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https://en.wikipedia.org/wiki/The%20Tower%20of%20Hanoi%20%E2%80%93%20Myths%20and%20Maths
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The Tower of Hanoi – Myths and Maths is a book in recreational mathematics, on the tower of Hanoi, baguenaudier, and related puzzles. It was written by Andreas M. Hinz, Sandi Klavžar, Uroš Milutinović, and Ciril Petr, and published in 2013 by Birkhäuser, with an expanded second edition in 2018. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries.
Topics
Although this book is in recreational mathematics, it takes its subject seriously, and brings in material from automata theory, computational complexity, the design and analysis of algorithms, graph theory, and group theory, topology, fractal geometry, chemical graph theory, and even psychology (where related puzzles have applications in psychological testing).
The 1st edition of the book had 10 chapters, and the 2nd edition has 11. In both cases they begin with chapter zero, on the background and history of the Tower of Hanoi puzzle, covering its real-world invention by Édouard Lucas and in the mythical backstory he invented for it. Chapter one considers the Baguenaudier puzzle (or, as it is often called, the Chinese rings), related to the tower of Hanoi both in the structure of its state space and in the fact that it takes an exponential number of moves to solve, and likely the inspiration for Lucas. Chapter two introduces the main topic of the book, the tower of Hanoi, in its classical form in which one must move disks one-by-one between three towers, always keeping the disks on each tower sorted by size. It provides several different algorithms for solving the classical puzzle (in which the disks begin and end all on a single tower) in as few moves as possible, and for collecting all disks on a single tower when they begin in other configurations, again as quickly as possible. It introduces the Hanoi graphs describing the state space of the puzzle, and relates numbers of puzzle steps to distances within this graph. After a chapter on "irregular" puzzles in which the initial placement of disks on their towers is not sorted, chapter four discusses the "Sierpiński graphs" derived from the Sierpiński triangle; these are closely related to the three-tower Hanoi graphs but diverge from them for higher numbers of towers of Hanoi or higher-dimensional Sierpinski fractals.
The next four chapters concern additional variants of the tower of Hanoi, in which more than three towers are used, the disks are only allowed to move between some of the towers or in restricted directions between the towers, or the rules for which disks can be placed on which are modified or relaxed. A particularly important case is the Reve's puzzle, in which the rules are unchanged except that there are four towers instead of three. An old conjecture concerning the minimum possible number of moves between two states with all disks on a single tower was finally proven in 2014, after the publication of the first edition of the book, and the
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https://en.wikipedia.org/wiki/Theoretical%20Biology%20and%20Medical%20Modelling
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Theoretical Biology and Medical Modelling is a peer-reviewed online-only medical journal covering mathematical and theoretical biology, as well as on applications of mathematics in the field of medicine. It was established in 2004 and is published by BioMed Central. The editor-in-chief is Prof. Hiroshi Nishiura (Kyoto University). According to the Journal Citation Reports, the journal has a 2021 impact factor of 2.432. The journal was ceased to be published by BioMed Central as of 31 December 2021.
References
External links
Academic journals established in 2004
BioMed Central academic journals
English-language journals
Mathematical and theoretical biology journals
General medical journals
Online-only journals
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https://en.wikipedia.org/wiki/Washington%20Commanders%20records
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This article details statistics relating to the Washington Commanders, a club member of the National Football League (NFL).
Passing
Yardage
Completions
Touchdowns
Receiving
Receptions
Receiving yards
Receiving touchdowns
Rushing
Rushes
Rushing yards
Touchdowns
Kick and punt returning
Kick return yards
Yards per return
Return touchdowns
References
External links
Pro Football Reference
records
American football team records and statistics
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https://en.wikipedia.org/wiki/Marilyn%20Seastrom
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Marilyn M. Seastrom (born 1951, née Miles, also published as Marilyn M. McMillen) is an American statistician specializing in educational statistics. She is the chief statistician at the National Center for Education Statistics.
Seastrom studied biology and sociology as an undergraduate, and went on to earn master's degrees in each. She also has a doctorate in demography and applied social statistics.
She is a Fellow of the American Statistical Association and a Fellow of the American Educational Research Association. In 2016 she was elected chair of the Government Statistics Section of the American Statistical Association.
References
1951 births
Living people
American statisticians
Women statisticians
Fellows of the American Statistical Association
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https://en.wikipedia.org/wiki/Alexander%20Schmidt%20%28mathematician%29
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Alexander Schmidt (born 1965) is a German mathematician at the University of Heidelberg. His research interests include algebraic number theory and algebraic geometry.
Life
Schmidt attended the Heinrich Heinrich-Hertz-Gymnasium in East Berlin, a special school for mathematics. In 1984 he received the bronze medal at the International Mathematical Olympiad in Prague. He studied mathematics at the Humboldt University in Berlin and was awarded the diploma in 1991. In 1993, he obtained his PhD at the University of Heidelberg by Kay Wingberg (Positive branched extensions of algebraic number fields). He then was a research assistant and later an assistant at the chair of Prof. Wingberg. He was also a Heisenberg fellow from 2002 to 2004. In 2000, he habilitated at the University of Heidelberg (with a thesis on the connection between algebraic cycle theory and higher-dimensional class field theory), was a private lecturer there, 2001 chair at the University of Cologne, and in 2004 became a professor at the University of Regensburg and is now a professor at the University of Heidelberg.
Publications
Einführung in die Algebraische Zahlentheorie, Springer 2007
with Kay Wingberg and Jürgen Neukirch Cohomology of number fields. Springer 2000, second edition 2008,
Editor of the new edition of Jürgen Neukirch's Klassenkörpertheorie, Springer 2011
Editor of Jürgen Neukirch's Class Field Theory - The Bonn Lectures, Springer Verlag 2011
References
The article contains translated materials from the corresponding article in German Wikipedia.
External links
Faculty page, University of Heidelberg
1965 births
Living people
20th-century German mathematicians
Academic staff of Heidelberg University
21st-century German mathematicians
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https://en.wikipedia.org/wiki/Kay%20Wingberg
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Kay Wingberg (born 1949) is a German mathematician at the University of Heidelberg. His research interests include algebraic number theory, Iwasawa theory, arithmetic geometry and the structure of profinite (or pro-p) groups.
Publications
with Jürgen Neukirch and Alexander Schmidt Cohomology of number fields. Springer 2000, second edition 2008,
References
External links
faculty page, University of Heidelberg
1949 births
Living people
20th-century German mathematicians
Academic staff of Heidelberg University
21st-century German mathematicians
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https://en.wikipedia.org/wiki/Muhammad%20Rafique%20%28mathematician%29
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Muhammad Rafique (2 January 1940 — 16 June 1996) was a Pakistani mathematician and professor of mathematics at the Punjab University. He was a versatile scholar who authored textbooks on computer language and special relativity. He was the co-author of textbook Group Theory for High Energy Physicists, which was eventually published years after his death in 2016.
Biographical overview
Rafique was born in Lahore, Punjab in British India on 2 January,1940 in Lahore, Punjab in India and was educated at the Punjab University where he graduated with BA with first-class honours in Mathematics in 1960. He served in the Faculty of Mathematics at the Punjab University where he graduated with MA in Mathematics in 1964, and earned a scholarship to study mathematics in the United Kingdom. He attended the University of North Wales where he graduated with a PhD in Mathematics in 1967.
Upon returning to Pakistan, he joined the Punjab University and taught there until 1971 when he joined the International Center for Theoretical Physics in Italy as a post-doctoral scholar. From 1972 to 1977, Rafique worked at the Institute of Nuclear Science and Technology where he contributed his work on fast neutron calculations for atomic weapons which built his interests in the theory of relativity and nuclear physics.
From 1977 to 1982, he served on the faculty of University of Tripoli in Libya, and served as the Head of Department of Mathematics at the Punjab University from 1983 until 1992 when he went to teach mathematics at the King Fahd University in Saudi Arabia. His tenure at the King Fahd University was short-lived. He died due to cardiac arrest in June 1996. Although a mathematician, Rafique was a prolific author on physics, was writing a college text on group theory's applications on high energy physics with Mohammad Saleem at the time of his death in 1992. The college book was eventually published in 2015-2016 by British publisher Taylor & Francis.
Textbooks
See also
Definite integral
References
External links
Punjab University
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R
R
R
R
R
Pakistani relativity theorists
R
R
R
R
R
R
R
R
R
Pakistani expatriates in Libya
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https://en.wikipedia.org/wiki/Wolfgang%20Martin%20Stroh
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Wolfgang Martin Stroh (born 1 July 1941) is a German musicologist and Emeritus professor at the Carl von Ossietzky Universität Oldenburg.
Life
Born in Stuttgart, Stroh studied mathematics, physics, musicology and modern German literature at the Universities of Erlangen, Munich, Freiburg and at the Eastman School of Music (Rochester). In 1973 he obtained his doctorate with Hans Heinrich Eggebrecht (Freiburg). In 2006 he acquired the HAF diploma for multimedia design. He was a teacher at several Gymnasiums, from 1973 to 1978 he was research fellow at the Oberstufen-Kolleg Bielefeld, since 1978 Professor for systematic musicology at the University of Oldenburg. In the he has become known for his "extended interface approach".
Publications
Anton Webern. Historische Legitimation als kompositorisches Problem. (Göppinger Akademische Beiträge 63). Verlag Kümmerle, Göppingen 1973.
Zur Soziologie der elektronischen Musik. Amadeus-Verlag, Zürich 1975.
Leben Ja. Zur Psychologie musikalischer Tätigkeit. Musik in Kellern, auf Plätzen und vor Natodraht. Marohl-Verlag, Stuttgart 1984. .
with Ralf Nebhuth: Carmen. Begründungen und Unterrichtsmaterialien (Szenische Interpretation von Opern, Band 1). Lugert-Verlag, Oldershausen 1990. .
Handbuch New Age Musik. Auf der Suche nach neuen musikalischen Erfahrungen. (ConBrio Fachbuch Band 1). Verlag ConBrio, Regensburg 1994. .
Szenische Interpretation von Musik. Eine Anleitung zur Entwicklung von Spielkonzepten anhand ausgewählter Beispiele.(Norbert Schläbitz (ed.): EinFach Musik, vol. 3). Schöningh-Verlag, Paderborn 2007. .
With Margherita D’Amelio: Tarantella in der Schule. Eine multimediale Lernumgebung. starfish music Production, Bremen 2012 / Lugert-Verlag, Oldershausen 2012. DVD 027191–670245.
References
External links
Website von Wolfgang Martin Stroh
1941 births
Living people
People from Stuttgart
20th-century German musicologists
Academic staff of the University of Oldenburg
German music educators
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https://en.wikipedia.org/wiki/Al%20Muqaraea
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Al Muqaraea () is a village in Al Udayn District. It is located in the Ibb Governorate, According to the 2004 census it had a population of 52 people.
External links
Central Statistics Agency of the Republic of Yemen
National Information Center in Yemen
References
Districts of Ibb Governorate
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https://en.wikipedia.org/wiki/Salaq
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Salaq () is a village in Kushar District . It is located in the Hajjah Governorate, According to the 2004 census it had a population of 231 people.
External links
Central Statistics Agency of the Republic of Yemen
National Information Center in Yemen
References
Populated places in Hajjah Governorate
Port cities in the Arabian Peninsula
Port cities and towns of the Red Sea
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https://en.wikipedia.org/wiki/1933%E2%80%9334%20Rochdale%20A.F.C.%20season
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The 1933–34 season saw Rochdale compete for their 13th season in the Football League Third Division North.
Statistics
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Final league table
Competitions
Football League Third Division North
FA Cup
Third Division North Cup
Lancashire Cup
Manchester Cup
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Peter%20Li%20%28mathematician%29
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Peter Wai-Kwong Li (born 18 April 1952) is an American mathematician whose research interests include differential geometry and partial differential equations, in particular geometric analysis. After undergraduate work at California State University, Fresno, he received his Ph.D. at University of California, Berkeley under Shiing-Shen Chern in 1979. Presently he is Professor Emeritus at University of California, Irvine, where he has been located since 1991.
His most notable work includes the discovery of the Li–Yau differential Harnack inequalities, and the proof of the Willmore conjecture in the case of non-embedded surfaces, both done in collaboration with Shing-Tung Yau. He is an expert on the subject of function theory on complete Riemannian manifolds.
He has been the recipient of a Guggenheim Fellowship in 1989 and a Sloan Research Fellowship. In 2002, he was an invited speaker in the Differential Geometry section of the International Congress of Mathematicians in Beijing, where he spoke on the subject of harmonic functions on Riemannian manifolds. In 2007, he was elected a member of the American Academy of Arts and Sciences, which cited his "pioneering" achievements in geometric analysis, and in particular his paper with Yau on the differential Harnack inequalities, and its application by Richard S. Hamilton and Grigori Perelman in the proof of the Poincaré conjecture and Geometrization conjecture.
Notable publications
See also
Ricci flow#Li–Yau inequalities
References
External links
Peter Li's website at University of California, Irvine
Differential geometers
UC Berkeley College of Letters and Science alumni
University of California, Irvine faculty
Fellows of the American Academy of Arts and Sciences
California State University, Fresno alumni
1952 births
Living people
20th-century American mathematicians
21st-century American mathematicians
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https://en.wikipedia.org/wiki/Samuel%20Kou
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Shingchang "Samuel" Kou (; born in 1974) is a Chinese American statistician and Professor of Statistics at Harvard University.
Biography
He earned a bachelor's degree in computational mathematics at Peking University. He graduated in 1997 and then moved to the United States to study statistics at Stanford University under Bradley Efron. He earned his Ph.D. in 2001 and subsequently joined the statistics faculty at Harvard University.
In 2008, he became a full professor of statistics at Harvard.
Honors and awards
In 2007, he was elected a fellow of the American Statistical Association. In 2013, he was awarded a Guggenheim fellowship.
He received the COPSS Presidents' Award in 2012. The reason for receiving the award was described as follows:
Selected publications
S. C. Kou, Qing Zhou, and Wing Hung Wong. "Equi-energy sampler with applications in statistical inference and statistical mechanics". Annals of Statistics, 34(4), 1581–1619, 2006.
References
External links
Faculty website
1974 births
Living people
American statisticians
Harvard University faculty
Peking University alumni
Stanford University alumni
Fellows of the American Statistical Association
People from Lanzhou
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https://en.wikipedia.org/wiki/Roswitha%20M%C3%A4rz
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Roswitha März (born October 15, 1940) is a German mathematician known for her research on differential-algebraic systems of equations. She is a professor emeritus of mathematics at the Humboldt University of Berlin.
Education and career
März was born on October 15, 1940, in Varnsdorf, now part of the Czech Republic. Beginning in 1960 she studied mathematics at the University of Leningrad, now Saint Petersburg State University, earning a diploma in 1965. She earned a doctorate (Dr. sc. nat.) from the Chemnitz University of Technology in 1970. Her dissertation, Interpolation mit Parameteroptimierung, was supervised by Frieder Kuhnert.
She worked at the Humboldt University of Berlin beginning in 1968, first as a researcher and later as a faculty member, serving as dean of the mathematics faculty from 1990 to 1991 and becoming University Professor in 1992.
Books
März is the author or coauthor of books including:
Differential-algebraic equations: a projector based analysis (with René Lamour and Caren Tischendorf, Springer, 2013)
Differential-algebraic equations and their numerical treatment (with Eberhard Griepentrog, Teubner, 1986)
Parametric multistep methods (Humboldt University, 1979)
References
External links
Home page
1940 births
Living people
People from Varnsdorf
20th-century German mathematicians
German women mathematicians
Saint Petersburg State University alumni
Chemnitz University of Technology alumni
Academic staff of the Humboldt University of Berlin
20th-century German women
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https://en.wikipedia.org/wiki/Dieter%20Puppe
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Siegmund Dieter Puppe (16 December 1930 – 13 August 2005) was a German mathematician who worked in algebraic topology, differential topology and homological algebra. He is known for the Puppe sequence in algebraic topology.
