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https://en.wikipedia.org/wiki/Kim%20Williams%20%28architect%29
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Kim Williams is an American architect, an independent scholar on the connections between architecture and mathematics, and a book publisher. She is the founder of the Nexus: Architecture and Mathematics conference series, the founder and co-editor-in-chief of Nexus Network Journal, and the author of several books on mathematics and architecture.
Williams has a degree in architectural studies from the University of Texas at Austin, and is a licensed architect in New York.
Books
Williams is the author of:
Italian Pavements: Patterns in Space (Anchorage Press, 1997)
The Villas of Palladio (illustrated by Giovanni Giaconi, Princeton Architectural Press, 2003)
She is an editor, translator, and commentator of older works on architecture and mathematics including:
The Mathematical Works of Leon Battista Alberti (with Lionel March and Stephen R. Wassell, Birkhäuser, 2010)
Daniele Barbaro's Vitruvius of 1567 (Birkhäuser, 2019)
She is also the editor or co-editor of several collections of papers on architecture and mathematics, including several volumes of the Nexus conference proceedings and:
Two Cultures: Essays in Honour of David Speiser (Birkhäuser, 2006)
Crossroads: History of Science, History of Art: Essays by David Speiser (Birkhäuser, 2011)
Architecture and Mathematics from Antiquity to the Future, Volume I: Antiquity to the 1500s; Volume II: The 1500s to the future (with Michael J. Ostwald, Birkhäuser, 2015)
Masonry Structures: Between Mechanics and Architecture (with Danila Aita and Orietta Pedemonte, Birkhäuser, 2015)
References
External links
Kim Williams Books, Williams's publishing company
Year of birth missing (living people)
Living people
20th-century American architects
American women architects
American historians of mathematics
University of Texas at Austin alumni
21st-century American women
21st-century American architects
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https://en.wikipedia.org/wiki/Lisa%20Piccirillo
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Lisa Marie Piccirillo (born 1990 or 1991) is an American mathematician who works on geometry and low-dimensional topology. In 2020, Piccirillo published a mathematical proof in the journal Annals of Mathematics determining that the Conway knot is not a slice knot, answering an unsolved problem in knot theory first proposed over fifty years prior by English mathematician John Horton Conway. In July 2020, she became an assistant professor of mathematics at Massachusetts Institute of Technology.
Early life
Piccirillo was raised in Greenwood, Maine, and attended Telstar Regional High School in Bethel, Maine. Her mother was a middle school math teacher. As a child, she had many hobbies, such as riding dressage, being involved in her church's youth group and she participated in drama and band in school.
Education
Piccirillo earned a B.S. in mathematics from Boston College in 2013 and a PhD in low-dimensional topology at the University of Texas at Austin under the supervision of John Luecke in 2019, followed by postdoctoral research at Brandeis University. Boston College professor Elisenda Grigsby cited Piccirillo's creativity as contributing to her success, adding that Piccirillo did not fit the mold of a "standard golden child math prodigy" during her undergraduate studies.
Work
The slice property of the Conway knot was a long-standing unsolved problem in knot theory. The knot was named after its discoverer, English mathematician John Horton Conway, who first wrote about the knot in 1970. The Conway knot was determined to be topologically slice in the 1980s; however, the nature of its sliceness, and whether or not it was smoothly slice, eluded mathematicians for decades up until Piccirillo's breakthrough. Piccirillo's work on the Conway knot completed the classification of slice knots with under thirteen crossings, as the Conway knot had been the last outstanding knot in its group fully unclassified.
Piccirillo first learned of the Conway knot problem in 2018 at a conference on low-dimensional topology and geometry. She was a graduate student at the time and spent less than a week working on the knot in her free time before finding an answer. The Washington Post reported that her proof had been "hailed as a thing of mathematical beauty, and her work could point to new ways to understand knots." Following the publication of Piccirillo's proof in Annals of Mathematics, she was offered a tenure-track position at the Massachusetts Institute of Technology set to begin fourteen months after the completion of her doctorate.
Recognition
In association with the 2021 Breakthrough Prizes, Piccirillo was awarded one of three 2021 Maryam Mirzakhani New Frontiers Prizes, for early-career achievements by a woman mathematician. The other two winners were Nina Holden and Urmila Mahadev. She was also awarded a 2021 Clay Research Fellowship for "her work in low-dimensional topology" and a 2021 Sloan Research Fellowship.
She was also counted as one of "The world
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https://en.wikipedia.org/wiki/Lattice%20disjoint
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In mathematics, specifically in order theory and functional analysis, two elements x and y of a vector lattice X are lattice disjoint or simply disjoint if , in which case we write , where the absolute value of x is defined to be .
We say that two sets A and B are lattice disjoint or disjoint if a and b are disjoint for all a in A and all b in B, in which case we write .
If A is the singleton set then we will write in place of .
For any set A, we define the disjoint complement to be the set .
Characterizations
Two elements x and y are disjoint if and only if .
If x and y are disjoint then and , where for any element z, and .
Properties
Disjoint complements are always bands, but the converse is not true in general.
If A is a subset of X such that exists, and if B is a subset lattice in X that is disjoint from A, then B is a lattice disjoint from .
Representation as a disjoint sum of positive elements
For any x in X, let and , where note that both of these elements are and with .
Then and are disjoint, and is the unique representation of x as the difference of disjoint elements that are .
For all x and y in X, and .
If y ≥ 0 and x ≤ y then x+ ≤ y.
Moreover, if and only if and .
See also
Solid set
Locally convex vector lattice
Vector lattice
References
Sources
Functional analysis
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https://en.wikipedia.org/wiki/ERMETH
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The ERMETH (Electronic Calculating Machine of the ETH) was one of the first computers in Europe and was developed and built by Eduard Stiefel and his team of the Institute for Applied Mathematics at the ETH Zurich between 1948 and 1956. It was in use until 1963 and is now displayed at the Museum of Communication Bern (Switzerland).
Models
Eduard Stiefel and his two senior assistants Heinz Rutishauser and Ambros Speiser were inspired by models in the USA and United Kingdom when developing the ERMETH. In 1949 Rutishauser and Speiser undertook study trips to Howard Aiken (Harvard University), John von Neumann (Princeton University) and to the University of Cambridge, which operated the EDSAC. In 1950, Stiefel rented for five years the only existing digital computer in continental Europe at that time, the Zuse Z4, completed by Konrad Zuse in 1945, for the ETH in order to gain experience with a calculating machine during the construction of the ERMETH.
Technical concept
The ERMETH had (in contrast to the Z4) a classical von Neumann architecture, i.e. it was a calculating machine in which program and processed data were stored in the same main memory; thus, numbers, as well as program parts, could be processed automatically. The ERMETH was designed for numerical calculations and worked in true decimal (not dual or hexadecimal) and had instructions for all four basic arithmetic operations with floating-point and fixed-point numbers, but not for processing letters. At the start of operation (1956), it consisted of devices (hardware) and stored user programs (software), but had no operating system, so that each user had to first read in his program, which had already been prepared on punch cards in machine language and then start it by setting the program counter to the first command. Under program control, user data was then read in (from punch cards) and parameter values were requested (via the keyboard) from the user.
Already in 1952, Heinz Rutishauser had presented the concept of the compiler for the use of machine-independent computer languages in his habilitation thesis on "automatic computation plan production". Thanks to the development of the higher programming language Algol (Algol 58 and Algol 60), machine-independent programming later became possible; for the input of letters, the ERMETH 1958 had to be supplemented with a paper tape reader.
The ERMETH had an arithmetic unit with 1,500 electron tubes. A 1.5-ton magnetic drum with space for 10,000 words to 16 decimal places (14 digits, sign, check digit), which rotated at 100 revolutions per second, served as the main memory. This also determined the operating speed of the ERMETH per command step, because the average access time to the commands and numbers stored on the drum was 5 milliseconds; the much higher operating speed of the electron tubes did not change this. The use of the 10'000 words of the working memory was very flexible. For each word (with 16 decimal places), either a flo
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https://en.wikipedia.org/wiki/Mary%20Graustein
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Mary Graustein (April 12, 1884 – July 18, 1972) was a mathematician and university professor, and was the first woman to earn a doctorate in mathematics (1917) at Radcliffe College.
Life and research
Mary Florence Curtis was the oldest of five children born to Jennie Esther (Lucas) (1857–1945) and Frank Abbott Curtis (1857–1937) in Westminster, Massachusetts. She attended Fitchburg High School in Massachusetts and in 1902 she began her undergraduate studies at Wellesley College. She was a Wellesley Honors Scholar throughout her college years and received her Bachelor of Art's degree in 1906.
As was common practice at that time, Mary Curtis took a teaching position at Leominster High School in Westminster, where she taught German, algebra and geometry for two years, traveling to Europe for the summer of 1907.
After her return, from 1908 to 1910, she taught German and natural science at the Cushing Academy in Ashburnham, Massachusetts. (During the summer break of 1909, she studied botany and pedagogy at Cornell University in Ithaca, New York.)
Returning to Germany, Curtis studied mathematics and science for three semesters (May 1910 until August 1911) at Leipzig University.
Upon her return from Leipzig, she joined the Wellesley College mathematics faculty where she taught from September 1911 to June 1914.
Even while she was on the Wellesley faculty, she started graduate school at nearby Radcliffe College in Cambridge, Mass. in September 1913 and was awarded a one-year Mary E. Horton fellowship to facilitate her schooling. Curtis earned her M.A. in 1915 and her Ph.D. in 1917 with a dissertation in differential geometry titled Curves invariant under point transformations of special type. Professors Charles Leonard Bouton and Julian Coolidge were her faculty reviewers. She was the first woman from Harvard-Radcliffe (the two are now combined) to earn a doctorate in math.
Professor
From 1917 to 1918, Dr. Mary Curtis taught at the College for Women at Case Western Reserve University in Cleveland, Ohio, From 1918 to 1920 she was an instructor and then until 1921 assistant professor at Wellesley College. In the summer of 1920 she returned to Leipzig, Germany. Mary's mathematical research did not go unnoticed. According to mathematician Judy Green:In a November 1920 letter extracted in the Bulletin of the AMS, the Italian geometer and historian of mathematics Gino Loria wrote to the American historian of mathematics D. E. Smith that 'Mary F. Curtis had established [a] remarkable result, that every rectifiable skew parabola is a helix” (27 (1921): 201). The extract from Loria’s letter referred to Curtis’s 1918 paper On the rectifiability of a twisted cubic and motivated her 1921 paper On skew parabolas.It was in Wellesley, on June 10, 1921, at the age of 37, that she married another mathematician William Caspar Graustein (1888-1941), who was born in Cambridge and teaching at Harvard when he met Curtis, one of his students. After their marriage
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https://en.wikipedia.org/wiki/Jyotiprasad%20Medhi
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Jyotiprasad Medhi was a professor of statistics at Gauhati University and Institute of Advanced Study in Science and Technology.
Work and education
Medhi started his schooling in Dibrugarh and in 1940 he passed matriculation from Dibrugarh Government High School. After matriculation, he did his graduate studies in Cotton College in 1946 and was a gold medalist in BSc with Honours in mathematics. There he received the Sudmerson Gold Medal and Rajanikant Barat Gold Medal. Medhi did his MSc in Pure Mathematics from Calcutta University, and got the Debendra Nath Gangopadhaya Gold medal for record marks obtained and the Post graduate First class first gold medal in 1948. In 1952, he took a loan of ten thousand rupees from Govt of Assam and moved to England to pursue Master of Statistics (MStat) from the University of Manchester and completed in 1954. He worked with M S Bartlett in the University of Manchester in 1955 on the topic 'Time Series Analysis'. Thereon Medhi moved to France to study for his DSc in the University of Paris in 1956 under the supervision of Robert Fortet. He had also taken a diploma in French Language with mention 'Honorable'. Its worthy to mention that he had written his doctoral thesis in French Language.
Medhi joined as a lecturer of statistics at Cotton University erstwhile Cotton College in 1948. However, in the same year Gauhati University was established and he was invited to work as professor in Gauhati University. Accepting the invitation, he joined the Department of Mathematics and Statistics as a lecturer. In between his tenure, he had taken MS degree from England and DSc from Paris. Medhi returned to Gauhati University where he became a professor and was the head of the department of statistics till he retired in 1985. Earlier in Gauhati University, both mathematics and statistics were in a common department, however, under the able leadership of Prof Medhi, statistics became a full-fledged individual department. In 1987, two years after retirement, he was entitled the honour of professor emeritus at the same university and remained so until his death in 2017. Under his guidance, several students got doctoral degrees and Tata Subba Rao is the first among them. From Southern India, Subba Rao had come to Assam to pursue his research under Prof Medhi and later he had joined Manchester University as a Professor. In 1979, he established the 'Population Research Centre' and served as a director. He played a prominent role in shaping the newly formed Institute of Advanced Study in Science and Technology, Assam, IASST by serving as director.
Publications
Medhi published many articles in peer reviewed international and national journals. He also published two books on stochastic processes each with over 500 citations.
Awards and honours
The J Medhi memorial lecture is annually held in the Indian Institute of Technology, Guwahati at the Department of Mathematics.
In 2016, Medhi was conferred an Honorary doctorate DSc by
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https://en.wikipedia.org/wiki/Crossing%20Numbers%20of%20Graphs
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Crossing Numbers of Graphs is a book in mathematics, on the minimum number of edge crossings needed in graph drawings. It was written by Marcus Schaefer, a professor of computer science at DePaul University, and published in 2018 by the CRC Press in their book series Discrete Mathematics and its Applications.
Topics
The main text of the book has two parts, on the crossing number as traditionally defined and on variations of the crossing number, followed by two appendices providing background material on topological graph theory and computational complexity theory.
After introducing the problem, the first chapter studies the crossing numbers of complete graphs (including Hill's conjectured formula for these numbers) and complete bipartite graphs (Turán's brick factory problem and the Zarankiewicz crossing number conjecture), again giving a conjectured formula). It also includes the crossing number inequality, and the Hanani–Tutte theorem on the parity of crossings. The second chapter concerns other special classes of graphs including graph products (especially products of cycle graphs) and hypercube graphs. After a third chapter relating the crossing number to graph parameters including skewness, bisection width, thickness, and (via the Albertson conjecture) the chromatic number, the final chapter of part I concerns the computational complexity of finding minimum-crossing graph drawings, including the results that the problem is both NP-complete and fixed-parameter tractable.
In the second part of the book, two chapters concern the rectilinear crossing number, describing graph drawings in which the edges must be represented as straight line segments rather than arbitrary curves, and Fáry's theorem that every planar graph can be drawn without crossings in this way. Another chapter concerns 1-planar graphs and the associated local crossing number, the smallest number such that the graph can be drawn with at most crossings per edge. Two chapters concern book embeddings and string graphs, and two more chapters concern variations of the crossing number that count crossings in different ways, for instance by the number of pairs of edges that cross or that cross an odd number of times. The final chapter of part II concerns thrackles and the problem of finding drawings with a maximum number of crossings.
Audience and reception
The book can be used as an advanced textbook, and has exercises provided for that use. However, it assumes that its readers are already familiar with both graph theory and the design and analysis of algorithms. Reviewing the book, L. W. Beineke calls it a "valuable contribution" for its presentation of the many results in this area.
