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https://en.wikipedia.org/wiki/The%20Higher%20Infinite	The Higher Infinite: Large Cardinals in Set Theory from their Beginnings is a monograph in set theory by Akihiro Kanamori, concerning the history and theory of large cardinals, infinite sets characterized by such strong properties that their existence cannot be proven in Zermelo–Fraenkel set theory (ZFC). This book was published in 1994 by Springer-Verlag in their series Perspectives in Mathematical Logic, with a second edition in 2003 in their Springer Monographs in Mathematics series, and a paperback reprint of the second edition in 2009 (). Topics Not counting introductory material and appendices, there are six chapters in The Higher Infinite, arranged roughly in chronological order by the history of the development of the subject. The author writes that he chose this ordering "both because it provides the most coherent exposition of the mathematics and because it holds the key to any epistemological concerns". In the first chapter, "Beginnings", the material includes inaccessible cardinals, Mahlo cardinals, measurable cardinals, compact cardinals and indescribable cardinals. The chapter covers the constructible universe and inner models, elementary embeddings and ultrapowers, and a result of Dana Scott that measurable cardinals are inconsistent with the axiom of constructibility. The second chapter, "Partition properties", includes the partition calculus of Paul Erdős and Richard Rado, trees and Aronszajn trees, the model-theoretic study of large cardinals, and the existence of the set 0# of true formulae about indiscernibles. It also includes Jónsson cardinals and Rowbottom cardinals. Next are two chapters on "Forcing and sets of reals" and "Aspects of measurability". The main topic of the first of these chapters is forcing, a technique introduced by Paul Cohen for proving consistency and inconsistency results in set theory; it also includes material in descriptive set theory. The second of these chapters covers the application of forcing by Robert M. Solovay to prove the consistency of measurable cardinals, and related results using stronger notions of forcing. Chapter five is "Strong hypotheses". It includes material on supercompact cardinals and their reflection properties, on huge cardinals, on Vopěnka's principle, on extendible cardinals, on strong cardinals, and on Woodin cardinals. The book concludes with the chapter "Determinacy", involving the axiom of determinacy and the theory of infinite games. Reviewer Frank R. Drake views this chapter, and the proof in it by Donald A. Martin of the Borel determinacy theorem, as central for Kanamori, "a triumph for the theory he presents". Although quotations expressing the philosophical positions of researchers in this area appear throughout the book, more detailed coverage of issues in the philosophy of mathematics regarding the foundations of mathematics are deferred to an appendix. Audience and reception Reviewer Pierre Matet writes that this book "will no doubt serve for many years
https://en.wikipedia.org/wiki/Other%20People%27s%20Letters	Other People's Letters () is a 1975 Soviet drama film directed by Ilya Averbakh. Plot The film tells about a teacher of mathematics, who takes her student to her family, who as a result begins to feel like a mistress in her house. Cast Irina Kupchenko as Vera Ivanovna (as I. Kupchenko) Svetlana Smirnova as Zina Begunkova (as S. Smirnova) Sergei Kovalenkov as Igor (as S. Kovalenko) Zinaida Sharko as Angelina Grigoryevna (as Z. Sharko) Oleg Yankovskiy as Priachin (as O. Yankovskiy) Ivan Bortnik as Shura (as I. Bortnik) Natalya Skvortsova as Valya (as N. Skvortsova) Pyotr Arzhanov as Nikolay Artomovich Mayya Bulgakova Valentina Vladimirova References External links 1975 films 1970s Russian-language films Soviet drama films 1975 drama films
https://en.wikipedia.org/wiki/Allison%20Henrich	Allison Henrich (born 1980) is an American mathematician specializing in knot theory and also interested in undergraduate-level mathematics research mentorship. She is a professor of mathematics at Seattle University. Education and career Henrich entered college planning for an undergraduate teaching career, graduated in 2003 from the University of Washington with a double major in mathematics and philosophy. She completed a Ph.D. at Dartmouth College in 2008. Her dissertation, A Sequence of Degree One Vassiliev Invariants for Virtual Knots, was supervised by Vladimir Chernov. At Dartmouth, Carolyn S. Gordon became another faculty mentor. She joined the Seattle University mathematics faculty in 2009, and was promoted to full professor in 2019. Books Henrich is the coauthor of a book on knot theory, An Interactive Introduction to Knot Theory (with Inga Johnson, Dover Publications, 2017). She also coauthored the book A Mathematician’s Practical Guide to Mentoring Undergraduate Research (with Michael Dorff and Lara Pudwell, Mathematical Association of America, American Mathematical Society, and Council on Undergraduate Research, 2019). With Emille D. Lawrence, Matthew Pons, and David Taylor, she co-edited the book Living Proof: Stories of Resilience Along the Mathematical Journey (American Mathematical Society and Mathematical Association of America, 2019). She is also an editor of Knots, Links, Spatial Graphs, and Algebraic Invariants (with Erica Flapan, Aaron Kaestner, and Sam Nelson, American Mathematical Society, 2017). Recognition In 2015, the Mathematical Association of America gave Henrich their Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member, and also their Paul R. Halmos – Lester R. Ford Award for expository excellence for her article "Unknotting unknots" coauthored with Louis Kauffman. The award citation for the Alder Award cited her work in interactive learning, in guiding undergraduate mathematics students to become mentors to elementary school students, and in founding a summer research program at for underrepresented undergraduates, hosted at Seattle University. References External links Home page 1980 births Living people 21st-century American mathematicians American women mathematicians University of Washington alumni Dartmouth College alumni Topologists Seattle University faculty 21st-century American women
https://en.wikipedia.org/wiki/A.%20R.%20B.%20Thomas	Andrew Rowland Benedick Thomas (11 October 1904 – 16 May 1985), was an amateur chess player from Devon, England. He taught mathematics at Blundell's School in Tiverton from 1927 until retiring in 1969, and continued to live in the town until his death. References 1904 births 1985 deaths English chess players People from Crosby, Merseyside Schoolteachers from Devon Sportspeople from Devon Game players from Merseyside
https://en.wikipedia.org/wiki/Treks%20into%20Intuitive%20Geometry	Treks into Intuitive Geometry: The World of Polygons and Polyhedra is a book on geometry, written as a discussion between a teacher and a student in the style of a Socratic dialogue. It was written by Japanese mathematician Jin Akiyama and science writer Kiyoko Matsunaga, and published by Springer-Verlag in 2015 (). Topics The term "intuitive geometry" of the title was used by László Fejes Tóth to refer to results in geometry that are accessible to the general public, and the book concerns topics of this type. The book has 16 self-contained chapters, each beginning with an illustrative puzzle or real-world application. It includes material on tessellations, polyhedra, and honeycombs, unfoldings of polyhedra and tessellations of unfoldings, cross sections of polyhedra, measuring boxes, gift wrapping, packing problems, wallpaper groups, pentagonal tilings, the Conway criterion for prototiles and Escher-like tilings of the plane by animal-shaped figures, aperiodic tilings including the Penrose tiling, the art gallery theorem, the Euler characteristic, dissection problems and the Dehn invariant, and the Steiner tree problem. The book is heavily illustrated. And although the results of the book are demonstrated in an accessible way, the book provides sequences of deductions leading to each major claim, and more-complete proofs and references are provided in an appendix. Audience and reception Although it was initially developed from course material offered to undergraduates at the Tokyo University of Science, the book is aimed at a broad audience, and assumes only a high-school level knowledge of geometry. It could be used to encourage children in mathematics as well as to provide material for teachers and public lecturers. There is enough depth of material to also retain the interest of readers with a more advanced mathematical background. Reviewer Matthieu Jacquemet writes that the ordering of topics is unintuitive and the dialogue-based format "artificial", but reviewer Tricia Muldoon Brown instead suggests that this format allows the work to flow very smoothly, "more like a novel or a play than a textbook ... with the ease of reading purely for pleasure". Jacquemet assesses the book as "well illustrated and entertaining", and Brown writes that it "is a delightful read". Reviewer Michael Fox disagrees, finding the dialogue irritating and the book overall "rather disappointing". He cites as problematic the book's cursory treatment of some of its topics, and in particular its treatment of tiling patterns as purely monochromatic, its omission of the frieze groups, and its use of demonstrations by special examples that do not have all the features of the general case. He also complains about idiosyncratic terminology, the use of decimal approximations instead of exact formulas for angles, the small scale of some figures, and an uneven level of difficulty of material. Nevertheless, he writes that "this is an interesting work, with much that cannot
https://en.wikipedia.org/wiki/1961%E2%80%9362%20Rochdale%20A.F.C.%20season	The 1961–62 season saw Rochdale compete for their 3rd season in the Football League Fourth Division. This season also saw Rochdale reach final of the League Cup. Statistics \|} Final League Table Competitions Football League Fourth Division Expunged Games F.A. Cup League Cup Lancashire Cup Rose Bowl References Rochdale A.F.C. seasons Rochdale
https://en.wikipedia.org/wiki/A%20Guide%20to%20the%20Classification%20Theorem%20for%20Compact%20Surfaces	A Guide to the Classification Theorem for Compact Surfaces is a textbook in topology, on the classification of two-dimensional surfaces. It was written by Jean Gallier and Dianna Xu, and published in 2013 by Springer-Verlag as volume 9 of their Geometry and Computing series (, ). The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate mathematics libraries. Topics The classification of surfaces (more formally, compact two-dimensional manifolds without boundary) can be stated very simply, as it depends only on the Euler characteristic and orientability of the surface. An orientable surface of this type must be topologically equivalent (homeomorphic) to a sphere, torus, or more general handlebody, classified by its number of handles. A non-orientable surface must be equivalent to a projective plane, Klein bottle, or more general surface characterized by an analogous number, its number of cross-caps. For compact surfaces with boundary, the only extra information needed is the number of boundary components. This result is presented informally at the start of the book, as the first of its six chapters. The rest of the book presents a more rigorous formulation of the problem, a presentation of the topological tools needed to prove the result, and a formal proof of the classification. Other topics in topology discussed as part of this presentation include simplicial complexes, fundamental groups, simplicial homology and singular homology, and the Poincaré conjecture. Appendices include additional material on embeddings and self-intersecting mappings of surfaces into three-dimensional space such as the Roman surface, the structure of finitely generated abelian groups, general topology, the history of the classification theorem, and the Hauptvermutung (the theorem that every surface can be triangulated). Audience and reception This is a textbook aimed at the level of advanced undergraduates or beginning graduate students in mathematics, perhaps after having already completed a first course in topology. Readers of the book are expected to already be familiar with general topology, linear algebra, and group theory. However, as a textbook, it lacks exercises, and reviewer Bill Wood suggests its use for a student project rather than for a formal course. Many other graduate algebraic topology textbooks include coverage of the same topic. However, by focusing on a single topic, the classification theorem, the book is able to prove the result rigorously while remaining at a lower overall level, provide a greater amount of intuition and history, and serve as "a motivating tour of the discipline’s fundamental techniques". Reviewer complains that parts of the book are redundant, and in particular that the classification theorem can be proven either with the fundamental group or with homology (not needing both), that on the other hand several important tools from topology including the Jordan–S
https://en.wikipedia.org/wiki/Hvar%20Arsenal	{ "type": "FeatureCollection", "features": [ { "type": "Feature", "properties": {}, "geometry": { "type": "Point", "coordinates": [ 16.441533565521244, 43.172047765944015 ] } } ] } The Hvar Arsenal is a historic building in the town of Hvar, Croatia. It was first constructed in the 14th century as a maintenance shipyard for the galley of the commune. Through the ages it was further expanded and gained additional functions. Most notable is the historic theater (), built in 1612 as part of the first floor, above the galley space. Today it is a multi-functional building centered on the theater. History The Arsenal in Hvar has developed and changed in accordance with the historical, social and technological changes of its day. It was first built in the period between 1292 (the decision to build) and 1331 (its existence confirmed). The location was chosen with regard to the dangers of weather and high seas to the port of Hvar and so to enable the integration of the building into the protection of the city walls. The later built city walls have never included Arsenal and multiple other important buildings. The first construction phase (1292/1317 - 1331) The existing ground floor walls in the area of the 2. - 8. bays are built in the first construction phase, in the beginning of the 14th century. The foundations of these walls lay directly on the historical layers from antiquity. These old structures have been formed to accommodate foundations for the arsenal, as well as the slipway inside the building. The slipway was covered with a clay finish and was used as a work surface for the maintenance of the galley. The first, 14th century arsenal was essentially a building protected from the weather by two walls and a roof. It was a precondition for the municipality to fulfill its commitment to the Republic of Venice: to maintain, equip and finance a municipal galley and to train and provide a crew from its own residents. The size and shape of the building was in accordance with the size of the 14th century galley. The first design of the arsenal was, according to the preserved parts and the practice of similar buildings, simple, industrial and without architectural decoration. After the Republic of Venice came to power the municipality of Hvar was under pressure to rapidly build the arsenal (and other infrastructure) to fulfill the municipal galley duty. The building was financed and controlled by the municipality. It was the work of local masters who made it as simple and cost-effective as possible. The 2nd – 8th bay arsenal is 40 meters long, what corresponds to the galley of the time. The side walls were about one meter higher than today's level of the first floor. The second construction phase (1528 - 1559) The arsenal has been preserved and used by the municipality despite the multiple changes of rule on the island until the 16th century (Venice had lost control
