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https://en.wikipedia.org/wiki/Haruki%20Saruta	is a Japanese footballer currently playing as a goalkeeper for Kashiwa Reysol. Career statistics Club . Notes References External links 1999 births Living people Japanese men's footballers Japan men's youth international footballers Men's association football goalkeepers J3 League players Kashiwa Reysol players Kagoshima United FC players Gamba Osaka players Gamba Osaka U-23 players Yokohama FC players
https://en.wikipedia.org/wiki/Ko%20Ise	is a Japanese footballer currently studying at the Waseda University. Career statistics Club . Notes References External links 2002 births Living people Waseda University alumni Japanese men's footballers Japanese expatriate men's footballers Men's association football midfielders J3 League players Gamba Osaka players Gamba Osaka U-23 players Japanese expatriate sportspeople in the United States Expatriate men's soccer players in the United States
https://en.wikipedia.org/wiki/Foguete	Wellington Cabral Costa (born 1 February 1996), commonly known as Foguete ou Taco de Piquete is a Brazilian footballer. Career statistics Club Honours Club Ventforet Kofu Emperor's Cup: 2022 References External links 1996 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Men's association football defenders Campeonato Brasileiro Série B players CR Vasco da Gama players São Paulo FC players Vila Nova Futebol Clube players Esporte Clube Santo André players FC Cascavel players Kagoshima United FC players Ventforet Kofu players J2 League players J3 League players Brazilian expatriate sportspeople in Japan Expatriate men's footballers in Japan Footballers from Rio de Janeiro (state) People from Itaboraí
https://en.wikipedia.org/wiki/Jessie%20Forbes%20Cameron	Jessie Forbes Cameron (1883 – 1968) was a British mathematician who in 1912 became the first woman to complete her doctorate in mathematics at the University of Marburg in Germany. Life and work Jessie Cameron was born on 8 January 1883 in Stanley, Scotland, one of eight children whose parents were James Cameron, a school principal at a village school in Perthshire, and his wife Jessie Forbes. After attending the Perth Academy in Scotland, Jessie Cameron studied for four semesters at University of Edinburgh. From 1905 to 1908, she studied mathematics at Newnham College, which is part of University of Cambridge, in England, and earned a Magister degree (MA). There, she was ranked the tenth best in her class (earning her the distinction "10th Wrangler"), passed the "Mathematical Tripos" and graduated with a Bachelor of Arts (BA). Postgraduate studies Cameron moved to the University of Göttingen, in Germany, to take two more semesters of math, and finally, she enrolled at the University of Marburg, for three semesters. Under the supervision of distinguished mathematician Kurt Hensel, Cameron wrote her dissertation On the decomposition of a prime number in a composed body. Before her degree was officially completed, however, there was one additional barrier for her to surmount. It seems she had completed the work and won the approval of her advisor, Dr. Hensel, without realizing a lesser-known caveat for graduation from a German university. According to Lorch-Göllner, she received the following letter from the university's Dean of Faculty of Philosophy on 10 November 1911. "Although your doctoral thesis was judged favorably by the representatives of mathematics, especially by Privy Councilor Hensel, your admission to the rigorous examination is unfortunately subject to legal difficulties, which have to be fixed before I make an appointment. According to the regulations of our faculty's doctoral regulations, admission to a doctorate is dependent on proof that at least six semesters were studied at a university in the German Reich or a foreign university set up in the German way. The universities of Great Britain are not among the latter. "You only studied five semesters at German universities and your ten semesters, which you have spent in Scotland and England, cannot be credited easily ... [you will need] a special dispensation from the Minister of Spiritual and Educational Affairs. ... "I wrote to the Minister for this purpose eight days ago. It is hoped that he will give his approval, and then I would presumably be able to schedule the day of rigorosum before Christmas as you requested it."She soon received the Minister's dispensation and passed her exams in "mathematics, physics and philosophy" on 20 December 1911, with the accolade magna cum laude. Thus, Cameron became the first female to earn a PhD in mathematics at that university and her dissertation was published in 1912. On 28 September 1912 Cameron married the lawyer Edward Vince
https://en.wikipedia.org/wiki/Hiroto%20Nakagawa%20%28footballer%2C%20born%202000%29	is a Japanese footballer. Club career Nakagawa made his professional debut on 3 July 2019 in an Emperor's Cup game against Tokushima Vortis. Career statistics Club . Notes References External links 2000 births Living people Association football people from Wakayama Prefecture Japanese men's footballers Men's association football forwards Cerezo Osaka players Ehime FC players
https://en.wikipedia.org/wiki/Takeaki%20Hommura	is a Japanese footballer currently playing as a defender for Giravanz Kitakyushu. Career statistics Club . Notes References External links 1997 births Living people Association football people from Tokyo Ryutsu Keizai University alumni Japanese men's footballers Men's association football defenders J2 League players JEF United Chiba players Giravanz Kitakyushu players
https://en.wikipedia.org/wiki/Nicholas%20Pirihi	Nicholas Gordon Pirihi (born 19 April 1977) is a New Zealand police officer and former first-class cricketer. Pirihi was born at Whangārei in April 1977. He later studied mathematics and science to masters level at the University of Waikato, before gaining a Rhodes Scholarship to read law at Merton College, Oxford. Prior to leaving for England, he was known as a field hockey player and had played for the New Zealand Māori field hockey team. While studying at Oxford, Pirihi played first-class cricket for Oxford University from 1997–99, making eight appearances. He scored 115 runs in his eight matches at an average of 9.58, with a high score of 23. After returning to New Zealand, Pihiri worked in the financial markets. Deciding to realise a lifelong dream of becoming a police officer, he joined the New Zealand Police in 2006. He is currently a detective in the Criminal Investigation Branch. Pirihi plays field hockey for the Northland Police, in addition to assisting the Waikato Hockey Association as an administrator. References External links 1977 births Living people People from Whangārei New Zealand Māori sportspeople New Zealand male field hockey players University of Waikato alumni New Zealand Rhodes Scholars Alumni of Merton College, Oxford New Zealand cricketers Oxford University cricketers New Zealand police officers
https://en.wikipedia.org/wiki/Dominik%20Kirnbauer	Dominik Kirnbauer (born 28 August 2002) is an Austrian footballer currently playing as a midfielder for SV Lafnitz. Career statistics Club Notes References 2002 births Living people Austrian men's footballers Men's association football midfielders Austrian Football Bundesliga players TSV Hartberg players People from Oberwart Footballers from Burgenland
https://en.wikipedia.org/wiki/Dardan%20Shabanhaxhaj	Dardan Shabanhaxhaj (born 23 April 2001) is an Austrian footballer who plays as a winger for Slovenian PrvaLiga club Mura. Career statistics Club References 2001 births Living people Austrian men's footballers Austria men's under-21 international footballers Austrian people of Kosovan descent Austrian people of Albanian descent Kosovan men's footballers Kosovo men's youth international footballers Men's association football wingers SK Sturm Graz players Kapfenberger SV players NŠ Mura players Austrian Football Bundesliga players 2. Liga (Austria) players Slovenian PrvaLiga players Austrian expatriate men's footballers Austrian expatriate sportspeople in Slovenia Expatriate men's footballers in Slovenia
https://en.wikipedia.org/wiki/Nicolas%20Vouilloz%20%28footballer%29	Nicolas Vouilloz (born 11 May 2001) is a Swiss professional footballer who plays as a defender for Swiss club Servette. Career statistics Club Notes References 2001 births Living people People from Chêne-Bougeries Sportspeople from the canton of Geneva Swiss men's footballers Switzerland men's under-21 international footballers Switzerland men's youth international footballers Men's association football defenders Swiss Super League players 2. Liga Interregional players Servette FC players
https://en.wikipedia.org/wiki/Bj%C3%B8rn%20M%C3%A6land	Bjørn Mæland (born 24 February 2001) is a Norwegian footballer currently playing as a defender for Egersund. Career statistics Club Notes References 2001 births Living people Norwegian men's footballers Norway men's youth international footballers Men's association football defenders Eliteserien players Odds BK players Sportspeople from Porsgrunn Footballers from Vestfold og Telemark
https://en.wikipedia.org/wiki/Tom%20Stranneg%C3%A5rd	Tom Henning Strannegård (born 29 April 2002) is a Swedish footballer currently playing as a midfielder for Start. Career statistics Club Notes References External links 2002 births Living people Swedish men's footballers Swedish expatriate men's footballers AIK Fotboll players Vasalunds IF players IK Start players Men's association football midfielders Allsvenskan players Superettan players Norwegian First Division players Sweden men's youth international footballers Expatriate men's footballers in Norway Swedish expatriate sportspeople in Norway Footballers from Stockholm 21st-century Swedish people
https://en.wikipedia.org/wiki/D%C3%A1niel%20Kov%C3%A1cs%20%28footballer%2C%20born%201994%29	Dániel Kovács (born 16 January 1994) is a Hungarian professional footballer who plays for Fehérvár FC. Career statistics . References External links 1994 births Living people People from Gyula Hungarian men's footballers Men's association football goalkeepers Zalaegerszegi TE players Aqvital FC Csákvár players Soroksár SC players Fehérvár FC players Nemzeti Bajnokság I players Footballers from Békés County 21st-century Hungarian people
https://en.wikipedia.org/wiki/Joakim%20Persson%20%28footballer%2C%20born%202002%29	Joakim Birger Persson (born 3 April 2002) is a Swedish footballer who plays as a forward for IK Sirius. Career statistics Club Notes References 2002 births Living people Swedish men's footballers Men's association football forwards IK Sirius Fotboll players IFK Luleå players IK Brage players Allsvenskan players Superettan players Ettan Fotboll players
https://en.wikipedia.org/wiki/Michael%20Eastwood	Michael G. Eastwood is a mathematician at the University of Adelaide, known for his work in twistor theory, conformal differential geometry and invariant differential operators. In 1976 he received a PhD at Princeton University in several complex variables under Robert C. Gunning. He was a member of the twistor research group of Roger Penrose at the University of Oxford and he coauthored the monograph The Penrose Transform: Its Interaction with Representation Theory with Robert Baston. After moving to South Australia in 1985 he was the 1992 recipient of the Australian Mathematical Society Medal and made a Fellow of the Australian Academy of Science in 2005. In 2012 he was named to the inaugural (2013) class of fellows of the American Mathematical Society. References Academic staff of the University of Adelaide Australian mathematicians Princeton University alumni Fellows of the American Mathematical Society Fellows of the Australian Academy of Science Year of birth missing (living people) Living people
https://en.wikipedia.org/wiki/Vrboec	Vrboec () is a village in the municipality of Kruševo, North Macedonia. Demographics In statistics gathered by Vasil Kanchov in 1900, the village of Vrboec was inhabited by 24 Christian Bulgarians and 150 Muslim Albanians. According to the 2021 census, the village had a total of 227 inhabitants. Ethnic groups in the village include: Macedonians 255 Others 1 References Villages in Kruševo Municipality
https://en.wikipedia.org/wiki/Journal%20of%20Agricultural%2C%20Biological%20and%20Environmental%20Statistics	Journal of Agricultural, Biological and Environmental Statistics (JABES) is a peer-reviewed academic journal published by Springer Science+Business Media. It is a joint publication of the International Biometric Society and the American Statistical Association. The journal publishes four issues a year composed of articles that introduce new statistical methods to solve practical problems in the agricultural sciences, the biological sciences, and the environmental sciences. Abstracting and indexing Journal of Agricultural, Biological and Environmental Statistics is abstracted and indexed in the Journal Citation Reports, Mathematical Reviews, Research Papers in Economics, SCImago Journal Rank, Scopus, Science Citation Index, Zentralblatt MATH, among others. According to the Journal Citation Reports, the journal has a 2019 impact factor of 1.650, ranking it 57th out of 93 journals in the category "Biology," 35th out of 59 journals in the category "Mathematical & Computational Biology" and 39th out of 124 journals in the category "Statistics & Probability". External links References Statistics journals Academic journals established in 2001 Springer Science+Business Media academic journals American Statistical Association academic journals English-language journals