References
Graph drawing
Topological graph theory
Geometric graph theory
Mathematics books
2018 non-fiction books
CRC Press books
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https://en.wikipedia.org/wiki/The%20History%20of%20Mathematical%20Tables
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The History of Mathematical Tables: from Sumer to Spreadsheets is an edited volume in the history of mathematics on mathematical tables. It was edited by Martin Campbell-Kelly, Mary Croarken, Raymond Flood, and Eleanor Robson, developed out of the presentations at a conference on the subject organised in 2001 by the British Society for the History of Mathematics, and published in 2003 by the Oxford University Press.
Topics
An introductory chapter classifies tables broadly according to whether they are intended as aids to calculation (based on mathematical formulas) or as analyses and records of data, and further subdivides them according to how they were compiled. Following this, the contributions to the book include articles on the following topics:
Tables of data in Babylonian mathematics, administration, and astronomy, by Eleanor Robson
Early tables of logarithms, by Graham Jagger
Life tables in actuarial science, by Christopher Lewin and Margaret de Valois
The work of Gaspard de Prony constructing mathematical tables in revolutionary France, by Ivor Grattan-Guinness
Difference engines, by Michael Williams
The uses and advantages of machines in table-making, and error correction in mechanical tables, by Doron Swade
Astronomical tables, by Arthur Norberg
The data processing and statistical analyses used to produce tables of census data from punched cards, by Edward Higgs
British table-making committees, and the transition from calculators to computers, by Mary Croarken
The Mathematical Tables Project of the Works Progress Administration, in New York during the Great Depression of the 1930s and early 1940s, by David Alan Grier
The work of the British Nautical Almanac Office, by George A. Wilkins
Spreadsheets, by Martin Campbell-Kelly.
The work is presented on VIII + 361 pages in a unified format with illustrations throughout, and with the historical and biographical context of the material set aside in separate text boxes.
Audience and reception
Reviewer Paul J. Campbell finds it ironic that, unlike the works it discusses, "there are no tables in the back of the book". Reviewer Sandy L. Zabell calls the book "interesting and highly readable".
Both Peggy A. Kidwell and Fernando Q. Gouvêa note several topics that would have been worthwhile to include, including tables in mathematics in medieval Islam or other non-Western cultures, the book printing industry that provided inexpensive books of tables in the 19th century, and the development of mathematical tables in Germany. As Kidwell writes, "like most good books, this one not only tells good stories, but leaves the reader hoping to learn more". Gouvêa evaluates the book as being useful in its coverage of a topic often missed in broader surveys of the history of mathematics, of interest both to historians of mathematics and to a more general audience interested in the development of these topics, and "a must-have for libraries".
References
External links
The History of Mathematical Tables on
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https://en.wikipedia.org/wiki/Marsaglia%27s%20theorem
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In computational number theory, Marsaglia's theorem connects modular arithmetic and analytic geometry to describe the flaws with the pseudorandom numbers resulting from a linear congruential generator. As a direct consequence, it is now widely considered that linear congruential generators are weak for the purpose of generating random numbers. Particularly, it is inadvisable to use them for simulations with the Monte Carlo method or in cryptographic settings, such as issuing a public key certificate, unless specific numerical requirements are satisfied. Poorly chosen values for the modulus and multiplier in a Lehmer random number generator will lead to a short period for the sequence of random numbers. Marsaglia's result may be further extended to a mixed linear congruential generator.
Main statement
Consider a Lehmer random number generator with
for any modulus and multiplier where each , and define a sequence
Define the points
on a unit -cube formed from successive terms of the sequence of . With such a multiplicative number generator, all -tuples of resulting random numbers lie in at most hyperplanes. Additionally, for a choice of constants which satisfy the congruence
there are at most parallel hyperplanes which contain all -tuples produced by the generator. Proofs for these claims may be found in Marsaglia's original paper.
References
Theorems in number theory
Random number generation
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https://en.wikipedia.org/wiki/Rachel%20Blodgett%20Adams
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Rachel Blodgett Adams (October 13, 1894–January 22, 1982) was a pioneering American mathematician and one of the first women to earn a doctorate in mathematics at Radcliffe College in 1921.
Biography
Rachel Blodgett was born in Woburn, Massachusetts, the oldest of three children of Mabel Edith Owen (b. 1874) and William Edward Blodgett (b. 1864); neither of whom attended college.
After graduating from Woburn High School in 1912, she entered Wellesley College and majored in mathematics and Latin. In addition to her studies, she joined the school's Shakespeare Society and performed cornet in the symphony orchestra. Academically, she was gifted and was named a Wellesley scholar in 1914 and a Durant scholar in 1915.
She graduated with her bachelor's degree (B.A.) in 1916, after which Blodgett moved to Montreal, Quebec, Canada to teach math at Miss Edgar's and Miss Cramp's School until 1918.She then returned to Massachusetts to further pursue her academic and professional endeavors
Research
For the next three years, Blodgett pursued advanced analysis at Radcliffe College, where she received an Edward Austin scholarship for at least two years and a Mary E. Horton fellowship for her final year. She earned her master's degree (M.A.) in 1919, and continued on to acquire her Ph.D. in mathematics in 1921. The following fall term, Dr. Blodgett took a teaching position at Wellesley.
Rachel Blodgett married Harvard-trained mathematician Clarence Raymond Adams (1898–1965) on August 17, 1922, in Eden Park, in Providence, Rhode Island. (He was widely known as "C.R. Adams.") At the time, C. R. Adams was a Sheldon traveling fellow from Harvard, which allowed the newly married couple to travel extensively overseas with stops in Rome and Göttingen, Germany. Upon their return to the U.S. in 1923, the two mathematicians settled down in Providence, Rhode Island, where C. R. established his career at Brown University and eventually headed the math department there.
Blodgett, now known as Dr. Rachel Adams, moved forward with her research for a few years, according to mathematician Judy Green, "At least through the 1920s Adams continued her interest in integral equations. G. C. Evans of Rice Institute used information from her dissertation in an extensive review of a book on linear integral equations for the Monthly in 1927. She presented her results to the AMS in 1926 and published them in the American Journal in 1929."Adams also spent many years tutoring math students at her alma mater, Radcliffe College, from 1926 to 1941, with her friend and colleague Mary Graustein, Ph.D., with the goal of encouraging young female students.
During World War II, Adams registered with the National Roster of Scientific and Specialized Personnel in Washington, D.C. to help with the war effort, but confirmation of any contribution she may have made as part of that program has not yet been found.
Later years
During their marriage Rachel and C. R. Adams traveled extensively by a
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https://en.wikipedia.org/wiki/Saturated%20family
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In mathematics, specifically in functional analysis, a family of subsets a topological vector space (TVS) is said to be saturated if contains a non-empty subset of and if for every the following conditions all hold:
contains every subset of ;
the union of any finite collection of elements of is an element of ;
for every scalar contains ;
the closed convex balanced hull of belongs to
Definitions
If is any collection of subsets of then the smallest saturated family containing is called the of
The family is said to if the union is equal to ;
it is if the linear span of this set is a dense subset of
Examples
The intersection of an arbitrary family of saturated families is a saturated family.
Since the power set of is saturated, any given non-empty family of subsets of containing at least one non-empty set, the saturated hull of is well-defined.
Note that a saturated family of subsets of that covers is a bornology on
The set of all bounded subsets of a topological vector space is a saturated family.
See also
References
Functional analysis
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https://en.wikipedia.org/wiki/Positive%20linear%20operator
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In mathematics, more specifically in functional analysis, a positive linear operator from an preordered vector space into a preordered vector space is a linear operator on into such that for all positive elements of that is it holds that
In other words, a positive linear operator maps the positive cone of the domain into the positive cone of the codomain.
Every positive linear functional is a type of positive linear operator.
The significance of positive linear operators lies in results such as Riesz–Markov–Kakutani representation theorem.
Definition
A linear function on a preordered vector space is called positive if it satisfies either of the following equivalent conditions:
implies
if then
The set of all positive linear forms on a vector space with positive cone called the dual cone and denoted by is a cone equal to the polar of
The preorder induced by the dual cone on the space of linear functionals on is called the .
The order dual of an ordered vector space is the set, denoted by defined by
Canonical ordering
Let and be preordered vector spaces and let be the space of all linear maps from into
The set of all positive linear operators in is a cone in that defines a preorder on .
If is a vector subspace of and if is a proper cone then this proper cone defines a on making into a partially ordered vector space.
If and are ordered topological vector spaces and if is a family of bounded subsets of whose union covers then the positive cone in , which is the space of all continuous linear maps from into is closed in when is endowed with the -topology.
For to be a proper cone in it is sufficient that the positive cone of be total in (that is, the span of the positive cone of be dense in ).
If is a locally convex space of dimension greater than 0 then this condition is also necessary.
Thus, if the positive cone of is total in and if is a locally convex space, then the canonical ordering of defined by is a regular order.
Properties
Proposition: Suppose that and are ordered locally convex topological vector spaces with being a Mackey space on which every positive linear functional is continuous. If the positive cone of is a weakly normal cone in then every positive linear operator from into is continuous.
Proposition: Suppose is a barreled ordered topological vector space (TVS) with positive cone that satisfies and is a semi-reflexive ordered TVS with a positive cone that is a normal cone. Give its canonical order and let be a subset of that is directed upward and either majorized (that is, bounded above by some element of ) or simply bounded. Then exists and the section filter converges to uniformly on every precompact subset of
See also
References
Functional analysis
Order theory
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https://en.wikipedia.org/wiki/Soifer
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Soifer is a surname. Notable people with the surname include:
Alexander Soifer (born 1948), Russian-born American mathematician and mathematics author
Aviam Soifer (born 1948), American legal scholar and academic administrator
See also
Sofer (disambiguation)
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https://en.wikipedia.org/wiki/The%20Geometry%20of%20Musical%20Rhythm
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The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good? is a book on the mathematics of rhythms and drum beats. It was written by Godfried Toussaint, and published by Chapman & Hall/CRC in 2013 and in an expanded second edition in 2020. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
Author
Godfried Toussaint (1944–2019) was a Belgian–Canadian computer scientist who worked as a professor of computer science for McGill University and New York University. His main professional expertise was in computational geometry, but he was also a jazz drummer, held a long-term interest in the mathematics of music and musical rhythm, and since 2005 held an affiliation as a researcher in the Centre for Interdisciplinary Research in Music Media and Technology in the Schulich School of Music at McGill. In 2009 he visited Harvard University as a Radcliffe Fellow in advancement of his research in musical rhythm.
Topics
In order to study rhythms mathematically, Toussaint abstracts away many of their features that are important musically, involving the sounds or strengths of the individual beats, the phasing of the beats, hierarchically-structured rhythms, or the possibility of music that changes from one rhythm to another. The information that remains describes the beats of each bar (an evenly-spaced cyclic sequence of times) as being either on-beats (times at which a beat is emphasized in the musical performance) or off-beats (times at which it is skipped or performed only weakly). This can be represented combinatorially as a necklace, an equivalence class of binary sequences under rotations, with true binary values representing on-beats and false representing off-beats. Alternatively, Toussaint uses a geometric representation as a convex polygon, the convex hull of a subset of the vertices of a regular polygon, where the vertices of the hull represent times when a beat is performed; two rhythms are considered the same if the corresponding polygons are congruent.
As an example, reviewer William Sethares (himself a music theorist and engineer) presents a representation of this type for the tresillo rhythm, in which three beats are hit out of an eight-beat bar, with two long gaps and one short gap between each beat. The tresillo may be represented geometrically as an isosceles triangle, formed from three vertices of a regular octahedron, with the two long sides and one short side of the triangle corresponding to the gaps between beats. In the figure, the conventional start to a tresillo bar, the beat before the first of its two longer gaps, is at the top vertex, and the chronological progression of beats corresponds to the clockwise ordering of vertices around the polygon.
The book uses this method to study and classify existing rhythms from world music, to analyze their mathematical properties (for instance, the fact that many of these rhythms have a spacing b
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https://en.wikipedia.org/wiki/Virasoro%20group
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In abstract algebra, the Virasoro group or Bott–Virasoro group (often denoted by Vir) is an infinite-dimensional Lie group defined as the universal central extension of the group of diffeomorphisms of the circle. The corresponding Lie algebra is the Virasoro algebra, which has a key role in conformal field theory (CFT) and string theory.
The group is named after Miguel Ángel Virasoro and Raoul Bott.
Background
An orientation-preserving diffeomorphism of the circle , whose points are labelled by a real coordinate subject to the identification , is a smooth map such that and . The set of all such maps spans a group, with multiplication given by the composition of diffeomorphisms. This group is the universal cover of the group of orientation-preserving diffeomorphisms of the circle, denoted as .
Definition
The Virasoro group is the universal central extension of . The extension is defined by a specific two-cocycle, which is a real-valued function of pairs of diffeomorphisms. Specifically, the extension is defined by the Bott–Thurston cocycle:
In these terms, the Virasoro group is the set of all pairs , where is a diffeomorphism and is a real number, endowed with the binary operation
This operation is an associative group operation. This extension is the only central extension of the universal cover of the group of circle diffeomorphisms, up to trivial extensions. The Virasoro group can also be defined without the use explicit coordinates or an explicit choice of cocycle to represent the central extension, via a description the universal cover of the group.
Virasoro algebra
The Lie algebra of the Virasoro group is the Virasoro algebra. As a vector space, the Lie algebra of the Virasoro group consists of pairs , where is a vector field on the circle and is a real number as before. The vector field, in particular, can be seen as an infinitesimal diffeomorphism . The Lie bracket of pairs then follows from the multiplication defined above, and can be shown to satisfy
where the bracket of vector fields on the right-hand side is the usual one: . Upon defining the complex generators
the Lie bracket takes the standard textbook form of the Virasoro algebra:
The generator commutes with the whole algebra. Since its presence is due to a central extension, it is subject to a superselection rule which guarantees that, in any physical system having Virasoro symmetry, the operator representing is a multiple of the identity. The coefficient in front of the identity is then known as a central charge.
Properties
Since each diffeomorphism must be specified by infinitely many parameters (for instance the Fourier modes of the periodic function ), the Virasoro group is infinite-dimensional.
Coadjoint representation
The Lie bracket of the Virasoro algebra can be viewed as a differential of the adjoint representation of the Virasoro group. Its dual, the coadjoint representation of the Virasoro group, provides the transformation law of a CFT stress t
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https://en.wikipedia.org/wiki/The%20Petersen%20Graph
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The Petersen Graph is a mathematics book about the Petersen graph and its applications in graph theory. It was written by Derek Holton and John Sheehan, and published in 1993 by the Cambridge University Press as volume 7 in their Australian Mathematical Society Lecture Series.
Topics
The Petersen graph is an undirected graph with ten vertices and fifteen edges, commonly drawn as a pentagram within a pentagon, with corresponding vertices attached to each other. It has many unusual mathematical properties, and has frequently been used as a counterexample to conjectures in graph theory. The book uses these properties as an excuse to cover several advanced topics in graph theory where this graph plays an important role. It is heavily illustrated, and includes both open problems on the topics it discusses and detailed references to the literature on these problems.
After an introductory chapter, the second and third chapters concern graph coloring, the history of the four color theorem for planar graphs, its equivalence to 3-edge-coloring of planar cubic graphs, the snarks (cubic graphs that have no such colorings), and the conjecture of W. T. Tutte that every snark has the Petersen graph as a graph minor. Two more chapters concern closely related topics, perfect matchings (the sets of edges that can have a single color in a 3-edge-coloring) and nowhere-zero flows (the dual concept to planar graph coloring). The Petersen graph shows up again in another conjecture of Tutte, that when a bridgeless graph does not have the Petersen graph as a minor, it must have a nowhere-zero 4-flow.