https://en.wikipedia.org/wiki/Variational%20series	In statistics, a variational series is a non-decreasing sequence composed from an initial series of independent and identically distributed random variables . The members of the variational series form order statistics, which form the basis for nonparametric statistical methods. is called the kth order statistic, while the values and (the 1st and th order statistics, respectively) are referred to as the extremal terms. The sample range is given by , and the sample median by when is odd and when is even. The variational series serves to construct the empirical distribution function , where is the number of members of the series which are less than . The empirical distribution serves as an estimate of the true distribution of the random variables, and according to the Glivenko–Cantelli theorem converges almost surely to . References Nonparametric statistics
https://en.wikipedia.org/wiki/Ill%C3%A9s%20Z%C3%B6ldesi	Illés Zöldesi (born 9 February 1998) is a Hungarian football goalkeeper. Career statistics . References External links 1998 births Footballers from Nyíregyháza Living people Hungarian men's footballers Hungary men's under-21 international footballers Men's association football goalkeepers Diósgyőri VTK players Fehérvár FC players Kisvárda FC players Zalaegerszegi TE players Debreceni VSC players Nemzeti Bajnokság I players Nemzeti Bajnokság II players
https://en.wikipedia.org/wiki/Takaya%20Sugasawa	is a Japanese former footballer. Career statistics Club Notes References 1987 births Living people Japanese men's footballers Men's association football midfielders Singapore Premier League players Lao Premier League players Japan Soccer College players Albirex Niigata Singapore FC players Master 7 FC players Japanese expatriate sportspeople in Singapore Expatriate men's footballers in Singapore Japanese expatriate sportspeople in Thailand Expatriate men's footballers in Thailand Japanese expatriate sportspeople in Laos Expatriate men's footballers in Laos
https://en.wikipedia.org/wiki/Michihisa%20Nagasawa	is a Japanese former footballer. Career statistics Club Notes References 1989 births Living people Japanese men's footballers Men's association football midfielders Albirex Niigata Singapore FC players Singapore Premier League players Japanese expatriate sportspeople in Singapore Expatriate men's footballers in Singapore
https://en.wikipedia.org/wiki/Yoshinobu%20Matsumura	is a Japanese former footballer. Career statistics Club Notes References 1988 births Living people Waseda University alumni Japanese men's footballers Men's association football forwards Club Guaraní players Club Olimpia footballers Albirex Niigata Singapore FC players Singapore Premier League players Segunda Divisão players Japanese expatriate men's footballers Japanese expatriate sportspeople in Paraguay Expatriate men's footballers in Paraguay Japanese expatriate sportspeople in Singapore Expatriate men's footballers in Singapore Japanese expatriate sportspeople in Portugal Expatriate men's footballers in Portugal
https://en.wikipedia.org/wiki/Akiya%20Wada	is a Japanese former footballer. Career statistics Club Notes References 1991 births Living people People from Hachiōji, Tokyo Sportspeople from Tokyo Metropolis Association football people from Tokyo Metropolis Tokyo International University alumni Japanese men's footballers Men's association football forwards Albirex Niigata Singapore FC players Singapore Premier League players Japanese expatriate sportspeople in Singapore Expatriate men's footballers in Singapore
https://en.wikipedia.org/wiki/Combinatorial%20Games%3A%20Tic-Tac-Toe%20Theory	Combinatorial Games: Tic-Tac-Toe Theory is a monograph on the mathematics of tic-tac-toe and other positional games, written by József Beck. It was published in 2008 by the Cambridge University Press as volume 114 of their Encyclopedia of Mathematics and its Applications book series (). Topics A positional game is a game in which players alternate in taking possession of a given set of elements, with the goal of forming a winning configuration of elements; for instance, in tic-tac-toe and gomoku, the elements are the squares of a grid, and the winning configurations are lines of squares. These examples are symmetric: both players have the same winning configurations. However, positional games also include other possibilities such as the maker-breaker games in which one player (the "maker") tries to form a winning configuration and the other (the "breaker") tries to put off that outcome indefinitely or until the end of the game. In symmetric positional games one can use a strategy-stealing argument to prove that the first player has an advantage, but realizing this advantage by a constructive strategy can be very difficult. According to the Hales–Jewett theorem, in tic-tac-toe-like games involving forming lines on a grid or higher-dimensional lattice, grids that are small relative to their dimension cannot lead to a drawn game: once the whole grid is partitioned between the two players, one of them will necessarily have a line. One of the main results of the book is that somewhat larger grids lead to a "weak win", a game in which one player can always force the formation of a line (not necessarily before the other player does), but that grid sizes beyond a certain threshold lead to a "strong draw", a game in which both players can prevent the other from forming a line. Moreover, the threshold between a weak win and a strong draw can often be determined precisely. The proof of this result uses a combination of the probabilistic method, to prove the existence of strategies for achieving the desired outcome, and derandomization, to make those strategies explicit. The book is long (732 pages), organized into 49 chapters and four sections. Part A looks at the distinction between weak wins (the player can force the existence of a winning configuration) and strong wins (the winning configuration can be forced to exist before the other player gets a win). It shows that, for maker-breaker games over the points on the plane in which the players attempt to create a congruent copy of some finite point set, the maker always has a weak win, but to do so must sometimes allow the breaker to form a winning configuration earlier. It also includes an extensive analysis of tic-tac-toe-like symmetric line-forming games, and discusses the Erdős–Selfridge theorem according to which sparse-enough sets of winning configurations lead to drawn maker-breaker games. Part B of the book discusses the potential-based method by which the Erdős–Selfridge theorem was proven, and
https://en.wikipedia.org/wiki/Drew%20Allbritten	Drew William Allbritten (born April 24, 1947) is a former member of the Michigan House of Representatives. Allbritten worked an educator, starting as middle school and high school mathematics and science teacher. He later worked as a college administrator. On November 7, 1978, Allbritten was elected to the Michigan House of Representatives where he represented the 93rd district from January 10, 1979 to 1980. References Living people 1947 births American academic administrators Republican Party members of the Michigan House of Representatives Schoolteachers from Michigan 20th-century American politicians
https://en.wikipedia.org/wiki/Luis%20Ni%C8%9Bu	Luis Emanuel Nițu (born 30 May 2001) is a Romanian professional footballer who plays as a forward for CSM Slatina. Career Statistics Club References External links 2001 births Living people Footballers from Slatina, Romania Romanian men's footballers Romania men's youth international footballers Men's association football forwards Liga I players Liga II players CS Universitatea Craiova players CS Gaz Metan Mediaș players CSM Slatina (football) players
https://en.wikipedia.org/wiki/Charles%20Pirie	Charles Pirie (8 January 1897 – 3 February 1960) was a Scottish chess player. Biography Charles Pirie graduated from University of Aberdeen in 1920. He worked as a mathematics teacher all his life. Charles Pirie took an active part in the work of the Aberdeen chess club Bon-Accord CC. His most notable organizing work is related to the Scottish Chess Championship of 1939, held in Aberdeen. Charles Pirie played for Scotland in the Chess Olympiad: In 1937, at reserve board in the 7th Chess Olympiad in Stockholm (+0, =1, -9). References External links Charles Pirie chess games at 365chess.com 1897 births 1960 deaths Sportspeople from Aberdeen Scottish chess players Chess Olympiad competitors 20th-century chess players Alumni of the University of Aberdeen
https://en.wikipedia.org/wiki/Sliding%20DFT	In applied mathematics, the sliding discrete Fourier transform is a recursive algorithm to compute successive STFTs of input data frames that are a single sample apart (hopsize − 1). The calculation for the sliding DFT is closely related to Goertzel algorithm. Definition Assuming that the hopsize between two consecutive DFTs is 1 sample, then From this definition above, the DFT can be computed recursively thereafter. However, implementing the window function on a sliding DFT is difficult due to its recursive nature, therefore it is done exclusively in a frequency domain. Sliding windowed infinite Fourier transform It is not possible to implement asymmetric window functions into sliding DFT. However, the IIR version called sliding windowed infinite Fourier transform (SWIFT) provides an exponential window and the αSWIFT calculates two sDFTs in parallel where slow-decaying one is subtracted by fast-decaying one, therefore a window function of . References FFT algorithms
https://en.wikipedia.org/wiki/Nixon%20Jew%20count	The "Nixon Jew count" of July 1971 is the name given to then-President of the United States Richard Nixon's attempts to demote and remove Jews from the Bureau of Labor Statistics (BLS). History In their 1976 book, The Final Days, Bob Woodward and Carl Bernstein suggest President Nixon had a history of antisemitic outbursts and became convinced that Jewish employees of BLS were undermining him by negatively altering labor numbers. Orchestrated by H. R. Haldeman, Charles Colson, and Fred Malek at Nixon's behest, a list of 13 employees of the BLS with "Jewish-sounding" surnames was drawn up, along with a list of political affiliations. In a letter to Nixon, subsequently referred to as the "Jew-counting" memo, Malek identified 25 Democrats and 13 other employees who "fit the other demographic criterion that was discussed". The 13 employees considered to be Jewish were demoted and sent to other positions within the United States Department of Labor, where they were deemed to be at lower risk of causing issues to Nixon. Reaction When the story was first reported in 1988, Malek resigned from his post as deputy chairman of the Republican National Committee. Malek apologised for his role in the count but denied involvement in the demotion of those identified as Jewish. Jewish leaders including Abraham Foxman and Senator Dianne Feinstein accepted Malek's apologies. Malek remained active in politics after his resignation, later serving as the campaign manager of President George H. W. Bush's re-election campaign in 1992 and the national finance co-chair of Senator John McCain's unsuccessful presidential campaign in 2008. Writing for Slate, Timothy Noah described the plan as "the last known act of official anti-Semitism conducted by the United States government". See also Antisemitism in the United States Judenzählung General Order No. 11 (1862) References 1971 in American politics Antisemitic attacks and incidents in the United States Bureau of Labor Statistics Nixon administration controversies
https://en.wikipedia.org/wiki/Word%20Processing%20in%20Groups	Word Processing in Groups is a monograph in mathematics on the theory of automatic groups, a type of abstract algebra whose operations are defined by the behavior of finite automata. The book's authors are David B. A. Epstein, James W. Cannon, Derek F. Holt, Silvio V. F. Levy, Mike Paterson, and William Thurston. Widely circulated in preprint form, it formed the foundation of the study of automatic groups even before its 1992 publication by Jones and Bartlett Publishers (). Topics The book is divided into two parts, one on the basic theory of these structures and another on recent research, connections to geometry and topology, and other related topics. The first part has eight chapters. They cover automata theory and regular languages, and the closure properties of regular languages under logical combinations; the definition of automatic groups and biautomatic groups; examples from topology and "combable" structure in the Cayley graphs of automatic groups; abelian groups and the automaticity of Euclidean groups; the theory of determining whether a group is automatic, and its practical implementation by Epstein, Holt, and Sarah Rees; extensions to asynchronous automata; and nilpotent groups. The second part has four chapters, on braid groups, isoperimetric inequalities, geometric finiteness, and the fundamental groups of three-dimensional manifolds. Audience and reception Although not primarily a textbook, the first part of the book could be used as the basis for a graduate course. More generally, reviewer Gilbert Baumslag recommends it "very strongly to everyone who is interested in either group theory or topology, as well as to computer scientists." Baumslag was an expert in a related but older area of study, groups defined by finite presentations, in which research was eventually stymied by the phenomenon that many basic problems are undecidable. Despite tracing the origins of automatic groups to early 20th-century mathematician Max Dehn, he writes that the book studies "a strikingly new class of groups" that "conjures up the fascinating possibility that some of the exploration of these automatic groups can be carried out by means of high-speed computers" and that the book is "very likely to have a great impact". Reviewer Daniel E. Cohen adds that two features of the book are unusual. First, that the mathematical results that it presents all have names, not just numbers, and second, that the cost of the book is low. In 2009, mathematician Mark V. Lawson wrote that despite its "odd title," the book made automata theory more respectable among mathematicians stating that it became part of "a quiet revolution in the diplomatic relations between mathematics and computer science". References Computational group theory Mathematics books 1992 non-fiction books
https://en.wikipedia.org/wiki/Andreas%20Buja	Andreas Buja is a Swiss statistician and professor of statistics. He is the Liem Sioe Liong/First Pacific Company professor in the Statistics department of The Wharton School at the University of Pennsylvania in Philadelphia, United States. Buja joined Center for Computational Mathematics (CCM) as a Senior Research Scientist in January 2020. Life and education Buja was born in Switzerland. He graduated from the Swiss Federal Institute of Technology (ETHZ, Zurich) in 1980 with a PhD in Mathematics and Statistics, where his dissertation was supervised jointly by Frank Hampel, Peter J. Huber, and H. Foellmer. Career and research Buja began working as research associate at ETH Zurich and Children's Hospital, until 1982. In 1982, Buja held his first academic position as an assistant professor at University of Washington, where he later became an associate professor in 1987. He also held positions in industry as a member of technical staff at Bell Communications Research and AT&T Bell Laboratories between 1994–1996 and 1996–Jan 2002, respectively. Then, he returned to academia as a professor at The Wharton School, University of Pennsylvania, where he was designated as the Liem Sioe Liong/First Pacific Company Professor in July 2003. Buja is a co-author of a data visualization system called XGobi, a predecessor of GGobi, for which Google provides more than 10,000 entries. His research interests include data visualization, data mining, multivariate statistics, and nonparametric statistics. Results of his research have been discussed in multiple articles like : Science Daily, Slate, knowledge@wharton. Notable papers Buja has authored several publications. Of which the following papers have more than 500 citations: “Linear Smoothers and the Additive Model,” Buja, A., Hastie, T., and Tibshirani, R., The Annals of Statistics, 17, 453–555 (1989). “Penalized Discriminant Analysis,” Hastie, T., Buja, A., and Tibshirani, R., The An- nals of Statistics, 23, 73–102 (1995). “Flexible Discriminant Analysis,” Hastie, T., Tibshirani, R., and Buja, A., Journal of the American Statistical Association, 89, 1255–1270 (1994). “Rare de novo and transmitted copy number variation in autistic spectrum disorders,” Levy, D., Ronemus, M., Yamrom, B., Lee, Y., Leotta, A., Kendall, J., Marks, S., Lakshmi, B., Ye, K., Buja, A., Yoon, S., Krieger, A., Troge, J., Rodgers, L., Iossifov, I., and Wigler M. Neuron, 70 (5) 886–897 (9 June 2011). “Remarks on Parallel Analysis,” Buja, A., and Eyuboglu, N., Multivariate Behavioral Research 27, 509–540 (1993). Awards Infovis best paper award for the article “Graphical inference for infovis” by Wickham, H., Cook, D., Hofmann, H., and Buja, A. IEEE Transactions on Visualization and Computer Graphics (Proc. InfoVis’10)., 2010 Journal of Marketing, finalist for the Harold H. Maynard Award and featured blog article of the October Issue, 2007 Fellow, Institute of Mathematical Statistics, 2006 IMS Medallion lecture, Joint Statisti