Life
Dieter Puppe was born the son of the lawyer Siegmund Puppe. The mathematician Volker Puppe (born 1938) and the legal scholar Ingeborg Puppe (born 1941) were his siblings. From 1948 he studied physics and mathematics in University of Göttingen and from 1951 at Heidelberg University. In 1954 he received his doctorate under Herbert Seifert (On the homotopy of images of a polyhedron. Mathematische Zeitschrift Bd. 61, 1954, S. 303). From 1951 he was an assistant in Heidelberg and after his habilitation in 1957, a lecturer. In 1960 he became a professor in Saarbrücken. In 1968 he returned to Heidelberg, where he stayed until his retirement in 1996, apart from guest stays at the Institute for Advanced Study in Princeton in 1957/58, in Chicago in 1961, and in Minneapolis in 1966/67.
Puppe worked on knot theory (with Martin Kneser as early as the 1950s) and homotopy theory.
From 1972 he was a member of the Heidelberg Academy of Sciences. In 1962 he gave a lecture at the International Congress of Mathematicians in Stockholm (Korrespondenzen in abelschen Kategorien).
His students included Tammo tom Dieck, Hans-Werner Henn, and Rudolf Fritsch.
Works
with Hans-Berndt Brinkmann: Kategorien und Funktoren (= Lecture Notes in Mathematics. 18). Springer, Berlin u. a. 1966.
Stabile Homotopietheorie I. In: Mathematische Annalen. Bd. 169, Nr. 2, 1967, S. 243–274.
Einhängungssätze im Aufbau der Homotopietheorie. In: Jahresbericht der Deutschen Mathematiker-Vereinigung. Bd. 71, 1969, S. 48–54.
with Hans-Berndt Brinkmann: Abelsche und exakte Kategorien, Korrespondenzen (= Lecture Notes in Mathematics. 96). Springer, Berlin u. a. 1969.
with Tammo tom Dieck, Klaus Heiner Kamps: Homotopietheorie (= Lecture Notes in Mathematics. 157). Springer, Berlin u. a. 1970, (originated by a lecture by Puppe at the University of Minnesota 1966/67).
with Hans-Werner Henn: Algebraische Topologie. In: Gerd Fischer, Friedrich Hirzebruch, Winfried Scharlau, Willi Törnig (Hrsg.): Ein Jahrhundert Mathematik 1890–1990. Festschrift zum Jubiläum des DMV (= Dokumente zur Geschichte der Mathematik. 6). Vieweg, Braunschweig u. a. 1990, , S. 673–716.
Literature
Puppe, Dieter. In: Dagmar Drüll: Heidelberger Gelehrtenlexikon. Bd. 3, Heidelberg 2009, S. 476.
See also
Puppe sequence
References
1930 births
2005 deaths
20th-century German mathematicians
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https://en.wikipedia.org/wiki/Pascal%20Massart
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Pascal Massart (born 23 January 1958) is a French Statistician.
His work focuses on probability and statistics, notably the Dvoretzky–Kiefer–Wolfowitz inequality, the Bousquet inequality, the concentration inequality, and the Efron-Stein inequality. With Lucien Birgé he worked on model selection.
He received his Ph.D. in statistics from Paris-Sud University under Jean Bretagnolle. He has worked at the University of Paris-Sud and at the University of Lyon.
Honors and awards
He was awarded the COPSS Presidents' Award in 1998. He was awarded the Prix Pierre-Simon de Laplace from the French Statistical Society in 2007 alongside Paul Deheuvels. He was a lecturer at the European Congress of Mathematics in 2004 in Stockholm.
Books
Concentration Inequalities: A Nonasymptotic Theory of Independence (2013)
Concentration Inequalities and Model Selection (2003)
References
External links
Official website
Living people
French statisticians
1958 births
Paris-Sud University alumni
Academic staff of Paris-Sud University
Mathematical statisticians
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https://en.wikipedia.org/wiki/1934%E2%80%9335%20Rochdale%20A.F.C.%20season
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The 1934–35 season saw Rochdale compete for their 14th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
FA Cup
Third Division North Cup
Lancashire Cup
Manchester Cup
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Kimberly%20Powers
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Kimberly A. Powers is an American epidemiologist who is an associate professor of epidemiology at the UNC Gillings School of Global Public Health. She combines epidemiology, statistics and mathematical modelling to understand the transmission of infectious diseases. In 2011 her work on antiretroviral therapy for the management of human immunodeficiency virus was selected by Science as the breakthrough of the year. During the COVID-19 pandemic, Powers looked to understand the spread of SARS-CoV-2.
Early life and education
As a child Powers considered becoming as physician. She eventually studied mathematics at Hamilton College and graduated in 1998. After graduating she joined a healthcare consultancy, where she was first introduced to epidemiology. She spent a year at The University of New Mexico where she studied tobacco use in the community. In 2002 she moved to Los Alamos National Laboratory, where she worked as a graduate assistant in the biophysics group. There she developed mathematical models that could describe viral transmission. She was eventually accepted as a graduate student at the University of North Carolina at Chapel Hill, where she eared a Master's in Public Health. During her second year at UNC she saw a talk from Myron S. Cohen, and became interest in the use of antiretroviral drugs to treat HIV. She remained at the University of North Carolina at Chapel Hill for her doctoral studies, where she studied the transmission dynamics of HIV in the laboratory of Cohen. During her doctoral research, Cohen realised that Powers would need formal training in epidemiology. She spent one year in the United Kingdom, studying at the London School of Hygiene & Tropical Medicine and Imperial College London. In particular, her research considered acute- and early-stage HIV infection in Lilongwe. She spent weeks at a time visiting a STD clinic in Lilongwe, where she looked to improve patient care as well as track trends in HIV transmission.
Research and career
In 2010 Powers started a postdoctoral research position at the UNC Gillings School of Global Public Health. She identified that almost 40% of HIV transmission occurred before patients or physicians knew about it, meaning that treatment often started after infection had occurred. People who are unaware about their own HIV infection contribute significantly to the ongoing transmission of virus. She was awarded the University of North Carolina at Chapel Hill award for research excellence in 2011.
Powers recognised that population-level prevention of HIV would require regular testing, to detect the virus in its early stages, as well as the provision of antiretroviral drugs. Powers was part of the HPTN 052 clinical trial, and demonstrated that there was a 96% reduction in transmission in couples who had been treated with antiretroviral therapy. She looked to apply this understanding to other populations, including in the US prison community. The proportion of HIV positive Americans in the U
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https://en.wikipedia.org/wiki/Simone%20Gutt
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Simone Gutt (born 1956) is a Belgian mathematician specializing in differential geometry. She is a professor of mathematics at the Université libre de Bruxelles.
Education and career
Gutt was born on 13 July 1956 in Uccle, near Brussels. She completed her doctorate in 1980 at the Université libre de Bruxelles; her dissertation, Déformations formelles de l'algèbre des fonctions différentiables sur une variété symplectique, was jointly supervised by Michel Cahen and .
She was a researcher for the National Fund for Scientific Research from 1981 until 1991, and became a professor at the Université libre de Bruxelles in 1992.
Recognition
Gutt was the 1998 winner of the quadrennial Francois Deruyts Prize in geometry of the Royal Academies for Science and the Arts of Belgium. She was elected to the Royal Academy of Science, Letters and Fine Arts of Belgium in 2004.
References
External links
Home page
1956 births
Living people
Belgian mathematicians
Belgian women mathematicians
Academic staff of the Université libre de Bruxelles
Members of the Royal Academy of Belgium
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https://en.wikipedia.org/wiki/Making%20Mathematics%20with%20Needlework
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Making Mathematics with Needlework: Ten Papers and Ten Projects is an edited volume on mathematics and fiber arts. It was edited by Sarah-Marie Belcastro and Carolyn Yackel, and published in 2008 by A K Peters, based on a meeting held in 2005 in Atlanta by the American Mathematical Society.
Topics
The book includes ten different mathematical fiber arts projects, by eight contributors. An introduction provides a history of the connections between mathematics, mathematics education, and the fiber arts. Each of its ten project chapters is illustrated by many color photographs and diagrams, and is organized into four sections: an overview of the project, a section on the mathematics connected to it, a section of ideas for using the project as a teaching activity, and directions for constructing the project. Although there are some connections between topics, they can be read independently of each other, in any order. The thesis of the book is that directed exercises in fiber arts construction can help teach both mathematical visualization and concepts from three-dimensional geometry.
The book uses knitting, crochet, sewing, and cross-stitch, but deliberately avoids weaving as a topic already well-covered in mathematical fiber arts publications. Projects in the book include a quilt in the form of a Möbius strip, a "bidirectional hat" connected to the theory of Diophantine equations, a shawl with a fractal design, a knitted torus connecting to discrete approximations of curvature, a sampler demonstrating different forms of symmetry in wallpaper group, "algebraic socks" with connections to modular arithmetic and the Klein four-group, a one-sided purse sewn together following a description by Lewis Carroll, a demonstration of braid groups on a cable-knit pillow, an embroidered graph drawing of an Eulerian graph, and topological pants.
Beyond belcastro and Yackel, the contributors to the book include Susan Goldstine, Joshua Holden, Lana Holden, Mary D. Shepherd, Amy F. Szczepański, and D. Jacob Wildstrom.
Audience and reception
Reviewers had mixed opinions on the appropriate audience for the book and its success in targeting that audience. Ketty Peeva writes that the book is "of interest to mathematicians, mathematics educators and crafters", and Mary Fortune writes that a wide group of people would enjoy browsing its contents, However, Kate Atherley warns that it is "not for the faint-of-heart" (either among mathematicians or crafters), and Mary Goetting complains that the audience for the book is not clearly defined, and is inconsistent across the book, with some chapters written for professional mathematicians and others for mathematical beginners. She writes that most readers will have to pick and choose among the chapters for material appealing to them. Similarly, reviewer Michelle Sipics writes that in aiming at multiple audiences, the book "sacrifices some accessibility". And although reviewer Gwen Fisher downplays the potential pedagogical app
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https://en.wikipedia.org/wiki/Susan%20Goldstine
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Susan Goldstine is an American mathematician active in mathematics and fiber arts. She is a professor of mathematics at St. Mary's College of Maryland, and (for 2019–2022) the Steven Muller Distinguished Professor in the Sciences at St. Mary's College.
Education and career
Goldstine graduated summa cum laude from Amherst College in 1993. She completed a Ph.D. in mathematics at Harvard University in 1998. Her dissertation, Spin Representations and Lattices, was supervised by Benedict Gross.
After postdoctoral and visiting assistant professorships at McMaster University, Ohio State University, and Amherst College, she joined the St. Mary's College faculty in 2004.
Contributions
Goldstine has made and exhibited many pieces of mathematical art, often involving textiles. A set of bead crochet jewelry pieces by her visualizing the map coloring problem on three different manifolds won the prize for "best textile, sculpture, or other medium" in the art show of the 2015 Joint Mathematics Meetings.
She is the coauthor of the book Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist (with Ellie Baker, A K Peters / CRC Press, 2014).
Combining her interests in mathematics and fiber arts she is one of 24 mathematicians and artists who make up the Mathemalchemy Team.
Personal life
Goldstine is the granddaughter of teacher and author Bel Kaufman and the great-great-granddaughter of Sholem Aleichem.
References
External links
Home page
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
Recreational mathematicians
Amherst College alumni
Harvard Graduate School of Arts and Sciences alumni
St. Mary's College of Maryland faculty
Mathematical artists
20th-century American women
21st-century American women
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https://en.wikipedia.org/wiki/Natalie%20Dean
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Natalie E. Dean (née Exner; born 1987) is an American biostatistician specializing in infectious disease epidemiology. Dean is currently an assistant professor of Biostatistics at the University of Florida. Her research involves epidemiological modeling of outbreaks, including Ebola, Zika and COVID-19.
Early life and education
Dean was born to Christine and Paul Exner. She grew up in Reading, Massachusetts, and attended Phillips Academy. She became interested in infectious diseases during high school. While Dean briefly considered becoming an experimental microbiologist, she quickly recognized that she preferred the computer to the laboratory.
In 2009, Dean earned a B.A. in mathematics/statistics and biology from Boston University, where she was first introduced to epidemiology. During her undergraduate degree she was inducted into the Phi Beta Kappa honor society. In 2011, Dean earned an A.M. master's degree in biostatistics from Harvard University where she developed surveillance methods to better understand the incidence of HIV. Dean received a PhD in biostatistics in 2014 with a dissertation on Surveillance methods for monitoring HIV incidence & drug resistance under the supervision of Marcello Pagano.
Research and career
In May 2014, Dean moved to Florida, where she joined the World Health Organization as a statistical consultant. In this capacity she designed surveys that could evaluate the drug resistant mutations to HIV treatment. In 2015 she joined the University of Florida Center for Statistics in Quantitative Infectious Diseases (CSQUID), where she worked as a postdoctoral researcher with Ira Longini. At CSQUID Dean conducts epidemiological analysis of disease outbreaks. She worked on the design of a vaccine trial for the Ebola virus epidemic in Guinea, which made use of a ring vaccination strategy. The ring vaccination approach had previously been used to eradicate smallpox in the 1970s. This strategy randomly selects and vaccinates the contacts of Ebola virus cases, and organizes populations into delayed and immediate-vaccination clusters. The ring vaccination approach was shown to be highly effective, and was replicated in the Democratic Republic of the Congo in 2018. Dean also studied asymptomatic Ebola cases.
After her success with the Ebola vaccine, Dean started to work on Zika virus. There were concerns that Zika virus caused microcephaly. Dean worked with Longini to better predict the spread of the infection through the Americas. She has described how challenging it is to design and evaluate effective vaccinations during public health emergencies, and why researchers must be both flexible and responsive.
Dean has provided expert commentary to the media and public throughout the COVID-19 pandemic. She has continued to work with the World Health Organization on the evaluation of a coronavirus vaccine. Mashable described Dean as one of the top coronavirus disease researchers to follow on Twitter. In discussion with her alma
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https://en.wikipedia.org/wiki/Mathology
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Mathology is:
a fictional religion from the US television program Young Sheldon
a part of mathematics
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https://en.wikipedia.org/wiki/LB-space
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In mathematics, an LB-space, also written (LB)-space, is a topological vector space that is a locally convex inductive limit of a countable inductive system of Banach spaces.
This means that is a direct limit of a direct system in the category of locally convex topological vector spaces and each is a Banach space.
If each of the bonding maps is an embedding of TVSs then the LB-space is called a strict LB-space. This means that the topology induced on by is identical to the original topology on
Some authors (e.g. Schaefer) define the term "LB-space" to mean "strict LB-space," so when reading mathematical literature, its recommended to always check how LB-space is defined.
Definition
The topology on can be described by specifying that an absolutely convex subset is a neighborhood of if and only if is an absolutely convex neighborhood of in for every
Properties
A strict LB-space is complete, barrelled, and bornological (and thus ultrabornological).
Examples
If is a locally compact topological space that is countable at infinity (that is, it is equal to a countable union of compact subspaces) then the space of all continuous, complex-valued functions on with compact support is a strict LB-space. For any compact subset let denote the Banach space of complex-valued functions that are supported by with the uniform norm and order the family of compact subsets of by inclusion.
