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https://en.wikipedia.org/wiki/Nikodem%20Fiedosewicz	Nikodem Fiedosewicz (born 30 May 1998) is a Polish professional footballer who plays as a left-back or a left midfielder for III liga club Wikęd Luzino. Career statistics Club References External links 1998 births Living people People from Grodzisk Wielkopolski Polish men's footballers Men's association football midfielders Warta Poznań players MKP Pogoń Siedlce players III liga players II liga players I liga players Ekstraklasa players Footballers from Greater Poland Voivodeship
https://en.wikipedia.org/wiki/Harold%20R.%20Jacobs	Harold R. Jacobs (born 1939), who authored three mathematics books, both taught the subject and taught those who teach it. Since retiring he has continued writing articles, and as of 2012 had lectured "at more than 200" math conferences. His books have been used by some homeschoolers and has inspired followup works. Biography Jacobs was born in North Hollywood and while in high school "realized that he wanted to become a teacher." The 1939-born educator began "in the late 1960s" what became his first book, originally published in 1970, as an attempt to address the needs of "those students who had not done well in mathematics." His works helped inspire other educators to extend areas such as "inquiry-based learning." He chaired a high school math department in California for 12 years. Works (1970): Mathematics: A Human Endeavor (revised 1982, 1994) A student workbook for this was subsequently written by Susan Knueven Wong. The 1994 edition was (re)titled as Mathematics, a Human Endeavor: A Textbook for Those Who Think They Don't Like the Subject. Jacobs' approach, described as ahead of its time, was to introduce concepts in an entertaining yet practical way. Jacobs' description of the mathematics of billiards inspired a teacher to write a simulation in the Logo educational computer programming language to help improve both his understanding and his teaching. (1974): Geometry: Seeing, Doing, Understanding (revised 1987, 2003). The 2003 edition makes reference to computer software such as The Geometer's Sketchpad. Even before this edition, the Teacher's notes for Geometry was used for developing new ways of teaching. One instructor credited the book's success to being "mathematically very sound" yet using a "little by little" approach. (1979): Elementary Algebra (revised 2016) The style of gently introducing new topics ahead of time, with details in a subsequent chapter, while accepted in homeschooling, has those who disagree for its use in classrooms. several articles for Encyclopædia Britannica and The Mathematics Teacher. The three books were published by W. H. Freeman and Company, and "overhead transparencies for" classroom use were subsequently developed. The Elementary Algebra text has attracted interest by homeschoolers, particularly when used in conjunction with an independently produced set of DVDs offering 36 hours of educational instruction. References 1939 births 20th-century American writers 21st-century American writers Living people People from North Hollywood, Los Angeles
https://en.wikipedia.org/wiki/Sug%20Woo%20Shin	Sug Woo Shin is a professor of mathematics at the University of California, Berkeley working in number theory, automorphic forms, and the Langlands program. Education From 1994 to 1996 when he was in Seoul Science High School, Shin won two gold medals (including a perfect score in 1995) and one bronze medal while representing South Korea at the International Mathematical Olympiad. He graduated from Seoul National University with a Bachelor of Science degree in mathematics in 2000. He received his PhD in mathematics from Harvard University in 2007 under the supervision of Richard Taylor. Career Shin was a member of the Institute for Advanced Study from 2007 to 2008, a Dickson Instructor at the University of Chicago from 2008 to 2010, and again a member at the Institute for Advanced Study from 2010 to 2011. He was an assistant professor of mathematics at the Massachusetts Institute of Technology from 2011 to 2014. In 2014, Shin moved to the Department of Mathematics at the University of California, Berkeley as an associate professor. In 2020, Shin became a full professor of mathematics at the University of California, Berkeley. Shin is a visiting KIAS scholar at the Korea Institute for Advanced Study and a visiting associate member of the Pohang Mathematics Institute. Research In 2011, Michael Harris and Shin resolved the dependencies on improved forms of the Arthur–Selberg trace formula in the conditional proofs of generalizations of the Sato–Tate conjecture by Harris (for products of non-isogenous elliptic curves) and Barnet-Lamb–Geraghty–Harris–Taylor (for arbitrary non-CM holomorphic modular forms of weight greater than or equal to two). Awards Shin received a Sloan Fellowship in 2013. Selected publications References External links 20th-century South Korean mathematicians 21st-century South Korean mathematicians Number theorists Living people Date of birth missing (living people) Place of birth missing (living people) University of California, Berkeley faculty Harvard University alumni Seoul National University alumni Massachusetts Institute of Technology School of Science faculty University of Chicago faculty Sloan Research Fellows Year of birth missing (living people) International Mathematical Olympiad participants
https://en.wikipedia.org/wiki/Symmetry%20in%20Mechanics	Symmetry in Mechanics: A Gentle, Modern Introduction is an undergraduate textbook on mathematics and mathematical physics, centered on the use of symplectic geometry to solve the Kepler problem. It was written by Stephanie Singer, and published by Birkhäuser in 2001. Topics The Kepler problem in classical mechanics is a special case of the two-body problem in which two point masses interact by Newton's law of universal gravitation (or by any central force obeying an inverse-square law). The book starts and ends with this problem, the first time in an ad hoc manner that represents the problem using a system of twelve variables for the positions and momentum vectors of the two bodies, uses the conservation laws of physics to set up a system of differential equations obeyed by these variables, and solves these equations. The second time through, it describes the positions and variables of the two bodies as a single point in a 12-dimensional phase space, describes the behavior of the bodies as a Hamiltonian system, and uses symplectic reductions to shrink the phase space to two dimensions before solving it to produce Kepler's laws of planetary motion in a more direct and principled way. The middle portion of the book sets up the machinery of symplectic geometry needed to complete this tour. Topics covered in this part include manifolds, vector fields and differential forms, pushforwards and pullbacks, symplectic manifolds, Hamiltonian energy functions, the representation of finite and infinitesimal physical symmetries using Lie groups and Lie algebras, and the use of the moment map to relate symmetries to conserved quantities. In these topics, as well, concrete examples are central to the presentation. Audience and reception The book is written as a textbook for undergraduate mathematics and physics students, with many exercises, and it assumes that the students are already familiar with multivariable calculus and linear algebra, a significantly lower level of background material than other books on symplectic geometry in mechanics. It is not comprehensive in its coverage of symplectic geometry and mechanics, but could be used as auxiliary reading in a class that covers that material from other sources, such as Abraham and Marsden's Foundations of Mechanics or Arnold's Mathematical Methods of Classical Mechanics. Alternatively, on its own, it can provide a more accessible first course in this material, before presenting it more comprehensively in another course. Reviewer William Satzer writes that this book "makes serious efforts to address real students and their potential difficulties" and shifts comfortably between mathematical and physical views of its problem. Similarly, reviewer J. R. Dorfman writes that it "removes some of the language barriers that divide the worlds of mathematics and physics", and reviewer Jiří Vanžura calls it "remarkable" in its dual ability to motivate mathematical methods for physics students and provide applications
https://en.wikipedia.org/wiki/Kathy%20Horadam	Kathryn Jennifer Horadam (born 1951) is an Australian mathematician known for her work on Hadamard matrices and related topics in mathematics and information security. She is an Emeritus Professor at the Royal Melbourne Institute of Technology (RMIT). Life Horadam is one of the three children of mathematicians Alwyn Horadam and Eleanor Mollie Horadam, and was born in 1951 in Armidale, New South Wales. She studied mathematics at Australian National University, earning a bachelor's degree in 1972 and completing her PhD in 1977. Her dissertation, The Homology of Groupnets, was supervised by Neville Smythe. She worked for over 30 years at RMIT, becoming a professor of mathematics there in 1995. Additionally, she worked for three years in the Defence Science and Technology Group. Book Horadam is the author of the book Hadamard Matrices and Their Applications (Princeton University Press, 2007). Recognition Horadam became a fellow of the Institute of Combinatorics and its Applications in 1991 and of the Australian Mathematical Society in 2001. An international workshop on Hadamard matrices was held at RMIT in 2011 in honour of her 60th birthday, and papers from the workshop were published in 2013 as a special issue of the Australasian Journal of Combinatorics. References External links 1951 births Living people Australian mathematicians Australian women mathematicians Combinatorialists Australian National University alumni Academic staff of RMIT University
https://en.wikipedia.org/wiki/Eleanor%20Mollie%20Horadam	Eleanor Mollie Horadam (29 June 1921 – 5 May 2002) was an English-Australian mathematician specialising in the number theory of generalised integers. Life Horadam was born in Dewsbury, Yorkshire. She read mathematics at Girton College, Cambridge. Then, while doing wartime service by day for Rolls-Royce performing stress–strain analysis of jet engines, she took night classes in engineering at the University of London, earning first-class honours there. She moved to Australia by herself in 1949, becoming a lecturer at the University of New England. There, she married mathematician Alwyn Horadam and raised three children, persuading the university to update their maternity policies so that (unusually for the time) she could keep her position as a lecturer. She completed a doctorate and became a senior lecturer in 1965, retired in 1983, and was named a fellow of the university in 1995. Her daughter Kathy Horadam, also became a mathematician. Mathematics Horadam's research concerned generalised integers, formed from a sequence of real numbers greater than one (called generalised prime numbers) as the products of finite multisets of generalised primes. She was also the author of a textbook published by the University of New England, Principles of mathematics for economists (1982). References Further reading 1921 births 2002 deaths British mathematicians British women mathematicians Australian mathematicians Australian women mathematicians Number theorists Alumni of Girton College, Cambridge Alumni of the University of London Academic staff of the University of New England (Australia) British emigrants to Australia
https://en.wikipedia.org/wiki/Olga%20Sorkine-Hornung	Olga Sorkine-Hornung (born 1981) is a professor of Computer Science at ETH Zurich working in the fields of computer graphics, geometric modeling and geometry processing. She has received multiple awards, including the ACM SIGGRAPH Significant New Researcher Award in 2011. Personal life and career Sorkine-Hornung was born in 1981 in the Soviet Union to a mother who is a mathematician and a Jewish father who is a physicist. They emigrated to Israel when she was twelve. She learnt the QBasic programming language when she was 13. She then studied math and computer science at Tel Aviv University graduating at the age of 19. She did her master's degree in parallel to her two-year military service, and completed her doctorate degree in 2006. Subsequently, she worked in the Technical University of Berlin as a postdoctoral researcher and as an assistant professor at the Courant Institute of Mathematical Sciences, before being appointed to ETH Zurich in 2011 at the age of 30 as the youngest professor at the time, where she leads the Interactive Geometry Lab. She is married to a computer scientist, and in 2015 they became parents of twins. Awards 2020: Fellow of the Association for Computing Machinery (ACM) 2017: Rössler Prize (accompanied by in research funds) 2017: Eurographics Outstanding Technical Contributions Award 2016: Best Paper Award at the International Conference on 3D Vision (3DV) 2016 2015: Symposium on Geometry Processing Software Award for libigl, a C++ geometry processing library 2015: Fellow of the Eurographics Associationlibrary 2014: Best Paper Award at Eurographics Symposium on Geometry Processing 2014 2013: Intel Early Career Faculty Award 2012: ERC Starting Grant 2012: Latsis Prize of ETH Zurich 2011: ACM SIGGRAPH Significant New Researcher Award 2008: EUROGRAPHICS Young Researcher Award 2006-2008: Alexander von Humboldt research fellowship 2003: Excellence award, School of Computer Science, Tel Aviv University 1999-2000: Dean’s List of Excellence, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University References Living people 1981 births Academic staff of ETH Zurich Tel Aviv University alumni Academics from Moscow Fellows of the Association for Computing Machinery
https://en.wikipedia.org/wiki/Kim%20Chan%20%28footballer%29	Kim Chan (; born 25 April 2000) is a Korean footballer currently playing as a forward for Busan IPark. Career statistics Club References External links 2000 births Living people South Korean men's footballers South Korea men's youth international footballers Men's association football forwards K League 1 players K League 2 players Pohang Steelers players Daejeon Hana Citizen players Chungnam Asan FC players Busan IPark players People from Pohang Footballers from North Gyeongsang Province
https://en.wikipedia.org/wiki/Luc%C3%A3o%20%28footballer%2C%20born%202001%29	Lucas Alexandre Galdino de Azevedo (born 26 February 2001), commonly known as Lucão, is a Brazilian footballer who plays as a goalkeeper for Red Bull Bragantino. Career statistics Club Notes Honours International Brazil U23 Summer Olympics: 2020 References External links 2001 births Living people Brazilian men's footballers Men's association football goalkeepers Campeonato Brasileiro Série A players Campeonato Brasileiro Série B players CR Vasco da Gama players Brazil men's youth international footballers Olympic footballers for Brazil Footballers at the 2020 Summer Olympics Olympic medalists in football Olympic gold medalists for Brazil Medalists at the 2020 Summer Olympics Footballers from Rio de Janeiro (state) People from Barra Mansa
https://en.wikipedia.org/wiki/Kaio%20Magno	Kaio Magno Bacelar Martins (born 13 August 1999), commonly known as Kaio Magno, is a Brazilian professional footballer who plays as a striker. Career statistics Club Notes References 1999 births Living people Brazilian men's footballers Men's association football forwards CR Vasco da Gama players Ceará Sporting Club players Botafogo Futebol Clube (SP) players People from Barra Mansa Footballers from Rio de Janeiro (state)
https://en.wikipedia.org/wiki/Janson%20inequality	In the mathematical theory of probability, Janson's inequality is a collection of related inequalities giving an exponential bound on the probability of many related events happening simultaneously by their pairwise dependence. Informally Janson's inequality involves taking a sample of many independent random binary variables, and a set of subsets of those variables and bounding the probability that the sample will contain any of those subsets by their pairwise correlation. Statement Let be our set of variables. We intend to sample these variables according to probabilities . Let be the random variable of the subset of that includes with probability . That is, independently, for every . Let be a family of subsets of . We want to bound the probability that any is a subset of . We will bound it using the expectation of the number of such that , which we call , and a term from the pairwise probability of being in , which we call . For , let be the random variable that is one if and zero otherwise. Let be the random variables of the number of sets in that are inside : . Then we define the following variables: Then the Janson inequality is: and Tail bound Janson later extended this result to give a tail bound on the probability of only a few sets being subsets. Let give the distance from the expected number of subsets. Let . Then we have Uses Janson's Inequality has been used in pseudorandomness for bounds on constant-depth circuits. Research leading to these inequalities were originally motivated by estimating chromatic numbers of random graphs. References Probabilistic inequalities
https://en.wikipedia.org/wiki/Taking%20Sudoku%20Seriously	Taking Sudoku Seriously: The math behind the world's most popular pencil puzzle is a book on the mathematics of Sudoku. It was written by Jason Rosenhouse and Laura Taalman, and published in 2011 by the Oxford University Press. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. It was the 2012 winner of the PROSE Awards in the popular science and popular mathematics category. Topics The book is centered around Sudoku puzzles, using them as a jumping-off point "to discuss a broad spectrum of topics in mathematics". In many cases these topics are presented through simplified examples which can be understood by hand calculation before extending them to Sudoku itself using computers. The book also includes discussions on the nature of mathematics and the use of computers in mathematics. After an introductory chapter on Sudoku and its deductive puzzle-solving techniques (also touching on Euler tours and Hamiltonian cycles), the book has eight more chapters and an epilogue. Chapters two and three discuss Latin squares, the thirty-six officers problem, Leonhard Euler's incorrect conjecture on Graeco-Latin squares, and related topics. Here, a Latin square is a grid of numbers with the same property as a Sudoku puzzle's solution of having each number appear once in each row and once in each column. They can be traced back to mathematics in medieval Islam, were studied recreationally by Benjamin Franklin, and have seen more serious application in the design of experiments and in error correction codes. Sudoku puzzles also constrain square blocks of cells to contain each number once, making a restricted type of Latin square called a gerechte design. Chapters four and five concern the combinatorial enumeration of completed Sudoku puzzles, before and after factoring out the symmetries and equivalence classes of these puzzles using Burnside's lemma in group theory. Chapter six looks at combinatorial search techniques for finding small systems of givens that uniquely define a puzzle solution; soon after the book's publication, these methods were used to show that the minimum possible number of givens is 17. The next two chapters look at two different mathematical formalizations of the problem of going from a Sudoku problem to its solution, one involving graph coloring (more precisely, precoloring extension of the Sudoku graph) and another involving using the Gröbner basis method to solve systems of polynomial equations. The final chapter studies questions in extremal combinatorics motivated by Sudoku, and (although 76 Sudoku puzzles of various types are scattered throughout the earlier chapters) the epilogue presents a collection of 20 additional puzzles, in advanced variations of Sudoku. Audience and reception This book is intended for a general audience interested in recreational mathematics, including mathematically inclined high school students. It is intended