https://en.wikipedia.org/wiki/Janis%20Johnston	Janis E. Johnston (born 1957) is an American statistician, sociologist, and book author known for her work on permutation tests in statistics. Johnston earned a Ph.D. in 2006 from Colorado State University, and works as a social science analyst for the Food and Nutrition Service of the United States Department of Agriculture. Her books include: A Chronicle of Permutation Statistical Methods: 1920–2000, and Beyond (with Kenneth J. Berry and Paul W. Mielke Jr., Springer, 2014) Inequality: Social Class and Its Consequences (edited with D. Stanley Eitzen, Paradigm Publishers, 2007, and Routledge, 2015) Permutation Statistical Methods: An Integrated Approach (with Kenneth J. Berry and Paul W. Mielke Jr., Springer, 2016) The Measurement of Association: A Permutation Statistical Approach (with Kenneth J. Berry and Paul W. Mielke Jr., Springer, 2018) A Primer of Permutation Statistical Methods (with Kenneth J. Berry and Paul W. Mielke Jr., Springer, 2019) References 1957 births Living people American women sociologists American sociologists American women statisticians Colorado State University alumni 21st-century American women
https://en.wikipedia.org/wiki/Combinatorics%20of%20Finite%20Geometries	Combinatorics of Finite Geometries is an undergraduate mathematics textbook on finite geometry by Lynn Batten. It was published by Cambridge University Press in 1986 with a second edition in 1997 (). Topics The types of finite geometry covered by the book include partial linear spaces, linear spaces, affine spaces and affine planes, projective spaces and projective planes, polar spaces, generalized quadrangles, and partial geometries. A central connecting concept is the "connection number" of a point and a line not containing it, equal to the number of lines that meet the given point and intersect the given line. The second edition adds a final chapter on blocking sets. Beyond the basic theorems and proofs of this subject, the book includes many examples and exercises, and some history and information about current research. Audience and reception The book is aimed at advanced undergraduates, assuming only an introductory-level of abstract algebra and some knowledge of linear algebra. Its coverage of recent research also makes it useful as background reading for researchers in this area. Reviewer Michael J. Kallaher cites as a "serious shortcoming" of the first edition its lack of coverage of applications of this subject, for instance to the design of experiments and to coding theory. The second edition has a section on applications but reviewer Tamás Szőnyi writes that it needs additional expansion. Because of the many types of geometry covered in the book, the coverage of each of them is, at times, shallow; for instance, reviewer Theodore G. Ostrom complains that there is only half a page on non-Desarguesian planes. Additionally, Kallaher feels that block designs should have been included in place of some of the more esoteric geometries described by Batten. Reviewer Thomas Brylawski criticizes the book for "glossing over or ignoring" important results, for overcomplicated proofs, and for missed cases in some of its case analysis. On the other hand, reviewer B. J. Wilson "enjoyed reading this book" and praises it for its "easily followed style", while reviewer R. J. M. Dawson writes that the book "succeeds admirably" in conveying to students "the living, active nature" of this area. Related books Other books on related topics include Finite Generalized Quadrangles by S. E. Payne and J. A. Thas, and Projective Planes by D. R. Hughes and F. C. Piper. References External links Combinatorics of Finite Geometries (1st ed.) on the Internet Archive Finite geometry Mathematics textbooks 1986 non-fiction books 1997 non-fiction books
https://en.wikipedia.org/wiki/Lynn%20Gamwell	Lynn Gamwell (born 1943) is an American nonfiction author and art curator known for her books on art history, the history of mathematics, the history of science, and their connections. Gamwell has a bachelor's degree from the University of Illinois at Chicago, an MFA from Claremont Graduate School, and a PhD from the University of California, Los Angeles. She is also a faculty member at the School of Visual Arts, and has curated exhibits for institutions including the Freud Museum, New York Academy of Sciences, and Loyola University Museum of Art. Her books include: Sigmund Freud and Art: His Personal Collection of Antiquities (catalog for exhibit The Sigmund Freud Antiquities: Fragments from a Buried Past, Sigmund Freud Museum, 1989) Madness in America: Cultural and Medical Perceptions of Mental Illness before 1914 (with Nancy Tomes, Cornell Studies in the History of Psychiatry, Cornell University Press, 1994). Dreams 1900-2000: Science, Art, and the Unconscious Mind (catalog for exhibit, Cornell University Press, 2000) Mathematics and Art: A Cultural History (Princeton University Press, 2016) Exploring the Invisible: Art, Science, and the Spiritual, revised and expanded edition (Princeton University Press, 2020) References 1943 births Living people American art historians Women art historians University of Illinois Chicago alumni Claremont McKenna College alumni University of California, Los Angeles alumni School of Visual Arts faculty Historians from California
https://en.wikipedia.org/wiki/Modes%20of%20variation	In statistics, modes of variation are a continuously indexed set of vectors or functions that are centered at a mean and are used to depict the variation in a population or sample. Typically, variation patterns in the data can be decomposed in descending order of eigenvalues with the directions represented by the corresponding eigenvectors or eigenfunctions. Modes of variation provide a visualization of this decomposition and an efficient description of variation around the mean. Both in principal component analysis (PCA) and in functional principal component analysis (FPCA), modes of variation play an important role in visualizing and describing the variation in the data contributed by each eigencomponent. In real-world applications, the eigencomponents and associated modes of variation aid to interpret complex data, especially in exploratory data analysis (EDA). Formulation Modes of variation are a natural extension of PCA and FPCA. Modes of variation in PCA If a random vector has the mean vector , and the covariance matrix with eigenvalues and corresponding orthonormal eigenvectors , by eigendecomposition of a real symmetric matrix, the covariance matrix can be decomposed as where is an orthogonal matrix whose columns are the eigenvectors of , and is a diagonal matrix whose entries are the eigenvalues of . By the Karhunen–Loève expansion for random vectors, one can express the centered random vector in the eigenbasis where is the principal component associated with the -th eigenvector , with the properties and Then the -th mode of variation of is the set of vectors, indexed by , where is typically selected as . Modes of variation in FPCA For a square-integrable random function , where typically and is an interval, denote the mean function by , and the covariance function by where are the eigenvalues and are the orthonormal eigenfunctions of the linear Hilbert–Schmidt operator By the Karhunen–Loève theorem, one can express the centered function in the eigenbasis, where is the -th principal component with the properties and Then the -th mode of variation of is the set of functions, indexed by , that are viewed simultaneously over the range of , usually for . Estimation The formulation above is derived from properties of the population. Estimation is needed in real-world applications. The key idea is to estimate mean and covariance. Modes of variation in PCA Suppose the data represent independent drawings from some -dimensional population with mean vector and covariance matrix . These data yield the sample mean vector , and the sample covariance matrix with eigenvalue-eigenvector pairs . Then the -th mode of variation of can be estimated by Modes of variation in FPCA Consider realizations of a square-integrable random function with the mean function and the covariance function . Functional principal component analysis provides methods for the estimation of and in detail, often involving poi
https://en.wikipedia.org/wiki/Giuliana%20Davidoff	Giuliana P. Davidoff is an American mathematician specializing in number theory and expander graphs. She is the Robert L. Rooke Professor of Mathematics and the chair of mathematics and statistics at Mount Holyoke College. Education and career Davidoff is a graduate of Rollins College. She completed her Ph.D. in 1984 at New York University, with Peter Sarnak as her doctoral advisor; her dissertation was Statistical Properties of Certain Exponential Sums. Books Davidoff is a coauthor of: Elementary Number Theory, Group Theory and Ramanujan Graphs (with Peter Sarnak and Alain Valette, 2003) The Geometry of Numbers (with Carl D. Olds and Anneli Cahn Lax, 2001) Laboratories in Mathematical Experimentation: A Bridge to Higher Mathematics (1997) References External links Home page Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians American women mathematicians Number theorists Graph theorists Rollins College alumni New York University alumni Mount Holyoke College faculty 20th-century American women 21st-century American women
https://en.wikipedia.org/wiki/Jennifer%20E.%20Smith	Jennifer Elizabeth Smith (born 1980) is an American author of young adult novels, including bestsellers The Statistical Probability of Love at First Sight, Windfall and Field Notes on Love. Biography Smith was born in Lake Forest, Illinois. She graduated from Colgate University in 2003 with an English degree, and she also holds a master's degree in creative writing from the University of St. Andrews in Scotland. She began working for a literary agent in New York City. Her first novel, The Comeback Season, was published by Simon & Schuster in 2008. Both this book and Smith's second book, You are Here, sold poorly. However, she encountered her first commercial success with The Statistical Probability of Love at First Sight, written after having taken a break from writing. Smith continued to work as an editor at Random House while also working on her own writing until 2015. Currently, her work has been translated into 33 languages. As of 2021, Smith has published ten novels, including nine young adult novels, and one novel aimed at middle graders. Her first picture book, The Creature of Habit, illustrated by Leo Espinosa, was released in 2021. Her first novel for adults, The Unsinkable Greta James, was released in 2022. Film adaptations The first film adaptation of one of Smith's novels to be released was the 2022 Netflix film Hello, Goodbye, and Everything in Between, based on the 2015 novel of the same name. It was directed by Michael Lewen, starring Jordan Fisher as Aidan and Talia Ryder as Clare. It was the first film that Jordan Fisher produced. The film was released to a mixed reception from both critics and general audiences. When it was published in 2011, The Statistical Probability of Love at First Sight became her first commercial success, being optioned as a film (with Dustin Lance Black assigned as the director, but later replaced by Vanessa Caswill). As of 2021, the movie adaptation of The Statistical Probability of Love at First Sight was in production in London. Starring Haley Lu Richardson as Hadley and Ben Hardy as Oliver., the film was released on Netflix on September 15, 2023. Her 2017 novel, Windfall, has also been optioned as a movie, with Lauren Graham intending to produce the adaptation. In 2019, it was announced that producers Roger Lay, Jr. and Eric Carnagey have acquired rights to the novels This is What Happy Looks Like and The Geography of You and Me. Bibliography The Comeback Season (Simon & Schuster, 2008) You are Here (Simon & Schuster, 2009) The Statistical Probability of Love at First Sight (Poppy/Little, Brown & Company, 2011) The Storm Makers (Little, Brown Books for Young Readers, 2013) This Is What Happy Looks Like (Little, Brown Books for Young Readers, 2013) The Geography of You and Me (Poppy/Little, Brown, 2014) Happy Again (Poppy, 2015) Hello, Goodbye, and Everything in Between (Poppy/Little, Brown, 2015) Windfall (Delacorte Press, 2017) Field Notes on Love (Delacorte Press, 2019) The Creature of
https://en.wikipedia.org/wiki/2020%20ICC%20Women%27s%20T20%20World%20Cup%20statistics	This is a list of statistics for the 2020 ICC Women's T20 World Cup. Each list contains the top five records except for the partnership records. Team statistics Highest team totals Largest winning margin By runs By wickets By balls remaining Lowest team totals Notes: This is a list of completed innings only; low totals in matches with reduced overs are omitted except when the team was all out. Successful run chases in the second innings are not counted. Smallest winning margin By runs Individual statistics Batting Most runs Highest scores Most boundaries Bowling Most wickets Best bowling figures Fielding Most dismissals This is a list of wicket-keepers with the most dismissals in the tournament. Most catches This is a list of the fielders who took the most catches in the tournament. Other statistics Highest partnerships The following tables are lists of the highest partnerships for the tournament. References External links Official 2020 World Cup site Cricket World Cup at icc-cricket.com statistics
https://en.wikipedia.org/wiki/Chases%20and%20Escapes	Chases and Escapes: The Mathematics of Pursuit and Evasion is a mathematics book on continuous pursuit–evasion problems. It was written by Paul J. Nahin, and published by the Princeton University Press in 2007. It was reissued as a paperback reprint in 2012. The Basic Library List Committee of the Mathematical Association of America has rated this book as essential for inclusion in undergraduate mathematics libraries. Topics The book has four chapters, covering the solutions to 21 continuous pursuit–evasion problems, with an additional 10 "challenge problems" left for readers to solve, with solutions given in an appendix. The problems are presented as entertaining stories that "breathe life into the mathematics and invite wider engagement", and their solutions use varied methods, including the computer calculation of numerical solutions for differential equations whose solutions have no closed form. Most of the material was previously known, but is collected here for the first time. The book also provides background material on the history of the problems it describes, although this is not its main focus. Even before beginning its main content, the preface of the book begins with an example of pure evasion from known pursuit, the path used by the Enola Gay to escape the blast of the nuclear bomb it dropped on Hiroshima. The first chapter of the book concerns the opposite situation of "pure pursuit" without evasion, including the initial work in this area by Pierre Bouguer in 1732. Bouger studied a problem of pirates chasing a merchant ship, in which the merchant ship (unaware of the pirates) travels on a straight line while the pirate ship always travels towards the current position of the merchant ship. The resulting pursuit curve is called a radiodrome, and this chapter studies several similar problems and stories involving a linearly moving target, including variations where the pursuer may aim ahead of the target and the tractrix curve generated by a pursuer that follows the target at constant distance. Chapter 2 considers targets moving to evade their pursuers, beginning with an example of circular evasive motion described in terms of a dog chasing a duck in a pond, with the dog beginning at the center and the duck moving circularly around the bank. Other variants considered in this chapter include cases where the target is hidden from view, and moving on an unknown trajectory. Chapter 3 considers "cyclic pursuit" problems in which multiple agents pursue each other, as in the mice problem. The fourth and final chapter is entitled "Seven classic evasion problems". It begins with a problem from Martin Gardner's Mathematical Games, the reverse of the dog-and-duck problem, in which a person on a raft in a circular lake tries to reach the shore before a pursuer on land reaches the same point. It also includes hide-and-seek problems and their formulation using game theory, and the work of Richard Rado and Abram Samoilovitch Besicovitch on a ma