https://en.wikipedia.org/wiki/Kim%20Yong-un	Kim Yong-un (; September 6, 1927 – May 30, 2020) was a South Korean mathematician, philosopher, and critic of civilisations. He was active in various fields of mathematics, philosophy, anthropology, and linguistics, and is considered to have established the history of mathematics in Korea. He was a professor of mathematics at Hanyang University. Life Kim Yong-un was born in Tokyo, Japan in 1927. He was liberated in the year he entered Waseda University and returned to his father's hometown of Naju, Jeollanam-do in 1946. While working as a math teacher at Mokpo High School and Gwangju Jeil High School since 1947, he felt the need to popularize math and later wrote several popular math books. After teaching for more than 10 years, he earned a doctorate in science while studying in the United States and Canada. In the late 1970s, he studied the history of mathematics, and since the 1980s, he has analyzed Korea and Japan in a comparative cultural way by combining mathematics and history. The original form, which means collective unconsciousness of the community, and the locality in which the community is located, were involved in the development of language and history. In 1983, he founded the Korean Mathematical History Association and became the first chairman, and in 1994, he participated in the development process of Ungjin Publishing (now Ungjin Thinkbig), a mathematics learning magazine brand of Ungjin Publishing (now Ungjin Thinkbig), along with his younger brother, Professor Kim Yong-guk of Hanyang University. This is also the predecessor of Thinkbig, a learning center brand of Ungjin. He wrote more than 150 books throughout his life. Academic background Bachelor's degree in mining at Waseda University in Japan (dropout) Bachelor's degree in mathematics at Chosun University Graduate School of Orburn University in the U.S. (Bachelor of Science) Graduate School of University of Alberta, Canada (Doctor of Science) Career Assistant Professor of University of Wisconsin (1962-1965) Visiting professor at Kobe University in Japan A visiting professor at Tokyo University in Japan Guest Professor of the Center for International Cultural Research in Japan Professor of Mathematics at Hanyang University (1969-1993) President of the Korean Mathematical History Society Professor emeritus of mathematics at Hanyang University (1994-current) Chairman of the Korea Broadcasting Culture Promotion Agency (2000-2003) Director of the Korean Mathematical and Cultural Institute Books References 20th-century South Korean mathematicians Academic staff of Hanyang University Waseda University alumni University of Alberta alumni 1927 births 2020 deaths Academics from Tokyo Historians of mathematics South Korean philosophers South Korean historians
https://en.wikipedia.org/wiki/Pauline%20Barrieu	Pauline Barrieu is a French financial statistician, probability theorist, and expert on financial risk assessment, risk transfer, and uncertainty quantification. She is a professor of statistics in the London School of Economics. Education and career Barrieu earned an MBA at the ESSEC Business School in 1997, a DEA in probability theory at Pierre and Marie Curie University in 1998, and a PhD in 2002, simultaneously in finance at HEC Paris and in applied mathematics at Pierre and Marie Curie University, supervised by at HEC Paris and by Nicole El Karoui at Pierre and Marie Curie University. She has been a member of the statistics department at the London School of Economics since 2002, becoming a professor in 2012 and serving as head of the department for 2016–2019. Recognition In 2003, Barrieu was one of the winners of the Prix de l'Actuariat, an annual international award for top doctoral dissertations in actuarial science. She was the 2018 winner of the Louis Bachelier Prize. The award cited her work on "how we address model risk, uncertainty, and risk sharing under uncertainty". References External links Home page Year of birth missing (living people) Living people French economists French statisticians Women economists Women statisticians Academics of the London School of Economics
https://en.wikipedia.org/wiki/Barrieu	Barrieu is a surname. Notable people with the surname include: Pauline Barrieu, French financial statistician and probability theorist Pierre Barrieu (born 1972), French football coach See also Barrie (name)
https://en.wikipedia.org/wiki/Knowledge%20graph	In knowledge representation and reasoning, a knowledge graph is a knowledge base that uses a graph-structured data model or topology to integrate data. Knowledge graphs are often used to store interlinked descriptions of entities objects, events, situations or abstract concepts while also encoding the semantics underlying the used terminology. Since the development of the Semantic Web, knowledge graphs are often associated with linked open data projects, focusing on the connections between concepts and entities. They are also prominently associated with and used by search engines such as Google, Bing, Yext and Yahoo; knowledge-engines and question-answering services such as WolframAlpha, Apple's Siri, and Amazon Alexa; and social networks such as LinkedIn and Facebook. History The term was coined as early as 1972 by the Austrian linguist Edgar W. Schneider, in a discussion of how to build modular instructional systems for courses. In the late 1980s, the University of Groningen and University of Twente jointly began a project called Knowledge Graphs, focusing on the design of semantic networks with edges restricted to a limited set of relations, to facilitate algebras on the graph. In subsequent decades, the distinction between semantic networks and knowledge graphs was blurred. Some early knowledge graphs were topic-specific. In 1985, Wordnet was founded, capturing semantic relationships between words and meanings an application of this idea to language itself. In 2005, Marc Wirk founded Geonames to capture relationships between different geographic names and locales and associated entities. In 1998 Andrew Edmonds of Science in Finance Ltd in the UK created a system called ThinkBase that offered fuzzy-logic based reasoning in a graphical context. In 2007, both DBpedia and Freebase were founded as graph-based knowledge repositories for general-purpose knowledge. DBpedia focused exclusively on data extracted from Wikipedia, while Freebase also included a range of public datasets. Neither described themselves as a 'knowledge graph' but developed and described related concepts. In 2012, Google introduced their Knowledge Graph, building on DBpedia and Freebase among other sources. They later incorporated RDFa, Microdata, JSON-LD content extracted from indexed web pages, including the CIA World Factbook, Wikidata, and Wikipedia. Entity and relationship types associated with this knowledge graph have been further organized using terms from the schema.org vocabulary. The Google Knowledge Graph became a successful complement to string-based search within Google, and its popularity online brought the term into more common use. Since then, several large multinationals have advertised their knowledge graphs use, further popularising the term. These include Facebook, LinkedIn, Airbnb, Microsoft, Amazon, Uber and eBay. In 2019, IEEE combined its annual international conferences on "Big Knowledge" and "Data Mining and Intelligent Computing" into the Int
https://en.wikipedia.org/wiki/Spatial%20Statistics	Spatial Statistics is an academic journal published by Elsevier about spatial statistics. Its editor-in-chief is Alfred Stein; its 2018 impact factor is 1.219. References Elsevier academic journals Statistics journals Geostatistics
https://en.wikipedia.org/wiki/Ideal%20polyhedron	In three-dimensional hyperbolic geometry, an ideal polyhedron is a convex polyhedron all of whose vertices are ideal points, points "at infinity" rather than interior to three-dimensional hyperbolic space. It can be defined as the convex hull of a finite set of ideal points. An ideal polyhedron has ideal polygons as its faces, meeting along lines of the hyperbolic space. The Platonic solids and Archimedean solids have ideal versions, with the same combinatorial structure as their more familiar Euclidean versions. Several uniform hyperbolic honeycombs divide hyperbolic space into cells of these shapes, much like the familiar division of Euclidean space into cubes. However, not all polyhedra can be represented as ideal polyhedra – a polyhedron can be ideal only when it can be represented in Euclidean geometry with all its vertices on a circumscribed sphere. Using linear programming, it is possible to test whether a given polyhedron has an ideal version, in polynomial time. Every two ideal polyhedra with the same number of vertices have the same surface area, and it is possible to calculate the volume of an ideal polyhedron using the Lobachevsky function. The surface of an ideal polyhedron forms a hyperbolic manifold, topologically equivalent to a punctured sphere, and every such manifold forms the surface of a unique ideal polyhedron. Examples and counterexamples An ideal polyhedron can be constructed as the convex hull of a finite set of ideal points of hyperbolic space, whenever the points do not all lie on a single plane. The resulting shape is the intersection of all closed half-spaces that have the given ideal points as limit points. Alternatively, any Euclidean convex polyhedron that has a circumscribed sphere can be reinterpreted as an ideal polyhedron by interpreting the interior of the sphere as a Klein model for hyperbolic space. In the Klein model, every Euclidean polyhedron enclosed by the sphere represents a hyperbolic polyhedron, and every Euclidean polyhedron with its vertices on the sphere represents an ideal hyperbolic polyhedron. Every isogonal convex polyhedron (one with symmetries taking every vertex to every other vertex) can be represented as an ideal polyhedron, in a way that respects its symmetries, because it has a circumscribed sphere centered at the center of symmetry of the polyhedron. In particular, this implies that the Platonic solids and the Archimedean solids all have ideal forms. However, another highly symmetric class of polyhedra, the Catalan solids, do not all have ideal forms. The Catalan solids are the dual polyhedra to the Archimedean solids, and have symmetries taking any face to any other face. Catalan solids that cannot be ideal include the rhombic dodecahedron and the triakis tetrahedron. Removing certain triples of vertices from the triakis tetrahedron separates the remaining vertices into multiple connected components. When no such three-vertex separation exists, a polyhedron is said to be 4-connec
https://en.wikipedia.org/wiki/M%C3%A1rk%20Bonnyai	Márk Bonnyai (born 28 June 1999) is a Hungarian professional footballer who plays for Veszprém. Career statistics . References 1999 births Living people People from Nagyatád Hungarian men's footballers Men's association football goalkeepers Kaposvári Rákóczi FC players Nagyatádi FC players FC Veszprém footballers Nemzeti Bajnokság I players Nemzeti Bajnokság II players Nemzeti Bajnokság III players Footballers from Somogy County
https://en.wikipedia.org/wiki/Karin%20Melnick	Karen Melnick is a mathematician and associate professor at University of Maryland, College Park. She specializes in differential geometry and was most recently awarded the 2020-2021 Joan and Joseph Birman Fellowship for Women Scholars by the American Mathematical Society. Research Melnick's primary research area is in differential-geometric aspects of rigidity, where she focuses on global and local results relating the automorphisms of a differential-geometric structure with the geometric and topological properties of the space. In addition, she is a leader in research in Lorentzian geometry and has done substantial work on the Lorentzian Lichnerowicz conjecture. Melnick also has research interests in conformal pseudo-Riemannian structures, parabolic Cartan geometries in general, and smooth dynamics. Her research has earned her recognition as a strong collaborator on groundbreaking work with her fellow mathematicians. Melnick has authored or co-authored fourteen academic papers in her field and has been cited by over sixty authors. She has also presented her work in a variety of seminars and colloquia internationally. Education Melnick received her Ph.D. in Mathematics from the University of Chicago in 2006, where she also earned her Master of Science in Mathematics in 2000, while working under the guidance of doctoral advisor Benson Farb. Her dissertation research focused on compact Lorentz manifolds with local symmetry. Prior to her graduate studies, Melnick received her Bachelor of Arts, also in Mathematics, from Reed College in 1999. Career Melnick currently works as an associate professor in the Department of Mathematics at University of Maryland, College Park, where she worked also worked as an assistant professor beginning in 2009 prior to her promotion. Before working at UMD, Melnick held the position of Gibbs Assistant Professor at Yale University while on an NSF Postdoctoral Research Fellowship. In her career, Melnick has contributed significant service to the mathematics profession. In spring 2020, she taught a graduate topics course in exterior differential systems. In addition, she is and has been involved in organizing multiple workshops and seminars, including a two-week workshop on Cartan Connections, Geometry of Homogeneous Spaces, and Dynamics at the Erwin Schrödinger Institute in 2011, the weekly Geometry-Topology Seminar at University of Maryland, and an upcoming conference on geometric structures at Goethe University Frankfurt in 2021. She is also an advocate for women in her field, speaking at events such as the 2014 Nebraska Conference for Undergraduate Women in Mathematics. Honors Most recently, Melnick was awarded the 2020-2021 Joan and Joseph Birman Fellowship for Women Scholars by the American Mathematical Society for her research on differential-geometric aspects of rigidity. This prestigious fellowship, founded by mathematician Joan Birman and physicist Joseph L. Birman, is awarded to talented, mid-career wome
https://en.wikipedia.org/wiki/D.%20W.%20J.%20Perera	D. W. J. Perera was a Ceylonese Sinhalese teacher and member of the Senate of Ceylon. Educated at Sri Sumangala College, Panadura, Perera became a mathematics master at Ananda College under Principal P. de S. Kularatne. Following Kularatne's retirement from Ananda College and subsequent appointment as Manager of the Buddhist Theosophical Society (BTS) Schools, Perera followed and joined the staff at Sri Sumangala College which was administrated by the Buddhist Theosophical Society (BTS) in 1944. A longstanding member of Lanka Sama Samaja Party, he was nominated by the Bolshevik–Leninist Party of India, Ceylon and Burma and elected to the Senate of Ceylon in 1947. References Alumni of Sri Sumangala College, Panadura Sinhalese teachers Members of the Senate of Ceylon People from British Ceylon Lanka Sama Samaja Party politicians Year of death missing
https://en.wikipedia.org/wiki/Abdoulaye%20Sall	Abdoulaye Sall (born 28 December 2000) is a Senegalese footballer who plays as a forward for Italian Serie D club Ghiviborgo. Career statistics Club Notes References External links 2000 births Living people Senegalese men's footballers Men's association football forwards Serie C players Serie D players ACD Pro Dronero players Imolese Calcio 1919 players Senegalese expatriate men's footballers Senegalese expatriate sportspeople in Italy Expatriate men's footballers in Italy
https://en.wikipedia.org/wiki/North-south%20traffic	In computer networking, north-south traffic is network traffic flowing into and out of a data center. Traffic Based on the most commonly deployed network topology of systems within a data center, north-south traffic typically indicates data flow that either enters or leaves the data center from/to a system physically residing outside the data center, such as user to server. Southbound traffic is data entering the data center (through a firewall and/or other networking infrastructure). Data exiting the data center is northbound traffic, commonly routed through a firewall to Internet space. The other direction of traffic flow is east-west traffic which typically indicates data flow within a data center. See also Virtual private network References Data processing Computer data
