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https://en.wikipedia.org/wiki/Rhombicuboctahedral%20prism | In geometry, a rhombicuboctahedral prism is a convex uniform polychoron (four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.
Images
Alternative names
small rhombicuboctahedral prism
(Small) rhombicuboctahedral dyadic prism (Norman W. Johnson)
Sircope (Jonathan Bowers: for small-rhombicuboctahedral prism)
(small) rhombicuboctahedral hyperprism
Related polytopes
Runcic snub cubic hosochoron
A related polychoron is the runcic snub cubic hosochoron, also known as a parabidiminished rectified tesseract, truncated tetrahedral alterprism, or truncated tetrahedral cupoliprism, s3{2,4,3}, . It is made from 2 truncated tetrahedra, 6 tetrahedra, and 8 triangular cupolae in the gaps, for a total of 16 cells, 52 faces, 60 edges, and 24 vertices. It is vertex-transitive, and equilateral, but not uniform, due to the cupolae. It has symmetry [2+,4,3], order 48.
It is related to the 16-cell in its s{2,4,3}, construction.
It can also be seen as a prismatic polytope with two parallel truncated tetrahedra in dual positions, as seen in the compound of two truncated tetrahedra. Triangular cupolae connect the triangular and hexagonal faces, and the tetrahedral connect edge-wise between.
References
External links
4-polytopes |
https://en.wikipedia.org/wiki/Nikolay%20Davydenko%20career%20statistics | This is a list of the main career statistics of tennis player Nikolay Davydenko.
Significant finals
Year-end championship finals
Singles: 2 (1 title, 1 runner-up)
Masters 1000 finals
Singles: 3 (3 titles)
ATP career finals
Singles: 28 (21 titles, 7 runner-ups)
Doubles: 4 (2 titles, 2 runner-ups)
Team competition: 2 (1–1)
Singles performance timeline
Doubles performance timeline
Head-to-head against other players
Davydenko's win-loss record against certain players who have been ranked World No. 10 or better is as follows:
Players who have been ranked World No. 1 are in boldface.
Tomáš Berdych 9–3
Fernando Verdasco 7–2
Fernando González 6–0
Jürgen Melzer 6–1
Radek Štěpánek 6–4
Rafael Nadal 6–5
Tommy Robredo 5–2
Mario Ančić 5–2
David Nalbandian 5–7
/ Greg Rusedski 4–0
Arnaud Clément 4–0
Tommy Haas 4–1
Dominik Hrbatý 4–1
David Ferrer 4–2
Mikhail Youzhny 4–2
Marat Safin 4–4
Ivan Ljubičić 4–4
Andy Murray 4–6
Robin Söderling 4–7
Rainer Schüttler 3–1
Juan Carlos Ferrero 3–2
Thomas Johansson 3–2
/ Janko Tipsarević 3–2
John Isner 3–3
Juan Martín del Potro 3–4
Sébastien Grosjean 2–0
Nicolás Massú 2–0
Jonas Björkman 2–1
Mariano Puerta 2–1
Stanislas Wawrinka 2–1
Gaël Monfils 2–2
Marcos Baghdatis 2–2
Mardy Fish 2–3
Marin Čilić 2–3
Guillermo Cañas 2–3
Paradorn Srichaphan 2–3
Nicolás Lapentti 2–3
Albert Costa 2–3
Jo-Wilfried Tsonga 2–4
Carlos Moyá 2–5
Gilles Simon 2–5
Gastón Gaudio 2–5
/ Novak Djokovic 2–6
Richard Gasquet 2–6
Roger Federer 2–19
Àlex Corretja 1–0
David Goffin 1–0
Mark Philippoussis 1–0
Marc Rosset 1–0
Yevgeny Kafelnikov 1–1
Jiří Novák 1–1
Karol Kučera 1–1
Félix Mantilla 1–1
Andre Agassi 1–2
Tim Henman 1–2
Guillermo Coria 1–2
Nicolás Almagro 1–3
Nicolas Kiefer 1–3
Andy Roddick 1–5
James Blake 1–7
Grigor Dimitrov 0–1
Richard Krajicek 0–1
Joachim Johansson 0–1
Todd Martin 0–1
Patrick Rafter 0–1
Milos Raonic 0–1
Gustavo Kuerten 0–2
Kei Nishikori 0–2
Lleyton Hewitt 0–4
*As of March 19, 2017.