https://en.wikipedia.org/wiki/Petros%20Drineas	Petros Drineas is a Greek-American computer scientist known for his contributions to the theory of data science and the development of Randomized Numerical Linear Algebra (RandNLA). In a 2012 paper Michael W. Mahoney and Drineas introduced CUR matrix approximation for improved big data analysis. Drineas' work on the application of principal component analysis to population genetics disproved the long-standing hypothesis that the Minoan civilization had North African origins. Drineas earned his BS in 1997 from University of Patras in Greece. He received his PhD in Computer Science from Yale University in 2003 where his advisor was Ravi Kannan. Drineas was on the faculty of Rensselaer Polytechnic Institute from 2003 to 2016 and was a visiting researcher at Microsoft Research, Yahoo! Research and Sandia National Laboratory. He is currently a professor of computer science at Purdue University. Drineas is a co-editor with Peter Bühlmann, Michael Kane and M. van der Laan of "Handbook of Big Data" published in 2016. References American computer scientists Purdue University faculty Yale School of Engineering & Applied Science alumni Year of birth missing (living people) Living people Greek computer scientists
https://en.wikipedia.org/wiki/L.%20Christine%20Kinsey	Laura Christine Kinsey is an American mathematician specializing in topology. She is a professor of mathematics at Canisius College. Education Kinsey graduated from the University of Maryland, College Park in 1975 with honors in mathematics. She returned to the University of Maryland, College Park for graduate study, completing a Ph.D. there in 1984. Her dissertation, Pseudoisotopies and Submersions of a Compact Manifold to the Circle, was jointly supervised by Henry C. King and Walter Neumann. Books Kinsey is the author of mathematics textbooks that include: Topology of Surfaces (Undergraduate Texts in Mathematics, Springer, 1993) Symmetry, Shape, and Space: An Introduction to Mathematics through Geometry (with Teresa Moore, Springer, 2002) Geometry and Symmetry (with Teresa Moore and Efstratios Prassidis, Wiley, 2010) References Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians American women mathematicians Topologists University of Maryland, College Park alumni Canisius University faculty 20th-century American women 21st-century American women
https://en.wikipedia.org/wiki/Legacy%20of%20Alan%20Turing	Alan Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. He left an extensive legacy in mathematics, science, society and popular culture. Awards, honours, and tributes Turing was appointed an officer of the Order of the British Empire 1946. He was also elected a Fellow of the Royal Society (FRS) in 1951. Several things are named in his honour: Alan Turing Institute Church–Turing thesis Good–Turing frequency estimation Turing completeness Turing degree Turing fixed-point combinator Turing Institute Turing Lecture Turing machine Turing patterns Turing reduction Turing switch Turing test Posthumous tributes Various institutions have paid tribute to Turing by naming things after him including: The computer room at King's College, Cambridge, Turing's alma mater, is called the Turing Room. The Turing Room at the University of Edinburgh's School of Informatics houses a bust of Turing by Eduardo Paolozzi, and a set (No. 42/50) of his Turing prints (2000). The University of Surrey has a statue of Turing on their main piazza and one of the buildings of Faculty of Engineering and Physical Sciences is named after him. Istanbul Bilgi University organises an annual conference on the theory of computation called "Turing Days". The University of Texas at Austin has an honours computer science programme named the Turing Scholars. In the early 1960s, Stanford University named the sole lecture room of the Polya Hall Mathematics building "Alan Turing Auditorium". One of the amphitheatres of the Computer Science department (LIFL) at the University of Lille in northern France is named in honour of Alan M. Turing (the other amphitheatre is named after Kurt Gödel). The University of Washington has a computer laboratory named after Turing. Oxford Brookes University has a building named after Turing. Alan Turing Road in the Surrey Research Park and the Alan Turing Way, part of the Manchester inner ring road. Alan Turing road in Loughborough are named after Turing. Carnegie Mellon University has a granite bench, situated in the Hornbostel Mall, with the name "A.M. Turing" carved across the top, "Read" down the left leg, and "Write" down the other. The University of Oregon has a bust of Turing on the side of Deschutes Hall, the computer science building. The École Polytechnique Fédérale de Lausanne has a road and a square named after Turing (Chemin Alan Turing and Place Alan Turing). The Faculty of Informatics and Information Technologies Slovak University of Technology in Bratislava, Slovakia, has a lecture room named "Turing Auditorium". The Paris Diderot University has a lecture room named "Amphithéâtre Turing". The Faculty of Mathematics and Computer Science at the University of Würzburg has a lecture hall named "Turing Hörsaal". The Paul Sabatier University in Toulouse has a lecture room named "Amphithéâtre Turing" (Bâtiment U4).
https://en.wikipedia.org/wiki/Hotaka%20Nakamura	is a Japanese footballer currently playing as a right back for FC Tokyo. Career statistics . Notes Honours Club FC Tokyo J.League Cup : 2020 References External links 1997 births Living people Japanese men's footballers Men's association football defenders J1 League players FC Tokyo players Sportspeople from Yokosuka, Kanagawa
https://en.wikipedia.org/wiki/Ryoya%20Morishita	is a Japanese professional footballer who plays as a wing-back or a left-back for Nagoya Grampus and the Japan national team. Career statistics Club . Notes Honours Nagoya Grampus J.League Cup: 2021 References External links 1997 births Living people Meiji University alumni Japanese men's footballers Men's association football midfielders J1 League players Júbilo Iwata players Sagan Tosu players Nagoya Grampus players Japan men's international footballers
https://en.wikipedia.org/wiki/Tatsuki%20Seko	is a Japanese footballer currently playing as a defensive midfielder for Kawasaki Frontale. Career statistics Club . Notes References External links 1997 births Living people Japanese men's footballers Men's association football midfielders J1 League players Yokohama FC players Kawasaki Frontale players
https://en.wikipedia.org/wiki/Norbert%20Sz%C3%A9lp%C3%A1l	Norbert Szélpál (born 3 March 1996) is a Hungarian football centre-back who plays for OTP Bank Liga club Paksi FC. Career statistics . References External links 1996 births Living people Hungarian men's footballers Hungary men's youth international footballers Men's association football defenders Békéscsaba 1912 Előre footballers Paksi FC players Nemzeti Bajnokság I players People from Szeged
https://en.wikipedia.org/wiki/Tomoya%20Fujii	is a Japanese professional footballer who plays as a winger for club Kashima Antlers. Career statistics Club . References External links 1998 births Living people Sportspeople from Gifu Association football people from Gifu Prefecture Ritsumeikan University alumni Japanese men's footballers Men's association football midfielders J1 League players Sanfrecce Hiroshima players Kashima Antlers players
https://en.wikipedia.org/wiki/Yuki%20Yamamoto%20%28footballer%29	is a Japanese footballer currently playing as a defensive midfielder for Gamba Osaka. Career statistics Club . Notes References External links 1997 births Living people Sportspeople from Shiga Prefecture Association football people from Shiga Prefecture Kwansei Gakuin University alumni Japanese men's footballers Men's association football midfielders J1 League players J3 League players Sagawa Shiga FC players Gamba Osaka players Gamba Osaka U-23 players 21st-century Japanese people
https://en.wikipedia.org/wiki/Koki%20Tachi	is a Japanese footballer currently playing as a centre back for Shonan Bellmare. Career statistics Club . Notes References External links 1997 births Living people Sportspeople from Mie Prefecture Association football people from Mie Prefecture Nihon University alumni Japanese men's footballers Men's association football defenders J1 League players Shonan Bellmare players
https://en.wikipedia.org/wiki/Shuma%20Mihara	is a Japanese footballer who plays as a defender for Ehime. Career statistics . Notes References External links 2001 births Living people Japanese men's footballers Japan men's youth international footballers Men's association football defenders J2 League players Ehime FC players Sportspeople from Matsuyama, Ehime
https://en.wikipedia.org/wiki/Takahiro%20Akimoto	is a Japanese footballer currently playing as a left winger or a left back for Urawa Red Diamonds. Career statistics Club . Notes Honours Club Urawa Red Diamonds Emperor's Cup: 2021 Japanese Super Cup: 2022 AFC Champions League: 2022 References External links 1998 births Living people Association football people from Tochigi Prefecture Kokushikan University alumni Japanese men's footballers Men's association football midfielders J2 League players J1 League players Tochigi SC players Urawa Red Diamonds players
https://en.wikipedia.org/wiki/Ryo%20Sato%20%28footballer%29	is a Japanese footballer currently playing as a forward for Giravanz Kitakyushu. Career statistics Club . Notes References External links 1997 births Living people Japanese men's footballers Men's association football forwards J2 League players Giravanz Kitakyushu players
https://en.wikipedia.org/wiki/Ryoya%20Yamashita	is a Japanese footballer currently playing as a forward for Yokohama FC. Career statistics Club . Notes References External links 1997 births Living people Sportspeople from Shizuoka Prefecture Association football people from Shizuoka Prefecture Nippon Sport Science University alumni Japanese men's footballers Men's association football forwards J2 League players Tokyo Verdy players Yokohama FC players
https://en.wikipedia.org/wiki/Ryoma%20Kida	is a Japanese footballer currently playing as a midfielder for Vegalta Sendai. Career statistics Club . Notes Honours Individual J.League Monthly MVP: 2022(May) References External links 1997 births Living people Japanese men's footballers Men's association football midfielders J1 League players J2 League players V-Varen Nagasaki players Vegalta Sendai players
https://en.wikipedia.org/wiki/Mutsuki%20Kato	is a Japanese footballer who plays as a forward for club Sanfrecce Hiroshima. Career statistics Club References External links 1997 births Living people Japanese men's footballers Men's association football forwards J1 League players J2 League players Sanfrecce Hiroshima players Ehime FC players Cerezo Osaka players
https://en.wikipedia.org/wiki/Daiki%20Nakashio	is a Japanese footballer currently playing as a defender for Thespakusatsu Gunma. Career statistics Club . Notes References External links 1997 births Living people Japanese men's footballers Men's association football defenders J1 League players J2 League players Ventforet Kofu players Yokohama FC players
https://en.wikipedia.org/wiki/Shunnosuke%20Matsuki	is a Japanese footballer currently playing as a midfielder for Fagiano Okayama. He is currently on loan to Suzuka Point Getters of the Japan Football League Career statistics Club . Notes References External links 1996 births Living people Japanese men's footballers Men's association football midfielders J2 League players Yokohama FC players Fagiano Okayama players
https://en.wikipedia.org/wiki/Intercollegiate%20Biomathematics%20Alliance	The Intercollegiate Biomathematics Alliance (IBA) is a syndicate of organizations focused on connecting both academic and non-academic institutions to promote the study of biomathematics, ecology, and other related fields. Biomathematics is a scientific area connecting biology, ecology, mathematics, and computer science. Founded in 2014 by Executive director Olcay Akman of Illinois State University, the Intercollegiate Biomathematics Alliance helps organizations to work together and share resources among one another that are not regularly available at all institutions. The IBA is still young and typically attracts smaller colleges around the United States who tend to benefit more from being part of a consortium. However, in recent years, universities such as Arizona State University have joined and the IBA continues to maintain connections with larger research groups such as the Mathematical Bioscience Institute (MBI) and the National Institute for Mathematical and Biological Synthesis (NIMBioS). History In 2007, Olcay Akman of mathematics and Steven Juliano of biological sciences started a master's degree program at Illinois State University. The program grew and is now operated under the same umbrella as the IBA, the Center for Collaborative Studies in Mathematical Biology. In 2008, the first BEER (Biomathematics Ecology Education and Research) conference was held at Illinois State University with only 10 speakers and less than 50 attendees. In 2014, the BEER conference was the second largest biomathematics conference globally with more than 100 speakers. Then in 2014, other universities were asked to collaborate with the common goal of educating students about biomathematics, and this led to the creation of the Intercollegiate Biomathematics Alliance (IBA). The IBA is not the first to create a network of institutions. Morehouse College in Atlanta, GA participates in its own network of institutions that helps to provide students with greater access to resources. Similarly, Massachusetts Institute of Technology houses a consortium for research in energy, the MIT Energy Initiative. This network brings together the university and companies to expand research experiences and broaden educational perspectives. By pooling together resources, these consortia attempt to unite organizations under a common goal and share resources in infrastructure, intellect, and academia. Member Institutions As of 2021, the Intercollegiate Biomathematics Alliance has 9 member institutions. In 2019, the IBA had 11 member institutions. IBA members pay dues based on their institutional size. Individuals are also able to become members of the IBA with reduced rates for students. There is some incentive beyond collaboration efforts to become an IBA member. The organization offers reduced registration fees to the International Symposium on BEER, access to distance education courses, a copy of Spora-Journal of Biomathematics, and travel funding. Programs and Resources