https://en.wikipedia.org/wiki/Johanna%20G.%20Ne%C5%A1lehov%C3%A1	Johanna G. Nešlehová (born July 26, 1977) is a Czech mathematical statistician who works in Canada at McGill University as a professor in the department of mathematics and statistics. Her research interests include copulas, extreme value theory, multivariate statistics, and operational risk. Education and career Nešlehová is originally from Prague, the daughter of painter Pavel Nešleha and art historian . She studied at the Charles University, the University of Hamburg, and the University of Oldenburg, earning a degree (vordiplom) from University of Hamburg in 1999, a master's degree (diplom) from the University of Hamburg in 2000, and a doctorate from the University of Oldenburg in 2004. Her dissertation, Dependence of Non-continuous Random Variables, was supervised by . After working as a postdoctoral researcher and Heinz Hopf Lecturer at ETH Zürich, she joined the McGill University faculty in 2009. Since October 2022 she is also a professor at WU Vienna University of Economics and Business. Book With Erhard Cramer, Nešlehová is the author of a German-language undergraduate textbook in introductory mathematics, Vorkurs Mathematik: Arbeitsbuch zum Studienbeginn in Bachelor-Studiengängen (Springer, 2005; 7th ed., 2018). Recognition Nešlehová was named as an Elected Member of the International Statistical Institute in 2011. In 2020 she was named a Fellow of the Institute of Mathematical Statistics. She was the 2019 winner of the CRM-SSC Prize in Statistics "for fundamental contributions to multivariate statistics, and in particular stochastic dependence modeling and extreme-value theory, and for her efforts to promote the sound application of statistics in risk management". In 2023, Nešlehová was the second statistician (after Nancy Reid in 1995) to receive the Krieger–Nelson Prize of the Canadian Mathematical Society. Personal life Nešlehová is married to mathematician Christian Genest. References External links Living people Czech statisticians Canadian statisticians Women statisticians Charles University alumni University of Hamburg alumni University of Oldenburg alumni Academic staff of McGill University Elected Members of the International Statistical Institute Fellows of the Institute of Mathematical Statistics 1977 births
https://en.wikipedia.org/wiki/Daniel%20McGee	Daniel McGee is an American statistician and professor emeritus of statistics at Florida State University, where he formerly chaired the department of statistics. Before joining the faculty of Florida State in 2002, he worked for the United States Public Health Service and in academic medicine. He chaired Florida State's department of statistics from 2005 to 2011 and retired from the faculty there in May 2019. He was elected a Fellow of the American Statistical Association in 1992. References External links Faculty page Living people American statisticians University of California, Berkeley alumni Johns Hopkins University alumni Florida State University faculty Fellows of the American Statistical Association United States Public Health Service personnel Year of birth missing (living people)
https://en.wikipedia.org/wiki/A%20Treatise%20on%20the%20Circle%20and%20the%20Sphere	A Treatise on the Circle and the Sphere is a mathematics book on circles, spheres, and inversive geometry. It was written by Julian Coolidge, and published by the Clarendon Press in 1916. The Chelsea Publishing Company published a corrected reprint in 1971, and after the American Mathematical Society acquired Chelsea Publishing it was reprinted again in 1997. Topics As is now standard in inversive geometry, the book extends the Euclidean plane to its one-point compactification, and considers Euclidean lines to be a degenerate case of circles, passing through the point at infinity. It identifies every circle with the inversion through it, and studies circle inversions as a group, the group of Möbius transformations of the extended plane. Another key tool used by the book are the "tetracyclic coordinates" of a circle, quadruples of complex numbers describing the circle in the complex plane as the solutions to the equation . It applies similar methods in three dimensions to identify spheres (and planes as degenerate spheres) with the inversions through them, and to coordinatize spheres by "pentacyclic coordinates". Other topics described in the book include: Tangent circles and pencils of circles Steiner chains, rings of circles tangent to two given circles Ptolemy's theorem on the sides and diagonals of quadrilaterals inscribed in circles Triangle geometry, and circles associated with triangles, including the nine-point circle, Brocard circle, and Lemoine circle The Problem of Apollonius on constructing a circle tangent to three given circles, and the Malfatti problem of constructing three mutually-tangent circles, each tangent to two sides of a given triangle The work of Wilhelm Fiedler on "cyclography", constructions involving circles and spheres The Mohr–Mascheroni theorem, that in straightedge and compass constructions, it is possible to use only the compass Laguerre transformations, analogues of Möbius transformations for oriented projective geometry Dupin cyclides, shapes obtained from cylinders and tori by inversion Legacy At the time of its original publication this book was called encyclopedic, and "likely to become and remain the standard for a long period". It has since been called a classic, in part because of its unification of aspects of the subject previously studied separately in synthetic geometry, analytic geometry, projective geometry, and differential geometry. At the time of its 1971 reprint, it was still considered "one of the most complete publications on the circle and the sphere", and "an excellent reference". References External links A Treatise on the Circle and the Sphere (1916 edition) at the Internet Archive Circles Spherical geometry Inversive geometry Mathematics books 1916 non-fiction books Treatises Clarendon Press books
https://en.wikipedia.org/wiki/G%C3%BCnther%20Frei	Günther Hans Frei (born 19 May 1942 in St. Gallen) is a Swiss mathematician and historian of mathematics. Education and career Frei studied mathematics, physics and languages at the University of Zurich. There he received his doctoral degree in 1968 with advisor Bartel Leendert van der Waerden and dissertation on geometry (Beiträge zur axiomatischen Inhaltstheorie). He became an instructor in 1968 at the University of Notre Dame and in 1970 at Quebec's Université Laval, where he became in 1971 a professor. He remained there until he retired as professor emeritus and returned to Switzerland to live in Hombrechtikon. Frei's research deals with number theory and the history of mathematics, especially the history of number theory in the 19th and 20th centuries and Swiss mathematics. He has written extensively on the life and work of Helmut Hasse. Frei is a member of the Euler Committee of the Swiss Academy of Sciences. Selected publications Felix Klein. A biographical sketch. In: Jahrbuch Überblicke Mathematik. 1984, pp. 229–254 (and Felix Klein. In: Collection Mathématique. Université Laval, vol. 40, 1981). Leben und Werk von Helmut Hasse. In: Collection Mathématique. Université Laval, 1977 (and Helmut Hasse. In: Collection Math. vol. 38, 1981). Helmut Hasse. In: Expositiones Mathematicae. vol. 3. 1985, pp. 55–69. with Urs Stammbach: Hermann Weyl und die Mathematik an der ETH Zürich 1913–1930. Birkhäuser 1992. with Urs Stammbach: Die Mathematik an den Zürcher Hochschulen. Birkhäuser 1994. with Urs Stammbach: Mathematicians and Mathematics in Zürich, at the university and the ETH. Schriftenreihe der ETH-Bibliothek 2007. as editor with Peter Roquette: Emil Artin und Helmut Hasse – die Korrespondenz 1923–1934. Universitätsverlag Göttingen 2008 (originally published in 1981 in Collection Mathématique. Universität Laval). 2014 hbk translation; Emil and Helmut Hasse: The Correspondence 1923–1958, 2014 ebook as editor: Der Briefwechsel David Hilbert–Felix Klein 1886–1918. Vandenhoeck und Ruprecht 1985. with Urs Stammbach: Heinz Hopf. In: Ioan James (ed.): History of Topology. Elsevier 1999. The unpublished section eight: on the way to function fields over finite fields. In: Catherine Goldstein, Joachim Schwermer, Norbert Schappacher (eds.) The shaping of arithmetic – after C. F. Gauss´s Disquisitiones Arithmeticae. Springer 2007 (also in Nachrichten Akad. Wiss. Göttingen 2006). Heinrich Weber and the emergence of class field theory. in David Rowe, John McCleary (eds.) History of modern mathematics. Academic Press, 1989, pp. 424–450. (See Heinrich Martin Weber.) Chapter 6. Developments in the theory of algebra over number fields: A new foundation for the Hasse norm residue symbol and new approaches to both the Artin reciprocity law and class field theory. in Jeremy Gray, Karen Parshall (eds.): Episodes in the history of modern algebra 1800–1950. American Mathematical Society 2007, pp. 117–151. Chapter 6, 2011 pbk edition The reciprocit
https://en.wikipedia.org/wiki/Tin%20Hrvoj	Tin Hrvoj (born 6 June 2001) is a Croatian footballer who plays as a right-back for Slovenian club Radomlje. Career statistics Club References External links 2001 births Living people Footballers from Zagreb Croatian men's footballers Men's association football fullbacks Croatia men's youth international footballers First Football League (Croatia) players Croatian Football League players Slovenian PrvaLiga players GNK Dinamo Zagreb II players GNK Dinamo Zagreb players NK Hrvatski Dragovoljac players NK Radomlje players Croatian expatriate men's footballers Croatian expatriate sportspeople in Slovenia Expatriate men's footballers in Slovenia
https://en.wikipedia.org/wiki/Erica%20Moodie	Erica Eleanor Margret Moodie is a Canadian biostatistician known for her work on dynamic treatment regimes. She is Canada Research Chair and Professor in the Department of Epidemiology, Biostatistics, and Occupational Health at McGill University. Education and career Moodie graduated from the University of Winnipeg in 2000 with a double major in mathematics and statistics. She earned a master's degree in epidemiology at the University of Cambridge in 2001, a second master's degree in biostatistics at the University of Washington in 2004, and a Ph.D. in biostatistics at the University of Washington in 2006. Her dissertation was Inference for optimal dynamic treatment regimes, and was supervised by Thomas Richardson. She has been on the McGill University faculty since 2006. Books With B. Chakraborty, Moodie is the coauthor of the book Statistical Methods for Dynamic Treatment Regimes: Reinforcement Learning, Causal Inference, and Personalized Medicine (Springer, 2013). She is the co-editor, with M. R. Kosorok, of Adaptive Treatment Strategies in Practice: Planning Trials and Analyzing Data for Personalized Medicine (SIAM, 2016). Recognition Moodie became an Elected Member of the International Statistical Institute in 2015. She was the 2020 winner of the CRM-SSC Prize in Statistics "for her outstanding contributions to biostatistics, notably in causal inference, precision medicine, and dynamic treatment regimes, and her influential contributions to substantive areas of application such as HIV and mental health". Family Moodie is originally from Winnipeg, Manitoba; her parents, Ric Moodie and Patricia F. Moodie, are a zoologist and biostatistician respectively, and her older sister Zoe Moodie, brother-in-law Jonathan Wakefield, and husband David A. Stephens are all also (bio)statisticians. References External links McGill home page Personal home page Year of birth missing (living people) Living people Canadian statisticians People from Winnipeg Women statisticians University of Winnipeg alumni Alumni of the University of Cambridge University of Washington alumni Academic staff of McGill University Elected Members of the International Statistical Institute
https://en.wikipedia.org/wiki/Lei%20Sun	Lei Sun is a Chinese and Canadian statistical geneticist at the University of Toronto, where she is affiliated both with the department of biostatistics in the Dalla Lana School of Public Health and the department of statistical sciences in the faculty of arts and science. Education and career Sun graduated in 1995 from Fudan University with a bachelor's degree in mathematics. She completed her Ph.D. in statistics in 2001 at the University of Chicago. Her dissertation, Two Statistical Problems in Human Genetics, was supervised by Mary Sara McPeek. She joined the Dalla Lana School of Public Health in 2001, and at the same time took a courtesy appointment in statistical sciences. On becoming a full professor in 2014, she changed her appointment to be 25% time in the School of Public Health and 75% time in statistical sciences. Recognition Sun was the 2017 winner of the CRM-SSC Prize in Statistics "for original and influential contributions to statistical methodology, statistical genetics, and human genetics, including important new developments in false discovery rate control and in robust methods for genetic association studies, and for her outstanding contributions to mentoring and training in statistical genetics in Canada". References External links Home page Year of birth missing (living people) Living people Chinese statisticians Canadian statisticians Statistical geneticists Women statisticians Fudan University alumni University of Chicago alumni Academic staff of the University of Toronto
https://en.wikipedia.org/wiki/Ioannis%20Kontoyiannis	Ioannis Kontoyiannis (born January 1972) is a Greek mathematician and information theorist. He is the Churchill Professor of Mathematics for Operational Research with the Statistical Laboratory, in the Department of Pure Mathematics and Mathematical Statistics, of the University of Cambridge. He is also a Fellow of Darwin College, Cambridge, an affiliated member of the Division of Information Engineering, Cambridge, a Research Fellow of the Foundation for Research and Technology - Hellas, a Senior Member of Robinson College, Cambridge, and a trustee of the Rollo Davidson Trust. His research interests are in information theory, probability and statistics, including their applications in data compression, bioinformatics, neuroscience, machine learning, and the connections between core information-theoretic ideas and results in probability theory and additive combinatorics. Academic biography Kontoyiannis earned a B.S. in mathematics from Imperial College, University of London (1992), he obtained a distinction in Part III of the Cambridge University Pure Mathematics Tripos (1993), and he earned an M.S. in statistics (1997) and a Ph.D. in electrical engineering (1998), both from Stanford University. Between 1998 and 2018 he taught at Purdue University, Brown University, Columbia University, and at the Athens University of Economics and Business. In January 2018 he joined the Information Engineering Division at Cambridge University, as Professor of Information and Communications, and Head of the Signal Processing and Communications Laboratory. Since June 2020 he has been with the Statistical Laboratory, in the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, where he holds the Churchill Chair in Mathematics. Awards and honors Manning endowed assistant professorship (2002) Alfred P. Sloan Foundation Research Fellowship (2004) Honorary Master of Arts Degree Ad Eundem, Brown University (2005) Marie Curie Fellowship (2009) IEEE Fellow (2011) References External links Ioannis Kontoyiannis' web page at Cambridge 1972 births Living people Information theorists Fellows of Darwin College, Cambridge Alumni of Imperial College London Greek expatriates in the United Kingdom Stanford University alumni Greek expatriates in the United States Purdue University faculty Brown University faculty Columbia University faculty Sloan Fellows Fellow Members of the IEEE 20th-century Greek mathematicians 21st-century Greek mathematicians Engineering professors at the University of Cambridge
