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https://en.wikipedia.org/wiki/Borel%20distribution | The Borel distribution is a discrete probability distribution, arising in contexts including branching processes and queueing theory. It is named after the French mathematician Émile Borel.
If the number of offspring that an organism has is Poisson-distributed, and if the average number of offspring of each organism is no bigger than 1, then the descendants of each individual will ultimately become extinct. The number of descendants that an individual ultimately has in that situation is a random variable distributed according to a Borel distribution.
Definition
A discrete random variable X is said to have a Borel distribution
with parameter μ ∈ [0,1] if the probability mass function of X is given by
for n = 1, 2, 3 ....
Derivation and branching process interpretation
If a Galton–Watson branching process has common offspring distribution Poisson with mean μ, then the total number of individuals in the branching process has Borel distribution with parameter μ.
Let X be the total number of individuals in a Galton–Watson branching process.
Then a correspondence between the total size of the branching process and a hitting time for an associated random walk gives
where Sn = Y1 + … + Yn, and Y1 … Yn are independent identically distributed random variables whose common distribution is the offspring distribution of the branching process.
In the case where this common distribution is Poisson with mean μ, the random variable
Sn has Poisson distribution with mean μn,
leading to the mass function of the Borel distribution given above.
Since the mth generation of the branching process has mean size μm − 1,
the mean of X is
Queueing theory interpretation
In an M/D/1 queue with arrival rate μ and common service time 1,
the distribution of a typical busy period of the queue is Borel with parameter μ.
Properties
If Pμ(n) is the probability mass function of a
Borel(μ) random variable, then the mass function
P(n)
of a sized-biased sample from the distribution
(i.e. the mass function proportional to nPμ(n) )
is given by
Aldous and Pitman
show that
In words, this says that a Borel(μ) random variable has the same distribution
as a size-biased Borel(μU) random variable, where U has the uniform distribution on [0,1].
This relation leads to various useful formulas, including
Borel–Tanner distribution
The Borel–Tanner distribution generalizes the Borel distribution.
Let k be a positive integer.
If X1, X2, … Xk
are independent and each has
Borel distribution with parameter μ, then their sum
W = X1 + X2 + … + Xk is said to have Borel–Tanner distribution with parameters μ and k.
This gives the distribution of the total number of individuals
in a Poisson–Galton–Watson process starting with k individuals in the first generation,
or of the time taken for an M/D/1 queue to empty starting with k jobs in the queue.
The case k = 1 is simply the Borel distribution above.
Generalizing the random walk correspondence given above for k = 1,
where Sn |
https://en.wikipedia.org/wiki/Manuel%20Bryennios | Manuel Bryennios or Bryennius (; c. 1275 – c. 1340) was a Byzantine scholar who flourished in Constantinople about 1300 teaching astronomy, mathematics and musical theory. His only surviving work is the Harmonika (Greek: Ἁρμονικά), which is a three-volume codification of Byzantine musical scholarship based on the classical Greek works of Ptolemy, Nicomachus, and the Neopythagorean authors on the numerological theory of music. One of Bryennios's students was Theodore Metochites, the grand logothete during the reign of Emperor Andronikos II Palaiologos (r. 1272–1328). Metochites studied astronomy under Bryennios.
References
Citations
Sources
Byzantine astronomers
Music theorists
Byzantine music
Manuel
1275 births
1340 deaths
13th-century scholars
14th-century scholars
13th-century Byzantine scientists
14th-century Byzantine scientists
13th-century Greek people
14th-century Greek people
13th-century Greek scientists
14th-century Greek scientists
13th-century Greek educators
14th-century Greek educators
13th-century Greek mathematicians
14th-century Greek mathematicians
13th-century Greek astronomers
14th-century Greek astronomers
13th-century Greek musicians
14th-century Greek musicians |
https://en.wikipedia.org/wiki/Ghana%20National%20Science%20and%20Maths%20Quiz | The National Science and Maths Quiz is an annual science and mathematics content-based national level quiz competition for senior high schools in Ghana. It has been produced by Primetime Limited, an education-interest advertising and public relations agency, since 1993.
The objective of the National Science & Maths Quiz is to promote the study of the sciences and mathematics, help students develop quick thinking and a probing and scientific mind about the everyday world around them, while fostering healthy academic rivalry among senior high schools.
The quiz, originally sponsored by Unilever's"Brillant Soap", is popularly referred to as “Brilla” by many who have gone through the secondary school system and it is one of the few academic events that brings all of Ghana's secondary schools together. The National Science and Maths Quiz is the longest running educational programme on Ghanaian television. It is broadcast on GTV during the quiz season every Saturday at 11am and Wednesdays at 4pm.
History
The idea for the production of a quiz programme aimed at encouraging the study of the sciences and mathematics was not mooted at a national science fair or conference. It happened on the tennis court of the University of Ghana, Legon in 1993. Kwaku Mensa-Bonsu, then managing director of Primetime, was on the court to play a tennis game with his playmates, the late Professors Marian Ewurama Addy and Ebenezer Kweku Awotwe. Mensa-Bonsu was curious as to why birds could stand on a live electric wire without getting electrocuted, but human beings could not do same. From Awotwe's explanation, Mensa-Bonsu got the idea of putting together a quiz programme on science and mathematics.
When the quiz started, it involved only 32 schools across the country, and these were divided into the Northern Sector and Southern Sector, with 16 schools per sector. Winners in both sectors were then brought to Accra for the national championship. Prempeh College won the maiden edition.
In 1997, the geographical sector system was abandoned, and two northern sector schools (from the old format), Opoku Ware School and Prempeh College made it to the finals where Opoku Ware School won its first trophy.
In 1998, the tournament became known as the National Science & Maths Quiz, when the quiz show lost its original sponsorship from Brillant Soap. Subsequently, in 2012, the Ghana Education Service, through the Conference of Heads of Assisted Secondary Schools (CHASS) took up the sponsorship of the programme. In terms of participation, beginning in 2000, the number of schools was increased to 40. The number of participating schools again, was increased in 2013 to 81, although 66 ultimately showed up for the competition. Thus, the participation format was changed to a three-team contest instead of the two-team contest which had characterized the competition since its inception in 1993. To give the programme a national character, the quiz has since 2014 involved 135 schools from all p |
https://en.wikipedia.org/wiki/Quarter%20hypercubic%20honeycomb | In geometry, the quarter hypercubic honeycomb (or quarter n-cubic honeycomb) is a dimensional infinite series of honeycombs, based on the hypercube honeycomb. It is given a Schläfli symbol q{4,3...3,4} or Coxeter symbol qδ4 representing the regular form with three quarters of the vertices removed and containing the symmetry of Coxeter group for n ≥ 5, with = and for quarter n-cubic honeycombs = .
See also
Hypercubic honeycomb
Alternated hypercubic honeycomb
Simplectic honeycomb
Truncated simplectic honeycomb
Omnitruncated simplectic honeycomb
References
Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition,
pp. 122–123, 1973. (The lattice of hypercubes γn form the cubic honeycombs, δn+1)
pp. 154–156: Partial truncation or alternation, represented by q prefix
p. 296, Table II: Regular honeycombs, δn+1
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
Honeycombs (geometry)
Polytopes |
https://en.wikipedia.org/wiki/Franz-Erich%20Wolter | Franz-Erich Wolter is a German computer scientist, chaired professor at Leibniz University Hannover, with research contributions especially in computational (differential) geometry and haptic/tactile Virtual reality.
He currently heads the Institute of Man-Machine Communication and is the Dean of Studies in Computer Science at Leibniz University Hannover.
He is the founder and actual director of the Welfenlab research laboratory.
Research
Wolter's early contributions were in the area of Differential Geometry dealing with the Cut Locus characterizing it as the closure of a set, where the shortest geodesics starting from a point (or a general source) set intersect or equivalently where the distance function is not directionally differentiable implying that a complete Riemannian manifold M must be diffeomorphic to R^n if there is a point p on M s.t. the (squared) distance function wrt. to p is (directionally) differentiable on all M. His Ph.D. thesis (1985) transferred the concept of Cut Locus to manifolds with and without boundary.
In 1992, essentially a specialisation of the latter works lead to his paper presenting a mathematical foundation of the medial axis of solid objects in Euclidean space. It showed that the medial axis of a solid body can be viewed as the interior Cut Locus of the solid`s boundary and the medial axis is a deformation retract of the solid. Therefore it represents the homotopy type of a solid thus including the solid's homology type. Furthermore the medial axis can be used to reconstruct the solid. Later on since 1997 the subject of the medial axis received a rapidly growing attention in computational geometry but also wrt. its applications in vision and robotics. A Voronoi diagram of a finite point set A in Euclidean space can be viewed as Cut Locus of that point set. In 1997, Wolter apparently pioneered computations of geodesic Voronoi diagrams and geodesic medial axis on general parametrized curved surfaces. In the surface case the length of a shortest geodesic join defines the distance between two points. In 2007, Wolter extended the computations of geodesic Voronoi diagrams and geodesic medial axis (inverse) transform to Riemannian 3D-manifolds.
Wolter's early works on computing Riemannian Laplace Beltrami spectra for surfaces and images lead to a patent application in (2005) for a method using those spectra as Shape DNA for recognizing and retrieving surfaces, solids and images from data repositories.
His works used the heat trace of a Riemannian Laplace Beltrami operator wrt. a surface patch to numerically compute area, length of boundary curves and Euler Characteristic of the patch. All this later on stimulated research in the area of spectral shape analysis wrt. shape retrieval and shape analysis, including applications in biomedical shape cognition and especially using the heat kernel more precisely the heat trace for partial shape cognition and the global point signature.
Wolter was responsible for creatin |
https://en.wikipedia.org/wiki/Grace%E2%80%93Walsh%E2%80%93Szeg%C5%91%20theorem | In mathematics, the Grace–Walsh–Szegő coincidence theorem is a result named after John Hilton Grace, Joseph L. Walsh, and Gábor Szegő.
Statement
Suppose ƒ(z1, ..., zn) is a polynomial with complex coefficients, and that it is
symmetric, i.e. invariant under permutations of the variables, and
multi-affine, i.e. affine in each variable separately.
Let A be a circular region in the complex plane. If either A is convex or the degree of ƒ is n, then for every there exists such that
Notes and references
Theorems in complex analysis
Theorems about polynomials |
https://en.wikipedia.org/wiki/Rectified%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the rectified tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a rectification of a tesseractic honeycomb which creates new vertices on the middle of all the original edges, rectifying the cells into rectified tesseracts, and adding new 16-cell facets at the original vertices. Its vertex figure is an octahedral prism, {3,4}×{}.
It is also called a quarter tesseractic honeycomb since it has half the vertices of the 4-demicubic honeycomb, and a quarter of the vertices of a tesseractic honeycomb.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
Demitesseractic honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
o4x3o3o4o, o3o3o *b3x4o, x3o3x *b3o4o, x3o3x *b3o *b3o - rittit - O87
Honeycombs (geometry)
5-polytopes |
https://en.wikipedia.org/wiki/G%C3%A1bor%20Gr%C3%A9czi | Gábor Gréczi (born 3 May 1993) is a Hungarian professional footballer.
Club statistics
Updated to games played as of 6 December 2014.
References
MLSZ
HLSZ
1993 births
Footballers from Szeged
Living people
Hungarian men's footballers
Men's association football forwards
Kecskeméti TE players
BFC Siófok players
Nyíregyháza Spartacus FC players
Tiszakécske FC footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Nemzeti Bajnokság III players |
https://en.wikipedia.org/wiki/Scott%20Sheffield | Scott Sheffield (born October 20, 1973) is a professor of mathematics at the Massachusetts Institute of Technology. His primary research field is theoretical probability.
Research
Much of Sheffield's work examines conformal invariant objects which arise in the study of two-dimensional statistical physics models. He studies the Schramm-Loewner evolution SLE(κ) and its relations to a variety of other random objects. For example, he proved that SLE describes the interface between two Liouville quantum gravity surfaces that have been conformally welded together. In joint work with Oded Schramm, he showed that contour lines of the Gaussian free field are related to SLE(4). With Jason Miller, he developed the theory of Gaussian free field flow lines, which include SLE(κ) for all values of κ, as well as many variants of SLE.
Sheffield and Bertrand Duplantier proved the Knizhnik-Polyakov-Zamolodchikov (KPZ) relation for fractal scaling dimensions in Liouville quantum gravity. Sheffield also defined the conformal loop ensembles, which serve as scaling limits of the collection of all interfaces in various statistical physics models. In joint work with Wendelin Werner, he described the conformal loop ensembles as the outer boundaries of clusters of Brownian loops.
In addition to these contributions, Sheffield has also proved results regarding internal diffusion limited aggregation, dimers, game theory, partial differential equations, and Lipschitz extension theory.
Teaching
Since 2011, Sheffield has taught 18.600 (formerly 18.440), the introductory probability course at MIT.
Sheffield was a visiting professor at the Institute for Advanced Study for the 2022 to 2023 academic year.
Education and career
Sheffield graduated from Harvard University in 1998 with an A.B. and A.M. in mathematics. In 2003, he received his Ph.D. in mathematics from Stanford University. Before becoming a professor at MIT, Sheffield held postdoctoral positions at Microsoft Research, the University of California at Berkeley, and the Institute for Advanced Study. He was also an associate professor at New York University.
Awards
Scott Sheffield received the Loève Prize, the Presidential Early Career Award for Scientists and Engineers, the Sloan Research Fellowship, and the Rollo Davidson Prize. He was also an invited speaker at the 2010 meeting of the International Congress of Mathematicians and a plenary speaker in 2022. In 2017 he received the Clay Research Award jointly with Jason Miller. He was elected to the American Academy of Arts and Sciences in 2021. In 2023 he received the Leonard Eisenbud Prize for Mathematics and Physics of the AMS jointly with Jason Miller.
Books
Scott Sheffield (2005), Random Surfaces, American Mathematical Society
References
1973 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Harvard University alumni
Probability theorists
Stanford University alumni
Fellows of the American Academy of Arts and Scien |
https://en.wikipedia.org/wiki/Rhonda%20Hughes | Rhonda Jo Hughes (born Rhonda Weisberg September 28, 1947) is an American mathematician, the Helen Herrmann Professor Emeritus of Mathematics at Bryn Mawr College.
Education
Hughes grew up on the South Side of Chicago. She attended Gage Park High School, where she was a cheerleader and valedictorian of her class. She studied engineering at the University of Illinois at Urbana–Champaign for one and a half years, then left school and worked for six months before resuming her education at the University of Illinois at Chicago on an Illinois State Scholarship studying mathematics. There, she came under the mentorship of Yoram Sagher, who encouraged her to pursue graduate studies in mathematics. She earned a Ph.D. from the same university in 1975, under the supervision of Shmuel Kantorovitz, with a dissertation entitled Semi-Groups of Unbounded Linear Operators in Banach Space.
Career
She began her teaching career at Tufts University then spent a year as a fellow at the Bunting Institute of Radcliffe College. She moved to Bryn Mawr College in 1980, where she served as department chair for six years.
She is the Helen Herrmann professor emeritus of mathematics at Bryn Mawr, and retired in 2011.
She was president of the Association for Women in Mathematics (AWM) 1987–1988. She has served on the Commission on Physical Science, Mathematics, and Applications of the United States National Research Council. She served as an American Mathematical Society (AMS) Council member at large from 1988 to 1990.
She and Sylvia Bozeman organized the Spelman-Bryn Mawr Summer Mathematics Program for female undergraduate students from 1992 to 1994. In 1998, they founded the EDGE Program (Enhancing Diversity in Graduate Education), a transition program for women entering graduate programs in the mathematical sciences.
The program is now in its twentieth year.
Her most recent research involves ill-posed problems.
Honors
Hughes received a Distinguished Teaching Award from the Mathematical Association of America in 1997. In 2004 she received the AAAS Mentor Award for Lifetime Achievement, in 2010 the Gweneth Humphreys Award for Mentorship of Undergraduate Women in Mathematics of the Association for Women in Mathematics, and in 2013 she received the Elizabeth Bingham Award of the Philadelphia Chapter of the Association for Women in Science.
In 2017, she was selected as a fellow of the Association for Women in Mathematics in the inaugural class.
References
External links
A Tribute to the Work of Professor Emeritus Rhonda Hughes
1947 births
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
University of Illinois Chicago alumni
Tufts University faculty
Bryn Mawr College faculty
Fellows of the Association for Women in Mathematics
20th-century women mathematicians
21st-century women mathematicians
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/David%20Sankoff | David Sankoff (born December 31, 1942) is a Canadian mathematician, bioinformatician, computer scientist and linguist. He holds the Canada Research Chair in Mathematical Genomics in the Mathematics and Statistics Department at the University of Ottawa, and is cross-appointed to the Biology Department and the School of Information Technology and Engineering. He was founding editor of the scientific journal Language Variation and Change (Cambridge) and serves on the editorial boards of a number of bioinformatics, computational biology and linguistics journals. Sankoff is best known for his pioneering contributions in computational linguistics and computational genomics. He is considered to be one of the founders of bioinformatics. In particular, he had a key role in introducing dynamic programming for sequence alignment and other problems in computational biology. In Pavel Pevzner's words,
"[ Michael Waterman ] and David Sankoff are responsible for transforming bioinformatics from a ‘stamp collection' of ill-defined problems into a rigorous discipline with important biological applications."
