pq(u,m) is a Jacobi elliptic function (p and q are one of s,c,n,d), then
Examples
Symmetry
Complex 3D plots
Implementation
NetvilleThetaC[z,m], NevilleThetaD[z,m], NevilleThetaN[z,m], and NevilleThetaS[z,m] are built-in functions of Mathematica.
Notes
References
Special functions
Theta functions
Elliptic functions
Analytic functions |
https://en.wikipedia.org/wiki/Castelnuovo%27s%20contraction%20theorem | In mathematics, Castelnuovo's contraction theorem is used in the classification theory of algebraic surfaces to construct the minimal model of a given smooth algebraic surface.
More precisely, let be a smooth projective surface over and a (−1)-curve on (which means a smooth rational curve of self-intersection number −1), then there exists a morphism from to another smooth projective surface such that the curve has been contracted to one point , and moreover this morphism is an isomorphism outside (i.e., is isomorphic with ).
This contraction morphism is sometimes called a blowdown, which is the inverse operation of blowup. The curve is also called an exceptional curve of the first kind.
References
Algebraic surfaces
Theorems in geometry |
https://en.wikipedia.org/wiki/Christina%20Sormani | Christina Sormani is a professor of mathematics at City University of New York affiliated with Lehman College and the CUNY Graduate Center. She is known for her research in Riemannian geometry, metric geometry, and Ricci curvature, as well as her work on the notion of intrinsic flat distance.
Career
Sormani received her Ph.D. from New York University in 1996 under Jeff Cheeger. She then took postdoctoral positions at Harvard University (under Shing-Tung Yau) and Johns Hopkins University (under William Minicozzi II). Sormani is now a Full Professor of Mathematics at Lehman College in the City University of New York
and member of the doctoral faculty at the CUNY Graduate Center.
Awards and honors
In 2009, Sormani was an invited speaker at the Geometry Festival. She received the Association for Women in Mathematics (AWM) Service Award in 2015. She was recognized for her work planning and coordinating AWM activities at the Joint Mathematics Meetings.
In 2015, Sormani became a Fellow of the American Mathematical Society. She was honored for her research in geometry, specifically Ricci curvature. Her mentorship of junior mathematicians from underrepresented groups was also cited in the recognition.
Sormani was selected as an Association for Women in Mathematics Fellow in the Class of 2024 "for utilizing every opportunity to open pathways to mathematics for more women and students by creating and maintaining online access to advice, mathematical resources, and information about women mathematicians; for organizing the “Inspiring Talks by Mathematicians” lecture series featuring under-represented speakers, and for her dedicated and active contributions to the AWM."
Selected publications
Sormani, Christina. (2000). Nonnegative Ricci curvature, small linear diameter growth and finite generation of fundamental groups. Journal of Differential Geometry, 54(3), 547–559. MR 1823314.
Sormani, Christina, & Wei, Guofang. Hausdorff convergence and universal covers. Transactions of the American Mathematical Society, 353 (2001), no. 9, 3585–3602. MR 1837249
Sormani, Christinam & Wei, Guofang. Universal covers for Hausdorff limits of noncompact spaces. Transactions of the American Mathematical Society, 356 (2004), no. 3, 1233–1270. MR 2021619
Sormani, Christina, & Wenger, Stefan. (2010). Weak convergence of currents and cancellation. Calculus of Variations and Partial Differential Equations, 38, 183–206. https://doi.org/10.1007/s00526-009-0282-x
Lee, Dan A, & Sormani, Christina. (2014). Stability of the positive mass theorem for rotationally symmetric Riemannian manifolds. Journal für die reine und angewandte Mathematik (Crelles Journal) 686. https://doi.org/10.1515/crelle-2012-0094
Sormani, Christina, & Wenger, Stefan. (2011). The intrinsic flat distance between Riemannian manifolds and other integral current spaces." Journal of Differential Geometry, 87(1), 117–199. MR 2786592
References
Hunter College High School alumni
Living people
American women mathema |
https://en.wikipedia.org/wiki/List%20of%20Portuguese%20municipalities%20by%20population | This is a list of Portugal's municipalities by population, according to the estimate of the resident population for the Census 2021 made by the National Statistics Institute (INE).