Final topology on the direct limit of finite-dimensional Euclidean spaces
Let
denote the , where denotes the space of all real sequences.
For every natural number let denote the usual Euclidean space endowed with the Euclidean topology and let denote the canonical inclusion defined by so that its image is
and consequently,
Endow the set with the final topology induced by the family of all canonical inclusions.
With this topology, becomes a complete Hausdorff locally convex sequential topological vector space that is a Fréchet–Urysohn space.
The topology is strictly finer than the subspace topology induced on by where is endowed with its usual product topology.
Endow the image with the final topology induced on it by the bijection that is, it is endowed with the Euclidean topology transferred to it from via
This topology on is equal to the subspace topology induced on it by
A subset is open (resp. closed) in if and only if for every the set is an open (resp. closed) subset of
The topology is coherent with family of subspaces
This makes into an LB-space.
Consequently, if and is a sequence in then in if and only if there exists some such that both and are contained in and in
Often, for every the canonical inclusion is used to identify with its image in explicitly, the elements and are identified together.
Under this identification, becomes a direct limit of the direct system where for every the map is the canonical inclusion defined by where there are trailing zeros.
Counter-examp
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https://en.wikipedia.org/wiki/Blumberg%20theorem
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In mathematics, the Blumberg theorem states that for any real function there is a dense subset of such that the restriction of to is continuous.
Examples
For instance, the restriction of the Dirichlet function (the indicator function of the rational numbers ) to is continuous, although the Dirichlet function is nowhere continuous in
Blumberg spaces
More generally, a Blumberg space is a topological space for which any function admits a continuous restriction on a dense subset of The Blumberg theorem therefore asserts that (equipped with its usual topology) is a Blumberg space.
If is a metric space then is a Blumberg space if and only if it is a Baire space.
Motivation and discussion
The restriction of any continuous function to any subset of its domain (dense or otherwise) is always continuous, so the conclusion of the Blumberg theorem is only interesting for functions that are not continuous. Given a function that is not continuous, it is typically not surprising to discover that its restriction to some subset is once again not continuous, and so only those restrictions that are continuous are (potentially) interesting.
Such restrictions are not all interesting, however. For example, the restriction of any function (even one as interesting as the Dirichlet function) to any subset on which it is constant will be continuous, although this fact is as uninteresting as constant functions.
Similarly uninteresting, the restriction of function (continuous or not) to a single point or to any finite subset of (or more generally, to any discrete subspace of such as the integers ) will be continuous.
One case that is considerably more interesting is that of a non-continuous function whose restriction to some dense subset (of its domain) continuous.
An important fact about continuous -valued functions defined on dense subsets is that a continuous extension to all of if one exists, will be unique (there exist continuous functions defined on dense subsets of such as that cannot be continuously extended to all of ).
Thomae's function, for example, is not continuous (in fact, it is discontinuous at rational number) although its restriction to the dense subset of irrational numbers is continuous.
Similarly, every additive function that is not linear (that is, not of the form for some constant ) is a nowhere continuous function whose restriction to is continuous (such functions are the non-trivial solutions to Cauchy's functional equation).
This raises the question: can such a dense subset always be found? The Blumberg theorem answer this question in the affirmative.
In other words, every function − no matter how poorly behaved it may be − can be restricted to some dense subset on which it is continuous.
Said differently, the Blumberg theorem shows that there does not exist a function that is so poorly behaved (with respect to continuity) that all of its restrictions to all possible dense subsets are discontinuous.
The t
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https://en.wikipedia.org/wiki/Tatyana%20Krivobokova
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Tatyana Krivobokova is a Kazakh statistician known for her work on spline estimators, with applications in biophysics and econometrics. She is University Professor for Statistics with Applications in Economics at the University of Vienna.
Education and career
Krivobokova earned a diploma in applied mathematics from Al-Farabi Kazakh National University in 1996, a master's degree in applied mathematics from the University of Kaiserslautern in 2002, and a doctorate (Dr. rer. pol.) in statistics from Bielefeld University in 2007. Her dissertation, Theoretical and Practical Aspects of Penalized Spline Smoothing, was jointly supervised by Göran Kauermann and . After postdoctoral research at KU Leuven in Belgium, she joined the Bielefeld University faculty in 2008. She moved to the University of Vienna in 2020.
References
External links
Home page
Year of birth missing (living people)
Living people
Kazakhstani academics
Women statisticians
Technical University of Kaiserslautern alumni
Bielefeld University alumni
Academic staff of the University of Vienna
Al-Farabi Kazakh National University alumni
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https://en.wikipedia.org/wiki/Paolo%20R%C3%ADos
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Paolo Santiago Ríos Vargas (born 14 February 2000) is a Mexican professional footballer who plays as a midfielder for MLS Next Pro club Houston Dynamo 2.
Career statistics
Club
References
2000 births
Living people
Mexican men's footballers
Men's association football midfielders
Club América footballers
Liga MX players
MLS Next Pro players
Houston Dynamo 2 players
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https://en.wikipedia.org/wiki/Spectral%20theory%20of%20normal%20C%2A-algebras
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In functional analysis, every C*-algebra is isomorphic to a subalgebra of the C*-algebra of bounded linear operators on some Hilbert space This article describes the spectral theory of closed normal subalgebras of . A subalgebra of is called normal if it is commutative and closed under the operation: for all , we have and that .
Resolution of identity
Throughout, is a fixed Hilbert space.
A projection-valued measure on a measurable space where is a σ-algebra of subsets of is a mapping such that for all is a self-adjoint projection on (that is, is a bounded linear operator that satisfies and ) such that
(where is the identity operator of ) and for every the function defined by is a complex measure on (that is, a complex-valued countably additive function).
A resolution of identity on a measurable space is a function such that for every :
;
;
for every is a self-adjoint projection on ;
for every the map defined by is a complex measure on ;
;
if then ;
If is the -algebra of all Borels sets on a Hausdorff locally compact (or compact) space, then the following additional requirement is added:
for every the map is a regular Borel measure (this is automatically satisfied on compact metric spaces).
Conditions 2, 3, and 4 imply that is a projection-valued measure.
Properties
Throughout, let be a resolution of identity.
For all is a positive measure on with total variation and that satisfies for all
For every :
(since both are equal to ).
If then the ranges of the maps and are orthogonal to each other and
<li> is finitely additive.
If are pairwise disjoint elements of whose union is and if for all then
However, is additive only in trivial situations as is now described: suppose that are pairwise disjoint elements of whose union is and that the partial sums converge to in (with its norm topology) as ; then since the norm of any projection is either or the partial sums cannot form a Cauchy sequence unless all but finitely many of the are
For any fixed the map defined by is a countably additive -valued measure on
Here countably additive means that whenever are pairwise disjoint elements of whose union is then the partial sums converge to in Said more succinctly,
In other words, for every pairwise disjoint family of elements whose union is , then (by finite additivity of ) converges to in the strong operator topology on : for every , the sequence of elements converges to in (with respect to the norm topology).
L∞(π) - space of essentially bounded function
The be a resolution of identity on
Essentially bounded functions
Suppose is a complex-valued -measurable function. There exists a unique largest open subset of (ordered under subset inclusion) such that
To see why, let be a basis for 's topology consisting of open disks and suppose that is the subsequence (possibly finite) consisting of those sets such that ; then Note that, in particular, if is
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https://en.wikipedia.org/wiki/Vanessa%20Robins
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Vanessa Robins is an Australian applied mathematician whose research interests include computational topology, image processing, and the structure of granular materials. She is a fellow in the departments of applied mathematics and theoretical physics at Australian National University, where she was ARC Future Fellow from 2014 to 2019.
Education
Robins earned a bachelor's degree in mathematics at Australian National University in 1994. She completed a PhD at the University of Colorado Boulder in 2000. Her dissertation, Computational Topology at Multiple Resolutions: Foundations and Applications to Fractals and Dynamics, was jointly supervised by James D. Meiss and Elizabeth Bradley.
Contributions
One of Robins's publications, from 1999, is one of the three works that independently introduced persistent homology in topological data analysis.
As well as working on mathematical research, she has collaborated with artist Julie Brooke, of the Australian National University School of Art & Design, on the mathematical visualization of topological surfaces.
References
External links
Year of birth missing (living people)
Living people
Australian mathematicians
Australian women mathematicians
Australian National University alumni
University of Colorado Boulder alumni
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https://en.wikipedia.org/wiki/Dan%20Margalit%20%28mathematician%29
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Dan Margalit (born March 6, 1976) is an American mathematician at Vanderbilt University. His research fields include geometric group theory and low-dimensional topology, with a particular focus on mapping class groups of surfaces.
Education and career
Margalit earned his bachelor's degree from Brown University. He earned his doctorate from the University of Chicago in 2003, advised by Benson Farb. His thesis was titled Algebra versus Topology in Mapping Class Groups. Margalit was a postdoctoral scholar at the University of Utah from 2003 to 2008. He was a faculty member at Tufts University from 2008 to 2010, before going to the Georgia Institute of Technology. In 2023, Margalit moved to Vanderbilt University as chair of the Department of Mathematics.
Margalit is known for his work in exposition of geometric group theory, particularly his book with Benson Farb, A Primer on Mapping Class Groups.
Awards and honors
Margalit became a fellow of the American Mathematical Society in 2019; he was recognized "for contributions to low-dimensional topology and geometric group theory, exposition, and mentoring." Margalit was a 2009 Sloan Research Fellow. For 2021 he received the Levi L. Conant Prize of the AMS.
Selected publications
Books
Translations
References
1976 births
Living people
21st-century American mathematicians
Tufts University faculty
Georgia Tech faculty
Brown University alumni
University of Chicago alumni
Fellows of the American Mathematical Society
Sloan Research Fellows
Topologists
Group theorists
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https://en.wikipedia.org/wiki/System%20of%20differential%20equations
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In mathematics, a system of differential equations is a finite set of differential equations. Such a system can be either linear or non-linear. Also, such a system can be either a system of ordinary differential equations or a system of partial differential equations.
Linear system of differential equations
Like any system of equations, a system of linear differential equations is said to be overdetermined if there are more equations than the unknowns.
For an overdetermined system to have a solution, it needs to satisfy the compatibility conditions. For example, consider the system:
Then the necessary conditions for the system to have a solution are:
See also: Cauchy problem and Ehrenpreis's fundamental principle.
Non-linear system of differential equations
Perhaps the most famous example of a non-linear system of differential equations is the Navier–Stokes equations. Unlike the linear case, the existence of a solution of a non-linear system is a difficult problem (cf. Navier–Stokes existence and smoothness.)
See also: h-principle.
Differential system
A differential system is a means of studying a system of partial differential equations using geometric ideas such as differential forms and vector fields.
For example, the compatibility conditions of an overdetermined system of differential equations can be succinctly stated in terms of differential forms (i.e., a form to be exact, it needs to be closed). See integrability conditions for differential systems for more.
See also: :Category:differential systems.
Notes
See also
Integral geometry
Cartan–Kuranishi prolongation theorem
References
L. Ehrenpreis, The Universality of the Radon Transform, Oxford Univ. Press, 2003.
Gromov, M. (1986), Partial differential relations, Springer,
M. Kuranishi, "Lectures on involutive systems of partial differential equations" , Publ. Soc. Mat. São Paulo (1967)
Pierre Schapira, Microdifferential systems in the complex domain, Grundlehren der Math- ematischen Wissenschaften, vol. 269, Springer-Verlag, 1985.
Further reading
https://mathoverflow.net/questions/273235/a-very-basic-question-about-projections-in-formal-pde-theory
https://www.encyclopediaofmath.org/index.php/Involutional_system
https://www.encyclopediaofmath.org/index.php/Complete_system
https://www.encyclopediaofmath.org/index.php/Partial_differential_equations_on_a_manifold
Differential equations
Differential systems
Multivariable calculus
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https://en.wikipedia.org/wiki/1990%20Chinese%20census
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The 1990 Chinese census, officially the Fourth National Population Census of the People's Republic of China, was conducted by the National Bureau of Statistics of the People's Republic of China. Based on the fourth census of July 1990, mainland China's population was estimated to be 1.133 billion. According to the 1990 census, there were 56 ethnic nationalities with a total population of 1,133 billion. Among them, the Han Chinese had a population of 1.042 billion (94% of overall population).
See also
Census in China
References
External links
1990
1990 in China
China
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https://en.wikipedia.org/wiki/Niquinohomo%20FC
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Niquinohomo FC is a Nicaraguan football club from Niquinohomo, Masaya Department. It was founded on 2000 and currently plays on Tercera División de Nicaragua.
References
Club profile on StatisticSports
Football clubs in Nicaragua
Association football clubs established in 2000
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https://en.wikipedia.org/wiki/Myles%20Stoddard
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Myles Stoddard (born January 7, 1977) is a former American soccer player.
Career statistics
Club
Notes
References
1977 births
Living people
American men's soccer players
United States men's youth international soccer players
Men's association football forwards
Reno Rattlers players
Nashville Metros players
Utah Freezz players
Cleveland Crunch players
California Cougars players
A-League (1995–2004) players
World Indoor Soccer League players
Major Indoor Soccer League (2001–2008) players
Sportspeople from Reno, Nevada
Soccer players from Nevada
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https://en.wikipedia.org/wiki/1935%E2%80%9336%20Rochdale%20A.F.C.%20season
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The 1935–36 season saw Rochdale compete for their 15th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
FA Cup
Third Division North Cup
Lancashire Cup
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Icositetrahedron
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In geometry, an icositetrahedron is a polyhedron with 24 faces. There are many symmetric forms, and the ones with highest symmetry have chiral icosahedral symmetry:
Four Catalan solids, convex:
Triakis octahedron - isosceles triangles
Tetrakis hexahedron - isosceles triangles
Deltoidal icositetrahedron - kites
Pentagonal icositetrahedron - pentagons
27 uniform star-polyhedral duals: (self-intersecting)
Small rhombihexacron, Great rhombihexacron
Small hexacronic icositetrahedron, Great hexacronic icositetrahedron
Great deltoidal icositetrahedron
Great triakis octahedron
References
Polyhedra
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https://en.wikipedia.org/wiki/Christos%20Liatsos
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Christos Liatsos (; born 1 September 2003) is a Greek professional footballer who plays as a midfielder for Super League 2 club Olympiacos B.
Career statistics
Club
Notes
Honours
Greek Cup : 2019-20
References
2003 births
Living people
Greece men's youth international footballers
Men's association football midfielders
Super League Greece players
Olympiacos F.C. players
Footballers from Athens
Greek men's footballers
Super League Greece 2 players
Olympiacos F.C. B players
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https://en.wikipedia.org/wiki/Wahyu%20Sukarta
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Wahyu Sukarta (born 12 June 1994) is an Indonesian professional footballer who plays as a defensive midfielder who plays for Liga 2 club Persipa Pati.
Career statistics
Club
Honours
Club
PSS Sleman
Liga 2: 2018
Menpora Cup third place: 2021
References
External links
Wahyu Sukarta at Liga Indonesia
1994 births
Living people
Indonesian men's footballers
Liga 2 (Indonesia) players
Liga 1 (Indonesia) players
PSS Sleman players
Men's association football midfielders
People from Sleman Regency
Sportspeople from Special Region of Yogyakarta
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https://en.wikipedia.org/wiki/Sophie%20Schbath
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Sophie Schbath (born 1969) is a French statistician whose research concerns the statistics of pattern matching in strings and formal languages, particularly as applied to genomics. She is a director of research for the French National Institute for Research in Agriculture, Food, and Environment (INRAE), and a former president of the French BioInformatics Society.