https://en.wikipedia.org/wiki/In%20Pursuit%20of%20the%20Traveling%20Salesman	In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation is a book on the travelling salesman problem, by William J. Cook, published in 2011 by the Princeton University Press, with a paperback reprint in 2014. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. Topics The travelling salesman problem asks to find the shortest cyclic tour of a collection of points, in the plane or in more abstract mathematical spaces. Because the problem is NP-hard, algorithms that take polynomial time are unlikely to be guaranteed to find its optimal solution; on the other hand a brute-force search of all permutations would always solve the problem exactly but would take far too long to be usable for all but the smallest problems. Threading a middle ground between these too-fast and too-slow running times, and developing a practical system that can find the exact solution of larger instances, raises difficult questions of algorithm engineering, which have sparked the development of "many of the concepts and techniques of combinatorial optimization". The introductory chapter of the book explores the limits of calculation on the problem, from 49-point problems solved by hand in the mid-1950s by George Dantzig, D. R. Fulkerson, and Selmer M. Johnson to a problem with 85,900 points solved optimally in 2006 by the Concorde TSP Solver, which Cook helped develop. The next chapters covers the early history of the problem and of related problems, including Leonhard Euler's work on the Seven Bridges of Königsberg, William Rowan Hamilton's Icosian game, and Julia Robinson first naming the problem in 1949. Another chapter describes real-world applications of the problem, ranging "from genome sequencing and designing computer processors to arranging music and hunting for planets". Reviewer Brian Hayes cites "the most charming revelation" of the book as being the fact that one of those real-world applications has been route planning for actual traveling salesmen in the early 20th century. Chapters four through seven, "core of the book", discuss methods for solving the problem, leading from heuristics and metaheuristics, linear programming relaxation, and cutting-plane methods, up to the branch and bound method that combines these techniques and is used by Concorde. The next two chapters also cover technical material, on the performance of computer implementations and on the Computational complexity theory of the problem. The remaining chapters are more human-centered, covering human and animal problem-solving strategies, and the incorporation of TSP solutions into the artworks of Julian Lethbridge, Robert A. Bosch, and others. A short final summary chapter suggests possible future directions, including the possibility of progress on the P versus NP problem. Audience The book is intended for a non-specialist audience, avoids technical detail and is written "in a
https://en.wikipedia.org/wiki/Olga%20Korosteleva	Olga Korosteleva is a Russian-American statistician. She is a professor of statistics at California State University, Long Beach, and the author of several books on statistics. Education and career Korosteleva grew up in the Soviet Union, but was educated in the US after her father, statistician Alexander Korostelev, became a professor at Wayne State University. She went to Wayne State herself as an undergraduate, completing a bachelor's degree there in 1996, and then earned a Ph.D. in statistics from Purdue University in 2002. Her dissertation, Limit theorem for the spread of branching process with stabilizing drift, was supervised by Thomas Sellke. As well as holding a faculty position at California State University, Long Beach, Korosteleva has served as president of the Southern California Chapter of the American Statistical Association, and editor-in-chief of the chapter newsletter. Books Korosteleva is the author or co-author of books including: Clinical Statistics: Introducing Clinical Trials, Survival Analysis, and Longitudinal Data Analysis (Jones and Bartlett, 2009) Mathematical Statistics: Asymptotic Minimax Theory (with Alexander Korostelev, Graduate Studies in Mathematics 119, American Mathematical Society, 2011) Nonparametric Methods in Statistics with SAS Applications (CRC Press, 2013) Advanced Regression Models with SAS and R (CRC Press, 2018) References Year of birth missing (living people) Living people American statisticians Russian statisticians Women statisticians Wayne State University alumni Purdue University alumni California State University, Long Beach faculty
https://en.wikipedia.org/wiki/Computing%20the%20Continuous%20Discretely	Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra is an undergraduate-level textbook in geometry, on the interplay between the volume of convex polytopes and the number of lattice points they contain. It was written by Matthias Beck and Sinai Robins, and published in 2007 by Springer-Verlag in their Undergraduate Texts in Mathematics series (Vol. 154). A second edition was published in 2015, and a German translation of the first edition by Kord Eickmeyer, Das Kontinuum diskret berechnen, was published by Springer in 2008. Topics The book begins with a motivating problem, the coin problem of determining which amounts of money can be represented (and what is the largest non-representable amount of money) for a given system of coin values. Other topics touched on include face lattices of polytopes and the Dehn–Sommerville equations relating numbers of faces; Pick's theorem and the Ehrhart polynomials, both of which relate lattice counting to volume; generating functions, Fourier transforms, and Dedekind sums, different ways of encoding sequences of numbers into mathematical objects; Green's theorem and its discretization; Bernoulli polynomials; the Euler–Maclaurin formula for the difference between a sum and the corresponding integral; special polytopes including zonotopes, the Birkhoff polytope, and permutohedra; and the enumeration of magic squares. In this way, the topics of the book connect together geometry, number theory, and combinatorics. Audience and reception This book is written at an undergraduate level, and provides many exercises, making it suitable as an undergraduate textbook. Little mathematical background is assumed, except for some complex analysis towards the end of the book. The book also includes open problems, of more interest to researchers in these topics. As reviewer Darren Glass writes, "Even people who are familiar with the material would almost certainly learn something from the clear and engaging exposition that these two authors use." Reviewer Margaret Bayer calls the book "coherent and tightly developed ... accessible and engaging", and reviewer Oleg Karpenkov calls it "outstanding". See also List of books about polyhedra References Polytopes Lattice points Volume Mathematics textbooks 2007 non-fiction books 2015 non-fiction books Springer Science+Business Media books
https://en.wikipedia.org/wiki/Cavell%20Brownie	Cavell Brownie (née Sherlock) is a Professor Emeritus of Statistics at the North Carolina State University. Her research considered biometric methods and wildlife sampling. Education and career Brownie is African-American, and was born in Jamaica. She earned her doctoral degree at Cornell University in 1973, developing mathematical models to estimate bird populations. Her dissertation, Stochastic Models Allowing Age-Dependent Survival Rates for Banding Experiments on Exploited Bird Populations, was supervised by D. S. Robson. Brownie was a faculty member at North Carolina State University from 1982 to 2007. Research Brownie's research involved wildlife sampling and biometric methods. Her publications include: Recognition Brownie was awarded the George W. Snedecor award in 1983 and 1990, and the North Carolina State University D.D. Mason Faculty Award in 1988. She was elected a Fellow of the American Statistical Association in 2003. The Department of Statistics at North Carolina State University award an annual Cavell Brownie Mentoring Faculty prize in her honor. Personal life Brownie married Cecil Brownie, a Veterinarian at North Carolina State University, in August 1968. Together they have two sons. References Living people Year of birth missing (living people) American people of Jamaican descent American statisticians North Carolina State University faculty Cornell University alumni Fellows of the American Statistical Association African-American statisticians Women statisticians 21st-century African-American scientists 21st-century African-American academics 21st-century American academics
https://en.wikipedia.org/wiki/Matrix%20factorization%20%28algebra%29	In homological algebra, a branch of mathematics, a matrix factorization is a tool used to study infinitely long resolutions, generally over commutative rings. Motivation One of the problems with non-smooth algebras, such as Artin algebras, are their derived categories are poorly behaved due to infinite projective resolutions. For example, in the ring there is an infinite resolution of the -module whereInstead of looking at only the derived category of the module category, David Eisenbud studied such resolutions by looking at their periodicity. In general, such resolutions are periodic with period after finitely many objects in the resolution. Definition For a commutative ring and an element , a matrix factorization of is a pair of square matrices such that . This can be encoded more generally as a graded -module with an endomorphism such that . Examples (1) For and there is a matrix factorization where for . (2) If and , then there is a matrix factorization where Periodicity definition Main theorem Given a regular local ring and an ideal generated by an -sequence, set and let be a minimal -free resolution of the ground field. Then becomes periodic after at most steps. https://www.youtube.com/watch?v=2Jo5eCv9ZVY Maximal Cohen-Macaulay modules page 18 of eisenbud article Categorical structure Support of matrix factorizations See also Derived noncommutative algebraic geometry Derived category Homological algebra Triangulated category References Further reading Homological Algebra on a Complete Intersection with an Application to Group Representations Geometric Study of the Category of Matrix Factorizations https://web.math.princeton.edu/~takumim/takumim_Spr13_JP.pdf https://arxiv.org/abs/1110.2918 Homological algebra
https://en.wikipedia.org/wiki/David%20Richeson	David S. Richeson is an American mathematician whose interests include the topology of dynamical systems, recreational mathematics, and the history of mathematics. He is a professor of mathematics at Dickinson College, where he holds the John J. & Ann Curley Faculty Chair in the Liberal Arts. Education and career Richeson was interested in mathematics from an early age, in part through Martin Gardner's Mathematical Games columns. He graduated from Hamilton College in 1993, and completed his Ph.D. at Northwestern University in 1998; his dissertation, Connection Matrix Pairs for the Discrete Conley Index, was supervised by John Franks. Richeson joined the Dickinson College faculty after postdoctoral research at Michigan State University. He was the editor of Math Horizons from 2014 to 2019. Books Richeson is the author of the book Euler's Gem: The Polyhedron Formula and the Birth of Topology (Princeton University Press, 2008; paperback, 2012), on the Euler characteristic of polyhedra. The book won the 2010 Euler Book Prize of the Mathematical Association of America. His second book, Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (Princeton University Press, 2019), concerns four famous problems of straightedge and compass construction, unsolved by the ancient Greek mathematicians and now known to be impossible: doubling the cube, squaring the circle, constructing regular polygons of any order, and trisecting the angle. References External links Division by zero, Richeson's personal web site Dave Richeson's Favorite Theorem, Evelyn Lamb, Scientific American Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians Hamilton College (New York) alumni Northwestern University alumni Dickinson College faculty
https://en.wikipedia.org/wiki/Susan%20H.%20Marshall	Susan Hammond Marshall is an American mathematician specializing in number theory, arithmetic geometry, and mathematical proof techniques. She is an associate professor of mathematics at Monmouth University. Education and career Marshall is a 1993 graduate of Wake Forest University, majoring in mathematics with a minor in psychology; she cites Wake Forest professors John Baxley and Stephen B. Robinson as early mentors in mathematics. After taking a position analyzing Hubble Space Telescope data at the Goddard Space Flight Center, she went to the University of Arizona for graduate study in mathematics, completing her Ph.D. in 2001. Her dissertation, Crystalline Representations and Neron Models, was supervised by Minhyong Kim. She was a postdoctoral researcher at the University of Texas at Austin from 2001 to 2004, and joined the Monmouth faculty in 2004. Recognition In 2014, Marshall won the Carl B. Allendoerfer Award of the Mathematical Association of America for her work with Monmouth colleague Donald R. Smith applying control theory to the distribution of prime numbers. In the same year, she also won the Paul R. Halmos – Lester R. Ford Award with Alexander Perlis for their work showing that Heronian tetrahedra can always be realized with integer coordinates. Her work with Smith also won the 2016 Chauvenet Prize. In 2019 the New Jersey Section of the Mathematical Association of America gave Marshall their Award for Distinguished College or University Teaching of Mathematics. References External links Home page Year of birth missing (living people) Living people 21st-century American mathematicians American women mathematicians Wake Forest University alumni University of Arizona alumni Monmouth University faculty 21st-century American women
https://en.wikipedia.org/wiki/Euler%27s%20Gem	Euler's Gem: The Polyhedron Formula and the Birth of Topology is a book on the formula for the Euler characteristic of convex polyhedra and its connections to the history of topology. It was written by David Richeson and published in 2008 by the Princeton University Press, with a paperback edition in 2012. It won the 2010 Euler Book Prize of the Mathematical Association of America. Topics The book is organized historically, and reviewer Robert Bradley divides the topics of the book into three parts. The first part discusses the earlier history of polyhedra, including the works of Pythagoras, Thales, Euclid, and Johannes Kepler, and the discovery by René Descartes of a polyhedral version of the Gauss–Bonnet theorem (later seen to be equivalent to Euler's formula). It surveys the life of Euler, his discovery in the early 1750s that the Euler characteristic is equal to two for all convex polyhedra, and his flawed attempts at a proof, and concludes with the first rigorous proof of this identity in 1794 by Adrien-Marie Legendre, based on Girard's theorem relating the angular excess of triangles in spherical trigonometry to their area. Although polyhedra are geometric objects, Euler's Gem argues that Euler discovered his formula by being the first to view them topologically (as abstract incidence patterns of vertices, faces, and edges), rather than through their geometric distances and angles. (However, this argument is undermined by the book's discussion of similar ideas in the earlier works of Kepler and Descartes.) The birth of topology is conventionally marked by an earlier contribution of Euler, his 1736 work on the Seven Bridges of Königsberg, and the middle part of the book connects these two works through the theory of graphs. It proves Euler's formula in a topological rather than geometric form, for planar graphs, and discusses its uses in proving that these graphs have vertices of low degree, a key component in proofs of the four color theorem. It even makes connections to combinatorial game theory through the graph-based games of Sprouts and Brussels Sprouts and their analysis using Euler's formula. In the third part of the book, Bradley moves on from the topology of the plane and the sphere to arbitrary topological surfaces. For any surface, the Euler characteristics of all subdivisions of the surface are equal, but they depend on the surface rather than always being 2. Here, the book describes the work of Bernhard Riemann, Max Dehn, and Poul Heegaard on the classification of manifolds, in which it was shown that the two-dimensional topological surfaces can be completely described by their Euler characteristics and their orientability. Other topics discussed in this part include knot theory and the Euler characteristic of Seifert surfaces, the Poincaré–Hopf theorem, the Brouwer fixed point theorem, Betti numbers, and Grigori Perelman's proof of the Poincaré conjecture. An appendix includes instructions for creating paper and soap-bub
https://en.wikipedia.org/wiki/Levente%20Szab%C3%B3	Levente Szabó (born 6 June 1999) is a Hungarian professional footballer who plays for Fehérvár. Club career On 31 August 2021, Szabó was loaned to Budafoki MTE for the season. Career statistics . References External links 1999 births Footballers from Székesfehérvár Living people Hungarian men's footballers Hungary men's youth international footballers Men's association football forwards Győri ETO FC players Atalanta BC players Genoa CFC players Fehérvár FC players Budaörsi SC footballers Budafoki MTE footballers Kecskeméti TE players Nemzeti Bajnokság I players Nemzeti Bajnokság II players Hungarian expatriate men's footballers Expatriate men's footballers in Italy Hungarian expatriate sportspeople in Italy