Education
Sankoff published his first paper in 1963 while he was an undergraduate student in Mathematics at McGill University. Starting with his doctoral research, he developed mathematical formulations to a number of pivotal concepts in socio- and historical linguistics, including glottochronology, variable rules analysis (with Henrietta Cedergren), the linguistic marketplace and code switching.
Career and research
After completing his Ph.D. in Mathematics, Sankoff began his academic career at the University of Montreal in 1969. In 1971, Sankoff became interested in molecular sequence comparison and devised the first quadratic-time variant of the Needleman–Wunsch algorithm for pairwise sequence alignment.
In 1973, Sankoff and Robert Cedergren developed a joint estimation method for phylogeny and multiple sequence alignment of 5S ribosomal RNA, laying the algorithmic foundations of comparative genomics. In 1975, Sankoff and Václav Chvátal studied the behavior of the longest common subsequence problem on random inputs; the constants of proportionality arising in this study have come to be known as the Chvátal–Sankoff constants.
In 1980, Robert Cedergen and David Sankoff created the first research group in bioinformatics at the University of Montreal. Sankoff's work in bioinformatics addresses RNA secondary structure, genome rearrangements, sequence alignment, genome evolution and phylogenetics.
Awards and honors
Inaugural recipient of the International Society for Computational Biology's Senior Scientist Award in 2003.
Elected a Fellow of the Royal Society of Canada (1995)
Elected an ISCB Fellow by the International Society for Computational Biology in 2009
Marcel-Vincent Prize (1977)
Ontario Distinguished Researcher Award (2002)
Weldon Memorial Prize (2004)
University of Ottawa Excellence in Research Award (2013)
Honorary doctorate, Tel Aviv Un |
https://en.wikipedia.org/wiki/Joan%20Hutchinson | Joan Prince Hutchinson (born 1945) is an American mathematician and Professor Emerita of Mathematics from Macalester College.
Education
Joan Hutchinson was born in Philadelphia, Pennsylvania; her father was a demographer and university professor, and her mother a mathematics teacher at the Baldwin School, which Joan also attended. She studied at Smith College in Northampton, Massachusetts, graduating in 1967 summa cum laude with an honors paper directed by Prof. Alice Dickinson.
After graduation she worked as a computer programmer at the Woods Hole Oceanographic Institute and at the Harvard University Computing Center then studied mathematics (and English change ringing on tower bells) at the University of Warwick in Coventry England. Returning to the United States, Hutchinson did graduate work at the University of Pennsylvania earning a Ph.D. in mathematics in 1973 under the supervision of Herbert S. Wilf.
Career
She was a John Wesley Young research instructor at Dartmouth College, 1973–1975.
She and her husband, fellow mathematician Stan Wagon, taught at Smith College, 1975–1990, and at Macalester College, 1990–2007. At both colleges they shared a full-time position in mathematics. She spent sabbaticals, taught, and held visiting positions at Tufts University, Carleton College, University of Colorado Boulder, University of Washington, University of Michigan, Mathematical Sciences Research Institute in Berkeley, California, and University of Colorado Denver.
She has served on committees of the American Mathematical Society, the Mathematical Association of America (MAA), SIAM Special Interest Group on Discrete Math (SIAM-DM), and the Association for Women in Mathematics, involved with the latter organization since a graduate student during its founding days in 1971. Mentoring women students and younger colleagues has been an important concern of her professional life. She served as the vice-chair of SIAM-DM, 2000–2002. She was a member of the editorial board of the American Mathematical Monthly, 1986–1996, and continues on the board of the Journal of Graph Theory since 1993.
Research
Her research has focused on graph theory and discrete mathematics, specializing mainly in topological and chromatic graph theory and on visibility graphs;
for overviews of this work see and .
She has published over 75 research and expository papers in graph theory, many with Michael O. Albertson, formerly of Smith College.
In one of their most cited works, Albertson and Hutchinson completed work of Gabriel Andrew Dirac related to the Heawood conjecture by proving that, on any surface other than the sphere or Klein bottle, the only graphs meeting Heawood's bound on the chromatic number of surface-embedded graphs are the complete graphs.
She has also considered algorithmic aspects in these areas, for example, generalizing the planar separator theorem to surfaces.
With S. Wagon she has co-authored papers on algorithmic aspects of the four color theorem.
Alber |
https://en.wikipedia.org/wiki/Carl%20B.%20Allendoerfer%20Award | The Carl B. Allendoerfer Award is presented annually by the Mathematical Association of America (MAA) for "expository excellence published in Mathematics Magazine." it is named after mathematician Carl B. Allendoerfer who was president of the MAA 1959–60.
Recipients
Recipients of the Carl B. Allendoerfer Award have included:
See also
List of mathematics awards
References
Awards of the Mathematical Association of America |
https://en.wikipedia.org/wiki/List%20of%20V%C3%A4xj%C3%B6%20Lakers%20seasons | This is a list of seasons of Växjö Lakers HC, a Swedish ice hockey club based in Växjö.
External links
Swedish Ice Hockey Association: Historical Statistics
Swedish Ice Hockey Association: Current Statistics
Eliteprospects.com: Club profile
Växjö Lakers |
https://en.wikipedia.org/wiki/Pegasus%20Academy | Pegasus Academy (formerly known as Holly Hall School and Holly Hall Maths and Computing College) is a mixed secondary school located in the Holly Hall area of Dudley, West Midlands, England. Situated by the Scotts Green roundabout near the Russells Hall Estate, it was originally opened in 1968 to replace an earlier, smaller building several hundred yards further along the road towards Brierley Hill.
It was originally a secondary modern school until adopting comprehensive status in September 1975, three years after the entry age was increased from 11 to 12. The school reverted to being an 11-16 comprehensive in September 1990. The school had grant-maintained status in the 1990s, before receiving Mathematics and Computing College specialist status in September 2002.
In December 2007, plans were unveiled by Dudley council for the school to be rebuilt and change to academy status, which would have made it the first school of its kind in the borough. The plan also included taking in some pupils from Pensnett High School, which was earmarked for closure with other pupils also transferring to The Crestwood School at Kingswinford. However, these plans were scrapped by the local council in March 2008 as the school was deemed "too successful" for academy status. However the school was converted to academy status in 2011.
In September 2017 the academy joined The Dudley Academies Trust, under the sponsorship of Dudley College. It was renamed the Pegasus Academy the following September.
References
Secondary schools in the Metropolitan Borough of Dudley
Academies in the Metropolitan Borough of Dudley
Educational institutions established in 1968
1968 establishments in England |
https://en.wikipedia.org/wiki/Vivienne%20Malone-Mayes | Vivienne Lucille Malone-Mayes (February 10, 1932 – June 9, 1995) was an American mathematician and professor. Malone-Mayes studied properties of functions, as well as methods of teaching mathematics. She was the fifth African-American woman to gain a PhD in mathematics in the United States, and the first African-American member of the faculty of Baylor University.
Early life and education
Vivienne Lucille Malone was born on February 10, 1932, in Waco, Texas, to Pizarro and Vera Estelle Allen Malone. She encountered educational challenges associated with growing up in an African-American community in the South, including racially segregated schools, but the encouragement of her parents, both educators, led her to avidly pursue her own education. She graduated from A. J. Moore High School in 1948. She entered Fisk University at the age of 16 where she earned a bachelor's degree (1952) and a master's degree (1954). Vivienne switched from medicine to mathematics after she began studying under Evelyn Boyd Granville and Lee Lorch. Granville was one of the first of five African-American women to earn her Ph.D. in mathematics.
Career
After earning her master's, she chaired the Mathematics department at Paul Quinn College for seven years and then at Bishop College for one year before deciding to take further graduate mathematics course. She was refused admission at Baylor University due to segregation and instead attend summer courses at the University of Texas. After another year of teaching she decided to attend the University of Texas full-time as a graduate student. She was the only African American and only woman in the class, and at first her classmates ignored her. She was not allowed to teach, was unable to attend professor Robert Lee Moore's lectures, and could not join off-campus meetings because they were held in a coffee shop which could not, under Texas law, serve African Americans. She wrote, "My mathematical isolation was complete", and that "it took a faith in scholarship almost beyond measure to endure the stress of earning a Ph.D. degree as a Black, female graduate student". She participated in civil rights demonstrations, and her friends and colleagues Etta Falconer and Lee Lorch wrote on her death that "With skill, integrity, steadfastness and love she fought racism and sexism her entire life, never yielding to the pressures or problems which beset her path".
As an educator, Malone-Mayes's developed novel methods of teaching mathematics including a program using self-paced audio-tutorials. Her mathematical research was in the field of functional analysis, particularly characterizing the growth properties of ranges of nonlinear operators. Malone-Mayes graduated in 1966, with a dissertation entitled "A structure problem in asymptotic analysis". Her doctoral supervisor was Don E. Edmondson.
Following graduation, Malone-Mayes was hired as a full-time professor in the mathematics department at Baylor University. Her research there cont |
https://en.wikipedia.org/wiki/Mustafa%20Re%C5%9Fit%20Ak%C3%A7ay | Mustafa Reşit Akçay (born 12 December 1958) is a Turkish professional football manager who is the manager of TFF Second League club Esenler Erokspor.
Managerial statistics
Honours
Manager
1461 Trabzon
TFF Second League: 2011–12 (Red Group)
Konyaspor
Turkish Super Cup: 2017
References
External links
Mustafa Reşit Akçay at TFF.org
Mustafa Reşit Akçay at Maçkolik.com
1958 births
Living people
Sportspeople from Trabzon
Turkish football managers
Süper Lig managers
Trabzonspor managers
Akhisarspor managers
Konyaspor managers
MKE Ankaragücü managers
Kocaelispor managers
Esenler Erokspor managers |
https://en.wikipedia.org/wiki/Structural%20complexity%20%28applied%20mathematics%29 | Structural complexity is a science of applied mathematics, that aims at relating fundamental physical or biological aspects of a complex system with the mathematical description of the morphological complexity that the system exhibits, by establishing rigorous relations between mathematical and physical properties of such system.
Structural complexity emerges from all systems that display morphological organization. Filamentary structures, for instance, are an example of coherent structures that emerge, interact and evolve in many physical and biological systems, such as mass distribution in the Universe, vortex filaments in turbulent flows, neural networks in our brain and genetic material (such as DNA) in a cell. In general information on the degree of morphological disorder present in the system tells us something important about fundamental physical or biological processes.
Structural complexity methods are based on applications of differential geometry and topology (and in particular knot theory) to interpret physical properties of dynamical systems. such as relations between kinetic energy and tangles of vortex filaments in a turbulent flow or magnetic energy and braiding of magnetic fields in the solar corona, including aspects of topological fluid dynamics.
Literature
References
Applied mathematics
Complex systems theory |
https://en.wikipedia.org/wiki/Ribbon%20%28mathematics%29 | In differential geometry, a ribbon (or strip) is the combination of a smooth space curve and its corresponding normal vector. More formally, a ribbon denoted by includes a curve given by a three-dimensional vector , depending continuously on the curve arc-length (), and a unit vector perpendicular to at each point. Ribbons have seen particular application as regards DNA.
Properties and implications
The ribbon is called simple if is a simple curve (i.e. without self-intersections) and closed and if and all its derivatives agree at and .
For any simple closed ribbon the curves given parametrically by are, for all sufficiently small positive , simple closed curves disjoint from .
The ribbon concept plays an important role in the Călugăreanu-White-Fuller formula, that states that
where is the asymptotic (Gauss) linking number, the integer number of turns of the ribbon around its axis; denotes the total writhing number (or simply writhe), a measure of non-planarity of the ribbon's axis curve; and is the total twist number (or simply twist), the rate of rotation of the ribbon around its axis.
Ribbon theory investigates geometric and topological aspects of a mathematical reference ribbon associated with physical and biological properties, such as those arising in topological fluid dynamics, DNA modeling and in material science.
See also
Bollobás–Riordan polynomial
Knots and graphs
Knot theory
DNA supercoil
Möbius strip
References
Bibliography
Differential geometry
Topology |
https://en.wikipedia.org/wiki/List%20of%20Bryn%C3%A4s%20IF%20seasons | This is a list of Brynäs IF seasons.
External links
Historical Statistics from the Swedish Ice Hockey Association
Bry
Brynäs IF |
https://en.wikipedia.org/wiki/Quarter%205-cubic%20honeycomb | In five-dimensional Euclidean geometry, the quarter 5-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 5-demicubic honeycomb, and a quarter of the vertices of a 5-cube honeycomb. Its facets are 5-demicubes and runcinated 5-demicubes.
Related honeycombs
See also
Regular and uniform honeycombs in 5-space:
5-cube honeycomb
5-demicube honeycomb
5-simplex honeycomb
Truncated 5-simplex honeycomb
Omnitruncated 5-simplex honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
x3o3o x3o3o *b3*e - spaquinoh
Honeycombs (geometry)
6-polytopes |
https://en.wikipedia.org/wiki/Bosnia%20and%20Herzegovina%20national%20football%20team%20records%20and%20statistics | This page lists national football team statistics regarding Bosnia 1992 – present, and also some statistics from Yugoslavia 1920–1990 period relevant to SRBiH.
Recent results and forthcoming fixtures
Player records
All scorers Bosnia national football team
Table correct as of 4 September 2020.
All appearances for Bosnia national football team
Table correct as of 26 March 2014
Not included unofficial matches: BiH-Uruguay, BiH-Chile, BiH-Slovakia, BiH-Malaysia U23, BiH-South Africa
All Bosnian scorers at Major Competitions (Bosnia 1992 – present)
Bosnian players at Major Competitions (Yugoslavia 1920–1990)
2+ BiH players playing at the same club
The table below lists notable instances of two or more Bosnian football team players in one foreign based club at the same time:
Note: Table contains some of the more prominent club sides of the world. Table does not yet contain clubs from other former Yugoslavia republics.
Youngest debutants
As of 7 June 2016, the youngest debutants for senior Bosnia-Herzegovina side are:
Match statistics
Biggest wins
Wins by five goals and up
Hat-tricks for Bosnia
The table below shows a list of Bosnia and Herzegovina players who scored three or more goals in one match.
Hat-tricks conceded by Bosnia
The table below shows a list of opponent players who scored three or more goals in one match against Bosnia and Herzegovina.
Memorable victories
Source: Results
Unofficial games not included.
Major Tournaments appearances and play-offs appearances
Bosnia and Herzegovina was the first former Yugoslav nation to qualify for a FIFA World Cup directly, and not via play-offs first;
Tino-Sven Sušić played for Bosnia at 2014 FIFA World Cup under his uncle - head coach Safet Sušić.
Play-offs win–draw–loss stats
Major Tournament win–draw–loss stats
Head-to-Head records against other countries
Tables correct as of match played on 1 June 2018.
The table lists opponents played, sorted by members of FIFA affiliated confederations.
Bosnia and Herzegovina's all-time record sorted by FIFA Confederations, 1995–present
Matches vs Ex-Yugoslav Republics
Bosnia and Herzegovina was one of six republics of Socialist Federal Republic of Yugoslavia. As such, meeting one of its neighbor republics on the sports pitch is of great significance.
Penalty shootout record
Managers and captains
Captains
Emir Spahić captained Bosnia at their first ever FIFA World Cup tournament.
This is a list of Bosnia and Herzegovina captains for ten or more matches.
Note: Some of the other players to have captained the team include: Mehmed Baždarević (2 caps) 1996, Meho Kodro (5) 1997 to 1998, Vlatko Glavaš (1) 1997, Suvad Katana (2) 1998, Elvir Bolić (6) 1999 to 2000, Bruno Akrapović (4) 1999 to 2003, Hasan Salihamidžić (1) 2004, Zlatan Bajramović (1) 2006, Džemal Berberović (1) 2007, Asmir Begović (6) 2011 to 2020, Haris Medunjanin (4) 2016 to 2018, Vedad Ibišević (1) 2017, Miralem Pjanić (6) 2019 to 2021, Ermin Bičakčić (1) 2019, Sead Kol |
https://en.wikipedia.org/wiki/Quarter%207-cubic%20honeycomb | In seven-dimensional Euclidean geometry, the quarter 7-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 7-demicubic honeycomb, and a quarter of the vertices of a 7-cube honeycomb. Its facets are 7-demicubes, pentellated 7-demicubes, and {31,1,1}×{3,3} duoprisms.
Related honeycombs
See also
Regular and uniform honeycombs in 7-space:
7-cube honeycomb
7-demicube honeycomb
7-simplex honeycomb
Truncated 7-simplex honeycomb
Omnitruncated 7-simplex honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
Honeycombs (geometry)
8-polytopes |
https://en.wikipedia.org/wiki/Quarter%206-cubic%20honeycomb | In six-dimensional Euclidean geometry, the quarter 6-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 6-demicubic honeycomb, and a quarter of the vertices of a 6-cube honeycomb. Its facets are 6-demicubes, stericated 6-demicubes, and {3,3}×{3,3} duoprisms.