Education and career
Schbath was born on 19 December 1969 in Nantes. She earned a master's degree in stochastic modeling and statistics in 1992 from Paris-Sud University, and completed a Ph.D. in 1995 at Paris Descartes University. Her dissertation was Étude asymptotique du nombre d'occurrences d'un mot dans une chaîne de Markov et application à la recherche de mots de fréquence exceptionnelle dans les séquences d'ADN. She earned a habilitation in 2003 at the University of Évry Val d'Essonne.
After postdoctoral research in 1996 at the University of Southern California, Schbath became a researcher for INRAE. She became a director of research in 2006, and director of research (1st class) in 2018. She was president of the French BioInformatics Society from 2010 to 2016.
Books
Schbath is the coauthor of the book ADN, mots et modèles, with S. Robin and F. Rodolphe, BELIN, 2003, translated into English as DNA, Words and Models: Statistics of Exceptional Words, Cambridge University Press, 2005.
She is also one of the contributors to the book Applied Combinatorics on Words, which lists its author as the collective pseudonym M. Lothaire.
References
External links
Home page
1969 births
Living people
French statisticians
Women statisticians
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https://en.wikipedia.org/wiki/2019%20Japanese%20Regional%20Leagues
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Statistics of Japanese Regional Leagues in the 2019 season.
Champions list
Hokkaido
Tohoku
Kantō
Vertfee Yaita were relegated to the Tochigi Prefectural League, Waseda United were relegated to the Tokyo Metropolitan Prefectural League, and Kanagawa Teachers were relegated to the Kanagawa Prefectural League.
Hokushinetsu
Tokai
Toyota Industries were relegated to the Aichi Prefectural League, and Ogaki Kogans were relegated to the Gifu Prefectural League.
Kansai
Chūgoku
Shikoku
Kyushu
<onlyinclude>
References
RSSSF
2019
2019 in Japanese football leagues
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https://en.wikipedia.org/wiki/1936%E2%80%9337%20Rochdale%20A.F.C.%20season
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The 1936–37 season saw Rochdale compete for their 16th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
F.A. Cup
Division 3 North Cup
Lancashire Cup
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Jan%20Saxl
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Jan Saxl (5 June 1948 – 2 May 2020) was a Czech-British mathematician, and a professor at the University of Cambridge. He was known for his work in finite group theory, particularly on consequences of the classification of finite simple groups.
Education and career
Saxl was born in Brno, in what was at the time Czechoslovakia. He came to the United Kingdom in 1968, during the Prague Spring.
After undergraduate studies at the University of Bristol, he completed his DPhil in 1973 at the University of Oxford under the direction of Peter M. Neumann, with the title of Multiply Transitive Permutation Groups.
Saxl held postdoctoral positions at Oxford and the University of Illinois at Chicago, and a lecturer position at the University of Glasgow. He moved to the University of Cambridge in 1976, and spent the rest of his career there. He was elected as a fellow of Gonville and Caius College in 1986, and he retired in 2015.
Saxl published around 100 papers, and according to MathSciNet, these have been cited over 1900 times. He is noted for his work in finite group theory, particularly on permutation groups, and often coauthored with Robert Guralnick, Martin Liebeck, and Cheryl Praeger. Some notable and highly-cited examples of this work are as follows. Liebeck, Saxl and Praeger gave a relatively simple and self-contained proof of the O'Nan–Scott theorem. It had long been known that every maximal subgroup of a symmetric group or alternating group was intransitive, imprimitive, or primitive, and the same authors in 1988 gave a partial description of which primitive subgroups could occur.
Personal life
Saxl was married to Cambridge mathematician Ruth M. Williams and they had one daughter, Miriam.
Death
Saxl died on 2 May 2020, after a long period of poor health.
Awards and honors
A three-day conference in the joint honor of Saxl and Martin Liebeck was held at the University of Cambridge in July 2015.
Publications
Books
Selected articles
References
1948 births
2020 deaths
Scientists from Brno
Czech mathematicians
Group theorists
Alumni of the University of Oxford
Cambridge mathematicians
Fellows of Gonville and Caius College, Cambridge
University of Illinois Chicago people
Czech emigrants to the United Kingdom
Alumni of the University of Bristol
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https://en.wikipedia.org/wiki/Bottema%27s%20theorem
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Bottema's theorem is a theorem in plane geometry by the Dutch mathematician Oene Bottema (Groningen, 1901–1992).
The theorem can be stated as follows: in any given triangle , construct squares on any two adjacent sides, for example and . The midpoint of the line segment that connects the vertices of the squares opposite the common vertex, , of the two sides of the triangle is independent of the location of .
The theorem is true when the squares are constructed in one of the following ways:
Looking at the figure, starting from the lower left vertex, , follow the triangle vertices clockwise and construct the squares to the left of the sides of the triangle.
Follow the triangle in the same way and construct the squares to the right of the sides of the triangle.
If is the projection of onto , Then .
If the squares are replaced by regular polygons of the same type, then a generalized Bottema theorem is obtained:
In any given triangle construct two regular polygons on two sides and .
Take the points and on the circumcircles of the polygons, which are diametrically opposed of the common vertex . Then, the midpoint of the line segment is independent of the location of .
See also
Van Aubel's theorem
Napoleon's theorem
References
External links
Bottema's Theorem: What Is It?
Wolfram Demonstrations Project – Bottema's Theorem
GeoGebra Demonstrations Project - A Generalized Theorem - Equilateral Triangles
GeoGebra Demonstrations Project - A Generalized Theorem - Regular Pentagons
Theorems about triangles
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https://en.wikipedia.org/wiki/Antonella%20Buccianti
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Antonella Buccianti (born 1960) is an Italian statistician and earth scientist, known for her work on the statistics of compositional data and its applications in geochemistry and geostatistics. She is an associate professor in the department of earth sciences at the University of Florence.
Education and career
Buccianti was born on 7 August 1960 in Florence. She earned a master's degree in stratigraphy from the University of Florence in 1988, including work done as a student with Agip, and completed a PhD at the University of Florence in 1994. She obtained a permanent research position at the university in 2001.
Books
Buccianti is the co-author, with Fabio Rosso, Fabio Vlacci, of the three-volume Italian book Metodi matematici e statistici nelle scienze della terra (2000). She is co-editor of Compositional Data Analysis in the Geosciences: From Theory to Practice (Geological Society, 2006) and Compositional Data Analysis: Theory and Applications (Wiley, 2011).
Recognition
Buccianti was the 2003 winner of the Felix Chayes Prize of the International Association for Mathematical Geosciences.
References
External links
1960 births
Living people
Italian earth scientists
Italian statisticians
Women earth scientists
Women statisticians
Geochemists
Women geochemists
Academic staff of the University of Florence
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https://en.wikipedia.org/wiki/Geometry%20From%20Africa
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Geometry From Africa: Mathematical and Educational Explorations is a book in ethnomathematics by . It analyzes the mathematics behind geometric designs and patterns from multiple African cultures, and suggests ways of connecting this analysis with the mathematics curriculum. It was published in 1999 by the Mathematical Association of America, in their Classroom Resource Materials book series.
Background
The book's author, Paulus Gerdes (1952–2014), was a mathematician from the Netherlands who became a professor of mathematics at the Eduardo Mondlane University in Mozambique, rector of Maputo University, and chair of the African Mathematical Union Commission on the History of Mathematics in Africa. He was a prolific author, especially of works on the ethnomathematics of Africa. However, as many of his publications were written in Portuguese, German, and French, or published only in Mozambique, this book makes his work in ethnomathematics more accessible to English-speaking mathematicians.
Topics
The book is heavily illustrated, and describes geometric patterns in the carvings, textiles, drawings and paintings of multiple African cultures. Although these are primarily decorative rather than mathematical, Gerdes adds his own mathematical analysis of the patterns, and suggests ways of incorporating this analysis into the mathematical curriculum.
It is divided into four chapters. The first of these provides an overview of geometric patterns in many African cultures, including examples of textiles, knotwork, architecture, basketry, metalwork, ceramics, petroglyphs, facial tattoos, body painting, and hair styles. The second chapter presents examples of designs in which squares and right triangles can be formed from elements of the patterns, and suggests educational activities connecting these materials to the Pythagorean theorem and to the theory of Latin squares. For instance, basket-weavers in Mozambique form square knotted buttons out of folded ribbons, and the resulting pattern of oblique lines crossing the square suggests a standard dissection-based proof of the theorem. The third chapter uses African designs, particularly in basket-weaving, to illustrate themes of symmetry, polygons and polyhedra, area, volume, and the theory of fullerenes. In the final chapter, the only one to concentrate on a single African culture, the book discusses the sona sand-drawings of the Chokwe people, in which a single self-crossing curve surrounds and separates a grid of points. These drawings connect to the theory of Euler tours, fractals, arithmetic series, and polyominos.
Audience and reception
The book is aimed at primary and secondary school mathematics teachers. Reviewer Karen Dee Michalowicz, a school teacher, writes that although the connections between culture and mathematics are sometimes contrived, "every mathematics educator would benefit" from the book.
Ethnomathematician Marcia Ascher suggests that the book would have benefited from an index and a
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https://en.wikipedia.org/wiki/Margaret%20Bayer
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Margaret M. Bayer is an American mathematician working in polyhedral combinatorics. She is a professor of mathematics at the University of Kansas.
Education
Bayer earned her Ph.D. in 1983 from Cornell University. Her dissertation, Facial Enumeration in Polytopes, Spheres and Other Complexes, was supervised by Louis Billera.
Recognition
Bayer was a Sigma Xi Distinguished Lecturer for 1998–1999.
In 2012 the university of Kansas named Bayer as one of 24 "Women of Distinction" among their students, faculty, and alumnae.
Bayer was one of the inaugural winners of the AWM Service Award of the Association for Women in Mathematics, in 2013, for her work editing book reviews for the AWM Newsletter. In 2020 Bayer was named a Fellow of the Association for Women in Mathematics "for her far-reaching work on the combinatorics and geometry of polytopes; for a long record of successfully mentoring, advising, and supervising women in mathematics at all levels; and for her service to AWM and the profession."
Personal life
She was married to Ralph Byers (1955–2007), also a mathematician at the University of Kansas; they had two daughters.
References
External links
Home page
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
Cornell University alumni
University of Kansas faculty
Fellows of the Association for Women in Mathematics
20th-century American women
21st-century American women academics
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https://en.wikipedia.org/wiki/Ricardo%20%C3%81lvarez%20%28footballer%2C%20born%201957%29
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Ricardo Álvarez de Mena (born 26 October 1957) is a retired Spanish footballer who played as a midfielder.
Career statistics
Club
Notes
References
1957 births
Living people
Spanish men's footballers
Men's association football midfielders
Real Madrid CF players
Real Madrid Castilla footballers
Racing de Santander players
Hércules CF players
Segunda División B players
Segunda División players
La Liga players
Palencia CF players
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https://en.wikipedia.org/wiki/Bal%C3%ADn
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Cristóbal Machín Fernández de la Puente (born 11 November 1957), commonly known as Balín, is a retired Spanish footballer who played as a forward.
Career statistics
Club
Notes
References
1957 births
Living people
Spanish men's footballers
Men's association football forwards
Real Madrid CF players
Real Madrid Castilla footballers
CA Osasuna players
UD Salamanca players
Segunda División players
La Liga players
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https://en.wikipedia.org/wiki/Deformed%20Hermitian%20Yang%E2%80%93Mills%20equation
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In mathematics and theoretical physics, and especially gauge theory, the deformed Hermitian Yang–Mills (dHYM) equation is a differential equation describing the equations of motion for a D-brane in the B-model (commonly called a B-brane) of string theory. The equation was derived by Mariño-Minasian-Moore-Strominger in the case of Abelian gauge group (the unitary group ), and by Leung–Yau–Zaslow using mirror symmetry from the corresponding equations of motion for D-branes in the A-model of string theory.
Definition
In this section we present the dHYM equation as explained in the mathematical literature by Collins-Xie-Yau. The deformed Hermitian–Yang–Mills equation is a fully non-linear partial differential equation for a Hermitian metric on a line bundle over a compact Kähler manifold, or more generally for a real -form. Namely, suppose is a Kähler manifold and is a class. The case of a line bundle consists of setting where is the first Chern class of a holomorphic line bundle . Suppose that and consider the topological constant
Notice that depends only on the class of and . Suppose that . Then this is a complex number
for some real and angle which is uniquely determined.
Fix a smooth representative differential form in the class . For a smooth function write , and notice that . The deformed Hermitian Yang–Mills equation for with respect to is
The second condition should be seen as a positivity condition on solutions to the first equation. That is, one looks for solutions to the equation such that . This is in analogy to the related problem of finding Kähler-Einstein metrics by looking for metrics solving the Einstein equation, subject to the condition that is a Kähler potential (which is a positivity condition on the form ).
Discussion
Relation to Hermitian Yang–Mills equation
The dHYM equations can be transformed in several ways to illuminate several key properties of the equations. First, simple algebraic manipulation shows that the dHYM equation may be equivalently written
In this form, it is possible to see the relation between the dHYM equation and the regular Hermitian Yang–Mills equation. In particular, the dHYM equation should look like the regular HYM equation in the so-called large volume limit. Precisely, one replaces the Kähler form by for a positive integer , and allows . Notice that the phase for depends on . In fact, , and we can expand
Here we see that
and we see the dHYM equation for takes the form
for some topological constant determined by . Thus we see the leading order term in the dHYM equation is
which is just the HYM equation (replacing by if necessary).
Local form
The dHYM equation may also be written in local coordinates. Fix and holomorphic coordinates such that at the point , we have
Here for all as we assumed was a real form. Define the Lagrangian phase operator to be
Then simple computation shows that the dHYM equation in these local coordinates takes the form
where
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https://en.wikipedia.org/wiki/Susan%20Tolman
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Susan Tolman is an American mathematician known for her work in symplectic geometry. She is a professor of mathematics at the University of Illinois at Urbana–Champaign, and Lynn M. Martin Professorial Scholar at Illinois.
Tolman earned her Ph.D. in 1993 at Harvard University. Her dissertation, Group Actions And Cohomology, was supervised by Raoul Bott. She was awarded a Sloan Research Fellowship in 1998, and was named Lynn M. Martin Professorial Scholar in 2008–2009.
References
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
University of Illinois Urbana-Champaign faculty
Sloan Research Fellows
Harvard University alumni
20th-century American women
21st-century American women
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https://en.wikipedia.org/wiki/Bridgeland%20stability%20condition
|
In mathematics, and especially algebraic geometry, a Bridgeland stability condition, defined by Tom Bridgeland, is an algebro-geometric stability condition defined on elements of a triangulated category. The case of original interest and particular importance is when this triangulated category is the derived category of coherent sheaves on a Calabi–Yau manifold, and this situation has fundamental links to string theory and the study of D-branes.
Such stability conditions were introduced in a rudimentary form by Michael Douglas called -stability and used to study BPS B-branes in string theory. This concept was made precise by Bridgeland, who phrased these stability conditions categorically, and initiated their study mathematically.
Definition
The definitions in this section are presented as in the original paper of Bridgeland, for arbitrary triangulated categories. Let be a triangulated category.
Slicing of triangulated categories
A slicing of is a collection of full additive subcategories for each such that
for all , where is the shift functor on the triangulated category,
if and and , then , and
for every object there exists a finite sequence of real numbers and a collection of triangles
with for all .
The last property should be viewed as axiomatically imposing the existence of Harder–Narasimhan filtrations on elements of the category .