Top 10 wins per season
Wins over top 10s per season
ATP Tour career earnings
* As of March 18, 2013.
Russian tournament timeline
Notes
External links
Davydenko, Nikolay
Russia sport-related lists |
https://en.wikipedia.org/wiki/Micha%C5%82%20Misiurewicz | Michał Misiurewicz (born 9 November 1948) is a Polish mathematician. He is known for his contributions to chaotic dynamical systems and fractal geometry, notably the Misiurewicz point.
Misiurewicz participated in the International Mathematical Olympiad for Poland, winning a bronze medal in 1965 and a gold medal (with perfect score and special prize) in 1966. He earned his Doctorate from University of Warsaw under supervision of Bogdan Bojarski.
In 1990 he moved to the United States, where he visited Northwestern University and Princeton University, eventually settling down at Indiana University–Purdue University Indianapolis at Indianapolis, Indiana, where he currently is a professor.
In 2012 he became a fellow of the American Mathematical Society.
See also
Mandelbrot set
Complex quadratic polynomial
Conley index theory
Topological entropy
Rotation number
Rule 90
References
External links
Website at IUPUI
1948 births
Living people
Polish mathematicians
University of Warsaw alumni
Indiana University–Purdue University Indianapolis faculty
Scientists from Warsaw
Fellows of the American Mathematical Society
International Mathematical Olympiad participants |
https://en.wikipedia.org/wiki/Ruanda%20%28Mbeya%20Urban%29 | Ruanda is an administrative ward in the Mbeya Urban district of the Mbeya Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 24,166 people in the ward, from 21,927 in 2012.
Neighborhoods
The ward has 11 neighborhoods.
Benki
Ilolo
Kabwe
Kati
Makunguru
Mkombozi
Mtoni
Mwenge
Soko
Soweto
Wakulima
References
Wards of Mbeya Region |
https://en.wikipedia.org/wiki/Sergei%20Konyagin | Sergei Vladimirovich Konyagin (; born 25 April 1957) is a Russian mathematician. He is a professor of mathematics at the Moscow State University.
Konyagin participated in the International Mathematical Olympiad for the Soviet Union, winning two consecutive gold medals with perfect scores in 1972 and 1973. At the age of 15, he became one of the youngest people to achieve a perfect score at the IMO.
In 1990 Konyagin was awarded the Salem Prize.
In 2012 he became a fellow of the American Mathematical Society.
Selected works
References
External links
1957 births
Living people
20th-century Russian mathematicians
21st-century Russian mathematicians
Academic staff of Moscow State University
International Mathematical Olympiad participants
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Periodic%20graph%20%28geometry%29 | A Euclidean graph (a graph embedded in some Euclidean space) is periodic if there exists a basis of that Euclidean space whose corresponding translations induce symmetries of that graph (i.e., application of any such translation to the graph embedded in the Euclidean space leaves the graph unchanged). Equivalently, a periodic Euclidean graph is a periodic realization of an abelian covering graph over a finite graph. A Euclidean graph is uniformly discrete if there is a minimal distance between any two vertices. Periodic graphs are closely related to tessellations of space (or honeycombs) and the geometry of their symmetry groups, hence to geometric group theory, as well as to discrete geometry and the theory of polytopes, and similar areas.
Much of the effort in periodic graphs is motivated by applications to natural science and engineering, particularly of three-dimensional crystal nets to crystal engineering, crystal prediction (design), and modeling crystal behavior. Periodic graphs have also been studied in modeling very-large-scale integration (VLSI) circuits.