https://en.wikipedia.org/wiki/Marcia%20Ascher	Marcia Alper Ascher (April 23, 1935 – August 10, 2013) was an American mathematician, and a leader and pioneer in ethnomathematics. She was a professor emerita of mathematics at Ithaca College. Life Ascher was born in New York City, the daughter of a glazier and a secretary. She graduated from Queens College, City University of New York in 1956, and married Robert Ascher, an anthropologist graduating from Queens College in the same year. They both became graduate students at the University of California, Los Angeles; she completed a master's degree in 1960, and moved with her husband to Ithaca, New York, where he had found a faculty position at Cornell University. She joined the mathematics department at Ithaca College in 1960, as one of the founders of the department. She retired as full professor emerita in 1995. She died on August 10, 2013. Books With her husband, Ascher co-authored the book Code of the Quipu: A Study in Media, Mathematics, and Culture (University of Michigan Press, 1981); it was republished in 1997 by Dover Books as Mathematics of the Incas: Code of the Quipu. She was also the sole author of two more books on ethnomathematics, Ethnomathematics: A Multicultural View of Mathematical Ideas (Brooks/Cole, 1991) and Mathematics Elsewhere: An Exploration of Ideas across Cultures (Princeton University Press, 2002). The Basic Library List Committee of the Mathematical Association of America has recommended the inclusion of all three books in undergraduate mathematics libraries. Mathematics Elsewhere won an honorable mention in the 2002 PROSE Awards in the mathematics and statistics category. References 1935 births 2013 deaths 20th-century American mathematicians 21st-century American mathematicians American women mathematicians Ethnomathematicians Queens College, City University of New York alumni Ithaca College faculty 20th-century American women academics 21st-century American women
https://en.wikipedia.org/wiki/Frank%20Calegari	Francesco Damien "Frank" Calegari is a professor of mathematics at the University of Chicago working in number theory and the Langlands program. Career Calegari won a bronze medal and a silver medal at the International Mathematical Olympiad while representing Australia in 1992 and 1993 respectively. Calegari received his PhD in mathematics from the University of California, Berkeley in 2002 under the supervision of Ken Ribet. Calegari was a von Neumann Fellow of mathematics at the Institute for Advanced Study from 2010 to 2011. He is a professor of mathematics at the University of Chicago. As of 2020, Calegari is an Editor at Mathematische Zeitschrift and an Associate Editor of the Annals of Mathematics. Research Calegari works in algebraic number theory, including Langlands reciprocity and torsion classes in the cohomology of arithmetic groups. Awards Calegari was a 5-year American Institute of Mathematics Fellow. Selected publications Personal life Mathematician Danny Calegari is Frank Calegari's brother. References External links 20th-century Australian mathematicians 21st-century American mathematicians Number theorists Living people Date of birth missing (living people) Place of birth missing (living people) University of Chicago faculty UC Berkeley College of Letters and Science alumni Institute for Advanced Study visiting scholars International Mathematical Olympiad participants Year of birth missing (living people)
https://en.wikipedia.org/wiki/List%20of%20Hibernian%20F.C.%20records%20and%20statistics	Hibernian Football Club (), commonly known as "Hibs", is a professional football club based in the Leith area of Edinburgh, Scotland. The club was founded in 1875 by members of Edinburgh's Irish community, and named after the Roman word for Ireland. Home matches are played at Easter Road Stadium, which has been in use since 1893. The club joined the Scottish Football League in that year, and has since played in the Scottish Premier League (1999–2013) and since 2013 it has played in the Scottish Professional Football League. This list encompasses the major honours won by Hibernian, records set by the club, their managers and their players. The player records section includes details of the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Hibernian players in international play, and the highest transfer fees paid and received by the club. Attendance records at Easter Road are also included in the list. Honours Hibernian have won the Scottish league championship four times, most recently in 1952. Three of those four championships were won between 1948 and 1952, when the club had the services of The Famous Five, a notable forward line. The club have won the Scottish Cup three times, in 1887, 1902 and 2016, with the latter victory ending a notorious drought. Hibs have also won the Scottish League Cup three times, in 1972, 1991 and 2007. Major domestic honours Scottish league, first tier Winners (4): 1902–03, 1947–48, 1950–51, 1951–52 Runners-up (6): 1896–97, 1946–47, 1949–50, 1952–53, 1973–74, 1974–75 Scottish Cup Winners (3): 1886–87, 1901–02, 2015–16 Runners-up (12): 1895–96, 1913–14, 1922–23, 1923–24, 1946–47, 1957–58, 1971–72, 1978–79, 2000–01, 2011–12, 2012–13, 2020–21 Scottish League Cup Winners (3): 1972–73, 1991–92, 2006–07 Runners-up (7): 1950–51, 1968–69, 1974–75, 1985–86, 1993–94, 2003–04, 2015–16 Other honours Scottish league, second tier Winners (6): 1893–94, 1894–95, 1932–33, 1980–81, 1998–99, 2016–17 Runners-up: 2014–15 Drybrough Cup Winners: 1972, 1973 Summer Cup Winners: 1941, 1964 Runners-up: 1942, 1945 Southern League Cup Winners: 1943–44 Edinburgh Football League/East of Scotland League (1894–1908) Winners: 1901–02 North-Eastern Cup (1908–1914) Winners: 1910–11 Rosebery Charity Cup (1882–1945) Winners: 22 times Wilson Cup (1906–1946) Winners: 14 times East of Scotland Shield (1875–1990) Winners: 49 times (record) Glasgow Merchants Charity Cup Winners: 1901–02 Coronation Cup Runners-up: 1953 Dunedin Cup (1909–1933) Winners: 1921–22, 1929–30 Youth honours Scottish Youth Cup: 3 1991–92, 2008–09, 2017–18 SPFL Development League: 2 (Previously SFL Youth/SPL U18/U19 league) 2008–09, 2017–18 Player records Appearances Most appearances in all competitions: Gordon Smith, 636. Most League appearances: Lewis Stevenson, 466. Most Scottish Cup appearances: Arthur Duncan, 51. Most League Cup appearances: Pat Stanton, 103. Youngest first-team playe
https://en.wikipedia.org/wiki/Random%20surfing%20model	The random surfing model is a graph model which describes the probability of a random user visiting a web page. The model attempts to predict the chance that a random internet surfer will arrive at a page by either clicking a link or by accessing the site directly, for example by directly entering the website's URL in the address bar. For this reason, an assumption is made that all users surfing the internet will eventually stop following links in favor of switching to another site completely. The model is similar to a Markov chain, where the chain's states are web pages the user lands on and transitions are equally probable links between these pages. Description A user navigates the internet in two primary ways; the user may access a site directly by entering the site's URL or clicking a bookmark, or the user may use a series of hyperlinks to get to the desired page. The random surfer model assumes that the link which the user selects next is picked at random. The model also assumes that the number of successive links is not infinite – the user will at some point lose interest and leave the current site for a completely new site. The random surfer model is presented as a series of nodes which indicate web pages that can be accessed at random by users. A new node is added to the a graph when a new website is published. The movement about the graphs nodes is modeled by choosing a start node at random, then performing a short and random traversal of the nodes, or random walk. This traversal is analogous to a user accessing a website, then following hyperlink number of times, until the user either exits the page or accesses another site completely. Connections to other nodes in this graph are formed when outbound links are placed on the page. Graph definitions In the random surfing model, webgraphs are presented as a sequence of directed graphs such that a graph has vertices and edges. The process of defining graphs is parameterized with a probability , thus we let . Nodes of the model arrive one at time, forming connections to the existing graph . In some models, connections represent directed edges, and in others, connections represent undirected edges. Models start with a single node and have self-loops. denotes a vertex added in the step, and denotes the total number of vertices. Model 1. (1-step walk with self-loop) At time , vertex makes connections by iterations of the following steps: Pick an existing node uniformly at random from With probability stay at ; with probability take a 1-step walk to a random neighbor of Add an edge from to the current node For directed graphs, edges added are directed from into the existing graph. Edges are undirected in respective undirected graphs. Model 2. (Random walks with coin flips) At time , vertex makes connections by iterations of the following steps: Pick an existing node uniformly at random from Flip a coin of bias If the coin comes up heads add an edge
https://en.wikipedia.org/wiki/Daniel%20Cremers	Daniel Cremers (born 1971) is a German computer scientist, Professor of Informatics and Mathematics and Chair of Computer Vision & Artificial Intelligence at the Technische Universität München. His research foci are computer vision, mathematical image, partial differential equations, convex and combinatorial optimization, machine learning and statistical inference. Career Cremers received a bachelor's degree in mathematics (1994) and Physics (1994), and later a master's degree in Theoretical Physics (1997) from the University of Heidelberg. He obtained a PhD in Computer Science from the University of Mannheim in 2002. He was a postdoctoral researcher at UCLA. He was associate professor at the University of Bonn from 2005 until 2009. He received a Starting Grant (2009), a Consolidator Grant (2015) and an Advanced Grant (2020) by the European Research Council. On March 1, 2016, Cremers received the Gottfried Wilhelm Leibniz Prize for having "brought the field of image processing and pattern recognition an important step closer to its goal of reproducing the abilities of human vision with camera systems and computers." Selected publications References Gottfried Wilhelm Leibniz Prize winners Academic staff of the Technical University of Munich Living people 1971 births
https://en.wikipedia.org/wiki/International%20Journal%20of%20Geometry	The International Journal of Geometry is a peer-reviewed academic journal that covers Euclidean, Non-Euclidean and Discrete geometry. It was established in 2012 with two volumes per year, and as of 2021 is published quarterly by the Department of Mathematics of the Vasile Alecsandri National College of Bacău. It is abstracted and indexed among others by Zentralblatt MATH, MathSciNet, the Electronic Journals Library and Ebsco. Its founding editor-in-chief is Cătălin Barbu, a professor of mathematics at the Vasile Alecsandri National College of Bacău. See also Forum Geometricorum References External links Mathematics journals Open access journals Academic journals established in 2012 English-language journals
https://en.wikipedia.org/wiki/Zsolt%20M%C3%A1t%C3%A9	Zsolt Máté (born 14 September 1997) is a Hungarian footballer who plays as a defender for Tiszakécske. Career statistics References External links Zsolt Máté at Magyarfutball.hu 1997 births People from Szabadszállás Footballers from Bács-Kiskun County Living people Hungarian men's footballers Men's association football defenders Budapest Honvéd FC players Újpest FC players Tiszakécske FC footballers Nemzeti Bajnokság I players Nemzeti Bajnokság II players Nemzeti Bajnokság III players
https://en.wikipedia.org/wiki/Stjepan%20O%C5%A1trek	Stjepan Oštrek (born 9 August 1996) is a Croatian professional footballer who plays for Nafta 1903. Career statistics References External links Profile at Magyarfutball.hu 1996 births Living people Footballers from Varaždin Men's association football midfielders Croatian men's footballers Croatia men's youth international footballers NK Nafta Lendava players Zalaegerszegi TE players FC Koper players Slovenian Second League players Nemzeti Bajnokság I players Slovenian PrvaLiga players Croatian expatriate men's footballers Expatriate men's footballers in Italy Expatriate men's footballers in Slovenia Expatriate men's footballers in Hungary Croatian expatriate sportspeople in Italy Croatian expatriate sportspeople in Slovenia Croatian expatriate sportspeople in Hungary
https://en.wikipedia.org/wiki/Wattanakorn%20Sawatlakhorn	Wattanakorn Sawatlakhorn (; born 23 May 1998) is a Thai professional footballer who plays as a left back for Thai League 1 club BG Pathum United. Career statistics Honours Club BG Pathum United Thai League Cup runners-up: 2022–23 References External links Wattanakorn Sawatlakhorn at livesoccer888.com Wattanakorn Sawatlakhorn at EnglishUDFC.com 1997 births Living people Wattanakorn Sawatlakhorn Wattanakorn Sawatlakhorn Men's association football defenders Wattanakorn Sawatlakhorn Wattanakorn Sawatlakhorn Wattanakorn Sawatlakhorn Wattanakorn Sawatlakhorn
https://en.wikipedia.org/wiki/Michal%20Irani	Michal Irani () is a professor in the Department of Computer Science and Applied Mathematics at the Weizmann Institute of Science, Israel. Education Irani received her Ph.D. degree in computer science from the Hebrew University of Jerusalem. Subsequently, she was a member of the Vision Technologies Laboratory at the Sarnoff Research Center (Princeton). Research Irani's research is in the area of computer vision, image processing, and artificial intelligence. In particular, she has done work on understanding the internal statistics of natural images and videos, the space-time analysis of videos, and on visual inference by composition. Selected awards 2020 Rothschild Prize in Mathematics/Computer Sciences and Engineering 2017 Helmholtz Prize for the paper "Actions as space-time shapes" 2016 Maria Petrou Prize (awarded by the International Association in Pattern Recognition) for outstanding contributions to the fields of Computer Vision and Pattern Recognition 2003 Morris L. Levinson Prize in Mathematics 2000, 2002 ECCV Best Paper Awards References Computer vision researchers Israeli women academics Academic staff of Weizmann Institute of Science Hebrew University of Jerusalem School of Computer Science & Engineering alumni Year of birth missing (living people) Living people
https://en.wikipedia.org/wiki/Crocheting%20Adventures%20with%20Hyperbolic%20Planes	Crocheting Adventures with Hyperbolic Planes is a book on crochet and hyperbolic geometry by Daina Taimiņa. It was published in 2009 by A K Peters, with a 2018 second edition by CRC Press. Topics The book is on the use of crochet to make physical surfaces with the geometry of the hyperbolic plane. The full hyperbolic plane cannot be embedded smoothly into three-dimensional space, but pieces of it can. Past researchers had made models of these surfaces out of paper, but Taimiņa's work is the first work to do so using textile arts. She had previously described these models in a research paper and used them as illustrations for an undergraduate geometry textbook, but this book describes more of the background for the project, makes it more widely accessible, and provides instructions for others to follow in making these models. The book has nine chapters. The first chapter introduces the notion of the curvature of a surface, provides instructions for an introductory project in crocheting a patch of the hyperbolic plane, and provides an initial warning about the exponential growth in the area of this plane as a function of its radius, which will cause larger crochet projects to take a very long time to complete. Chapter two covers more concepts in the geometry of the hyperbolic plane, connecting them to crocheted models of the plane. The next three chapters take a step back to look at the broader history of the topics discussed in the book: geometry and its connection to human arts and architecture in chapter 3, crochet in chapter 4, and non-Euclidean geometry in chapter 5. Chapters 6, 7, and 8 cover specific geometric objects with negatively-curved surfaces, including the pseudosphere, helicoid, and catenoid, investigate mathematical toys, and use these crocheted models "to explore otherwise hard to visualize objects". A final chapter covers the applications of hyperbolic geometry and its ongoing research interest. Audience and reception The book is written for a general audience. However, although suggesting that it has a place on mathematical coffee tables, reviewer Keith Leatham wonders who its real readers are likely to be. Reviewer Hinke Osinga, however, feels that the book can be of interest to readers interested in either crochet or mathematics, rather than (as Leatham suggests) requiring both interests. She writes "I highly recommend this book, perhaps not only as a beautiful coffee-table book with the subtle message that mathematics is fun, but also because crochet is a perfect tool for testing and exploring deep mathematical theories." Recognition Crocheting Adventures with Hyperbolic Planes won the 2009 Bookseller/Diagram Prize for Oddest Title of the Year. It also won the 2012 Euler Book Prize of the Mathematical Association of America. References Crochet Hyperbolic geometry Mathematics books 2009 non-fiction books
https://en.wikipedia.org/wiki/Chusak%20Sriphum	Chusak Sriphum (; born 16 September 1976) is a Thai football manager, who is currently the manager of Thai League 2 side Kasetsart. Managerial statistics References External links https://us.soccerway.com/coaches/chusak-sriphum/644189/ Living people Chusak Sriphum 1976 births Chusak Sriphum
https://en.wikipedia.org/wiki/List%20of%20Fenerbah%C3%A7e%20S.K.%20records%20and%20statistics	List of Fenerbahçe S.K. records and statistics contains the records and statistics of the footballers of Fenerbahçe. Honours European competitions Balkans Cup Winners (1): 1966–67 Domestic competitions National Championships Turkish Super League Winners (19): 1959, 1960–61, 1963–64, 1964–65, 1967–68, 1969–70, 1973–74, 1974–75, 1977–78, 1982–83, 1984–85, 1988–89, 1995–96, 2000–01, 2003–04, 2004–05, 2006–07, 2010–11, 2013–14 Runners-up (24): 1959–60, 1961–62, 1966–67, 1970–71, 1972–73, 1975–76, 1976–77, 1979–80, 1983–84, 1989–90, 1991–92, 1993–94, 1997–98, 2001–02, 2005–06, 2007–08, 2009–10, 2011–12, 2012–13, 2014–15, 2015–16, 2017–18, 2021–22, 2022–23 Turkish National Division Winners (6) (record): 1937, 1940, 1943, 1945, 1946, 1950 Runners-up (2): 1944, 1947 Turkish Football Championship Winners (3) (shared-record): 1933, 1935, 1944 Runners-up (2): 1940, 1947 National Cups Turkish Cup Winners (7): 1967–68, 1973–74, 1978–79, 1982–83, 2011–12, 2012–13, 2022–23 Runners-up (11): 1962–63, 1964–65, 1988–89, 1995–96, 2000–01, 2004–05, 2005–06, 2008–09, 2009–10, 2015–16, 2017–18 Turkish Super Cup Winners (9): 1968, 1973, 1975, 1984, 1985, 1990, 2007, 2009, 2014 Runners-up (9): 1970, 1974, 1978, 1979, 1983, 1989, 1996, 2012, 2013 Atatürk Cup Winners (2) (record): 1964, 1998 Prime Minister's Cup Winners (8) (record): 1945, 1946, 1950, 1973, 1980, 1989, 1993, 1998 Runners-up (7): 1944, 1971, 1976, 1977, 1992, 1994, 1995 Spor Toto Cup Winners (1): 1967 Regional competitions Istanbul Football League Winners (16) (record): 1911–12, 1913–14, 1914–15, 1920–21, 1922–23, 1929–30, 1932–33, 1934–35, 1935–36, 1936–37, 1943–44, 1946–47, 1947–48, 1952–53, 1956–57, 1958–59 Istanbul Cup Winners (1): 1945 Istanbul Shield Winners (4) (record): 1930, 1934, 1938, 1939 Others General Harrington Cup Winners (1): 1923 Fleet Cup Winners (4) (record): 1982, 1983, 1984, 1985 TSYD Cup Winners (12) (shared-record): 1969, 1973, 1975, 1976, 1978, 1979, 1980, 1982, 1985, 1986, 1994, 1995 TSYD Challenge Cup Winners (2) (record): 1976, 1980 Player records Most appearances All official and unofficial competitions are included in the list. Top goalscorers All official and unofficial competitions are included in the list. Managers First manager: Hüseyin Dalaklı, became the first manager in 1907. Manager who managed for the longest time: Ignace Molnar, 6 seasons. Manager who held the most title: Didi and Todor Veselinović, each has 8 titles. Club records Goals Most goals scored in a season: 103 goals (1988–89 season) Least goals scored in a season: 31 goals (1969–70, 1976–77, 1979–80 seasons) Most goals conceded in a season: 53 goals (1990–91 season) Least goals conceded in a season: 6 goals (1969–70 season) Points Most points in a season: 93 points (1988–89 season in 36 matches) Least points in a season: 29 points (1980–81 season in 30 matches) Matches First First Süper Lig match: Fenerbahçe 3–1 Ankaragücü (21 February 19