Chapter six of the book concerns cages, the smallest regular graphs with no cycles shorter than a given length. The Petersen graph is an example: it is the smallest 3-regular graph with no cycles of length shorter than 5. Chapter seven is on hypohamiltonian graphs, the graphs that do not have a Hamiltonian cycle through all vertices but that do have cycles through every set of all but one vertices; the Petersen graph is the smallest example. The next chapter concerns the symmetries of graphs, and types of graphs defined by their symmetries, including the distance-transitive graphs and strongly regular graphs (of which the Petersen graph is an example) and the Cayley graphs (of which it is not). The book concludes with a final chapter of miscellaneous topics too small for their own chapters.
Audience and reception
The book assumes that its readers already have some familiarity with graph theory. It can be used as a reference work for researchers in this area, or as the basis of an advanced course in graph theory.
Although Carsten Thomassen describes the book as "elegant", and Robin Wilson evaluates its exposition as "generally good", reviewer Charles H. C. Little takes the opposite view, finding fault with its copyediting, with some of its mathematical notation, and with its failure to discuss the lattice of integer combinations of perfect matchings, in which the number
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https://en.wikipedia.org/wiki/Statistics%20of%20the%20COVID-19%20pandemic%20in%20Tamil%20Nadu
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Statistics
Total confirmed cases, active cases, recoveries and deaths
Active cases
Confirmed cases by districts
Case completion percentage
Daily new cases
Daily new recovered
Daily new deaths
Note: On 22 July, 444 previous deaths were added to Chennai district after reconciliation; which are not included in the chart.
Daily new cases by type of spread
Positive sampling rate
Case fatality rate
The trend of case fatality rate for COVID-19 from 25 March, the day first death in the state was recorded.
Total samples tested
Daily new samples tested
Plot of new samples tested per day vs new confirmed positive per day
References
External links
COVID-19 dashboard
StopCoronaTN – Department of Health and Family Welfare, Tamil Nadu
Minister of Health and Family Welfare – Ministry of Health and Family Welfare's homepage
– National Health Mission Tamil Nadu channel
COVID-19 pandemic in India
Tamil Nadu
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https://en.wikipedia.org/wiki/Subodha%20Kumar
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Subodha Kumar is known for his work on web advertising, social media, healthcare, analytics, and disruptive technologies. He is the Paul R. Anderson Distinguished Chair Professor of Statistics, Operations, and Data Science (with a secondary appointment in Information Systems) at the Fox School of Business, Temple University. He founded the Center for Business Analytics and Disruptive Technologies at Temple University and directs the Ph.D. Program in Operations and Supply Chain Management.
Kumar is the Deputy Editor for the Production and Operations Management journal, a journal in the field of operations and supply chain management. He is the Founding Executive Editor of the Management and Business Review journal. Kumar's research expertise lies in web advertising. He has (co)-authored two books in the areas of web analytics - Optimization Issues in Web and Mobile Advertising: Past and Future Trends Social Media Analytics and Practical Applications: The Change to the Competition Landscape.
Kumar has received several awards for research, teaching, and service to the academic community. He has been invited by media to provide expert opinion on matters related to social media, marketing, and business management.
Education and Academic Career
Kumar was born in India where he received his Bachelor of Mechanical Engineering from BIT Sindri, India. He later went on to get his masters in Industrial and Management Engineering from Indian Institute of Technology Kanpur. He received his MBA and PhD (2001) in Management Sciences and Information Systems from University of Texas, Dallas. Kumar started his academic career as an Assistant Professor of Information Systems at Foster School of Business, University of Washington. He later joined Mays Business School at Texas A&M University in 2009, where he held Mays Research Fellow (2012), Shelley and Joe Tortorice '70 Faculty Research Fellow (2012 – 2013), and Carol and G. David Van Houten, Jr. '71 Professorship (2013 – 2017).
Patent and Writing
Kumar holds a patent (United States Patent # 6,556,893, approved on April 29, 2003) on “Robotic System Control.”
Books
Subodha is the author of Optimization Issues in Web and Mobile Advertising: Past and Future Trends, which summarizes the state of the art research on the web and mobile advertising. He is also a co-author of Social Media Analytics and Practical Applications: The Change to the Competition Landscape, which illustrates how social media analytics can help firms build transformational strategies and cope with the challenges of social media technology.
Journal and Refereed Conference Publications
Subodha has published more than 90 papers in scientific journals including Operations Research, Management Science, Information Systems Research, Production and Operations Management, MIS Quarterly, Manufacturing & Service Operations Management, Journal of Operations Management, Journal of Management Information Systems, Decision Sciences, IIE Transactions, E
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https://en.wikipedia.org/wiki/Ernesto%20Laura
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Ernesto Laura (23 March 1879 – 29 December 1949) was an Italian mathematician born in Porto Maurizio.
Biography
He graduated in mathematics in 1901 at the University of Turin, where he was a student of Morera and of Somigliana.
He taught rational mechanics at the Universities of Messina, Pavia and Padua.
Laura has dealt with uncommon elasticity problems, namely related to indefinitely extended elastic means and, especially in the last part of his University career, the mechanics of flexible and inextensible surfaces.
Notes
External links
An Italian short biography of Ernesto Laura in Edizione Nazionale Mathematica Italiana online.
1879 births
1949 deaths
20th-century Italian mathematicians
University of Turin alumni
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https://en.wikipedia.org/wiki/Angela%20Kunoth
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Angela Kunoth (born 22 June 1963) is a German mathematician specializing in the numerical analysis of partial differential equations. She is a professor of mathematics at the University of Cologne, and the editor-in-chief of SIAM Journal on Numerical Analysis.
Education and career
Kunoth studied mathematics at Bielefeld University beginning in 1982, and earned a diploma there in 1990. After visiting the University of South Carolina as a Fulbright Scholar, she completed a doctorate (Dr. rer. nat.) at the Free University of Berlin in 1994. Her dissertation, Multilevel Preconditioning, was supervised by Wolfgang Dahmen.
After research positions at SINTEF in Norway, at the Weierstrass Institute in Berlin, at Texas A&M University, and at RWTH Aachen University, she became an associate professor at the University of Bonn in 1999, and earned a habilitation through RWTH Aachen in 2000 with the habilitation thesis Wavelet Methods for Minimization Problems Involving Elliptic Partial Differential Equations. She moved to Paderborn University as a full professor and chair of complex systems in 2007, and at Paderborn served as director of the mathematical institute and vice-dean of the faculty for electrotechnics from 2010 to 2012. She moved again to the University of Cologne as professor and chair for applied mathematics in 2013.
Kunoth was elected to the 2023 Class of SIAM Fellows.
Book
Kunoth is the author of the monograph Wavelet Methods — Elliptic Boundary Value Problems and Control Problems (Springer, 2001), a book version of her habilitation thesis.
References
External links
Home page
1963 births
Living people
20th-century German mathematicians
German women mathematicians
Bielefeld University alumni
Free University of Berlin alumni
Academic staff of the University of Bonn
Academic staff of Paderborn University
Academic staff of the University of Cologne
20th-century German women
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https://en.wikipedia.org/wiki/The%20Unimaginable%20Mathematics%20of%20Borges%27%20Library%20of%20Babel
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The Unimaginable Mathematics of Borges' Library of Babel is a popular mathematics book on Jorge Luis Borges and mathematics. It describes several mathematical concepts related to the short story "The Library of Babel", by Jorge Luis Borges. Written by mathematics professor William Goldbloom Bloch, and published in 2008 by the Oxford University Press, it received an honorable mention in the 2008 PROSE Awards.
Topics
"The Library of Babel" was originally written by Borges in 1941,
based on an earlier essay he had published in 1939 while working as a librarian. It concerns a fictional library containing every possible book of a certain fixed length, over a 25-symbol alphabet (which, including spacing and punctuation, is sufficient for the Spanish language). These assumptions, based on the dimensions of his own library and spelled out in more detail in the story, imply that the total number of books in the library is 251312000, an enormous number. The story also describes, with an attitude of some horror, the physical layout of the library that holds all of these books, and some of the behavior of its inhabitants.
After a copy of "The Library of Babel" itself, as translated into English by Andrew Hurley, The Unimaginable Mathematics of Borges' Library of Babel has seven chapters on its mathematics. The first chapter, on combinatorics, repeats the calculation above, of the number of books in the library, putting it in context with the size of the known universe and with other huge numbers, and uses this material as an excuse to branch off into a discussion of logarithms and their use in estimation. The second chapter concerns a line in the story about the existence of a library catalog for the library, using information theory to prove that such a catalog would necessarily equal in size the library itself, and touching on topics including the prime number theorem. The third chapter considers the mathematics of the infinite, and the possibility of books with infinitely many, infinitely thin pages, connecting these topics both to a footnote in "The Library of Babel" and to another Borges story, "The Book of Sand", about such an infinite book.
Chapters four and five concern the architecture of the library, described as a set of interconnected hexagonal rooms, exploring the possibilities for their connections in terms of geometry, topology, and graph theory. They also use mathematics to deduce unexpected conclusions about the library's structure: it must have at least one room whose shelves are not full (because the number of books per room does not divide the total number of books evenly), and the rooms on each floor of the library must either be connected into a single Hamiltonian cycle, or possibly be disconnected into subsets that cannot reach each other. Chapter six considers the ways the books might be distributed through these rooms, and chapter seven views the library and its interactions with its inhabitants as analogous to Turing machines. A
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https://en.wikipedia.org/wiki/Alassane%20Sow
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Alassane Sow (born 3 January 1997) is a Senegalese footballer who last played for Bizertin.
Career statistics
Club
Notes
References
1997 births
Living people
Senegalese men's footballers
Senegal men's youth international footballers
Senegalese expatriate men's footballers
Men's association football midfielders
Tunisian Ligue Professionnelle 1 players
Real Zaragoza players
CA Bizertin players
Expatriate men's footballers in Spain
Expatriate men's footballers in Tunisia
Senegalese expatriate sportspeople in Spain
Senegalese expatriate sportspeople in Tunisia
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https://en.wikipedia.org/wiki/Mouhameth%20San%C3%A9
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Mouhameth Sané (born 26 January 1996) is a Senegalese footballer who currently plays as a defender for Mulhouse.
Career statistics
Club
Notes
References
1996 births
Living people
Senegalese men's footballers
Senegal men's youth international footballers
Senegalese expatriate men's footballers
Men's association football defenders
Championnat National 3 players
Championnat National 2 players
Dijon FCO players
AJ Auxerre players
FC Mulhouse players
Expatriate men's footballers in France
Senegalese expatriate sportspeople in France
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https://en.wikipedia.org/wiki/Michel%20Tab%C3%A1rez
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Michel Emanuel Tabárez Soria (born 29 March 1995) is an Uruguayan footballer who last played for CA Fénix.
Career statistics
Club
Notes
References
1995 births
Living people
Men's association football goalkeepers
Uruguayan men's footballers
Uruguay men's youth international footballers
Uruguayan Primera División players
Centro Atlético Fénix players
People from Treinta y Tres
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https://en.wikipedia.org/wiki/Kim%20Seung-woo%20%28footballer%29
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Kim Seung-woo (; born 25 March 1998) is a South Korean professional footballer who plays as a centre-back for Gwangju FC.
Career statistics
Club
References
1998 births
Living people
South Korean men's footballers
South Korea men's youth international footballers
Men's association football defenders
K League 1 players
K League 2 players
Jeju United FC players
Gwangju FC players
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https://en.wikipedia.org/wiki/Lee%20Jung-moon
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Lee Jung-moon (; born 18 March 1998) is a South Korean footballer who plays for K League 2 side Seoul E-Land.
Career statistics
Club
References
1998 births
Living people
Footballers from Seoul
South Korean men's footballers
South Korea men's under-20 international footballers
Men's association football utility players
Daejeon Hana Citizen players
Jeju United FC players
Seoul E-Land FC players
K League 2 players
K League 1 players
Yonsei University alumni
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https://en.wikipedia.org/wiki/Lee%20Kyu-hyuk%20%28footballer%29
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Lee Kyu-hyuk (; born 4 May 1999) is a South Korean footballer currently playing as a defender for the Jeonnam Dragons.
Career statistics
Club
References
1999 births
Living people
South Korean men's footballers
South Korea men's youth international footballers
Men's association football defenders
K League 2 players
Jeju United FC players
South Korea men's under-20 international footballers
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https://en.wikipedia.org/wiki/Paraguay%20national%20football%20team%20results%20%282020%E2%80%93present%29
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This page details the match results and statistics of the Paraguay national football team from 2020 to present.
Key
Key to matches
Att.=Match attendance
(H)=Home ground
(A)=Away ground
(N)=Neutral ground
Key to record by opponent
Pld=Games played
W=Games won
D=Games drawn
L=Games lost
GF=Goals for
GA=Goals against
Results
Notes
Record by opponent
References
Paraguay national football team results
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https://en.wikipedia.org/wiki/Philip%20Adjah
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Philip Adjah Tettey-Narh (born 25 June 1998) is a Ghanaian professional footballer who plays as a forward for Rahmatganj MFS in the Bangladesh Premier League.
Career statistics
Club
Honours
Gokulam Kerala
I-League: 2020–21
References
External links
Living people
1998 births
Ghanaian men's footballers
Ghanaian expatriate men's footballers
Expatriate men's footballers in India
NEROCA FC players
Men's association football forwards
Rahmatganj MFS players
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https://en.wikipedia.org/wiki/Oum%20Sang-il
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Oum Sang-il (; born 1976) is a Korean mathematician working in graph theory and discrete mathematics. He is a tenured professor in the Department of Mathematical Sciences at KAIST and the chief investigator of the Discrete Mathematics Group in the Pioneer Research Center for Mathematical and Computational Sciences at the Institute for Basic Science. He is known for his work on structural graph theory and in particular for structures and algorithms relating to rank-width, clique-width, and branch-width. He published more than 45 journal papers.
He won the Young Scientist Award from the South Korean government in 2012.
and the TJ Park Young Professor Fellowship from the POSCO TJ Park Foundation in 2009.
He has been an editor of the Journal of the Korean Mathematical Society since 2011 and a founding member of Young Korean Academy of Science and Technology.
He wrote a monthly pieces for the monthly magazine "Math Donga" (ko) for 4 years from 2016, sharing the latest research breakthroughs in mathematics.
In the Korean Mathematical Society, he was appointed twice (2011-2012, 2017-2018) as an executive member of the board of trustees in charge of the Korean Mathematical Olympiad. He was a member of the Korean Mathematical Olympiad Committee for 2011-2018 and was the deputy leader of the South Korean team at the International Mathematical Olympiad in 2012 and 2018.
Education
Born in Yecheon County, Oum attended Daegu Science High School in Daegu from 1992. He then went to KAIST where he majored in mathematics and graduated with a B.S. in 1998. Studying in the Program of Applied and Computational Mathematics of Princeton University, he majored in graph theory and discrete mathematics. His dissertation was overseen by Professor Paul Seymour and Ph.D. was awarded in 2005.
Career
From 1999 to 2002, Oum worked as a computer programmer in Korea.
He was a visiting assistant professor in the School of Mathematics, Georgia Tech for 2005-2006 and a postdoctoral fellow under Jim Geelen in the Department of Combinatorics & Optimization in the University of Waterloo in 2007. In 2008, he joined the Department of Mathematical Sciences KAIST as an assistant professor before coming an associate professor and then full professor in 2011 and 2016, respectively. He was an affiliate professor in the School of Mathematics, Korea Institute for Advanced Study for several years. In 2018, he was appointed as the CI (Chief Investigator) of the Discrete Mathematics Group in the Pioneer Research Center for Mathematical and Computational Sciences at the Institute for Basic Science (IBS). This and the Pioneer Research Center for Biomolecular and Cellular Structure are the first of two such centers at IBS.