Related honeycombs
See also
Regular and uniform honeycombs in 5-space:
6-cube honeycomb
6-demicube honeycomb
6-simplex honeycomb
Truncated 6-simplex honeycomb
Omnitruncated 6-simplex honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
Honeycombs (geometry)
7-polytopes |
https://en.wikipedia.org/wiki/Quarter%208-cubic%20honeycomb | In seven-dimensional Euclidean geometry, the quarter 8-cubic honeycomb is a uniform space-filling tessellation (or honeycomb). It has half the vertices of the 8-demicubic honeycomb, and a quarter of the vertices of a 8-cube honeycomb. Its facets are 8-demicubes h{4,36}, pentic 8-cubes h6{4,36}, {3,3}×{32,1,1} and {31,1,1}×{31,1,1} duoprisms.
See also
Regular and uniform honeycombs in 8-space:
8-cube honeycomb
8-demicube honeycomb
8-simplex honeycomb
Truncated 8-simplex honeycomb
Omnitruncated 8-simplex honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
Honeycombs (geometry)
9-polytopes |
https://en.wikipedia.org/wiki/Statistics%20Botswana | Statistics Botswana (StatsBots) is the National statistical bureau of Botswana. The organization was previously under the Ministry of Finance and development planning as a department and was called Central Statistics Office. The organisation was initially set up in 1967 through an Act of Parliament – the Statistics Act (Cap 17) and thereafter transformed into a parastatal through the revised Statistics Act of 2009. This act gives the Statistics Botswana the mandate and authority to collect, process, compile, analyse, publish, disseminate and archive official national statistics. It is also responsible for "coordinating, monitoring and supervising the National Statistical System" in Botswana. The office has its main offices in Gaborone and three satellite offices in Maun, Francistown and Ghanzi. The different areas in statistics that should be collected are covered under this Act and are clearly specified. The other statistics that are not specified can be collected as long as they are required by the Government, stakeholders and the users.
Legal Mandate
Statistics Botswana conducts the Population and Housing Census (PHC) within the jurisdiction of two (2) key legal instruments namely:
Census Act (Cap 17:02) of 1904
Statistics Act (Cap 17:01) of 2009
The legal instruments stipulates that the census population of Botswana should be carried out every 10 years and any other censuses and surveys as it is determined or necessary. The Statistics Act 2009 authorizes the Statistician General to have access to records (administrative data, financial, geographic information etc.) from other statistics producing agencies.
The Statistics Act 2009 provides for confidentiality and disclosure of information. All staff of Statistics Botswana, including any contractors of Statistics Botswana are sworn to secrecy to not disclose any information that they came across by virtue of their employment (Section 20) of the Act and penalties are also provided for in the Act. In addition, .
Data collection
Data collection is the process of gathering data for purposes of measuring information on variables of interest in an established systematic fashion that enables one to
answer stated research question, test hypothesis and evaluate outcomes. Data is collected through various methods. The primary methods used by Statistics Botswana include questionnaires, face to face interviews, online interviews and desktop data collection.
Uses of Data
Survey and census data update the demographic, social and economic data to support national development activities. The data also is used for informed decision making in various government, private and individual activities such as:
Provision of data for constituency delimitation processes;
Increase availability and accessibility of accurate, timely and reliable baseline data on demographic and socio-economic characteristics of the population;
Provision of various demographic baseline indicators, such as cu |
https://en.wikipedia.org/wiki/GotoBLAS | In scientific computing, GotoBLAS and GotoBLAS2 are open source implementations of the BLAS (Basic Linear Algebra Subprograms) API with many hand-crafted optimizations for specific processor types. GotoBLAS was developed by Kazushige Goto at the Texas Advanced Computing Center. , it was used in seven of the world's ten fastest supercomputers.
GotoBLAS remains available, but development ceased with a final version touting optimal performance on Intel's Nehalem architecture (contemporary in 2008).
OpenBLAS is an actively maintained fork of GotoBLAS, developed at the Lab of Parallel Software and Computational Science, ISCAS.
GotoBLAS was written by Goto during his sabbatical leave from the Japan Patent Office in 2002. It was initially optimized for the Pentium 4 processor and managed to immediately boost the performance of a supercomputer based on that CPU from 1.5 TFLOPS to 2 TFLOPS. , the library was available at no cost for noncommercial use. A later open source version was released under the terms of the BSD license.
GotoBLAS's matrix-matrix multiplication routine, called GEMM in BLAS terms, is highly tuned for the x86 and AMD64 processor architectures by means of handcrafted assembly code. It follows a similar decomposition into smaller "kernel" routines that other BLAS implementations use, but where earlier implementations streamed data from the L1 processor cache, GotoBLAS uses the L2 cache.
The kernel used for GEMM is a routine called GEBP, for "General block-times-panel multiply", which was experimentally found to be "inherently superior" over several other kernels that were considered in the design.
Several other BLAS routines are, as is customary in BLAS libraries, implemented in terms of GEMM.
As of January 2022, the Texas Advanced Computing Center website states that Goto BLAS in no more maintained and suggests the use of BLIS or MKL.
See also
Automatically Tuned Linear Algebra Software (ATLAS)
Intel Math Kernel Library (MKL)
References
Numerical linear algebra
Numerical software
Software using the BSD license |
https://en.wikipedia.org/wiki/Tetrahedral%20cupola | In 4-dimensional geometry, the tetrahedral cupola is a polychoron bounded by one tetrahedron, a parallel cuboctahedron, connected by 10 triangular prisms, and 4 triangular pyramids.
Related polytopes
The tetrahedral cupola can be sliced off from a runcinated 5-cell, on a hyperplane parallel to a tetrahedral cell. The cuboctahedron base passes through the center of the runcinated 5-cell, so the Tetrahedral cupola contains half of the tetrahedron and triangular prism cells of the runcinated 5-cell. The cupola can be seen in A2 and A3 Coxeter plane orthogonal projection of the runcinated 5-cell:
See also
Tetrahedral pyramid (5-cell)
References
External links
Segmentochora: tetaco, tet || co, K-4.23
4-polytopes |
https://en.wikipedia.org/wiki/Cubic%20cupola | In 4-dimensional geometry, the cubic cupola is a 4-polytope bounded by a rhombicuboctahedron, a parallel cube, connected by 6 square prisms, 12 triangular prisms, 8 triangular pyramids.
Related polytopes
The cubic cupola can be sliced off from a runcinated tesseract, on a hyperplane parallel to cubic cell. The cupola can be seen in an edge-centered (B3) orthogonal projection of the runcinated tesseract:
See also
Cubic pyramid
Octahedral cupola
Runcinated tesseract
References
External links
Segmentochora: cube || sirco, K-4.71
4-polytopes |
https://en.wikipedia.org/wiki/Octahedral%20cupola | In 4-dimensional geometry, the octahedral cupola is a 4-polytope bounded by one octahedron and a parallel rhombicuboctahedron, connected by 20 triangular prisms, and 6 square pyramids.
Related polytopes
The octahedral cupola can be sliced off from a runcinated 24-cell, on a hyperplane parallel to an octahedral cell. The cupola can be seen in a B2 and B3 Coxeter plane orthogonal projection of the runcinated 24-cell:
See also
Octahedral pyramid
Cubic cupola
Runcinated 24-cell
References
External links
Segmentochora: oct || sirco, K-4.107
4-polytopes
Four-dimensional geometry |
https://en.wikipedia.org/wiki/Dodecahedral%20cupola | In 4-dimensional geometry, the dodecahedral cupola is a polychoron bounded by a rhombicosidodecahedron, a parallel dodecahedron, connected by 30 triangular prisms, 12 pentagonal prisms, and 20 tetrahedra.
Related polytopes
The dodecahedral cupola can be sliced off from a runcinated 120-cell, on a hyperplane parallel to a dodecahedral cell. The cupola can be seen in a pentagonal centered orthogonal projection of the runcinated 120-cell:
See also
Dodecahedral pyramid
References
External links
Segmentochora: doe || srid
4-polytopes
Four-dimensional geometry |
https://en.wikipedia.org/wiki/Centre%20for%20Theoretical%20Cosmology | The Centre for Theoretical Cosmology is a research center within the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. Founded by Stephen Hawking in 2007, it encourages new thinking on some of the most challenging problems in science, intending to advance the scientific understanding of the universe.
References
External links
Centre for Theoretical Cosmology, University of Cambridge
Theoretical Cosmology, Centre for |
https://en.wikipedia.org/wiki/Twist%20%28mathematics%29 | In differential geometry, the twist of a ribbon is its rate of axial rotation. Let a ribbon be composed of space curve , where is the arc length of , and the a unit normal vector, perpendicular at each point to . Since the ribbon has edges and , the twist (or total twist number) measures the average winding of the edge curve around and along the axial curve . According to Love (1944) twist is defined by
where is the unit tangent vector to .
The total twist number can be decomposed (Moffatt & Ricca 1992) into normalized total torsion and intrinsic twist as
where is the torsion of the space curve , and denotes the total rotation angle of along . Neither nor are independent of the ribbon field . Instead, only the normalized torsion is an invariant of the curve (Banchoff & White 1975).
When the ribbon is deformed so as to pass through an inflectional state (i.e. has a point of inflection), the torsion becomes singular. The total torsion jumps by and the total angle simultaneously makes an equal and opposite jump of (Moffatt & Ricca 1992) and remains continuous. This behavior has many important consequences for energy considerations in many fields of science (Ricca 1997, 2005; Goriely 2006).
Together with the writhe of , twist is a geometric quantity that plays an important role in the application of the Călugăreanu–White–Fuller formula in topological fluid dynamics (for its close relation to kinetic and magnetic helicity of a vector field), physical knot theory, and structural complexity analysis.
See also
Twist (screw theory)
Twist (rational trigonometry)
Twisted sheaf
References
Banchoff, T.F. & White, J.H. (1975) The behavior of the total twist and self-linking number of a closed space curve under inversions. Math. Scand. 36, 254–262.
Goriely, A. (2006) Twisted elastic rings and the rediscoveries of Michell’s instability. J Elasticity 84, 281-299.
Love, A.E.H. (1944) A Treatise on the Mathematical Theory of Elasticity. Dover, 4th Ed., New York.
Moffatt, H.K. & Ricca, R.L. (1992) Helicity and the Calugareanu invariant. Proc. R. Soc. London A 439, 411-429. Also in: (1995) Knots and Applications (ed. L.H. Kauffman), pp. 251-269. World Scientific.
Ricca, R.L. (1997) Evolution and inflexional instability of twisted magnetic flux tubes. Solar Physics 172, 241-248.
Ricca, R.L. (2005) Inflexional disequilibrium of magnetic flux tubes. Fluid Dynamics Research 36, 319-332.
Differential geometry
Topology |
https://en.wikipedia.org/wiki/Bio-Med%20Science%20Academy | Bio-Med Science Academy is a public STEM+M (Science, Technology, Engineering, Mathematics, plus Medicine) school in Portage County, Ohio, United States. The school's original location, now known as the Rootstown campus, is on the campus of Northeast Ohio Medical University (NEOMED) in Rootstown, and houses grades 7 through 12. The school, originally a grades 9–12 high school, has expanded to include lower grade levels, with grades 5 and 6 at its Ravenna campus and grades K-4 at the Shalersville campus. Bio-Med opened as a community charter school in August 2012, but in April 2013 the school received a formal STEM designation for the State of Ohio. This new designation required the closing of the community school which occurred June 30, 2013, and the opening of Bio-Med Science Academy STEM School on July 1, 2013. With its new title it became an official independent and public STEM school.
The academy began with an initial freshmen class of 70 students. 119 students were admitted for the 2013–14 academic year, 109 were accepted for the 2014–15 year and 110 for the 2015–16 year. For the 2017–18 school year, Bio-Med expanded to grades 6–12 with the opening of the Lower Academy in Shalersville Township. Total enrollment in the academy now surpasses 1,000 students from over 41 district across eight counties. There is a 50/50 male to female ratio.
For the 2020–21 year an addition was completed at the Rootstown campus to house 7th and 8th graders who had previously been at the Shalersville campus, making the Shalersville campus open for 2nd, 3rd, and 4th grades while 6th grade was moved to the Ravenna campus with the 5th graders.
The school operates on a year-round academic schedule and is a member of the Akron hub of the Ohio Stem Learning Network. The Upper Academy is housed on the third floor of the NEOMED Education and Wellness (NEW) Center, which opened in August 2014. Previously, the school was located in another part of the NEOMED campus for the first two academic years. Bio-Med Science Academy was granted Ohio STEM designation in April 2013. Within its first year, the school claimed first place at the Regional Engineer Career Day. Bio-Med Science Academy was one of seven schools recognized by Ohio Governor John Kasich in January 2017 as a recipient of the governor's innovation awards.
Clubs and activities
The academy is home to over 28 different clubs with many different activities to choose from depending on the student's interests. Various interest clubs such as science fiction, science Olympiad, and student government.
References
External links
Educational institutions established in 2012
High schools in Portage County, Ohio
Public high schools in Ohio
2012 establishments in Ohio |
https://en.wikipedia.org/wiki/Vladimir%20Krsti%C4%87%20%28footballer%29 | Vladimir Krstić (Serbian Cyrillic: Владимир Крстић; born 28 June 1987) is a retired Serbian footballer.
Career statistics
Honours
Napredak Kruševac
Serbian First League: 2015–16
References
Krstić: Mislio sam da su golovi u Bečeju povratna karta za "Marakanu"
Vladimir Krstić at srbijafudbal
1987 births
Living people
Footballers from Valjevo
Serbian men's footballers
Men's association football defenders
OFK Bečej 1918 players
FK Kolubara players
FK Voždovac players
FK BSK Borča players
FK Sloboda Užice players
FK Borac Čačak players
FK Sloga Petrovac na Mlavi players
FK Napredak Kruševac players
FK Budućnost Valjevo players
FK Jedinstvo Ub players
Serbian First League players
Serbian SuperLiga players |
https://en.wikipedia.org/wiki/Limiting%20case%20%28mathematics%29 | In mathematics, a limiting case of a mathematical object is a special case that arises when one or more components of the object take on their most extreme possible values. For example:
In statistics, the limiting case of the binomial distribution is the Poisson distribution. As the number of events tends to infinity in the binomial distribution, the random variable changes from the binomial to the Poisson distribution.
A circle is a limiting case of various other figures, including the Cartesian oval, the ellipse, the superellipse, and the Cassini oval. Each type of figure is a circle for certain values of the defining parameters, and the generic figure appears more like a circle as the limiting values are approached.
Archimedes calculated an approximate value of π by treating the circle as the limiting case of a regular polygon with 3 × 2n sides, as n gets large.
In electricity and magnetism, the long wavelength limit is the limiting case when the wavelength is much larger than the system size.
In economics, two limiting cases of a demand curve or supply curve are those in which the elasticity is zero (the totally inelastic case) or infinity (the infinitely elastic case).
In finance, continuous compounding is the limiting case of compound interest in which the compounding period becomes infinitesimally small, achieved by taking the limit as the number of compounding periods per year goes to infinity.
A limiting case is sometimes a degenerate case in which some qualitative properties differ from the corresponding properties of the generic case. For example:
A point is a degenerate circle, namely one with radius 0.
A parabola can degenerate into two distinct or coinciding parallel lines.
An ellipse can degenerate into a single point or a line segment.
A hyperbola can degenerate into two intersecting lines.
See also
Degeneracy (mathematics)
Limit (mathematics)
References
Mathematical concepts |
https://en.wikipedia.org/wiki/Bitruncated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the bitruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a bitruncation of a tesseractic honeycomb. It is also called a cantic quarter tesseractic honeycomb from its q2{4,3,3,4} construction.
Other names
Bitruncated tesseractic tetracomb (batitit)
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
Demitesseractic honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x3x3x *b3o *b3o, x3x3x *b3o4o, o3x3o *b3x4o, o4x3x3o4o - batitit - O92
5-polytopes
Honeycombs (geometry)
Bitruncated tilings |
https://en.wikipedia.org/wiki/Bitruncated%2016-cell%20honeycomb | In four-dimensional Euclidean geometry, the bitruncated 16-cell honeycomb (or runcicantic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Symmetry constructions
There are 3 different symmetry constructions, all with 3-3 duopyramid vertex figures. The symmetry doubles on in three possible ways, while contains the highest symmetry.
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
16-cell honeycomb
24-cell honeycomb
Rectified 24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x3x3x *b3x *b3o, x3x3o *b3x4o, o3x3x4o3o - bithit - O107
Honeycombs (geometry)
5-polytopes
Bitruncated tilings |
https://en.wikipedia.org/wiki/Birectified%2016-cell%20honeycomb | In four-dimensional Euclidean geometry, the birectified 16-cell honeycomb (or runcic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Symmetry constructions
There are 3 different symmetry constructions, all with 3-3 duoprism vertex figures. The symmetry doubles on in three possible ways, while contains the highest symmetry.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
16-cell honeycomb
24-cell honeycomb
Rectified 24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x3o3x *b3x *b3o, x3o3o *b3x4o, o3o3x4o3o - bricot - O106
Honeycombs (geometry)
5-polytopes |
https://en.wikipedia.org/wiki/Cohn-Vossen%27s%20inequality | In differential geometry, Cohn-Vossen's inequality, named after Stefan Cohn-Vossen, relates the integral of Gaussian curvature of a non-compact surface to the Euler characteristic. It is akin to the Gauss–Bonnet theorem for a compact surface.