https://en.wikipedia.org/wiki/Integrally%20convex%20set	An integrally convex set is the discrete geometry analogue of the concept of convex set in geometry. A subset X of the integer grid is integrally convex if any point y in the convex hull of X can be expressed as a convex combination of the points of X that are "near" y, where "near" means that the distance between each two coordinates is less than 1. Definitions Let X be a subset of . Denote by ch(X) the convex hull of X. Note that ch(X) is a subset of , since it contains all the real points that are convex combinations of the integer points in X. For any point y in , denote near(y) := {z in \| \|zi - yi\| < 1 for all i in {1,...,n} }. These are the integer points that are considered "nearby" to the real point y. A subset X of is called integrally convex if every point y in ch(X) is also in ch(X ∩ near(y)). Example Let n = 2 and let X = { (0,0), (1,0), (2,0), (2,1) }. Its convex hull ch(X) contains, for example, the point y = (1.2, 0.5). The integer points nearby y are near(y) = {(1,0), (2,0), (1,1), (2,1) }. So X ∩ near(y) = {(1,0), (2,0), (2,1)}. But y is not in ch(X ∩ near(y)). See image at the right. Therefore X is not integrally convex. In contrast, the set Y = { (0,0), (1,0), (2,0), (1,1), (2,1) } is integrally convex. Properties Iimura, Murota and Tamura have shown the following property of integrally convex set. Let be a finite integrally convex set. There exists a triangulation of ch(X) that is integral, i.e.: The vertices of the triangulation are the vertices of X; The vertices of every simplex of the triangulation lie in the same "cell" (hypercube of side-length 1) of the integer grid . The example set X is not integrally convex, and indeed ch(X) does not admit an integral triangulation: every triangulation of ch(X), either has to add vertices not in X, or has to include simplices that are not contained in a single cell. In contrast, the set Y = { (0,0), (1,0), (2,0), (1,1), (2,1) } is integrally convex, and indeed admits an integral triangulation, e.g. with the three simplices {(0,0),(1,0),(1,1)} and {(1,0),(2,0),(2,1)} and {(1,0),(1,1),(2,1)}. See image at the right. References Discrete geometry
https://en.wikipedia.org/wiki/Discrete%20fixed-point%20theorem	In discrete mathematics, a discrete fixed-point is a fixed-point for functions defined on finite sets, typically subsets of the integer grid . Discrete fixed-point theorems were developed by Iimura, Murota and Tamura, Chen and Deng and others. Yang provides a survey. Basic concepts Continuous fixed-point theorems often require a continuous function. Since continuity is not meaningful for functions on discrete sets, it is replaced by conditions such as a direction-preserving function. Such conditions imply that the function does not change too drastically when moving between neighboring points of the integer grid. There are various direction-preservation conditions, depending on whether neighboring points are considered points of a hypercube (HGDP), of a simplex (SGDP) etc. See the page on direction-preserving function for definitions. Continuous fixed-point theorems often require a convex set. The analogue of this property for discrete sets is an integrally-convex set. A fixed point of a discrete function f is defined exactly as for continuous functions: it is a point x for which f(x)=x. For functions on discrete sets We focus on functions , where the domain X is a nonempty subset of the Euclidean space . ch(X) denotes the convex hull of X. Iimura-Murota-Tamura theorem: If X is a finite integrally-convex subset of , and is a hypercubic direction-preserving (HDP) function, then f has a fixed-point. Chen-Deng theorem: If X is a finite subset of , and is simplicially direction-preserving (SDP), then f has a fixed-point. Yang's theorems: [3.6] If X is a finite integrally-convex subset of , is simplicially gross direction preserving (SGDP), and for all x in X there exists some g(x)>0 such that , then f has a zero point. [3.7] If X is a finite hypercubic subset of , with minimum point a and maximum point b, is SGDP, and for any x in X: and , then f has a zero point. This is a discrete analogue of the Poincaré–Miranda theorem. It is a consequence of the previous theorem. [3.8] If X is a finite integrally-convex subset of , and is such that is SGDP, then f has a fixed-point. This is a discrete analogue of the Brouwer fixed-point theorem. [3.9] If X = , is bounded and is SGDP, then f has a fixed-point (this follows easily from the previous theorem by taking X to be a subset of that bounds f). [3.10] If X is a finite integrally-convex subset of , a point-to-set mapping, and for all x in X: , and there is a function f such that and is SGDP, then there is a point y in X such that . This is a discrete analogue of the Kakutani fixed-point theorem, and the function f is an analogue of a continuous selection function. [3.12] Suppose X is a finite integrally-convex subset of , and it is also symmetric in the sense that x is in X iff -x is in X. If is SGDP w.r.t. a weakly-symmetric triangulation of ch(X) (in the sense that if s is a simplex on the boundary of the triangulation iff -s is), and for every pair of simplicially-co
https://en.wikipedia.org/wiki/List%20of%20Canadian%20provinces%20and%20territories%20by%20homicide%20rate	This is a list of Canadian provinces and territories by homicide rate according to Statistics Canada. Homicide rate by province Note: The rate columns can be sorted in ascending or descending order. Sort the province/territory column to return to alphabetical order. Rates are calculated per 100,000 inhabitants per year and sorted by population (note that homicide rates fluctuate a lot for areas with low population). Table 2 Intentional homicide rate (per 100,000) See also List of countries by intentional homicide rate List of cities by murder rate Crime in Canada List of United States cities by crime rate (2014). Cities with population of 250,000+ List of countries by firearm-related death rate Homicide in world cities Notes References Homicide rate Canada provinces and territories Homicide rate Subdivisions of Canada Canada, homicide rate
https://en.wikipedia.org/wiki/Carlos%20Eduardo%20Parreira	Carlos Eduardo Parreira is a Brazilian football manager. He is the current manager of Saudi club Al-Qaisumah. Managerial statistics References External links Living people Carlos Eduardo Parreira Brazilian football managers 1981 births Expatriate football managers in Saudi Arabia Brazilian expatriate sportspeople in Saudi Arabia Saudi First Division League managers
https://en.wikipedia.org/wiki/Ryan%20Hirooka	Ryan Yuuki Hirooka (広岡勇輝, Hirooka Yuuki, born 18 February 1990) is a Japanese professional footballer who plays for Portuguese club Estrela B as a right winger. Career statistics References Living people English men's footballers National League (English football) players Japanese people of English descent English people of Japanese descent Japanese men's footballers 1990 births Men's association football wingers Ramsgate F.C. players Lewes F.C. players JEF United Chiba players Associação Naval 1º de Maio players Campeonato de Portugal (league) players Boavista F.C. players C.D. Feirense players Liga Portugal 2 players Leixões S.C. players S.C. Covilhã players RSD Alcalá players Tercera División players Japanese expatriate men's footballers English expatriate men's footballers Expatriate men's footballers in Portugal Expatriate men's footballers in Spain Japanese expatriate sportspeople in Portugal Japanese expatriate sportspeople in Spain
https://en.wikipedia.org/wiki/International%20Linear%20Algebra%20Society	The International Linear Algebra Society (ILAS) is a professional mathematical society organized to promote research and education in linear algebra, matrix theory and matrix computation. It serves the international community through conferences, publications, prizes and lectures. Membership in ILAS is open to all mathematicians and scientists interested in furthering its aims and participating in its activities. History ILAS was founded in 1989. Its genesis occurred at the Combinatorial Matrix Analysis Conference held at the University of Victoria in British Columbia, Canada, May 20–23, 1987, hosted by Dale Olesky and Pauline van den Driessche. ILAS was initially known as the International Matrix Group, founded in 1987. The founding officers of ILAS were Hans Schneider, President; Robert C. Thompson, Vice President; Daniel Hershkowitz, Secretary; and James R. Weaver, Treasurer. ILAS Conferences The inaugural meeting of ILAS took place at Brigham Young University (including one day at the Sundance Mountain Resort) in Provo, Utah, USA, from August 12–15, 1989. The organizing committee consisted of Wayne Barrett, Daniel Hershkowitz, Charles Johnson, Hans Schneider, and Robert C. Thompson. Much additional support came from Don Robinson, Chair of the BYU Mathematics Department, and James R. Weaver, ILAS Treasurer. The conference received support from Brigham Young University, the National Security Agency, and the National Science Foundation. There were 85 in attendance at the conference from 15 countries including Olga Taussky-Todd, a renowned mathematician in Matrix Theory. The proceedings of the Conference appeared in volume 150 of the journal Linear Algebra and Its Applications. The 2nd ILAS conference was held in Lisbon, Portugal, August 3–7, 1992. The chair of the organizing committee was José Dias da Silva. There were 150 participants from 27 countries and the conference was supported by 11 different organizations. The proceedings of the conference can be found in volumes 197-198 of Linear Algebra and Its Applications. ILAS conferences were held the next 4 years, alternating between the United States and Europe, before beginning the standard pattern of holding the Conference two of every three years (with a few exceptions). The number of participants at each ILAS conference has grown steadily through the years. The first ILAS conference outside of the United States and Europe was held in Haifa, Israel in 2001. The first in the Far East was in Shanghai in 2007 and the first in Latin America was in Cancun, Mexico in 2008. The complete list of locations hosting ILAS conferences follows: 1. Provo, Utah, USA (1989) 2. Lisbon, Portugal (1992) 3. Pensacola, Florida, USA (1993) 4. Rotterdam, The Netherlands (1994) 5. Atlanta, Georgia, USA (1995) 6. Chemnitz, Germany (1996) 7. Madison, Wisconsin, USA (1998) 8. Barcelona, Spain (1999) 9. Haifa, Israel (2001) 10. Auburn, Alabama, USA (2002) 11. Coimbra, Portugal (
https://en.wikipedia.org/wiki/Charles%20L.%20Dolph	Charles Laurie Dolph (August 27, 1918 – June 1, 1994) was an American mathematician known for his research in applied mathematics and engineering. Biography Dolph graduated from the University of Michigan with A.B. in 1939 and from Princeton University with M.A. in 1941 and Ph.D. in 1944. His thesis advisor was Salomon Bochner. Dolph was from 1943 to 1944 a physicist in the U.S. Naval Research Laboratory and from 1944 to 1945 an ensign in the U.S. Navy. From 1945 to 1946 Dolph worked for Michigan Bell Telephone Laboratories. In 1946 he joined the University of Michigan faculty as a lecturer with a joint appointment in the department of mathematics and in the department of engineering research at the Engineering Research Institute. At the University of Michigan's department of mathematics he became in 1947 an assistant professor, in 1954 an associate professor, and in 1960 a full professor, retiring in 1988 as professor emeritus. In 1982 Dolph, an Ann Arbor native, and his first wife donated the land for the Dolph Park Nature Area to the City of Ann Arbor. The land, consisting of 57 acres with 2 lakes, was originally owned by his parents. He directed four doctoral theses and was three times a visiting professor at German universities. He was an associate editor for the Journal of Mathematical Analysis and Applications. In 1944 in New Jersey, Dolph married Marjorie Louise Tibert (1918–2010). They divorced after three of their four children died, and Dolph remarried. He died in 1994. Awards and honors 1946 Thompson Prize from the Institute of Radio Engineers 1947 J. Browder Thompson Award from the Institute of Electrical and Electronics Engineers 1957–58 Guggenheim Fellowship, spent as a sabbatical year at the Technical Universities of Munich and Aachen Selected publications References 1918 births 1994 deaths University of Michigan alumni Princeton University alumni 20th-century American mathematicians Applied mathematicians United States Navy personnel of World War II United States Navy officers
https://en.wikipedia.org/wiki/Jonas%20F.%20Ludvigsson	Jonas Filip Ludvigsson is a Swedish physician and epidemiologist. He is a professor at the Department of Medical Epidemiology and Biostatistics at Karolinska Institutet, Sweden, and a senior paediatrician in the Department of Pediatrics at Örebro University Hospital, Sweden. Ludvigsson is known for being one of the 47 initial signees of the Great Barrington Declaration. Biography Jonas Ludvigsson was born in Sweden. He studied medicine at Linköping University, in Sweden, where he received his M.D. in 1995, and defended his PhD thesis - Some epidemiological aspects of perinatal gastrointestinal disease - in 2001 (Medicine). Ludvigsson became a professor at the Karolinska Institutet, in 2013. Since then, he has conducted extensive epidemiological research in the field of gastroenterology, focusing on, among other things, celiac disease, inflammatory bowel disease, microscopic colitis, and liver disease. Moreover, he has performed extensive research in paediatrics. He is an Honorary Professor at the Columbia University School of Medicine in New York, NY, and, previously, also at the Nottingham University School of Medicine, in the UK. Between 2015 and 2017, Ludvigsson initiated and led a nationwide effort to collect data on all biopsies from the gastrointestinal tract taken in Sweden from 1967-2017. This histopathology data constitutes the foundation for the ESPRESSO study (Epidemiology Strengthened by histoPathology Reports in Sweden).. Ludvigsson also serves as a member of the steering group of the Swedish Inflammatory Bowel Disease Register (Swibreg). Between 2011 and 2014, Ludvigsson chaired the Swedish Epidemiological Association. and in 2014, he was elected to serve as chairman of the Swedish Society of Pediatrics (2014-2016).. In June 2023, he assumed the position of scientific secretary at the Swedish Medical Society Ludvigsson has received numerous awards for his epidemiological research and leadership. He was named the 2010 "Rising Star in Gastroenterology" by the European Gastroenterology Association, and he also received the award for the 2013 Alumnus of the year, from Linköping University. Ludvigsson also serves as an active member of the Editorial Boards of both the European Journal of Epidemiology and Alimentary, Pharmacology & Therapeutics. Beginning in 2019, he was named the staff pediatrician at the Swedish Television station, TV4. In 2022, Ludvigsson was awarded the prestigious Jubilee-prizefrom the Swedish Medical Society in recognition of his research on chronic viral hepatitis where he could show that use of aspirin is associated with a reduced risk of liver cancer. Moreover, in 2023, with the motivation: “For his amazing talent to explain important pediatric research to the public and to healthcare staff.” he also received the Hugo Lagercrantz award He has also been named "Örebro-person of the year by the readers of the Swedish daily Nerikes Allehanda. References External links Swedish epidemiologists Academic st
https://en.wikipedia.org/wiki/Instituto%20Nacional%20de%20Estat%C3%ADstica	Instituto Nacional de Estatística (Portuguese for "National Institute for Statistics") may refer to: Instituto Nacional de Estatística (Cape Verde) - the national statistical agency of Cape Verde Instituto Nacional de Estatística (Mozambique) - the national statistical agency of Mozambique Instituto Nacional de Estatística (Portugal) - the national statistical agency of Portugal Instituto Nacional de Estatística (São Tomé and Príncipe) - the national statistical agency of São Tomé and Príncipe Instituto Nacional de Estatística - the original name of the present Instituto Brasileiro de Geografia e Estatística, the national statistical agency of Brazil
https://en.wikipedia.org/wiki/Thomas%20E.%20Nichols	Thomas E. Nichols is an American statistician. He is Professor of Neuroimaging Statistics and a Wellcome Trust Senior Research Fellow in Basic Biomedical Science at the Nuffield Department of Population Health of the University of Oxford, where he is also affiliated with the Big Data Institute. Previously, he taught in the Department of Biostatistics at the University of Michigan and at the University of Warwick; he also worked for GlaxoSmithKline as director of modeling and genetics at their Clinical Imaging Centre. He received the Wiley Young Investigator Award from the Organization for Human Brain Mapping in 2009 and was elected a Fellow of the American Statistical Association in 2012. References External links Faculty page Group page Living people American statisticians Fellows of the American Statistical Association University of Michigan faculty Carnegie Mellon University alumni Neuroimaging researchers Academics of the University of Oxford Academics of the University of Warwick GSK plc people Year of birth missing (living people)
https://en.wikipedia.org/wiki/Power%20in%20Numbers%3A%20The%20Rebel%20Women%20of%20Mathematics	Power in Numbers: The Rebel Women of Mathematics is a book on women in mathematics, by Talithia Williams. It was published in 2018 by Race Point Publishing. Topics and related works This book is a collection of biographies of 27 women mathematicians, and brief sketches of the lives of many others. It is similar to previous works including Osen's Women in Mathematics (1974), Perl's Math Equals (1978), Henrion's Women in Mathematics (1997), Murray's Women Becoming Mathematicians (2000), Complexities: Women in Mathematics (2005), Green and LaDuke's Pioneering Women in American Mathematics (2009), and Swaby's Headstrong (2015). The book is divided into three sections. The first two cover mathematics before and after World War II, when women's mathematical contributions to codebreaking and other aspects of the war effort became crucial; together they include the biographies of 11 mathematicians. The final section, on modern (post-1965) mathematics has another 16. Mathematics is interpreted in a broad sense, including people who trained as mathematicians and worked in industry, or who made mathematical contributions in other fields. It includes people from more diverse backgrounds than previous such collections, including 18th-century Chinese astronomer Wang Zhenyi, Native American engineer Mary G. Ross, African-American rocket scientist Annie Easley, Iranian mathematician Maryam Mirzakhani, and Mexican-American mathematician Pamela E. Harris. Mathematicians The mathematicians discussed in this book include: Part I: The Pioneers Marie Crous Émilie du Châtelet Maria Gaetana Agnesi Philippa Fawcett Isabel Maddison Grace Chisholm Young Wang Zhenyi Sophie Germain Winifred Edgerton Merrill Sofya Kovalevskaya Emmy Noether Euphemia Haynes Part II: From Code Breaking to Rocket Science Grace Hopper Mary G. Ross Dorothy Vaughan Katherine Johnson Mary Jackson Shakuntala Devi Annie Easley Margaret Hamilton Part III: Modern Math Mavens Sylvia Bozeman Eugenia Cheng Carla Cotwright-Williams Pamela E. Harris Maryam Mirzakhani Ami Radunskaya Daina Taimiņa Tatiana Toro Chelsea Walton Sara Zahedi Audience and reception The book is aimed at a young audience, with many images and few mathematical details. Nevertheless, each biography is accompanied by a general-audience introduction to the subject's mathematical work, and beyond images of the women profiled, the book includes many mathematical illustrations and historical images that bring to life these contributions. Reviewer Emille Davie Lawrence suggests that the book could also find its way to the coffee tables of professional mathematicians, and spark conversations with guests. Reviewer Amy Ackerberg-Hastings criticizes the book for overlooking much scholarly work on the subject of women in mathematics, for its lack of detail for some notable women including Émilie du Châtelet and Maria Gaetana Agnesi, and for omitting others such as Mary Somerville. Nevertheless, she recommends it as a "gift book for middl