https://en.wikipedia.org/wiki/Danylo%20Ryabenko	Danylo Romanovych Ryabenko (; born 9 October 1998) is a Ukrainian professional footballer. Career statistics . References 1998 births Living people Ukrainian men's footballers Ukrainian expatriate men's footballers Men's association football goalkeepers Lori FC players CSKA Pamir Dushanbe players Mezőkövesdi SE footballers Nemzeti Bajnokság I players Expatriate men's footballers in Armenia Expatriate men's footballers in Tajikistan Expatriate men's footballers in Hungary Ukrainian expatriate sportspeople in Armenia Ukrainian expatriate sportspeople in Tajikistan Ukrainian expatriate sportspeople in Hungary Footballers from Makiivka
https://en.wikipedia.org/wiki/Keanin%20Ayer	Keanin Ayer Boya (born 21 April 2000) is a South African soccer player currently playing as a midfielder for Sandefjord. Career statistics Notes References 2000 births Living people South African men's soccer players South African expatriate men's soccer players Men's association football midfielders Superettan players Allsvenskan players Right to Dream Academy players Varbergs BoIS players South African expatriate sportspeople in Sweden Expatriate men's footballers in Ghana Expatriate men's footballers in Sweden Soccer players from Johannesburg
https://en.wikipedia.org/wiki/J%C3%BCrg%20Peter%20Buser	Jürg Peter Buser, known as Peter Buser, (born 27 February 1946 in Basel) is a Swiss mathematician, specializing in differential geometry and global analysis. Education and career Buser received his doctorate in 1976 from the University of Basel with advisor Heinz Huber and thesis Untersuchungen über den ersten Eigenwert des Laplaceoperators auf kompakten Flächen (Studies on the first eigenvalue of the Laplace operator on compact surfaces). As a post-doctoral student he was at the University of Bonn, the University of Minnesota. and the State University of New York at Stony Brook, before he habilitated at the University of Bonn with a thesis on the length spectrum of Riemann surfaces. Buser is known for his construction of curved isospectral surfaces (published in 1986 and 1988). His 1988 construction led to a negative solution to Mark Kac's famous 1966 problem Can one hear the shape of a drum?. The negative solution was published in 1992 by Scott Wolpert, David Webb and Carolyn S. Gordon. The is named after him and Jeff Cheeger. He has been a professor at the École Polytechnique Fédérale de Lausanne (EPFL) since 1982. From 2004 to 2005 he was president of the Swiss Mathematical Society. In 2003 he was made an honorary doctor of the University of Helsinki. Selected publications with Hermann Karcher: with Hermann Karcher: Gromov`s almost flat manifolds, Astérisque 1981, Nr. 81, p. 148 "A note on the isoperimetric constant." In Annales scientifiques de l'École Normale Supérieure, vol. 15, no. 2, 1982, pp. 213-230. "On the bipartition of graphs." Discrete Applied Mathematics 9, no. 1 (1984): 105–109. Isospectral Riemann Surfaces, Annales Institut Fourier (Grenoble), vol. 36, 1986, pp. 167–192 Cayley graphs and planar isospectral domains, in Toshikazu Sunada (ed.), Geometry and Analysis on Manifolds, Springer Verlag, Lecture Notes in Mathematics, vol. 1339, 1988, pp. 64–77 Geometry and Spectra of Compact Riemann Surfaces, Birkhäuser 1992; 2010 pbk reprint with John Horton Conway, Peter Doyle, and Klaus-Dieter Semmler: with Peter Sarnak: with Mika Seppälä: References External links Homepage at EPFL Swiss mathematicians Differential geometers University of Basel alumni University of Bonn alumni Academic staff of the École Polytechnique Fédérale de Lausanne 1946 births Living people
https://en.wikipedia.org/wiki/List%20of%20Paris%20Saint-Germain%20F%C3%A9minine%20records%20and%20statistics	Paris Saint-Germain Féminine have won four titles. Domestically, the capital side have clinched one Division 1 championship, three French Cups and one Division 2 title. In international club football, Paris have reached the UEFA Champions League final twice (2015 and 2017). Additionally, PSG have won one unofficial title. Influential officials and players in the club's history include most decorated president Nasser Al-Khelaifi, trophy-winning managers Sébastien Thierry, Camillo Vaz, Bernard Mendy, Olivier Echouafni and Didier Ollé-Nicolle, record appearance maker and longest-serving captain Sabrina Delannoy, and all-time top scorer Marie-Antoinette Katoto. Honours . Official shared record Unofficial shared record Competitive record . Missing data from matches of the Ligue de Paris Île-de-France (1971–1979) and Division 2 (1993–94, 1996–97 and 1997–98 seasons). Club Matches All-time record win: 19–0 (away to Bourges 18, Coupe de France, 8 January 2017). All-time record defeat: 1–9 (away to Hénin-Beaumont, Division 1, 18 September 1994). Record win in Division 1: 14–0 (away to Issy, 14 November 2020). Record defeat in Division 1: 0–7 (home to Montpellier, 8 June 2008). Record win in Coupe de France: 19–0 (away to Bourges 18, 8 January 2017). Record defeat in Coupe de France: 0–7 (home to Paris FC, 5 May 2005). Record win in UEFA Champions League: 9–0 (home to Olimpia Cluj, 14 October 2015). Record defeat in UEFA Champions League: 0–7 (away to Lyon, 23 April 2016). Highest home attendance (National Record): 43,254 (vs. Lyon at the Parc des Princes, UEFA Champions League, 30 April 2022). First match at the Parc des Princes: home to Paris FC (1–0 win), Division 1, 18 October 2009. Seasons Most matches played in all competitions: 38 in 2022–23. Most goals scored in all competitions: 118 in 2021–22. Most goals scored in Division 1: 88 in 2014–15. Fewest goals conceded in all competitions: 11 in 1979–80, 1982–83 and 2000–01. Fewest goals conceded in Division 1: 4 in 2020–21. Most wins in all competitions: 28 in 2021–22. Most wins in Division 1: 20 in 2014–15 and 2020–21. Most points in Division 1: 62 in 2020–21. Personnel Presidents Most decorated: 3 titles – Nasser Al-Khelaifi. Longest-serving: 13 years, 4 months, 23 days – Francis Borelli. Managers Most decorated: 1 title – Olivier Echouafni, Camillo Vaz, Bernard Mendy, Didier Ollé-Nicolle and Sébastien Thierry. Most matches managed: 126 matches – Farid Benstiti. Most matches won: 97 wins – Farid Benstiti. Highest win percentage: 80.00% – Didier Ollé-Nicolle. Longest-serving: 5 years – Sébastien Thierry. Players Appearances Most appearances in Division 1: 244 – Sabrina Delannoy. Most appearances in Coupe de France: 45 – Sabrina Delannoy. Most appearances in the UEFA Champions League: 41 – Grace Geyoro. All-time most appearances . Goalscorers Most goals in Division 1: 109 – Marie-Antoinette Katoto. Most goals in Coupe de France: 35 – Marie-Laure Delie. Most goals in t
https://en.wikipedia.org/wiki/Lily%20Wang	Li Lily Wang is a Chinese statistician whose research interests include nonparametric statistics, semiparametric statistics, large data sets and high-dimensional data, and official statistics. She is an associate professor of statistics at George Mason University . Education and career Wang studied economics at Tongji University, graduating in 2000, and earned a master's degree in mathematics from Tongji University in 2003. She completed a Ph.D. in statistics at Michigan State University in 2007. Her dissertation, Polynomial Spline Smoothing for Nonlinear Time Series, was supervised by Li-Jian Yang. She became a faculty member in the University of Georgia department of statistics in 2007, and moved to Iowa State University as an associate professor in 2014. While holding these faculty positions, she has also worked as a visiting scholar at the United States Census Bureau, Bureau of Labor Statistics, and U.S. Securities and Exchange Commission. Recognition Wang was named an Elected Member of the International Statistical Institute in 2008. In 2020 she was named a Fellow of the Institute of Mathematical Statistics "for contributions to spatial, survey, image and functional analysis using nonparametric and semiparametric methods, especially to partially linear models, confidence envelopes and bivariate smoothing". She became a Fellow of the American Statistical Association in 2021. References External links Home page Year of birth missing (living people) Living people Chinese statisticians American statisticians Women statisticians Tongji University alumni Michigan State University alumni University of Georgia faculty Iowa State University faculty Elected Members of the International Statistical Institute Fellows of the Institute of Mathematical Statistics Fellows of the American Statistical Association
https://en.wikipedia.org/wiki/How%20Round%20Is%20Your%20Circle%3F	How Round Is Your Circle? Where Engineering and Mathematics Meet is a book on the mathematics of physical objects, for a popular audience. It was written by chemical engineer John Bryant and mathematics educator Chris Sangwin, and published by the Princeton University Press in 2008. Topics The book has 13 chapters, whose topics include: Lines, the thickness of physically drawn or cut lines, and the problem of testing straightness of physical objects The construction of physical measuring and calculating devices including rulers, protractors, pantographs, planimeters, integrators, and slide rules Mechanical linkages, pantographs, four-bar linkages, and the problem of converting rotary to linear motion, solved by the Peaucellier–Lipkin linkage and by Hart's inversor Geometric dissections, straightedge and compass constructions, angle trisection, and mathematical origami The catenary and the tractrix, curves formed from physical forces, and their use in bridges and bearings Approximation by rational numbers, discretization and pixelization, gear ratios, and the approximations involved in calendar systems The roundness of objects, non-circular objects of constant width, including the Reuleaux triangle and certain coins, and their use in drilling square holes Stability and mechanical equilibrium of objects, overhanging objects and the block-stacking problem, supereggs, and objects with only one stable resting position (unfortunately not including the Gömböc, which was discovered too recently to be included) The book emphasizes the construction of physical models, and includes many plates of the authors' own models, detailed construction plans, and illustrations. Audience and reception Doug Manchester characterizes the topic of the book as "recreational engineering". It only requires a standard background in mathematics including basic geometry, trigonometry, and a small amount of calculus. Owen Smith calls it "a great book for engineers and mathematicians, as well as the interested lay person", writing that it is particularly good at laying bare the mathematical foundations of seemingly-simple problems. Similarly, Ronald Huston recommends it to "mathematicians, engineers, and physicists", as well as interested members of the general public. Matthew Killeya writes approvingly of the book's intuitive explanations for its calculations and the motivation it adds to the mathematics it applies. However, although reviewer Tim Erickson calls the book "exuberant and eclectic", reviewers Andrew Whelan and William Satzer disagree, both finding fault with the book's lack of focus. References Applied mathematics Mathematics books 2008 non-fiction books
https://en.wikipedia.org/wiki/Antoine%20Song	Antoine Song (born 18 July 1992 in Paris) is a French mathematician whose research concerns differential geometry. In 2018, he proved Yau's conjecture. He is a Clay Research Fellow (2019–2024). He obtained his Ph.D. from Princeton University in 2019 under the supervision of Fernando Codá Marques. Existence of minimal surfaces It is known that any closed surface possesses infinitely many closed geodesics. The first problem in the minimal submanifolds section of Yau's list asks whether any closed three-manifold has infinitely many closed smooth immersed minimal surfaces. At the time it was known from Almgren–Pitts min-max theory the existence of at least one minimal surface. Kei Irie, Fernando Codá Marques, and André Neves solved this problem in the generic case and later Antoine Song claimed it in full generality. Selected publications "Existence of infinitely many minimal hypersurfaces in closed manifolds" (2018) Joint with Marques and Neves: "Equidistribution of minimal hypersurfaces for generic metrics" (2019), Inventiones mathematicae References Living people Differential geometers Princeton University alumni 1992 births Scientists from Paris French mathematicians
https://en.wikipedia.org/wiki/Togo%20Umeda	is a Japanese professional footballer currently playing as a goalkeeper for Shimizu S-Pulse. Career statistics Club . References External links Profile at Shimizu S-Pulse 2000 births Living people Sportspeople from Shizuoka Prefecture Association football people from Shizuoka Prefecture Japanese men's footballers Japan men's youth international footballers Men's association football goalkeepers J1 League players Shimizu S-Pulse players Fagiano Okayama players
https://en.wikipedia.org/wiki/Yuma%20Obata	is a Japanese footballer currently playing as a goalkeeper for Vegalta Sendai. Career statistics Club . Notes International Japan national under-18 football team 2020 AFC U-19 Championship qualification（Group J 1st） Japan national under-19 football team Japan national under-20 football team Japan national under-22 football team 2022 AFC U-23 Asian Cup qualification（Group K 1st） References External links 2001 births Living people Japanese men's footballers Japan men's youth international footballers Men's association football goalkeepers J1 League players J2 League players Vegalta Sendai players
https://en.wikipedia.org/wiki/Rikito%20Sugiura	is a Japanese footballer currently playing as a forward for Tegevajaro Miyazaki from 2023, on loan from Zweigen Kanazawa as a designated special player. Career statistics Club . Notes References External links 2002 births Living people Japanese men's footballers Men's association football forwards J2 League players J3 League players Zweigen Kanazawa players Ococias Kyoto AC players Tegevajaro Miyazaki players