Stability conditions
A Bridgeland stability condition on a triangulated category is a pair consisting of a slicing and a group homomorphism , where is the Grothendieck group of , called a central charge, satisfying
if then for some strictly positive real number .
It is convention to assume the category is essentially small, so that the collection of all stability conditions on forms a set . In good circumstances, for example when is the derived category of coherent sheaves on a complex manifold , this set actually has the structure of a complex manifold itself.
Technical remarks about stability condition
It is shown by Bridgeland that the data of a Bridgeland stability condition is equivalent to specifying a bounded t-structure on the category and a central charge on the heart of this t-structure which satisfies the Harder–Narasimhan property above.
An element is semi-stable (resp. stable) with respect to the stability condition if for every surjection for , we have where and similarly for .
Examples
From the Harder–Narasimhan filtration
Recall the Harder–Narasimhan filtration for a smooth projective curve implies for any coherent sheaf there is a filtrationsuch that the factors have slope . We can extend this filtration to a bounded complex of sheaves by considering the filtration on the cohomology sheaves and defining the slope of , giving a functionfor the central charge.
Elliptic curves
There is an analysis by Bridgeland for the case of Elliptic curves. He finds there is an equivalencewhere is the set of stability conditions and is the set of autoequi
|
https://en.wikipedia.org/wiki/Statistics%20of%20the%20COVID-19%20pandemic%20in%20Portugal
|
Statistics
The following graphs show the evolution of the pandemic starting from 2 March 2020, the day the first cases were confirmed in the country.
Cumulative cases
Nationwide
Daily cases
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Total confirmed cases by age and gender
The following chart displays the proportion of total cases by age and gender on August 20, 2021.
Total confirmed deaths
Severe cases
Total confirmed deaths by age and gender
The following chart displays the proportion of total deaths by age and gender on December 6, 2021.
Confirmed cases and deaths, by region
The following graph shows the daily cases of COVID-19 for each region of Portugal (updated on the 10th of June) according to DGS visualising the table above.
Similarly, the following graph presents the daily deaths by COVID-19 for each region of Portugal (updated on the 10th of June) according to DGS.
Growth of cases by Municipalities
The following graph presents the total number of COVID-19 cases per day for the municipalities of Portugal with more than 1000 confirmed cases (updated on 30 May), according to the Data Science for Social Good Portugal.
2009–20 deaths cases comparison
According to the Portuguese mortality surveillance (EVM), the following chart presents the total number of deaths per day in Portugal for the years 2009–2020 (updated on 10 June).
In the following two graphs, the total deaths per day and by age group are presented for the years 2019 and 2020.
References
statistics
Portugal
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https://en.wikipedia.org/wiki/Caroline%20Klivans
|
Caroline Jane (Carly) Klivans is an American mathematician specializing in algebraic combinatorics, including work on cell complexes associated with matroids and on chip-firing games. She is an associate professor of applied mathematics at Brown University, and associate director of the Institute for Computational and Experimental Research in Mathematics at Brown.
Education and career
As an undergraduate at Cornell University, Klivans was the 1999 winner of the Alice T. Schafer Prize of the Association for Women in Mathematics for excellence in mathematics by an undergraduate woman, for an undergraduate research project involving robot navigation algorithms. She graduated from Cornell in 1999, and completed her Ph.D. at the Massachusetts Institute of Technology in 2003. Her dissertation, Combinatorial Properties of Shifted Complexes, was supervised by Richard P. Stanley.
After postdoctoral research at the Mathematical Sciences Research Institute and the University of Chicago, where she was an L. E. Dickson Instructor, and positions as a researcher and lecturer at the University of Chicago and Brown University, she became associate director of the Institute for Computational and Experimental Research in Mathematics at Brown in 2015, and obtained a regular-rank faculty position as associate professor there in 2018. In 2022, she was elected member-at-large of the AWM Executive Committee.
Contributions
Klivans is the author of the book The Mathematics of Chip-Firing (CRC Press, 2018).
Her research contributions include a disproof of a 50-year-old conjecture of Richard Stanley that every abstract simplicial complex whose face ring is a Cohen–Macaulay ring can be partitioned into disjoint intervals, each including a facet of the complex. Such a partition generalizes a shelling and (if it always existed) would have been helpful in understanding the -vectors of these complexes.
References
External links
Home page
Year of birth missing (living people)
Living people
21st-century American mathematicians
American women mathematicians
Cornell University alumni
Massachusetts Institute of Technology alumni
Brown University faculty
21st-century American women
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https://en.wikipedia.org/wiki/1937%E2%80%9338%20Rochdale%20A.F.C.%20season
|
The 1937–38 season saw Rochdale compete for their 17th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
F.A. Cup
Division 3 North Cup
Lancashire Cup
References
Rochdale A.F.C. seasons
Rochdale
|
https://en.wikipedia.org/wiki/Joo%20Ik-seong
|
Joo Ik-seong (; born 10 September 1992) is a South Korean professional footballer who plays as a midfielder for Taichung Futuro and the South Korea national team.
Career statistics
Club
Notes
References
1992 births
Living people
South Korean men's footballers
South Korean expatriate men's footballers
Men's association football midfielders
K League 2 players
K3 League players
Taiwan Football Premier League players
FC Seoul players
Daejeon Hana Citizen players
Hwaseong FC players
Hang Yuan FC players
Taichung Futuro F.C. players
South Korean expatriate sportspeople in Taiwan
Expatriate men's footballers in Taiwan
Footballers from Seoul
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https://en.wikipedia.org/wiki/Serxhio%20Emini
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Serxhio Emini (born 3 December 2002) is an Albanian professional footballer who plays as a winger for Albanian club Bylisi.
Career statistics
Club
References
External links
2002 births
Living people
People from Sarandë
Sportspeople from Vlorë County
Sportspeople from Vlorë
Men's association football midfielders
Men's association football forwards
Albanian men's footballers
KF Luftëtari players
Kategoria Superiore players
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https://en.wikipedia.org/wiki/Statistics%20of%20the%20COVID-19%20pandemic%20in%20Germany
|
Statistics
Progression charts
Total confirmed cases, active cases, deaths, and recoveries
On 8 April 2020, the Robert Koch Institute began using another method to estimate the numbers of recoveries, now also incorporating cases where the date of the first symptoms is unknown. This caused the singular sharp drop in active cases on that date.
New cases per day
New deaths per day
Reproduction rate
The effective reproduction number or reproduction rate, symbolised with Re, is a rate of how many more people are infected from a positive COVID-19 case. In order to suppress an outbreak, the reproduction rate must be constantly below 1, which means each positive case infects less than one person.
The Robert Koch Institute measures the reproduction rate as a moving 4-day average of the number of new symptomatic cases using a nowcasting according to the 4-day average number of new cases on a specific day and comparing it with the corresponding mean 4 days before, reflecting the spread of the disease roughly one to two weeks before any specific day. As it is however prone to larger fluctuation, taking into account possible delays in reporting, a 7-day rate is then introduced, which compares the 7-day average of cases at one specific date with 4 days before. Specific values have been published since its daily report on 7 April, while the R-rate has been calculated from 6 March.
Effective reproduction number. Logarithmic scaling highlights the important changes near 1. Above 1, the number of active infections will grow exponentially, but even below 1 the decline will be very slow, if Re is too close to 1.
Number of tests per week
Since the beginning of testing in Germany up to and including week 25/2021 (Jun 21–27), 64,551,021 laboratory tests in at least 212 laboratories have been recorded, 4,245,186 of which have been positive. The number of tests is not the same as the number of persons tested, as the data may include multiple tests of patients.
Vaccinations
Vaccination numbers were obtained from the RKI and updated every business day. Starting from April, vaccinations can also be administered at a doctor's office alongside the existing vaccination center and mobile teams.
All-cause deaths
Weekly all-cause deaths in Germany based on mortality.org data.
Comparison of 2020 weekly mortality to the average of the 4 preceding years (data at mortality.org is available as of 2016 for Germany).
By age and gender
Number of COVID-19 cases per 100,000 people per week by age group (as of 13 May 2022)
}
Data discussion
Testing
Until late March, due to the restrictive Robert Koch Institute (RKI) testing criteria, Germans without specific symptoms could not be tested. On 25 March 2020, the RKI announced that people no longer needed to come from risk areas to be tested. In the revised criteria, acute respiratory symptoms were generally maintained, with one additional criterion of the following having to be fulfilled: contact to a confirmed positive cas
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https://en.wikipedia.org/wiki/Infrabarrelled%20space
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In functional analysis, a discipline within mathematics, a locally convex topological vector space (TVS) is said to be infrabarrelled (also spelled infrabarreled) if every bounded barrel is a neighborhood of the origin.
Characterizations
If is a Hausdorff locally convex space then the canonical injection from into its bidual is a topological embedding if and only if is infrabarrelled.
Properties
Every quasi-complete infrabarrelled space is barrelled.
Examples
Every barrelled space is infrabarrelled.
A closed vector subspace of an infrabarrelled space is, however, not necessarily infrabarrelled.
Every product and locally convex direct sum of any family of infrabarrelled spaces is infrabarrelled.
Every separated quotient of an infrabarrelled space is infrabarrelled.
See also
References
Bibliography
Functional analysis
Topological vector spaces
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https://en.wikipedia.org/wiki/Victoria%20Howle
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Victoria E. Howle is an American applied mathematician specializing in numerical linear algebra and known as one of the developers of the Trilinos open-source software library for scientific computing. She is a full professor in the Department of Mathematics and Statistics at
Texas Tech University.
Education and career
Howle graduated from Rutgers University in 1988 with a bachelor's degree in English literature. She earned her Ph.D. in 2001 from Cornell University. Her dissertation, Efficient Iterative Methods for Ill-Conditioned Linear and Nonlinear Network Problems, was supervised by Stephen Vavasis.
After working as a researcher at Sandia National Laboratories from 2000 to 2007, she took a faculty position at Texas Tech in 2007.
Service and recognition
Howle was one of the inaugural winners of the AWM Service Award of the Association for Women in Mathematics, in 2013. The award honored her service to the association, including founding its annual essay contest in which students write biographies of women mathematicians.
References
External links
Home page
Year of birth missing (living people)
Living people
21st-century American mathematicians
American women mathematicians
Applied mathematicians
Rutgers University alumni
Cornell University alumni
Sandia National Laboratories people
Texas Tech University faculty
21st-century American women
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https://en.wikipedia.org/wiki/Strong%20dual%20space
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In functional analysis and related areas of mathematics, the strong dual space of a topological vector space (TVS) is the continuous dual space of equipped with the strong (dual) topology or the topology of uniform convergence on bounded subsets of where this topology is denoted by or The coarsest polar topology is called weak topology.
The strong dual space plays such an important role in modern functional analysis, that the continuous dual space is usually assumed to have the strong dual topology unless indicated otherwise.
To emphasize that the continuous dual space, has the strong dual topology, or may be written.
Strong dual topology
Throughout, all vector spaces will be assumed to be over the field of either the real numbers or complex numbers
Definition from a dual system
Let be a dual pair of vector spaces over the field of real numbers or complex numbers
For any and any define
Neither nor has a topology so say a subset is said to be if for all
So a subset is called if and only if
This is equivalent to the usual notion of bounded subsets when is given the weak topology induced by which is a Hausdorff locally convex topology.
Let denote the family of all subsets bounded by elements of ; that is, is the set of all subsets such that for every
Then the on also denoted by or simply or if the pairing is understood, is defined as the locally convex topology on generated by the seminorms of the form
The definition of the strong dual topology now proceeds as in the case of a TVS.
Note that if is a TVS whose continuous dual space separates point on then is part of a canonical dual system
where
In the special case when is a locally convex space, the on the (continuous) dual space (that is, on the space of all continuous linear functionals ) is defined as the strong topology and it coincides with the topology of uniform convergence on bounded sets in i.e. with the topology on generated by the seminorms of the form
where runs over the family of all bounded sets in
The space with this topology is called of the space and is denoted by
Definition on a TVS
Suppose that is a topological vector space (TVS) over the field
Let be any fundamental system of bounded sets of ;
that is, is a family of bounded subsets of such that every bounded subset of is a subset of some ;
the set of all bounded subsets of forms a fundamental system of bounded sets of
A basis of closed neighborhoods of the origin in is given by the polars:
as ranges over ).
This is a locally convex topology that is given by the set of seminorms on :
as ranges over
If is normable then so is and will in fact be a Banach space.
If is a normed space with norm then has a canonical norm (the operator norm) given by ;
the topology that this norm induces on is identical to the strong dual topology.
Bidual
The bidual or second dual of a TVS often denoted by is the strong dual of the stron
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https://en.wikipedia.org/wiki/The%20Mathematics%20of%20Chip-Firing
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The Mathematics of Chip-Firing is a textbook in mathematics on chip-firing games and abelian sandpile models. It was written by Caroline Klivans, and published in 2018 by the CRC Press.
Topics
A chip-firing game, in its most basic form, is a process on an undirected graph, with each vertex of the graph containing some number of chips. At each step, a vertex with more chips than incident edges is selected, and one of its chips is sent to each of its neighbors. If a single vertex is designated as a "black hole", meaning that chips sent to it vanish, then the result of the process is the same no matter what order the other vertices are selected. The stable states of this process are the ones in which no vertex has enough chips to be selected; two stable states can be added by combining their chips and then stabilizing the result. A subset of these states, the so-called critical states, form an abelian group under this addition operation. The abelian sandpile model applies this model to large grid graphs, with the black hole connected to the boundary vertices of the grid; in this formulation, with all eligible vertices selected simultaneously, it can also be interpreted as a cellular automaton. The identity element of the sandpile group often has an unusual fractal structure.
The book covers these topics, and is divided into two parts. The first of these parts covers the basic theory outlined above, formulating chip-firing in terms of algebraic graph theory and the Laplacian matrix of the given graph. It describes an equivalence between states of the sandpile group and the spanning trees of the graph, and the group action on spanning trees, as well as similar connections to other combinatorial structures, and applications of these connections in algebraic combinatorics. And it studies chip-firing games on other classes of graphs than grids, including random graphs.
The second part of the book has four chapters devoted to more advanced topics in chip-firing. The first of these generalizes chip-firing from Laplacian matrices of graphs to M-matrices, connecting this generalization to root systems and representation theory. The second considers chip-firing on abstract simplicial complexes instead of graphs. The third uses chip-firing to study graph-theoretic analogues of divisor theory and the Riemann–Roch theorem. And the fourth applies methods from commutative algebra to the study of chip-firing.
The book includes many illustrations, and ends each chapter with a set of exercises making it suitable as a textbook for a course on this topic.
Audience and reception
Although the book may be readable by some undergraduate mathematics students, reviewer David Perkinson suggests that its main audience should be graduate students in mathematics, for whom it could be used as the basis of a graduate course or seminar. He calls it "a thorough introduction to an exciting and growing subject", with "clear and concise exposition". Reviewer Paul Dreyer calls it
|
https://en.wikipedia.org/wiki/Shelly%20M.%20Jones
|
Shelly Monica Jones (born November 2, 1964) is an American mathematics educator. She is an associate professor of mathematics education at Central Connecticut State University.
Early life and education
Jones is African-American; she was raised in Bridgeport, Connecticut and went on to study computer science at Spelman College, graduating in 1986. Jones received a master's degree in mathematics education from the University of Bridgeport and a Ph.D. in mathematics education from Illinois State University.
Career and research
Jones is an associate professor at Central Connecticut State University in New Britain, Connecticut. She teaches undergraduate and graduate content, curriculum, and methods courses. Her focus includes culturally relevant mathematics, where she explains cognitively demanding mathematics skills from a relevant cultural perspective. In addition, Jones's specialties include integrating elementary school mathematics and music, and the effects of college students’ attitudes and beliefs about mathematics on their success in college.