A divergent path within a Riemannian manifold is a smooth curve in the manifold that is not contained within any compact subset of the manifold. A complete manifold is one in which every divergent path has infinite length with respect to the Riemannian metric on the manifold. Cohn-Vossen's inequality states that in every complete Riemannian 2-manifold S with finite total curvature and finite Euler characteristic, we have
where K is the Gaussian curvature, dA is the element of area, and χ is the Euler characteristic.
Examples
If S is a compact surface (without boundary), then the inequality is an equality by the usual Gauss–Bonnet theorem for compact manifolds.
If S has a boundary, then the Gauss–Bonnet theorem gives
where is the geodesic curvature of the boundary, and its integral the total curvature which is necessarily positive for a boundary curve, and the inequality is strict. (A similar result holds when the boundary of S is piecewise smooth.)
If S is the plane R2, then the curvature of S is zero, and χ(S) = 1, so the inequality is strict: 0 < 2.
Notes and references
External links
Gauss–Bonnet theorem, in the Encyclopedia of Mathematics, including a brief account of Cohn-Vossen's inequality
Theorems in differential geometry
Inequalities |
https://en.wikipedia.org/wiki/Harold%20R.%20Parks | Harold Raymond Parks (born May 22, 1949) is an American mathematician and is a professor emeritus of mathematics at Oregon State University.
Parks obtained his Ph.D. in 1974 from Princeton University, under the supervision of Frederick J. Almgren, Jr. In 2012, he became a fellow of the American Mathematical Society.
He has developed and implemented a computational technique for computing parametric area minimizing surfaces. He derived an existence and regularity theory for a class of constrained variational problems. Parks has discovered, and characterized, a type of minimal surface with surprising properties, defined in terms of the Jacobi elliptic functions.
References
1949 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Mathematical Society
Princeton University alumni
Oregon State University faculty |
https://en.wikipedia.org/wiki/NWSL%20records%20and%20statistics | The following is a compilation of notable records and statistics for teams and players in the National Women's Soccer League, which started in 2013.
Statistics for the NWSL Challenge Cup, a competition originally created in place of the 2020 season that was cancelled due to the COVID-19 pandemic, are treated separately from regular season statistics.
Champions and shield winners
By season
Total trophies by team
Italics indicates a defunct team.
Team records
Wins
Most wins in a season (24 games): 17, North Carolina Courage (2018)
Fewest wins in a season (20 games): 3, Boston Breakers (2016)
Fewest wins in a season (24 games): 1, Sky Blue FC (2018)
Most consecutive wins in a season: 7, joint record:
FC Kansas City (2014)
Seattle Reign FC (2014)
Portland Thorns FC (2017)
Most consecutive games without a win: 23, Sky Blue FC (2018)
Most consecutive away games without a win: 19, Boston Breakers (between August 6, 2014 and July 10, 2016)
Most consecutive home wins in a season: 7, joint record:
Portland Thorns FC (between June 28, 2017 and September 30, 2017)
North Carolina Courage (between July 5, 2019 and October 12, 2019)
Most consecutive home wins: 8, Portland Thorns FC (between June 28, 2017 and April 15, 2018)
Most wins in total (204 games): 99, Portland Thorns FC
Losses
Fewest losses in a season (24 games): 1, North Carolina Courage (2018)
Longest unbeaten run: 20 games, Washington Spirit (between 26 September 2021 and 7 May 2022)
Most losses in total (204 games): 94, NJ/NY Gotham FC
Fewest home losses in a season (12 games): 0, Seattle Reign FC (2014)
Most consecutive losses in a season: 11, NJ/NY Gotham FC (2022)
Most consecutive home games undefeated: 22, Seattle Reign FC (between 13 April 2014 and 29 August 2015)
Attendance
1 A semifinal that would have been played in North Carolina was moved to Portland due to Hurricane Florence.
2 Due to restrictions related to the COVID-19 pandemic, many teams had reduced capacities for part or all of the season, including some games with zero fans.
Goals
Most goals scored in a season: 54, North Carolina Courage (2019)
Fewest goals scored in a season: 12, Washington Spirit (2018)
Most goals conceded in a season: 53, Orlando Pride (2019)
Fewest goals conceded in a season (joint record): 17, North Carolina Courage (2018), Portland Thorns (2021)
Best goal difference in a season: 36, North Carolina Courage (2018)
Most goals scored in total: 283, Portland Thorns FC
Most goals conceded in total: 279, Sky Blue FC/NJ/NY Gotham FC
Most consecutive games scoring: 28 games, FC Kansas City (2013–2014) includes 3 playoff games
Most consecutive games scoring 2+ goals: 7 games, Western New York Flash (2013)
Longest shutout streak (joint record): 5 games, Seattle Reign FC (2016), North Carolina Courage (2021)
Regular season records
Through 2022 season (regular season games only)
Sort order is points, finishing positions, wins
Playoff records
Through 2022 playoffs
Sort orde |
https://en.wikipedia.org/wiki/Benjamin%20Weiss | Benjamin Weiss (; born 1941) is an American-Israeli mathematician known for his contributions to ergodic theory, topological dynamics, probability theory, game theory, and descriptive set theory.
Biography
Benjamin ("Benjy") Weiss was born in New York City. In 1962 he received B.A. from Yeshiva University and M.A. from the Graduate School of Science, Yeshiva University. In 1965, he received his Ph.D. from Princeton under the supervision of William Feller.
Academic career
Between 1965 and 1967, Weiss worked at the IBM Research. In 1967, he joined the faculty of the Hebrew University of Jerusalem; and since 1990 occupied the Miriam and Julius Vinik Chair in Mathematics (Emeritus since 2009). Weiss held visiting positions at Stanford, MSRI, and IBM Research Center.
Weiss published over 180 papers in ergodic theory, topological dynamics, orbit equivalence, probability, information theory, game theory, descriptive set theory; with notable contributions including introduction of Markov partitions (with Roy Adler), development of ergodic theory of amenable groups (with Don Ornstein), mean dimension (with Elon Lindenstrauss), introduction of sofic subshifts and sofic groups. The road coloring conjecture was also posed by Weiss with Roy Adler.
One of Weiss's students is Elon Lindenstrauss, a 2010 recipient of the Fields Medal.
Awards and recognition
Weiss gave an invited address at the International Congress of Mathematicians 1974,
was twice the main speaker at a Conference Board of Mathematical Sciences (1979 and 1995),
gave the M.B.Porter Distinguished Lecture Series at Rice University (1998).
In 2000 Weiss was elected as a Foreign Honorary Member of the American Academy of Arts and Sciences.
In 2006 he was awarded the Rothschild Prize in Mathematics.
In 2012 Weiss was elected a Fellow of the American Mathematical Society.
See also
Daniel Rudolph - contemporary of and academic collaborator with Weiss
References
Living people
Israeli mathematicians
Dynamical systems theorists
Princeton University alumni
Academic staff of the Hebrew University of Jerusalem
Fellows of the American Mathematical Society
1941 births |
https://en.wikipedia.org/wiki/Chandola%20Lake | {
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"type": "Feature",
"properties": {"title": "Chandola Lake", "marker-symbol": "water", "marker-size": "small",},
"geometry": {
"type": "Point",
"coordinates": [
72.5871605880093,
22.986789130656533
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Chandola Lake is located near Dani Limda Road, Ahmedabad, Gujarat state, India and covers an area of 1200 hectares. It is a water reservoir, embanked and circular in form. It is also home for cormorants, painted storks and spoonbill birds. During the evening time, many people visit this place and take a leisure stroll.
History
Chandola Lake was in existence when Asha Bhil founded Ashaval.
The historic Salt March around nine in the morning, after covering a distance of seven miles from the Sabarmati Ashram and a few minutes after the trucks and the taxis carrying radio and print journalists had disappeared down the road, had reached the Chandola Lake. Mahatma Gandhi had stopped under a large pipal tree next to the lake, no bigger than a small pond in the middle of a vast expanse of mud during March, 1930.
Usage
Water from this lake is used for irrigation and industrial purposes. It is also being used for agriculture, as well as for other purposes like processing of waste oil and plastics.
The Kharicut Canal Scheme which is one of the oldest irrigation schemes of Gujarat was constructed with the main purpose of providing irrigation to 1,200 acres of rice land near Chandola lake in Ahmedabad.
Pollution and encroachment
Large-scale encroachment have been built on this water body. Kharicut, the lake’s feeder canal is choked with filth and garbage.
Chandola Lake Development Plans
The Ahmedabad Municipal Corporation (AMC) has ambitious plans for developing Chandola lake in a big way. AMC has also drawn an exhaustive plan for the upkeep of Chandola lake, which till now was a neglected public space. The AMC has tendered jobs for cleaning and sanitation activities to be carried out around Chandola. The civic body has earmarked Rs 3.70 lakh for clearing the garbage from the lake.
References
External links
Chandola Lake at ahmedabad.org.uk
Chandola Lake at ahmedabad.clickindia.com
Chandola Lake at touristplaces.org
See also
Kankaria Lake
Vastrapur Lake
Thol Lake
Lakes of Gujarat
Tourist attractions in Ahmedabad district
Reservoirs in India |
https://en.wikipedia.org/wiki/Fine%20structure%20theory | Fine structure theory may refer to:
Fine structure, a property in quantum physics
Fine structure theory, the study of the levels of the Jensen hierarchy of sets in set theory |
https://en.wikipedia.org/wiki/Blaze%20and%20the%20Monster%20Machines | Blaze and the Monster Machines (or shortened to BATMM) is a computer-animated interactive children's television series with a focus on teaching science, technology, engineering, and mathematics (STEM) that premiered on Nickelodeon on October 13, 2014. The series revolves around Blaze, a monster truck, and his human driver, AJ, as they have adventures in Axle City and learn about various STEM concepts which help them on their way. Joining them is the human mechanic Gabby and their monster truck friends Stripes, Starla, Darington and Zeg as well as their rival Crusher and his goofy sidekick Pickle. Then later on, Watts joins the main cast in Season 3.
Plot
Blaze and the Monster Machines focuses on Blaze, an orange-red monster truck, and his smart, young driver, AJ. They live in a world that involves many living monster trucks called "Monster Machines". Their friends include their truck friends, Starla, Stripes, Zeg, Darington, and Watts (as of Season 3), as well as Gabby, who is a mechanic who can fix anything and later on Watts' Monster Machine driver and close friend (as of Season 3). Each episode also features Crusher, a very evil sneaky blue lightning bolted tractor-trailer who cheats in races, but slowly evolves into a nicer character. Crusher is always accompanied by a small truck named Pickle, his goofy sidekick.
Format
Each episode has Blaze and AJ go on various adventures and solve problems along the way, normally three per episode, with "assistance" from the viewing audience. Blaze might also transform into a different vehicle or artifact depending on the situation. Blaze may sometimes get a task done with the help of his Blazing Speed, a special power that allows him to go super fast. Animals in this Monster Machine world have blended windows (which have been removed as of season 5) and wheels. Despite this, AJ and Gabby are both humans. In some episodes, Blaze, AJ and their friends are in a race against Crusher. During the race, Crusher cheats, usually with the help of his gray robot parts. However, Blaze and AJ manage to get through his traps, and they always beat him in time. Not all episodes involve a proper race, but still have Blaze competing against Crusher, sometimes by racing against him to get an item. Other episodes involve helping a truck friend such as Starla, Zeg, Darington, Stripes, Watts, or even Crusher and/or Pickle. Each episode features two or three original songs usually performed by Blaze and AJ offscreen, when they are setting off on their adventure or demonstrating the episode's STEM concept.
Episodes
Characters
Main
Blaze (voiced by Nolan North, Donald Reignoux in the French version, Lorenzo Scattorin in the Italian version and Karlo Hackenberger in the German version) is the show's host and central character, an orange-red monster truck who is good-hearted, loyal, and brave. He has blue eyes, and is the only main Monster Machine character to have an eye color in the entire series. He is based on the first- |
https://en.wikipedia.org/wiki/Legendre%27s%20theorem%20on%20spherical%20triangles | In geometry, Legendre's theorem on spherical triangles, named after Adrien-Marie Legendre, is stated as follows:
Let ABC be a spherical triangle on the unit sphere with small sides a, b, c. Let A'B'C' be the planar triangle with the same sides. Then the angles of the spherical triangle exceed the corresponding angles of the planar triangle by approximately one third of the spherical excess (the spherical excess is the amount by which the sum of the three angles exceeds ).
The theorem was very important in simplifying the heavy numerical work in calculating the results of traditional (pre-GPS and pre-computer) geodetic surveys from about 1800 until the middle of the twentieth century.
The theorem was stated by who provided a proof (1798) in a supplement to the report of the measurement of the French meridional arc used in the definition of the metre . Legendre does not claim that he was the originator of the theorem despite the attribution to him. maintains that the method was in common use by surveyors at the time and may have been used as early as 1740 by La Condamine for the calculation of the Peruvian meridional arc.
Girard's theorem states that the spherical excess of a triangle, E, is equal to its area, Δ, and therefore Legendre's theorem may be written as
The excess, or area, of small triangles is very small. For example, consider an equilateral spherical triangle with sides of 60 km on a spherical Earth of radius 6371 km; the side corresponds to an angular distance of 60/6371=.0094, or approximately 10−2 radians (subtending an angle of 0.57° at the centre). The area of such a small triangle is well approximated by that of a planar equilateral triangle with the same sides: a2sin(/3) = 0.0000433 radians corresponding to 8.9″.
When the sides of the triangles exceed 180 km, for which the excess is about 80″, the relations between the areas and the differences of the angles must be corrected by terms of fourth order in the sides, amounting to no more than 0.01″:
(Δ′ is the area of the planar triangle.) This result was proved by —an extended proof may be found in (Appendix D13). Other results are surveyed by .
The theorem may be extended to the ellipsoid if a, b, c are calculated by dividing the true lengths by the square root of the product of the principal radii of curvature (see Chapter 5) at the median latitude of the vertices (in place of a spherical radius). provided more exact formulae.
References
Spherical trigonometry |
https://en.wikipedia.org/wiki/Steriruncitruncated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the steriruncitruncated tesseractic honeycomb is a uniform space-filling honeycomb.
Alternate names
Celliprismatotruncated tesseractic tetracomb
Great tomocubic-diprismatotesseractic tetracomb
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
16-cell honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
References
Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x4x3o3x4x - captatit - O102
5-polytopes
Honeycombs (geometry)
Truncated tilings |
https://en.wikipedia.org/wiki/Stericantellated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the stericantellated tesseractic honeycomb is a uniform space-filling honeycomb.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
16-cell honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
References
Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x4o3x3o4x - scartit - O98
5-polytopes
Honeycombs (geometry) |
https://en.wikipedia.org/wiki/Omnitruncated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the omnitruncated tesseractic honeycomb is a uniform space-filling honeycomb. It has omnitruncated tesseract, truncated cuboctahedral prism, and 8-8 duoprism facets in an irregular 5-cell vertex figure.
Related honeycombs
See also
Truncated square tiling
Omnitruncated cubic honeycomb
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
16-cell honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
References
Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x4x3x3x4x - otatit - O103
5-polytopes
Honeycombs (geometry)
Truncated tilings |
https://en.wikipedia.org/wiki/Truncated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the truncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a truncation of a tesseractic honeycomb creating truncated tesseracts, and adding new 16-cell facets at the original vertices.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
Demitesseractic honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
o3o3o *b3x4x, x4x3o3o4o - tattit - O89
5-polytopes
Honeycombs (geometry)
Truncated tilings |
https://en.wikipedia.org/wiki/Cantellated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the cantellated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a cantellation of a tesseractic honeycomb creating cantellated tesseracts, and new 24-cell and octahedral prism facets at the original vertices.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
Demitesseractic honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
o3x3o *b3o4x, x4o3x3o4o - srittit - O90
Honeycombs (geometry)
5-polytopes |
https://en.wikipedia.org/wiki/Runcinated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the runcinated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a runcination of a tesseractic honeycomb creating runcinated tesseracts, and new tesseract, rectified tesseract and cuboctahedral prism facets.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
Demitesseractic honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x3o3x *b3o4x, x4o3o3x4o - sidpitit - O91
Honeycombs (geometry)
5-polytopes |
https://en.wikipedia.org/wiki/Cantitruncated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the cantitruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
Demitesseractic honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
o3x3o *b3x4x, x4x3x3o4o - grittit - O94
Honeycombs (geometry)
5-polytopes
Truncated tilings |
https://en.wikipedia.org/wiki/European%20Cup%2C%20Euroleague%20and%20LEN%20Champions%20League%20records%20and%20statistics | This page details statistics of the European Cup, Euroleague and Champions League.
General performances
By club
By nation
Notes
Results until the Breakup of Yugoslavia in early 1990s. Clubs from present day Serbia won the title six times and were runners-up additional three times, clubs from present day Croatia won the title seventh and were runners-up once times.
Results until the Dissolution of the Soviet Union in 1991. Clubs from present day Russia won the title two times and were runners-up additional five times, clubs from present day Kazakhstan were runners-up once times.