https://en.wikipedia.org/wiki/Ryotaro%20Nakamura	is a Japanese professional footballer who plays as a defensive midfielder for club Ventforet Kofu, on loan from Kashima Antlers. Career statistics Club . References External links Profile at Kashima Antlers 1997 births Living people Japanese men's footballers Men's association football midfielders Chuo University alumni J2 League players J1 League players Ventforet Kofu players Kashima Antlers players Sportspeople from Niigata (city)
https://en.wikipedia.org/wiki/Masahiko%20Sugita	is a Japanese footballer currently playing as a midfielder for Fujieda MYFC. Career statistics Club . Notes References External links 1995 births Living people Japanese men's footballers Men's association football midfielders Juntendo University alumni Japan Football League players J3 League players Sony Sendai FC players Fujieda MYFC players
https://en.wikipedia.org/wiki/1949%E2%80%9350%20Rochdale%20A.F.C.%20season	The 1949–50 season saw Rochdale compete for their 22nd season in the Football League Third Division North. Statistics \|} Final league table Competitions Football League Third Division North F.A. Cup Lancashire Cup References Rochdale A.F.C. seasons Rochdale
https://en.wikipedia.org/wiki/Samson%20Iyede	Samson Iyede Onomigho (born 28 January 1998) is a Nigerian footballer currently playing as a forward for Ukrainian club Chornomorets Odesa, on loan from AC Horsens in Denmark. Career statistics Club . Notes References External links 1998 births Living people Nigerian men's footballers Men's association football forwards F.C. Ebedei players FC Midtjylland players Paide Linnameeskond players Fremad Amager players Lommel S.K. players FC Fredericia players AC Horsens players FC Chornomorets Odesa players Danish 1st Division players Challenger Pro League players Ukrainian Premier League players Nigerian expatriate men's footballers Nigerian expatriate sportspeople in Denmark Nigerian expatriate sportspeople in Belgium Nigerian expatriate sportspeople in Ukraine Expatriate men's footballers in Denmark Expatriate men's footballers in Belgium Expatriate men's footballers in Ukraine
https://en.wikipedia.org/wiki/Ra%C5%A1tak	Raštak () is a village in the municipality of Gazi Baba, North Macedonia. Demographics In statistics gathered by Vasil Kanchov in 1900, the village was inhabited by 270 Muslim Albanians and 230 Orthodox Bulgarians. According to the 2021 census, the village had a total of 457 inhabitants. Ethnic groups in the village include: Macedonians 430 Persons for whom data are taken from administrative sources 17 Serbs 2 Others 8 Sports The local football club is FK Raštak. References Villages in Gazi Baba Municipality
https://en.wikipedia.org/wiki/Basic%20Number%20Theory	Basic Number Theory is an influential book by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on valuation-theoretic methods. Based in part on a course taught at Princeton University in 1961-2, it appeared as Volume 144 in Springer's Grundlehren der mathematischen Wissenschaften series. The approach handles all 'A-fields' or global fields, meaning finite algebraic extensions of the field of rational numbers and of the field of rational functions of one variable with a finite field of constants. The theory is developed in a uniform way, starting with topological fields, properties of Haar measure on locally compact fields, the main theorems of adelic and idelic number theory, and class field theory via the theory of simple algebras over local and global fields. The word `basic’ in the title is closer in meaning to `foundational’ rather than `elementary’, and is perhaps best interpreted as meaning that the material developed is foundational for the development of the theories of automorphic forms, representation theory of algebraic groups, and more advanced topics in algebraic number theory. The style is austere, with a narrow concentration on a logically coherent development of the theory required, and essentially no examples. Mathematical context and purpose In the foreword, the author explains that instead of the “futile and impossible task” of improving on Hecke’s classical treatment of algebraic number theory, he “rather tried to draw the conclusions from the developments of the last thirty years, whereby locally compact groups, measure and integration have been seen to play an increasingly important role in classical number theory”. Weil goes on to explain a viewpoint that grew from work of Hensel, Hasse, Chevalley, Artin, Iwasawa, Tate, and Tamagawa in which the real numbers may be seen as but one of infinitely many different completions of the rationals, with no logical reason to favour it over the various p-adic completions. In this setting, the adeles (or valuation vectors) give a natural locally compact ring in which all the valuations are brought together in a single coherent way in which they “cooperate for a common purpose”. Removing the real numbers from a pedestal and placing them alongside the p-adic numbers leads naturally – “it goes without saying” to the development of the theory of function fields over finite fields in a “fully simultaneous treatment with number-fields”. In a striking choice of wording for a foreword written in the United States in 1967, the author chooses to drive this particular viewpoint home by explaining that the two classes of global fields “must be granted a fully simultaneous treatment […] instead of the segregated status, and at best the separate but equal facilities, which hitherto have been their lot. That, far from losing by such treatment, both races stand to gain by it, is one fact which will, I hope, clearly emerge from this book.” After Wor
https://en.wikipedia.org/wiki/Dinamo%20Zagreb%20records%20and%20statistics	This page is containing records and statistics of Croatian football club GNK Dinamo Zagreb. It shows club records as well as individual records achieved by the club's players. Domestic and international titles Number in parentheses indicates number of titles, while competition in bold indicates record number of titles. Croatian First Football League (23): 1993, 1996, 1997, 1998, 1999, 2000, 2003, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2018, 2019, 2020, 2021, 2022 Croatian Football Cup (16): 1994, 1996, 1997, 1998, 2001, 2002, 2004, 2007, 2008, 2009, 2011, 2012, 2015, 2016, 2018, 2021 Croatian Football Super Cup (7): 2002, 2003, 2006, 2010, 2013, 2019, 2022 Yugoslav First League (10): 1923, 1926, 1928, 1937, 1940, 1943, 1948, 1954, 1958, 1982 Yugoslav Cup (7): 1951, 1960, 1963, 1965, 1969, 1980, 1983 Inter-Cities Fairs Cup (1): 1967 Reference: Results and sequences Record of biggest wins and loses in domestic league, domestic cup and official European matches (from 1992). Biggest league win: 10–1 vs NK Pazinka, 12 December 1993 Biggest cup win: 13–0 vs NK Rudeš, 7 October 1992, round of 32 Biggest European win: 6–0 vs B68 Toftir, 1 September 1993, (UEFA Champions League) preliminary round; 6–0 vs Zalaegerszegi TE, 19 September 2002, (UEFA Cup) 1st round Biggest league defeat: 0–4 vs NK Varteks, 26 May 1992; 0–4 vs NK Varteks, 19 November 2000 Biggest cup defeat: 1–4 vs Hajduk Split, 19 May 1993, final Biggest European defeat: 1–7 vs Olympique Lyonnais, 7 December 2011, (UEFA Champions League) group stage Record of longest league sequences in terms of winning, losing, scoring and conceding (from 1992). Most games won in a row: 28 - from 8 November 2006 to 15 September 2007 Most games without defeat: 50 - from 17 May 2014 to 16 October 2015 Most games without winning: 6 - from 10 October 2001 to 4 November 2001 Most games lost in a row: 3 - from 4 October 2001 to 21 October 2001 Most games scored in a row: 61 - from 22 April 2006 to 15 March 2008 Most games without conceding: 10 - from 2 March 2013 to 11 May 2013 Most games without scoring: 4 - from 9 April 2005 to 30 April 2005 Most games conceded in a row: 13 - from 12 March 1995 to 4 June 1995 Reference: Appearances and goals GNK Dinamo Zagreb record players in terms of appearances and goals in official matches (domestic league and cup games, all official European games). Last game updated: Rijeka - Dinamo 2–7 (13 November 2022) Appearances Goals Minutes without conceding in league Updated on 21 August 2022 Reference: Transfers Reference: Dinamo Zagreb players on major international tournaments Lists below show Dinamo Zagreb players who represented their countries on major senior continental and world competitions. All players were on the squad list of their national team and under contract as Dinamo Zagreb players at the time. Flag in front of the name indicates national team that the player has represented. Gold, silver and bronze icon afte
https://en.wikipedia.org/wiki/Icons%20of%20Mathematics	Icons of Mathematics: An Exploration of Twenty Key Images is a book on elementary geometry for a popular audience. It was written by Roger B. Nelsen and Claudi Alsina, and published by the Mathematical Association of America in 2011 as volume 45 of their Dolciani Mathematical Expositions book series. Topics Each of the book's 20 chapters begins with an iconic mathematical diagram, and discusses an interrelated set of topics inspired by that diagram, including results in geometry, their proofs and visual demonstrations, background material, biographies of mathematicians, historical illustrations and quotations, and connections to real-world applications. The topics include: The geometry of circles and triangles, star polygons, Platonic solids, and figurate numbers The Pythagorean theorem, Thales's theorem on right triangles in semicircles, and geometric interpretations of the arithmetic mean, geometric mean, and harmonic mean Dido's problem on surrounding as large an area as possible with a given perimeter, and curves of constant width Tessellations, polygon triangulations, and rep-tiles Similar figures and spirals The mathematics of the yin and yang symbol and other self-complementary shapes, and of tatami arrangements. Audience and reception Reviewer E. J. Barbeau recommends the book to high-school level mathematics students and teachers. Cheryl McAllister suggests it as auxiliary material for both high school and general-audience college mathematics courses, and Hans-Wolfgang Henn adds that it also makes enjoyable light reading for professional mathematicians. References Elementary geometry Popular mathematics books 2011 non-fiction books Mathematical Association of America
https://en.wikipedia.org/wiki/Matrix%20factorization%20of%20a%20polynomial	In mathematics, a matrix factorization of a polynomial is a technique for factoring irreducible polynomials with matrices. David Eisenbud proved that every multivariate real-valued polynomial p without linear terms can be written as a AB = pI, where A and B are square matrices and I is the identity matrix. Given the polynomial p, the matrices A and B can be found by elementary methods. Example: The polynomial x2 + y2 is irreducible over R[x,y], but can be written as References External links A Mathematica implementation of a algorithm to matrix-factorize polynomials Polynomials Algebra Polynomials factorization algorithms
https://en.wikipedia.org/wiki/Manastirec	Manastirec () is a village in the municipality of Rosoman, North Macedonia. Demographics According to the statistics of the Bulgarian ethnographer Vasil Kanchov from 1900, 188 inhabitants lived in Manastirec, 116 Christian Bulgarians and 72 Muslim Bulgarians. On the 1927 ethnic map of Leonhard Schulze-Jena, the village is written as "Monastirče" and shown as having a mixed population of Bulgarians and Muslim Bulgarians. According to the 2002 census, the village had a total of 321 inhabitants. Ethnic groups in the village include: Macedonians 305 Serbs 16 References Villages in Rosoman Municipality
https://en.wikipedia.org/wiki/Palikura	Palikura () is a village in the municipality of Rosoman, North Macedonia. Demographics According to the statistics of the Bulgarian ethnographer Vasil Kanchov from 1900, 130 inhabitants lived in Palikura, all Christian Bulgarians. On the 1927 ethnic map of Leonhard Schulze-Jena, the village is written as "Çiftlik Palikura" and shown as a Christian Bulgarian village. According to the 2002 census, the village had a total of 183 inhabitants. Ethnic groups in the village include: Macedonians 161 Serbs 17 Romani 4 Others 1 References Villages in Rosoman Municipality
https://en.wikipedia.org/wiki/Trstenik%2C%20Rosoman	Trstenik () is a village in the municipality of Rosoman, North Macedonia. Demographics According to the statistics of the Bulgarian ethnographer Vasil Kanchov from 1900, 140 inhabitants lived in Trstenik, all Christian Bulgarians. On the 1927 ethnic map of Leonhard Schulze-Jena, the village is written as "Trstani" and shown as a Christian Bulgarian village. According to the 2002 census, the village had a total of 246 inhabitants. Ethnic groups in the village include: Macedonians 239 Serbs 7 References Villages in Rosoman Municipality
https://en.wikipedia.org/wiki/Berlin%20workshops%20on%20Babylonian%20mathematics	The Berlin workshops were a series of six workshops that took place between 1983 and 1994 and focused on mathematical conceptualization and notation in a number of early writing systems. Although the names of the workshops varied slightly over time, most included the phase "conceptual development of Babylonian mathematics" and were supported by the Archaische Texte aus Uruk Project at Freie Universität Berlin and the Max Planck Institute for the History of Science. The first meeting was held at the Altorientalisches Seminar und Seminar für Vorderasiatische Altertumskunde on August 5, 1983. Subsequent meetings were held in 1984, 1985, 1988 and 1994. List of workshops The workshops played a significant role in advancing the decipherment of Proto-cuneiform and Proto-Elamite numerals as well as the comparative study of early mathematical notation. Workshop on Mathematical Concepts in Babylonian Mathematics Date: August 1-5, 1983. Place: Seminar für Vorderasiatische Altertumskunde und altorientalische Philologie der Freien Universität. Second Workshop on Concept Development in Babylonian Mathematics Date: June 18-22, 1984. Place: Seminar für Vorderasiatische Altertumskunde der Freien Universität Berlin. Third Workshop on Concept Development in Babylonian Mathematics Date: December 9-13, 1985. Place: Seminar für Vorderasiatische Altertumskunde der Freien Universität Berlin. Fourth Workshop on Concept Development in Babylonian Mathematics Date: May 5-9, 1988. Place: Seminar für Vorderasiatische Altertumskunde der Freien Universität Berlin. Fifth Workshop on Mathematical Concepts in Babylonian Mathematics Date: January 21-23, 1994. Place: Seminar für Vorderasiatische Altertumskunde der Freien Universität Berlin. Standardisierung der elektronischen Transliteration von Keilschrifttexten Date: September 7-9, 1994. Place: Max Planck Institute for the History of Science References Babylonian mathematics International conferences in Germany Free University of Berlin