https://en.wikipedia.org/wiki/Hiptmair%E2%80%93Xu%20preconditioner	In mathematics, Hiptmair–Xu (HX) preconditioners are preconditioners for solving and problems based on the auxiliary space preconditioning framework. An important ingredient in the derivation of HX preconditioners in two and three dimensions is the so-called regular decomposition, which decomposes a Sobolev space function into a component of higher regularity and a scalar or vector potential. The key to the success of HX preconditioners is the discrete version of this decomposition, which is also known as HX decomposition. The discrete decomposition decomposes a discrete Sobolev space function into a discrete component of higher regularity, a discrete scale or vector potential, and a high-frequency component. HX preconditioners have been used for accelerating a wide variety of solution techniques, thanks to their highly scalable parallel implementations, and are known as AMS and ADS precondition. HX preconditioner was identified by the U.S. Department of Energy as one of the top ten breakthroughs in computational science in recent years. Researchers from Sandia, Los Alamos, and Lawrence Livermore National Labs use this algorithm for modeling fusion with magnetohydrodynamic equations. Moreover, this approach will also be instrumental in developing optimal iterative methods in structural mechanics, electrodynamics, and modeling of complex flows. HX preconditioner for Consider the following problem: Find such that with . The corresponding matrix form is The HX preconditioner for problem is defined as where is a smoother (e.g., Jacobi smoother, Gauss–Seidel smoother), is the canonical interpolation operator for space, is the matrix representation of discrete vector Laplacian defined on , is the discrete gradient operator, and is the matrix representation of the discrete scalar Laplacian defined on . Based on auxiliary space preconditioning framework, one can show that where denotes the condition number of matrix . In practice, inverting and might be expensive, especially for large scale problems. Therefore, we can replace their inversion by spectrally equivalent approximations, and , respectively. And the HX preconditioner for becomes HX Preconditioner for Consider the following problem: Find with . The corresponding matrix form is The HX preconditioner for problem is defined as where is a smoother (e.g., Jacobi smoother, Gauss–Seidel smoother), is the canonical interpolation operator for space, is the matrix representation of discrete vector Laplacian defined on , and is the discrete curl operator. Based on the auxiliary space preconditioning framework, one can show that For in the definition of , we can replace it by the HX preconditioner for problem, e.g., , since they are spectrally equivalent. Moreover, inverting might be expensive and we can replace it by a spectrally equivalent approximations . These leads to the following practical HX preconditioner for problem, Derivation The de
https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Oklahoma	As of December 22, 2022, Oklahoma has been impacted more by Covid than the average U.S. state. Statistics for the U.S. as a whole are 331 deaths per 100,000 population with 68 percent of the population fully vaccinated. The comparable statistics for Oklahoma are 405 deaths per 100,000 population with 59 percent of the population fully vaccinated. 16,041 deaths from Covid have been recorded in Oklahoma. A wide variation in deaths from Covid exists between counties in Oklahoma. Greer County recorded a death rate of .00753 (753 deaths per 100,000 residents). Payne County recorded a death rate of only .00231 (231 deaths per 100,000 residents. The first case of COVID-19 in the U.S. state of Oklahoma was reported on March 7, 2020, with the first confirmed COVID-19 death occurring on March 18. For the 7 days ending May 19, 2021, Oklahoma public health authorities reported 965 new cases of COVID-19, for a cumulative total of 451,280 cases since the start of the pandemic. The state's death toll increased to 6,918 with 40 deaths reported over the previous 7 days. As of August 18, 2021, Oklahoma has administered 3,642,556 COVID-19 vaccine doses, equivalent to 51.05% of the state's population. Timeline March 2020 On March 7, 2020, the first case of COVID-19 was confirmed in Oklahoma in a patient who had returned from Italy on February 23 and began showing symptoms on February 29. On March 13, there were 4 cases in Oklahoma, including the first case in Oklahoma City, a woman in her 60s who recently returned from Florida. On March 15, the number of cases grew to 7, an increase of 75% from March 13. The three new cases were in Cleveland, Payne, and Tulsa counties. The age range of patients was 20 to 69. Governor Stitt held a press conference to announce executive orders. On March 16, there were 10 cases, an increase of 43% from the previous day. The first case of known community spread was reported on this day. and a few hours later Governor Stitt declared a State of emergency. On March 17, there were 17 cases. This was an increase of 70% over the previous day. On March 18, there were 29 cases, an increase of 71% from the previous day's total. In addition, the first COVID-19 patient died of the disease in Tulsa. He was a man in his 50s who had been admitted the day before. Testing capabilities remain limited in Oklahoma. On March 19, there were 44 cases, an increase of 51% over the previous day. On March 20, there were 49 cases, an increase of 11%. The majority of the cases were in two counties: Oklahoma (19 cases) and Cleveland (11) Counties. On March 21, there were 53 cases (an increase of 8%) according to the Oklahoma State Department of Health (OSDH). The U.S. Small Business Administration approved the State of Oklahoma's request for disaster loans for small businesses that are and will be affected by the COVID-19 pandemic. On March 22, there were 67 cases, an increase of 26% from the day before. In addition, a second patient died. So fa
https://en.wikipedia.org/wiki/Euclid%20Speidell	Euclid Speidell (died 1702) was an English customs official and mathematics teacher known for his writing on logarithms. Speidell published revised and expanded versions of texts by his father, John Speidell. He also published a book called Logarithmotechnia, or, The making of numbers called logarithms to twenty five places from a geometrical figure in 1688. Speidell lived in Angel Alley in the 1680s and 1690s, according to the Survey of London. Speidell's name appears on an instrument made by his contemporary Henry Sutton. References 17th-century English mathematicians 17th-century births Year of birth uncertain 1702 deaths
https://en.wikipedia.org/wiki/Algorithmic%20Geometry	Algorithmic Geometry is a textbook on computational geometry. It was originally written in the French language by Jean-Daniel Boissonnat and Mariette Yvinec, and published as Géometrie algorithmique by Edusciences in 1995. It was translated into English by Hervé Brönnimann, with improvements to some proofs and additional exercises, and published by the Cambridge University Press in 1998. Topics The book covers the theoretical background and analysis of algorithms in computational geometry, their implementation details, and their applications. It is grouped into five sections, the first of which covers background material on the design and analysis of algorithms and data structures, including computational complexity theory, and techniques for designing randomized algorithms. Its subsequent sections each consist of a chapter on the mathematics of a subtopic in this area, presented at the level of detail needed to analyze the algorithms, followed by two or three chapters on algorithms for that subtopic. The topics presented in these sections and chapters include convex hulls and convex hull algorithms, low-dimensional randomized linear programming, point set triangulation for two- and three-dimensional data, arrangements of hyperplanes, of line segments, and of triangles, Voronoi diagrams, and Delaunay triangulations. Audience and reception The book can be used as a graduate textbook, or as a reference for computational geometry research. Reviewer Peter McMullen calls it "a welcome addition to the shelves of anyone interested in algorithmic geometry". References Computational geometry Mathematics textbooks 1995 non-fiction books 1998 non-fiction books
https://en.wikipedia.org/wiki/Ingrid%20Kristine%20Glad	Ingrid Kristine Glad (born 1965) is a Norwegian statistician whose research topics have included nonparametric regression, DNA microarray data, and image processing. She is a professor of statistics and data science at the University of Oslo. Education and career Glad was born in Oslo. After rebelling against her family by preferring mathematics to language, Glad studied physics and statistics at the Norwegian Institute of Technology. She is married to statistician Arnoldo Frigessi, and followed Frigessi to Italy for postdoctoral research before returning to Norway for her position at the University of Oslo. As a teenager she worked a stint on a cargo ship, and her later research has also included using statistics to prevent shipping disasters. In 2022 Glad and Frigessi obtained the founding for the center of excellence (SFF) Integreat. Recognition Glad is an Elected Member of the International Statistical Institute. She was elected to the Norwegian Academy of Science and Letters in 2019. References External links 1965 births Living people Norwegian statisticians Women statisticians Norwegian Institute of Technology alumni Academic staff of the University of Oslo Elected Members of the International Statistical Institute Members of the Norwegian Academy of Science and Letters
https://en.wikipedia.org/wiki/LMS%20Journal%20of%20Computation%20and%20Mathematics	LMS Journal of Computation and Mathematics was a peer-reviewed online mathematics journal covering computational aspects of mathematics published by the London Mathematical Society. The journal published its first article in 1998 and ceased operation in 2017. An open access archive of the journal is maintained by Cambridge University Press. Abstracting and indexing The journal is abstracted and indexed in MathSciNet, Scopus, and Zentralblatt MATH. References External links English-language journals Hybrid open access journals Mathematics education in the United Kingdom Mathematics journals
https://en.wikipedia.org/wiki/International%20Day%20of%20Mathematics	The International Day of Mathematics is 14 March. It is also known as the Pi Day, because the mathematical constant (pi) can be rounded down to 3.14. UNESCO's 40th General Conference decided Pi Day as the International Day of Mathematics in November 2019. See also (pi) Pi Day References External links Official website of the International Day of Mathematics UNESCO page on the International Day of Mathematics 数学漫谈 (A Tour of Mathematics), a public lecture (in Chinese) delivered by Professor Ya-xiang Yuan (President of International Council for Industrial and Applied Mathematics) on 14 March 2020, the first International Day of Mathematics (slides) Mathematics and culture Pi
https://en.wikipedia.org/wiki/David%20Nadler%20%28mathematician%29	David Erie Nadler (born 1973) is an American mathematician who specializes in geometric representation theory and symplectic geometry. He is currently a professor at the University of California, Berkeley. Education and career Nadler graduated from Brown University with a B.S. in mathematics in 1996. He completed his doctoral studies at Princeton University under the supervision of Robert MacPherson, earning a Ph.D. in mathematics in 2001. He worked as an instructor at the University of Chicago for several years before taking a tenure track position at Northwestern University in 2005, where he became a Full Professor in 2011. He moved to his current position at the University of California at Berkeley in 2012. Recognition In 2007 Nadler was selected as a Sloan Research Fellow, and in 2013 he became a member of the inaugural class of Fellows of the American Mathematical Society. Nadler delivered the Arf Lecture in 2012. Selected works References External links David Erie Nadler at the Mathematics Genealogy Project David Nadler author profile at MathSciNet David Nadler author profile at zbMath David Nadler researcher profile at University of California, Berkeley 1973 births Living people 21st-century American mathematicians Brown University alumni Princeton University alumni Northwestern University faculty University of California, Berkeley College of Letters and Science faculty Fellows of the American Mathematical Society
https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Sabah	The COVID-19 pandemic was confirmed to have reached Sabah, Malaysia, in March 2020. As of 16 November 2022, there are 402,031 confirmed cases. Statistics The top plot shows the total number of cases as a function of time (by date) since 12 March 2020, the date of the first reported case in Sabah. The middle plot shows the number of new cases as reported each day. The bottom plot shows the number of active cases in Sabah. Timeline March 2020 On 12 March 2020, Sabah reported its first positive case involving a male resident from Tawau District who had been one of the participant in the Muslim religious gathering at Sri Petaling in Kuala Lumpur. He began to develop symptoms after returning and was subsequently transferred to Tawau Hospital. A second positive case was reported the following day in Benoni's Papar District which also originated from the religious gathering where he was then transferred to Queen Elizabeth Hospital for further treatment. A total of 14 new confirmed cases were recorded within the day. On 14 March, the Sabah State Health Department reported that another 11 new cases were confirmed in the state, bringing the total to 26. A further spike to 82 positive cases was then reported making Sabah the third most affected in Malaysia by the virus after Selangor and Kuala Lumpur. Earlier since the first positive case was reported, the State Health Department had warned that more positive cases were expected. By 18 March, the total positive cases had risen to 103. A further seven infections were recorded on 20 March, raising the total infected to 119 with the first death caused by the virus reported in Tawau involving a 58-year-old man who had been one of the participant of the religious gathering. The religious gathering also caused the closure of palm oil plantations in three districts of Tawau, Lahad Datu and Kinabatangan in late March after several plantation workers who had participated in the gathering were found positive with the virus. On 26 March, Sabah reported its first recovery of a coronavirus patient in Sandakan District. The entire Gaya Island inhabitants in the western coast of Sabah had also been put under close monitoring. 65.6% of the inhabitants were tested and 1,600 samples were taken. By 29 March, Tawau District was declared a red zone with a significant increase in positive cases, surpassing other districts within the state. April 2020 By early April, a total of 7,173 coronavirus tests had been conducted with the results of positive cases rising to 209. Within the same month, more than 90 people recovered from the virus with three deaths reported since March; the latest involving a 66-year-old man in Tambunan District with a medical history of diabetes, high blood pressure and kidney disease on 5 April along with a 62-year-old retired senior Sabah government official and tabligh worker with diabetes who died in Kota Kinabalu District on 10 April. On 9 April, a total of 231,980 people had been screened in t
https://en.wikipedia.org/wiki/%C3%81rp%C3%A1d%20Varecza	Árpád Varecza (6 September 1941 – 26 September 2005), was a Hungarian mathematician, former lecturer at the College of Nyíregyháza, head of the Institute of Mathematics and Informatics, and deputy director general of the institution for three years. Biography He was born on September 6, 1941, in Vác. He graduated from the teacher training college in Szeged in 1963, then graduated from ELTE with a degree in mathematics, physics and technology. His first jobs were tied to his birthplace. He taught at the Primary School in Váchartyán and Verőce, then at the Géza Király Secondary School and Vocational Secondary School in Vác. He was admitted to the Department of Mathematics of the Teacher Training College in Nyíregyháza in 1969 as an assistant lecturer, in 1971 he was appointed an assistant professor, in 1977 he was appointed an associate professor and in 1983 he was appointed a college teacher. Between 1977 and 1980 he was an aspirant at the Mathematical Research Institute of the Hungarian Academy of Sciences. In 1975 he received his Ph.D. at Kossuth Lajos University, and in 1982 he defended his Ph.D. Following the era marked by the name of Gyula Bereznai, he was head of the Department of Mathematics in 1984, then Head of the Institute of Mathematics and Informatics in 2000, and served as Deputy Director General of the institution for three years. Work He specialized in combinatorics, including "sorting algorithms". He obtained his candidate's degree in his dissertation on "Optimal sorting algorithms". Honorary Heir President of the János Bolyai Mathematical Society, President of the Department of Mathematics, Physics and Astronomy of the DAB, Chairman of the College's Scientific Committee, Member of the MM Intensive Further Education Council and of the MM Computer Science Advisory Board, He was the editor of the Mathematics series. Under his guidance, in 1985, four colleagues earned their Ph.D. Books Mathematics competitions for teacher training colleges A tanárképző főiskolák Péter Rózsa matematikai versenyei Notes External links Varecza Árpád On the smallest and largest elements In memoriam 1941 births 2005 deaths 20th-century Hungarian mathematicians 21st-century Hungarian mathematicians People from Szabolcs-Szatmár-Bereg County People from Nyíregyháza Eötvös Loránd University alumni
https://en.wikipedia.org/wiki/Giannis%20Tatsis	Giannis Tatsis (; born 15 August 1972) is a Greek professional football manager and former player. Managerial statistics As of 6 February 2023. References 1972 births Living people Footballers from Ioannina Greek men's footballers PAS Giannina F.C. players Apollon Smyrnis F.C. players Paniliakos F.C. players A.P.O. Akratitos Ano Liosia players Athens Kallithea F.C. players Kavala F.C. players Super League Greece players Men's association football midfielders Greek football managers Platanias F.C. managers Athlitiki Enosi Larissa F.C. managers Athens Kallithea F.C. managers Apollon Smyrnis F.C. managers Panachaiki F.C. managers Super League Greece managers
https://en.wikipedia.org/wiki/Dimitrios%20Spanos	Dimitris Spanos (; born 13 July 1969) is a Greek professional football manager. Managerial Statistics References 1969 births Living people Footballers from Aigio Greek football managers Anagennisi Arta F.C. managers Vyzas F.C. managers A.E. Rodos managers Panachaiki F.C. managers Panegialios F.C. managers Aiolikos F.C. managers Panelefsiniakos F.C. managers PAS Lamia 1964 managers Apollon Smyrnis F.C. managers Aris Thessaloniki F.C. managers PAE Kerkyra managers Doxa Drama F.C. managers Levadiakos F.C. managers Ionikos F.C. managers
https://en.wikipedia.org/wiki/Slicing%20the%20Truth	Slicing the Truth: On the Computability Theoretic and Reverse Mathematical Analysis of Combinatorial Principles is a book on reverse mathematics in combinatorics, the study of the axioms needed to prove combinatorial theorems. It was written by Denis R. Hirschfeldt, based on a course given by Hirschfeldt at the National University of Singapore in 2010, and published in 2014 by World Scientific, as volume 28 of the Lecture Notes Series of the Institute for Mathematical Sciences, National University of Singapore. Topics The book begins with five chapters that discuss the field of reverse mathematics, which has the goal of classifying mathematical theorems by the axiom schemes needed to prove them, and the big five subsystems of second-order arithmetic into which many theorems of mathematics have been classified. These chapters also review some of the tools needed in this study, including computability theory, forcing, and the low basis theorem. Chapter six, "the real heart of the book", applies this method to an infinitary form of Ramsey's theorem: every edge coloring of a countably infinite complete graph or complete uniform hypergraph, using finitely many colors, contains a monochromatic infinite induced subgraph. The standard proof of this theorem uses the arithmetical comprehension axiom, falling into one of the big five subsystems, ACA0. However, as David Seetapun originally proved, the version of the theorem for graphs is weaker than ACA0, and it turns out to be inequivalent to any one of the big five subsystems. The version for uniform hypergraphs of fixed order greater than two is equivalent to ACA0, and the version of the theorem stated for all numbers of colors and all orders of hypergraphs simultaneously is stronger than ACA0. Chapter seven discusses conservative extensions of theories, in which the statements of a powerful theory (such as one of the forms of second-order arithmetic) that are both provable in that theory and expressible in a weaker theory (such as Peano arithmetic) are only the ones that are already provably in the weaker theory. Chapter eight summarizes the results so far in diagrammatic form. Chapter nine discusses ways to weaken Ramsey's theorem, and the final chapter discusses stronger theorems in combinatorics including the Dushnik–Miller theorem on self-embedding of infinite linear orderings, Kruskal's tree theorem, Laver's theorem on order embedding of countable linear orders, and Hindman's theorem on IP sets. An appendix provides a proof of a theorem of Jiayi Liu, part of the collection of results showing that the graph Ramsey theorem does not fall into the big five subsystems. Audience and reception This is a technical monograph, requiring its readers to have some familiarity with computability theory and Ramsey theory. Prior knowledge of reverse mathematics is not required. It is written in a somewhat informal style, and includes many exercises, making it usable as a graduate textbook or beginning work in