Jones' accomplishments have earned her recognition by Mathematically Gifted & Black as a Black History Month 2019 Honoree.
Book
Jones is the author of the book Women Who Count: Honoring African American Women Mathematicians, published in 2019 by the American Mathematical Society.
References
External links
Women Who Count: Honoring African American Women Mathematicians (official website)
Culturally relevant pedagogy in mathematics: A critical need (TEDxCCSU video)
Living people
People from Bridgeport, Connecticut
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
African-American mathematicians
Spelman College alumni
University of Bridgeport alumni
Illinois State University alumni
Central Connecticut State University faculty
21st-century American women
1964 births
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https://en.wikipedia.org/wiki/Avernold%20Qyrani
|
Avernold Qyrani (born 20 April 1998) is an Albanian professional footballer who plays as a goalkeeper for Albanian club KF Korabi Peshkopi.
Career statistics
Club
References
External links
1998 births
Living people
Sportspeople from Gjirokastër County
People from Gjirokastër
Men's association football goalkeepers
Albanian men's footballers
KF Luftëtari players
KF Naftëtari players
KF Korabi Peshkopi players
Kategoria Superiore players
Kategoria e Parë players
|
https://en.wikipedia.org/wiki/1938%E2%80%9339%20Rochdale%20A.F.C.%20season
|
The 1938–39 season saw Rochdale compete for their 18th season in the Football League Third Division North.
Statistics
|}
Final league table
Competitions
Football League Third Division North
F.A. Cup
Football League Third Division North Cup
Lancashire Cup
Football League Jubilee
References
Rochdale A.F.C. seasons
Rochdale
|
https://en.wikipedia.org/wiki/Margaret%20Maxfield
|
Margaret Alice Waugh Maxfield (February 23, 1926 – December 20, 2016) was an American mathematician and mathematics book author.
Education and personal life
Margaret Waugh was born on February 23, 1926, in Willimantic, Connecticut. Her father was agricultural economist Frederick V. Waugh and her grandfather was horticulturist Frank Albert Waugh.
She was active in the mathematics club at Oberlin College in the mid-1940s, and graduated from Oberlin in 1947.
After earning a master's degree in 1948 from the University of Wisconsin, she completed her Ph.D. in 1951 at the University of Oregon. Her dissertation, Fermat's Theorem for Matrices over a Modular Ring, was supervised by Ivan M. Niven. In 1948 she had married John Edward Maxfield, another student at Wisconsin and the University of Oregon who became her frequent collaborator.
As students, both Maxfields visited the Naval Air Weapons Station China Lake, then known as the Naval Ordnance Test Station, in the summers. After completing their doctorates they worked at the station from 1951 until 1960, when John Maxfield took a succession of academic posts at the University of Florida, Kansas State University, and (beginning in 1981) at Louisiana Tech University. Margaret, also, became a professor of business at Kansas State, and a professor of mathematics and statistics at Louisiana Tech.
By 2011 Maxfield had retired, but was still active in mathematics, and noted to her alumni magazine that she was using Wikipedia to find bibliographic material for her papers. She died on December 20, 2016, in Placerville, California.
Contributions
While at the Naval Ordnance Test Station, Maxfield coauthored the book Statistics Manual: With Examples Taken from Ordnance Development, with Edwin L. Crow and Frances A. Davis. It was published by the station in 1955, and reprinted by Dover Books in 1960.
With John Maxfield, she was also the coauthor of Contemporary Mathematics for General Education: Algebra (Allyn and Bacon, 1963, also with S. Gould Sadler) Abstract Algebra and Solution By Radicals (W. B. Saunders, 1971; reprinted by Dover Books, 1992), Discovering Number Theory (W. B. Saunders, 1972), and Keys to Mathematics (W. B. Saunders, 1973)
Maxfield was one of the 1968 winners of the Lester R. Ford Award of the Mathematical Association of America for a paper with her father on the rational approximation of square roots.
References
1926 births
2016 deaths
People from Willimantic, Connecticut
20th-century American mathematicians
American women mathematicians
Oberlin College alumni
University of Wisconsin–Madison alumni
University of Oregon alumni
Kansas State University faculty
Louisiana Tech University faculty
20th-century American women
21st-century American women
|
https://en.wikipedia.org/wiki/K%C3%A4ina%20Bay
|
{
"type": "FeatureCollection",
"features": [
{
"type": "Feature",
"properties": {},
"geometry": {
"type": "Point",
"coordinates": [
22.786331,
58.805207
]
}
}
]
}
Käina Bay () is almost isolated and very shallow approximately marine area between the Estonian islands Hiiumaa and Kassari, which is connected to the surrounding Väinameri and adjacent Vaemla Bay via three tiny channels - Orjaku channel, Orjaku sill and Vaemla (Laisna, Õunaku) channel. The maximum depth of Käina Bay is about 1 meter. Käina Bay is separated from the Väinameri Sea by Kassari Island, Õunaku Bay and Jausa Bay by a dyke road. There are many thickets of reeds and islets (23). In the southern part of the bay there is mineral curative mud.
Water regime
Average high water level in Käina Bay lasts from November until March and critically low water level period is from April until June. Most extreme changes in the sea level; onto which water level in the bay reacts with certain time lag, occur in the open sea from September until March, when stronger winds prevail. Sea level variability in the Käina Bay is smaller comparing to Baltic Sea. Two types of water exchange regime occur in the Käina Bay, which depend on the water level in the open sea. In the case of higher sea level water in the Vaemla Bay rises faster due to transport through Õunaku sill comparing to Käina Bay and as a consequence, open sea water arrives to the Käina bay also through Vaemla channel. In the case of lower sea level water exchange through Õunaku sill does not occur and therefor saltier water inflow (outflow) to (from) the Vaemla Bay occurs through Käina Bay.
Protected nature area
Landscape Reserve
Käina Bay-Kassari Landscape Conservation Area (KLO1000508) is one of 152 protected areas of Estonia. Total area of the reserve is , including areas permanently covered by water . The history of this protected area dates back to 1939, when the Kassari and Vaemla Bay curative mud areas were protected. In 1962, two protected areas were established: the Kassari Island Landscape Protection Area and the Käina Bay Ornithological Protection Area, which were merged to form the Käina Bay-Kassari Landscape Protection Area in 1998.
This area is maintained and improved with the support of various public funds, including support from the European Union Cohesion Fund and Environmental Investment Centre environmental programme. Vaemla region at the Käina Bay-Kassari Landscape Reserve on the south-eastern edge received the necessary tools for coastal meadow maintenance.
The channels would ensure normal water exchange in the bay and at the same time create a favorable condition for the local habitats and species. Based on the 2017 study of the Taltech Department of Marine Systems about the condition of Käina Bay and Vaemla Bay, and the efficiency of water regulators and recommendations therein, the works in the watercourses were implemented
|
https://en.wikipedia.org/wiki/Ray%20Evans%20%28footballer%2C%20born%201929%29
|
Raymond Frederick Evans (8 October 1929 – 2005) was an English professional footballer who played in the Football League for Crewe Alexandra.
Career statistics
Source:
References
1929 births
2005 deaths
English men's footballers
Men's association football goalkeepers
English Football League players
Crewe Alexandra F.C. players
Stoke City F.C. players
Footballers from Carlisle, Cumbria
|
https://en.wikipedia.org/wiki/Zero%20dynamics
|
In mathematics, zero dynamics is known as the concept of evaluating the effect of zero on systems.
History
The idea was introduced thirty years ago as the nonlinear approach to the concept of transmission of zeros. The original purpose of introducing the concept was to develop an asymptotic stabilization with a set of guaranteed regions of attraction (semi-global stabilizability), to make the overall system stable.
Initial working
Given the internal dynamics of any system, zero dynamics refers to the control action chosen in which the output variables of the system are kept identically zero. While, various systems have an equally distinctive set of zeros, such as decoupling zeros, invariant zeros, and transmission zeros. Thus, the reason for developing this concept was to control the non-minimum phase and nonlinear systems effectively.
Applications
The concept is widely utilized in SISO mechanical systems, whereby applying a few heuristic approaches, zeros can be identified for various linear systems. Zero dynamics adds an essential feature to the overall system’s analysis and the design of the controllers. Mainly its behavior plays a significant role in measuring the performance limitations of specific feedback systems. In a Single Input Single Output system, the zero dynamics can be identified by using junction structure patterns. In other words, using concepts like bond graph models can help to point out the potential direction of the SISO systems.
Apart from its application in nonlinear standardized systems, similar controlled results can be obtained by using zero dynamics on nonlinear discrete-time systems. In this scenario, the application of zero dynamics can be an interesting tool to measure the performance of nonlinear digital design systems (nonlinear discrete-time systems).
Before the advent of zero dynamics, the problem of acquiring non-interacting control systems by using internal stability was not specifically discussed. However, with the asymptotic stability present within the zero dynamics of a system, static feedback can be ensured. Such results make zero dynamics an interesting tool to guarantee the internal stability of non-interacting control systems.
References
Differential equations
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https://en.wikipedia.org/wiki/Matt%20Keeling
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Matthew James Keeling (born June 1970) is a professor in the Mathematics Institute and the School of Life Sciences of the University of Warwick. He has been editor of the journal Epidemics since 2007.
Keeling was appointed Officer of the Order of the British Empire (OBE) in the 2021 Birthday Honours for services to SAGE during the Covid-19 response.
Awards
Philip Leverhulme Prize in Mathematics (2005)
Royal Zoological Society of London, Scientific Medal (2007)
References
Academics of the University of Warwick
Living people
1970 births
Officers of the Order of the British Empire
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https://en.wikipedia.org/wiki/1999%E2%80%932000%20Ferencv%C3%A1rosi%20TC%20season
|
Transfers
Summer
In:
Out:
Winter
In:
Out:
Nemzeti Bajnokság I
League table
Results summary
Results by round
Matches
Hungarian Cup
UEFA Cup
Qualifying round
First round
Statistics
Appearances and goals
Last updated on 27 May 2000.
|-
|colspan="14"|Players no longer at the club:
|}
Top scorers
Includes all competitive matches. The list is sorted by shirt number when total goals are equal.
Last updated on 27 May 2000.
Disciplinary record
Includes all competitive matches. Players with 1 card or more included only.
Last updated on 27 May 2000.
Overall
{|class="wikitable"
|-
|Games played || 38 (33 PNB, 2 Hungarian Cup and 4 UEFA Cup)
|-
|Games won || 17 (15 PNB, 1 Hungarian Cup and 1 UEFA Cup)
|-
|Games drawn || 10 (8 PNB, 0 Hungarian Cup and 2 UEFA Cup)
|-
|Games lost || 12 (10 PNB, 1 Hungarian Cup and 1 UEFA Cup)
|-
|Goals scored || 73
|-
|Goals conceded || 49
|-
|Goal difference || +25
|-
|Yellow cards || 80
|-
|Red cards || 5
|-
|rowspan="1"|Worst discipline || Attila Kriston (9 , 1 )
|-
|rowspan="1"|Best result || 8–0 (H) v Vác - (PNB) - 11-3-2000
|-
|rowspan="2"|Worst result || 1–4 (A) v Vasas - (Hungarian Cup) - 1-12-1999
|-
| 0–3 (A) v Nyíregyháza - (PNB) - 1-4-2000
|-
|rowspan="2"|Most appearances || Péter Horváth (39 appearances)
|-
| Lajos Szűcs (39 appearances)
|-
|rowspan="1"|Top scorer || Péter Horváth (24 goals)
|-
|Points || 61/117 (52.13%)
|-
References
External links
Official Website
UEFA
fixtures and results
1999-00
Hungarian football clubs 1999–2000 season
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https://en.wikipedia.org/wiki/Rosamund%20Sutherland
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Rosamund Sutherland (née Hatfield, 1947–2019) was a British mathematics educator. She was a professor emeritus at the University of Bristol, and the former head of the school of education at Bristol.
Education and career
Sutherland was born in Birmingham; her mother taught geography and her father was a physicist. The family moved to south Wales when she was young, and after attending Haberdashers' Monmouth School for Girls she became a student at the University of Bristol, where she met and married her husband, mechanical and biomedical engineer Ian Sutherland.
She worked briefly as a computer programmer, and then as a researcher at the University of Bristol while her husband completed his doctorate. After she and her family moved to Hertfordshire, she taught for The Open University and the Borehamwood College of Further Education. Through her position at The Open University she came to work with Celia Hoyles, who encouraged her to become an academic researcher in a project combining mathematics education with computer programming in the Logo programming language. She worked at the University of London from 1983 until 1995, when she was given a Chair in Education at the University of Bristol.
At Bristol, in 1997, she chaired a national committee that helped bring algebra to a more prominent position in secondary-school mathematics education. She was the head of the school from 2003 to 2006, and again in 2014. She also played a key role in improving educational opportunities for underprivileged youth in south Bristol.
She died on 26 January 2019.
Books
Sutherland was the author or coauthor of several books or booklets on mathematics education, including:
Logo Mathematics in the Classroom (Routledge / Chapman & Hall, 1989)
Exploring Mathematics with Spreadsheets (with Lulu Healy, Blackwell, 1992)
Key Aspects of Teaching Algebra in Schools (with John Mason, QCA, 2002)
A Comparative Study of Algebra Curricula (QCA, 2002)
Screenplay: Children and Computing in the Home (with Keri Facer, John Furlong, and Ruth Furlong, RoutledgeFalmer, 2003)
Teaching for Learning Mathematics (Open University Press / McGraw Hill, 2007)
Improving Classroom Learning With ICT (with Susan Robertson and Peter John, Routledge, 2009)
Education and Social Justice in a Digital Age (Bristol University Press, 2014)
She also edited books including:
Theory of Didactical Situations in Mathematics (Didactique des Mathématiques, 1970–1990) (by Guy Brousseau, edited and translated by Balacheff, Cooper, Sutherland, and Warfield, Kluwer, 1997)
Learning and Teaching Where Worldviews Meet (edited with Guy Claxton and Andrew Pollard, Trentham, 2004)
References
External links
1947 births
2019 deaths
British mathematicians
British women mathematicians
Mathematics educators
Alumni of the University of Bristol
Academics of the University of London
Academics of the University of Bristol
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https://en.wikipedia.org/wiki/Fichier%20des%20personnes%20d%C3%A9c%C3%A9d%C3%A9es
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In France, the ("Register of deceased persons") is a central register of persons who have died in the country since 1970. It is maintained by the national statistics bureau (Insee). Since October 2019, the register has been accessible online free of charge and without registration.
Data in the register
The register contains deaths since 1970, inclusively. For the current year, there are monthly and quarterly files. For past years, the data are summarised in one file per calendar year.
Each entry concerns one person and contains the surname, first names, sex, date of birth, the Insee code of the place of birth (or country of birth for those born abroad), the name of the place of birth (for those born abroad also the name of the country of birth), the date of death, the Insee code of the place of death and the number in the death register of the respective municipality. The text fields contain only capital letters without diacritics.
Each data set is included in the file that corresponds to its date of processing at the Insee, not the date of death. The law gives French civil registry offices one week to report deaths to the Insee. For reports submitted in paper form by traditional mail, postal delivery and processing at the statistics bureau will cause an additional delay before the data are recorded. Public holidays or other circumstances affecting the work of the authorities involved may also cause delays. A file of the register published by Insee for a given period therefore usually contains a significant number of entries for previous reporting periods; conversely, not all deaths occurring during the reporting period are included in the file for that period. For example, the monthly file for March 2020 contained about 8,700 entries concerning deaths before 1 March, but the file was missing 9,500 cases of deaths in March that were not recorded until April.