By city
Clubs
By semi-final appearances (European Cup, Euroleague and LEN Champions League)
All-time table for semi-finalists and clubs with at least 10 participations
As of the end of 2022/23 season
Qualifications for the main tournament are NOT included, except in 'total participations' and 'qualifications' columns.
Total participations - includes unsuccessful participations in qualifications for the main tournament in addition to participations in the main tournament.
Wins/Defeats after penalty shootout counted as draws.
SF/F4 appearances in brackets denote finishes in the top 4 (out of total) when group stage was played to determine the winner.
Season 2019/20 is ONLY included in participations column, because teams didn't play equal amount of games in the group stage.
Euroleague and LEN Champions League Final4, Final6, Final8
The history of the LEN Champions League (Euroleague) Final Four system, which was permanently introduced in the 1996–97 season.
By season
Final4
Final6
Final8
Countries
Only on three occasions has the final of the tournament involved two teams from the same country:
1971 Yugoslavia: Partizan vs HAVK Mladost 4–4
1993 Croatia: Jadran Split vs HAVK Mladost 13–12 (7–8, 6–4)
1998 Italy: Posillipo vs Pescara 8–6
The country providing the highest number of wins is Yugoslavia with 13 victories, shared by two teams, Partizan (6), HAVK Mladost (6) and Jug Dubrovnik (1)
Country representation in the main tournament
Qualifications not included.
Notes
References
External links
http://www.len.eu
https://web.archive.org/web/20150513034438/http://www.len.eu/Disciplines/water-polo/clubs-pages/champions-league.aspx
+
LEN Champions League |
https://en.wikipedia.org/wiki/Runcitruncated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the runcitruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
Demitesseractic honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x3o3x *b3x4x, x4x3o3x4o - potatit - O95
Honeycombs (geometry)
5-polytopes
Truncated tilings |
https://en.wikipedia.org/wiki/Steritruncated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the steritruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
Demitesseractic honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x4x3o3o4x - capotat - O96
Honeycombs (geometry)
5-polytopes
Truncated tilings |
https://en.wikipedia.org/wiki/Runcicantitruncated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the runcicantitruncated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
Demitesseractic honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x3x3x *b3x4x, x4x3x3x4o - gippittit - O100
Honeycombs (geometry)
5-polytopes
Truncated tilings |
https://en.wikipedia.org/wiki/Runcicantellated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the runcicantellated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
Demitesseractic honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
Notes
References
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p318
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x3x3x *b3o4x, x4o3x3x4o - prittit - O97
Honeycombs (geometry)
5-polytopes
Truncated tilings |
https://en.wikipedia.org/wiki/Stericantitruncated%20tesseractic%20honeycomb | In four-dimensional Euclidean geometry, the stericantitruncated tesseractic honeycomb is a uniform space-filling honeycomb. It is composed of runcitruncated 16-cell, cantitruncated tesseract, rhombicuboctahedral prism, truncated cuboctahedral prism, and 4-8 duoprism facets, arranged around an irregular 5-cell vertex figure.
Related honeycombs
See also
Regular and uniform honeycombs in 4-space:
Tesseractic honeycomb
16-cell honeycomb
24-cell honeycomb
Truncated 24-cell honeycomb
Snub 24-cell honeycomb
5-cell honeycomb
Truncated 5-cell honeycomb
Omnitruncated 5-cell honeycomb
References
Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, p. 296, Table II: Regular honeycombs
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
x4x3x3o4x - gicartit - O101
5-polytopes
Honeycombs (geometry)
Truncated tilings |
https://en.wikipedia.org/wiki/Ashot%20Petrosian | Ashot Vezirovich Petrosian (; June 2, 1930 – February 23, 1998) was a Soviet Armenian mathematician. He completed his PhD in Computational Mathematics in 1964 under the supervision of Julius Anatolyevich Schrader. He was a founding member of the Mergelyan Institute of Mathematical Machines and the Computing Center of the Armenian National Academy of Sciences. He also contributed to the development of several generations of advanced digital computer systems in Armenia, including the Nairi (computer) and ES EVM.
Biography
Ashot V. Petrosian was born in 1930 in a small village near Vardenis, Armenia. He finished high school as a valedictorian in 1949 in Dilijan, Armenia, where his parents settled after escaping the massacre of Armenians in eastern Turkey back in 1915. He went on to study mathematics and graduated with honors from the Yerevan State University, faculty of Physics and Math in 1954. He taught Math courses at the same University until 1955, when he was admitted to Moscow State University to pursue a Ph.D. degree (under supervision of Lazar Lyusternik).
Upon completion of his studies he was offered a position at the Steklov Institute of Mathematics, however he decided to return to his native country of Armenia. In 1957 he was appointed to serve as a Chief Engineer and then as a Director of Mathematical Division at the Yerevan Computer Research and Development Institute (YCRDI, known as Mergelyan Institute). During his tenure at the YCRDI, the institute became one of the largest producers of computer equipment in the former USSR. He also worked as the Vice-Principal (1963–65) and Principal (1965–70) of the Institute for Informatics and Automation Problems (IIAP), formerly known as the Computing Center of the Armenian National Academy of Sciences. During his scientific career, Prof. Petrosian taught various mathematics courses at the Yerevan State University (1957–78) and at the Yerevan Polytechnic Institute (1978–86). He has authored several textbooks, patents, and monographs in the areas of computational mathematics, algorithmic information theory, automata and discrete mathematics. He has edited five volumes of the Proceedings of the Computing Center of the Armenian National Academy of Sciences and served as a Ph.D. adviser to over 20 post-graduate students, mainly in the Graph Theory field.
Selected publications
References
1930 births
1998 deaths
20th-century Armenian mathematicians
Moscow State University alumni
Academic staff of Moscow State University
Soviet mathematicians |
https://en.wikipedia.org/wiki/List%20of%20European%20Cup%2C%20Euroleague%20and%20LEN%20Champions%20League%20winning%20players |
See also
LEN Champions League
European Cup, Euroleague and LEN Champions League records and statistics
References
External links
LEN Champions League
+
LEN Champions League
European |
https://en.wikipedia.org/wiki/Sebastian%20Rudol | Sebastian Rudol (born 21 February 1995) is a Polish professional footballer who plays as a centre-back for Motor Lublin.
Career statistics
Club
References
External links
1995 births
Living people
Sportspeople from Koszalin
Footballers from West Pomeranian Voivodeship
Polish men's footballers
Polish expatriate men's footballers
Poland men's youth international footballers
Poland men's under-21 international footballers
Men's association football defenders
Pogoń Szczecin players
Sepsi OSK Sfântu Gheorghe players
Widzew Łódź players
Sandecja Nowy Sącz players
Motor Lublin players
Ekstraklasa players
I liga players
II liga players
Liga I players
Expatriate men's footballers in Romania
Polish expatriate sportspeople in Romania |
https://en.wikipedia.org/wiki/Mateusz%20Lewandowski | Mateusz Lewandowski (born 18 March 1993) is a Polish former professional footballer. Playing mostly as a left-back throughout his career, he was also deployed in a midfielder role.
Career statistics
Club
Honours
Lechia Gdańsk
Polish Cup: 2018–19
References
External links
1993 births
Living people
Polish men's footballers
Poland men's under-21 international footballers
Poland men's youth international footballers
Polish expatriate men's footballers
Men's association football midfielders
Wisła Płock players
Pogoń Szczecin players
Virtus Entella players
Śląsk Wrocław players
Lechia Gdańsk players
Radomiak Radom players
Ekstraklasa players
I liga players
IV liga players
Serie B players
Expatriate men's footballers in Italy
Polish expatriate sportspeople in Italy
Sportspeople from Płock
Footballers from Masovian Voivodeship |
https://en.wikipedia.org/wiki/L%20series | L series may refer to:
L-series trains in China
Saturn L series – sedans and station wagons
L-function
Honda L engine
Nissan L engine
Dirichlet L-function - mathematical functions in number theory
Rover L-series engine
Ford L series – trucks
Canon L lens
International Harvester L series – trucks
Lincoln L series – 1920 luxury cars
Cummins L-series engine
ThinkPad L series – laptop computers
Mercedes-Benz L-series truck
Rolls-Royce–Bentley L-series V8 engine
Sony Vaio L series – desktop computers
Subaru Leone
System Sensor L-Series fire alarm notification appliances
Artin L-function
QI (L series), the twelfth series of quiz show QI
See also
K series (disambiguation)
M series (disambiguation)
1 series (disambiguation) |
https://en.wikipedia.org/wiki/List%20of%20Carolina%20Panthers%20records%20and%20statistics | The Carolina Panthers are an American professional football club based in Charlotte, North Carolina and representing the Carolinas. The team, which plays in the South division of the National Football Conference (NFC) of the National Football League (NFL), began play in 1995 as an expansion team. From 1995-2001, the team was a member of the West division of the NFC.
This list encompasses the major honors won by the Carolina Panthers as well as records set by the team, its coaches, and its players. Attendance records at Bank of America Stadium, the team's home stadium since 1996, are also included in this list. All records are accurate as of the end of the 2017 season.
Honors
NFC championship games
Winners (2): 2003, 2015
Losers (2): 1996, 2005
Division championships
Winners (6): 1996, 2003, 2008, 2013, 2014, 2015
Runners-up (6): 1997, 1999, 2005, 2006, 2007, 2012
Playoff appearances
Appearances (8): 1996, 2003, 2005, 2008, 2013, 2014, 2015, 2017
Retired numbers
Player records
Top scorers (season)
Top scorers (career)
Passing (season)
Passing (career)
Rushing (season)
Rushing (career)
Receiving (season)
Receiving (career)
Sacks (season)
Sacks (career)
Interceptions (season)
Interceptions (career)
Single-game records
Most passing yards in a game: 432 (Cam Newton, September 18, 2011 vs. Green Bay Packers)
Most rushing yards in a game: 210 (DeAngelo Williams, December 30, 2012 at New Orleans Saints)
Most receiving yards in a game: 218 (Steve Smith, January 15, 2006 at Chicago Bears)
Coaching records
First head coach: Dom Capers (1995-98)
Longest-serving head coach: John Fox (2002-2010)
Most regular season games as head coach: John Fox - 144 Games
Most regular season wins for a head coach: Ron Rivera - 76 Wins
Best regular season winning % for a head coach: Ron Rivera - .546
Most playoff appearances as head coach: Ron Rivera - 4 Appearances
Most playoff games as head coach: John Fox - 8 Games
Most playoff wins for a head coach: John Fox - 5 Wins
Best playoff winning % for a head coach: John Fox - .625
Team records
Overall
Games
First game: 20-14 win over Jacksonville (July 29, 1995; preseason, Pro Football Hall of Fame Game)
First regular-season game: 23-20 OT loss to Atlanta (September 3, 1995)
First playoff game: 26-17 win over Dallas (January 5, 1997)
First Super Bowl: 32-29 loss to New England (February 1, 2004; Super Bowl XXXVIII)
Record results
Record win: 38-0 vs. Atlanta (December 13, 2015)
Record regular-season win: 38-0 vs. Atlanta (December 13, 2015)
Record playoff win: 23-0 at New York Giants (January 8, 2006)
Record loss: 9-52 at Oakland (December 24, 2000)
Record regular-season loss: 9-52 at Oakland (December 24, 2000)
Record playoff loss: 14-34 at Seattle (January 22, 2006)
Streaks
Longest winning streak (within one season): 14 (2015)
Longest winning streak (excluding playoffs): 17 (2014 - 2015)
Longest winning streak (Start of season): 14 (2015)
Longest losing streak (regular season): 15 (2001)
Longest losing s |
https://en.wikipedia.org/wiki/Binge-watching | Binge-watching (also called binge-viewing) is the practice of watching entertainment or informational content for a prolonged time span, usually a single television show.
Statistics
Binge-watching overlaps with marathon viewing which places more emphasis on stamina and less on self-indulgence. In a survey conducted by Netflix in February 2014, 73% of people define binge-watching as "watching between 2–6 episodes of the same TV show in one sitting". Some researchers have argued that binge-watching should be defined based on the context and the actual content of TV show. Others suggested that what is normally called binge-watching in fact refers to more than one type of TV viewing experience. They proposed that the notion of binge-watching should be expanded to include both the prolonged sit (watching 3 or more episodes in a row, in one sitting) and the accelerated consumption of an entire season (or seasons) of a show, one episode at a time, over several days.
Binge-watching as an observed cultural phenomenon has become popular with the rise of video streaming services in the 2006–2007 time frame, such as Netflix, Amazon Prime Video, and Hulu through which the viewer can watch television shows and movies on-demand. For example, 61% of the Netflix survey participants said they binge-watch regularly. Recent research based on video-on-demand data from major US video streaming providers shows that over 64% of the customers binged-watched once during a year.
History
The first uses of “binge” in reference to television appeared in Variety under the byline of TV industry reporter George Rosen, in 1948, according to archival research by media scholar Emil Steiner. The term “TV binge” first appeared in a U.S. newspaper on July 27, 1952, in the Atlanta Journal-Constitution. Sports editor Ed Danforth used the term to describe a Bob Hope–Bing Crosby telethon to raise money for the U.S. Olympic team. While the term "TV marathon" was used frequently in the 1950s, "TV binge" rarely appeared in English language periodicals from 1952-1986 and was most commonly used as a side effect of technological improvements in broadcast television around multi-game sporting events such as the NCAA Division I men's basketball tournament, the Olympics, and the World Cup. An October 1970 Vogue trendspotting feature described how people were talking about “the television binge of sports with more networks finding live action healthier than canned plots.” The first printed usage of the term "binge viewing" appeared in a December, 1986 Philadelphia Inquirer last-minute Christmas list by TV Critic Andy Wickstrom who suggested Scotch tape to mend worn VCR tape if "you're a confirmed weekday time-shifter, saving up the soap operas for weekend binge viewing." This first use of "binge viewing" as a gerund predated "binge-watching" uses by nearly a decade. The first known usage of binge-watching as an active verb is credited to GregSerl, an X-Files Usenet newsgroup commenter. On Dece |
https://en.wikipedia.org/wiki/Mehrdad%20Bayrami | Mehrdad Bayrami (, September 21, 1990 in Ardabil, Iran) an Iranian professional football player who plays for Padideh in the Persian Gulf Pro League.
Club career
Club career statistics
Assist Goals
References
"مهرداد بایرامی" به آلومینیوم اراک پیوست Retaved in Persian www.tasnimnews.com خبرگزاری تسنیم
مهرداد بایرامی راهی آلومینیوم اراک شد Retaved in Persian www.isna.ir خبرگزاری ایسنا
3. مهرداد بایرامی به نساجی مازندران پیوست Retaved in Persian www.farsnews.com خبرگزاری فارس
4. بایرامی: انتظار کسب سهمیه از پدیده منطقی نبود/ کار کردن با رحمتی راحت است Retaved in Persian www.tasnimnews.com خبرگزاری تسنیم
5. بایرامی و گلزنی به تیم سابق؛ چند متر فاصله بود (عکس Retaved in Persian www.varzesh3.com ورزش 3
6. مهرداد بایرامی گربه سیاه پرسپولیس Retaved in Persian www.ilna.news خبرگزاری ایلنا
7. Biography Mehrdad Bayrami Retaved in Persian بیوگرافی مهرداد بایرامی
External links
Mehrdad Bayrami at PersianLeague.com
Mehrdad Bayrami at metafootball
Iranian men's footballers
1990 births
Sportspeople from Ardabil
Living people
Machine Sazi F.C. players
Gostaresh Foulad F.C. players
Tractor S.C. players
Foolad F.C. players
Persian Gulf Pro League players
Azadegan League players
Men's association football forwards
Gol Gohar Sirjan F.C. players |
https://en.wikipedia.org/wiki/Instat | Instat may refer to:
InStat, sports performance analysis company.
Institute of Statistics (Albania), the statistical agency. |
https://en.wikipedia.org/wiki/Trees%20Dream%20in%20Algebra | Trees Dream in Algebra is the first studio album from Irish alternative-rock group Codes.
Track listing
Peak positions
External links
Codes' official site
2009 debut albums
Codes (band) albums |
https://en.wikipedia.org/wiki/Hyperharmonic%20number | In mathematics, the n-th hyperharmonic number of order r, denoted by , is recursively defined by the relations:
and
In particular, is the n-th harmonic number.
The hyperharmonic numbers were discussed by J. H. Conway and R. K. Guy in their 1995 book The Book of Numbers.
Identities involving hyperharmonic numbers
By definition, the hyperharmonic numbers satisfy the recurrence relation
In place of the recurrences, there is a more effective formula to calculate these numbers:
The hyperharmonic numbers have a strong relation to combinatorics of permutations. The generalization of the identity
reads as
where is an r-Stirling number of the first kind.
Asymptotics
The above expression with binomial coefficients easily gives that for all fixed order r>=2 we have.
that is, the quotient of the left and right hand side tends to 1 as n tends to infinity.
An immediate consequence is that
when m>r.
Generating function and infinite series
The generating function of the hyperharmonic numbers is
The exponential generating function is much more harder to deduce. One has that for all r=1,2,...
where 2F2 is a hypergeometric function. The r=1 case for the harmonic numbers is a classical result, the general one was proved in 2009 by I. Mező and A. Dil.