https://en.wikipedia.org/wiki/Rayleigh%20theorem%20for%20eigenvalues	In mathematics, the Rayleigh theorem for eigenvalues pertains to the behavior of the solutions of an eigenvalue equation as the number of basis functions employed in its resolution increases. Rayleigh, Lord Rayleigh, and 3rd Baron Rayleigh are the titles of John William Strutt, after the death of his father, the 2nd Baron Rayleigh. Lord Rayleigh made contributions not just to both theoretical and experimental physics, but also to applied mathematics. The Rayleigh theorem for eigenvalues, as discussed below, enables the energy minimization that is required in many self-consistent calculations of electronic and related properties of materials, from atoms, molecules, and nanostructures to semiconductors, insulators, and metals. Except for metals, most of these other materials have an energy or a band gap, i.e., the difference between the lowest, unoccupied energy and the highest, occupied energy. For crystals, the energy spectrum is in bands and there is a band gap, if any, as opposed to energy gap. Given the diverse contributions of Lord Rayleigh, his name is associated with other theorems, including Parseval's theorem. For this reason, keeping the full name of "Rayleigh Theorem for Eigenvalues" avoids confusions. Statement of the theorem The theorem, as indicated above, applies to the resolution of equations called eigenvalue equations. i.e., the ones of the form HѰ = λѰ, where H is an operator, Ѱ is a function and λ is number called the eigenvalue. To solve problems of this type, we expand the unknown function Ѱ in terms of known functions. The number of these known functions is the size of the basis set. The expansion coefficients are also numbers. The number of known functions included in the expansion, the same as that of coefficients, is the dimension of the Hamiltonian matrix that will be generated. The statement of the theorem follows. Let an eigenvalue equation be solved by linearly expanding the unknown function in terms of N known functions. Let the resulting eigenvalues be ordered from the smallest (lowest), λ1, to the largest (highest), λN. Let the same eigenvalue equation be solved using a basis set of dimension N + 1 that comprises the previous N functions plus an additional one. Let the resulting eigenvalues be ordered from the smallest , 1, to the largest, N+1. Then, the Rayleigh theorem for eigenvalues states that i ≤ λi for A subtle point about the above statement is that the smaller of the two sets of functions must be a subset of the larger one. The above inequality does not hold otherwise. Self-consistent calculations In quantum mechanics, where the operator H is the Hamiltonian, the lowest eigenvalues are occupied (by electrons) up to the applicable number of electrons; the remaining eigenvalues, not occupied by electrons, are empty energy levels. The energy content of the Hamiltonian is the sum of the occupied eigenvalues. The Rayleigh theorem for eigenvalues is extensively utilized in calculations of electronic
https://en.wikipedia.org/wiki/Sacred%20Mathematics	Sacred Mathematics: Japanese Temple Geometry is a book on Sangaku, geometry problems presented on wooden tablets as temple offerings in the Edo period of Japan. It was written by Fukagawa Hidetoshi and Tony Rothman, and published in 2008 by the Princeton University Press. It won the PROSE Award of the Association of American Publishers in 2008 as the best book in mathematics for that year. Topics The book begins with an introduction to Japanese culture and how this culture led to the production of Sangaku tablets, depicting geometry problems, their presentation as votive offerings at temples, and their display at the temples. It also includes a chapter on the Chinese origins of Japanese mathematics, and a chapter on biographies of Japanese mathematicians from the time. The Sangaku tablets illustrate theorems in Euclidean geometry, typically involving circles or ellipses, often with a brief textual explanation. They are presented as puzzles for the viewer to prove, and in many cases the proofs require advanced mathematics. In some cases, booklets providing a solution were included separately, but in many cases the original solution has been lost or was never provided. The book's main content is the depiction, explanation, and solution of over 100 of these Sangaku puzzles, ranked by their difficulty, selected from over 1800 catalogued Sangaku and over 800 surviving examples. The solutions given use modern mathematical techniques where appropriate rather than attempting to model how the problems would originally have been solved. Also included is a translation of the travel diary of Japanese mathematician Yamaguchi Kanzan (or Kazu), who visited many of the temples where these tablets were displayed and in doing so built a collection of problems from them. The final three chapters provide a scholarly appraisal of precedence in mathematical discoveries between Japan and the west, and an explanation of the techniques that would have been available to Japanese problem-solvers of the time, in particular discussing how they would have solved problems that in western mathematics would have been solved using calculus or inversive geometry. Audience and reception Sacred Geometry can be read by historians of mathematics, professional mathematicians, "people who are simply interested in geometry", and "anyone who likes mathematics", and the puzzles it presents also span a wide range of expertise. Readers are not expected to already have a background in Japanese culture and history. The book is heavily illustrated, with many color photographs, also making it suitable as a mathematical coffee table book despite the depth of the mathematics it discusses. Reviewer Paul J. Campbell calls this book "the most thorough account of Japanese temple geometry available", reviewer calls it "exquisite, artfull, well-thought and particularly well-documented",, reviewer Frank J. Swetz calls it "a well crafted work that combines mathematics, history and cultural considera
https://en.wikipedia.org/wiki/Signed%20set	In mathematics, a signed set is a set of elements together with an assignment of a sign (positive or negative) to each element of the set. Representation Signed sets may be represented mathematically as an ordered pair of disjoint sets, one set for their positive elements and another for their negative elements. Alternatively, they may be represented as a Boolean function, a function whose domain is the underlying unsigned set (possibly specified explicitly as a separate part of the representation) and whose range is a two-element set representing the signs. Signed sets may also be called -graded sets. Application Signed sets are fundamental to the definition of oriented matroids. They may also be used to define the faces of a hypercube. If the hypercube consists of all points in Euclidean space of a given dimension whose Cartesian coordinates are in the interval , then a signed subset of the coordinate axes can be used to specify the points whose coordinates within the subset are or (according to the sign in the signed subset) and whose other coordinates may be anywhere in the interval . This subset of points forms a face, whose codimension is the cardinality of the signed subset. Combinatorics Enumeration The number of signed subsets of a given finite set of elements is , a power of three, because there are three choices for each element: it may be absent from the subset, present with positive sign, or present with negative sign. For the same reason, the number of signed subsets of cardinality is and summing these gives an instance of the binomial theorem, Intersecting families An analogue of the Erdős–Ko–Rado theorem on intersecting families of sets holds also for signed sets. The intersection of two signed sets is defined to be the signed set of elements that belong to both and have the same sign in both. According to this theorem, for any a collection of signed subsets of an -element set, all having cardinality and all pairs having a non-empty intersection, the number of signed subsets in the collection is at most For instance, an intersecting family of this size can be obtained by choosing the sign of a single fixed element, and taking the family to be all signed subsets of cardinality that contain this element with this sign. For this theorem follows immediately from the unsigned Erdős–Ko–Rado theorem, as the unsigned versions of the subsets form an intersecting family and each unsigned set can correspond to at most signed sets. However, for larger values of a different proof is needed. References Set theory
https://en.wikipedia.org/wiki/Jaime%20G%C3%B3mez-Hern%C3%A1ndez	J. Jaime Gómez-Hernández (born 1960) is a Spanish civil engineer specialized in geostatistics and hydrogeology. He is a full professor of hydraulic engineering at the School of Civil Engineering of the Technical University of Valencia. He was conferred the William Christian Krumbein Medal in 2020 from the International Association for Mathematical Geosciences. He also received the 2020 Prince Sultan bin Abdulaziz International Prize for Water in the field of groundwater. Education BS in Civil Engineering from Technical University of Valencia in 1983 MS in Applied Hydrogeology from Stanford University in 1987 PhD in Geostatistics for Natural Resources Evaluation from Stanford University in 1990 Biography Born on 28 October, 1960, in Requena, Spain, Gómez-Hérnandez earned his Civil Engineering Bachelor's degree from the Technical University of Valencia in 1983. After a year working for the Valencian delegation of the Spanish company EPTISA, where he implemented the first aquifer numerical models using just his ZX Spectrum connected to a portable TV, he moved to Stanford University in 1984 to pursue an MS in Applied Hydrogeology under the supervision of Irwin Remson of the Applied Earth Sciences Department. This was followed by a PhD at Stanford in Geostatistics for Natural Resources Characterization under the supervision of Andre Journel. Upon his return to Spain in 1990, he worked for the Spanish company EVREN as a civil engineer, and in 1994, he joined the School of Civil Engineering at the Technical University of Valencia as an associate professor. He became a full professor in 2000, the position at which he remains active. Research Gómez-Hernández's MS thesis (1987) dealt with the application of the Kalman filter for network design in aquifers. 30 years later, he would supervise several PhD theses and publish a number of important papers on the use of the ensemble Kalman filter for inverse modeling in aquifers. His PhD thesis dealt with the use of geostatistics for the upscaling of hydraulic conductivity in heterogeneous aquifers. Heterogeneity, aquifer characterization, and uncertainty quantification have been the main topics around which his research has revolved. His research can also be grouped into the following four main subjects: Algorithm and code development Gómez-Hernández developed for his PhD a stochastic simulation technique for random functions that was much more precise and versatile than other contemporary codes, and, more importantly, without limitations on the size of the realizations to be generated. This technique is included in the public domain codes ISIM3D and GCOSIM3D. These codes have been incorporated into commercial programs and have been used routinely by institutions such as the University of Arizona, the British Nuclear Waste Management Agency (NIREX), and the Polytechnic University of Catalonia. Upscaling The need to establish a link between laboratory measurements of parameters, such as permeability, a
https://en.wikipedia.org/wiki/Worldometer	Worldometer, formerly Worldometers, is a reference website that provides counters and real-time statistics for diverse topics. It is owned and operated by a data company Dadax which generates revenue through online advertising. It is available in 31 languages and covers subjects such as government, world population, economics, society, media, environment, food and water, energy, and health. In early 2020, the website attained greater popularity due to hosting statistics relating to the COVID-19 pandemic. History The website was founded by Andrey Alimetov, a Russian immigrant to the United States, in 2004. In 2011, it was voted as one of the best free reference websites by the American Library Association. This site changed its name from "Worldometers" to "Worldometer" in January 2020 and announced that it would migrate to the singular domain name. COVID-19 pandemic In early 2020, the website gained popularity during the COVID-19 pandemic. It came under cyber attack in March 2020. The site was hit with a DDoS attack, and was then hacked a few days later, resulting in incorrect information being shown on its COVID-19 statistics page for approximately 20 minutes. The hacked site showed a dramatic rise in COVID-19 cases in Vatican City, which caused panic among some users of social media. The Spanish government used its figures to claim that it had carried out more tests than all but four other countries. Worldometers' COVID-19 figures have also been cited by Financial Times, The New York Times, The Washington Post, CNN, and Rede Globo. Worldometer has faced some criticism over transparency of ownership, lack of citations to data sources, and unreliability of its COVID-19 statistics and live rankings. In April 2020, editors of the English Wikipedia decided that Worldometer's COVID-19 figures are often unreliable and should not be cited in any pages related to the pandemic. Reception Edouard Mathieu, the data manager of Our World in Data, stated that "Their main focus seems to be having the latest number [of COVID-19 cases] wherever it comes from, whether it's reliable or not, whether it's well-sourced or not." Virginia Pitzer, a Yale University epidemiologist, said that the site is "legitimate", but flawed, inconsistent, and containing errors. According to Axios, at the peak of user interest, the website was the #28 most visited website in the world in April 2020. A plurality (25.8%) of visitors came from the United States, followed by Japan (17.9%), India (8.67%), the United Kingdom (6.6%), South Korea (5.8%), Canada (5.18%), Germany (3.13%), Australia (2.49%), Poland (2.18%), France (1.73%), Turkey (1.66%), Brazil (1.65%) and Argentina (1.52%). By March 2023, according to traffic data from Similarweb, Worldometer had dropped to the 5,963rd global place. References External links American websites Internet properties established in 2008 Reference websites Web analytics
https://en.wikipedia.org/wiki/Mary%20Leng	Mary Leng is a British philosopher specialising in the philosophy of mathematics and philosophy of science. She is a professor at the University of York. Career Leng studied as an undergraduate at Balliol College, University of Oxford and as postgraduate student at the University of Toronto. She worked at the University of Cambridge from 2002 to 2006, and then the University of Liverpool from 2006 to 2011. In 2007, she co-edited a collection called Mathematical Knowledge with Alexander Paseau and Michael Potter, which was published by Oxford University Press, and, in 2010, she published a monograph called Mathematics and Reality, again with Oxford University Press. In Mathematics and Reality, Leng defends mathematical fictionalism. Leng joined the University of York in 2012, where she is now a professor. References Living people Year of birth missing (living people) British women philosophers British philosophers Philosophers of mathematics Academics of the University of York Academics of the University of Liverpool Academics of the University of Cambridge University of Toronto alumni Alumni of Balliol College, Oxford
https://en.wikipedia.org/wiki/Alban%20%C3%87ejku	Alban Çejku (born 23 July 2001) is an Albanian professional footballer who plays as a left back for Albanian club Teuta Durrës. Career statistics Club Honours Tirana Albanian Superliga: 2019–20 References External links 2001 births Living people Footballers from Tirana Albanian men's footballers People from Tirana County Men's association football midfielders Kategoria Superiore players KF Tirana players Albania men's youth international footballers
https://en.wikipedia.org/wiki/Illinois%20Council%20of%20Teachers%20of%20Mathematics	The Illinois Council of Teachers of Mathematics (ICTM) is an organization of mathematics educators in the US state of Illinois. An affiliate of the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics, the ICTM was founded in 1949 with 90 members. Professional Activities The ICTM is involved in a number of professional activities, including: Hosting conferences on math education Hosting webinars for professional development Publishing its journal, Illinois Mathematics Teacher. Offering scholarships to college students. In 2017, the ICTM gave $7,500 in scholarships. Math Contests The ICTM offers several math competitions for primary and secondary school students in Illinois. Grade School Contest The Grade School Contest is a series of three tests that are given at elementary schools. Each grade level (3-8) competes in its own division. The contest has two components: an individual competition and a team competition. The team competition consists of five student teams who work on 20 questions in 25 minutes. There is no limit to the number of teams that a school may enter. The individual competition is an eight question, 20 minute exam to be completed by each competitor individually. The use of calculators during the contest is encouraged. The top two team scores and top ten individual scores contribute to each school's total score. Algebra Contest The Algebra Contest is an individual, 60 minute, 20 question contest for elementary and junior high school students. Each school can submit as many competitors as it wishes. The ten highest individual scores in each school contributes to the school's total score, and the top ten individuals and top ten schools receive special recognition from the ICTM. High School Contest Started in 1981, the High School Contest consists of a number of team and individual events, with a regional competition being held in late February and the state competition being held in late April or early May. Schools are separated into divisions by enrollment. Events †In all cases, a member of a lower grade may substitute for a member of a higher grade. For example, freshmen, sophomores, and juniors may all compete in the Algebra II Written competition, but not seniors. Each school can have a maximum of one team per level per event, with the exception of the relay competition, in which schools are permitted a maximum of two teams per level per event. This gives a maximum possible team score of 1306 at the state finals, and a maximum score of 1150 at the regional competition. References Mathematics education in the United States
https://en.wikipedia.org/wiki/Konstantin%20Ardakov	Konstantin Ardakov (born 1979) is professor of pure mathematics at the Mathematical Institute, University of Oxford and fellow and tutor in mathematics at Brasenose College, Oxford. After education at the University of Oxford and the University of Cambridge, he held positions at Cambridge, the University of Sheffield, the University of Nottingham, and Queen Mary University of London, before returning to Oxford. He was awarded the 2019–20 Adams Prize for making "substantial contributions to noncommutative Iwasawa theory, and to the p-adic representation theory of p-adic Lie groups". References Living people 1979 births British mathematicians Fellows of Brasenose College, Oxford Academics of the University of Sheffield
https://en.wikipedia.org/wiki/Non-skid	Non-skid is a surface applied to the deck of a ship to increase the coefficient of friction and reduce the probability of footwear or vehicle tires sliding along a smooth wet surface. When decks are painted for protection against wear and corrosion, non-skid may be formed by either mixing a granular material like sand into the paint prior to application, or by sprinkling dry sand onto a newly painted surface before the paint hardens by drying or curing. Examples Sources Watercraft components