https://en.wikipedia.org/wiki/Proofs%20That%20Really%20Count	Proofs That Really Count: the Art of Combinatorial Proof is an undergraduate-level mathematics book on combinatorial proofs of mathematical identies. That is, it concerns equations between two integer-valued formulas, shown to be equal either by showing that both sides of the equation count the same type of mathematical objects, or by finding a one-to-one correspondence between the different types of object that they count. It was written by Arthur T. Benjamin and Jennifer Quinn, and published in 2003 by the Mathematical Association of America as volume 27 of their Dolciani Mathematical Expositions series. It won the Beckenbach Book Prize of the Mathematical Association of America. Topics The book provides combinatorial proofs of thirteen theorems in combinatorics and 246 numbered identities (collated in an appendix). Several additional "uncounted identities" are also included. Many proofs are based on a visual-reasoning method that the authors call "tiling", and in a foreword, the authors describe their work as providing a follow-up for counting problems of the Proof Without Words books by Roger B. Nelson. The first three chapters of the book start with integer sequences defined by linear recurrence relations, the prototypical example of which is the sequence of Fibonacci numbers. These numbers can be given a combinatorial interpretation as the number of ways of tiling a strip of squares with tiles of two types, single squares and dominos; this interpretation can be used to prove many of the fundamental identities involving the Fibonacci numbers, and generalized to similar relations about other sequences defined similarly, such as the Lucas numbers, using "circular tilings and colored tilings". For instance, for the Fibonacci numbers, considering whether a tiling does or does not connect positions and of a strip of length immediately leads to the identity Chapters four through seven of the book concern identities involving continued fractions, binomial coefficients, harmonic numbers, Stirling numbers, and factorials. The eighth chapter branches out from combinatorics to number theory and abstract algebra, and the final chapter returns to the Fibonacci numbers with more advanced material on their identities. Audience and reception The book is aimed at undergraduate mathematics students, but the material is largely self-contained, and could also be read by advanced high school students. Additionally, many of the book's chapters are themselves self-contained, allowing for arbitrary reading orders or for excerpts of this material to be used in classes. Although it is structured as a textbook with exercises in each chapter, reviewer Robert Beezer writes that it is "not meant as a textbook", but rather intended as a "resource" for teachers and researchers. Echoing this, reviewer Joe Roberts writes that despite its elementary nature, this book should be "valuable as a reference ... for anyone working with such identities". In an initial revie
https://en.wikipedia.org/wiki/L%C3%A1szl%C3%B3%20Deutsch	László Deutsch (born 9 March 1999) is a Hungarian football defender who plays for Nemzeti Bajnokság II club Vasas. Club career On 29 June 2022, Deutsch moved to Vasas. Career statistics . References External links 1999 births Footballers from Budapest Living people Hungarian men's footballers Hungary men's youth international footballers Hungary men's under-21 international footballers Men's association football defenders Puskás Akadémia FC II players Puskás Akadémia FC players Aqvital FC Csákvár players Vasas SC players Nemzeti Bajnokság I players Nemzeti Bajnokság II players Nemzeti Bajnokság III players
https://en.wikipedia.org/wiki/Convexity%20%28algebraic%20geometry%29	In algebraic geometry, convexity is a restrictive technical condition for algebraic varieties originally introduced to analyze Kontsevich moduli spaces in quantum cohomology. These moduli spaces are smooth orbifolds whenever the target space is convex. A variety is called convex if the pullback of the tangent bundle to a stable rational curve has globally generated sections. Geometrically this implies the curve is free to move around infinitesimally without any obstruction. Convexity is generally phrased as the technical condition since Serre's vanishing theorem guarantees this sheaf has globally generated sections. Intuitively this means that on a neighborhood of a point, with a vector field in that neighborhood, the local parallel transport can be extended globally. This generalizes the idea of convexity in Euclidean geometry, where given two points in a convex set , all of the points are contained in that set. There is a vector field in a neighborhood of transporting to each point . Since the vector bundle of is trivial, hence globally generated, there is a vector field on such that the equality holds on restriction. Examples There are many examples of convex spaces, including the following. Spaces with trivial rational curves If the only maps from a rational curve to are constants maps, then the pullback of the tangent sheaf is the free sheaf where . These sheaves have trivial non-zero cohomology, and hence they are always convex. In particular, Abelian varieties have this property since the Albanese variety of a rational curve is trivial, and every map from a variety to an Abelian variety factors through the Albanese. Projective spaces Projective spaces are examples of homogeneous spaces, but their convexity can also be proved using a sheaf cohomology computation. Recall the Euler sequence relates the tangent space through a short exact sequence If we only need to consider degree embeddings, there is a short exact sequence giving the long exact sequence since the first two -terms are zero, which follows from being of genus , and the second calculation follows from the Riemann–Roch theorem, we have convexity of . Then, any nodal map can be reduced to this case by considering one of the components of . Homogeneous spaces Another large class of examples are homogenous spaces where is a parabolic subgroup of . These have globally generated sections since acts transitively on , meaning it can take a bases in to a basis in any other point , hence it has globally generated sections. Then, the pullback is always globally generated. This class of examples includes Grassmannians, projective spaces, and flag varieties. Product spaces Also, products of convex spaces are still convex. This follows from the Kunneth theorem in coherent sheaf cohomology. Projective bundles over curves One more non-trivial class of examples of convex varieties are projective bundles for an algebraic vector bundle over a smoo
https://en.wikipedia.org/wiki/Ren%20Ikeda	is a Japanese footballer currently playing as a midfielder for Oita Trinita. Career statistics Club . Notes References External links 1997 births Living people Japanese men's footballers Men's association football midfielders J2 League players FC Ryukyu players
https://en.wikipedia.org/wiki/Yu%20Yong-hyeon	Yu Yong-hyeon (; born 27 February 2000) is a South Korean footballer currently playing as a midfielder for Thai League 1 clubChiangrai United. Club statistics Notes References External links 2000 births Living people South Korean men's footballers South Korean expatriate men's footballers Men's association football midfielders J2 League players Fagiano Okayama players Yu Yong-hyeon Yu Yong-hyeon South Korean expatriate sportspeople in Japan Expatriate men's footballers in Japan
https://en.wikipedia.org/wiki/Felipe%20Tavares	Felipe Pereira Tavares (born 24 February 1994) is a Brazilian footballer who currently plays for FC Ryukyu. Career statistics Club Notes References External links 1994 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football defenders J2 League players Clube Atlético Linense players Duque de Caxias Futebol Clube players Associação Esportiva Santacruzense players Rio Branco Esporte Clube players Associação Esportiva Velo Clube Rioclarense players Associação Atlética Anapolina players Mirassol Futebol Clube players Olímpia Futebol Clube players Sociedade Esportiva do Gama players Anápolis Futebol Clube players FC Ryukyu players Expatriate men's footballers in Japan Brazilian expatriate sportspeople in Japan Footballers from São Paulo
https://en.wikipedia.org/wiki/Albert%20Puig%20%28football%20manager%29	Albert Puig Ortoneda (born 15 April 1968) is a Spanish footballer manager He most recently managed J1 League club of FC Tokyo. Managerial statistics References 1968 births Living people Spanish football managers Albirex Niigata managers FC Tokyo managers Spanish expatriate sportspeople in Japan Expatriate football managers in Japan J1 League managers J2 League managers
https://en.wikipedia.org/wiki/David%20Soudry	David Soudry (born 1956) is a professor of mathematics at Tel Aviv University working in number theory and automorphic forms. Career Soudry was born in 1956. He received his PhD in mathematics from Tel Aviv University in 1983 under the supervision of Ilya Piatetski-Shapiro. From 1983 to 1984, he was a member of the Institute for Advanced Study. He is a professor of mathematics at Tel Aviv University. Research Together with Stephen Rallis and David Ginzburg, Soudry wrote a series of papers about automorphic descent culminating in their book The descent map from automorphic representations of GL(n) to classical groups. Their automorphic descent method constructs an explicit inverse map to the (standard) Langlands functorial lift and has had major applications to the analysis of functoriality. Also, using the "Rallis tower property" from Rallis's 1984 paper on the Howe duality conjecture, they studied global exceptional correspondences and found new examples of functorial lifts. Selected publications References External links 20th-century Israeli mathematicians 21st-century Israeli mathematicians Number theorists Living people Date of birth missing (living people) Place of birth missing (living people) Tel Aviv University alumni Academic staff of Tel Aviv University Institute for Advanced Study visiting scholars 1956 births
https://en.wikipedia.org/wiki/Dihua%20Jiang	Dihua Jiang (, born 1958) is a Chinese-born American mathematician. He is a professor of mathematics at the University of Minnesota working in number theory, automorphic forms, and the Langlands program. Early life and education In 1958, Jiang was born in the Lucheng District of Wenzhou, Zhejiang. He studied at Wenzhou No. 3 Middle School before studying at Zhejiang Normal University, where he received his bachelor's degree in mathematics in 1982. He received a master's degree from East China Normal University in 1987 and a PhD in mathematics from Ohio State University in 1994 under the supervision of Stephen Rallis. Career Jiang joined the faculty at the Department of Mathematics at the University of Minnesota in 1998 and became a full professor in 2004. Awards Jiang was a recipient of a Sloan Research Fellowship and was inducted as a Fellow of the American Mathematical Society in 2019. Selected publications Degree 16 standard L-function of GSp(2)×GSp(2). Mem. Amer. Math. Soc. 123 (1996), no. 588, viii+196 pp. With Ilya Piatetski-Shapiro: Arithmeticity of discrete subgroups and automorphic forms. Geom. Funct. Anal. 8 (1998), no. 3, 586–605. With Wee Teck Gan and Nadya Gurevich: Cubic unipotent Arthur parameters and multiplicities of square integrable automorphic forms. Invent. Math. 149 (2002), no. 2, 225-265. With David Soudry: The local converse theorem for SO(2n+1) and applications. Annals of Mathematics (2) 157 (2003), no. 3, 743-806. With David Ginzburg and Stephen Rallis: On the nonvanishing of the central value of the Rankin-Selberg L-functions. J. Amer. Math. Soc. 17 (2004), no. 3, 679–722. On the fundamental automorphic L-functions of SO(2n+1). Int. Math. Res. Not. 2006, Art. ID 64069, 26 pp. With Jian-Shu Li and Shou-Wu Zhang: Periods and distribution of cycles on Hilbert modular varieties. Pure Appl. Math. Q. 2 (2006), no. 1, Special Issue: In honor of John H. Coates. Part 1, 219–277. With Binyong Sun and Chen-Bo Zhu: Uniqueness of Bessel models: the Archimedean case. Geom. Funct. Anal. 20 (2010), no. 3, 690–709. Automorphic integral transforms for classical groups I: Endoscopy correspondences. Automorphic forms and related geometry: assessing the legacy of I. I. Piatetski-Shapiro, 179–242, Contemp. Math., 614, Amer. Math. Soc., Providence, RI, 2014. With Chufeng Nien and Shaun Stevens: Towards the Jacquet conjecture on the local converse problem for p-adic GLn. J. Eur. Math. Soc. (JEMS) 17 (2015), no. 4, 991–1007. With Lei Zhang: Arthur parameters and cuspidal automorphic modules of classical groups. Annals of Mathematics (2) 191 (2020), no. 3, 739-827. With Baiying Liu and Bin Xu: A reciprocal branching problem for automorphic representations and global Vogan packets. J. Reine Angew. Math. 765 (2020), 249–277. References External links 1958 births Living people 20th-century Chinese mathematicians 21st-century American mathematicians Date of birth missing (living people) East China Normal University alumni Educators from
https://en.wikipedia.org/wiki/Kei%20Okawa	is a Japanese footballer who last plays for Albirex Niigata Singapore. Career statistics Club Notes Honours Club Albirex Niigata Singapore Singapore Premier League: 2020 References 1998 births Living people Japanese men's footballers Japanese expatriate men's footballers Men's association football goalkeepers Singapore Premier League players Urawa Red Diamonds players Albirex Niigata Singapore FC players Japanese expatriate sportspeople in Singapore Expatriate men's footballers in Singapore
https://en.wikipedia.org/wiki/Ryosuke%20Nagasawa	is a Japanese professional footballer who plays for Indonesian side Persikabo 1973. Career statistics Club International Statistics U17 International caps U17 International goals U16 International caps U16 International goals References 1998 births Living people Japanese men's footballers Japan men's youth international footballers Japanese expatriate men's footballers Men's association football forwards Singapore Premier League players Gamba Osaka players Vissel Kobe players Albirex Niigata Singapore FC players FK Radnički Niš players Japanese expatriate sportspeople in Thailand Expatriate men's footballers in Thailand Japanese expatriate sportspeople in Singapore Expatriate men's footballers in Singapore Japanese expatriate sportspeople in Serbia Expatriate men's footballers in Serbia
https://en.wikipedia.org/wiki/Kamolidin%20Tashiyev	Kamolidin Nazhimidinovich Tashiyev (; ; born 9 February 2000) is a Kyrgyzstani footballer who currently plays for Abdysh-Ata Kant. Career statistics Club References 2000 births Living people Kyrgyzstani men's footballers Kyrgyzstani expatriate men's footballers Men's association football defenders Singapore Premier League players Geylang International FC players Kyrgyzstani expatriate sportspeople in Singapore Expatriate men's footballers in Singapore
https://en.wikipedia.org/wiki/Azri%20Suhaili	Muhammad Azri Suhaili Bin Muhammad Azar (born 12 July 2002) is a Singaporean footballer currently playing as a midfielder for Geylang International. Career statistics Club Notes References External links Azri Suhaili Interview Geylang midfielder Azri Suhaili, 16, is third youngest to play in SPL 2002 births Living people Singaporean men's footballers Men's association football midfielders Singapore Premier League players Geylang International FC players
https://en.wikipedia.org/wiki/Ryuya%20Mitsuzuka	is a Japanese footballer who currently plays for SC Sagamihara Career statistics Club Notes References 1999 births Living people Japanese men's footballers Japanese expatriate men's footballers Men's association football midfielders Singapore Premier League players UE Cornellà players SC Sagamihara players Albirex Niigata Singapore FC players Japanese expatriate sportspeople in Spain Expatriate men's footballers in Spain Japanese expatriate sportspeople in Singapore Expatriate men's footballers in Singapore
https://en.wikipedia.org/wiki/Ga%C3%A7k%C3%AB	Gaçkë is a village in Ferizaj Municipality, Kosovo. According to the Kosovo Agency of Statistics (KAS) estimate from the 2011 census, there were 2,368 people residing in Gaçkë, with Albanians constituting the majority of the population. References Villages in Ferizaj