The next relation connects the hyperharmonic numbers to the Hurwitz zeta function:
Integer hyperharmonic numbers
It is known, that the harmonic numbers are never integers except the case n=1. The same question can be posed with respect to the hyperharmonic numbers: are there integer hyperharmonic numbers? István Mező proved that if r=2 or r=3, these numbers are never integers except the trivial case when n=1. He conjectured that this is always the case, namely, the hyperharmonic numbers of order r are never integers except when n=1. This conjecture was justified for a class of parameters by R. Amrane and H. Belbachir. Especially, these authors proved that is not integer for all r<26 and n=2,3,... Extension to high orders was made by Göral and Sertbaş. These authors have also shown that is never integer when n is even or a prime power, or r is odd.
Another result is the following. Let be the number of non-integer hyperharmonic numbers such that . Then, assuming the Cramér's conjecture,
Note that the number of integer lattice points in is , which shows that most of the hyperharmonic numbers cannot be integer.
The problem was finally settled by D. C. Sertbaş who found that there are infinitely many hyperharmonic integers, albeit they are quite huge. The smallest hyperharmonic number which is an integer found so far is
References
Number theory |
https://en.wikipedia.org/wiki/Michiel%20Hazewinkel | Michiel Hazewinkel (born 22 June 1943) is a Dutch mathematician, and Emeritus Professor of Mathematics at the Centre for Mathematics and Computer Science and the University of Amsterdam, particularly known for his 1978 book Formal groups and applications and as editor of the Encyclopedia of Mathematics.
Biography
Born in Amsterdam to Jan Hazewinkel and Geertrude Hendrika Werner, Hazewinkel studied at the University of Amsterdam. He received his BA in mathematics and physics in 1963, his MA in mathematics with a minor in philosophy in 1965 and his PhD in 1969 under supervision of Frans Oort and Albert Menalda for the thesis "Maximal Abelian Extensions of Local Fields".
After graduation Hazewinkel started his academic career as assistant professor at the University of Amsterdam in 1969. In 1970 he became associate professor at the Erasmus University Rotterdam, where in 1972 he was appointed professor of mathematics at the Econometric Institute. Here he was thesis advisor of Roelof Stroeker (1975), M. van de Vel (1975), Jo Ritzen (1977), and Gerard van der Hoek (1980). From 1973 to 1975 he was also Professor at the Universitaire Instelling Antwerpen, where Marcel van de Vel was his PhD student.
From 1982 to 1985 he was appointed part-time professor extraordinarius in mathematics at the Erasmus Universiteit Rotterdam, and part-time head of the Department of Pure Mathematics at the Centre for Mathematics and Computer (CWI) in Amsterdam. In 1985 he was also appointed professor extraordinarius in mathematics at the University of Utrecht, where he supervised the promotion of Frank Kouwenhoven (1986), Huib-Jan Imbens (1989), J. Scholma (1990) and F. Wainschtein (1992). At the Centre for Mathematics and Computer CWI in Amsterdam in 1988 he became professor of mathematics and head of the Department of Algebra, Analysis and Geometry until his retirement in 2008.
Hazewinkel has been managing editor for journals as Nieuw Archief voor Wiskunde since 1977; for Acta Applicandae Mathematicae since its foundation in 1983; and associate editor for Chaos, Solitons & Fractals since 1991. He was managing editor for the book series Mathematics and Its Applications for Kluwer Academic Publishers in 1977; Mathematics and Geophysics for Reidel Publishing in 1981; Encyclopedia of Mathematics for Kluwer Academic Publishers from 1987 to 1994; and Handbook of Algebra in 6 volumes for Elsevier Science Publishers from 1995 to 2009.
Hazewinkel was member of 15 professional societies in the field of mathematics, and participated in numerous administrative tasks in institutes, program committee, steering committee, consortiums, councils and boards. In 1994 Hazewinkel was elected member of the International Academy of Computer Sciences and Systems.
Publications
Hazewinkel has authored and edited several books, and numerous articles. Books, selection :
1970. Géométrie algébrique-généralités-groupes commutatifs. With Michel Demazure and Pierre Gabriel. Masson & Cie.
1976. On |
https://en.wikipedia.org/wiki/Proceedings%20-%20Mathematical%20Sciences | Proceedings - Mathematical Sciences is a peer-reviewed scientific journal that covers current research in mathematics. Papers in pure and applied areas are also published on the basis of the mathematical content. It is published by Springer Science+Business Media on behalf of the Indian Academy of Sciences. The editor-in-chief is Parameswaran Sankaran (Chennai Mathematical Institute).
History
The journal was originally part of the Proceedings of the Indian Academy of Sciences. This journal was established in 1934, but in 1978 it was split into three different journals: Proceedings of the Indian Academy of Sciences – Mathematical Sciences, Journal of Earth System Science, and Journal of Chemical Sciences, all of them continuing as "volume 87". The journal was later renamed as Proceedings - Mathematical Sciences.
Abstracting and indexing
The journal is abstracted and indexed in:
According to the Journal Citation Reports, the journal has a 2019 impact factor of 0.272.
References
External links
Springer Science+Business Media academic journals
Quarterly journals
Academic journals established in 1978
English-language journals
Mathematics journals |
https://en.wikipedia.org/wiki/Department%20of%20Statistics%20%28Bermuda%29 | The Bermuda Department of Statistics, subject to the Bermuda Statistics Act of 2002 as further amended, reports to the head of Cabinet Office. It was created mainly for the collection, compilation, analysis and publication of statistical information and so facilitate the development of a statistical system for Bermuda which is also a component of the regional statistical systems of CARICOM, together with other member countries of this regional institution.
Mission
In accordance with the provisions of the Statistics Act
to collect, compile, collate, analyse, abstract and publish statistical information relating to the commercial, industrial, social, financial, economic, and general activities and conditions of the people of Bermuda;
to take any census of population and housing in Bermuda;
to collaborate with Ministries, other Government Departments and public authorities in the collection, compilation, collation and publication of statistical information, including statistics derived from the activities of those Ministries, departments or public authorities;
to promote the avoidance of duplication in the information collected by Ministries, other Government Departments and public authorities;
and generally to promote, organise and develop an integrated scheme of economic and social statistics relating to Bermuda
Organisation
The department is organised in five work divisions:
Administration Division
Business Statistics Division
Social Statistics Division
Economic Statistics Division
Census and Survey Research Statistics Division
History
{| class="wikitable"
|+ Previous heads of the Department of statistics
! width=300 | Name
! width=100
Valerie Robinson James
| - Qt2 2014
|}
See also
Sub-national autonomous statistical services
United Nations Statistics Division
References
External links
Cabinet Office
Bermuda Department of Statistics
CARICOM Statistics
Official statistics
Bermuda |
https://en.wikipedia.org/wiki/Harm%20Bart | Harm Bart (born 5 August 1942) is a Dutch mathematician, economist, and Professor of Mathematics at the Erasmus University Rotterdam, particularly known for his work on "factorization problems for matrix and operator functions."
Biography
Born in Enkhuizen, Bart started his study at the Vrije Universiteit in Amsterdam in 1960. Here he received his BA in Mathematics and Astronomy in 1964, his MA in Mathematics with a minor in Dogmatics in 1969, and his PhD in 1973 with the thesis "Meromorphic operator valued functions" under supervision of Rien Kaashoek.
After graduation Bart started his academic career at the Faculty of Mathematics at the Vrije Universiteit as Assistant Professor in 1973, and Associate Professor at the Faculty of Mathematics and Computer Science in 1977. In 1982 he was appointed Professor at the Faculty of Mathematics and Computer Science of the Eindhoven University of Technology. In 1984 he became Extraordinary Professor of Mathematics and since 1985 Professor of Mathematics at the Erasmus School of Economics of the Erasmus University Rotterdam. From 1987 to 1992 he was Co-Director of the Econometric Institute, first with Teun Kloek and later with Ton Vorst. From 1996 to 2000 he was also Dean of the Erasmus School of Economics.
In 2004 Bart was decorated as Officer in the Order of Orange-Nassau. He has been elected Fellow of the Stieltjes Institute for Mathematics, and Fellow of the Tinbergen Institute.
Publications
Bart authored and co-authored three books and over fifty articles.
1973. Meromorphic Operator Valued Functions. Vrije Universiteit, Amsterdam
1979. Minimal Factorization of Matrix and Operator Functions, Operator Theory: Advances and Applications, Vol. 1 With I. Gohberg and M.A. Kaashoek. Birkhauser Verlag
2008. Factorization of matrix and operator functions: The State Space Method (Operator Theory: Advances and Applications / Linear Operators and Linear Systems). With Israel Gohberg, Marinus A. Kaashoek and André C.M. Ran. Vol. 178. Springer.
Articles, a selection:
Bart, Harm, and Seymour Goldberg. "Characterizations of almost periodic strongly continuous groups and semigroups." Mathematische Annalen 236.2 (1978): 105–116.
Bart, H., Gohberg, I., Kaashoek, M. A., & Van Dooren, P. (1980). Factorizations of transfer functions. SIAM Journal on Control and Optimization, 18(6), 675–696.
Bart, Harm, and H. Hoogland. "Complementary triangular forms of pairs of matrices, realizations with prescribed main matrices, and complete factorization of rational matrix functions." Linear Algebra and its Applications 103 (1988): 193–228.
References
External links
Harm Bart Curriculum Vitae at few.eur.nl
1942 births
Living people
Dutch economists
Dutch mathematicians
Vrije Universiteit Amsterdam alumni
Academic staff of Vrije Universiteit Amsterdam
Academic staff of the Eindhoven University of Technology
Academic staff of Erasmus University Rotterdam
People from Enkhuizen |
https://en.wikipedia.org/wiki/Mars%20Cramer | Jan Salomon (Mars) Cramer (28 April 1928 – 15 March 2014) was a Dutch economist, Professor of Statistics and Econometrics at the University of Amsterdam, known for his work of empirical econometrics.
Biography
Born in The Hague, Mars Cramer was the son of biologist and Professor P. J. S. Cramer (1879–1952) He received his PhD in Mathematics in 1961 at the University of Amsterdam with a thesis entitled "A Statistical Model of the Ownership of Major Consumer Durables with an Application to some Findings of the 1953 Oxford Savings Survey" under supervision of .
In the 1950s Cramer started his career as researcher for the Bureau for Economic Policy Analysis. After graduation in 1961 at the University of Amsterdam he was appointed Professor of Econometrics, a newly established chair. He was Director of the SEO Economic Research from 1985 to 1992 as successor of Wim Driehuis. Among his doctoral students were Arnold Merkies (1972), Geert Ridder (1987) and Mirjam van Praag (2005).
In 1980 Cramer was elected member of the Royal Netherlands Academy of Arts and Sciences, and later Fellow of the Tinbergen Institute. Cramer died on 15 March 2014 in Amsterdam
The University of Amsterdam's Faculty of Economics and Business (2014) recalled that "Mars was known for his originality and his wit. He possessed a genuine academic curiosity and a rather characteristic style of writing. For example, his research into the velocity of money led him to study the velocity of particular coins. As a student he served as editor of the literary student periodical Propria Cures, and he continued to intermittently publish short stories and opinion pieces. In 2012, the Washington Post published his moving account of his wife Til’s euthanasia four years earlier." Cramer "continued working on new research projects and contributing to the supervision of students until the very last day before his passing."
Publications
Cramer authored and co-authored numerous publications in the field of econometrics. Books, a selection:
1958. Economic forecasts and policy. With Henri Theil assisted by J.S. Cramer, H. Moerman, and A. Russchen.
1961. A Statistical Model of the Ownership of Major Consumer Durables with an Application to some Findings of the 1953 Oxford Savings Survey.
1969. Empirical econometrics. Amsterdam : North-Holland Pub. Co.
1991. The logit model: an introduction for economists. London: Edward Arnold.
2003. Logit models from economics and other fields. Cambridge University Press, 2003.
Articles, a selection:
References
External links
In memoriam: Mars Cramer on uva.nl
1928 births
2014 deaths
Dutch economists
Dutch mathematicians
Members of the Royal Netherlands Academy of Arts and Sciences
University of Amsterdam alumni
Academic staff of the University of Amsterdam
Writers from The Hague
Fellows of the Econometric Society |
https://en.wikipedia.org/wiki/Continuum%20percolation%20theory | In mathematics and probability theory, continuum percolation theory is a branch of mathematics that extends discrete percolation theory to continuous space (often Euclidean space ). More specifically, the underlying points of discrete percolation form types of lattices whereas the underlying points of continuum percolation are often randomly positioned in some continuous space and form a type of point process. For each point, a random shape is frequently placed on it and the shapes overlap each with other to form clumps or components. As in discrete percolation, a common research focus of continuum percolation is studying the conditions of occurrence for infinite or giant components. Other shared concepts and analysis techniques exist in these two types of percolation theory as well as the study of random graphs and random geometric graphs.
Continuum percolation arose from an early mathematical model for wireless networks, which, with the rise of several wireless network technologies in recent years, has been generalized and studied in order to determine the theoretical bounds of information capacity and performance in wireless networks. In addition to this setting, continuum percolation has gained application in other disciplines including biology, geology, and physics, such as the study of porous material and semiconductors, while becoming a subject of mathematical interest in its own right.
Early history
In the early 1960s Edgar Gilbert proposed a mathematical model in wireless networks that gave rise to the field of continuum percolation theory, thus generalizing discrete percolation. The underlying points of this model, sometimes known as the Gilbert disk model, were scattered uniformly in the infinite plane according to a homogeneous Poisson process. Gilbert, who had noticed similarities between discrete and continuum percolation, then used concepts and techniques from the probability subject of branching processes to show that a threshold value existed for the infinite or "giant" component.
Definitions and terminology
The exact names, terminology, and definitions of these models may vary slightly depending on the source, which is also reflected in the use of point process notation.
Common models
A number of well-studied models exist in continuum percolation, which are often based on homogeneous Poisson point processes.
Disk model
Consider a collection of points in the plane that form a homogeneous Poisson process with constant (point) density . For each point of the Poisson process (i.e. ), place a disk with its center located at the point . If each disk has a random radius (from a common distribution) that is independent of all the other radii and all the underlying points , then the resulting mathematical structure is known as a random disk model.
Boolean model
Given a random disk model, if the set union of all the disks is taken, then the resulting structure is known as a Boolean–Poisson model (also known as simply t |
https://en.wikipedia.org/wiki/Supreme%20Prosecutors%20Office | The Supreme Prosecutors Office () is the highest prosecution authority in the Republic of China, commonly known as Taiwan.
Organizational structure
Statistics Office
Accounting Office
Civil Service Ethics Office
Personnel Office
Information Management Office
Prosecutor General
The Prosecutor General of the Supreme Prosecutors Office is the highest ranking member of the prosecution system. The position is appointed by the president, and must be confirmed by the Legislative Yuan. The position carries a term limit of four years, and the appointee cannot serve consecutive terms. Notably, the prosecutor general has the exclusive authority to file extraordinary appeals.
List of prosecutor generals
Huang Shih-ming (- April 2014)
Yen Da-ho (April 2014 - May 2018)
Chiang Hui-min (May 2018 - May 2022)
Xing Tai-Zhao (May 2022 -)
Transportation
The office is accessible within walking distance South of Ximen Station of the Taipei Metro.
See also
History of law in Taiwan
Law of Taiwan
Six Codes
Constitution of the Republic of China
Judicial Yuan
Supreme Court of the Republic of China
High Court (Taiwan)
District Courts (Taiwan)
Ministry of Justice (Taiwan)
Taiwan High Prosecutors Office
List of law schools in Taiwan
Director of Public Prosecutions
Supreme People's Procuratorate
References
External links
1928 establishments in China
Government agencies established in 1928
Law enforcement agencies of Taiwan |
https://en.wikipedia.org/wiki/Stochastic%20geometry%20models%20of%20wireless%20networks | In mathematics and telecommunications, stochastic geometry models of wireless networks refer to mathematical models based on stochastic geometry that are designed to represent aspects of wireless networks. The related research consists of analyzing these models with the aim of better understanding wireless communication networks in order to predict and control various network performance metrics. The models require using techniques from stochastic geometry and related fields including point processes, spatial statistics, geometric probability, percolation theory, as well as methods from more general mathematical disciplines such as geometry, probability theory, stochastic processes, queueing theory, information theory, and Fourier analysis.
In the early 1960s a stochastic geometry model was developed to study wireless networks. This model is considered to be pioneering and the origin of continuum percolation. Network models based on geometric probability were later proposed and used in the late 1970s and continued throughout the 1980s for examining packet radio networks. Later their use increased significantly for studying a number of wireless network technologies including mobile ad hoc networks, sensor networks, vehicular ad hoc networks, cognitive radio networks and several types of cellular networks, such as heterogeneous cellular networks. Key performance and quality of service quantities are often based on concepts from information theory such as the signal-to-interference-plus-noise ratio, which forms the mathematical basis for defining network connectivity and coverage.