https://en.wikipedia.org/wiki/COVID-19%20pandemic%20in%20Northern%20Ireland	The COVID-19 pandemic reached Northern Ireland in February 2020. The Department of Health reports 3,445 deaths overall among people who had recently tested positive. The Northern Ireland Statistics and Research Agency reports 5,444 where the death certificate mentioned COVID as one possible cause (see Statistics). Northern Ireland has the lowest COVID death rate per population in the United Kingdom. The vast majority of deaths have been among those over the age of 60 and almost half were in care homes. According to figures, over 1 in 10 of over 5,400 who have passed have been under 65. On 23 March 2020, Northern Ireland went into lockdown with the rest of the UK. A stay-at-home order banned "non-essential" travel and contact with others, and schools, businesses, venues, amenities and places of worship were shut. Major events such as Saint Patrick's Day were cancelled. A lengthy lockdown was forecast to severely damage the economy and lead to a large rise in unemployment. The health service worked to raise hospital capacity. In mid-April, Department of Health modeling indicated the health service in Northern Ireland could cope with the expected peak in cases. On 21 April, Northern Ireland's chief scientific advisor said the curve of new cases had flattened, and the peak had passed. The lockdown was gradually lifted in June–July, as infection and death rates dropped. Schools remained closed for summer break, but re-opened in September. The infection rate (or positivity rate) rose again that month and restrictions were re-imposed. On 16 October, Northern Ireland went into an eight-week lockdown, although schools remained open, and some restrictions were eased for one week. The lockdown was mostly lifted on 11 December. Following a brief easing of restrictions at Christmas, another lockdown was imposed on 26 December, including schools, as the positivity rate rose sharply. A mass vaccination program began, and the infection rate fell in early 2021. Schools re-opened in March, and the lockdown was gradually lifted from late April. In December, proof of vaccination or non-infection became mandatory to enter indoor venues. Timeline Health care in the United Kingdom is devolved, with England, Northern Ireland, Scotland and Wales each having their own publicly funded healthcare systems, funded by devolved block grants via the Barnett formula and accountable to separate governments and parliaments, together with smaller private sector and voluntary provision. As a result of each country having different policies and priorities, differences now exist between these systems. First wave and national lockdown (March–May 2020) The HSC began testing for COVID-19 during February 2020, as of 19 February there were 35 completed tests all of which returned negative results. On 27 February, the HSC confirmed that the first presumptive case had been discovered in Northern Ireland in a woman who had returned from Italy, the case was sent to the Public Health Englan
https://en.wikipedia.org/wiki/List%20of%20Bashundhara%20Kings%20records%20and%20statistics	The Bashundhara Kings is a professional football club based in Bashundhara Residential Area, Dhaka, Bangladesh. History Bashundhara Kings played their first match in 2017 against Uttar Baridhara SC. They won their first-ever title in the same year, lifting 2017 Bangladesh Championship League. Major titles League Bangladesh Premier League Winners (1): 2018–19 Bangladesh Championship League Winners (1): 2017–18 Cup Bangladesh Federation Cup Winners (1): 2019–20 Independence Cup Winners (1): 2018–19 Goalscoring records Top scorers in Premier League Top scorers in Federation Cup Top scorers in Independence Cup Top scorers in AFC Cup \|- \|2\|\|align=left\|\|\|Mohammad Ibrahim\|\|2018–2023\|\|1 \|} Top scorers in Sheikh Kamal Club Cup Clean sheets Bangladesh Premier League only. Head Coach's records First Head Coach: S. M. Asifuzzaman, from August 2017 to November 2017. Longest-serving Head Coach by time: Óscar Bruzón, from 5 September 2018 to Present (1 year, 9 months, 28 days). Longest-serving Head Coach by matches: Óscar Bruzón managed the club for 51 matches over a period of 1 year and nine months, from September 2018 to Present. Player records Goalscorers Most goals in all competitions:: Daniel Colindres, 26. Most league goals: Robson Azevedo da Silva, 21. Most Federation Cup goals: Daniel Colindres, 8. Most Independence Cup goals: Motin Mia & Bakhtiyar Duyshobekov, 2. Most Continental goals: Hernan Barcos, 4. First player to score for Bashundhara: Ripon Biswas (against Uttar Baridhara SC, 7 August 2017). Most goals in a season: Robson Azevedo da Silva, 24 (during the 2020–21 season). Most goals in a debut season: Robson Azevedo da Silva, 24 (during the 2020–21 season). Most league goals in a season: Robson Azevedo da Silva, 21 (during the 2020–21 season). Most continental goals in a season: Hernan Barcos, 4. Most hat-tricks: 5 Players, 1. Fastest hat-trick: Daniel Colindres, 13 minutes, (against Team BJMC, 11 November 2018). Highest-scoring substitute in Premier League: Tawhidul Alam Sabuz, 3. Most games without scoring for an outfield player in Premier League: Masuk Mia Jony, 40. Youngest goalscorer: Arif Hossain, 16 years (2017). Oldest goalscorer: Hernan Barcos, 35 years, 11 months, 1 day (against TC Sports Club, 11 March 2020). Club records Matches Firsts First Match: Bashundhara Kings 2–2 Uttar Baridhara SC, 7 August 2017. First Premier League Match: Bashundhara Kings 1–0 Sheikh Jamal Dhanmondi Club, 19 January 2019. First Federation Cup Match: Bashundhara Kings 5–2 Dhaka Mohammedan, 29 October 2018. First Independence Cup Match: Bashundhara Kings 2–0 Sheikh Jamal Dhanmondi Club, 2 December 2018. First AFC Cup Match: Bashundhara Kings 5–1 TC Sports Club, 11 March 2020. Wins Record win: Bashundhara Kings 5–0 Brothers Union, 16 July 2019. Record Premier League win: Bashundhara Kings 5–0 Brothers Union, 16 July 2019. Record Federation Cup win: Bashundhara Kings 5–1 Team BJMC, 11 Nove
https://en.wikipedia.org/wiki/Mary%20Perry%20Smith	Mary Perry Smith (May 29, 1926 – August 10, 2015) was an American mathematics educator who cofounded the Mathematics, Engineering, Science Achievement program and the Black Filmmakers Hall of Fame. Early life and education Perry Smith was born on May 29, 1926, and was originally from Evansville, Indiana, one of six children of a minister in the African Methodist Episcopal Church; her maternal grandfather, Henry Allen Perry had been a chaplain and mathematics teacher at the Tuskegee Institute, where her parents met. As a child she moved frequently, to Kokomo, Logansport, Anderson, Crawfordsville, and Frankfort, all in Indiana. She earned a bachelor's degree from Ball State University in mathematics and science in three years, as one of a small number of African-American students there, and continued at Purdue University for a master's degree in counseling and guidance (with minors in biochemistry and statistics), finishing in 1948. Later life and career Unable to find a job because of the discrimination in teacher hiring in Indiana, she followed her older brother to the newly opened Texas State University for Negroes in Houston, where she taught mathematics for three years. After marrying Norvel L. Smith (later to become the president of Merritt College and the first African American head of a college in California) and moving with her husband to Oakland, California, she joined a doctoral program in educational psychology at the University of California, Berkeley, but moved to part-time study and then stopped out to become a teacher, first in a junior high school in San Francisco from 1953 until 1961, and then at Oakland Technical High School, where she taught geometry for 17 years. Service In 1969, Perry Smith cofounded the Mathematics, Engineering, Science Achievement (MESA) program for under-privileged pre-college students in California. In 1974, she cofounded the Black Filmmakers Hall of Fame in Oakland, California, initially as part of the Oakland Museum’s Cultural and Ethnics Affairs Guild and, in 1978, as a separate organization; she also served as its president. She left her teaching position to work for the MESA program in 1977, as statewide program director, and also served on the board of the Oakland Museum of California. She died in 2015. Legacy Her papers are kept in the Bancroft Library of the University of California, Berkeley. References External links In memoriam: Mary Perry Smith, UCLA Center for Excellence in Engineering and Diversity 2015 deaths Ball State University alumni Purdue University alumni 20th-century American mathematicians American women mathematicians African-American mathematicians Mathematics educators Texas Southern University faculty 1926 births 20th-century African-American women 20th-century African-American people 21st-century African-American people 21st-century African-American women
https://en.wikipedia.org/wiki/Equivalents%20of%20the%20Axiom%20of%20Choice	Equivalents of the Axiom of Choice is a book in mathematics, collecting statements in mathematics that are true if and only if the axiom of choice holds. It was written by Herman Rubin and Jean E. Rubin, and published in 1963 by North-Holland as volume 34 of their Studies in Logic and the Foundations of Mathematics series. An updated edition, Equivalents of the Axiom of Choice, II, was published as volume 116 of the same series in 1985. Topics At the time of the book's original publication, it was unknown whether the axiom of choice followed from the other axioms of Zermelo–Fraenkel set theory (ZF), or was independent of them, although it was known to be consistent with them from the work of Kurt Gödel. This book codified the project of classifying theorems of mathematics according to whether the axiom of choice was necessary in their proofs, or whether they could be proven without it. At approximately the same time as the book's publication, Paul Cohen proved that the negation of the axiom of choice is also consistent, implying that the axiom of choice, and all of its equivalent statements in this book, are indeed independent of ZF. The first edition of the book includes over 150 statements in mathematics that are equivalent to the axiom of choice, including some that are novel to the book. This edition is divided into two parts, the first involving notions expressed using sets and the second involving classes instead of sets. Within the first part, the topics are grouped into statements related to the well-ordering principle, the axiom of choice itself, trichotomy (the ability to compare cardinal numbers), and Zorn's lemma and related maximality principles. This section also includes three more chapters, on statements in abstract algebra, statements for cardinal numbers, and a final collection of miscellaneous statements. The second section has four chapters, on topics parallel to four of the first section's chapters. The book includes the history of each statement, and many proofs of their equivalence. Rather than ZF, it uses Von Neumann–Bernays–Gödel set theory for its proofs, mainly in a form called NBG0 that allows urelements (contrary to the axiom of extensionality) and also does not include the axiom of regularity. The second edition adds many additional equivalent statements, more than twice as many as the first edition, with an additional list of over 80 statements that are related to the axiom of choice but not known to be equivalent to it. It includes two added sections, one on equivalent statements that need the axioms of extensionality and regularity in their proofs of equivalence, and another on statements in topology, mathematical analysis, and mathematical logic. It also includes more recent developments on the independence of the axiom of choice, and an improved account of the history of Zorn's lemma. Audience and reception This book is written as a reference for professional mathematicians, especially those working in set
https://en.wikipedia.org/wiki/Davenport%E2%80%93Schinzel%20Sequences%20and%20Their%20Geometric%20Applications	Davenport–Schinzel Sequences and Their Geometric Applications is a book in discrete geometry. It was written by Micha Sharir and Pankaj K. Agarwal, and published by Cambridge University Press in 1995, with a paperback reprint in 2010. Topics Davenport–Schinzel sequences are named after Harold Davenport and Andrzej Schinzel, who applied them to certain problems in the theory of differential equations. They are finite sequences of symbols from a given alphabet, constrained by forbidding pairs of symbols from appearing in alternation more than a given number of times (regardless of what other symbols might separate them). In a Davenport–Schinzel sequence of order , the longest allowed alternations have length . For instance, a Davenport–Schinzel sequence of order three could have two symbols and that appear either in the order or , but longer alternations like would be forbidden. The length of such a sequence, for a given choice of , can be only slightly longer than its number of distinct symbols. This phenomenon has been used to prove corresponding near-linear bounds on various problems in discrete geometry, for instance showing that the unbounded face of an arrangement of line segments can have complexity that is only slightly superlinear. The book is about this family of results, both on bounding the lengths of Davenport–Schinzel sequences and on their applications to discrete geometry. The first three chapters of the book provide bounds on the lengths of Davenport–Schinzel sequences whose superlinearity is described in terms of the inverse Ackermann function . For instance, the length of a Davenport–Schinzel sequence of order three, with symbols, can be at most , as the second chapter shows; the third concerns higher orders. The fourth chapter applies this theory to line segments, and includes a proof that the bounds proven using these tools are tight: there exist systems of line segments whose arrangement complexity matches the bounds on Davenport–Schinzel sequence length. The remaining chapters concern more advanced applications of these methods. Three chapters concern arrangements of curves in the plane, algorithms for arrangements, and higher-dimensional arrangements, following which the final chapter (comprising a large fraction of the book) concerns applications of these combinatorial bounds to problems including Voronoi diagrams and nearest neighbor search, the construction of transversal lines through systems of objects, visibility problems, and robot motion planning. The topic remains an active area of research and the book poses many open questions. Audience and reception Although primarily aimed at researchers, this book (and especially its earlier chapters) could also be used as the textbook for a graduate course in its material. Reviewer Peter Hajnal calls it "very important to any specialist in computational geometry" and "highly recommended to anybody who is interested in this new topic at the border of combinatorics, geo
https://en.wikipedia.org/wiki/Nikos%20Peios	Nikos Peios (; born 17 June 1999) is a Greek professional footballer who plays as a centre-back for Super League club Kifisia. Career statistics Club References 1999 births Living people Greek men's footballers Super League Greece 2 players Ergotelis F.C. players Men's association football defenders Footballers from Veria
https://en.wikipedia.org/wiki/Antonis%20Alexakis	Antonis Alexakis (; born 2 July 2001) is a Greek professional footballer who plays as a midfielder for Super League 2 club Irodotos. Career statistics Club References 2001 births Living people Super League Greece 2 players Ergotelis F.C. players Men's association football midfielders Footballers from Heraklion Greek men's footballers
https://en.wikipedia.org/wiki/Georgios%20Manousakis	Georgios Manousakis (; born 10 April 1998) is a Greek professional footballer who plays as a striker for Super League 2 club Chania. Career statistics References 1998 births Living people Gamma Ethniki players Football League (Greece) players Super League Greece 2 players Super League Greece players Ergotelis F.C. players PAS Lamia 1964 players Iraklis F.C. (Thessaloniki) players Men's association football forwards Footballers from Heraklion Greek men's footballers
https://en.wikipedia.org/wiki/Neritan%20Novi	Neritan Novi (born 3 September 1970) is an Albanian football manager and former player. International statistics References 1970 births Living people Sportspeople from Gjirokastër County People from Gjirokastër Footballers from Gjirokastër Albanian men's footballers Albania men's international footballers Men's association football midfielders KF Luftëtari players Kategoria Superiore players KF Luftëtari managers Kategoria Superiore managers Albanian football managers
https://en.wikipedia.org/wiki/Peter%20Teichner	Peter Teichner (born June 30, 1963 in Bratislava, Czechoslovakia) is a German mathematician and one of the directors of the Max Planck Institute for Mathematics in Bonn. His main areas of work are topology and geometry. Life In 1988, Peter Teichner graduated from the University of Mainz with a degree in mathematics. After graduating, he worked for one year in Canada, funded by the "Government of Canada Award", at McMaster University in Hamilton (Ontario). From 1989 to 1990 he was affiliated with the Max Planck Institute for Mathematics. From 1990 to 1992 he worked at the University of Mainz as a research assistant, and in 1992 he received his doctorate with Matthias Kreck as his advisor. The title of his doctoral thesis was Topological four-manifolds with finite fundamental group. With a Feodor Lynen Scholarship from the Humboldt Foundation, he went to UC San Diego from 1992 to 1995 and collaborated with Michael Freedman. In 1995 he worked at the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France. From 1995 to 1996 he was again at the University of Mainz. From 1996 to 1997 he was at UC Berkeley as a Miller Research Fellow. From 1996 he was an associate professor at UC San Diego, and in 1999 he was granted tenure. He stayed at UC San Diego until 2004, since then he has been a full professor at UC Berkeley, where he retired in 2019. He has been a director at the Max Planck Institute for Mathematics in Bonn since 2008. He has also been the managing director from 2011 until 2019. His students include Arthur Bartels, James Conant, and Christopher Schommer-Pries. Academic work Peter Teichner's work lies in the field of topology, which deals with qualitative properties of geometric objects. His early achievements were on the classification of 4-manifolds. Together with the Fields medalist Mike Freedman, Peter Teichner made contributions to the classification of 4-manifolds whose fundamental group only grows sub-exponentially. Later in his career, he moved on to study Euclidean and topological field theories. In particular, in an ongoing project, Peter Teichner and Stephan Stolz try to refine the mathematical term quantum field theory in such a way that deformation classes of quantum field theories can be interpreted as a qualitative property of a manifold. More specifically, these should form a cohomology theory. The emerging language should be flexible enough to formulate new physical theories, but also so precise that predictions can be made about the impossibility of certain combinations of space-time and quantum fields. References External links 1963 births Living people Topologists 21st-century German mathematicians Max Planck Institute directors Johannes Gutenberg University Mainz alumni
https://en.wikipedia.org/wiki/Oresti%20Kacurri	Oresti Kacurri (born 25 February 1998) is an Albanian professional footballer who plays as a midfielder for Greek Super League 2 club Chania. Career statistics Club References External links 1998 births Living people Albanian men's footballers Football League (Greece) players Super League Greece 2 players Ergotelis F.C. players Men's association football midfielders Footballers from Heraklion Greek men's footballers
https://en.wikipedia.org/wiki/Roger%20Peng	Roger D. Peng is an author and professor of Statistics and Data Science at the University of Texas at Austin. Peng originally received a Bachelor of Science in Applied Mathematics from Yale University in 1999, before going on to study at the University of California, Los Angeles, where he completed a Master of Science in Statistics in 2001 and a PhD in Statistics in 2003. The focus of his research has been on environmental health, specifically focusing on air pollution and climate change in his research. Peng is also a software engineer who has authored numerous R packages focused on applying statistical methods necessary for a variety of topics. He has also created numerous resources including books, online courses, podcasts, blogs, and other articles to aid those learning data analysis. Career Peng has written or contributed to ten different books, including R Programming for Data Science, which lays the foundation for using the R programming language. He, along with Jeff Leek and Rafa Irizarry, actively contribute to Simply Statistics, a website containing courses, articles, interviews, blog posts, and other materials for statisticians and those interested in data focused on various biostatistics topics. Peng and Leek join Brian Caffo as co-creators of the Data Science Specialization massive open online course (MOOC) offered through Johns Hopkins University, which is a collection of courses geared towards individuals seeking to develop skills in data science and data analysis. Peng is the co-host with Hilary Parker of the data science podcast Not So Standard Deviations. Parker and Peng also have co-authored Conversations on Data Science, which compiles many of the topics covered on their podcast, as well as other discussions related to data science. Peng actively contributes journal articles to several publications, most commonly related to providing evidence to the prevalence of air pollution. He has written on the importance of creating reproducible research and the practice of using various statistical methods. Awards Peng's work in biostatistics, especially related to environmental health, has led to numerous awards. In 2016, Peng received the American Public Health Association Mortimer Spiegelman Award to honor his contributions to public health statistics, given to a member under the age of 40. Additionally, Peng has received several awards for his publications, including multiple honors for NIEHS Extramural Paper of the Month. In 2017, Peng was elected a Fellow of the American Statistical Association. References Year of birth missing (living people) Living people American statisticians Biostatisticians Johns Hopkins Bloomberg School of Public Health faculty University of California, Los Angeles alumni Yale University alumni Fellows of the American Statistical Association R (programming language) people