For this reason, the numbers of deaths listed in the monthly files of the death register do not correspond to consolidated death statistics per period, such as the figures published by the Insee since the beginning of the COVID-19 pandemic in France, broken down by département.
Access
Until 2017, access to the central death register was available only to certain commercial genealogy services, which Insee charged about 7,000 euros per year. Access subsequently became free of charge, but remained restricted to authorized companies bound by a licensing agreement with Insee.
However, on 17 May 2019, the French state's commission in charge of questions related to freedom of information and access to official data, CADA (Commission d'accès aux documents administratifs), decided at the request of a genealogical association that the central death register must immediately be made publicly accessible. The commission argued that the register was a set of administrative documents not containing any personal data in need of protection, since the persons concerned were not alive anymore. This
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https://en.wikipedia.org/wiki/Carolyn%20Kieran
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Carolyn Kieran is a Canadian mathematics educator known for her studies of how students learn algebra. She is a professor emerita of mathematics at the Université du Québec à Montréal.
Education and career
Kieran has bachelor's degrees from Marianopolis College and the Université de Montréal, a master's degree from Concordia University, and a doctorate from McGill University. She joined the mathematics department at the Université du Québec à Montréal in 1983 and became a full professor there in 1991. She retired in 2008 and was named a professor emerita in 2010.
Books
Kieran is a co-author, with J. Pang, D. Schifter, and S. F. Ng, of Early Algebra: Research into its Nature, its Learning, its Teaching (Springer Open, 2016).
She is a co-editor of volumes including:
Research Issues in the Learning and Teaching of Algebra, Vol. 4 (1989)
Selected Lectures from the Seventh International Congress on Mathematical Education (1994)
Approaches to Algebra: Perspectives for Research and Teaching
Computer Algebra Systems in Secondary School Mathematics Education (2003).
References
External links
Year of birth missing (living people)
Living people
Canadian mathematicians
Canadian women mathematicians
Université de Montréal alumni
Concordia University alumni
McGill University alumni
Academic staff of the Université du Québec à Montréal
}
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https://en.wikipedia.org/wiki/Brent%20Coull
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Brent Andrew Coull is an American statistician and Professor of Biostatistics at Harvard University.
Biography
He received his Ph.D. in Statistics from the University of Florida in 1997. His thesis advisor was Alan Agresti. He and his advisor came up with the Agresti–Coull interval, an approximate method for calculating binomial confidence intervals.
Honors and awards
He was named a fellow of the American Statistical Association in 2010.
References
American statisticians
Living people
University of Florida alumni
Fellows of the American Statistical Association
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Eleanor%20Feingold
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Eleanor Feingold is an American statistical geneticist. She is a professor of human genetics and of biostatistics, and executive associate dean, in the University of Pittsburgh Graduate School of Public Health.
Feingold's research results include the discovery that the human genome includes at least 49 different genes that contribute to the shape of the earlobe.
Education and career
Feingold graduated from the Massachusetts Institute of Technology in 1985, with an interdisciplinary bachelor's degree that combined mathematics, public policy, and English. She completed a Ph.D. in statistics at Stanford University in 1993. Her dissertation, Modeling a New Genetic Mapping Method, was supervised by David Siegmund.
After her bachelor's degree, and continuing part-time into her graduate studies, she worked as a mathematician and statistician for the Pacific Gas and Electric Company. After completing her doctorate she became an assistant professor of biostatistics at Emory University. She moved to the University of Pittsburgh in 1997, became a full professor and associate dean there in 2010, and was named executive associate dean in 2015.
Recognition
In 2010 Feingold was named a Fellow of the American Statistical Association.
References
External links
Home page
Year of birth missing (living people)
Living people
American geneticists
American women statisticians
American women geneticists
Statistical geneticists
Massachusetts Institute of Technology alumni
Stanford University alumni
Emory University faculty
University of Pittsburgh faculty
Fellows of the American Statistical Association
21st-century American women
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https://en.wikipedia.org/wiki/Erd%C5%91s%20on%20Graphs
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Erdős on Graphs: His Legacy of Unsolved Problems is a book on unsolved problems in mathematics collected by Paul Erdős in the area of graph theory. It was written by Fan Chung and Ronald Graham, based on a 1997 survey paper by Chung, and published in 1998 by A K Peters. A softcover edition with some updates and corrections followed in 1999.
Topics
The book has eight chapters, the first being a short introduction.
Its main content are six chapters of unsolved problems, grouped by subtopic.
Chapters two and three are on Ramsey theory and extremal graph theory. The fourth covers topics in graph coloring, packing problems, and covering problems. The fifth concerns graph enumeration and random graphs, the sixth generalizes from graphs to hypergraphs, and the seventh concerns infinite graphs. The book concludes with a chapter of stories about Erdős from one of his oldest friends, Andrew Vázsonyi.
Each chapter begins with a survey of the history and major results in the subtopic of graph theory that it covers; Erdős himself figures prominently in the history of several of these subtopics. The individual history, motivation, known progress, and bibliographic references for each problem are included, along with (in some cases) prizes for a solution originally offered by Erdős and maintained by Chung and Graham.
Audience and reception
One target audience for the book is researchers in graph theory, for whom these problems may provide material for much future research.
They may also provide an inspiration for students of mathematics,
and reviewer Arthur Hobbs suggests that the book could even be used as the basis for a graduate course.
Additionally, reviewers Robert Beezer and W. T. Tutte suggest that the book may be of interests to mathematicians in other areas, and to historians of mathematics, for the insight it provides into Erdős's life and work. Ralph Faudree writes that the book is suitable both as reference material and for browsing.
Tutte notes, for those not familiar with the topic, that in mathematics, a well-posed and unsolved problem can itself be a significant contribution, a success rather than a failure. In a similar vein of thought, Faudree adds that the book provides "an appropriate tribute" to Erdős and his history of both formulating and solving problems.
References
External links
Erdős' Problems on Graphs, web site by students of Fan Chung based on the book
Unsolved problems in graph theory
Paul Erdős
Mathematics books
1998 non-fiction books
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https://en.wikipedia.org/wiki/Ma%C3%A2mar%20Ousser
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Maâmar Ousser (born 7 February 1935) was a professional Algerian footballer who played as a full-back.
Honour
Career statistics
Club
References
1935 births
Algerian men's footballers
USM Blida players
Men's association football defenders
Living people
People from Blida
21st-century Algerian people
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https://en.wikipedia.org/wiki/Mustapha%20Begga
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Mustapha Begga (10 June 1934) was a professional Algerian footballer who played as a defender.
Honour
Career statistics
Club
References
1934 births
Algerian men's footballers
USM Blida players
Men's association football defenders
Living people
People from Blida
21st-century Algerian people
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https://en.wikipedia.org/wiki/Mokhtar%20Dahmane
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Mokhtar Dahmane (27 December 1931) was an Algerian professional footballer who played as a forward.
Honour
Career statistics
Club
References
1931 births
Algerian men's footballers
Footballers from Algiers
USM Blida players
Men's association football defenders
Living people
People from Blida
21st-century Algerian people
20th-century Algerian people
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https://en.wikipedia.org/wiki/Ahmed%20Zahzah
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Ahmed Zahzah (10 June 1934) was a professional Algerian footballer who played as a defender.
Career statistics
Club
References
1934 births
Algerian men's footballers
Footballers from Algiers
USM Blida players
Men's association football defenders
Living people
People from Blida
21st-century Algerian people
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https://en.wikipedia.org/wiki/Ordered%20topological%20vector%20space
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In mathematics, specifically in functional analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order ≤ making it into an ordered vector space whose positive cone is a closed subset of X.
Ordered TVS have important applications in spectral theory.
Normal cone
If C is a cone in a TVS X then C is normal if , where is the neighborhood filter at the origin, , and is the C-saturated hull of a subset U of X.
If C is a cone in a TVS X (over the real or complex numbers), then the following are equivalent:
C is a normal cone.
For every filter in X, if then .
There exists a neighborhood base in X such that implies .
and if X is a vector space over the reals then also:
There exists a neighborhood base at the origin consisting of convex, balanced, C-saturated sets.
There exists a generating family of semi-norms on X such that for all and .
If the topology on X is locally convex then the closure of a normal cone is a normal cone.
Properties
If C is a normal cone in X and B is a bounded subset of X then is bounded; in particular, every interval is bounded.
If X is Hausdorff then every normal cone in X is a proper cone.
Properties
Let X be an ordered vector space over the reals that is finite-dimensional. Then the order of X is Archimedean if and only if the positive cone of X is closed for the unique topology under which X is a Hausdorff TVS.
Let X be an ordered vector space over the reals with positive cone C. Then the following are equivalent:
the order of X is regular.
C is sequentially closed for some Hausdorff locally convex TVS topology on X and distinguishes points in X
the order of X is Archimedean and C is normal for some Hausdorff locally convex TVS topology on X.
See also
References
Functional analysis
Order theory
Topological vector spaces
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https://en.wikipedia.org/wiki/Archimedean%20ordered%20vector%20space
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In mathematics, specifically in order theory, a binary relation on a vector space over the real or complex numbers is called Archimedean if for all whenever there exists some such that for all positive integers then necessarily
An Archimedean (pre)ordered vector space is a (pre)ordered vector space whose order is Archimedean.
A preordered vector space is called almost Archimedean if for all whenever there exists a such that for all positive integers then
Characterizations
A preordered vector space with an order unit is Archimedean preordered if and only if for all non-negative integers implies
Properties
Let be an ordered vector space over the reals that is finite-dimensional. Then the order of is Archimedean if and only if the positive cone of is closed for the unique topology under which is a Hausdorff TVS.
Order unit norm
Suppose is an ordered vector space over the reals with an order unit whose order is Archimedean and let
Then the Minkowski functional of (defined by ) is a norm called the order unit norm.
It satisfies and the closed unit ball determined by is equal to (that is,
Examples
The space of bounded real-valued maps on a set with the pointwise order is Archimedean ordered with an order unit (that is, the function that is identically on ).
The order unit norm on is identical to the usual sup norm:
Examples
Every order complete vector lattice is Archimedean ordered.
A finite-dimensional vector lattice of dimension is Archimedean ordered if and only if it is isomorphic to with its canonical order.
However, a totally ordered vector order of dimension can not be Archimedean ordered.
There exist ordered vector spaces that are almost Archimedean but not Archimedean.
The Euclidean space over the reals with the lexicographic order is Archimedean ordered since for every but
See also
References
Bibliography
Functional analysis
Order theory
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https://en.wikipedia.org/wiki/Order%20bound%20dual
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In mathematics, specifically in order theory and functional analysis, the order bound dual of an ordered vector space is the set of all linear functionals on that map order intervals, which are sets of the form to bounded sets.
The order bound dual of is denoted by This space plays an important role in the theory of ordered topological vector spaces.
Canonical ordering
An element of the order bound dual of is called positive if implies
The positive elements of the order bound dual form a cone that induces an ordering on called the .
If is an ordered vector space whose positive cone is generating (meaning ) then the order bound dual with the canonical ordering is an ordered vector space.
Properties
The order bound dual of an ordered vector spaces contains its order dual.
If the positive cone of an ordered vector space is generating and if for all positive and we have then the order dual is equal to the order bound dual, which is an order complete vector lattice under its canonical ordering.
Suppose is a vector lattice and and are order bounded linear forms on
Then for all
if and then and are lattice disjoint if and only if for each and real there exists a decomposition with
See also
References
Functional analysis
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https://en.wikipedia.org/wiki/Solid%20set
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In mathematics, specifically in order theory and functional analysis, a subset of a vector lattice is said to be solid and is called an ideal if for all and if then
An ordered vector space whose order is Archimedean is said to be Archimedean ordered.
If then the ideal generated by is the smallest ideal in containing
An ideal generated by a singleton set is called a principal ideal in
Examples
The intersection of an arbitrary collection of ideals in is again an ideal and furthermore, is clearly an ideal of itself;
thus every subset of is contained in a unique smallest ideal.
In a locally convex vector lattice the polar of every solid neighborhood of the origin is a solid subset of the continuous dual space ;
moreover, the family of all solid equicontinuous subsets of is a fundamental family of equicontinuous sets, the polars (in bidual ) form a neighborhood base of the origin for the natural topology on (that is, the topology of uniform convergence on equicontinuous subset of ).
Properties
A solid subspace of a vector lattice is necessarily a sublattice of
If is a solid subspace of a vector lattice then the quotient is a vector lattice (under the canonical order).
See also
References
Functional analysis
Order theory
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https://en.wikipedia.org/wiki/Order%20complete
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In mathematics, specifically in order theory and functional analysis, a subset of an ordered vector space is said to be order complete in if for every non-empty subset of that is order bounded in (meaning contained in an interval, which is a set of the form for some ), the supremum ' and the infimum both exist and are elements of
An ordered vector space is called order complete, Dedekind complete, a complete vector lattice, or a complete Riesz space, if it is order complete as a subset of itself, in which case it is necessarily a vector lattice.
An ordered vector space is said to be countably order complete if each countable subset that is bounded above has a supremum.
Being an order complete vector space is an important property that is used frequently in the theory of topological vector lattices.
Examples
The order dual of a vector lattice is an order complete vector lattice under its canonical ordering.
If is a locally convex topological vector lattice then the strong dual is an order complete locally convex topological vector lattice under its canonical order.
Every reflexive locally convex topological vector lattice is order complete and a complete TVS.
Properties
If is an order complete vector lattice then for any subset is the ordered direct sum of the band generated by and of the band of all elements that are disjoint from For any subset of the band generated by is If and are lattice disjoint then the band generated by contains and is lattice disjoint from the band generated by which contains
See also
References
Bibliography
Functional analysis
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https://en.wikipedia.org/wiki/Order%20topology%20%28functional%20analysis%29
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In mathematics, specifically in order theory and functional analysis, the order topology of an ordered vector space is the finest locally convex topological vector space (TVS) topology on for which every order interval is bounded, where an order interval in is a set of the form where and belong to
The order topology is an important topology that is used frequently in the theory of ordered topological vector spaces because the topology stems directly from the algebraic and order theoretic properties of rather than from some topology that starts out having.
This allows for establishing intimate connections between this topology and the algebraic and order theoretic properties of
For many ordered topological vector spaces that occur in analysis, their topologies are identical to the order topology.
Definitions
The family of all locally convex topologies on for which every order interval is bounded is non-empty (since it contains the coarsest possible topology on ) and the order topology is the upper bound of this family.
A subset of is a neighborhood of the origin in the order topology if and only if it is convex and absorbs every order interval in
A neighborhood of the origin in the order topology is necessarily an absorbing set because for all
For every let and endow with its order topology (which makes it into a normable space).
The set of all 's is directed under inclusion and if then the natural inclusion of into is continuous.
If is a regularly ordered vector space over the reals and if is any subset of the positive cone of that is cofinal in (e.g. could be ), then with its order topology is the inductive limit of (where the bonding maps are the natural inclusions).
The lattice structure can compensate in part for any lack of an order unit:
In particular, if is an ordered Fréchet lattice over the real numbers then is the ordered topology on if and only if the positive cone of is a normal cone in
If is a regularly ordered vector lattice then the ordered topology is the finest locally convex TVS topology on making into a locally convex vector lattice. If in addition is order complete then with the order topology is a barreled space and every band decomposition of is a topological direct sum for this topology.
In particular, if the order of a vector lattice is regular then the order topology is generated by the family of all lattice seminorms on
Properties
Throughout, will be an ordered vector space and will denote the order topology on
The dual of is the order bound dual of
If separates points in (such as if is regular) then is a bornological locally convex TVS.