The principal idea underlying the research of these stochastic geometry models, also known as random spatial models, is that it is best to assume that the locations of nodes or the network structure and the aforementioned quantities are random in nature due to the size and unpredictability of users in wireless networks. The use of stochastic geometry can then allow for the derivation of closed-form or semi-closed-form expressions for these quantities without resorting to simulation methods or (possibly intractable or inaccurate) deterministic models.
Overview
The discipline of stochastic geometry entails the mathematical study of random objects defined on some (often Euclidean) space. In the context of wireless networks, the random objects are usually simple points (which may represent the locations of network nodes such as receivers and transmitters) or shapes (for example, the coverage area of a transmitter) and the Euclidean space is either 3-dimensional, or more often, the (2-dimensional) plane, which represents a geographical region. In wireless networks (for example, cellular networks) the underlying geometry (the relative locations of nodes) plays a fundamental role due to the interference of other transmitters, whereas in wired networks (for example, the Internet) the underlying geometry is less important.
Channels in a wireless network
A wireless network |
https://en.wikipedia.org/wiki/Robert%20S.%20Doran | Robert Stuart Doran (born December 21, 1937) is an American mathematician. He held the John William and Helen Stubbs Potter Professorship in mathematics at Texas Christian University (TCU) from 1995 until his retirement in 2016. Doran served as chair of the TCU mathematics department for 21 years. He has also held visiting appointments at the Massachusetts Institute of Technology, the University of Oxford, and the Institute for Advanced Study. He was elected to the board of trustees of the Association of Members of the Institute for Advanced Study, serving as president of the organization for 10 years. He has been an editor for the Encyclopedia of Mathematics and its Applications, Cambridge University Press, a position he has held since 1988. Doran is known for his research-level books, his award-winning teaching, and for his solution to a long-standing open problem due to Irving Kaplansky on a symmetric *-algebra.
Personal background
Robert Stuart Doran was born on December 21, 1937 in Winthrop, Iowa. In 1959, he married Shirley Ann Lange. They have two sons, Bruce and Brad.
Military service
In 1956, Doran served in the 82nd Airborne Division at Fort Bragg, North Carolina. He served as a Special Forces Instructor at the US Army Jungle Survival Center at Fort Sherman, Colón, Panama. He left active duty in the military in 1958 and he served in the US Army reserves until 1962 when he was honorably discharged.
Educational background
Doran studied mathematics at the University of Iowa from 1959 until 1964, earning a Bachelor's degree and a Master of Science degree. He received a Ph.D in mathematics from the University of Washington in 1968, under the direction of J. M. G. Fell and Ramesh Gangolli. His doctoral dissertation, titled Representations of C*-algebras by Uniform CT-bundles and Operator Theory, dealt with topological representations in spaces of cross-sections of fiber bundles of a non-commutative C*-algebra. This work was motivated in part by the classical Gelfand–Naimark theorem for C*-algebras and by the work of M. Takesaki and J. Tomiyama.
Professional background
Doran held the John William and Helen Stubbs Potter Professor of Mathematics at Texas Christian University from 1995 to 2016. He was faculty sponsor of the TCU chapter of Campus Crusade for Christ (Cru) for 43 years, and he was the founding faculty sponsor in 1989 of the TCU chapter of Brothers Under Christ (Beta Upsilon Chi).
He has held visiting appointments at the Massachusetts Institute of Technology (1980), Oxford University in England (1988), and the Institute for Advanced Study (1981). His areas of research involve representation theory, C*-algebra characterizations, the notion of an approximate identity in a Banach algebra, and Banach bundle theory.
Doran taught at both the undergraduate and graduate levels. In 1988 he published an article titled "A care package for undergraduate mathematics students" that outlined his teaching methods. He has received nation |
https://en.wikipedia.org/wiki/Chiral%20homology | In mathematics, chiral homology, introduced by Alexander Beilinson and Vladimir Drinfeld, is, in their words, "a “quantum” version of (the algebra of functions on) the space of global horizontal sections of an affine -scheme (i.e., the space of global solutions of a system of non-linear differential equations)."
Jacob Lurie's topological chiral homology gives an analog for manifolds.
See also
Ran space
Chiral Lie algebra
Factorization homology
References
Homological algebra |
https://en.wikipedia.org/wiki/Jos%C3%A9%20Luis%20Gonz%C3%A1lez%20Velarde | José Luis González Velarde is a professor and researcher with the Tec de Monterrey, Monterrey Campus.
González Velarde’s educational background consists of a bachelor's degree in mathematics from Tec de Monterrey, Campus Monterrey (1971), a master's degree in mathematics from the Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (1973) (earned through a scholarship obtained from CONACYT), a master's degree in industrial engineering and operations research from the University of California, Berkeley (1978) and a doctorate in industrial engineering and operations research from the University of Texas, Austin (1990).
González Velarde primarily considers himself a researcher and even performs this work on his own time, rarely taking vacations. He has worked in this capacity with the Center for Quality and Manufacturing, School of Engineering at Campus Monterrey since 1990 and with the Cátedra de Investigación Tecnológico de Monterrey en Cadenas de Suministro since 2003. His specialties include computational optimization and algorithm design for logistics and manufacturing. He has participated in over 15,000 peer-reviewed publications in Spanish and English and has had his work published in journals such as IIE Transactions, Journal of Heuristics, Annals of OR, Computers and OR, Journal of Intelligent Manufacturing, EJOR, Transportation Science, Journal of the Operational Research Society, and Computers and Industrial Engineering.
However, he began his academic career as a teacher and is still involved in this activity. From 1973 to 1985 he was a professor in mathematics at the Universidad Autónoma de Nuevo León, then worked as an assistant instructor with the Department of Mechanical Engineering of the University of Texas, Austin from 1985 to 1990. Since joining the Tec de Monterrey in 1990, his teaching foci include production, manufacturing and logistics systems, and computational optimization at the graduate level, supervising more than thirty master’s level theses and five doctorate level ones. Since the 1990s, he has also been a visiting professor in institutions such as Universidad del Norte de Barranquilla, the University of Colorado, the University of Texas and the Polytechnic University of Catalonia .
In addition to academic work, González Velardo has also worked on several reorganization and modernization projects such as those with Bancomer, De Acero, and Aeromexico in the 1990s and a project with the state of Nuevo León in 2008.
González Velarde has been noted for his work in Who's Who in Science and Engineering (2003-2004) and has received third place at the Premio Rómulo Garza de la Investigación y el Desarrollo Tecnológico (1993, 2001, 2010) . He also has level II membership in Mexico’s Sistema Nacional de Investigadores.
Recent publications
Hybrid Estimation of Distribution Algorithm for the Quay Crane Scheduling Problem
Co-Autores: Christopher Expósito Izquierdo, Belén Melián Batista, J. Marcos |
https://en.wikipedia.org/wiki/Andor%20Margitics | Andor Margitics (born 3 January 1991) is a Hungarian professional footballer.
Club statistics
Updated to games played as of 15 May 2021.
References
MLSZ
HLSZ
1991 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football defenders
Vác FC players
Fehérvár FC players
Budafoki MTE footballers
Puskás Akadémia FC players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/%C3%81d%C3%A1m%20Hajd%C3%BA | Ádám Hajdú (born 16 January 1993 in Dunaújváros) is a Hungarian professional footballer who plays for Gyirmót.
Club statistics
Updated to games played as of 15 May 2022.
References
External links
Ádám Hajdú at HLSZ
Ádám Hajdú at MLSZ
1993 births
Living people
Sportspeople from Dunaújváros
Footballers from Fejér County
Hungarian men's footballers
Men's association football midfielders
MTK Budapest FC players
Budapest Honvéd FC players
Paksi FC players
Vasas SC players
Gyirmót FC Győr players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Hungarian expatriate men's footballers
Expatriate men's footballers in England
Hungarian expatriate sportspeople in England |
https://en.wikipedia.org/wiki/Tau-leaping | In probability theory, tau-leaping, or τ-leaping, is an approximate method for the simulation of a stochastic system. It is based on the Gillespie algorithm, performing all reactions for an interval of length tau before updating the propensity functions. By updating the rates less often this sometimes allows for more efficient simulation and thus the consideration of larger systems.
Many variants of the basic algorithm have been considered.
Algorithm
The algorithm is analogous to the Euler method for deterministic systems, but instead of making a fixed change
the change is
where is a Poisson distributed random variable with mean .
Given a state with events occurring at rate and with state change vectors (where indexes the state variables, and indexes the events), the method is as follows:
Initialise the model with initial conditions .
Calculate the event rates .
Choose a time step . This may be fixed, or by some algorithm dependent on the various event rates.
For each event generate , which is the number of times each event occurs during the time interval .
Update the state by
where is the change on state variable due to event . At this point it may be necessary to check that no populations have reached unrealistic values (such as a population becoming negative due to the unbounded nature of the Poisson variable ).
Repeat from Step 2 onwards until some desired condition is met (e.g. a particular state variable reaches 0, or time is reached).
Algorithm for efficient step size selection
This algorithm is described by Cao et al. The idea is to bound the relative change in each event rate by a specified tolerance (Cao et al. recommend , although it may depend on model specifics). This is achieved by bounding the relative change in each state variable by , where depends on the rate that changes the most for a given change in . Typically is equal the highest order event rate, but this may be more complex in different situations (especially epidemiological models with non-linear event rates).
This algorithm typically requires computing auxiliary values (where is the number of state variables ), and should only require reusing previously calculated values . An important factor in this since is an integer value, then there is a minimum value by which it can change, preventing the relative change in being bounded by 0, which would result in also tending to 0.
For each state variable , calculate the auxiliary values
For each state variable , determine the highest order event in which it is involved, and obtain
Calculate time step as
This computed is then used in Step 3 of the leaping algorithm.
References
Chemical kinetics
Computational chemistry
Monte Carlo methods
Stochastic simulation |
https://en.wikipedia.org/wiki/Secondary%20School%20Mathematics%20Curriculum%20Improvement%20Study | The Secondary School Mathematics Curriculum Improvement Study (SSMCIS) was the name of an American mathematics education program that stood for both the name of a curriculum and the name of the project that was responsible for developing curriculum materials. It is considered part of the second round of initiatives in the "New Math" movement of the 1960s. The program was led by Howard F. Fehr, a professor at Columbia University Teachers College.
The program's signature goal was to create a unified treatment of mathematics and eliminate the traditional separate per-year studies of algebra, geometry, trigonometry, and so forth, that was typical of American secondary schools. Instead, the treatment unified those branches by studying fundamental concepts such as sets, relations, operations, and mappings, and fundamental structures such as groups, rings, fields, and vector spaces. The SSMCIS program produced six courses' worth of class material, intended for grades 7 through 12, in textbooks called Unified Modern Mathematics. Some 25,000 students took SSMCIS courses nationwide during the late 1960s and early 1970s.
Background
The program was led by Howard F. Fehr, a professor at Columbia University Teachers College who was internationally known and had published numerous mathematics textbooks and hundreds of articles about mathematics teaching. In 1961 he had been the principal author of the 246-page report "New Thinking in School Mathematics", which held that traditional teaching of mathematics approaches did not meet the needs of the new technical society being entered into or of the current language of mathematicians and scientists. Fehr considered the separation of mathematical study into separate years of distinct subjects to be an American failing that followed an educational model two hundred years old.
The new curriculum was inspired by the seminar reports from the Organisation for Economic Co-operation and Development in the early 1960s and by the Cambridge Conference on School Mathematics (1963), which also inspired the Comprehensive School Mathematics Program. There were some interactions among these initiatives in the early stages, and the development of SSMCIS was part of a general wave of cooperation in the mathematics education reform movement between Europe and the U.S.
Curriculum
Work on the SSMCIS program began in 1965 and took place mainly at Teachers College. Fehr was the director of the project from 1965 to 1973. The principal consultants in the initial stages and subsequent yearly planning sessions were Marshall H. Stone of the University of Chicago, Albert W. Tucker of Princeton University, Edgar Lorch of Columbia University, and Meyer Jordan of Brooklyn College. The program was targeted at the junior high and high school level and the 15–20 percent best students in a grade.
Funding for the initiative began with the U.S. Office of Education and covered the development of the first three courses produced; the la |
https://en.wikipedia.org/wiki/Quotient%20space | Quotient space may refer to a quotient set when the sets under consideration are considered as spaces. In particular:
Quotient space (topology), in case of topological spaces
Quotient space (linear algebra), in case of vector spaces
Quotient space of an algebraic stack
Quotient metric space
See also
Quotient object |
https://en.wikipedia.org/wiki/Alfred%20Legoyt | Alfred Legoyt (1812–1885) was a French statistician who organised the census of France in 1856, 1861 and 1866. With his access to vital statistics Legoyt was the most important official statistician of France and was the official delegate to the International Statistical Congresses held in different European cities between 1853 and 1876.
Early career
Legoyt started his career as a clerk in the Ministry of the Interior and went on to be the deputy chief of the ministry's Bureau of Statistics in 1839. In 1833 the Statistique Générale de la France was created as the division of statistics of the Ministry of Commerce. Legoyt replaced Alexandre Moreau De Jonnes as director of the Statistique Générale de la France in 1852. Unlike Moreau de Jonnès Legoyt placed more importance on the practical work of data collection rather than on classification and analysis.
The 1856 Census
When Legoyt became director of SGF he took over the responsibility of organising the census from the bureau of statistics of the Ministry of the Interior and placed it under the stewardship of the SGF. As the Census Commissioner, of the forthcoming quinquennial census of 1856 Legoyt instructed his officials to use the households as the basis for the enumeration and to confine to the recording the occupation of the head of the family. It differed significantly from the 1851 Census in which the profession of all enumerated persons, including family dependents were recorded. In the words of Legoyt,
Legoyt held the position of director of SGF until the fall of the Second Empire in 1870.
He also served as the first permanent secretary of Société de Statistique de Paris from its creation in 1861 throughout the Second Empire.
He received an award from the Alliance Israélite Universelle for his book, De la vitalité de la race juive en Europe (1865).
References
External links
1812 births
1885 deaths
French statisticians |
https://en.wikipedia.org/wiki/List%20of%20AFC%20Wimbledon%20records%20and%20statistics | AFC Wimbledon is an English professional association football club, based at Plough Lane in Wimbledon, Greater London. The club was formed on 30 May 2002 by supporters of Wimbledon Football Club, led by Kris Stewart, Marc Jones and Trevor Williams who strongly opposed the decision of an independent commission appointed by the FA to allow the relocation of Wimbledon F.C. to Milton Keynes, to be subsequently rebranded as MK Dons.
The club was accepted into the Combined Counties League for the 2002–03 season and proceeded to rise through the non-League system, winning five promotions in nine seasons to return to the Football League less than a decade after the original Wimbledon Football Club had still been competing in the top flight of English football. AFC Wimbledon's average home attendance at league fixtures for their first season exceeded 3,000 – higher than the average attendance in the same season of Wimbledon F.C., who were still playing in the First Division (now the Football League Championship).
This list encompasses the major honours won by AFC Wimbledon and records set by the club, its managers and its players. The player records section includes details of the club's leading goalscorers and those who have made the most competitive first-team appearances. The club's attendance records are also included in the list.
As of 2020, AFC Wimbledon still hold the record for the longest run of unbeaten league games at any level of senior football in the United Kingdom. The club remained unbeaten for 78 league matches between 26 February 2003 (a 3–1 away win at Chessington United) and 27 November 2004 (a 2–1 away win at Bashley).
The club's record appearance maker is defender Barry Fuller, who made 233 appearances in all competitions between 2013 and 2018 and the club's record goalscorer is Kevin Cooper, who scored 104 goals in 99 appearances in all competitions between 2002 and 2004.
Honours
Following the move of Wimbledon F.C. to Milton Keynes and its rebranding as Milton Keynes Dons, there was much debate over the rightful home of all the honours won by Wimbledon F.C.. Former supporters argued that the trophies won by Wimbledon F.C. rightfully belong to the community of Wimbledon and should be returned to the local area. AFC Wimbledon believe that the honours of Wimbledon F.C. belong to the fans, as illustrated by the following statement on the club's official website:
In October 2006, an agreement was reached between Milton Keynes Dons F.C., the MK Dons Supporters Association, the Wimbledon Independent Supporters Association and the Football Supporters Federation. The replica of the FA Cup plus all club patrimony gathered under the name of Wimbledon F.C. would be returned to the London Borough of Merton. Ownership of trademarks and website domain names related to Wimbledon F.C. would also be transferred to the Borough. It was also agreed that any reference made to Milton Keynes Dons F.C. should refer only to events after 7 August 2004, |
https://en.wikipedia.org/wiki/KK%20Partizan%20accomplishments%20and%20records | This page details the all-time statistics, records, and other achievements pertaining to the KK Partizan. Partizan is the professional basketball club based in Belgrade, Serbia. The club competes in the Basketball League of Serbia, Adriatic League and Euroleague. Partizan has won as many as 49 trophies, and it is most successful basketball club in Serbia.
Honours
Total titles: 49
Shared record
Individual awards
International record
Road to the 1992 Euroleague victory
Domestic record
Regional record
Adriatic League
The biggest wins in Adriatic League
Home wins
Away wins
Positions by year
Longest winning streak
16 games in the 2022–23 season.
Longest losing streak
5 games in the 2020–21 season.