The 308 Portuguese municipalities are divided among the 25 sub-regions and the 7 national regions, the population density of each municipality, and the area it totals.
About 64.88% of the national population, 6,760,989 inhabitants, live in the 56 municipalities with more than 50,000 inhabitants, about 18.2% of all national municipalities. While there are 122 municipalities, about 39.6% of all national municipalities, with a population of less than 10,000 inhabitants, a total of 678,855 inhabitants, about 6.51% of the national population.
See also
Subdivisions of Portugal
List of cities in Portugal
List of towns in Portugal
List of municipalities of Portugal
List of parishes of Portugal
List of cities in Europe
References
External links
National Association of Portuguese Municipalities
Cities
Portugal, List of Cities in
05 |
https://en.wikipedia.org/wiki/Paul%20C.%20Yang | Paul C. Yang () is a Taiwanese-American mathematician specializing in differential geometry, partial differential equations and CR manifolds. He is best known for his work in Conformal geometry for his study of extremal metrics and his research on scalar curvature and Q-curvature. In CR Geometry he is known for his work on the CR embedding problem, the CR Paneitz operator
and for introducing the Q' curvature in CR Geometry.
Career
Yang earned his doctorate at the University of California, Berkeley in 1973 under the supervision of Hung-Hsi Wu（).
He held positions at Rice University, the University of Maryland, Indiana University and the
University of Southern California before joining
Princeton University in 2001.
Awards and honors
Yang was a Sloan Foundation Fellow in 1981. In 2012, he
became a fellow of the American Mathematical Society.
Selected publications
Chang, Sun-Yung A.; Yang, Paul C. Conformal deformation of metrics on . J. Differential Geom. 27 (1988), no. 2, 259–296.
Chang, Sun-Yung A.; Yang, Paul C. Prescribing Gaussian curvature on . Acta Math. 159 (1987), no. 3–4, 215–259.
Chang, Sun-Yung A.; Yang, Paul C. Extremal metrics of zeta function determinants on 4-manifolds. Ann. of Math. (2) 142 (1995), no. 1, 171–212.
Chang, Sun-Yung A.; Gursky, Matthew J.; Yang, Paul C. The scalar curvature equation on 2- and 3-spheres. Calc. Var. Partial Differential Equations 1 (1993), no. 2, 205–229.
Chang, Sun-Yung A.; Gursky, Matthew J.; Yang, Paul C. An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature. Ann. of Math. (2) 155 (2002), no. 3, 709–787.
Yang, Paul C.; Yau, Shing-Tung Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7 (1980), no. 1, 55–63.
Chanillo, Sagun; Chiu, Hung-Lin; Yang, Paul C. Embeddability for Three Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants, Duke Math. J.,161(15), (2012), 2909–2921.
References
Living people
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Mathematical Society
University of California, Berkeley alumni
Rice University faculty
University of Maryland, College Park faculty
Indiana University faculty
University of Southern California faculty
Princeton University faculty
American people of Chinese descent
Differential geometers
Chinese mathematicians
Year of birth missing (living people)
People from Changhua County |
https://en.wikipedia.org/wiki/Semigroup%20with%20three%20elements | In abstract algebra, a semigroup with three elements is an object consisting of three elements and an associative operation defined on them. The basic example would be the three integers 0, 1, and −1, together with the operation of multiplication. Multiplication of integers is associative, and the product of any two of these three integers is again one of these three integers.
There are 18 inequivalent ways to define an associative operation on three elements: while there are, altogether, a total of 39 = 19683 different binary operations that can be defined, only 113 of these are associative, and many of these are isomorphic or antiisomorphic so that there are essentially only 18 possibilities.
One of these is C3, the cyclic group with three elements. The others all have a semigroup with two elements as subsemigroups. In the example above, the set {−1,0,1} under multiplication contains both {0,1} and {−1,1} as subsemigroups (the latter is a subgroup, C2).
Six of these are bands, meaning that all three elements are idempotent, so that the product of any element with itself is itself again. Two of these bands are commutative, therefore semilattices (one of them is the three-element totally ordered set, and the other is a three-element semilattice that is not a lattice). The other four come in anti-isomorphic pairs.