Awards and honors
2022: Choi Seok-jeong Award
2017: Founding member of Young Korean Academy of Science and Technology
2012: Young Scientist Award, President of Korea
2011: Excellent Young Researcher Research Award, National Research Foundation of Korea
2010: Excellent Resea
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https://en.wikipedia.org/wiki/Ismar%20Voli%C4%87
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Ismar Volić is a Bosnian-American mathematician. He is a professor of mathematics at Wellesley College and a co-founder of the Institute for Mathematics and Democracy.
Education and career
Volić completed his undergraduate degree at Boston University in 1998 and his Ph.D. in mathematics at Brown University in 2003 under the direction of Thomas Goodwillie. He was a Whyburn Research Instructor at the University of Virginia from 2003 to 2006. He has been teaching at Wellesley College since 2006. He was a visiting professor at MIT, Louvain-la-Neuve University, and the University of Virginia.
In 2019, he co-founded the Institute for Mathematics and Democracy to "promote a deeper understanding of mathematics as a pivotal force in creating a democracy where people make informed political decisions and enact change based on objective and rigorous quantitative criteria".
Volić is an active member of the Bosnian-Herzegovinian American Academy of Arts and Sciences, an organization dedicated to advancement of arts and science in Bosnia and Herzegovina. He was its treasurer in 2016–2019, vice-president in 2019–20, and its president in 2020–21. He travels to Bosnia and Herzegovina frequently through his involvement in various education and research activities, including advising Ph.D. students and working with various agencies to bring quality STEM education to the country.
Research
Volić's research is in algebraic topology. He is the author of over thirty articles and two books and has delivered more than two hundred lectures in some twenty countries. He has contributed to the fields of calculus of functors, spaces of embeddings and immersions, configuration space integrals, finite type invariants, Milnor invariants, rational homotopy theory, topological data analysis, and social choice theory.
Selected papers
"Formality of the little N-discs operad", with P. Lambrechts, Memoirs of the American Mathematical Society, 239 (2014), no. 1079, 116 pp.
"The rational homology of spaces of long knots in codimension >2", with P. Lambrechts and V. Turchin, Geometry & Topology, 14 (2010), 2151–2187.
"Calculus of functors, operad formality, and rational homology of embedding spaces", with G. Arone and P. Lambrechts, Acta Mathematica, 199 (2007), no. 2, 153-198.
"Finite type knot invariants and calculus of functors", Compositio Mathematica, 142 (2006), 222-250.
Books
Cubical homotopy theory, with B. Munson, New Mathematical Monographs, 25. Cambridge University Press, Cambridge, 2015. 625 pp.
Awards
Volić was awarded a 2017-2018 Fulbright U.S. Scholar grant, which he used to visit University of Sarajevo. He was also selected as a Fulbright Specialist for three years in 2020. He has received several grants form the National Science Foundation as well as grants from the Simons Foundation and the Open Society Foundation.
References
Year of birth missing (living people)
Living people
Wellesley College faculty
Boston University alumni
Brown University alum
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https://en.wikipedia.org/wiki/Franco%20Sosa%20%28footballer%2C%20born%201995%29
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Franco Tomás Sosa (born 9 September 1995) is an Argentine footballer who plays as a forward for Italian club Cerignola.
Career statistics
Notes
References
1995 births
Living people
Argentine men's footballers
Argentine expatriate men's footballers
Men's association football forwards
Primera B Metropolitana players
Serie D players
Defensores de Belgrano footballers
Club Atlético Aldosivi footballers
Club Atlético Fénix players
Polisportiva Olympia Agnonese players
ASD Sorrento players
USD Città di Fasano players
SS Audace Cerignola players
Argentine expatriate sportspeople in Italy
Expatriate men's footballers in Italy
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https://en.wikipedia.org/wiki/Conway%20circle%20theorem
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In plane geometry, the Conway circle theorem states that when the sides meeting at each vertex of a triangle are extended by the length of the opposite side, the six endpoints of the three resulting line segments lie on a circle whose centre is the incentre of the triangle. The circle on which these six points lie is called the Conway circle of the triangle. The theorem and circle are named after mathematician John Horton Conway.
The radius of the Conway circle is
where and are the inradius and semiperimeter of the triangle.
Conway's circle is a special case of a more general circle for a triangle that can be obtained as follows: Given any △ABC with an arbitrary point P on line AB. Construct BQ = BP, CR = CQ, AS = AR, BT = BS, CU = CT. Then AU = AP, and PQRSTU is cyclic.
See also
List of things named after John Horton Conway
References
External links
Conway’s Circle Theorem as special case of Side Divider Theorem at Dynamic Geometry Sketches, interactive geometry sketches.
Theorems about triangles and circles
John Horton Conway
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https://en.wikipedia.org/wiki/Anna%20Irwin%20Young
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Anna Irwin Young (1873–1920) was an American professor of mathematics, physics and astronomy and in 1916 was a charter member of the Mathematical Association of America.
Biography
Young was born in what is now Chicago Heights, Illinois on November 25, 1873. Her father was Rev. Samuel Young of Ireland, and her mother was Eliza Caskey Young.
Early years
She attended Westminster College in 1892, and the following year, she began her studies at the Agnes Scott Institute (now Agnes Scott College), in Decatur, Georgia, completing her initial work there in 1895. She later continued her studies earning her A.B. degree in 1898, and she was the institute's librarian from 1898 to 1902. She also taught summer school at the University of Chicago in 1898 and 1901.
Teaching years
In 1897, as was the custom at the time, Young began her teaching career as a lecturer at Agnes Scott even before earning her bachelor's degree. The following year she was appointed to the Department of Mathematics. According to McNair, "When Agnes Scott became a college in 1905-1906, [Young] continued in the college faculty; however, feeling that she should have a degree, she took the requisite courses and received her B.A. degree in 1910." (According to a different source, she earned her A.B. degree in 1898.)
From 1910 until her sudden passing in 1920, she served as Professor of Mathematics, Physics and Astronomy at Agnes Scott. She also taught summer school at the University of Georgia.
In 1914, Young took a leave of absence to earn her master's degree in education from Columbia University in New York.
According to McNair, she was known as an exceptional teacher. "One account is of a senior who repeatedly failed trigonometry 'until the day came when she had the last exam that she could have on it. And she'd studied so hard and was so scared that in the glare of the classroom and under the sound of the thumping of her own heart she forgot everything she knew and didn't try to work some of the problems. That night she was sent for and she went to Miss Young's room. 'Now,' said Miss Young sweetly and firmly, 'I know you know this, and I know you can work these problems. Sit down in that chair and work them.' And there in the quiet she worked them. And so — she passed."She was a charter member of the school's alumnae association and was very active in campus life until the time of her death.
Sudden death
During a 1920 trip to Pittsburgh, Pennsylvania to visit relatives, Young contracted pneumonia and died at 46 years of age on September 3. She was buried in Westview Cemetery, Atlanta, Georgia.
At her funeral service, Agnes Scott President Frank Henry Gaines said, "A truer woman, a finer character, a more devoted Christian, a more useful member of the College community, it would be difficult to find."
The 1920 class of Agnes Scott student, the last group to graduate while Young was alive, dedicated their college yearbook to her with this: "To her whose loyal devotion has eve
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https://en.wikipedia.org/wiki/Park%20Kyung-mee
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Park Kyung-mee (; born 15 October 1965) is a South Korean politician who served as the Spokesperson of President Moon Jae-in from 2021 to 2022. She was previously a professor of mathematics education at Hongik University and Chungbuk National University.
She is widely known to the public for her educational books on mathematics. After becoming a politician, she continues such effort through her YouTube channel. She also hosted a famous TV debate programme at MBC in 2014 becoming its first female host in its history which dates back to 1999.
In the 2016 general election, Park was the first candidate to be named for Democratic Party's proportional representation list. As a parliamentarian, she took numerous roles in her party such as its spokesperson, floor spokesperson and deputy floor leader - twice from 2017 to 2018 and again in 2019 to 2020.
After losing her re-election in 2020, Park was brought to the Office of the President as President Moon's secretary for education. In April 2021, she was promoted to his spokesperson.
Park holds three degrees - a bachelor in mathematics education from Seoul National University and a master's in mathematics and a doctorate in mathematics education from University of Illinois at Urbana–Champaign.
Electoral history
References
Living people
1965 births
21st-century South Korean politicians
Members of the National Assembly (South Korea)
20th-century South Korean mathematicians
Seoul National University alumni
Academic staff of Hongik University
Academic staff of Chungbuk National University
University of Illinois College of Education alumni
Democratic Party of Korea politicians
South Korean government officials
South Korean women academics
21st-century South Korean women politicians
21st-century South Korean mathematicians
Female members of the National Assembly (South Korea)
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https://en.wikipedia.org/wiki/Namibia%20Statistics%20Agency
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The Namibia Statistics Agency (NSA), formerly the Central Bureau of Statistics (CBS), is the national statistical authority of Namibia, which is located in the capital Windhoek.
History
Before Namibian Independence in 1990, there was no stand-alone statistical authority. Statistical data was managed through a department of the South African Statistical Services. After independence, the Central Statistical Office was launched as a division of the National Planning Commission. It was later renamed the Central Bureau of Statistics.
In 2011, the Namibia Statistics Agency was formalised on the basis of the Statistics Act, 20 (Act No 9 of 2011) after it had already existed for several years. It reports to the National Planning Commission (NPC).
Legal Basis
The statistical authority until 2011 operated on the basis of the Statistics Act, No 66 of 1976. A new Statistics Bill was discussed by the national assembly during 2010 to 2011, including the formation of an entirely independent Namibia Statistics Agency. With the endorsement of the Statistics Act, 2011 (Act No 9 of 2011) this was implemented.
Mandate and Organisation
The main responsibility of NSA are the preparation, publication and dissemination of objective, relevant, comparable, trustworthy, timely and easy to access official statistics in all areas of national interest. In addition, NSA coordinates the creation of official datasets, ensuring compliance with defined quality criteria.
NSA is headed by the Statistician General, currently Alex Shimuafeni.
Statistical Information
The NSA regularly publishes various statistical datasets and publications.
Economic Data
In the area of economics, NSA mainly publishes information on agriculture, consumer prices, foreign trade and macroeconomic data.
National Accounts: quarterly publications as well as summaries spanning across several years (example 2000–2009)
Annual Agricultural Survey and industrial statistics
Consumer Price Index (NCPI) and inflation: monthly publication since February 2005, following the Interim Consumer Price Index for Windhoek that existed since January 1993
Foreign Trade: quarterly publications
Demographic and Geospatial Data
This department deals with the social structure of Namibia.
Demography
Social sciences
Geographic Information Systems and Cartography
The main surveys include the Namibia Household Income and Expenditure Survey (NHIES) as well as the Namibia Inter-censal Demographic Survey (NIDS) conducted every five years, as well as the National Household Census conducted once in ten years. The first Geographic Information System created under the National Spatial Data Infrastructure (NSDI) policy, is the Bush Information System that provides a national dataset on bush encroachment.
External links
Official website of Namibia Statistics Agency
Central Bureau of Statistics, website of the National Planning Commission
References
Government of Namibia
National statistical services
Government agencies
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https://en.wikipedia.org/wiki/List%20of%20largest%20hospital%20campuses
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This is a list of large hospitals ranked by bed capacity and staffing within a single campus.
Hospital networks that consist of several campuses are not considered as a whole, and statistics from satellite campuses are not included. Campuses that do not have reliable sources may not be included; it is not necessarily a complete list.
Ranked by capacity
This is a list of hospital campuses with a capacity of more than 1,500 beds.
Ranked by staff
This is a list of hospital campuses with more than 10,000 staff.
See also
Lists of hospitals
List of largest hospital networks
List of tallest hospitals
List of the oldest hospitals in the United States
Notes
References
Capacity
Hospitals by capacity
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https://en.wikipedia.org/wiki/Total%20subset
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In mathematics, more specifically in functional analysis, a subset of a topological vector space is said to be a total subset of if the linear span of is a dense subset of
This condition arises frequently in many theorems of functional analysis.
Examples
Unbounded self-adjoint operators on Hilbert spaces are defined on total subsets.
See also
References
Functional analysis
Topological vector spaces
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https://en.wikipedia.org/wiki/Sequentially%20complete
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In mathematics, specifically in topology and functional analysis, a subspace of a uniform space is said to be sequentially complete or semi-complete if every Cauchy sequence in converges to an element in .
is called sequentially complete if it is a sequentially complete subset of itself.
Sequentially complete topological vector spaces
Every topological vector space is a uniform space so the notion of sequential completeness can be applied to them.
Properties of sequentially complete topological vector spaces
A bounded sequentially complete disk in a Hausdorff topological vector space is a Banach disk.
A Hausdorff locally convex space that is sequentially complete and bornological is ultrabornological.
Examples and sufficient conditions
Every complete space is sequentially complete but not conversely.
A metrizable space then it is complete if and only if it is sequentially complete.
Every complete topological vector space is quasi-complete and every quasi-complete topological vector space is sequentially complete.
See also
Cauchy net
Complete space
Complete topological vector space
Quasi-complete space
Topological vector space
Uniform space
References
Bibliography
Functional analysis
Topological vector spaces
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https://en.wikipedia.org/wiki/Milenko%20Bo%C5%A1njakovi%C4%87
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Milenko Bošnjaković (born 4 March 1968) is a Bosnian professional football manager. He was most recently manager of Bosnian Premier League club Tuzla City.
Managerial statistics
Honours
Manager
Tuzla City
Second League of FBiH: 2014–15 (North), 2015–16 (North)
References
External links
1968 births
Living people
Sportspeople from Tuzla
Bosnia and Herzegovina football managers
FK Tuzla City managers
FK Radnički Lukavac managers
FK Sloboda Tuzla managers
FK Drina Zvornik managers
FK Zvijezda 09 managers
FK Budućnost Banovići managers
Premier League of Bosnia and Herzegovina managers
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https://en.wikipedia.org/wiki/Order%20summable
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In mathematics, specifically in order theory and functional analysis, a sequence of positive elements in a preordered vector space (that is, for all ) is called order summable if exists in .
For any , we say that a sequence of positive elements of is of type if there exists some and some sequence in such that for all .
The notion of order summable sequences is related to the completeness of the order topology.
See also
References
Bibliography
Functional analysis
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https://en.wikipedia.org/wiki/Faires
|
Faires is a surname. Notable people with the surname include:
Barbara Trader Faires (born 1943), British mathematics professor
Daniel Grady Faires (born 1983), American contractor, interior designer, and craftsman
Jay Faires, American entrepreneur and investor
See also
Fairs (surname)
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https://en.wikipedia.org/wiki/Jang%20Hong-won
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Jang Hong-won (; born 21 May 1990) is a South Korean former footballer.
Career statistics
Club
Notes
References
1990 births
Living people
South Korean men's footballers
Men's association football goalkeepers
Bucheon FC 1995 players
Lion City Sailors FC players
Singapore Premier League players
South Korean expatriate sportspeople in Singapore
Expatriate men's footballers in Singapore
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https://en.wikipedia.org/wiki/Jung%20Hee-bong
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Jung Hee-bong (; born 17 March 1986) is a South Korean former footballer.