Most Won Games in a Season
24 out of 26 games for the 2007–08 season.
Most Lost Games in a Season
Lost 14 out of 26 games for the 2015–16 season.
Player records
*Players in bold are still active
Records in EuroLeague
NBA
Players in the NBA draft
Moved to an NBA team
Signed from an NBA team
External links
Official website
KK Partizan
P |
https://en.wikipedia.org/wiki/Feature%20geometry | Feature geometry is a phonological theory which represents distinctive features as a structured hierarchy rather than a matrix or a set. Feature geometry grew out of autosegmental phonology, which emphasizes the autonomous nature of distinctive features and the non-uniform relationships among them. Feature geometry recognizes that some sets of features often pattern together in phonological and phonotactic generalizations, while others rarely interact. Feature geometry thus formally encodes groups of features under nodes in a tree: features that commonly pattern together are said to share a parent node, and operations on this set can be encoded as operation on the parent node.
One node in feature geometries is the Laryngeal node. The Laryngeal node is an organizing node that dominates the features of the larynx, usually taken to be [voice], [constricted glottis], and [spread glottis]. It is common for these three features to pattern together in the phonology of the world's languages to the exclusion of every other feature, and in feature geometry, this follows from the tree representation. Similarly, feature geometries generally include a Place node that is the dominant node of the place features, which also often pattern together. Feature geometry is easily compatible with theories of underspecification and can represent incomplete segments by missing nodes.
The Root node is the topmost node of the feature tree and works as the formal organizing unit of the segment, and in some frameworks encodes the major class features such as [consonantal], [sonorant], and [approximant]. Some features such as [nasal] and [lateral] are sometimes dependent of the root node, or sometimes of a Supralaryngeal node along with Place. Other features such as [anterior] and [distributed] are usually dependent from the Coronal place feature.
The first formal model of feature geometry was introduced in print by George N. Clements in 1985, drawing on unpublished work by K.P. Mohanan and Joan Mascaró. Another precursor to feature geometry was proposed by Roger Lass in 1976, in which he proposed a laryngeal feature submatrix within a distinctive feature matrix. Other important models have been proposed by Elizabeth Sagey (1986), John J. McCarthy (1988), and Clements & Hume (1995). Models vary widely in the number of the hierarchical nodes and in how consonant and vowel features are treated.
Feature geometry has attracted formal and conceptual criticism. In 2003, Charles Reiss argued that feature geometry is insufficiently powerful to account for a class of phonological rules that involve dependencies between segments, such as partial and total identity and nonidentity. Feature geometry is unable to encode these properties. In 2008, Jeff Mielke argued that feature geometry merely recapitulated physiological organization, and that since the influence of articulation on sound change will independently create patterns in the behavior of features, feature geometry recapitula |
https://en.wikipedia.org/wiki/Amplituhedron | In mathematics and theoretical physics (especially twistor string theory), an amplituhedron is a geometric structure introduced in 2013 by Nima Arkani-Hamed and Jaroslav Trnka. It enables simplified calculation of particle interactions in some quantum field theories. In planar N = 4 supersymmetric Yang–Mills theory, also equivalent to the perturbative topological B model string theory in twistor space, an amplituhedron is defined as a mathematical space known as the positive Grassmannian.
Amplituhedron theory challenges the notion that spacetime locality and unitarity are necessary components of a model of particle interactions. Instead, they are treated as properties that emerge from an underlying phenomenon.
The connection between the amplituhedron and scattering amplitudes is a conjecture that has passed many non-trivial checks, including an understanding of how locality and unitarity arise as consequences of positivity. Research has been led by Nima Arkani-Hamed. Edward Witten described the work as "very unexpected" and said that "it is difficult to guess what will happen or what the lessons will turn out to be".
Description
When subatomic particles interact, different outcomes are possible. The evolution of the various possibilities is called a "tree" and the probability amplitude of a given outcome is called its scattering amplitude. According to the principle of unitarity, the sum of the probabilities (the squared moduli of the probability amplitudes) for every possible outcome is 1.
The on-shell scattering process "tree" may be described by a positive Grassmannian, a structure in algebraic geometry analogous to a convex polytope, that generalizes the idea of a simplex in projective space. A polytope is the n-dimensional analogue of a 3-dimensional polyhedron, the values being calculated in this case are scattering amplitudes, and so the object is called an amplituhedron.
Using twistor theory, Britto–Cachazo–Feng–Witten recursion (BCFW recursion) relations involved in the scattering process may be represented as a small number of twistor diagrams. These diagrams effectively provide the recipe for constructing the positive Grassmannian, i.e. the amplituhedron, which may be captured in a single equation. The scattering amplitude can thus be thought of as the volume of a certain polytope, the positive Grassmannian, in momentum twistor space.
When the volume of the amplituhedron is calculated in the planar limit of N = 4 D = 4 supersymmetric Yang–Mills theory, it describes the scattering amplitudes of particles described by this theory. The amplituhedron thus provides a more intuitive geometric model for calculations with highly abstract underlying principles.
The twistor-based representation provides a recipe for constructing specific cells in the Grassmannian which assemble to form a positive Grassmannian, i.e., the representation describes a specific cell decomposition of the positive Grassmannian.
The recursion relations can be r |
https://en.wikipedia.org/wiki/Quotient%20stack | In algebraic geometry, a quotient stack is a stack that parametrizes equivariant objects. Geometrically, it generalizes a quotient of a scheme or a variety by a group: a quotient variety, say, would be a coarse approximation of a quotient stack.
The notion is of fundamental importance in the study of stacks: a stack that arises in nature is often either a quotient stack itself or admits a stratification by quotient stacks (e.g., a Deligne–Mumford stack.) A quotient stack is also used to construct other stacks like classifying stacks.
Definition
A quotient stack is defined as follows. Let G be an affine smooth group scheme over a scheme S and X an S-scheme on which G acts. Let the quotient stack be the category over the category of S-schemes:
an object over T is a principal G-bundle together with equivariant map ;
an arrow from to is a bundle map (i.e., forms a commutative diagram) that is compatible with the equivariant maps and .
Suppose the quotient exists as an algebraic space (for example, by the Keel–Mori theorem). The canonical map
,
that sends a bundle P over T to a corresponding T-point, need not be an isomorphism of stacks; that is, the space "X/G" is usually coarser. The canonical map is an isomorphism if and only if the stabilizers are trivial (in which case exists.)
In general, is an Artin stack (also called algebraic stack). If the stabilizers of the geometric points are finite and reduced, then it is a Deligne–Mumford stack.
has shown: let X be a normal Noetherian algebraic stack whose stabilizer groups at closed points are affine. Then X is a quotient stack if and only if it has the resolution property; i.e., every coherent sheaf is a quotient of a vector bundle. Earlier, Robert Wayne Thomason proved that a quotient stack has the resolution property.
Examples
An effective quotient orbifold, e.g., where the action has only finite stabilizers on the smooth space , is an example of a quotient stack.
If with trivial action of (often is a point), then is called the classifying stack of (in analogy with the classifying space of ) and is usually denoted by . Borel's theorem describes the cohomology ring of the classifying stack.
Moduli of line bundles
One of the basic examples of quotient stacks comes from the moduli stack of line bundles over , or over for the trivial -action on . For any scheme (or -scheme) , the -points of the moduli stack are the groupoid of principal -bundles .
Moduli of line bundles with n-sections
There is another closely related moduli stack given by which is the moduli stack of line bundles with -sections. This follows directly from the definition of quotient stacks evaluated on points. For a scheme , the -points are the groupoid whose objects are given by the setThe morphism in the top row corresponds to the -sections of the associated line bundle over . This can be found by noting giving a -equivariant map and restricting it to the fiber gives the same data as a section of |
https://en.wikipedia.org/wiki/Jes%C3%BAs%20Mar%C3%ADa%20Sanz-Serna | Jesús María Sanz-Serna (born 12 June 1953 in Valladolid, Spain) is a mathematician who specializes in applied mathematics. Sanz-Serna pioneered the field of geometric integration and wrote the first book on this subject. From 1998 to 2006, he was rector of the University of Valladolid.
He received the inaugural Dahlquist Prize from the Society for Industrial and Applied Mathematics in 1995 and became one of the inaugural fellows of the American Mathematical Society in 2012. His 60th birthday was celebrated at the 2013 International Conference on Scientific Computation and Differential Equations (SciCADE) in Valladolid.
Notes
Numerical analysts
1953 births
Living people
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Jblas%3A%20Linear%20Algebra%20for%20Java | jblas is a linear algebra library, created by Mikio Braun, for the Java programming language built upon BLAS and LAPACK. Unlike most other Java linear algebra libraries, jblas is designed to be used with native code through the Java Native Interface (JNI) and comes with precompiled binaries. When used on one of the targeted architectures, it will automatically select the correct binary to use and load it. This allows it to be used out of the box and avoid a potentially tedious compilation process. jblas provides an easier to use high level API on top of the archaic API provided by BLAS and LAPACK, removing much of the tediousness.
Since its initial release, jblas has been gaining popularity in scientific computing. With applications in a range of applications, such as text classification, network analysis, and stationary subspace analysis. It is part of software packages, such as JLabGroovy, and Universal Java Matrix Library (UJMP). In a performance study of Java matrix libraries, jblas was the highest performing library, when libraries with native code are considered.
Capabilities
The following is an overview of jblas's capabilities, as listed on the project's website:
Eigen – eigendecomposition
Solve – solving linear equations
Singular – singular value decomposition
Decompose – LU, Cholesky, ...
Geometry – centering, normalizing, ...
Usage example
Example of Eigenvalue Decomposition:
DoubleMatrix[] evd = Eigen.symmetricEigenvectors(matA);
DoubleMatrix V = evd[0];
DoubleMatrix D = evd[1];
Example of matrix multiplication:
DoubleMatrix result = matA.mmul(matB);
See also
NumPy
SciPy
ND4J: NDArrays & Scientific Computing for Java
References
Java (programming language) libraries |
https://en.wikipedia.org/wiki/Blake%20Young%20%28motorcyclist%29 | Blake Young (born September 20, 1987, in Madison, Wisconsin) is an American motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
Superbike World Championship
Races by year
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)
References
External links
1987 births
Living people
Sportspeople from Madison, Wisconsin
American motorcycle racers
MotoGP World Championship riders
Superbike World Championship riders
AMA Superbike Championship riders |
https://en.wikipedia.org/wiki/Ioan%20Dzi%C8%9Bac | Ioan Dzițac (14 February 1953 – 6 February 2021) was a Romanian professor (of Ukrainian descent) of mathematics and computer science. He obtained his B.S. and M.Sc. in Mathematics (1977) and PhD in Computer Science (2002) from Babeș-Bolyai University of Cluj-Napoca. He was a professor at the Aurel Vlaicu University of Arad and part of the leadership of Agora University in Oradea until his sudden death in 2021.
Education and career
Dzițac was born in Poienile de sub Munte, Maramureș County. After attending elementary school in Repedea (1960–1968), he studied at the Dragoș Vodă High School in Sighetu Marmației (1968–1972) and then at the Faculty of Mathematics, Babeș-Bolyai University (1972–1977). In 2002 he obtained his PhD in computer science at the Faculty of Mathematics and Informatics, Babeș-Bolyai University with thesis "Methods for parallel and distributed computing in solving operational equations" under the supervision of Grigor Moldovan.
Between 1977 and 1991, Dzițac taught mathematics in pre-university education, obtaining a permanent teacher certification on all levels (1980), second grade teacher certification (1985), and first grade teacher certification (1990). In 1986 he received the title of Distinguished Professor.
Since 1991, he accessed through competition in the higher education system the position of Lecturer (1991–2003) and associate professor (2003–2005) at the University of Oradea, associate professor (2005–2009) at Agora University, and then Professor (2009–2021) at Aurel Vlaicu University of Arad. At Agora University he founded, together with Florin Gheorghe Filip and Mișu-Jan Manolescu, the International conference on Computers, Communications & Control (ICCCC) and the International Journal of Computers, Communications & Control (IJCCC) journals which, in less than two years, have been covered by Thomson ISI. Since 2006 he was the associate editor-in-chief of the IJCCC journal until his sudden death in 2021.
Dzițac was a visiting professor at the Chinese Academy of Science (2013–2016), as well as a consulting member of the Hoseo University in South Korea.
Management positions
In 1996, Dzițac was elected Vice President of the Romanian Society of Applied and Industrial Mathematics (ROMAI), a position he occupied until 2011 (he was re-elected in 1999–2009). In April 2004, he was elected as Director of the Department of Mathematics and Computer Science of the University of Oradea, a position he occupied for a year, and in October 2005 he was elected Head of Department at Agora University. Since October 2009 he was the Director of the Centre "Agora Research & Development".
As of 2012, Dzițac was Rector of Agora University.
Awards
In recognition of his merits, Dzițac was awarded the following degrees and titles (see [1])
Title of “Distinguished Professor” accorded by the Romanian Ministry of Education (1988)
The Award for Young Researcher accorded by the Romanian Society of Applied and Industrial Mathematics (2003)
|
https://en.wikipedia.org/wiki/McKay%27s%20approximation%20for%20the%20coefficient%20of%20variation | In statistics, McKay's approximation of the coefficient of variation is a statistic based on a sample from a normally distributed population. It was introduced in 1932 by A. T. McKay. Statistical methods for the coefficient of variation often utilizes McKay's approximation.
Let , be independent observations from a normal distribution. The population coefficient of variation is . Let and denote the sample mean and the sample standard deviation, respectively. Then is the sample coefficient of variation. McKay's approximation is
Note that in this expression, the first factor includes the population coefficient of variation, which is usually unknown. When is smaller than 1/3, then is approximately chi-square distributed with degrees of freedom. In the original article by McKay, the expression for looks slightly different, since McKay defined with denominator instead of . McKay's approximation, , for the coefficient of variation is approximately chi-square distributed, but exactly noncentral beta distributed
.
References
Statistical deviation and dispersion |
https://en.wikipedia.org/wiki/Barry%20Veneman | Barry Veneman (born 22 March 1977) is a Dutch former motorcycle racer. He was born in Zwolle, Netherlands.
Career statistics
By season
Races by year
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)
Supersport World Championship
Races by year
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)
Superbike World Championship
Races by year
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)
References
External links
Living people
Dutch motorcycle racers
500cc World Championship riders
1972 births
21st-century Dutch people |
https://en.wikipedia.org/wiki/Kha%20%28Indic%29 | Kha is the second consonant of Indic abugidas. In modern Indic scripts, kha is derived from the Brahmi letter , which is probably derived from the Aramaic ("Q").
Mathematics
Āryabhaṭa numeration
Aryabhata used Devanagari letters for numbers, very similar to the Greek numerals, even after the invention of Indian numerals.
The values of the different forms of are:
= 2 (२)
= 200 (२००)
= 20,000 (२० ०००)
= 2,000,000 (२० ०० ०००)
= 2 (२×१०८)
= 2 (२×१०१०)
= 2 (२×१०१२)
= 2 (२×१०१४)
= 2 (२×१०१६)
Historic Kha
There are three different general early historic scripts - Brahmi and its variants, Kharoshthi, and Tocharian, the so-called slanting Brahmi. Kha as found in standard Brahmi, was a simple geometric shape, with slight variations toward the Gupta . The Tocharian Kha did not have an alternate Fremdzeichen form. The third form of kha, in Kharoshthi () was probably derived from Aramaic separately from the Brahmi letter.
Brahmi Kha
The Brahmi letter , Kha, is probably derived from the Aramaic Qoph , and is thus related to the modern Latin Q and Greek Koppa. Several identifiable styles of writing the Brahmi Kha can be found, most associated with a specific set of inscriptions from an artifact or diverse records from an historic period. As the earliest and most geometric style of Brahmi, the letters found on the Edicts of Ashoka and other records from around that time are normally the reference form for Brahmi letters, with vowel marks not attested until later forms of Brahmi back-formed to match the geometric writing style.
Tocharian Kha
The Tocharian letteris derived from the Brahmi , but does not have an alternate Fremdzeichen form.
Kharoshthi Kha
The Kharoshthi letter is generally accepted as being derived from the Aramaic Qoph , and is thus related to Q and Koppa, in addition to the Brahmi Kha.
Devanagari Kha
Kha (ख) is the second consonant of the Devanagari abugida. It ultimately arose from the Brahmi letter , after having gone through the Gupta letter . Letters that derive from it are the Gujarati letter ખ and the Modi letter 𑘏.
Devanagari-using Languages
In all languages, is pronounced as or when appropriate. Because of borrowings from languages with different phonemic inventories, Devanagari has employed the nukta to create an additional related letter ḫa that is pronounced as and can be used to retain non-native distinctions in Hindi texts.
Conjuncts With ख
Devanagari exhibits conjunct ligatures, as is common in Indic scripts. Like most Devanagari letters, in modern texts forms very few irregular ligatures, and assumes a half form to create most conjuncts, such as + = . Earlier texts show many more ligature forms, with vertically stacked conjuncts being common. The use of modern ligatures and vertical conjuncts may vary across languages using the Devanagari script, with Marathi in particular preferring the use of half forms where texts in other languages would show ligatures and vertical stacks.
L |
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