https://en.wikipedia.org/wiki/Komogllav%C3%AB	Komogllavë is a village in Ferizaj Municipality, Kosovo. According to the Kosovo Agency of Statistics (KAS) estimate from the 2011 census, there were 4,404 people residing in Komogllavë, with Albanians constituting the majority of the population. References Villages in Ferizaj
https://en.wikipedia.org/wiki/Koshare%2C%20Ferizaj	Koshare is a village in Ferizaj Municipality, Kosovo. According to the Kosovo Agency of Statistics (KAS) estimate from the 2011 census, there were 2,077 people residing in Koshare, with Albanians constituting the majority of the population. References Villages in Ferizaj
https://en.wikipedia.org/wiki/Lloshkobare	Lloshkobare is a village in Ferizaj Municipality, Kosovo. According to the Kosovo Agency of Statistics (KAS) estimate from the 2011 census, there were 2,075 people residing in Gaçkë, with Albanians constituting the majority of the population. References Villages in Ferizaj
https://en.wikipedia.org/wiki/Nekodim	Nekodim is a village in Ferizaj Municipality, Kosovo. According to the Kosovo Agency of Statistics (KAS) estimate from the 2011 census, there were 3,718 people residing in Nekodim, with Albanians constituting the majority of the population. History On September 12–13, 1943, during World War II, many of the village's Serb civilian population were murdered by Albanian paramilitaries. References Villages in Ferizaj
https://en.wikipedia.org/wiki/Pleshin%C3%AB	Pleshinë is a village in Ferizaj Municipality, Kosovo. According to the Kosovo Agency of Statistics (KAS) estimate from the 2011 census, there were 4,506 people residing in Pleshinë, with Albanians and Ashkali constituting the majority of the population. References Villages in Ferizaj
https://en.wikipedia.org/wiki/Varosh%2C%20Ferizaj	Varosh is a village in Ferizaj Municipality, Kosovo. According to the Kosovo Agency of Statistics (KAS) estimate from the 2011 census, there were 2,483 people residing in Gaçkë, with Albanians constituting the majority of the population. References Villages in Ferizaj
https://en.wikipedia.org/wiki/Se%C3%A7isht%C3%AB	Seçishtë is a village in Han i Elezit Municipality, Kosovo. According to the Kosovo Agency of Statistics (KAS) estimate from the 2011 census, there were 2,252 people residing in Seçishtë, with Albanians constituting the majority of the population. References Villages in Elez Han
https://en.wikipedia.org/wiki/Jack%20Yung%20Chang	Jack Yung Chang (; 9 March 1911 – 16 December 1939), courtesy name Junzhi (), was a Chinese historian of mathematics. His most significant work was on calendar systems in Asia. Biography Yung Chang was the second son of Chinese politician Zhang Shizhao. His mother was Wu Ruonan (), a feminist and the first female member of Kuomintang. He was born in Aberdeen, Scotland, and soon returned to China with his mother. He and his two brothers were home-schooled in Beiping. Among their teachers was Li Dazhao, one of the founders of Communist Party of China and a friend of Zhang Shizhao. At age 17, he went to Britain with his parents, then to Germany to learn German and French. In the spring of 1930, he took the national matriculation examination for foreigners in Berlin and was ranked second out of three thousand candidates from over ten countries. He entered University of Göttingen to study mathematics, and he also took classes in physics, chemistry, philosophy and Latin. He met Otto E. Neugebauer and was impressed by his research on Babylonian and Egyptian mathematics. Chang was well learned in classical Chinese literature from his upbringing, and he knew English, French, German, Latin and Greek well, so he was able to research in ancient Chinese texts and Western works. He was a reclusive person and did not mingle with other Chinese students, of which there were but a handful. However, when Ji Xianlin arrived in Göttingen in 1935, due to Ji's wide range of interests in literature, arts and religion, Chang and Ji became good friends. Chang showed Ji around the city and helped Ji settle down, and he often visited Ji and stayed for long hours. His mother told Ji that Chang seemed to have changed to a different person after knowing Ji. In the summer of 1936, due to financial problem, Chang returned to China and taught at National Shantung University. The following year, when the Japanese invasion of China had just started, he was invited to the Department of Mathematics of National Chekiang University to be a professor in the area of algebra, as there were none after Chiungtze Tsen's departure earlier that year. On 8 September 1937, when Chang was on his way to National Chekiang University, he took a train from Shanghai to Hangzhou. At 12:20 pm, when the train stopped at Songjiang station, eight Japanese warplanes came and bombed the station. Chang held tightly in his arms a 1607 edition of the book Jihe Yuanben, Chinese translation of Euclid's Elements, which he had borrowed from Yu Ta-wei. The carriage which he was in was not destroyed, but 5 other carriages of the 10-carriage train were destroyed in the airstrike, more than 300 civilians were killed and more than 400 were injured. Soon after Chang's arrival, the university was evacuated westwards, first from Hangzhou to Jiande in Zhejiang province, then to Taihe in Jiangxi province, and finally settled in Yishan in Guangxi province. He moved with the university and lived in harsh environment. Acc
https://en.wikipedia.org/wiki/Tatjana%20Stykel	Tatjana Stykel is a Russian mathematician who works as a professor of computational mathematics in the Institute of Mathematics of the University of Augsburg in Germany. Her research interests include numerical linear algebra, control theory, and differential-algebraic systems of equations. Education and career Stykel earned bachelor's and master's degrees from Novosibirsk State University in 1994 and 1996. After postgraduate study as a research institute at the Humboldt University of Berlin and Chemnitz University of Technology, she earned a doctorate (Dr. rer. nat.) from the Technical University of Berlin in 2002, and a habilitation from the Technical University of Berlin in 2008. Her doctoral dissertation, Analysis and Numerical Solution of Generalized Lyapunov Equation, was supervised by Volker Mehrmann. After completing her doctorate, she was a postdoctoral researcher at the University of Calgary, and then a researcher and guest professor at the Technical University of Berlin from 2003 until 2011, when she took her current position in Augsburg. Recognition In 2003, Stykel was one of the Second Prize winners of the Leslie Fox Prize for Numerical Analysis. She won the Richard von Mises Prize of the Gesellschaft für Angewandte Mathematik und Mechanik in 2007. References External links Home page Year of birth missing (living people) Living people Russian mathematicians Russian women mathematicians 20th-century German mathematicians Women mathematicians Novosibirsk State University alumni Technical University of Berlin alumni Academic staff of the University of Augsburg 21st-century German mathematicians
https://en.wikipedia.org/wiki/Dawoud%20Iraqi	Daoud Younis Abdallah Iraqi (born 13 September 1999) is a Palestinian professional footballer who plays as a forward for SV Babelsberg 03. Career statistics Club Notes International References 1999 births Living people Palestinian men's footballers Palestinian expatriate men's footballers Men's association football forwards Hertha Zehlendorf players Tennis Borussia Berlin players Berliner AK 07 players Expatriate men's footballers in Germany Palestinian expatriate sportspeople in Germany Palestine men's international footballers Palestine men's youth international footballers
https://en.wikipedia.org/wiki/Mladen%20Kova%C4%8Devi%C4%87	Mladen Kovačević (; born 30 December 1994) is a Serbian footballer who plays as a forward. Career statistics References 1994 births Living people Serbian men's footballers Serbian expatriate men's footballers Men's association football forwards Serbian First League players China League One players FK Radnički Sombor players FK Ozren Sokobanja players OFK Bečej 1918 players Nantong Zhiyun F.C. players FK Radnički Niš players Serbian expatriate sportspeople in China Expatriate men's footballers in China Sportspeople from Sombor Footballers from West Bačka District
https://en.wikipedia.org/wiki/Mathematics%20in%20Ancient%20Egypt%3A%20A%20Contextual%20History	Mathematics in Ancient Egypt: A Contextual History is a book on ancient Egyptian mathematics by Annette Imhausen. It was published by the Princeton University Press in 2016. Topics The history of ancient Egyptian mathematics covers roughly three thousand years, and as well as sketching the mathematics of this period, the book also provides background material on the culture and society of the period, and the role played by mathematics in society. These aspects of the subject advance the goal of understanding Egyptian mathematics in its cultural context rather than (as in much earlier work on the mathematics of ancient cultures) trying to translate it into modern mathematical ideas and notation. Particular emphases of the book are the elite status of the scribes, the Egyptian class entrusted with mathematical calculations, the practical rather than theoretical approach to mathematics taken by the scribes, and the ways that Egyptian conceptualizations of numbers affected the methods they used to solve mathematical problems. In keeping with that change in emphasis, the book is ordered by time period rather than by mathematical topics. After an introduction that reviews past studies of the subject and calls for a reassessment of their conclusions, it divides its history into five major eras: prehistoric Egypt and the Early Dynastic Period, the Old Kingdom of Egypt, the Middle Kingdom of Egypt, the New Kingdom of Egypt, and Hellenistic and Roman Egypt. The topics covered in the book include the Egyptian numbering systems, in both spoken and written (hieroglyphic) form, arithmetic, Egyptian fractions, and systems of measurement, their lunar calendar, calculations of volumes of solids, and word problems involving the measurement of beer and grain. As well, it covers the use of mathematics by the scribes in architectural design and the measurement of land. Although much past effort has gone into questions such as trying to deduce the rules used by the scribes to calculate their tables of representations of fractions of the form 2/n, that sort of mathematical exercise has been avoided here in place of a description of how the Egyptians used these tables and their other mathematical methods in solving practical problems. Because documents recording Egyptian mathematical knowledge are scarce, much of the book's history comes from other less directly mathematical objects, including the Egyptian architectural accomplishments, their burial goods, and their tax records, administrative writings, and literature. The book also discusses the mathematical problems and their solutions recorded from the small number of surviving mathematical documents including the Rhind papyrus, Lahun Mathematical Papyri, Moscow Mathematical Papyrus, Egyptian Mathematical Leather Roll, Papyrus Harris I, Wilbour Papyrus, Carlsberg papyrus and Ostraca Senmut 153 and Turin 57170, placed in context by comparison with other less directly mathematical objects and texts from ancient Eg
https://en.wikipedia.org/wiki/Bin%20Ukishima	is a Japanese footballer manager. Career statistics Club Notes Managerial statistics References External links Bin Ukishima at Eurosport 1967 births Living people Sportspeople from Tokyo Metropolis Association football people from Tokyo Metropolis Japanese men's footballers Japan Soccer League players Japan Football League (1992–1998) players Yokohama F. Marinos players Kawasaki Frontale players Japanese football managers J1 League managers Shonan Bellmare managers Men's association football players not categorized by position
https://en.wikipedia.org/wiki/Theophilus%20Eagles	Theophilus R. Eagles Jr. (November 10, 1885 – June 7, 1936) was an American college football coach and collegiate mathematics faculty member. He served as the head football coach at Catawba College in Salisbury, North Carolina in 1908, compiling a record of 0–4. Eagles was also as a mathematics professor at the school. Later in his academic career, he was a math professor at Bethany College in Bethany, West Virginia. References External links 1885 births 1936 deaths Barton College alumni Bethany College (West Virginia) faculty Catawba College faculty Catawba Indians football coaches University of North Carolina at Chapel Hill alumni People from Wilson County, North Carolina
https://en.wikipedia.org/wiki/Algebra%20and%20Tiling	Algebra and Tiling: Homomorphisms in the Service of Geometry is a mathematics textbook on the use of group theory to answer questions about tessellations and higher dimensional honeycombs, partitions of the Euclidean plane or higher-dimensional spaces into congruent tiles. It was written by Sherman K. Stein and Sándor Szabó, and published by the Mathematical Association of America as volume 25 of their Carus Mathematical Monographs series in 1994. It won the 1998 Beckenbach Book Prize, and was reprinted in paperback in 2008. Topics The seven chapters of the book are largely self-contained, and consider different problems combining tessellations and algebra. Throughout the book, the history of the subject as well as the state of the art is discussed, and there are many illustrations. The first chapter concerns a conjecture of Hermann Minkowski that, in any lattice tiling of a Euclidean space by unit hypercubes (a tiling in which a lattice of translational symmetries takes any hypercube to any other hypercube) some two cubes must meet face-to-face. This result was resolved positively by Hajós's theorem in group theory, but a generalization of this question to non-lattice tilings (Keller's conjecture) was disproved shortly before the publication of the book, in part by using similar group-theoretic methods. Following this, three chapters concern lattice tilings by polycubes. The question here is to determine, from the shape of the polycube, whether all cubes in the tiling meet face-to-face or, equivalently, whether the lattice of symmetries must be a subgroup of the integer lattice. After a chapter on the general version of this problem, two chapters consider special classes of cross and "semicross"-shaped polycubes, both with regard to tiling and then, when these shapes do not tile, with regard to how densely they can be packed. In three dimensions, this is the notorious tripod packing problem. Chapter five considers Monsky's theorem on the impossibility of partitioning a square into an odd number of equal-area triangles, and its proof using the 2-adic valuation, and chapter six applies Galois theory to more general problems of tiling polygons by congruent triangles, such as the impossibility of tiling a square with 30-60-90 right triangles. The final chapter returns to the topic of the first, with material on László Rédei's generalization of Hajós's theorem. Appendices cover background material on lattice theory, exact sequences, free abelian groups, and the theory of cyclotomic polynomials. Audience and reception Algebra and Tiling can be read by undergraduate or graduate mathematics students who have some background in abstract algebra, and provides a source of applications for this topic. It can be used as a textbook, with exercises scattered throughout its chapters. Reviewer William J. Walton writes that "The student or mathematician whose area of interest is algebra should enjoy this text". In 1998, the Mathematical Association of Ame
https://en.wikipedia.org/wiki/Papal%C3%A9l%C3%A9	Hélio Alberto Delgado Silva (born 16 March 1998), commonly known as Papalélé, is a Cape Verdean footballer who plays as a forward for Czech club MFK Karviná. Career statistics Club Notes International International goals Scores and results list Cape Verde's goal tally first. References 1998 births Living people Cape Verdean men's footballers Cape Verde men's international footballers Men's association football forwards CS Mindelense players FC Porto B players Leixões S.C. players C.D.C. Montalegre players C.F. Estrela da Amadora players Anadia F.C. players Liga Portugal 2 players Cape Verdean expatriate men's footballers Expatriate men's footballers in Portugal Cape Verdean expatriate sportspeople in Portugal MFK Karviná players Expatriate men's footballers in the Czech Republic