One of these non-commutative bands results from adjoining an identity element to LO2, the left zero semigroup with two elements (or, dually, to RO2, the right zero semigroup). It is sometimes called the flip-flop monoid, referring to flip-flop circuits used in electronics: the three elements can be described as "set", "reset", and "do nothing". This semigroup occurs in the Krohn–Rhodes decomposition of finite semigroups. The irreducible elements in this decomposition are the finite simple groups plus this three-element semigroup, and its subsemigroups.
There are two cyclic semigroups, one described by the equation x4 = x3, which has O2, the null semigroup with two elements, as a subsemigroup. The other is described by x4 = x2 and has C2, the group with two elements, as a subgroup. (The equation x4 = x describes C3, the group with three elements, already mentioned.)
There are seven other non-cyclic non-band commutative semigroups, including the initial example of {−1, 0, 1}, and O3, the null semigroup with three elements. There are also two other anti-isomorphic pairs of non-commutative non-band semigroups.
See also
Special classes of semigroups
Semigroup with two elements
Semigroup with one element
Empty semigroup
References
Algebraic structures
Semigroup theory |
https://en.wikipedia.org/wiki/Christel%20Rotthaus | Christel Rotthaus is a professor of mathematics at Michigan State University. She is known for her research in commutative algebra.
Career
Rotthaus received her Ph.D. from Westfälische Wilhelms-Universität Münster in 1975 under Hans-Joachim Nastold. Rotthaus now works at Michigan State University.
Awards and honors
In 2012, Rotthaus became a fellow of the American Mathematical Society.
Selected publications
Brodmann, M.; Rotthaus, Ch.; Sharp, R. Y. On annihilators and associated primes of local cohomology modules. J. Pure Appl. Algebra 153 (2000), no. 3, 197–227.
Heinzer, William; Rotthaus, Christel; Sally, Judith D. Formal fibers and birational extensions. Nagoya Math. J. 131 (1993), 1–38.
Rotthaus, Christel. On rings with low-dimensional formal fibres. J. Pure Appl. Algebra 71 (1991), no. 2–3, 287–296.
Rotthaus, Christel; Şega, Liana M. Some properties of graded local cohomology modules. J. Algebra 283 (2005), no. 1, 232–247.
Rotthaus, Christel. On the approximation property of excellent rings. Invent. Math. 88 (1987), no. 1, 39–63.
References
Living people
American women mathematicians
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Mathematical Society
20th-century women mathematicians
21st-century women mathematicians
Year of birth missing (living people)
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/Nancy%20K.%20Stanton | Nancy Kahn Stanton is a professor emeritus of mathematics at University of Notre Dame. She is known for her research in complex analysis, partial differential equations, and differential geometry.
Career
Stanton received her Ph.D. from Massachusetts Institute of Technology in 1973 under Isadore Singer. Stanton now works at University of Notre Dame.
Awards and honors
In 1981, Stanton became a Sloan Research Fellow.
In 2012, Stanton became a fellow of the American Mathematical Society.
Selected publications
Stanton, Nancy K. Infinitesimal CR automorphisms of real hypersurfaces. Amer. J. Math. 118 (1996), no. 1, 209–233.
Beals, Richard; Greiner, Peter C.; Stanton, Nancy K. The heat equation on a CR manifold. J. Differential Geom. 20 (1984), no. 2, 343–387.
Stanton, Nancy K. Infinitesimal CR automorphisms of rigid hypersurfaces. Amer. J. Math. 117 (1995), no. 1, 141–167.
Pinsky, Mark A.; Stanton, Nancy K.; Trapa, Peter E. Fourier series of radial functions in several variables. J. Funct. Anal. 116 (1993), no. 1, 111–132.
References
Living people
American women mathematicians
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Mathematical Society
20th-century women mathematicians
21st-century women mathematicians
Year of birth missing (living people)
20th-century American women
21st-century American women
Massachusetts Institute of Technology alumni |
https://en.wikipedia.org/wiki/Lynne%20H.%20Walling | Lynne Heather Walling (October 9, 1958 – May 28, 2021) was an American mathematician specializing in number theory, who became a reader in pure mathematics at the University of Bristol. She was known for her research in number theory. She died on 28 May 2021.