Career statistics
Club
Notes
References
1986 births
Living people
South Korean men's footballers
Men's association football forwards
Geylang International FC players
Gombak United FC players
Balestier Khalsa FC players
Singapore Premier League players
South Korean expatriate sportspeople in Singapore
Expatriate men's footballers in Singapore
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https://en.wikipedia.org/wiki/Karen%20D.%20King
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Karen Denise King (July 6, 1971 – December 24, 2019) was an African-American mathematics educator, a program director at National Science Foundation, and a 2012 AWM/MAA Falconer Lecturer.
Early life
Karen Denise King was born on July 6, 1971, in Washington, D.C. She was selected for the National Aeronautics and Space Administration Women in Science and Engineering (WISE) Scholars Program at Spelman College as an undergraduate and finished her degree in mathematics magna cum laude in 3 years. King next attended University of Maryland with a National Science Foundation fellowship and earned her Ph.D. in Mathematics Education in 1997. Her dissertation advisor was Patricia F. Campbell.
Professional career
King began her career as an assistant professor at San Diego State University in 1997. In 1999 she moved to Michigan State University. In 2006 King relocated to New York University as an associate professor. While a professor, King focused her research and publications on urban mathematics reform, the mathematical preparation of K-12 teachers, and mathematics professional development policies. King became the Director of Research for National Council of Teachers of Mathematics in 2011 where she co-authored the book Disrupting Tradition: Research and Practice in Mathematics. She later became a program director at the National Science Foundation of Education and Human Resources. In 2012 she was honored as an AWM/MAA Falconer Lecturer and served on the writing team that wrote The Mathematical Education of Teachers II. King also served as an associate editor for the Journal for Research in Mathematics Education from 2001 to 2004 and was a member of the Mathematics Association of America for nineteen years.
King's work earned her recognition by Mathematically Gifted & Black, where she was featured as a Black History Month 2020 Honoree.
Publications
Co-Author
King, K.D., Tate, William F., Anderson, Celia R., (2011) Disrupting Tradition: Research and Practice in Mathematics. Reston, VA:National Council of Teachers of Mathematics
Contributor
American Mathematical Society. (2012) The Mathematical Education of Teachers II (Cbms Issues in Mathematics Education). American Mathematical Society
RAND Mathematics Study Panel. (2003). Mathematical proficiency for all students: Toward a strategic research and development program in mathematics education. Santa Monica, CA: RAND Education.
Book Chapter
Rasmussen, C., Yackel, E., & King, K. (2003). Social and sociomathematical norms in the mathematics classroom. In R. Charles (Ed.). Teaching mathematics through problem solving: It's about learning mathematics. Reston, VA: National Council of Teachers of Mathematics.
King, K. D., Hillel, J., & Artigue, M. (2001) Technology. In D. Holton (Ed.). Teaching and Learning in University Level Mathematics (Results of the ICMI Study). Dordrecht: Kluwer Academic Publishers.
References
External links
MAA Memoriam page
Karen D King Curricula Vita 2006
Cadre Bio
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https://en.wikipedia.org/wiki/Combinatorics%20of%20Experimental%20Design
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Combinatorics of Experimental Design is a textbook on the design of experiments, a subject that connects applications in statistics to the theory of combinatorial mathematics. It was written by mathematician Anne Penfold Street and her daughter, statistician Deborah Street, and published in 1987 by the Oxford University Press under their Clarendon Press imprint.
Topics
The book has 15 chapters. Its introductory chapter covers the history and applications of experimental designs, it has five chapters on balanced incomplete block designs and their existence, and three on Latin squares and mutually orthogonal Latin squares. Other chapters cover resolvable block designs, finite geometry, symmetric and asymmetric factorial designs, and partially balanced incomplete block designs.
After this standard material, the remaining two chapters cover less-standard material. The penultimate chapter covers miscellaneous types of designs including circular block designs, incomplete Latin squares, and serially balanced sequences. The final chapter describes specialized designs for agricultural applications. The coverage of the topics in the book includes examples, clearly written proofs, historical references, and exercises for students.
Audience and reception
Although intended as an advanced undergraduate textbook, this book can also be used as a graduate text, or as a reference for researchers. Its main prerequisites are some knowledge of linear algebra and linear models, but some topics touch on abstract algebra and number theory as well.
Although disappointed by the omission of some topics, reviewer D. V. Chopra writes that the book "succeeds remarkably well" in connecting the separate worlds of combinatorics and statistics.
And Marshall Hall, reviewing the book, called it "very readable" and "very satisfying".
Related books
Other books on the combinatorics of experimental design include Statistical Design and Analysis of Experiments (John, 1971), Constructions and Combinatorial Problems in Design of Experiments (Rao, 1971), Design Theory (Beth, Jungnickel, and Lenz, 1985), and Combinatorial Theory and Statistical Design (Constantine, 1987). Compared to these, Combinatorics of Experimental Design makes the combinatorial aspects of the subjects more accessible to statisticians, and its last two chapters contain material not covered by the other books. However, it omits several other topics that were included in Rao's more comprehensive text.
See also
The Design of Experiments (1935), by Ronald Fisher
References
Design of experiments
Mathematics textbooks
Statistics books
1987 non-fiction books
Clarendon Press books
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https://en.wikipedia.org/wiki/Kim%20Jae-hong
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Kim Jae-hong (; born 10 August 1984) is a South Korean former footballer.
Career statistics
Club
Notes
References
1984 births
Living people
South Korean men's footballers
Men's association football midfielders
Daegu FC players
Geylang International FC players
Singapore Premier League players
South Korean expatriate sportspeople in Singapore
Expatriate men's footballers in Singapore
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https://en.wikipedia.org/wiki/Sonajharia%20Minz
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Sonajharia Minz is an academician, trained in Mathematics and Computer Science, and engages with adivasi issues. She is the second tribeswoman hailing from Chotanagpur and appointed as a Vice-Chancellor in Sido Kanhu Murmu University, Dumka.
Early life
Minz hails from Oraon tribe, and from Gumla district in Jharkhand. She is the oldest of the four daughters of Nirmal Minz, a social ideologue and activist. She completed her schooling in Ranchi and graduated from Women's Christian College, Chennai. She passed M.Sc in Mathematics from Madras Christian College, Chennai.
Academic career
She completed her M.Phil, Ph.D in Computer Science from Jawaharlal Nehru University (JNU). Minz worked as the assistant professor in the Department of Computer Science, Madurai Kamaraj University in 1991, as well as Barkatullah University of Bhopal since 1990. She published several research papers in national and international journals.
In 1992, Minz joined in the post of assistant professor of Computer Science in Jawaharlal Nehru University.
Later, she was also appointed in the post of Associate Professor in 1997 and was promoted to be professor since 2005 at the School of Computer & Systems Sciences, Jawaharlal Nehru University. She worked for the rights of underprivileged and group of Dalit students. She also became the President of JNU’s Teacher Association (JNUTA).
On 27 May 2020, the Governor of Jharkhand, Draupadi Murmu appointed her as the Vice-Chancellor to the Sido Kanhu Murmu University in Dumka.
After successful completion of her term as Vice Chancellor, Sido Kanhu Murmu University, Dumka, Jharkhand, Sonajharia Minz has returned to her parent institution, School of Computer and Systems Sciences, Jawaharlal Nehru University, New Delhi.
References
Living people
Adivasi activists
Indian women activists
21st-century Indian educators
21st-century Indian women educators
Adivasi women
People from Adi Community
People from Gumla district
Indian women scholars
Indian women academics
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Sergio%20Boixo
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Sergio Boixo has degrees in computer engineering, philosophy, mathematics, and master and PhD in physics, and is best known for his work on quantum computing. He is currently working as Chief Scientist Quantum Computer Theory for Google's Quantum Artificial Intelligence Lab, a team he joined in 2013, shortly after its foundation.
Education years
Boixo began his university education with a computer engineering degree at the newly instituted Faculty of Computer Science (Complutense University of Madrid) from 1993 to 1996. He got the best qualifications in that first promotion, being awarded with the Chip de Oro prize for his academic achievements. In the meantime, he also took degrees both in philosophy (2002) and mathematics (2003) at the National University of Distance Education (UNED).
After a traineeship at the European Central Bank as a C++ developer (Frankfurt, 1999), he continued his professional career as a computer engineer in the German banking sector, system architect for Semanticedge, and software consultant and analyst for several international companies.
He then focused on his academic career, with a specialisation in physics. In 2004 he was awarded with a LaCaixa fellowship to specialise in the University of New Mexico and Los Alamos National Laboratory. In 2008 he was also awarded a scholarship by the Mutua Madrileña Foundation. He completed a master's degree in physics in the Autonomous University of Barcelona in 2008 and published some of his first research focusing on quantum annealing. He received his PhD in physics from the University of New Mexico in 2008, under the supervision of Carlton M. Caves for his thesis on nonlinear quantum metrology. Part of the theory developed on this thesis was later implemented in an optical experiment.
Research in Quantum Computing
His postdoctoral research began at the California Institute of Technology (Caltech) with John Preskill, who had coined the term "quantum advantage (supremacy)" which Boixo's Quantum Artificial Intelligence Lab would later demonstrate. There he specialised in quantum information and quantum computing, topics in which he continued his postdoctoral research at Harvard. In 2011, he moved to the University of Southern California, where he focused his research on quantum computing and began working on the first-ever commercial quantum processor for the Quantum Artificial Intelligence Lab, a joint initiative of NASA, Universities Space Research Association, and Google.
He joined Google's quantum computing team in 2013. This team has focused on topics such as quantum simulation, quantum neural networks and quantum metrology. In 2019 they published the landmark paper demonstrating they had achieved quantum advantage (supremacy), completing with a quantum computer in just three minutes a task that would take 10000 years to be done by the world's most powerful classical supercomputer. Boixo played the leading role on the development of the theory backing that experimen
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https://en.wikipedia.org/wiki/Rebecca%20Andridge
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Rebecca Roberts Andridge is an American statistician. Her statistical research concerns the imputation of missing data and the statistics of group-randomized trials; she has also performed highly-cited applied statistical work on omega-3 nutritional supplements and on the health benefits of using yoga to lower stress. Andridge is an associate professor of biostatistics at the Ohio State University.
Education and career
Andridge majored in economics at Stanford University, graduating in 1999. She went to the University of Michigan for graduate study, earning a master's degree in 2005 and completing her Ph.D. in biostatistics in 2009. Her dissertation, Statistical Methods for Missing Data in Complex Sample Surveys, was supervised by Roderick J. A. Little.
In 2009, after completing her Ph.D., she joined the Ohio State University College of Public Health as an assistant professor of biostatistics. She was tenured as an associate professor in 2016. At Ohio State, she also holds affiliations with the Institute for Population Research, Food Innovation Center, and Decision Sciences Collaborative.
Recognition
Andridge was elected as a Fellow of the American Statistical Association in 2020.
References
External links
Home page
Year of birth missing (living people)
Living people
American statisticians
Women statisticians
Stanford University School of Humanities and Sciences alumni
University of Michigan alumni
Ohio State University faculty
Fellows of the American Statistical Association
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https://en.wikipedia.org/wiki/Hollylynne%20Lee
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Hollylynne Stohl Lee (also published as Hollylynne Stohl and Hollylynne Stohl Drier) is an American mathematics educator and statistics educator who describes herself as an "educational designer" focusing on technology-based learning. She is a professor of mathematics education in the College of Education at North Carolina State University, where she directs the Hub for Innovation and Research in Statistics Education in the William and Ida Friday Institute for Educational Innovation.
Education and career
Lee graduated from Pennsylvania State University in 1991 with a bachelor's degree in secondary mathematics education. After earning a master's degree from the College of William and Mary in 1995, she completed a doctorate in mathematics education at the University of Virginia in 2000. Her dissertation, Children's Probabilistic Reasoning with a Computer Microworld, was supervised by Joe Garofalo.
While a student, she also worked as a mathematics and statistics teacher at the elementary school, middle school, and high school levels from 1992 to 2000. After completing her Ph.D., she became an assistant professor of mathematics education at North Carolina State University in 2000. She was promoted to full professor in 2013.
Recognition
In 2020, Lee was elected as a Fellow of the American Statistical Association. She has also won the University of North Carolina Board of Governors 2020 Award for Excellence in Teaching and the 2022 Robert Foster Cherry Award.
References
External links
Home page
Year of birth missing (living people)
Living people
21st-century American mathematicians
American women mathematicians
American statisticians
Women statisticians
Mathematics educators
Statistics educators
Penn State College of Education alumni
College of William & Mary alumni
Curry School of Education alumni
North Carolina State University faculty
Fellows of the American Statistical Association
21st-century American women
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https://en.wikipedia.org/wiki/Quinten%20Huybers
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Quinten Huybers (born 6 December 2001) is a Dutch footballer who currently plays as a defender for Eindhoven.
Career statistics
Club
Notes
References
2001 births
Living people
Dutch men's footballers
Men's association football defenders
FC Eindhoven players
Eerste Divisie players
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https://en.wikipedia.org/wiki/Youri%20Roseboom
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Youri Roseboom (born 19 January 2000) is a Dutch footballer who plays for MASV Arnhem.
Career statistics
Club
Notes
References
2000 births
Living people
Dutch men's footballers
Dutch expatriate men's footballers
Men's association football forwards
SBV Vitesse players
NEC Nijmegen players
Achilles '29 players
De Treffers players
FC Eindhoven players
VV DOVO players
K.F.C. Diest players
Tweede Divisie players
Eerste Divisie players
Dutch expatriate sportspeople in Poland
Dutch expatriate sportspeople in Belgium
Expatriate men's footballers in Poland
Expatriate men's footballers in Belgium
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https://en.wikipedia.org/wiki/Gijs%20van%20Otterdijk
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Gijs van Otterdijk (born 15 February 2002) is a Dutch footballer who currently plays as a defender for Eindhoven.
Career statistics
Club
Notes
References
2002 births
Living people
Dutch men's footballers
Men's association football defenders
FC Eindhoven players
Eerste Divisie players
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https://en.wikipedia.org/wiki/Robert%20Mej%C3%ADa
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Robert Andrés Mejía Navarrete (born 6 October 2000) is a Colombian footballer who plays as a midfielder for Atlético Nacional on loan from Once Caldas.
Career statistics
Club
Notes
References
2000 births
Footballers from Cauca Department
21st-century Colombian people
Living people
Colombian men's footballers
Colombia men's youth international footballers
Men's association football midfielders
Deportes Quindío footballers
Boca Juniors de Cali footballers
Universitario Popayán footballers
Once Caldas footballers
Giresunspor footballers
Atlético Nacional footballers
Categoría Primera B players
Categoría Primera A players
Süper Lig players
Colombian expatriate men's footballers
Expatriate men's footballers in Turkey
Colombian expatriate sportspeople in Turkey
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https://en.wikipedia.org/wiki/Guo%20Hui
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Guo Hui (; born 9 April 1978) is a former Chinese footballer.
Career statistics
Club
Notes
References
1978 births
Living people
Chinese men's footballers
Men's association football midfielders
Chinese Super League players
China League Two players
China League One players
Bayi Football Team players
Liaoning F.C. players
Beijing Guoan F.C. players
Dalian Professional F.C. players
Chinese expatriate sportspeople in Denmark
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https://en.wikipedia.org/wiki/Roselyn%20E.%20Williams
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Roselyn Elaine Williams is an American mathematician who is an Associate Professor and former chair of the mathematics department at Florida Agricultural and Mechanical University. Her decades long involvement in the National Association of Mathematicians includes a 14 year term as secretary-treasurer.