https://en.wikipedia.org/wiki/Modular%20forms%20modulo%20p	In mathematics, modular forms are particular complex analytic functions on the upper half-plane of interest in complex analysis and number theory. When reduced modulo a prime p, there is an analogous theory to the classical theory of complex modular forms and the p-adic theory of modular forms. Reduction of modular forms modulo 2 Conditions to reduce modulo 2 Modular forms are analytic functions, so they admit a Fourier series. As modular forms also satisfy a certain kind of functional equation with respect to the group action of the modular group, this Fourier series may be expressed in terms of . So if is a modular form, then there are coefficients such that . To reduce modulo 2, consider the subspace of modular forms with coefficients of the -series being all integers (since complex numbers, in general, may not be reduced modulo 2). It is then possible to reduce all coefficients modulo 2, which will give a modular form modulo 2. Basis for modular forms modulo 2 Modular forms are generated by and :.. It is then possible to normalize and to and , having integers coefficients in their -series. This gives generators for modular forms, which may be reduced modulo 2. Note the Miller basis has some interesting properties Once reduced modulo 2, and are just . That is, a trivial reduction. To get a non-trivial reduction, mathematicians use the modular discriminant . It is introduced as a "priority" generator before and . Thus, modular forms are seen as polynomials of , and (over the complex in general, but seen over integers for reduction), once reduced modulo 2, they become just polynomials of over . The modular discriminant modulo 2 The modular discriminant is defined by an infinite product: The coefficients that matches are usually denoted , and correspond to the Ramanujan tau function. Results from Kolberg and Jean-Pierre Serre allows to show that modulo 2, we have: i.e., the -series of modulo 2 consists of to powers of odd squares. Hecke operators modulo 2 Hecke operators are commonly considered as the most important operators acting on modular forms. It is therefore justified to try to reduce them modulo 2. The Hecke operators for a modular form are defined as follows with . Hecke operators may be defined on the -series as follows: if , then with Since modular forms were reduced using the -series, it makes sense to use the -series definition. The sum simplifies a lot for Hecke operators of primes (i.e. when is prime): there are only two summands. This is very nice for reduction modulo 2, as the formula simplifies a lot. With more than two summands, there would be many cancellations modulo 2, and the legitimacy of the process would be doubtable. Thus, Hecke operators modulo 2 are usually defined only for primes numbers. With a modular form modulo 2 with -representation , the Hecke operator on is defined by where It is important to note that Hecke operators modulo 2 have the interesting property of being nil
https://en.wikipedia.org/wiki/Henryk%20Hi%C5%BC	Henryk Hiż (8 October 1917 – 19 December 2006) was a Polish analytical philosopher specializing in linguistics, philosophy of language, logic, mathematics and ethics, active for most of his life in the United States, one of the youngest representatives of the Lwów–Warsaw school. A disciple of Tadeusz Kotarbiński, Hiż studied at the University of Warsaw. During the German occupation of Poland in the World War II, he participated in the Polish resistance movement as a cryptographer in the Home Army. In 1944 he took part in the Warsaw Uprising. In 1948, he defended his Ph.D. at Harvard University under W.V.O. Quine. In 1950, he permanently emigrated to the United States. He kept in touch with the American logical environment, including with Alfred Tarski, and maintained lively contact with the Polish academic community. He lectured at the University of Pennsylvania between 1960 and 1988. In 1976 he was a Guggenheim Fellow and a visiting fellow at the University of Cambridge. In 1982 he received the Alfred Jurzykowski Foundation Award. He was a member of the Warsaw Scientific Society. He published about one hundred original papers in peer-reviewed scientific journals. Strongly influenced by the Lwów–Warsaw school, initially in his research he was interested in semantics, formal logic and methodology of the sciences. From the late 1950s, he dealt mainly with linguistics in relation to logic and philosophy. He described himself as a naturalist and linguistic behaviorist, assuming that the linguistic work is primarily about linguistic behavior. He called himself a “negative utilitarian”; and was also a pacifist and an atheist. Biography Early life and German occupation He was born on October 8, 1917, in Petrograd as the son of Tadeusz Hiż and Emilia née Elżanowska. He had an older brother, Stanisław (1915–1999). In 1920, the family came to Poland, settling in Warsaw. Henryk's mother, Emilia, was an architect, while his father Tadeusz Hiż was a journalist, who kept in touch with the Warsaw's bohemian circles. Franciszek Fiszer was, among others, a frequent guest in their house. Years later, Henryk Hiż said that “he obtained a lot from his parental home”. He attended the Mikołaj Rej High School in Warsaw, where he passed the matriculation examination in 1937. For two years he was an actor at the School Theater of the Reduta Institute. In 1938, he performed in the play Kościuszko near Racławice (Kościuszko pod Racławicami) directed by Maria Dulęba, portraying historical figure Bartosz Głowacki. In the theater, he also met Ewa Kunina, Juliusz Osterwa and Iwo Gall. In the late 1930s he associated with the so-called “democratic youth”, becoming one of the founding members of the anti-fascist Democratic Club in Warsaw. In 1937 he enrolled at the University of Warsaw to study philosophy. He attended lectures and seminars in logic led by Jan Łukasiewicz, Stanisław Leśniewski and Alfred Tarski. He was most influenced by Tadeusz Kotarbiński, to which he la
https://en.wikipedia.org/wiki/Zsombor%20B%C3%A9v%C3%A1rdi	Zsombor Bévárdi (born 30 January 1999) is a Hungarian professional footballer who plays for Nemzeti Bajnokság I club Debreceni VSC. Career statistics . External links 1999 births Living people People from Siófok Hungarian men's footballers Men's association football midfielders Fehérvár FC players BFC Siófok players Vasas SC players Debreceni VSC players Kaposvári Rákóczi FC players Nemzeti Bajnokság I players Hungary men's youth international footballers Footballers from Somogy County
https://en.wikipedia.org/wiki/Aur%C3%A9l%20Farkas	Aurél Farkas (born 31 March 1994) is a Hungarian football midfielder who plays for Csákvár. Career statistics References External links 1994 births Living people Footballers from Budapest Hungarian men's footballers Men's association football midfielders Szigetszentmiklósi TK footballers Erzsébeti Spartacus MTK LE footballers Ferencvárosi TC footballers Szeged-Csanád Grosics Akadémia footballers Szolnoki MÁV FC footballers Aqvital FC Csákvár players Kaposvári Rákóczi FC players Nyíregyháza Spartacus FC players Nemzeti Bajnokság I players Nemzeti Bajnokság II players Hungary men's youth international footballers
https://en.wikipedia.org/wiki/Zimbabwe%20National%20Statistics%20Agency	Zimbabwe National Statistics Agency (ZIMSTAT) is the statistics agency of Zimbabwe. It is headquartered in the Kaguvi Building in Harare. Census and Statistics Act of 2007 created the agency. It replaced the Central Statistical Office (CSO). It was headquartered in the Kaguvi Building in Harare. References External links Zimbabwe National Statistics Agency Government of Zimbabwe National statistical services Government agencies established in 2007 2007 establishments in Zimbabwe
https://en.wikipedia.org/wiki/Eridon%20Qardaku	Eridon Qardaku (born 10 August 2000) is an Albanian professional footballer who plays as an attacking midfielder for Albanian club Bylis. Career statistics Club References External links 2000 births Living people People from Shkodër County Sportspeople from Shkodër Footballers from Shkodër Albanian men's footballers Men's association football midfielders KF Bylis players Kategoria Superiore players
https://en.wikipedia.org/wiki/Valentino%20Murataj	Valentino Murataj (born 15 August 1996) is an Albanian professional footballer who plays as a midfielder for Albanian club Partizani. Career statistics Clubs References External links 1996 births Living people People from Fier County Footballers from Fier Men's association football midfielders Albanian men's footballers KF Bylis players Kategoria Superiore players Kategoria e Parë players Kategoria e Dytë players
https://en.wikipedia.org/wiki/Somchai%20Makmool	Somchai Makmool (; born 17 November 1980) is a Thai football manager He is the current head coach of Thai League 3 club Khon Kaen. Managerial statistics Honours Sukhothai FC 2016 Thai FA Cup Winners : 2016 References External links Living people 1980 births Somchai Makmool Somchai Makmool
https://en.wikipedia.org/wiki/Carlo%20Masi	Ruggero Freddi (born October 6, 1976) is an Italian mathematics lecturer and former gay pornographic film actor known professionally as Carlo Masi. Early life and education Freddi was born in Rome in 1976 to a poor family. His parents divorced when he was three years old. At the age of 14, he began to work out at a local gym, practicing bodybuilding assiduously. In 2002, when he was about to complete his first cycle of study at the Sapienza University of Rome, he moved to Canada, and subsequently to New York. Career In 2003, Masi completed a Master of Science (MSc) degree in computer engineering at the Sapienza University of Rome and worked in an artificial intelligence laboratory. Pornography In 2004, after being contacted by a Colt Studio Group (CSG) recruiter, he made his debut in the gay pornography industry participating in his first porn movie, Big N 'Plenty. After his debut, he signed an exclusive model contract with CSG. He has always promoted safe sex, fraternising with the Italian LGBT community. In 2006, he was selected to appear on the cover of COLT 40, a coffee table book published to celebrate the fortieth anniversary of the production company. In 2007, Masi and his future husband, Adam Champ (), were selected to appear on the cover of the Damron 2007 Men's Travel Guide. In 2008, CSG and Calaexotic released a dildo reproduction of Masi's penis. That same year, he was named the first and only Colt Man Emeritus and his contract was extended to a lifetime one. In 2008, Masi and Champ, were selected to appear on the cover of Adam Gay Film & Video Directory Magazine. During his porn career, he was a guest on national Italian TV shows such as , L'Infedele and . Moreover, he was featured in several tours across America, Mexico and Europe to promote the CSG brand. His porn career lasted six years (from age 28 to 34). Following a disagreement with Colt in 2009, Masi retired from the pornography industry. He then entered the theatre industry. In 2010, he was officially announced as a permanent member of the cast of Saturday Night Live Italia but he never appeared on the show. In 2011, he was included in the anthologies Porn from Andy Warhol to X-Tube and Gay Porn Heroes: 100 Most Famous Porn Stars. In 2013, he was interviewed for the documentary HUSTLABALL BERLIN - A Documentary That Bares All. In 2014, he was included in the coffee table book produced by Colt entitled Hairy Chested Men. Theatre In 2009, he made his theatre debut with Senzaparole, a reinterpretation of Samuel Beckett's Act Without Words I, directed by and staged in Bologna with the theatre company. and later in Rome at the . Academia After working in the theatre, Masi decided to return to the Sapienza University of Rome. There he earned a Bachelor of Science degree (cum laude) in mathematics, with a score of 110/110 and then a Master of Science degree (cum laude) in mathematics with a score of 110/110. In 2020, he completed a Ph.D. in Mathematical Models for Eng
https://en.wikipedia.org/wiki/Georgios%20Nikas	Georgios Nikas (; born 17 September 1999) is a Greek professional footballer who plays as a midfielder for Super League 2 club Levadiakos, on loan from Panathinaikos. Career Statistics Club Honours Levadiakos Super League 2: 2021–22 References 1999 births Living people Super League Greece players Super League Greece 2 players Levadiakos F.C. players Men's association football midfielders Footballers from Athens Greek men's footballers
https://en.wikipedia.org/wiki/Dorothy%20McCoy	Dorothy McCoy (August 9, 1903 – November 21, 2001) was an American mathematician and university professor. She was the first woman to earn a doctorate in mathematics from the University of Iowa, and she worked for many years as a professor of mathematics at Belhaven College and Wayland Baptist College. Early life and education McCoy was born on August 9, 1903, in Waukomis, Oklahoma, then part of the Oklahoma Territory, one of two children of a homesteading family. She and the rest of the family moved to Chesapeake, Missouri in 1906 after the death of her father. She received a bachelor's degree from Baylor University in Texas with distinction, worked for a year as a mathematics teacher, and completed a doctorate in mathematics from the University of Iowa in 1929, under the supervision of Edward Wilson Chittenden. Her dissertation was The Complete Existential Theory of Eight Fundamental Properties of Topological Spaces. She earned both degrees at the same time as her younger brother, Neal, who became a professor of mathematics at Smith College. She became the first woman to earn a doctorate in mathematics at the University of Iowa, and (with Winifred Asprey, Barbara Beechler, and Kathryn Powell Ellis) one of only four who did so before 1960. Later life and career McCoy became professor and head of the mathematics department at Belhaven College in Mississippi in 1929, and chaired the Louisiana–Mississippi Section of the Mathematical Association of America in 1937 and 1938. In 1949 she became professor of mathematics and chair of the division of physical and biological sciences at Wayland Baptist College. She was a Fulbright Scholar in 1954, visiting Iraq, and later traveled professionally to many other countries. She also consulted for the US government's missile defense program. She retired as distinguished professor emerita in 1975, "the only member of the faculty to have received the title of both emeritus and distinguished". She died on November 21, 2001. Recognition The Wayland Baptist Association of Former Students gave McCoy their Distinguished Lifetime Service Award in 1999. Wayland Baptist named a dorm in her honor in 2001, and displays a bust of her in one of its buildings. Two photographs of her are included in the collection of the National Museum of American History, as part of a set of photos on women with doctorates in mathematics. References 1903 births 2001 deaths 20th-century American mathematicians American women mathematicians Baylor University alumni University of Iowa alumni Belhaven University Wayland Baptist University 20th-century American women
https://en.wikipedia.org/wiki/Gury	Gury may refer to: People Gury Kolosov (1867–1936), Russian and Soviet mathematician and engineer Gury Marchuk (1925–2013), Soviet and Russian scientist in the fields of computational mathematics and physics of the atmosphere Gury Nikitin (1620–1691), Russian painter Gury of Metz, also known as Goeric of Metz, French bishop and saint Jean-Pierre Gury (1801–1866), French Jesuit moral theologian Places Gury, Oise, commune in the Oise department in northern France
https://en.wikipedia.org/wiki/Meca%20%28footballer%29	José Manuel Meca García (born 19 January 1978), commonly known as Meca, is a retired Spanish footballer who played as a forward. Career statistics Club Notes References 1978 births Living people Spanish men's footballers Men's association football forwards Real Madrid Castilla footballers Real Madrid CF players Cultural y Deportiva Leonesa players Elche CF players Racing de Ferrol footballers Real Jaén footballers UD Lanzarote players UDA Gramenet footballers Orihuela CF players CF Atlético Ciudad players Lorca Atlético CF players Segunda División B players Segunda División players La Liga players
https://en.wikipedia.org/wiki/H%C3%A9ctor%20Moreira	Héctor Osberto Moreira Pérez (born 27 December 1987) is a Guatemalan professional footballer who plays as a defender for Liga Nacional club Xelajú. Career statistics International goal Scores and results list. Guatemala's goal tally first. Honours Municipal Liga Nacional de Guatemala: Apertura 2019 Xelajú Liga Nacional de Guatemala: Clausura 2023 References External links 1987 births Living people People from Escuintla Department Guatemalan men's footballers Guatemala men's international footballers Men's association football defenders Deportivo Zacapa players Universidad SC players Club Xelajú MC players C.S.D. Municipal players
https://en.wikipedia.org/wiki/Mathematical%20Excursions	Mathematical Excursions: Side Trips along Paths Not Generally Traveled in Elementary Courses in Mathematics is a book on popular mathematics. It was written by Helen Abbot Merrill, published in 1933 by the Norwood Press, and reprinted (posthumously) by Dover Publications in 1957. Topics The book is devoted to mathematical puzzles and pastimes, gathered from Merrill's experience as a teacher. It has 15 chapters, most on arithmetic and number theory but with one on geometry. Its topics include squared triangular numbers and other sums of powers, Russian peasant multiplication, binary numbers, repeating decimals, magic squares, the irrationality of , mechanical linkages, linear Diophantine equations, the 15 puzzle, perfect numbers, and some unsolved problems in number theory. Audience and reception The book is written for a general audience, and is intended to spark the interest of high school students in mathematics. In general, only high school levels of algebra and geometry are needed to appreciate the book and solve its problems. It could be used as individual reading, or in mathematics clubs, and also for mathematics teachers looking for examples and demonstrations for their classes. Of the original edition, reviewer David Eugene Smith wrote "the book ought to be in the hands of all teachers and on the shelves of all high schools and colleges". By the time of the 1957 reprint, reviewer Samuel L. Greitzer complained about its obsolete notation, as well as its uneven level of exposition and non-uniform inclusion of solutions to problems, and reviewer Roland Sprague noted that its treatment of perfect numbers was out of date. Nevertheless, Greitzer suggested that it would be appropriate as "enrichment" for high-school students. References External links Mathematical Excursions in the Hathitrust Digital Library: Norwood Press edition, ; Dover edition, Popular mathematics books 1933 non-fiction books