Early life and education
Walling was born on October 9, 1958, and grew up in northern California. She began her undergraduate studies at the University of California, San Diego, and after a two-year gap continued at Sonoma State University, studying accounting at first but then finishing a bachelor's degree in mathematics. She received her Ph.D. from Dartmouth College in 1987 under Thomas Richard Shemanske.
Career and later life
She then taught at St. Olaf College, Minnesota. She lived in an old farmhouse, which had no indoor plumbing. She built a hand-operated pump, enabling her to install a bathtub in the kitchen, beside a wood-burning stove.
She became a tenure-track Assistant Professor at the University of Colorado, Boulder in 1990. In 1995 she received tenure, and in 2000 became a full Professor. She came to Bristol as a reader in mathematics in 2007. From 2011 to 2015 she was Head of Pure Mathematics, and from 2018 was Director of the Institute of Pure Mathematics.
Awards and honors
In 2012, Walling became a fellow of the American Mathematical Society.
Selected publications
Hafner, James Lee; Walling, Lynne H. Explicit action of Hecke operators on Siegel modular forms. J. Number Theory 93 (2002), no. 1, 34–57.
Walling, Lynne H. Hecke operators on theta series attached to lattices of arbitrary rank. Acta Arith. 54 (1990), no. 3, 213–240.
Merrill, Kathy D.; Walling, Lynne H. Sums of squares over function fields. Duke Math. J. 71 (1993), no. 3, 665–684.
References
External links and references
Lynne walling's homepage at University of Bristol
Lynne Walling's homepage at CU Boulder
Lyne Walling's research
Lynne Walling's math genealogy page
American women mathematicians
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Mathematical Society
Year of birth missing (living people)
20th-century women mathematicians
21st-century women mathematicians
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/FIFA%20Women%27s%20World%20Cup%20records%20and%20statistics | This is a list of the records of the FIFA Women's World Cup.
General statistics by tournament
Debut of national teams
Overall team records
In this ranking 3 points are awarded for a win, 1 for a draw and 0 for a loss. As per statistical convention in football, matches decided in extra time are counted as wins and losses, while matches decided by penalty shoot-outs are counted as draws. Teams are ranked by total points, then by goal difference, then by goals scored.
Medal table
Comprehensive team results by tournament
Legend
– Champions
– Runners-up
– Third place
– Fourth place
QF – Quarter-finals
R2 – Round 2 (2015–present: knockout round of 16)
R1 – Round 1 (1991–present: group stage)
– Did not qualify
– Qualified but withdrew
– Withdrew during qualification / Disqualified during qualification (after playing matches)
– Did not enter / Kicked / Banned / Permanently banned
– Hosts
Q – Qualified for forthcoming tournament
For each tournament, the number of teams in each finals tournament are shown (in parentheses).
Hosts
Host nations are granted an automatic spot in the World Cup group stage.
Results of defending finalists
Results by confederation
— Hosts are from this confederation
AFC
CAF
CONCACAF
CONMEBOL
OFC
UEFA
Droughts
This section is a list of droughts associated with the participation of women's national football teams in the FIFA Women's World Cups.
Longest active World Cup appearance droughts
Does not include teams that have not yet made their first appearance or teams that no longer exist.
Longest World Cup appearance droughts overall
Only includes droughts begun after a team's first appearance and until the team ceased to exist; updated to include qualification for the 2023 FIFA Women's World Cup.
Teams: tournament position
Teams having equal quantities in the tables below are ordered by the tournament the quantity was attained in (the teams that attained the quantity first are listed first). If the quantity was attained by more than one team in the same tournament, these teams are ordered alphabetically.
Most titles won 4: (1991, 1999, 2015, 2019).
Most finishes in the top two 5: (1991, 1999, 2011, 2015, 2019).
Most finishes in the top three 8: (1991–2019).
Most finishes in the top four 8: (1991–2019).
Most finishes in the top eight 8: , (1991–2019).
Most World Cup appearances 9: , , , , , , (every tournament).