Research
Williams’ dissertation was in the field of finite dimensional Hopf algebras and she also has research interest in application of mathematics to physics and chemistry.
Education
Williams attended Spelman College in Atlanta, Georgia, where she was mentored by Dr. Etta Falconer who was chair of the mathematics department at the time. She graduated in 1972 with a Bachelor of Science degree in mathematics. She then went to the University of Florida where she was the first African American master's degree student in mathematics. After some time away from school, she returned to her graduate studies at Florida State University and earned a PhD in 1988 under the advisement of Warren Douglas Nichols.
Career
After earning her master's degree Williams became an instructor at Florida Agricultural and Mechanical University in Tallahassee, Florida for five years before returning to graduate school to earn a PhD. She returned to Florida Agricultural and Mechanical University as an Associate Professor of Mathematics after completing her doctoral degree in 1988. While chair of the mathematics department she co-founded the Alliance for the Production of African American PhDs in the Mathematical Sciences, which is now known as the National Alliance for Doctoral Studies in the Mathematical Sciences. Williams has been very involved in the National Association of Mathematicians (NAM), including serving as Secretary-Treasurer for the National Association of Mathematicians (NAM) from 2005-2019. She has won several National Science Foundation (NSF) grants, many for undergraduate research experiences as well as other programs at historically Black colleges and universities. Additional in 2011, she was the local coordinator for the EDGE (Enhancing Diversity in Graduate Education) program which support female students starting graduate degrees in mathematics.
Honors
Williams was awarded the Dr. Etta Z. Falconer Award for Mentoring and Commitment to Diversity at the Infinite Possibilities Conference in 2012. In 2020, she became an Association for Women in Mathematics (AWM) fellow for "her lifelong promotion of Historically Black Colleges and Universities and support of the EDGE Program; for her unwavering dedication to the National Association of Mathematicians; and for her unsung work to create AIM/ICERM’s REUF and the National Math Alliance." Also in 2020, Williams was awarded the NAM Lifetime Achievement Award which is "given to a Mathematician-Mathematics Educator who has provided at least twenty-five years of exemplary service to the mathematical sciences community and who has affirmed by others as having been the kind of professional and role model whose pr
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https://en.wikipedia.org/wiki/Order%20convergence
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In mathematics, specifically in order theory and functional analysis, a filter in an order complete vector lattice is order convergent if it contains an order bounded subset (that is, is contained in an interval of the form ) and if
where is the set of all order bounded subsets of X, in which case this common value is called the order limit of in
Order convergence plays an important role in the theory of vector lattices because the definition of order convergence does not depend on any topology.
Definition
A net in a vector lattice is said to decrease to if implies and in
A net in a vector lattice is said to order-converge to if there is a net in that decreases to and satisfies for all .
Order continuity
A linear map between vector lattices is said to be order continuous if whenever is a net in that order-converges to in then the net order-converges to in
is said to be sequentially order continuous if whenever is a sequence in that order-converges to in then the sequence order-converges to in
Related results
In an order complete vector lattice whose order is regular, is of minimal type if and only if every order convergent filter in converges when is endowed with the order topology.
See also
References
Functional analysis
Order theory
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https://en.wikipedia.org/wiki/Daniel%20Rudolph
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Daniel Jay Rudolph (1949–2010) was a mathematician who was considered a leader in ergodic theory and dynamical systems. He studied at Caltech and Stanford and taught postgraduate mathematics at Stanford University, the University of Maryland and Colorado State University, being appointed to the Albert C. Yates Endowed Chair in Mathematics at Colorado State in 2005. He jointly developed a theory of restricted orbit equivalence which unified several other theories. He founded and directed an intense preparation course for graduate math studies and began a Math circle for middle-school children. Early in life he was a modern dancer. He died in 2010 from amyotrophic lateral sclerosis, a degenerative motor neuron disease.
Early life and education
Rudolph was born to William Franklin Rudolph (1922–2000) and Betty Johnalou Waldner (1921–2004). He was the second of three sons, the others being Gregory and James. The family moved to Fort Collins when Daniel was very young. He attended Fort Collins High School where he was active in the chemistry, physics, computer and flying clubs, and was on the student council. He was a semifinalist in the Westinghouse Science Talent Search.
He graduated from Fort Collins High School in 1968 and matriculated at the California Institute of Technology. He attended Caltech on a Sloan Research Fellowship, and planned to major in theoretical physics. He soon changed his mind and graduated with a bachelor's degree in mathematics in 1972. Before graduating he won Caltech's Bell Prize for Undergraduate Mathematics Research.
Career
Rudolph moved to Stanford University in 1972 where revolutionary work was being done on ergodic theory. He was awarded a Master of Science in 1973 and completed his PhD under the supervision of Don Ornstein in 1975, with the thesis "Non-Bernoulli Behavior of the Roots of K-automorphisms". His work in ergodic theory focused on measure theory, as opposed to the functional analysis approach that dominated ergodic theory.
His description of ergodic theory:
From August 1975 to August 1976, Rudolph was a postdoctoral fellow at the Hebrew University of Jerusalem, where he devised a solution to a problem in ergodic theory that had resisted solutions by Ornstein and others, entitled "When are two-point extensions of Bernoulli shifts also Bernoulli shifts?". In so doing he devised the method of "nesting" which evolved into a powerful tool. He also began his studies into varieties of orbit equivalence.
He became a fellow of the Miller Institute at U.C. Berkeley from late 1976 to 1978 and was appointed assistant professor at Stanford University from 1978 to 1981. He spent part of 1979 at the University of Maryland where he studied dynamics. At Maryland, he lived at "Ergodic House" with Bruce Kitchens, Brian Marcus and Laif Swanson; they were regularly visited by Doug Lind and Andres del Junco.
In 1981 Rudolph was appointed associate professor at the University of Maryland and was awarded a Sloan Research
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https://en.wikipedia.org/wiki/List%20of%20men%27s%20Olympic%20water%20polo%20tournament%20records%20and%20statistics
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This is a list of records and statistics of the men's Olympic water polo tournament since the inaugural official edition in 1900.
Abbreviations
General statistics
This is a summary of men's water polo at the Summer Olympics by tournament.
The following table shows winning teams, coaches and captains by tournament. Last updated: 8 August 2021.
Legend
– Olympic winning streak (winning three or more Olympic titles in a row)
– Winning all matches during the tournament
– Host team
Team† – Defunct team
The following table shows top goalscorers, goalkeepers, sprinters and Most Valuable Players by tournament. Last updated: 8 August 2021.
Notes:
Top goalscorer: the water polo player who scored the most goals in a tournament.
Top goalkeeper: the water polo player who saved the most shots in a tournament.
Top sprinter: the water polo player who won the most sprints in a tournament.
Most Valuable Player: the water polo player who was named the Most Valuable Player of a tournament.
Legend and abbreviation
– Olympic winning streak
– Winning all matches during the tournament
– Host team
Team† – Defunct team
Player‡ – Player who won the tournament with his team
Eff % – Save efficiency (Saves / Shots)
Confederation statistics
Best performances by tournament
This is a summary of the best performances of each confederation in each tournament. Last updated: 8 August 2021.
Note: italic number in header means unofficial tournament was held.
Legend
– Champions
– Runners-up
– Third place
– Fourth place
– Qualified for forthcoming tournament
All-time best performances
This is a summary of the best performances of each confederation at the Olympics. Last updated: 8 August 2021.
Legend
Year* – As host team
Team† – Defunct team
Team statistics
Comprehensive team results by tournament
Note: Results of Olympic qualification tournaments are not included. Numbers refer to the final placing of each team at the respective Games; italic number in header means unofficial tournament was held. Last updated: 8 August 2021.
Legend
– Champions
– Runners-up
– Third place
– Fourth place
– Qualified but were not allowed to compete
– Disqualified
– The nation did not participate in the Games
– Qualified for forthcoming tournament
– Hosts
= – More than one team tied for that rank
Team† – Defunct team
Abbreviation
stats – Olympic water polo team statistics
EUA – United Team of Germany
FRG – West Germany
FRY – FR Yugoslavia
GDR – East Germany
SCG – Serbia and Montenegro
Number of appearances by team
The following table is pre-sorted by number of appearances (in descending order), year of the last appearance (in ascending order), year of the first appearance (in ascending order), name of the team (in ascending order), respectively. Last updated: 8 August 2021.
Legend and abbreviation
Year* – As host team
Team† – Defunct team
Apps – Appearances
stats – Olympic water polo team statistics
Best finishes by team
The
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https://en.wikipedia.org/wiki/List%20of%20women%27s%20Olympic%20water%20polo%20tournament%20records%20and%20statistics
|
This is a list of records and statistics of the women's Olympic water polo tournament since the inaugural official edition in 2000.
Abbreviations
General statistics
This is a summary of women's water polo at the Summer Olympics by tournament.
The following table shows winning teams, coaches and captains by tournament. Last updated: 31 March 2021.
Legend
– Olympic winning streak (winning three or more Olympic titles in a row)
– Winning all matches during the tournament
– Host team
Team† – Defunct team
The following table shows top goalscorers, goalkeepers, sprinters and Most Valuable Players by tournament. Last updated: 31 March 2021.
Notes:
Top goalscorer: the water polo player who scored the most goals in a tournament.
Top goalkeeper: the water polo player who saved the most shots in a tournament.
Top sprinter: the water polo player who won the most sprints in a tournament.
Most Valuable Player: the water polo player who was named the Most Valuable Player of a tournament.
Legend and abbreviation
– Olympic winning streak
– Winning all matches during the tournament
– Host team
Team† – Defunct team
Player‡ – Player who won the tournament with her team
Eff % – Save efficiency (Saves / Shots)
Confederation statistics
Best performances by tournament
This is a summary of the best performances of each confederation in each tournament. Last updated: 7 August 2021.
Legend
– Champions
– Runners-up
– Third place
– Fourth place
– Qualified for forthcoming tournament
All-time best performances
This is a summary of the best performances of each confederation at the Olympics. Last updated: 15 January 2021.
Legend
Year* – As host team
Team statistics
Comprehensive team results by tournament
Note: Results of Olympic qualification tournaments are not included. Last updated: 7 August 2021.
Legend
– Champions
– Runners-up
– Third place
– Fourth place
– Qualified for forthcoming tournament
– Hosts
Abbreviation
stats – Olympic water polo team statistics
Number of appearances by team
The following table is pre-sorted by number of appearances (in descending order), year of the last appearance (in ascending order), year of the first appearance (in ascending order), name of the team (in ascending order), respectively. Last updated: 7 August 2021.
Legend and abbreviation
Year* – As host team
Apps – Appearances
stats – Olympic water polo team statistics
Best finishes by team
The following table is pre-sorted by best finish (in descending order), name of the team (in ascending order), respectively. Last updated: 7 August 2021.
Legend and abbreviation
Year* – As host team
Apps – Appearances
stats – Olympic water polo team statistics
Finishes in the top four
The following table is pre-sorted by total finishes in the top four (in descending order), number of Olympic gold medals (in descending order), number of Olympic silver medals (in descending order), number of Olympic bronze medals (in descending order),
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https://en.wikipedia.org/wiki/Jan-Erik%20Roos
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Jan-Erik Ingvar Roos (16 October 1935 – 15 December 2017) was a Swedish mathematician whose research interests were in abelian category theory, homological algebra, and related areas.
He was born in Halmstad, in the province of Halland on the Swedish west coast. Roos enrolled at Lund University in 1954, and started studying mathematics with Lars Gårding in 1957. Under Gårding's direction he wrote a thesis on ordinary differential equation, and graduated in 1958 with a licentiate degree. Later that year he went to Paris on a doctoral scholarship; there, he gravitated towards the mathematical environment at the Institut Henri Poincaré, and the various seminars held there. After a while, he started attending Alexander Grothendieck's seminar at the Institut des hautes études scientifiques in Bures-sur-Yvette, where he became interested in abstract algebra and algebraic geometry. In 1967 he was invited by Saunders Mac Lane to visit the University of Chicago for three months; Mac Lane was impressed by Roos and later wrote a very positive letter of recommendation for him.
Upon his return to Sweden, Roos was appointed Professor of Mathematics at Stockholm University in 1970, and started building a strong algebra school. He was elected to the Royal Swedish Academy of Sciences in 1980 and was its President from 1980 to 1982. While serving on the Academy, he was on the committees deciding the Rolf Schock Prizes in Mathematics and the Crafoord Prize in Astronomy and Mathematics.
Roos made important contributions to homological algebra, and did extensive computer-assisted studies of Hilbert–Poincaré series and their rationality. A special issue of the journal Homology, Homotopy and Applications ("The Roos Festschrift volume") was published in 2002, on the occasion of his 65th birthday.
He died on 15 December 2017 at his home in Uppsala and is buried at the Uppsala old cemetery.
Publications
References
1935 births
2017 deaths
People from Halmstad
20th-century Swedish mathematicians
21st-century Swedish mathematicians
Algebraists
Lund University alumni
Swedish expatriates in France
Members of the Royal Swedish Academy of Sciences
Academic staff of Stockholm University
Burials at Uppsala old cemetery
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https://en.wikipedia.org/wiki/Jaap%20Murre
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Jacob Pieter "Jaap" Murre (18 September 1929 – 9 April 2023) was a Dutch mathematician specializing in algebraic geometry. He was a professor of mathematics at Leiden University.
Career
Murre was born on 18 September 1929 in Baarland. At his small primary school one of his classmates and friends was later botanist . Murre studied mathematics at Leiden University and in 1957 he obtained his doctorate under Hendrik Kloosterman with a thesis titled: "Over multipliciteiten van maximaal samenhangende bossen". In 1959 he was appointed associate professor (lector) at Leiden University. In 1961 he became professor of mathematics at the same institute, with a teaching assignment in algebraic geometry. He retired in 1994.
Murre was elected a member of the Royal Netherlands Academy of Arts and Sciences in 1971. He was elected a foreign member of the in 2004.
Murre died on 9 April 2023 at the age of 93.
References
External links
Profile at Leiden University
1929 births
2023 deaths
Algebraic geometers
Dutch mathematicians
Leiden University alumni
Academic staff of Leiden University
Members of the Royal Netherlands Academy of Arts and Sciences
People from Borsele
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https://en.wikipedia.org/wiki/Karl-G%C3%B6ran%20M%C3%A4ler
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Karl-Göran Mäler (1939 – May 20, 2020) was a Swedish economist.
Mäler was born in 1939 in Sollefteå. He pursued undergraduate study in mathematics, statistics and economics at Stockholm University. Mäler specialized in economics at the graduate level, attending the Massachusetts Institute of Technology and Stanford University in the United States before earning a doctorate from Stockholm University in 1972. He was a professor at the Stockholm School of Economics between 1975 and 2002. Mäler was elected to the Royal Swedish Academy of Sciences in 1981, and served on its Committee for the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel until 1994. Mäler and Partha Dasgupta founded the Beijer Institute of Ecological Economics in 1992, and Mäler served as the institute's director through 2006. He and Dasgupta shared the Volvo Environment Prize in 2002. Mäler died in a Stockholm retirement home on 20 May 2020.