Each positive linear operator between two ordered vector spaces is continuous for the respective order topologies.
Each order unit of an ordered TVS is interior to the positive cone for the order topology.
If the order of an ordered vector space is a regular order and if each positive sequence of type i
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https://en.wikipedia.org/wiki/Topological%20vector%20lattice
|
In mathematics, specifically in functional analysis and order theory, a topological vector lattice is a Hausdorff topological vector space (TVS) that has a partial order making it into vector lattice that is possesses a neighborhood base at the origin consisting of solid sets.
Ordered vector lattices have important applications in spectral theory.
Definition
If is a vector lattice then by the vector lattice operations we mean the following maps:
the three maps to itself defined by , , , and
the two maps from into defined by and.
If is a TVS over the reals and a vector lattice, then is locally solid if and only if (1) its positive cone is a normal cone, and (2) the vector lattice operations are continuous.
If is a vector lattice and an ordered topological vector space that is a Fréchet space in which the positive cone is a normal cone, then the lattice operations are continuous.
If is a topological vector space (TVS) and an ordered vector space then is called locally solid if possesses a neighborhood base at the origin consisting of solid sets.
A topological vector lattice is a Hausdorff TVS that has a partial order making it into vector lattice that is locally solid.
Properties
Every topological vector lattice has a closed positive cone and is thus an ordered topological vector space.
Let denote the set of all bounded subsets of a topological vector lattice with positive cone and for any subset , let be the -saturated hull of .
Then the topological vector lattice's positive cone is a strict -cone, where is a strict -cone means that is a fundamental subfamily of that is, every is contained as a subset of some element of ).
If a topological vector lattice is order complete then every band is closed in .
Examples
The Banach spaces () are Banach lattices under their canonical orderings.
These spaces are order complete for .
See also
References
Bibliography
Functional analysis
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https://en.wikipedia.org/wiki/Weak%20order%20unit
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In mathematics, specifically in order theory and functional analysis, an element of a vector lattice is called a weak order unit in if and also for all
Examples
If is a separable Fréchet topological vector lattice then the set of weak order units is dense in the positive cone of
See also
Citations
References
Functional analysis
|
https://en.wikipedia.org/wiki/Quasi-interior%20point
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In mathematics, specifically in order theory and functional analysis, an element of an ordered topological vector space is called a quasi-interior point of the positive cone of if and if the order interval is a total subset of ; that is, if the linear span of is a dense subset of
Properties
If is a separable metrizable locally convex ordered topological vector space whose positive cone is a complete and total subset of then the set of quasi-interior points of is dense in
Examples
If then a point in is quasi-interior to the positive cone if and only it is a weak order unit, which happens if and only if the element (which recall is an equivalence class of functions) contains a function that is almost everywhere (with respect to ).
A point in is quasi-interior to the positive cone if and only if it is interior to
See also
References
Bibliography
Functional analysis
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https://en.wikipedia.org/wiki/Abstract%20L-space
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In mathematics, specifically in order theory and functional analysis, an abstract L-space, an AL-space, or an abstract Lebesgue space is a Banach lattice whose norm is additive on the positive cone of X.
In probability theory, it means the standard probability space.
Examples
The strong dual of an AM-space with unit is an AL-space.
Properties
The reason for the name abstract L-space is because every AL-space is isomorphic (as a Banach lattice) with some subspace of
Every AL-space X is an order complete vector lattice of minimal type;
however, the order dual of X, denoted by X+, is not of minimal type unless X is finite-dimensional.
Each order interval in an AL-space is weakly compact.
The strong dual of an AL-space is an AM-space with unit.
The continuous dual space (which is equal to X+) of an AL-space X is a Banach lattice that can be identified with , where K is a compact extremally disconnected topological space;
furthermore, under the evaluation map, X is isomorphic with the band of all real Radon measures 𝜇 on K such that for every majorized and directed subset S of we have
See also
References
Functional analysis
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https://en.wikipedia.org/wiki/Abstract%20m-space
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In mathematics, specifically in order theory and functional analysis, an abstract m-space or an AM-space is a Banach lattice whose norm satisfies for all x and y in the positive cone of X.
We say that an AM-space X is an AM-space with unit if in addition there exists some in X such that the interval is equal to the unit ball of X;
such an element u is unique and an order unit of X.
Examples
The strong dual of an AL-space is an AM-space with unit.
If X is an Archimedean ordered vector lattice, u is an order unit of X, and pu is the Minkowski functional of then the complete of the semi-normed space (X, pu) is an AM-space with unit u.
Properties
Every AM-space is isomorphic (as a Banach lattice) with some closed vector sublattice of some suitable .
The strong dual of an AM-space with unit is an AL-space.
If X ≠ { 0 } is an AM-space with unit then the set K of all extreme points of the positive face of the dual unit ball is a non-empty and weakly compact (i.e. -compact) subset of and furthermore, the evaluation map defined by (where is defined by ) is an isomorphism.
See also
Vector lattice
AL-space
References
Bibliography
Functional analysis
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https://en.wikipedia.org/wiki/Regularly%20ordered
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In mathematics, specifically in order theory and functional analysis, an ordered vector space is said to be regularly ordered and its order is called regular if is Archimedean ordered and the order dual of distinguishes points in .
Being a regularly ordered vector space is an important property in the theory of topological vector lattices.
Examples
Every ordered locally convex space is regularly ordered.
The canonical orderings of subspaces, products, and direct sums of regularly ordered vector spaces are again regularly ordered.
Properties
If is a regularly ordered vector lattice then the order topology on is the finest topology on making into a locally convex topological vector lattice.
See also
References
Bibliography
Functional analysis
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https://en.wikipedia.org/wiki/Cybelle%20Al%20Ghoul
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Cybelle Al Ghoul (; born 20 October 1998) is a Lebanese former footballer who played as a winger.
Career statistics
International
Scores and results list Lebanon's goal tally first, score column indicates score after each Al Ghoul goal.
See also
List of Lebanon women's international footballers
References
External links
1998 births
Living people
People from Matn District
Lebanese women's footballers
Women's association football wingers
Zouk Mosbeh SC footballers
Eleven Football Pro players
Lebanese Women's Football League players
Lebanon women's youth international footballers
Lebanon women's international footballers
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https://en.wikipedia.org/wiki/Locally%20convex%20vector%20lattice
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In mathematics, specifically in order theory and functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space.
LCVLs are important in the theory of topological vector lattices.
Lattice semi-norms
The Minkowski functional of a convex, absorbing, and solid set is a called a lattice semi-norm.
Equivalently, it is a semi-norm such that implies
The topology of a locally convex vector lattice is generated by the family of all continuous lattice semi-norms.
Properties
Every locally convex vector lattice possesses a neighborhood base at the origin consisting of convex balanced solid absorbing sets.
The strong dual of a locally convex vector lattice is an order complete locally convex vector lattice (under its canonical order) and it is a solid subspace of the order dual of ;
moreover, if is a barreled space then the continuous dual space of is a band in the order dual of and the strong dual of is a complete locally convex TVS.
If a locally convex vector lattice is barreled then its strong dual space is complete (this is not necessarily true if the space is merely a locally convex barreled space but not a locally convex vector lattice).
If a locally convex vector lattice is semi-reflexive then it is order complete and (that is, ) is a complete TVS;
moreover, if in addition every positive linear functional on is continuous then is of is of minimal type, the order topology on is equal to the Mackey topology and is reflexive.
Every reflexive locally convex vector lattice is order complete and a complete locally convex TVS whose strong dual is a barreled reflexive locally convex TVS that can be identified under the canonical evaluation map with the strong bidual (that is, the strong dual of the strong dual).
If a locally convex vector lattice is an infrabarreled TVS then it can be identified under the evaluation map with a topological vector sublattice of its strong bidual, which is an order complete locally convex vector lattice under its canonical order.
If is a separable metrizable locally convex ordered topological vector space whose positive cone is a complete and total subset of then the set of quasi-interior points of is dense in
If is a locally convex vector lattice that is bornological and sequentially complete, then there exists a family of compact spaces and a family of -indexed vector lattice embeddings such that is the finest locally convex topology on making each continuous.
Examples
Every Banach lattice, normed lattice, and Fréchet lattice is a locally convex vector lattice.
See also
References
Bibliography
Functional analysis
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https://en.wikipedia.org/wiki/Fr%C3%A9chet%20lattice
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In mathematics, specifically in order theory and functional analysis, a Fréchet lattice is a topological vector lattice that is also a Fréchet space.
Fréchet lattices are important in the theory of topological vector lattices.
Properties
Every Fréchet lattice is a locally convex vector lattice.
The set of all weak order units of a separable Fréchet lattice is a dense subset of its positive cone.
Examples
Every Banach lattice is a Fréchet lattice.
See also
References
Bibliography
Functional analysis
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https://en.wikipedia.org/wiki/Normed%20vector%20lattice
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In mathematics, specifically in order theory and functional analysis, a normed lattice is a topological vector lattice that is also a normed space whose unit ball is a solid set.
Normed lattices are important in the theory of topological vector lattices. They are closely related to Banach vector lattices, which are normed vector lattices that are also Banach spaces.
Properties
Every normed lattice is a locally convex vector lattice.
The strong dual of a normed lattice is a Banach lattice with respect to the dual norm and canonical order.
If it is also a Banach space then its continuous dual space is equal to its order dual.
Examples
Every Banach lattice is a normed lattice.
See also
References
Bibliography
Functional analysis
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https://en.wikipedia.org/wiki/Cone-saturated
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In mathematics, specifically in order theory and functional analysis, if is a cone at 0 in a vector space such that then a subset is said to be -saturated if where
Given a subset the -saturated hull of is the smallest -saturated subset of that contains
If is a collection of subsets of then
If is a collection of subsets of and if is a subset of then is a fundamental subfamily of if every is contained as a subset of some element of
If is a family of subsets of a TVS then a cone in is called a -cone if is a fundamental subfamily of and is a strict -cone if is a fundamental subfamily of
-saturated sets play an important role in the theory of ordered topological vector spaces and topological vector lattices.
Properties
If is an ordered vector space with positive cone then
The map is increasing; that is, if then
If is convex then so is When is considered as a vector field over then if is balanced then so is
If is a filter base (resp. a filter) in then the same is true of
See also
References
Bibliography
Functional analysis
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https://en.wikipedia.org/wiki/Normal%20cone%20%28functional%20analysis%29
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In mathematics, specifically in order theory and functional analysis, if is a cone at the origin in a topological vector space such that and if is the neighborhood filter at the origin, then is called normal if where and where for any subset is the -saturatation of
Normal cones play an important role in the theory of ordered topological vector spaces and topological vector lattices.
Characterizations
If is a cone in a TVS then for any subset let be the -saturated hull of and for any collection of subsets of let
If is a cone in a TVS then is normal if where is the neighborhood filter at the origin.
If is a collection of subsets of and if is a subset of then is a fundamental subfamily of if every is contained as a subset of some element of
If is a family of subsets of a TVS then a cone in is called a -cone if is a fundamental subfamily of and is a strict -cone if is a fundamental subfamily of
Let denote the family of all bounded subsets of
If is a cone in a TVS (over the real or complex numbers), then the following are equivalent:
is a normal cone.
For every filter in if then
<li> There exists a neighborhood base in such that implies
and if is a vector space over the reals then we may add to this list:
There exists a neighborhood base at the origin consisting of convex, balanced, -saturated sets.
There exists a generating family of semi-norms on such that for all and
and if is a locally convex space and if the dual cone of is denoted by then we may add to this list:
For any equicontinuous subset there exists an equicontiuous such that
The topology of is the topology of uniform convergence on the equicontinuous subsets of
and if is an infrabarreled locally convex space and if is the family of all strongly bounded subsets of then we may add to this list:
The topology of is the topology of uniform convergence on strongly bounded subsets of
is a -cone in
this means that the family is a fundamental subfamily of
is a strict -cone in
this means that the family is a fundamental subfamily of
and if is an ordered locally convex TVS over the reals whose positive cone is then we may add to this list:
<li>there exists a Hausdorff locally compact topological space such that is isomorphic (as an ordered TVS) with a subspace of where is the space of all real-valued continuous functions on under the topology of compact convergence.
If is a locally convex TVS, is a cone in with dual cone and is a saturated family of weakly bounded subsets of then
if is a -cone then is a normal cone for the -topology on ;
if is a normal cone for a -topology on consistent with then is a strict -cone in
If is a Banach space, is a closed cone in , and is the family of all bounded subsets of then the dual cone is normal in if and only if is a strict -cone.
If is a Banach space and is a cone in then the following are equivalent:
is a -cone in ;
;
is
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https://en.wikipedia.org/wiki/Band%20%28order%20theory%29
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In mathematics, specifically in order theory and functional analysis, a band in a vector lattice is a subspace of that is solid and such that for all such that exists in we have
The smallest band containing a subset of is called the band generated by in
A band generated by a singleton set is called a principal band.
Examples
For any subset of a vector lattice the set of all elements of disjoint from is a band in
If () is the usual space of real valued functions used to define Lp spaces then is countably order complete (that is, each subset that is bounded above has a supremum) but in general is not order complete.
If is the vector subspace of all -null functions then is a solid subset of that is a band.
Properties
The intersection of an arbitrary family of bands in a vector lattice is a band in
See also
References
Functional analysis
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https://en.wikipedia.org/wiki/T%C3%ADmea%20Babos%20career%20statistics
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This is a list of the main career statistics of Hungarian professional tennis player Tímea Babos. To date, Babos has won three singles titles and 24 career doubles titles. During her career, she get more recognized by her results in doubles events. Among her doubles titles, there are four Grand Slam doubles titles at the Australian Open in 2018 and 2020 and at the French Open in 2019 and 2020. She also won three WTA Finals doubles titles, as well as, two WTA Premier 5 doubles titles. In addition, she has more significant results in doubles such as finishing as a runner-up at Wimbledon in 2014 and 2016, the US Open in 2018 and Australian Open in 2019. Babos gained world No. 1 in doubles on 16 July 2018, while in singles, she has peak at the place No. 25 that she achieved in September 2016.
Performance timelines
Only main-draw results in WTA Tour, Grand Slams tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 Budapest Grand Prix.
Doubles
Current after the 2023 Italian Open.
Significant finals
Grand Slam tournaments
Doubles: 8 (4 titles, 4 runner–ups)
Mixed doubles: 2 (2 runner–ups)
WTA Finals
Doubles: 3 (3 titles)
Premier Mandatory/Premier-5 tournaments
Doubles: 7 (2 titles, 5 runner–ups)
WTA career finals
Singles: 8 (3 titles, 5 runner-ups)
Doubles: 37 (24 titles, 13 runner-ups)
WTA Challenger finals
Singles: 2 (1 title, 1 runner-up)
Doubles: 3 (1 title, 2 runner–ups)
ITF Circuit finals
Singles: 25 (15 titles, 10 runner–ups)
Doubles: 23 (12 titles, 11 runner–ups)
Junior Grand Slam finals
Girls' doubles: 5 (3 titles, 2 runner–ups)
WTA Tour career earnings
As of 1 November 2021
Career Grand Slam statistics
Seedings
The tournaments won by Babos are in boldface, and advanced into finals by Babos are in italics.
Singles
Doubles
Wins over top-10 players
Singles
Doubles
Players that were in the top 10 in that moment are in boldface.
Longest winning streaks
15–match doubles winning streak (2017–18)
Notes
References
External links
Babos, Tímea
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Subsets and Splits
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