https://en.wikipedia.org/wiki/Banphikot%20Rural%20Municipality	Banphikot () is a rural municipality located in Western Rukum District of Karnali Province of Nepal. According to 2011 Census conducted by Central Bureau of Statistics (CBS), Banphikot Rural Municipality had total population of 18,696. Banphikot Rural Municipality was established in 2015 through the merging five the former Village development committees of Aathbiskot, Pipal, Duli (ward no. 4, 5 &6) and Magma (ward no. 1-6 & 9). This Municipality shares boarder with Sisne Rural Municipality (East Rukum district) in the East, Sani Bheri Rural Municipality in the West, Aathbiskot Municipality in the North, and Musikot Municipality in the South. Demographics At the time of the 2011 Nepal census, Banphikot Rural Municipality had a population of 18,696. Of these, 99.8% spoke Nepali and 0.1% other languages as their first language. In terms of ethnicity/caste, 55.5% were Chhetri, 12.0% Kami, 9.7% Magar, 8.9% Thakuri, 7.2% Hill Brahmin, 4.2% Damai/Dholi, 1.4% Sarki, 0.4% Sanyasi/Dasnami, 0.2% Gaine, 0.1% Badi, 0.1% other Dalit, 0.1% Gurung and 0.1% others. In terms of religion, 99.1% were Hindu, 0.4% Christian, 0.2% Buddhist and 0.3% others. In terms of literacy, 61.0% could read and write, 3.1% could only read and 35.8% could neither read nor write. References External links Official website Populated places in Western Rukum District Rural municipalities in Karnali Province Rural municipalities of Nepal established in 2017
https://en.wikipedia.org/wiki/Werner%20Flechsig	Werner Flechsig (June 8, 1900 - October 12, 1981) was a German physicist and television pioneer. Life Werner Flechsig was born on June 8, 1900, in Cologne, Germany. He began studying mathematics and physics at the Technical University of Hanover. He continued his education at the Georg August University of Göttingen. There, Flechsig assisted Robert Wichard Pohl. In 1925, Flechsig completed his doctorate with the dissertation "Science of Photoelectric Primary Current in Crystals." In this document, Flechsig dealt with hot cathodes and photocells. He also considered the work of Pohl assistant Bernhard Gudden. Flechsig became an employee of Fernseh-AG in Berlin, where he developed TV camera tubes. In 1936, he made the orthicon technology practical. At the Olympic summer games, orthicon camera tubes supplanted the earlier iconoscope tubes. In 1937, the Internationale Funkausstellung of the Reichspost Research Institute displayed a color television method. (The Internationale Funkausstellung is the International Radio Exposition.) The new color television method used two primary colors. The process failed to produce satisfactory pictures. Members of the organization discussed developing a more accurate method to produce a full-color display: Additive color mixing with three primary colors. Flechsig invented the principle of color picture generation with shadow-mask picture tubes., He registered his shadow-mask process in July 1938 as a German Reichspatent. The patent title was "Cathode Ray Tube for the Development of Multicolored Pictures on a Fluorescent Screen." An exhibit at the 1939 Internationale Funkausstellung Berlin displayed a prototype of Flechsig's color television receiver. The war put an end to technical implementation of Flechsig's shadow mask picture tube. The Radio Corporation of America produced the first commercial realization in 1949. Flechsig was an honorary member of the Television and Cinema Engineering Society. Werner Flechsig died on October 12, 1981, in Wolfenbüttel. Writings "Science of Photoelectric Primary Current in Crystals," 1926, dissertation. "About the Saturation of Photoelectric Primary Current in Crystals," 1928. "Cathode Ray Tube for Development of Multicolored Pictures on a Fluorescent Screen," 1938, Reichspatent 736,575. Bibliography History of Electronic Entertainment, David L. Morton, 1999. Physical Sheets 37, No. 5, 1981. Andreas Fickers: "Politics of Grandeur" versus "Made in Germany." Political Cultural History of Technology, Using the Example of the PAL-SECAM Controversy. Oldenbourg, Munich 2007, . Footnotes External links Werner Flechsig: First Practical Color CRT, 1938 Internationale Funkausstellung Berlin, "History" section (IFA)IFA Berlin#History The story of the shadow mask picture tubemask 20th-century German inventors 1900 births Scientists from Cologne 1981 deaths 20th-century German physicists University of Hanover alumni University of Göttingen alumni
https://en.wikipedia.org/wiki/Ahmed%20Atef	Ahmed Atef (born 21 March 1998) was an Egyptian professional footballer who played as a forward for Wadi Degla. Career statistics Club Notes References 1998 births Living people Egyptian men's footballers Egyptian expatriate men's footballers Men's association football forwards Wadi Degla S.C. players Ergotelis F.C. players Super League Greece 2 players Egyptian expatriate sportspeople in Greece Expatriate men's footballers in Greece Future FC players
https://en.wikipedia.org/wiki/Ramez%20Medhat	Wassef Ramez Medhat (born 10 August 1999) is an Egyptian professional footballer who plays as a forward for Wadi Degla. Career statistics Club Notes References 1999 births Living people Egyptian men's footballers Egyptian expatriate men's footballers Men's association football forwards ENPPI SC players Al Ahly SC players Zamalek SC players Al Mokawloon Al Arab SC players Pyramids FC players Wadi Degla S.C. players Ergotelis F.C. players Super League Greece 2 players Egyptian expatriate sportspeople in Greece Expatriate men's footballers in Greece
https://en.wikipedia.org/wiki/Arthur%20Bote	Arthur César Reis Castro (born 7 January 1997), commonly known as Arthur Bote, is a Brazilian professional footballer who plays as a defender. Career statistics Club Notes References 1997 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football defenders Santos FC players S.U. Sintrense players Sertanense F.C. players Ergotelis F.C. players Super League Greece 2 players Liga III Brazilian expatriate sportspeople in Greece Expatriate men's footballers in Greece Brazilian expatriate sportspeople in Romania Expatriate men's footballers in Romania
https://en.wikipedia.org/wiki/2019%20Tajikistan%20First%20League	The Tajikistan First League is the second division of the Tajikistan Football Federation. Teams League table Season statistics Top scorers References Tajikistan First League seasons 1 Tajik
https://en.wikipedia.org/wiki/Women%20in%20Mathematics%20%28book%29	Women in Mathematics is a book on women in mathematics. It was written by Lynn M. Osen, and published by the MIT Press in 1974. Topics The main content of the book is a collection of eight biographies of women mathematicians, arranged chronologically, with an additional introductory chapter and two closing chapters. The mathematicians profiled here are Hypatia, Maria Gaetana Agnesi, Émilie du Châtelet, Caroline Herschel, Sophie Germain, Mary Somerville, Sofya Kovalevskaya, and Emmy Noether. One of the two closing chapters features shorter profiles of additional women mathematicians, "rather curiously selected" and "mostly working in America". The scientists mentioned in this chapter are Mary W. Gray, Mina Rees, Lise Meitner, Maria Goeppert Mayer, Charlotte Scott, Hanna Neumann, Maria Pastori, Maria Cibrario, Jacqueline Lelong-Ferraud, Paulette Libermann (misspelled Liberman), Sophie Piccard (misspelled Picard), Olga Taussky-Todd, Emma Lehmer (misspelled Lermer), Julia Robinson, Elizabeth Scott, Grace Hopper and Dorothy Maharam Stone. Reception Although reviewer Philip Peak found the book "interesting and useful", and reviewer writes that it is written in a pleasant style, most reviewers were not as positive. Hardy Grant writes that Osen's profile of Hypatia has treated her "very badly" by being based primarily on a piece of fiction for children written in the early 20th century by Elbert Hubbard. Reviewer R. P. Infante writes that "Osen does not seem to know much mathematics or its history", pointing to several errors in both. Infante also bemoans the book's "narrow" and "slipshod" scholarship, consisting of vague attributions to "some scholars" in the text of the work that "invariably" lead to the work of a single author, early 20th century writer John Augustine Zahm. Reviewer suggests that Grace Chisholm Young should have been mentioned. And reviewers Margaret Hayman and Edith Robinson both complain about the book's focus on its subjects' victimization by society, rather than either their personal lives and personalities or their mathematical accomplishments. Michael A. B. Deakin wrote, "Sadly, the standard of Osen's scholarship did not match the importance of her subject matter." References External links Women in Mathematics at the Internet Archive Women in mathematics Biographies and autobiographies of mathematicians 1974 non-fiction books
https://en.wikipedia.org/wiki/Chair%20tiling	In geometry, a chair tiling (or L tiling) is a nonperiodic substitution tiling created from L-tromino prototiles. These prototiles are examples of rep-tiles and so an iterative process of decomposing the L tiles into smaller copies and then rescaling them to their original size can be used to cover patches of the plane. Chair tilings do not possess translational symmetry, i.e., they are examples of nonperiodic tilings, but the chair tiles are not aperiodic tiles since they are not forced to tile nonperiodically by themselves. The trilobite and cross tiles are aperiodic tiles that enforce the chair tiling substitution structure and these tiles have been modified to a simple aperiodic set of tiles using matching rules enforcing the same structure. Barge et al. have computed the Čech cohomology of the chair tiling and it has been shown that chair tilings can also be obtained via a cut-and-project scheme. References External links Tilings Encyclopedia, Chair Aperiodic tilings
https://en.wikipedia.org/wiki/Weyl%20integration%20formula	In mathematics, the Weyl integration formula, introduced by Hermann Weyl, is an integration formula for a compact connected Lie group G in terms of a maximal torus T. Precisely, it says there exists a real-valued continuous function u on T such that for every class function f on G: Moreover, is explicitly given as: where is the Weyl group determined by T and the product running over the positive roots of G relative to T. More generally, if is only a continuous function, then The formula can be used to derive the Weyl character formula. (The theory of Verma modules, on the other hand, gives a purely algebraic derivation of the Weyl character formula.) Derivation Consider the map . The Weyl group W acts on T by conjugation and on from the left by: for , Let be the quotient space by this W-action. Then, since the W-action on is free, the quotient map is a smooth covering with fiber W when it is restricted to regular points. Now, is followed by and the latter is a homeomorphism on regular points and so has degree one. Hence, the degree of is and, by the change of variable formula, we get: Here, since is a class function. We next compute . We identify a tangent space to as where are the Lie algebras of . For each , and thus, on , we have: Similarly we see, on , . Now, we can view G as a connected subgroup of an orthogonal group (as it is compact connected) and thus . Hence, To compute the determinant, we recall that where and each has dimension one. Hence, considering the eigenvalues of , we get: as each root has pure imaginary value. Weyl character formula The Weyl character formula is a consequence of the Weyl integral formula as follows. We first note that can be identified with a subgroup of ; in particular, it acts on the set of roots, linear functionals on . Let where is the length of w. Let be the weight lattice of G relative to T. The Weyl character formula then says that: for each irreducible character of , there exists a such that . To see this, we first note The property (1) is precisely (a part of) the orthogonality relations on irreducible characters. References Theodor Bröcker and Tammo tom Dieck, Representations of compact Lie groups, Graduate Texts in Mathematics 98, Springer-Verlag, Berlin, 1995. Differential geometry
https://en.wikipedia.org/wiki/Pioneering%20Women%20in%20American%20Mathematics	Pioneering Women in American Mathematics: The Pre-1940 PhD's is a book on women in mathematics. It was written by Judy Green and Jeanne LaDuke, based on a long study beginning in 1978, and was published in 2009 by the American Mathematical Society and London Mathematical Society as volume 34 in their joint History of Mathematics series. Unlike many previous works on the topic, it aims at encyclopedic coverage of women in mathematics in the pre-World War II United States, rather than focusing only on the biographies of individual women or on collecting stories of only the most famous women in mathematics. The Basic Library List Committee of the Mathematical Association of America has strongly recommended its inclusion in undergraduate mathematics libraries. Topics The first part of the book discusses the institutions that granted doctorates to women in mathematics before 1940, and the milieu in which they operated, including typical practices of the time of that demanded that women resign on marriage, that forbade institutions from hiring wives or other relatives of their male faculty, or in some cases prevented women who had done all the work for a graduate degree from being granted one. It also discusses the patterns the authors' found in these women's lives, including the discovery that their life expectancies were higher than typical for their time. Its eight chapters include material on the family background of the subjects, their undergraduate and graduate education, hiring and careers, and their contributions to mathematics. The second part of the book provides biographical profiles of every woman that the authors could identify as having earned a doctorate in mathematics in the US before 1940, as well as four American women who earned doctorates abroad, giving 228 in all. The typical biography in this section is approximately 2/3 of a page to a page in length, with information drawn from reference works, review journals, and archival material as well as interviews with the subjects still living at the time of the study. The 1940 cutoff for the biographies in the book represents both a time of "a precipitous drop in enrollment" for women in mathematics, and the starting time for two previous studies on women in mathematics and science by Margaret A. M. Murray and Margaret W. Rossiter. The rate of doctorates given to women in the period covered by the book, approximately 14%, would not be reached again until the 1980s. A companion web site provides additional information on the subjects of the book, and can be considered as a third and "potentially most valuable" section of the book itself. Audience and reception This book is readable by a general audience, but reviewer Charles Ashbacher writes that "only people deeply interested in the history of mathematics, particularly in the role of women, will find it a critical read", and suggests that the second half should be used as reference material rather than reading it through. Reviewer Am
https://en.wikipedia.org/wiki/Coronavirus%20deaths	Coronavirus deaths may refer to: List of deaths from the 2019–20 coronavirus pandemic, a list of notable people 2019–20 coronavirus pandemic deaths, statistics on the numbers of deaths
https://en.wikipedia.org/wiki/Yuliya%20Mishura	Yuliya Stepanivna Mishura () is a Ukrainian mathematician specializing in probability theory and mathematical finance. She is a professor at the Taras Shevchenko National University of Kyiv. Education and career Mishura earned a Ph.D. in 1978 from the Taras Shevchenko National University of Kyiv with a dissertation on Limit Theorems for Functionals from Stochastic Fields supervised by Dmitrii Sergeevich Silvestrov. She earned a Dr. Sci. from the National Academy of Sciences of Ukraine in 1990 with a dissertation Martingale Methods in the Theory of Stochastic Fields. She became an assistant professor in the Faculty of Mechanics and Mathematics at National Taras Shevchenko University of Kyiv in 1976. She has been a full professor since 1991, and head of the Department of Probability, Statistics and Actuarial Mathematics since 2003. With Kęstutis Kubilius, she is the founding co-editor-in-chief of the journal Modern Stochastics: Theory and Applications. She is the editor-in-chief of the journal Theory of Probability and Mathematical Statistics. Books Mishura is the author of many monographs and textbooks. They include: Discrete-Time Approximations and Limit Theorems In Applications to Financial Markets (with Kostiantyn Ralchenko, De Gruyter Series in Probability and Stochastics, 2021) Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations (with G. Kulinich, S. Kushnirenko, Vol.9 Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics, 2020) Fractional Brownian Motion. Approximations and Projections (with Oksana Banna, Kostiantyn Ralchenko, Sergiy Shklyar, Wiley-ISTE, 2019) Stochastic Analysis of Mixed Fractional Gaussian Processes (ISTE Press, 2018) Theory and Statistical Applications of Stochastic Processes (with Georgiy Shevchenko, ISTE Press and John Wiley & Sons, 2017) Parameter Estimation in Fractional Diffusion Models (with Kęstutis Kubilius and Kostiantyn Ralchenko, Bocconi University Press and Springer, 2017) Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach (with Olena Ragulina, ISTE Press, 2016) Financial Mathematics: Optimization in Insurance and Finance Set (ISTE Press, 2016) Theory of Stochastic Processes: With Applications to Financial Mathematics And Risk Theory (with Gusak, Kukush, Kulik, and Pilipenko, Problem Books in Mathematics, Springer, 2010) Stochastic Calculus for Fractional Brownian Motion and Related Processes (Lecture Notes in Mathematics 1929, Springer, 2008) References External links Year of birth missing (living people) Living people Ukrainian women mathematicians 21st-century Ukrainian mathematicians 20th-century Ukrainian mathematicians Probability theorists Taras Shevchenko National University of Kyiv alumni Academic staff of the Taras Shevchenko National University of Kyiv 20th-century women mathematicians 21st-century women mathematicians
https://en.wikipedia.org/wiki/Magda%20Kandil	Magda ElSayed Kandil (; 5 May 1958 – 17 June 2020) was an Egyptian economist, and most notably the chief economist and head of the research and statistics department at the Central Bank of the United Arab Emirates. Previously she was a senior economist at the IMF and a professor at University of Wisconsin–Milwaukee. She was on the editorial board of the Journal of Economic Studies and Management Decision. Education and career She graduated with a Bachelor of Science in economics from Cairo University in 1978. She then obtained an M.A. from the University of Notre Dame in 1982 and an M.B.A. from Indiana University two years later. In 1988, she received her PhD from Washington State University. From 1992 to 1999, she was professor and economics department chair at the University of Wisconsin-Milwaukee. In 1999, she joined the International Monetary Fund (IMF) as Advisor to Executive Director. She then obtained successive promotions and in 2013, she was nominated as Senior Economist for the Eastern II Division in the African Department. She was the Chief Economist and Head of Research and Statistics Department at the Central Bank of the United Arab Emirates. Kandil died on 17 June 2020 in Abu Dhabi. Research Her research focuses on Macroeconomics, International Economics and growth economics. She has published in the Journal of Macroeconomics, the Journal of Economics and Business, the Southern Economic Journal, the Journal of International Money and Finance and Applied Economics. She is the 87th most cited woman in economics according to the ranking on IDEAS. Her research has been featured in The Washington Post, The Wall Street Journal, Reuters, The Jerusalem Post, Aljazeera, The Saudi Gazette, The New York Times, and CNBC. Selected bibliography Kandil, Magda; Woods, Jeffrey G. (1995). "A cross-industry examination of the Lucas misperceptions model". Journal of Macroeconomics. 17 (1): 55–76. Kandil, Magda (1997-02-01). "What differentiates industrial business cycles? A cross-country investigation". Applied Economics. 29 (2): 197–212. Ben Naceur, Samy; Kandil, Magda (2009-01-01). "The impact of capital requirements on banks' cost of intermediation and performance: The case of Egypt". Journal of Economics and Business. 61 (1): 70–89. Kandil, Magda (2001). "Variation in the Effects of Aggregate Demand Shocks: Evidence and Implications across Industrial Countries". Southern Economic Journal. 67 (3): 552 References 1958 births 2020 deaths University of Wisconsin–Milwaukee faculty Cairo University alumni University of Notre Dame alumni Indiana University alumni Washington State University alumni International Monetary Fund people
https://en.wikipedia.org/wiki/Bal%C3%A1zs%20T%C3%B3th%20%28footballer%2C%20born%201997%29	Balázs Tóth (born 4 September 1997) is a Hungarian football goalkeeper who plays for Fehérvár on loan from Puskás Akadémia FC. Career statistics . References External links 1997 births Living people People from Kazincbarcika Hungarian men's footballers Hungary men's youth international footballers Men's association football goalkeepers Puskás Akadémia FC players Puskás Akadémia FC II players Aqvital FC Csákvár players Fehérvár FC players Nemzeti Bajnokság I players Nemzeti Bajnokság III players Footballers from Borsod-Abaúj-Zemplén County

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