https://en.wikipedia.org/wiki/Karma%20Dajani	Karma Dajani is a Lebanese-Dutch mathematician whose research interests include ergodic theory, probability theory, and their applications in number theory. She is an associate professor of mathematics at Utrecht University. Education and career Dajani was born in Lebanon, and did her undergraduate studies at the American University of Beirut, initially in medicine but switching after a year to mathematics. Because of the Lebanese Civil War, she and her family moved to the US, where she earned her Ph.D. in 1989 from George Washington University. Again, she switched topics, beginning in functional analysis and trying graph theory but ending in ergodic theory. Her dissertation, Simultaneous Recurrence of Weighted Cocycles, was supervised by E. Arthur Robinson Jr., after a previous advisor, Daniel Ullman, shifted his own interests away from ergodic theory. As a student at George Washington University, Dajani was a two-time winner of the university's Taylor Prize in Mathematics. After completing her doctorate, she was a postdoctoral researcher at the University of Maryland, College Park and the University of North Carolina at Chapel Hill. She took a faculty position at the University of Alabama. After marrying a Dutch mathematician, Cor Kraaikamp, she obtained a visiting position at Delft University of Technology and then joined Utrecht University. She spent 25 years as the only female mathematics professor at Utrecht. Book With her husband Cor Kraaikamp, Dajani is the author of the book Ergodic Theory of Numbers, published in 2002 by the Mathematical Association of America as volume 29 of their Carus Mathematical Monographs. The book grew out of a course given by Dajani in a 1996 summer program for women in mathematics. References External links Home page Year of birth missing (living people) Living people Lebanese academics Dutch mathematicians Women mathematicians American University of Beirut alumni George Washington University alumni University of Alabama faculty Academic staff of the Delft University of Technology Academic staff of Utrecht University
https://en.wikipedia.org/wiki/2000%E2%80%9301%20Rochdale%20A.F.C.%20season	The 2000–01 Rochdale A.F.C. season was the club's 80th season in the Football League, and the 27th consecutive season in the fourth tier (League Division Three). Statistics \|} Competitions Football League Third Division FA Cup Football League Cup (Worthington Cup) Football League Trophy (LDV Vans Trophy) References Rochdale A.F.C. seasons 2000–01 Football League Third Division by team
https://en.wikipedia.org/wiki/Direction-preserving%20function	In discrete mathematics, a direction-preserving function (or mapping) is a function on a discrete space, such as the integer grid, that (informally) does not change too drastically between two adjacent points. It can be considered a discrete analogue of a continuous function. The concept was first defined by Iimura. Some variants of it were later defined by Yang, Chen and Deng, Herings, van-der-Laan, Talman and Yang, and others. Basic concepts We focus on functions , where the domain X is a finite subset of the Euclidean space . ch(X) denotes the convex hull of X. There are many variants of direction-preservation properties, depending on how exactly one defines the "drastic change" and the "adjacent points". Regarding the "drastic change" there are two main variants: Direction preservation (DP) means that, if x and y are adjacent, then for all : . In words: every component of the function f must not switch signs between adjacent points. Gross direction preservation (GDP) means that, if x and y are adjacent, then . In words: the direction of the function f (as a vector) does not change by more than 90 degrees between adjacent points. Note that DP implies GDP but not vice versa. Regarding the "adjacent points" there are several variants: Hypercubic means that x and y are adjacent iff they are contained in some axes-parallel hypercube of side-length 1. Simplicial means that x and y are adjacent iff they are vertices of the same simplex, in some triangulation of the domain. Usually, simplicial adjacency is much stronger than hypercubic adjacency; accordingly, hypercubic DP is much stronger than simplicial DP. Specific definitions are presented below. All examples below are for dimensions and for X = { (2,6), (2,7), (3, 6), (3, 7) }. Properties and examples Hypercubic direction-preservation A cell is a subset of that can be expressed by for some . For example, the square is a cell. Two points in are called cell connected if there is a cell that contains both of them. Hypercubic direction-preservation properties require that the function does not change too drastically in cell-connected points (points in the same hypercubic cell). f is called hypercubic direction preserving (HDP) if, for any pair of cell-connected points x,y in X, for all : . The term locally direction-preserving (LDP) is often used instead. The function fa on the right is DP. Some authors use a variant requiring that, for any pair of cell-connected points x,y in X, for all : . A function f(x) is HDP by the second variant, iff the function g(x):=f(x)-x is HDP by the first variant. f is called hypercubic gross direction preserving (HGDP), or locally gross direction preserving (LGDP), if for any pair of cell-connected points x,y in X, . Every HDP function is HGDP, but the converse is not true. The function fb is HGDP, since the scalar product of every two vectors in the table is non-negative. But it is not HDP, since the second component switches sign bet
https://en.wikipedia.org/wiki/Introduction%20to%20Tropical%20Geometry	Introduction to Tropical Geometry is a book on tropical geometry, by Diane Maclagan and Bernd Sturmfels. It was published by the American Mathematical Society in 2015 as volume 161 of Graduate Studies in Mathematics. Topics The tropical semiring is an algebraic structure on the real numbers in which addition takes the usual place of multiplication, and minimization takes the usual place of addition. This combination of the two operations of addition and minimization comes up naturally, for instance, in the shortest path problem, where concatenating paths causes their distances to be added and where the shortest of two parallel paths is the one with minimum length, and where some shortest path algorithms can be interpreted as tropical matrix multiplication. Tropical geometry applies the machinery of algebraic geometry to this system by defining polynomials using addition and minimization in place of multiplication and addition (yielding piecewise linear functions), and studying the "roots" of these polynomials, the breakpoints where they fail to be linear. The field is named after the Brazilian adopted home of one of its pioneering researchers, Imre Simon. Although past work in the area has studied it through methods of enumerative combinatorics, this book instead is centered around explicit calculations related to the tropicalization of classical varieties. Although it is much more comprehensive than the two previous introductory books in this area by Itenberg et al., some topics in tropical geometry are (deliberately) omitted, including enumerative geometry and mirror symmetry. The book has six chapters. Its first introduces the subject and gives an overview of some important result, after which the second chapter provides background material on non-Archimedean ordered field, algebraic varieties, convex polytopes, and Gröbner bases. Chapter three concerns tropical varieties, defined in several different ways, correspondences between classical varieties and their tropicalizations, the "Fundamental Theorem of Tropical Geometry" proving that these definitions are equivalent, and tropical intersection theory. Chapter four studies tropical connections to the Grassmannian, neighbor joining in the space of metric trees, and matroids. chapter five considers tropical analogues of some of the important concepts in linear algebra, and chapter six connects tropical varieties to toric varieties and polyhedral geometry. Audience and reception This book is written as a textbook, with problems testing readers' understanding of the material. Reviewer Patrick Popescu-Pampu claims that even though it is a graduate-level book series, undergraduates with a sufficient background in algebraic geometry should be able to access it. Reviewer Felipe Zaldivar writes that it "makes the subject accessible and enjoyable", and makes "a beautiful addition" to its book series. Reviewer Michael Joswig concludes that Introduction to Tropical Geometry "will become a standard re
https://en.wikipedia.org/wiki/Eric%20Urban	Eric Jean-Paul Urban is a professor of mathematics at Columbia University working in number theory and automorphic forms, particularly Iwasawa theory. Career Urban received his PhD in mathematics from Paris-Sud University in 1994 under the supervision of Jacques Tilouine. He is a professor of mathematics at Columbia University. Research Together with Christopher Skinner, Urban proved many cases of Iwasawa–Greenberg main conjectures for a large class of modular forms. As a consequence, for a modular elliptic curve over the rational numbers, they prove that the vanishing of the Hasse–Weil L-function L(E, s) of E at s = 1 implies that the p-adic Selmer group of E is infinite. Combined with theorems of Gross-Zagier and Kolyvagin, this gave a conditional proof (on the Tate–Shafarevich conjecture) of the conjecture that E has infinitely many rational points if and only if L(E, 1) = 0, a (weak) form of the Birch–Swinnerton-Dyer conjecture. These results were used (in joint work with Manjul Bhargava and Wei Zhang) to prove that a positive proportion of elliptic curves satisfy the Birch–Swinnerton-Dyer conjecture. Awards Urban was awarded a Guggenheim Fellowship in 2007. Selected publications References External links 20th-century French mathematicians 21st-century French mathematicians Number theorists Living people Date of birth missing (living people) Place of birth missing (living people) Columbia University faculty University of Paris alumni Year of birth missing (living people)
https://en.wikipedia.org/wiki/Jacques%20Tilouine	Jacques Tilouine is a professor of mathematics at Université Sorbonne Paris Nord working in number theory and automorphic forms, particularly Iwasawa theory. Career Tilouine received his PhD in mathematics from Paris-Sud University in 1989 under the supervision of John H. Coates. He is a professor of mathematics at Université Sorbonne Paris Nord. Research Tilouine has worked on the anticyclotomic main conjecture of Iwasawa theory, special values of L-functions, and Serre-type conjectures for symplectic groups. Selected publications References External links 20th-century French mathematicians 21st-century French mathematicians Number theorists Living people Date of birth missing (living people) Place of birth missing (living people) University of Paris alumni Academic staff of the University of Paris Year of birth missing (living people)
https://en.wikipedia.org/wiki/Geodesic%20bicombing	In metric geometry, a geodesic bicombing distinguishes a class of geodesics of a metric space. The study of metric spaces with distinguished geodesics traces back to the work of the mathematician Herbert Busemann. The convention to call a collection of paths of a metric space bicombing is due to William Thurston. By imposing a weak global non-positive curvature condition on a geodesic bicombing several results from the theory of CAT(0) spaces and Banach space theory may be recovered in a more general setting. Definition Let be a metric space. A map is a geodesic bicombing if for all points the map is a unit speed metric geodesic from to , that is, , and for all real numbers . Different classes of geodesic bicombings A geodesic bicombing is: reversible if for all and . consistent if whenever and . conical if for all and . convex if is a convex function on for all . Examples Examples of metric spaces with a conical geodesic bicombing include: Banach spaces. CAT(0) spaces. injective metric spaces. the spaces where is the first Wasserstein distance. any ultralimit or 1-Lipschitz retraction of the above. Properties Every consistent conical geodesic bicombing is convex. Every convex geodesic bicombing is conical, but the reverse implication does not hold in general. Every proper metric space with a conical geodesic bicombing admits a convex geodesic bicombing. Every complete metric space with a conical geodesic bicombing admits a reversible conical geodesic bicombing. References Geodesic (mathematics)
https://en.wikipedia.org/wiki/Takuya%20Hidaka	is a Japanese former footballer. Career statistics Club Notes References 1990 births Living people People from Shinagawa Association football people from Tokyo Japanese men's footballers Men's association football defenders Japan Soccer College players Albirex Niigata Singapore FC players ReinMeer Aomori players Singapore Premier League players Japan Football League players Japanese expatriate sportspeople in Singapore Expatriate men's footballers in Singapore
https://en.wikipedia.org/wiki/Lee%20Gee-hyeon	Lee Gee-hyeon (; born 5 March 1996) is a South Korean footballer currently playing as a defender for Trayal. Career statistics Club Notes References Living people 1996 births South Korean men's footballers South Korean expatriate men's footballers Men's association football defenders Serbian First League players FK Zlatibor Čajetina players South Korean expatriate sportspeople in Serbia Expatriate men's footballers in Serbia
https://en.wikipedia.org/wiki/Gram%E2%80%93Euler%20theorem	In geometry, the Gram–Euler theorem, Gram-Sommerville, Brianchon-Gram or Gram relation (named after Jørgen Pedersen Gram, Leonhard Euler, Duncan Sommerville and Charles Julien Brianchon) is a generalization of the internal angle sum formula of polygons to higher-dimensional polytopes. The equation constrains the sums of the interior angles of a polytope in a manner analogous to the Euler relation on the number of d-dimensional faces. Statement Let be an -dimensional convex polytope. For each k-face , with its dimension (0 for vertices, 1 for edges, 2 for faces, etc., up to n for P itself), its interior (higher-dimensional) solid angle is defined by choosing a small enough -sphere centered at some point in the interior of and finding the surface area contained inside . Then the Gram–Euler theorem states: In non-Euclidean geometry of constant curvature (i.e. spherical, , and hyperbolic, , geometry) the relation gains a volume term, but only if the dimension n is even:Here, is the normalized (hyper)volume of the polytope (i.e, the fraction of the n-dimensional spherical or hyperbolic space); the angles also have to be expressed as fractions (of the (n-1)-sphere). When the polytope is simplicial additional angle restrictions known as Perles relations hold, analogous to the Dehn-Sommerville equations for the number of faces. Examples For a two-dimensional polygon, the statement expands into:where the first term is the sum of the internal vertex angles, the second sum is over the edges, each of which has internal angle , and the final term corresponds to the entire polygon, which has a full internal angle . For a polygon with faces, the theorem tells us that , or equivalently, . For a polygon on a sphere, the relation gives the spherical surface area or solid angle as the spherical excess: . For a three-dimensional polyhedron the theorem reads:where is the solid angle at a vertex, the dihedral angle at an edge (the solid angle of the corresponding lune is twice as big), the third sum counts the faces (each with an interior hemisphere angle of ) and the last term is the interior solid angle (full sphere or ). History The n-dimensional relation was first proven by Sommerville, Heckman and Grünbaum for the spherical, hyperbolic and Euclidean case, respectively. See also Euler characteristic Dehn-Sommerville equations Angular defect Gauss-Bonnet theorem References Polytopes Real algebraic geometry Geometry
https://en.wikipedia.org/wiki/Aleks%20%C5%81awniczak	Aleks Ławniczak (born 5 May 1999) is a Polish professional footballer who plays as a centre-back for Zagłębie Lubin. Career statistics Club References External links 1999 births Living people Footballers from Poznań Polish men's footballers Men's association football defenders Miedź Legnica players Warta Poznań players Zagłębie Lubin players Ekstraklasa players I liga players III liga players

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