Most second-place finishes 1: (1991), (1995), (1999), (2003), (2007), (2011), (2015), (2019), (2023).
Most third-place finishes 4: (1991, 2011, 2019, 2023).
Most fourth-place finishes 2: (1991, 2015), (1999, 2007).
Most 3rd-4th-place finishes 4: (1991, 2011, 2019, 2023).
Most 5th-8th-place finishes 4: (1991, 2003, 2007, 2015).
Most 9th-16th-place finishes 7: (1991, 1995, 2003, 2007, 2011, 2019, 2023).
Consecutive
Most consecutive championships 2: (2003–2007), (2015–2019).
Most consecutive finishes in the top two 3: (2011–2019).
Most consecutive finishes |
https://en.wikipedia.org/wiki/Projective%20set%20%28disambiguation%29 | Projective Set may refer to:
A set in the Projective hierarchy, a sequence of subsets of a Polish space in descriptive set theory
Projective Set (game), a 2-dimensional analogue of the award-winning 1991 card game Set |
https://en.wikipedia.org/wiki/Saddlepoint%20approximation%20method | The saddlepoint approximation method, initially proposed by Daniels (1954) is a specific example of the mathematical saddlepoint technique applied to statistics. It provides a highly accurate approximation formula for any PDF or probability mass function of a distribution, based on the moment generating function. There is also a formula for the CDF of the distribution, proposed by Lugannani and Rice (1980).
Definition
If the moment generating function of a distribution is written as and the cumulant generating function as then the saddlepoint approximation to the PDF of a distribution is defined as:
and the saddlepoint approximation to the CDF is defined as:
where is the solution to , and .
When the distribution is that of a sample mean, Lugannani and Rice's saddlepoint expansion for the cumulative distribution function may be differentiated to obtain Daniels' saddlepoint expansion for the probability density function (Routledge and Tsao, 1997). This result establishes the derivative of a truncated Lugannani and Rice series as an alternative asymptotic approximation for the density function . Unlike the original saddlepoint approximation for , this alternative approximation in general does not need to be renormalized.
References
Asymptotic analysis
Perturbation theory |
https://en.wikipedia.org/wiki/1985%E2%80%9386%20VfL%20Bochum%20season | The 1985–86 VfL Bochum season was the 48th season in club history.
Review and events
Matches
Legend
Bundesliga
DFB-Pokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
VfL Bochum II
|}
Sources
External links
1985–86 VfL Bochum season at Weltfussball.de
1985–86 VfL Bochum season at kicker.de
1985–86 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/Sergei%20Tabachnikov | Sergei Tabachnikov, also spelled Serge, (in born in 1956) is an American mathematician who works in geometry and dynamical systems. He is currently a Professor of Mathematics at Pennsylvania State University.
Biography
He earned his Ph.D. from Moscow State University in 1987 under the supervision of Dmitry Fuchs and Anatoly Fomenko. He has been living and working in the USA since 1990.
From 2013 to 2015 Tabachnikov served as Deputy Director of the Institute for Computational and Experimental Research in Mathematics (ICERM) in Providence, Rhode Island. He is now Emeritus Deputy Director of ICERM.
He is a fellow of the American Mathematical Society. He currently serves as Editor in Chief of the journal Experimental Mathematics.
A paper on the variability hypothesis by Theodore Hill and Tabachnikov was accepted and retracted by The Mathematical Intelligencer and later The New York Journal of Mathematics (NYJM). There was some controversy over the mathematical model, the peer-review process, and the lack of an official retraction notice from the NYJM.
Selected publications
References
External links
Homepage
American mathematicians
Fellows of the American Mathematical Society
1956 births
Living people
Moscow State University alumni
Dynamical systems theorists
Topologists
Russian expatriates in the United States
Pennsylvania State University faculty |
https://en.wikipedia.org/wiki/1986%E2%80%9387%20VfL%20Bochum%20season | The 1986–87 VfL Bochum season was the 49th season in club history.
Review and events
Matches
Legend
Bundesliga
DFB-Pokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
Sources
External links
1986–87 VfL Bochum season at Weltfussball.de
1986–87 VfL Bochum season at kicker.de
1986–87 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
Subsets and Splits
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