References
1939 births
2020 deaths
20th-century Swedish economists
21st-century Swedish economists
People from Sollefteå Municipality
MIT School of Humanities, Arts, and Social Sciences alumni
Stanford University alumni
Stockholm University alumni
Members of the Royal Swedish Academy of Sciences
Academic staff of the Stockholm School of Economics
Swedish expatriates in the United States
Environmental economists
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https://en.wikipedia.org/wiki/Babette%20Brumback
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Babette Anne Brumback is an American biostatistician known for her work on causal inference. She is a professor of biostatistics at the University of Florida.
Education and career
Brumback earned a bachelor's degree in electrical engineering at the University of Virginia in 1988. She went to the University of California, Berkeley for graduate study, originally in electrical engineering and computer science but then switching to statistics; she earned a master's degree in 1992 and completed her Ph.D. in 1996. Her dissertation, Statistical Methods for Hormone Data, was supervised by John A. Rice.
After postdoctoral research at Harvard University she became an assistant professor of biostatistics at the University of Washington in 1999, and while there also became affiliated with the Fred Hutchinson Cancer Research Center. She moved to the University of California, Los Angeles in 2002 and again to the University of Florida in 2004.
Honors and awards
Brumback chaired the Statistics in Epidemiology Section of the American Statistical Association for the 2015 term. She was president of the Florida Chapter of the American Statistical Association for 2015–2016.. Brumback was elected as a Fellow of the American Statistical Association in 2019.
Bibliography
Books
Selected papers
References
External links
Home page
Year of birth missing (living people)
Living people
American women statisticians
Biostatisticians
University of Virginia School of Engineering and Applied Science alumni
UC Berkeley College of Letters and Science alumni
University of Washington faculty
UCLA School of Public Health faculty
University of Florida faculty
Fellows of the American Statistical Association
American women scientists
American women academics
21st-century American women
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https://en.wikipedia.org/wiki/List%20of%20FC%20Desna%20Chernihiv%20records%20and%20statistics
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FC Desna Chernihiv () is a Ukrainian football club based in Chernihiv. The original name of the club was "Avanhard" (FC Avanhard Chernihiv) during its first year of existence as part of a republican Avanhard sports society. Between 1961 and 1970 the club was called Desna. In 1972 it was replaced with SC Chernihiv (team of the SKA Kyiv) that played in Chernihiv for the next couple of years. In 1977 Desna was revived now in place of the amateur club "Khimik Chernihiv" that won regional competitions.
Players in national teams
In September 2021, Vladyslav Kalitvintsev become the first player belong Desna to be called in the Ukraine national football team against Finland. For the same match has been included also Serhiy Bolbat who played in Desna on loan from Shakhtar Donetsk. There are other players who took part in the national team before and after playing in the club like Pylyp Budkivskyi, Yevhen Selin, Andriy Totovytskyi, Denys Bezborodko and Vladislav Nosenko. The first player to be called Ukraine national football team was Yukhym Konoplya in 2020 but the player was on loan to the club by Shakhtar Donetsk There are other players who took part in the national team before and after playing in the club like Pylyp Budkivskyi, Yevhen Selin, Andriy Totovytskyi, Denys Bezborodko. Regarding other country, Desna had the Estonian international experience Joonas Tamm and the Constantin Dima who served only the under 21 team. The club had also Andriy Biba that he played one match for Soviet Union national football team, Oleh Kuznetsov, thatafter left the club got into the final of the European Football Championship in 1988 and Viktor Bannikov that he also got into the final of the European Football Championship in 1972.
Ukraine
The lists of players who took part in the national team during their time at the club. In bold the player corrently playing for the club.
Estonia
The lists of players who took part in the national team during their time at the club.
Romania
The lists of players who took part in the national team during their time at the club.
Player records and statistics
Appearances
Most player appearances in all competitions: Serhiy Sapronov, 474 matches
Most foreign player appearances in all competitions: Kakhaberi Sartania, 136 matches
Goalkeepers
Most clean sheets in Ukrainian Premier League: Yevhen Past, 11 matches in the season 2019–20 (with Andriy Pyatov)
Most appearances in all competitions: Yuriy Ovcharov, 198 matches
Most appearances in UEFA Europa League: Yevhen Past, 1 match
Most appearances as foreigner goalkeeper: Nikoloz Kheladze, 2 matches
Most appearances goalkeeper with dual citizenship: Dmytro Tyapushkin, 116 matches
Goalscorers
Most goals in all competitions: Oleksandr Kozhemyachenko, 128 goals
Most goals by season in Ukrainian Premier League: Oleksandr Filippov Season 2019–20 (16 goals)
Top goalscorers
Top Scorer Ukrainian Second League: Oleksandr Kozhemyachenko season 2010–11 (12 goals)
Top Scor
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https://en.wikipedia.org/wiki/Ordered%20algebra
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In mathematics, an ordered algebra is an algebra over the real numbers with unit e together with an associated order such that e is positive (i.e. e ≥ 0), the product of any two positive elements is again positive, and when A is considered as a vector space over then it is an Archimedean ordered vector space.
Properties
Let A be an ordered algebra with unit e and let C* denote the cone in A* (the algebraic dual of A) of all positive linear forms on A.
If f is a linear form on A such that f(e) = 1 and f generates an extreme ray of C* then f is a multiplicative homomorphism.
Results
Stone's Algebra Theorem: Let A be an ordered algebra with unit e such that e is an order unit in A, let A* denote the algebraic dual of A, and let K be the -compact set of all multiplicative positive linear forms satisfying f(e) = 1. Then under the evaluation map, A is isomorphic to a dense subalgebra of . If in addition every positive sequence of type l1 in A is order summable then A together with the Minkowski functional pe is isomorphic to the Banach algebra .
See also
Ordered vector space
Riesz space
References
Sources
Functional analysis
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https://en.wikipedia.org/wiki/43%2C112%2C609
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43,112,609 (forty-three million, one hundred twelve thousand, six hundred nine) is the natural number following 43,112,608 and preceding 43,112,610.
In mathematics
43,112,609 is a prime number. Moreover, it is the exponent of the 47th Mersenne prime, equal to M43,112,609 = 243,112,609 − 1, a prime number with 12,978,189 decimal digits. It was discovered on August 23, 2008 by Edson Smith, a volunteer of the Great Internet Mersenne Prime Search. The 45th Mersenne prime, M37,156,667 = 237,156,667 − 1, was discovered two weeks later on September 6, 2008, marking the shortest chronological gap between discoveries of Mersenne primes since the formation of the online collaborative project in 1996. It was the first time since 1963 when two Mersenne primes were discovered less than 30 days apart from each other. Less than a year later, on June 4, 2009, the 46th Mersenne prime, M42,643,801 = 242,643,801 − 1, was discovered by Odd Magnar Strindmo, a GIMPS participant from Norway. The result for this prime was first reported to the server in April 2009, but due to a bug, remained unnoticed for nearly two months. Having 12,837,064 decimal digits, it is only 141,125 digits, or 1.09%, shorter than M43,112,609. These two Mersenne primes hold the record for the ones with the smallest ratio between their exponents.
43,112,609 is the degree of four of the seven largest primitive binary trinomials over GF(2) found in 2016. and were the four largest in 2011.
43,112,609 is a Sophie Germain prime, the largest of only eight known Mersenne prime indexes to have this property.
43,112,609 is not a Gaussian prime, the largest of only 28 known Mersenne prime indexes to have this property.
References
Further reading
George Woltman, Scott Kurowski, On the discovery of the 45th and 46th known Mersenne primes", Fibonacci Quarterly, vol. 46/47, no. 3, pp. 194–197, August 2008.
Integers
Prime numbers
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https://en.wikipedia.org/wiki/David%20Parker%20%28footballer%2C%20born%201915%29
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William David Parker (27 May 1915 – October 1980) was an English professional footballer who played in the Football League for Hull City and Wolverhampton Wanderers as a full back.
Career statistics
References
English men's footballers
English Football League players
1915 births
1980 deaths
Footballers from Liverpool
Men's association football fullbacks
Marine A.F.C. players
Hull City A.F.C. players
Wolverhampton Wanderers F.C. players
South Liverpool F.C. players
Formby F.C. players
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https://en.wikipedia.org/wiki/Kan-Thurston%20theorem
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In mathematics, particularly algebraic topology, the Kan-Thurston theorem associates a discrete group to every path-connected topological space in such a way that the group cohomology of is the same as the cohomology of the space . The group might then be regarded as a good approximation to the space , and consequently the theorem is sometimes interpreted to mean that homotopy theory can be viewed as part of group theory.
More precisely, the theorem states that every path-connected topological space is homology-equivalent to the classifying space of a discrete group , where homology-equivalent means there is a map inducing an isomorphism on homology.
The theorem is attributed to Daniel Kan and William Thurston who published their result in 1976.
Statement of the Kan-Thurston theorem
Let be a path-connected topological space. Then, naturally associated to , there is a Serre fibration where is an aspherical space. Furthermore,
the induced map is surjective, and
for every local coefficient system on , the maps and induced by are isomorphisms.
Notes
References
Homotopy theory
Homology theory
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https://en.wikipedia.org/wiki/Louis%20Shapiro%20%28mathematician%29
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Louis Welles Shapiro (born 1941) is an American mathematician working in the fields of combinatorics and finite group theory. He is an emeritus professor at Howard University.
Shapiro attended Harvard University for his undergraduate studies and then the University of Maryland, College Park for graduate school. Shapiro is most known for creating the Riordan array, named after mathematician John Riordan, and developing the theory around it. He has been an organizer of and speaker at the yearly International Conference on Riordan Arrays and Related Topics, which has been held annually beginning 2014.
References
1941 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Howard University faculty
Harvard University alumni
University of Maryland, College Park alumni
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https://en.wikipedia.org/wiki/Moduli%20of%20abelian%20varieties
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Abelian varieties are a natural generalization of elliptic curves, including algebraic tori in higher dimensions. Just as elliptic curves have a natural moduli space over characteristic 0 constructed as a quotient of the upper-half plane by the action of , there is an analogous construction for abelian varieties using the Siegel upper half-space and the symplectic group .
Constructions over characteristic 0
Principally polarized Abelian varieties
Recall that the Siegel upper-half plane is given bywhich is an open subset in the symmetric matrices (since is an open subset of , and is continuous). Notice if this gives matrices with positive imaginary part, hence this set is a generalization of the upper half plane. Then any point gives a complex torus with a principal polarization from the matrix page 34. It turns out all principally polarized Abelian varieties arise this way, giving the structure of a parameter space for all principally polarized Abelian varieties. But, there exists an equivalence where for hence the moduli space of principally polarized abelian varieties is constructed from the stack quotientwhich gives a Deligne-Mumford stack over . If this is instead given by a GIT quotient, then it gives the coarse moduli space .
Principally polarized Abelian varieties with level n-structure
In many cases, it is easier to work with the moduli space of principally polarized Abelian varieties with level n-structure because it creates a rigidification of the moduli problem which gives a moduli functor instead of a moduli stack. This means the functor is representable by an algebraic manifold, such as a variety or scheme, instead of a stack. A level n-structure is given by a fixed basis of
where is the lattice . Fixing such a basis removes the automorphisms of an abelian variety at a point in the moduli space, hence there exists a bona-fide algebraic manifold without a stabilizer structure. Denoteand defineas a quotient variety.
References
See also
Schottky problem
Siegel modular variety
Moduli stack of elliptic curves
Moduli of algebraic curves
Hilbert scheme
Deformation Theory
Abelian varieties
Elliptic curves
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https://en.wikipedia.org/wiki/Qais%20Hameed
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Qais Hameed is a former Iraqi football forward who played for Iraq between 1962 and 1966. He played 13 matches and scored 2 goals.
Career statistics
International goals
Scores and results list Iraq's goal tally first.
References
Iraqi men's footballers
Iraq men's international footballers
Living people
Men's association football forwards
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/The%20Ancient%20Tradition%20of%20Geometric%20Problems
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The Ancient Tradition of Geometric Problems is a book on ancient Greek mathematics, focusing on three problems now known to be impossible if one uses only the straightedge and compass constructions favored by the Greek mathematicians: squaring the circle, doubling the cube, and trisecting the angle. It was written by Wilbur Knorr (1945–1997), a historian of mathematics, and published in 1986 by Birkhäuser. Dover Publications reprinted it in 1993.
Topics
The Ancient Tradition of Geometric Problems studies the three classical problems of circle-squaring, cube-doubling, and angle trisection throughout the history of Greek mathematics, also considering several other problems studied by the Greeks in which a geometric object with certain properties is to be constructed, in many cases through transformations to other construction problems. The study runs from Plato and the story of the Delian oracle to the second century BC, when Archimedes and Apollonius of Perga flourished; Knorr suggests that the decline in Greek geometry after that time represented a shift in interest to other topics in mathematics rather than a decline in mathematics as a whole. Unlike the earlier work on this material by Thomas Heath, Knorr sticks to the source material as it is, reconstructing the motivation and lines of reasoning followed by the Greek mathematicians and their connections to each other, rather than adding justifications for the correctness of the constructions based on modern mathematical techniques.
In modern times, the impossibility of solving the three classical problems by straightedge and compass, finally proven in the 19th century, has often been viewed as analogous to the foundational crisis of mathematics of the early 20th century, in which David Hilbert's program of reducing mathematics to a system of axioms and calculational rules struggled against logical inconsistencies in its axiom systems, intuitionist rejection of formalism and dualism, and Gödel's incompleteness theorems showing that no such axiom system could formalize all mathematical truths and remain consistent. However, Knorr argues in The Ancient Tradition of Geometric Problems that this point of view is anachronistic, and that the Greek mathematicians themselves were more interested in finding and classifying the mathematical tools that could solve these problems than they were in imposing artificial limitations on themselves and in the philosophical consequences of these limitations.
When a geometric construction problem does not admit a compass-and-straightedge solution, then either the constraints on the problem or on the solution techniques can be relaxed, and Knorr argues that the Greeks did both. Constructions described by the book include the solution by Menaechmus of doubling the cube by finding the intersection points of two conic sections, several neusis constructions involving fitting a segment of a given length between two points or curves, and the use of the Quadratrix of H
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https://en.wikipedia.org/wiki/Eva%20Petkova
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Eva Petkova is a Bulgarian-American biostatistician interested in the application of statistics to psychiatry, and known for her research on regression model comparison, brain imaging, and mental disorders. She is a professor of population health and of child and adolescent psychology at the New York University School of Medicine, and a research scientist at the Nathan Kline Institute for Psychiatric Research.
Education and career
Petkova a bachelor's degree in mathematics in 1982, a master's degree in mathematics in 1984, and a Ph.D. in physics in 1987 from Sofia University in Bulgaria. She completed a second Ph.D. in 1992 in statistics, at Pennsylvania State University. Her statistics dissertation, General Procedures for Analysis of Collapsibility in Generalized Linear Models, was supervised by Clifford Clogg.
After postdoctoral research at Harvard University, she joined the Columbia University faculty in 1994, in biostatistics and psychiatry, and as director of biostatistics at the New York State Psychiatric Institute. She moved to New York University in 2006.
Petkova was one of the founders of the Annual Symposium on Statistics in Psychiatry, later renamed as the Thomas R. Ten Have Symposium on Statistics in Mental Health.
Recognition
In 2014 Petkova was elected as a Fellow of the American Statistical Association "for significant research contributions to statistical methodology in mental health research; for dedicated leadership in advancing the use of statistical methods for the analysis of mental health data; and for devoted mentoring of students and medical researchers".