https://en.wikipedia.org/wiki/Mar%C3%ADa%20Luisa%20Aguilar	María Luisa Aguilar Hurtado (20 June 1938 - 29 October 2015), was the first professional astronomer of Peru. She studied at the Institute of Mathematics and Physics of the National University of San Marcos in Lima, Peru. She graduated as an astronomer from the National University of La Plata, Argentina. In 1981, motivated to develop astronomy at a professional level, she founded and served as director of the "Astronomy and Astrophysics Seminar", nowadays called "Permanent Astronomy and Space Sciences Seminar" of the National University of San Marcos. Biography She was born in Jauja, the city where she lived during her first three years. Her primary and secondary studies were carried out in Lima, in the Elvira García y García Mayor School Unit. In 1958 she entered the School of Mathematics of the National University of San Marcos. She traveled to Argentina to study astronomy at the Astronomy and Geophysics Observatory of the National University of La Plata; there was no such professional specialty in Peru during that time. She specialized in astronomical spectroscopy, stellar atmospheres, and variable stars. In 1969, she returned to Peru and began teaching at the National University of Engineering and at the National University of San Marcos. In those first years, she created the "Astronomical Fridays", a space for the dissemination of astronomy that has remained until today, becoming the oldest series of uninterrupted talks and conferences in the history of Peru. In 1981, Maria Aguilar founded the Astronomy and Astrophysics Seminar, renamed in 2001 as the Permanent Astronomy and Space Sciences Seminar - SPACE. In 1982 she was recognized as a Member of the International Astronomical Union, being part of commission 46 Astronomy Education and Development, and commission C1 WG Network for Astronomy School Education (NASE). In January 1984, she promoted and managed the "San Marcos - International Astronomical Union agreement", enabling the first Visiting Lecturer Program of the International Astronomical Union in Peru. In 1985, she coordinated the arrival of doctors José Luis Sérsic, Argentine, and specialist in galaxies, Josip Kleczek, Czech, Sun scholar, and Jorge Sahade, first Latin American president of the International Astronomical Union. She was an enthusiastic collaborator in science and astronomy topics in Sunday's supplement of the Peruvian newspaper "El Comercio" between 1999 and 2000. As part of the global activities for the celebrations of the International Year of Astronomy 2009, she was designated as "Single Point of Contact" between Peru and the International Astronomical Union, promoting and participating in a series of activities of education and outreach in Peru for that year, such as the "Astronomical Fridays", "Itinerant Telescope", the "Galileo Teacher Training Program" and "Galileo Mobile", among others. Aguilar was the promoter of the San Marcos Astronomical Observatory for Education and Tourism Project in Maranganí, C
https://en.wikipedia.org/wiki/Joel%20Spruck	Joel Spruck (born 1946) is a mathematician, J. J. Sylvester Professor of Mathematics at Johns Hopkins University, whose research concerns geometric analysis and elliptic partial differential equations. He obtained his PhD from Stanford University with the supervision of Robert S. Finn in 1971. Mathematical contributions Spruck is well known in the field of elliptic partial differential equations for his series of papers "The Dirichlet problem for nonlinear second-order elliptic equations," written in collaboration with Luis Caffarelli, Joseph J. Kohn, and Louis Nirenberg. These papers were among the first to develop a general theory of second-order elliptic differential equations which are fully nonlinear, with a regularity theory that extends to the boundary. Caffarelli, Nirenberg & Spruck (1985) has been particularly influential in the field of geometric analysis since many geometric partial differential equations are amenable to its methods. With Basilis Gidas, Spruck studied positive solutions of subcritical second-order elliptic partial differential equations of Yamabe type. With Caffarelli, they studied the Yamabe equation on Euclidean space, proving a positive mass-style theorem on the asymptotic behavior of isolated singularities. In 1974, Spruck and David Hoffman extended a mean curvature-based Sobolev inequality of James H. Michael and Leon Simon to the setting of submanifolds of Riemannian manifolds. This has been useful for the study of many analytic problems in geometric settings, such as for Gerhard Huisken's study of mean curvature flow in Riemannian manifolds and for Richard Schoen and Shing-Tung Yau's study of the Jang equation in their resolution of the positive energy theorem in general relativity. In the late 80s, Stanley Osher and James Sethian developed the level-set method as a computational tool in numerical analysis. In collaboration with Lawrence Evans, Spruck pioneered the rigorous study of the level-set flow, as adapted to the mean curvature flow. The level-set approach to mean curvature flow is important in the technical ease with topological change can occur along the flow. The same approach was independently developed by Yun Gang Chen, Yoshikazu Giga, and Shun'ichi Goto. The works of Evans-Spruck and Chen-Giga-Goto found significant application in Gerhard Huisken and Tom Ilmanen's solution of the Riemannian Penrose inequality of general relativity and differential geometry, where they adapted the level-set approach to the inverse mean curvature flow. In 1994 Spruck was an invited speaker at the International Congress of Mathematicians in Zurich. Major publications Hoffman, David; Spruck, Joel. Sobolev and isoperimetric inequalities for Riemannian submanifolds. Comm. Pure Appl. Math. 27 (1974), 715–727. Gidas, B.; Spruck, J. A priori bounds for positive solutions of nonlinear elliptic equations. Comm. Partial Differential Equations 6 (1981), no. 8, 883–901. Gidas, B.; Spruck, J. Global and local behavior of
https://en.wikipedia.org/wiki/Kaili%20Shimbo	is a Japanese footballer currently playing as a winger for Renofa Yamaguchi. He is the son of the former Japanese international defender, Hayuma Tanaka and fashion model, Malia. Career statistics Club . Notes References External links 2002 births Living people Japanese men's footballers Men's association football defenders J3 League players J2 League players Kashiwa Reysol players Cerezo Osaka players Cerezo Osaka U-23 players Renofa Yamaguchi FC players
https://en.wikipedia.org/wiki/Naoki%20Yoshikawa%20%28footballer%29	is a Japanese footballer currently studying at the Niigata University of Health and Welfare. Career statistics Club . Notes References External links 2002 births Living people Association football people from Osaka Prefecture Niigata University of Health and Welfare alumni Japanese men's footballers Men's association football goalkeepers J3 League players Gamba Osaka players Gamba Osaka U-23 players
https://en.wikipedia.org/wiki/Kota%20Ohashi	is a Japanese footballer currently playing as a defender for Cerezo Osaka. Career statistics Club . Notes References External links 2002 births Living people Japanese men's footballers Men's association football defenders J3 League players Cerezo Osaka players Cerezo Osaka U-23 players
https://en.wikipedia.org/wiki/Tatsuya%20Tabira	is a Japanese footballer currently playing as a defender for Iwate Grulla Morioka, on loan from Cerezo Osaka. Career statistics Club . Notes References External links 2001 births Living people Association football people from Osaka Prefecture Japanese men's footballers Japan men's youth international footballers Men's association football defenders J3 League players Cerezo Osaka players Cerezo Osaka U-23 players Iwate Grulla Morioka players Association football people from Osaka
https://en.wikipedia.org/wiki/Tatsuhiko%20Noguchi	is a Japanese footballer currently playing as a forward for Fagiano Okayama. Career statistics Club . Notes References External links 1997 births Living people Japanese men's footballers Men's association football forwards Chuo University alumni J2 League players Fagiano Okayama players
https://en.wikipedia.org/wiki/Peano%20surface	In mathematics, the Peano surface is the graph of the two-variable function It was proposed by Giuseppe Peano in 1899 as a counterexample to a conjectured criterion for the existence of maxima and minima of functions of two variables. The surface was named the Peano surface () by Georg Scheffers in his 1920 book Lehrbuch der darstellenden Geometrie. It has also been called the Peano saddle. Properties The function whose graph is the surface takes positive values between the two parabolas and , and negative values elsewhere (see diagram). At the origin, the three-dimensional point on the surface that corresponds to the intersection point of the two parabolas, the surface has a saddle point. The surface itself has positive Gaussian curvature in some parts and negative curvature in others, separated by another parabola, implying that its Gauss map has a Whitney cusp. Although the surface does not have a local maximum at the origin, its intersection with any vertical plane through the origin (a plane with equation or ) is a curve that has a local maximum at the origin, a property described by Earle Raymond Hedrick as "paradoxical". In other words, if a point starts at the origin of the plane, and moves away from the origin along any straight line, the value of will decrease at the start of the motion. Nevertheless, is not a local maximum of the function, because moving along a parabola such as (in diagram: red) will cause the function value to increase. The Peano surface is a quartic surface. As a counterexample In 1886 Joseph Alfred Serret published a textbook with a proposed criteria for the extremal points of a surface given by "the maximum or the minimum takes place when for the values of and for which and (third and fourth terms) vanish, (fifth term) has constantly the sign − , or the sign +." Here, it is assumed that the linear terms vanish and the Taylor series of has the form where is a quadratic form like , is a cubic form with cubic terms in and , and is a quartic form with a homogeneous quartic polynomial in and . Serret proposes that if has constant sign for all points where then there is a local maximum or minimum of the surface at . In his 1884 notes to Angelo Genocchi's Italian textbook on calculus, Calcolo differenziale e principii di calcolo integrale, Peano had already provided different correct conditions for a function to attain a local minimum or local maximum. In the 1899 German translation of the same textbook, he provided this surface as a counterexample to Serret's condition. At the point , Serret's conditions are met, but this point is a saddle point, not a local maximum. A related condition to Serret's was also criticized by Ludwig Scheeffer, who used Peano's surface as a counterexample to it in an 1890 publication, credited to Peano. Models Models of Peano's surface are included in the Göttingen Collection of Mathematical Models and Instruments at the University of Göttingen, and in the
https://en.wikipedia.org/wiki/1950%E2%80%9351%20Rochdale%20A.F.C.%20season	The 1950–51 season saw Rochdale compete for their 23rd season in the Football League Third Division North. Statistics \|} Final league table Competitions Football League Third Division North F.A. Cup Lancashire Cup References Rochdale A.F.C. seasons Rochdale
https://en.wikipedia.org/wiki/Ded%C3%A9%20%28footballer%2C%20born%202002%29	Vitor Hugo Oliveira Corrêa da Silva (born 17 April 2002), commonly known as Dedé, is a Brazilian footballer who currently plays for Botafogo. Career statistics Club Notes References External links 2002 births Living people Brazilian men's footballers Men's association football forwards Boavista Sport Club players Botafogo de Futebol e Regatas players
https://en.wikipedia.org/wiki/Gorgis%20Ismail	Gorgis Ismail is a former Iraqi football forward who played for Iraq between 1962 and 1969. He played 9 matches and scored 3 goals. Career statistics International goals Scores and results list Iraq's goal tally first. References Iraqi men's footballers Iraq men's international footballers Living people Men's association football forwards Year of birth missing (living people)
https://en.wikipedia.org/wiki/List%20of%20busiest%20airports%20by%20passenger%20traffic%20%282010%E2%80%932015%29	Below is a list of busiest airports by passenger traffic from 2010 to 2015. 2015 statistics Airports Council International's full-year figures are as follows: 2014 statistics Airports Council International's full-year figures are as follows: 2013 statistics Airports Council International's full-year figures are as follows: 2012 statistics Airports Council International's preliminary full-year figures are as follows: 2011 statistics Airports Council International's final full-year figures are as follows: 2010 statistics Airports Council International's final full-year figures are as follows: See also List of the busiest airports List of busiest airports by aircraft movements Busiest airports by continent References Lists of airports Passenger traffic 2010-2015
https://en.wikipedia.org/wiki/Kim%20Yeong-uk	Kim Yeong-uk (; born 2 March 2000) is a South Korean footballer currently playing as a right-back for Jeonnam Dragons FC. Career statistics Club Notes References 2000 births Living people South Korean men's footballers Men's association football defenders K League 2 players Jeju United FC players
https://en.wikipedia.org/wiki/Jeon%20Seung-min	Jeon Seung-min (; born 15 December 2000) is a South Korean footballer who plays as a midfielder for Busan IPark. Career statistics References 2000 births Living people South Korean men's footballers South Korea men's youth international footballers Men's association football midfielders Yong In University alumni K League 1 players K League 2 players Seongnam FC players Jeonnam Dragons players Busan IPark players
https://en.wikipedia.org/wiki/Mateusz%20Kaczmarek	Mateusz Kaczmarek (born 26 February 2003) is a Polish professional footballer who plays as a midfielder for II liga club Wisła Puławy. Career statistics Club Notes Honours Miedź Legnica I liga: 2021–22 References 2003 births Living people Polish men's footballers Poland men's youth international footballers Men's association football midfielders Raków Częstochowa players Miedź Legnica players Wisła Puławy players Ekstraklasa players I liga players II liga players III liga players Sportspeople from Częstochowa Footballers from Silesian Voivodeship