References
Year of birth missing (living people)
Living people
Bulgarian statisticians
Bulgarian women mathematicians
American statisticians
Women statisticians
Biostatisticians
Sofia University alumni
Eberly College of Science alumni
New York University Grossman School of Medicine faculty
Fellows of the American Statistical Association
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https://en.wikipedia.org/wiki/Thomas%20S.%20Ferguson
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Thomas Shelburne Ferguson (born December 14, 1929) is an American mathematician and statistician. He is a professor emeritus of mathematics and statistics at the University of California, Los Angeles.
Education and career
Ferguson was born in Oakland, California and was raised nearby in Alameda, California. He majored in mathematics at the University of California, Berkeley, and completed his Ph.D. there in 1956. His dissertation had two separately-titled parts, On Existence of Linear Regression in Linear Structural Relations and A Method of Generating Best Asymptotically Normal Estimates with Application to the Estimation of Bacterial Densities; it was supervised by Lucien Le Cam.
After another year teaching at Berkeley, he moved to the University of California, Los Angeles in 1957.
Contributions
Ferguson is the author of:
Mathematical Statistics: A Decision Theoretic Approach (Academic Press, 1967)
A Course in Large Sample Theory (Chapman & Hall, 1996)
A Course in Game Theory (World Scientific, 2020)
His research contributions include the analysis of the "big match" zero-sum game with David Blackwell, a result that eventually led to the proof of existence of equilibrium values for limiting average payoff in all stochastic games; the Ferguson distribution on prior probability; Ferguson's Dirichlet process; Ferguson's pairing property in the analysis of misère subtraction games; and contributions to the theory of optimal stopping as e.g. co-authored work on Robbins' problem.
Recognition
Ferguson was named a Fellow of the Institute of Mathematical Statistics in 1967, and a Fellow of the American Statistical Association in 1985.
He was given the Belgian International Francqui Chair of Science in 1998. A festschrift in Ferguson's honor edited by F. Thomas Bruss and Lucien Le Cam was published in 2000.
Personal life
Ferguson married mathematician Beatriz Rossello, and is the father of poker player Chris Ferguson. He has coauthored papers with Chris Ferguson on the mathematics of poker and other games of chance.
References
External links
Home page
1929 births
Living people
20th-century American mathematicians
21st-century American mathematicians
American statisticians
University of California, Berkeley alumni
University of California, Berkeley College of Letters and Science faculty
University of California, Los Angeles alumni
Fellows of the American Statistical Association
Fellows of the Institute of Mathematical Statistics
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https://en.wikipedia.org/wiki/Nigel%20Davey
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Nigel Geoffrey Davey (born 20 June 1946) is an English former footballer who played in the Football League for Leeds United.
Career statistics
References
1946 births
Living people
English men's footballers
Men's association football defenders
Leeds United F.C. players
Rotherham United F.C. players
English Football League players
People from Garforth
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https://en.wikipedia.org/wiki/Nguy%E1%BB%85n%20V%C4%83n%20To%E1%BA%A3n
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Nguyễn Văn Toản (born 26 November 1999) is a Vietnamese professional footballer who plays as a goalkeeper for V.League 1 side Hải Phòng and the Vietnam national team.
Career statistics
International
Honours
Vietnam U23/Olympic
Southeast Asian Games: 2019, 2021
Vietnam
AFF Championship runners-up: 2022
VFF Cup: 2022
References
1999 births
Living people
Vietnamese men's footballers
Vietnam men's youth international footballers
Men's association football goalkeepers
V.League 1 players
Haiphong FC players
People from Haiphong
Competitors at the 2021 SEA Games
SEA Games competitors for Vietnam
SEA Games gold medalists for Vietnam
SEA Games medalists in football
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https://en.wikipedia.org/wiki/Hong%20Jin-song
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Hong Jin-song (, born 20 February 1994) is a North Korean footballer who currently plays as a defender.
Career statistics
International
References
External links
1994 births
Living people
North Korean men's footballers
North Korea men's international footballers
North Korea men's youth international footballers
Men's association football defenders
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https://en.wikipedia.org/wiki/Pak%20Myong-song
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Pak Myong-song (, born 31 March 1994) is a North Korean footballer who currently plays as a defender for April 25 SC.
Career statistics
International
References
External links
1994 births
Living people
North Korean men's footballers
North Korea men's international footballers
North Korea men's youth international footballers
Men's association football defenders
Sobaeksu Sports Club players
April 25 Sports Club players
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https://en.wikipedia.org/wiki/Han%20Thae-hyok
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Han Thae-hyok (, born 20 June 1988) is a North Korean footballer who currently plays as a midfielder for Kigwancha SC.
Career statistics
International
References
External links
1988 births
Living people
North Korean men's footballers
North Korea men's international footballers
Men's association football midfielders
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https://en.wikipedia.org/wiki/Song%20Jong-hyok
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Song Jong-hyok (, born 28 June 1995) is a North Korean footballer who currently plays as a midfielder for Hwaebul SC.
Career statistics
International
References
External links
1995 births
Living people
North Korean men's footballers
North Korea men's international footballers
Men's association football midfielders
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https://en.wikipedia.org/wiki/Song%20Kum-il
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Song Kum-il (, born 10 May 1994) is a North Korean footballer who currently plays as a defender for Rimyongsu SC.
Career statistics
International
References
External links
1994 births
Living people
North Korean men's footballers
North Korea men's international footballers
Men's association football defenders
Rimyongsu Sports Club players
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https://en.wikipedia.org/wiki/Ri%20Un-il
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Ri Un-il (, born 15 August 1998) is a North Korean footballer who currently plays as a midfielder for Kigwancha SC.
Career statistics
International
References
External links
1998 births
Living people
North Korean men's footballers
North Korea men's international footballers
Men's association football midfielders
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https://en.wikipedia.org/wiki/Jo%20Sol-song
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Jo Sol-song (, born 27 October 1995) is a North Korean footballer who currently plays as a forward for Pyongyang SC.
Career statistics
International
References
External links
1995 births
Living people
North Korean men's footballers
North Korea men's international footballers
North Korea men's youth international footballers
Men's association football forwards
Pyongyang Sports Club players
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https://en.wikipedia.org/wiki/Paul%20Douglas%20%28footballer%29
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Paul Douglas (born 7 August 1997) is a Bermudan footballer who currently plays as a midfielder for Alvechurch.
Career statistics
International
References
1997 births
Living people
Bermudian men's footballers
Bermudian expatriate men's footballers
Bermuda men's under-20 international footballers
Bermuda men's international footballers
Men's association football midfielders
Ilkeston Town F.C. players
Redditch United F.C. players
Alvechurch F.C. players
Stratford Town F.C. players
Bermudian expatriate sportspeople in England
Expatriate men's footballers in England
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https://en.wikipedia.org/wiki/Rahzir%20Jones
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Rahzir Smith-Jones (born 1 November 2000) is a Bermudan footballer who currently plays as a midfielder for Welwyn Garden City.
Career statistics
International
References
2000 births
Living people
Bermudian men's footballers
Bermudian expatriate men's footballers
Bermuda men's youth international footballers
Bermuda men's international footballers
Men's association football midfielders
Queens Park Rangers F.C. players
Welwyn Garden City F.C. players
Bermudian expatriate sportspeople in England
Expatriate men's footballers in England
Bermuda men's under-20 international footballers
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https://en.wikipedia.org/wiki/William%20White%20%28footballer%29
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William Kyree Marcus White (born 10 January 1995) is a Bermudan footballer who plays as a midfielder.
Career statistics
Club
Notes
International
References
External links
William White at Sewanee: The University of the South
William White at the University of Alabama at Birmingham
1995 births
Living people
Bermudian men's footballers
Bermudian expatriate men's footballers
Bermuda men's youth international footballers
Bermuda men's international footballers
Men's association football midfielders
UAB Blazers men's soccer players
Närpes Kraft Fotbollsförening players
Detroit City FC players
Bermudian expatriate sportspeople in the United States
Expatriate men's soccer players in the United States
Expatriate men's footballers in Finland
Kakkonen players
Sewanee Tigers men's soccer players
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https://en.wikipedia.org/wiki/WNAF
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WNAF may refer to:
w-ary non-adjacent form (wNAF) in mathematics
Western part of the North Anatolian Fault in geology
Willie Nelson & Friends – Stars & Guitars, a music album
Former call sign of the radio station WPVD (AM)
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https://en.wikipedia.org/wiki/Janet%20Sinsheimer
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Janet Suzanne Sinsheimer (died March 14, 2023) was an American expert in statistical genetics who worked as a professor of human genetics, biomathematics and biostatistics in the Fielding School of Public Health at the University of California, Los Angeles. Topics in her research included genome-wide association studies, epigenetics, and Bayesian methods for phylogenetics.
Education
Sinsheimer graduated from Brown University in 1979, majoring in chemistry. She earned a master's degree in biochemistry in 1985 from Brandeis University, a second master's degree in biomathematics in 1988 from the University of California, Los Angeles (UCLA), and a Ph.D. in biomathematics in 1994 from UCLA. Her dissertation, Extensions to Evolutionary Parsimony, concerned phylogeny (the inference of evolutionary trees), and was jointly supervised by evolutionary biologist James A. Lake and biostatistician Roderick J. A. Little.
Recognition
Sinsheimer became a Fellow of the American Statistical Association in 2013. The Linnean Society of London elected her as a fellow in 2014. In 2017 the Boston University Department of Biostatistics gave her the L. Adrienne Cupples Award for Excellence in Teaching, Research, and Service in Biostatistics.
References
External links
Year of birth missing (living people)
2023 deaths
American statisticians
Women statisticians
Biostatisticians
Brown University alumni
Brandeis University alumni
University of California, Los Angeles alumni
UCLA School of Public Health faculty
Fellows of the American Statistical Association
Fellows of the Linnean Society of London
|
https://en.wikipedia.org/wiki/L%C3%A9o%20Gomes%20%28footballer%2C%20born%201997%29
|
Leonardo da Silva Gomes (born 30 April 1997), known as Léo Gomes, is a Brazilian footballer who plays as a midfielder for EC Vitória, on loan from Athletico Paranaense.
Career statistics
References
External links
1997 births
Living people
Brazilian men's footballers
Men's association football midfielders
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Esporte Clube Vitória players
Club Athletico Paranaense players
América Futebol Clube (MG) players
Associação Chapecoense de Futebol players
Footballers from Fortaleza
|
https://en.wikipedia.org/wiki/Vin%C3%ADcius%20Mingotti
|
Vinicius Alessandro Mingotti (born 7 January 2000) is a Brazilian footballer who plays as a forward for Bahia, on loan from Athletico Paranaense.
Career statistics
Club
Honours
Athletico Paranaense
Campeonato Paranaense: 2020
Mirassol
Campeonato Brasileiro Série C: 2022
References
2000 births
Living people
People from São Carlos
Footballers from São Paulo (state)
Brazilian men's footballers
Men's association football forwards
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Campeonato Paranaense players
Club Athletico Paranaense players
Tombense Futebol Clube players
Mirassol Futebol Clube players
Operário Ferroviário Esporte Clube players
Esporte Clube Bahia players
|
https://en.wikipedia.org/wiki/Ramon%20Vinicius
|
Ramon Vinicius dos Santos (born 13 May 2000) is a Brazilian footballer who plays as a midfielder for Bahia.
Career statistics
Club
Honours
Athletico Paranaense
Campeonato Paranaense: 2020
References
External links
Athletico Paranaense profile
2000 births
Living people
Footballers from Piracicaba
Brazilian men's footballers
Men's association football midfielders
Campeonato Paranaense players
Club Athletico Paranaense players
Esporte Clube Bahia players
|
https://en.wikipedia.org/wiki/Kawan
|
Kawan Gabriel da Silva (born 6 March 2002), simply known as Kawan, is a Brazilian footballer who plays as a defensive midfielder for Athletico Paranaense.
Career statistics
Club
Honours
Athletico Paranaense
Campeonato Paranaense: 2020
References
External links
Athletico Paranaense profile
2002 births
Living people
Footballers from Paraná (state)
Brazilian men's footballers
Brazil men's youth international footballers
Men's association football midfielders
Campeonato Brasileiro Série A players
Club Athletico Paranaense players
|
https://en.wikipedia.org/wiki/Elias%20Carioca
|
Elias Rezende de Oliveira (born 21 December 1999), known as Elias Carioca or simply Elias, is a Brazilian footballer who plays for Athletico Paranaense, as a forward.
Career statistics
Club
References
External links
Athletico Paranaense profile
1999 births
Living people
Footballers from Rio de Janeiro (state)
Brazilian men's footballers
Men's association football forwards
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Nova Iguaçu FC players
Santa Cruz Futebol Clube players
Club Athletico Paranaense players
Guarani FC players
|
https://en.wikipedia.org/wiki/Pedro%20do%20Rio
|
Pedro Bernardo do Rio (born 21 November 2000) is a Brazilian footballer who plays for Athletico Paranaense as a midfielder.
Career statistics
Club
References
2000 births
Living people
Brazilian men's footballers
Men's association football midfielders
Associação Ferroviária de Esportes players
Club Athletico Paranaense players
|
https://en.wikipedia.org/wiki/W%C3%A1lber
|
José Wálber Mota de Amorim (born 12 June 1997), commonly known as Wálber, is a Brazilian footballer who plays as a central defender for Guarani, on loan from Athletico Paranaense.
Career statistics
Club
References
External links
1997 births
Living people
Brazilian men's footballers
Men's association football defenders
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série C players
Botafogo Futebol Clube (PB) players
Sport Club do Recife players
Club Athletico Paranaense players
Figueirense FC players
Guarani FC players
Cuiabá Esporte Clube players
CR Vasco da Gama players
Footballers from Paraíba
|
https://en.wikipedia.org/wiki/Giva%20%28footballer%2C%20born%201999%29
|
Geovane Silva Santos (born 22 February 1999), simply known as Giva, is a Brazilian footballer who plays as a midfielder for Avaí.
Career statistics
Club
References
External links
Athletico Paranaense profile
1999 births
Living people
Footballers from Goiás
Brazilian men's footballers
Men's association football midfielders
Campeonato Brasileiro Série B players
Club Athletico Paranaense players
Associação Atlética Internacional (Limeira) players
Figueirense FC players
Centro Sportivo Alagoano players
Avaí FC players
People from Mineiros
|
https://en.wikipedia.org/wiki/Guilherme%20Castilho
|
Guilherme Castilho Carvalho (born 19 September 1999) is a Brazilian footballer who plays for as a midfielder for Ceará.
Career statistics
Club
Honours
Atlético Mineiro
Supercopa do Brasil: 2022
Campeonato Mineiro: 2022
Ceará
Copa do Nordeste: 2023
References
1999 births
Living people
Sportspeople from Tocantins
Brazilian men's footballers
Men's association football midfielders
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série D players
Mirassol Futebol Clube players
Clube Atlético Mineiro players
Associação Desportiva Confiança players
Esporte Clube Juventude players
Ceará Sporting Club players
|
https://en.wikipedia.org/wiki/Ralph%20%28footballer%2C%20born%201998%29
|
Ralph Machado Dias (born 7 March 1998), commonly known as Ralph, is a Brazilian footballer who plays for Ypiranga, on loan from Atlético Mineiro, as a midfielder.
Career statistics
Club
References
1998 births
Living people
Brazilian men's footballers
Men's association football midfielders
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série D players
Clube Atlético Mineiro players
Criciúma Esporte Clube players
Boavista Sport Club players
Coimbra Sports players
Associação Ferroviária de Esportes players
Clube Náutico Capibaribe players
Ypiranga Futebol Clube players
People from São Fidélis
|
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