https://en.wikipedia.org/wiki/Adrian%20Ni%C8%9B%C4%83	Adrian Romeo Niță (born 8 March 2003) is a Romanian professional footballer who plays as a winger for CSM Slatina. Career statistics Club Honours Club FCSB Cupa României: 2019–20 References External links 2003 births Living people Romanian men's footballers Romania men's youth international footballers Men's association football forwards Liga I players FC Steaua București players Liga II players AFC Turris-Oltul Turnu Măgurele players FC Unirea Constanța players CS Concordia Chiajna players Footballers from Slatina, Romania
https://en.wikipedia.org/wiki/Otto%20Hindrich	Otto Hindrich (born 5 August 2002) is a Romanian professional footballer who plays as a goalkeeper for Liga I club CFR Cluj. Hindrich stems from a Transylvanian Saxon family. Career statistics Club Honours CFR Cluj Liga I: 2019–20, 2021–22 References External links 2002 births Living people Footballers from Cluj-Napoca Romanian sportspeople of Hungarian descent Romanian people of German descent Transylvanian Saxon people Romanian men's footballers Men's association football goalkeepers Liga I players CFR Cluj players Liga II players SSU Politehnica Timișoara players Expatriate men's footballers in Hungary Romanian expatriate sportspeople in Hungary Nemzeti Bajnokság I players Kisvárda FC players Romania men's youth international footballers Romania men's under-21 international footballers
https://en.wikipedia.org/wiki/2019%20FIFA%20Women%27s%20World%20Cup%20statistics	These are statistics for the 2019 FIFA Women's World Cup, which took place in France from 7 June to 7 July 2019. The World Cup started with 6 groups, there were 4 national teams in each group, it is a round-robin tournament in group stage and the top two to three teams qualify. It then goes to an elimination tournament among the 16 qualified teams. Goals, assist, performance analyses, and squad performance are shown here. Goals scored from penalty shoot-outs are not counted, and matches decided by penalty shoot-outs are counted as draws. Goalscorers Assists Scoring Overall Timing First goal of the tournament: Eugénie Le Sommer for France against South Korea First brace of the tournament: Wendie Renard for France against South Korea First hat-trick of the tournament: Cristiane for Brazil against Jamaica Last goal of the tournament: Rose Lavelle for United States against Netherlands Last brace of the tournament: Megan Rapinoe for United States against France Last hat-trick of the tournament: Cristiana Girelli for Italy against Jamaica Fastest goal in a match from kickoff: 3rd minute Jill Scott for England against Norway Fastest goal in a match after coming on as a substitute: Latest goal in a match without extra time: 90+6th minute Elin Rubensson for Sweden against Thailand Latest goal in a match with extra time: 107th minute Amandine Henry for France against Brazil Latest winning goal in a match without extra time: 95th minute Ajara Nchout for Senegal against New Zealand Latest winning goal in a match with extra time: 107th minute Amandine Henry for France against Brazil Shortest time difference between two goals scored by the same team in a match: 1 minute Alex Morgan and Sam Mewis for United States against Thailand Teams Most goals scored by a team: 26 United States Fewest goals scored by a team: 1 China, Jamaica, New Zealand, South Africa, South Korea, Thailand Most goals conceded by a team: 20 Thailand Fewest goals conceded by a team: 2 Germany Best goal difference: +23 United States Worst goal difference: –19 Thailand Most goals scored in a match by both teams: 13 United States 13–0 Thailand Most goals scored in a match by one team: 13 United States against Thailand Most goals scored in a match by the losing team: 2 Brazil against Australia Biggest margin of victory: 13 goals United States 13–0 Thailand Most clean sheets achieved by a team: 4 Germany and United States Fewest clean sheets achieved by a team: 0 Australia, Cameroon, Jamaica, New Zealand, Scotland, South Africa, South Korea, Thailand Most clean sheets given by an opposing team: 3 China Fewest clean sheets given by an opposing team: 0 Australia, Brazil, England, France, Germany, Scotland, United States Most consecutive clean sheets achieved by a team: 4 Germany Most consecutive clean sheets given by an opposing team: 2 Argentina, China, Jamaica, New Zealand, Nigeria, South Africa, South Korea, Spain Individual Most goals scored by one player in a matc
https://en.wikipedia.org/wiki/Basilis%20Gidas	Basilis Gidas is an applied mathematician at Brown University, interested in many applications of mathematics. Following degrees in electrical engineering, mechanical engineering, and mathematics, he obtained a combined Ph.D. in physics and nuclear engineering at the University of Michigan in 1970. He is an elected fellow of the Institute of Mathematical Statistics. He has had past appointments in various mathematics and physics departments at the Institute for Advanced Study, Rutgers University, Rockefeller University, Bielefeld University, University of Washington, and University of Michigan. His collaborations with Luis Caffarelli, Wei-Ming Ni, Louis Nirenberg, and Joel Spruck resulted in six papers in pure mathematics, five of which rank among the most cited in the field of elliptic partial differential equations. The collaboration of Gidas, Ni, and Nirenberg in particular was cited in the awarding of the Abel Prize to Nirenberg. Selected publications B. Gidas, Wei Ming Ni, and L. Nirenberg. Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68 (1979), no. 3, 209–243. B. Gidas, Wei Ming Ni, and L. Nirenberg. Symmetry of positive solutions of nonlinear elliptic equations in . Mathematical analysis and applications, Part A, pp. 369–402, Adv. in Math. Suppl. Stud., 7a, Academic Press, New York-London, 1981. B. Gidas and J. Spruck. A priori bounds for positive solutions of nonlinear elliptic equations. Comm. Partial Differential Equations 6 (1981), no. 8, 883–901. B. Gidas and J. Spruck. Global and local behavior of positive solutions of nonlinear elliptic equations. Comm. Pure Appl. Math. 34 (1981), no. 4, 525–598. Luis A. Caffarelli, Basilis Gidas, and Joel Spruck. Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Comm. Pure Appl. Math. 42 (1989), no. 3, 271–297. References Year of birth missing (living people) Living people University of Michigan alumni Fellows of the Institute of Mathematical Statistics 20th-century American mathematicians 21st-century American mathematicians Brown University faculty
https://en.wikipedia.org/wiki/2011%20FIFA%20Women%27s%20World%20Cup%20statistics	The following article outlines the statistics for the 2011 FIFA Women's World Cup, which took place in Germany from 26 June to 17 July. Goals scored from penalty shoot-outs are not counted, and matches decided by penalty shoot-outs are counted as draws. Goalscorers Assists Scoring Overall Overall Timing First goal of the tournament: Marie-Laure Delie for France against Nigeria First brace of the tournament: Marta for Brazil against Norway Only hat-trick of the tournament: Homare Sawa for Japan against Mexico Last goal of the tournament: Homare Sawa for Japan against United States Last brace of the tournament: Nahomi Kawasumi for Japan against Sweden Fastest goal in a match from kickoff: 2nd minute Stephany Mayor for Mexico against New Zealand Latest goal in a match without extra time: 90+4th minute Hannah Wilkinson for New Zealand against Mexico Latest goal in a match with extra time: 120+2 minutesAbby Wambach for United States against Brazil Teams Most goals scored by one player in a match: 3 Homare Sawa for Japan against Mexico Wins and losses Most wins: 5 – Sweden Fewest wins: 0 – Canada, Colombia, Equatorial Guinea, Mexico, New Zealand, North Korea Most losses: 3 – Canada, Equatorial Guinea, France Fewest losses: 0 – Brazil, England Most draws: 2 – England, Mexico, United States Match awards Player of the Match Clean sheets Squads Multiple World Cups Scoring at three or more World Cups Appearing at four or more World Cups Overall results Bold numbers indicate the maximum values in each column. By team By confederation References statistics
https://en.wikipedia.org/wiki/Thomas%20Goodwillie%20%28mathematician%29	Thomas G. Goodwillie (born 1954) is an American mathematician and professor at Brown University who has made fundamental contributions to algebraic and geometric topology. He is especially famous for developing the concept of calculus of functors, often also named Goodwillie calculus. Life While studying at Harvard University, Goodwillie became a Putnam Fellow in 1974 and 1975. He then studied at Princeton University, where he completed his PhD at in 1982, under the supervision of Wu-Chung Hsiang. He returned to Harvard as Junior Fellow in 1979, and was an associate professor (without tenure) at Harvard from 1982 to 1987. In 1987 he was hired with tenure by Brown University, where he was promoted to full professor in 1991. He developed the calculus of functors in a series of three papers in the 1990s and 2000s, which has since been expanded and applied in a number of areas, including the theory of smooth manifolds, algebraic K-theory, and homotopy theory. He has advised 11 PhD students. Goodwillie is interested in issues of racial and gender equality and has taught a course on this topic. He is an active user on MathOverflow. Recognition Goodwillie received a Sloan Fellowship and the Harriet S. Sheridan Award. He is a Fellow of the American Mathematical Society. A conference with leading topologists as speakers was organized on the occasion of his 60th birthday. References External links Website at Brown University Topologists 20th-century American mathematicians 21st-century American mathematicians Harvard University alumni Princeton University alumni Harvard University Department of Mathematics faculty Harvard University faculty Brown University faculty 1954 births Living people Fellows of the American Mathematical Society Putnam Fellows
https://en.wikipedia.org/wiki/Takumi%20Mase	is a Japanese footballer currently playing as a defender for Vegalta Sendai. Playing career Right-back good at attacking. At Hannan University, he served as captain. Career statistics Club . Notes References External links Profile at Vegalta Sendai 1998 births Living people Japanese men's footballers Men's association football defenders Hannan University alumni J1 League players Vegalta Sendai players
https://en.wikipedia.org/wiki/1951%E2%80%9352%20Rochdale%20A.F.C.%20season	The 1951–52 season saw Rochdale compete for their 24th season in the Football League Third Division North. Statistics \|} Final League Table Competitions Football League Third Division North F.A. Cup Lancashire Cup References Rochdale A.F.C. seasons Rochdale
https://en.wikipedia.org/wiki/David%20Dego	David Teshager Dego (born 9 May 2001) is an Israeli footballer who currently plays as a midfielder for Hapoel Ramat HaSharon. Career statistics Club Notes References 2001 births Living people Israeli men's footballers Footballers from Ness Ziona Beitar Jerusalem F.C. players Hapoel Nir Ramat HaSharon F.C. players Hapoel Ironi Kiryat Shmona F.C. players Israeli Premier League players Jewish Israeli sportspeople Israeli people of Ethiopian-Jewish descent Men's association football midfielders
https://en.wikipedia.org/wiki/Kevin%20Scannell	Kevin Scannell (born 11 May 1970) is an American professor of mathematics and computer science at Saint Louis University. Career Kevin Scannell is the professor of mathematics and computer science at Saint Louis University. His work focuses on developing online computing resources for small, minority or under-resourced languages, with a particular interest in Irish and other Celtic languages. He has developed an Irish thesaurus, grammar checker, and spell checker, and dictionaries and translation engines for Irish, Scottish, and Manx Gaelics. Scannell is a member of the team which localises platforms including Gmail, Twitter and WhatsApp into Irish. He founded Indigenous Tweets in 2011 to promote the use of social media through indigenous and minority languages. He translated 20 hours worth of coding material into Irish for the Hour of Code in 2016. In 2019 he created an Irish language name generator called . In 2019, he won a Fulbright Scholarship working on developing language technologies for Irish using deep learning and neural networks in collaboration with researchers at in Carna, County Galway. He is active in developing the Irish-language Wikipedia, and adding Irish content to Wikidata. Personal life Scannell was born on 11 May 1970 in Boston, Massachusetts. He graduated from Massachusetts Institute of Technology (MIT) with a BS in 1991. In 1996 he was awarded his doctorate from University of California, Los Angeles. He started learning Irish in the 1990s. References External links Scannell on the podcast Bitesize Irish 1970 births American translation scholars Living people Saint Louis University faculty American Wikimedians Irish-language writers Linguists from the United States 21st-century linguists
https://en.wikipedia.org/wiki/Christiane%20Tammer	Christiane Tammer (née Gerstewitz, also published as Christiane Gerth) is a German mathematician known for her work on mathematical optimization. She is a professor in the Institute of Mathematics of Martin Luther University of Halle-Wittenberg, and editor-in-chief of Optimization: A Journal of Mathematical Programming and Operations Research. Tammer is the namesake of the Gerstewitz functions or Gerstewitz functionals in vector optimization and its generalizations. Education Tammer earned a doctorate (Dr. rer. nat.) in 1984 at the Technical University Leuna-Merseburg. Her dissertation, Beiträge zur Dualitätstheorie der nichtlinearen Vektoroptimierung, was supervised by . She earned a habilitation at Halle in 1991. Books Tammer is the author of books including: Variational Methods in Partially Ordered Spaces (with Alfred Göpfert, Hassan Riahi, and Constantin Zălinescu, Springer, 2003) Set-valued Optimization: An Introduction with Applications (with Akhtar A. Khan and Constantin Zălinescu, Springer, 2014) Scalarization and Separation by Translation Invariant Functions (with Petra Weidner, Springer, 2020) She is the co-editor, with Frank Heyde, of Festschrift in celebration of Prof. Dr. Wilfried Grecksch's 60th birthday (Shaker, 2008). References Year of birth missing (living people) Living people 20th-century German mathematicians German women mathematicians Academic staff of the Martin Luther University of Halle-Wittenberg 21st-century German mathematicians 20th-century German women 21st-century German women
https://en.wikipedia.org/wiki/Sylvester%27s%20triangle%20problem	Sylvester's theorem or Sylvester's formula describes a particular interpretation of the sum of three pairwise distinct vectors of equal length in the context of triangle geometry. It is also referred to as Sylvester's (triangle) problem in literature, when it is given as a problem rather than a theorem. The theorem is named after the British mathematician James Joseph Sylvester. Theorem Consider three pairwise distinct vectors of equal length , and each of them acting on the same point thus creating the points , and . Those points form the triangle with as the center of its circumcircle. Now let denote the orthocenter of the triangle, then connection vector is equal to the sum of the three vectors: Furthermore, since the points and are located on the Euler line together with the centroid the following equation holds: Generalisation If the condition of equal length in Sylvester's theorem is dropped and one considers merely three arbitrary pairwise distinct vectors, then the equation above does not hold anymore. However the relation with the centroid remains true, that is: This follows directly from the definition of the centroid for a finite set of points in , which also yields a version for vectors acting on : Here is the centroid of the vertices of the polygon generated by the vectors acting on . References External links Darij Grinberg: Solution to American Mathematical Monthly Problem 11398 by Stanley Huang – contains Sylvester's theorem including its proof as a lemma Theorems about triangles Triangle problems
https://en.wikipedia.org/wiki/Milan%20Kr%C3%A1l%C3%AD%C4%8Dek	Milan Králíček (born 18 July 2001) is a Czech footballer who currently plays as a forward for Slovan Liberec. Career statistics Club Notes References 2001 births Living people Czech men's footballers Czech Republic men's youth international footballers Men's association football forwards FC Hradec Králové players FC Slovan Liberec players Czech First League players
https://en.wikipedia.org/wiki/Gerhard%20Wanner	Gerhard Wanner (born 1942 in Innsbruck) is an Austrian mathematician. Education and career Wanner grew up in Seefeld in Tirol and studied mathematics at the University of Innsbruck, where he received his doctorate in 1965 with advisor Wolfgang Gröbner and dissertation Ein Beitrag zur numerischen Behandlung von Randwertproblemen gewöhnlicher Differentialgleichungen (A contribution to the numerical treatment of boundary value problems of ordinary differential equations). He taught in Innsbruck and from 1973 at the University of Geneva. Wanner's research deals with numerical analysis of ordinary differential equations (about which he wrote a two-volume monograph with Ernst Hairer). Wanner is the co-author of an analysis undergraduate textbook and a geometry undergraduate textbook, both of which give historically oriented explanations of mathematics. In 2003 he was awarded, jointly with Ernst Hairer, the Peter Henrici Prize. In 2015 Wanner received SIAM's George Pólya Prize for Mathematical Exposition. He was president of the Swiss Mathematical Society from 1998 to 1999. Selected publications Articles Books with Ernst Hairer: with Alexander Ostermann: Geometry by Its History. Springer, Berlin/Heidelberg 2012, . with Ernst Hairer and Christian Lubich: 2nd edition. Springer, Berlin/Heidelberg 2010, . pbk reprint with Ernst Hairer and Sylvert Nørsett: 3rd corrected printing. Springer, Berlin/Heidelberg 2009, . with Ernst Hairer and Sylvert Nørsett: 2nd edition. Springer, Berlin/Heidelberg 1996, . 2013 pbk reprint Integration gewöhnlicher Differentialgleichungen: Lie-Reihen (mit Programmen), Runge-Kutta-Methoden. BI-Hochschultaschenbücher. Bibliographisches Institut, Mannheim/Zürich 1969. References External links Homepage Austrian mathematicians University of Innsbruck alumni Academic staff of the University of Geneva 1942 births Living people Austrian expatriates in Switzerland
https://en.wikipedia.org/wiki/Doris%20Fischer-Colbrie	Doris Fischer-Colbrie is a ceramic artist and former mathematician. She received her Ph.D. in mathematics in 1978 from University of California at Berkeley, where her advisor was H. Blaine Lawson. Many of her contributions to the theory of minimal surfaces are now considered foundational to the field. In particular, her collaboration with Richard Schoen is a landmark contribution to the interaction of stable minimal surfaces with nonnegative scalar curvature. A particular result, also obtained by Manfredo do Carmo and Chiakuei Peng, is that the only complete stable minimal surfaces in are planes. Her work on unstable minimal surfaces gave the basic tools by which to relate the assumption of finite index to conditions on stable subdomains and total curvature. After positions at Columbia University and San Diego State University, Fischer-Colbrie left academia to become a ceramic artist. She is married to Schoen, with whom she has two children. Publication list References 20th-century women mathematicians 21st-century women mathematicians Columbia University faculty San Diego State University faculty American women artists American women academics
https://en.wikipedia.org/wiki/Igor%20Sergeyev%20%28footballer%2C%20born%201969%29	Igor Nikolaevich Sergeyev (; born 11 September 1969) is a Kyrgyzstani former football player. Career statistics International Scores and results list Kyrgyzstan's goal tally first, score column indicates score after each Kyrgyzstan goal. Honours Ak-Maral Tokmok Kyrgyzstan Cup (1): 1994 References External links 1968 births Living people Soviet men's footballers FC Orenburg players Kyrgyzstani men's footballers Kyrgyzstan men's international footballers Kyrgyzstani expatriate men's footballers Expatriate men's footballers in Russia Kyrgyzstani expatriate sportspeople in Russia Expatriate men's footballers in Israel Kyrgyzstani expatriate sportspeople in Israel Men's association football forwards FC Nosta Novotroitsk players
https://en.wikipedia.org/wiki/Homotopy%20associative%20algebra	In mathematics, an algebra such as has multiplication whose associativity is well-defined on the nose. This means for any real numbers we have . But, there are algebras which are not necessarily associative, meaning if then in general. There is a notion of algebras, called -algebras, which still have a property on the multiplication which still acts like the first relation, meaning associativity holds, but only holds up to a homotopy, which is a way to say after an operation "compressing" the information in the algebra, the multiplication is associative. This means although we get something which looks like the second equation, the one of inequality, we actually get equality after "compressing" the information in the algebra. The study of -algebras is a subset of homotopical algebra, where there is a homotopical notion of associative algebras through a differential graded algebra with a multiplication operation and a series of higher homotopies giving the failure for the multiplication to be associative. Loosely, an -algebra is a -graded vector space over a field with a series of operations on the -th tensor powers of . The corresponds to a chain complex differential, is the multiplication map, and the higher are a measure of the failure of associativity of the . When looking at the underlying cohomology algebra , the map should be an associative map. Then, these higher maps should be interpreted as higher homotopies, where is the failure of to be associative, is the failure for to be higher associative, and so forth. Their structure was originally discovered by Jim Stasheff while studying A∞-spaces, but this was interpreted as a purely algebraic structure later on. These are spaces equipped with maps that are associative only up to homotopy, and the A∞ structure keeps track of these homotopies, homotopies of homotopies, and so forth. They are ubiquitous in homological mirror symmetry because of their necessity in defining the structure of the Fukaya category of D-branes on a Calabi–Yau manifold who have only a homotopy associative structure. Definition Definition For a fixed field an -algebra is a -graded vector space such that for there exist degree , -linear maps which satisfy a coherence condition: , where . Understanding the coherence conditions The coherence conditions are easy to write down for low degreespgs 583–584. d=1 For this is the condition that , since giving and . These two inequalities force in the coherence condition, hence the only input of it is from . Therefore represents a differential. d=2 Unpacking the coherence condition for gives the degree map . In the sum there are the inequalities of indices giving equal to . Unpacking the coherence sum gives the relation , which when rewritten with and as the differential and multiplication, it is , which is the Leibniz rule for differential graded algebras. d=3 In this degree the associativity structure comes to light. Note if then ther
https://en.wikipedia.org/wiki/Maxwell%20Woledzi	Maxwell Woledzi (born 2 July 2001) is a Ghanaian professional footballer who plays as a centre-back for Norwegian club Fredrikstad. Career statistics Club Notes References 2001 births Living people Ghanaian men's footballers Men's association football defenders Right to Dream Academy players FC Nordsjælland players Vitória S.C. B players Danish Superliga players Ghanaian expatriate men's footballers Expatriate men's footballers in Denmark Ghanaian expatriate sportspeople in Denmark Expatriate men's footballers in Portugal Ghanaian expatriate sportspeople in Portugal
https://en.wikipedia.org/wiki/Yudai%20Nagano%20%28footballer%29	is a Japanese footballer currently playing as a midfielder for Giravanz Kitakyushu. Career statistics Club . Notes References External links 1998 births Living people Japanese men's footballers Men's association football midfielders Hannan University alumni J2 League players Giravanz Kitakyushu players
https://en.wikipedia.org/wiki/Vector-valued%20Hahn%E2%80%93Banach%20theorems	In mathematics, specifically in functional analysis and Hilbert space theory, vector-valued Hahn–Banach theorems are generalizations of the Hahn–Banach theorems from linear functionals (which are always valued in the real numbers or the complex numbers ) to linear operators valued in topological vector spaces (TVSs). Definitions Throughout and will be topological vector spaces (TVSs) over the field and will denote the vector space of all continuous linear maps from to , where if and are normed spaces then we endow with its canonical operator norm. Extensions If is a vector subspace of a TVS then has the extension property from to if every continuous linear map has a continuous linear extension to all of . If and are normed spaces, then we say that has the metric extension property from to if this continuous linear extension can be chosen to have norm equal to . A TVS has the extension property from all subspaces of (to ) if for every vector subspace of , has the extension property from to . If and are normed spaces then has the metric extension property from all subspace of (to ) if for every vector subspace of , has the metric extension property from to . A TVS has the extension property if for every locally convex space and every vector subspace of , has the extension property from to . A Banach space has the metric extension property if for every Banach space and every vector subspace of , has the metric extension property from to . 1-extensions If is a vector subspace of normed space over the field then a normed space has the immediate 1-extension property from to if for every , every continuous linear map has a continuous linear extension such that . We say that has the immediate 1-extension property if has the immediate 1-extension property from to for every Banach space and every vector subspace of . Injective spaces A locally convex topological vector space is injective if for every locally convex space containing as a topological vector subspace, there exists a continuous projection from onto . A Banach space is 1-injective or a -space if for every Banach space containing as a normed vector subspace (i.e. the norm of is identical to the usual restriction to of 's norm), there exists a continuous projection from onto having norm 1. Properties In order for a TVS to have the extension property, it must be complete (since it must be possible to extend the identity map from to the completion of ; that is, to the map ). Existence If is a continuous linear map from a vector subspace of into a complete Hausdorff space then there always exists a unique continuous linear extension of from to the closure of in . Consequently, it suffices to only consider maps from closed vector subspaces into complete Hausdorff spaces. Results Any locally convex space having the extension property is injective. If is an injective Banach space, then for every Banach spa
https://en.wikipedia.org/wiki/Tetsuya%20Chinen	is a Japanese professional footballer who plays as a centre back for J1 League club Urawa Red Diamonds. Career statistics Club Honours Club Urawa Red Diamonds Japanese Super Cup: 2022 AFC Champions League: 2022 References External links Profile at Urawa Red Diamonds 1997 births Living people People from Naha Association football people from Okinawa Prefecture Kindai University alumni Japanese men's footballers Men's association football defenders J1 League players J2 League players FC Ryukyu players Urawa Red Diamonds players
https://en.wikipedia.org/wiki/Ren%20Yamamoto%20%28footballer%2C%20born%201999%29	is a Japanese footballer currently playing as a midfielder for Tochigi SC. Career statistics Club . Notes References External links 1999 births Living people Sportspeople from Akita Prefecture Association football people from Akita Prefecture Japanese men's footballers Men's association football midfielders J2 League players Blaublitz Akita players FC Ryukyu players Arterivo Wakayama players
https://en.wikipedia.org/wiki/Kanta%20Makino	is a Japanese footballer currently playing as a midfielder for Nagano Parceiro. Career statistics Club . Notes References External links 1997 births Living people Japanese men's footballers Men's association football midfielders Kansai University alumni J3 League players Gamba Osaka players AC Nagano Parceiro players
https://en.wikipedia.org/wiki/Jorn%20Pedersen	is a Japanese footballer currently playing as a forward for YSCC Yokohama. Career statistics Club . Notes References External links 1997 births Living people Japanese men's footballers Danish men's footballers Men's association football forwards Keio University alumni J3 League players YSCC Yokohama players
https://en.wikipedia.org/wiki/Hiromu%20Kamada	is a Japanese footballer currently playing as a midfielder for Vegalta Sendai. Career statistics Club . Notes Personal life His elder brother Daichi is also a professional footballer. References External links 2001 births Living people Japanese men's footballers Men's association football midfielders J3 League players Fukushima United FC players J2 League players Vegalta Sendai players
https://en.wikipedia.org/wiki/Takumi%20Katai	is a Japanese footballer currently playing as a forward for FC Imabari. Career statistics Club . Notes References External links 1995 births Living people Japanese men's footballers Men's association football forwards National Institute of Fitness and Sports in Kanoya alumni Japan Football League players J3 League players FC Imabari players Kochi United SC players

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