Basic formulation
A Euclidean graph is a pair (V, E), where V is a set of points (sometimes called vertices or nodes) and E is a set of edges (sometimes called bonds), where each edge joins two vertices. While an edge connecting two vertices u and v is usually interpreted as the set { u, v }, an edge is sometimes interpreted as the line segment connecting u and v so that the resulting structure is a CW complex. There is a tendency in the polyhedral and chemical literature to refer to geometric graphs as nets (contrast with polyhedral nets), and the nomenclature in the chemical literature differs from that of graph theory. Most of the literature focuses on periodic graphs that are uniformly discrete in that there exists e > 0 such that for any two distinct vertices, their distance apart is |u – v| > e.
From the mathematical view, a Euclidean periodic graph is a realization of an infinite-fold abelian covering graph over a finite graph.
Obtaining periodicity
The identification and classification of the crystallographic space groups took much of the Nineteenth century, and the confirmation of the completeness of the list was finished by the theorems of Evgraf Fedorov and Arthur Schoenflies. The problem was generalized in David Hilbert's eighteenth Problem, and the Fedorov–Schoenflies Theorem was generalized to higher dimensions by Ludwig Bieberbach.
The Fedorov–Schoenflies theorem asserts the following. Suppose that one is given a Euclidean graph in 3-space such that the following are true:
It is uniformly discrete in that there exists e > 0 such that for any two distinct vertices, their distance apart is |u – v| > e.
It fills space in the sense that for any plane in 3-space, there exist vertices of the graph on both sides of the plane.
Each vertex is of finite degree or valency.
There are finitely many orbits of vertices under the symmetry group of the geometric graph. |
https://en.wikipedia.org/wiki/Periodic%20graph%20%28graph%20theory%29 | In graph theory, a branch of mathematics, a periodic graph with respect to an operator F on graphs is one for which there exists an integer n > 0 such that Fn(G) is isomorphic to G. For example, every graph is periodic with respect to the complementation operator, whereas only complete graphs are periodic with respect to the operator that assigns to each graph the complete graph on the same vertices. Periodicity is one of many properties of graph operators, the central topic in graph dynamics.
References
Graph invariants
Graph operations |
https://en.wikipedia.org/wiki/Periodic%20graph | Periodic graph may refer to:
Periodic graph (crystallography) or crystal net, a Euclidean graph representing the atomic or molecular structure of a crystal
Periodic graph (geometry), a Euclidean graph preserved under a lattice of translations
Periodic graph (graph theory), a graph that is periodic with respect to a graph theoretic operator |
https://en.wikipedia.org/wiki/K%C3%A1roly%20Bezdek | Károly Bezdek (born May 28, 1955 in Budapest, Hungary) is a Hungarian-Canadian mathematician. He is a professor as well as a Canada Research Chair of mathematics and the director of the Centre for Computational and Discrete Geometry at the University of Calgary in Calgary, Alberta, Canada. Also he is a professor (on leave) of mathematics at the University of Pannonia in Veszprém, Hungary. His main research interests are in geometry in particular, in combinatorial, computational, convex, and discrete geometry. He has authored 3 books and more than 130 research papers. He is a founding Editor-in-Chief of the e-journal Contributions to Discrete Mathematics (CDM).
Early life and family
Károly Bezdek was born in Budapest, Hungary, but grew up in Dunaújváros, Hungary. His parents are Károly Bezdek, Sr. (mechanical engineer) and Magdolna Cserey. His brother András Bezdek is also a mathematician. Károly and his brother have scored at the top level in several Mathematics and Physics competitions for high school and university students in Hungary. Károly's list of awards include winning the first prize in the traditional KöMal (Hungarian Math. Journal for Highschool Students) contest in the academic year 1972–1973, as well as winning the first prize for the research results presented at the National Science Conference for Hungarian Undergraduate Students (TDK) in 1978. Károly entered the Faculty of Science of the Eötvös Loránd University in Hungary, and completed his Diploma in Mathematics in 1978. Bezdek is married to Éva Bezdek, and has three sons: Dániel, Máté and Márk .
Career
Károly Bezdek received his Ph.D. (1980) as well as his Habilitation degree (1997) in mathematics from Eötvös Loránd University, in Budapest, Hungary and his Candidate of Mathematical Sciences degree (1985) as well as his Doctor of
Mathematical Sciences degree (1995) from the Hungarian Academy of Sciences. He has been a faculty member of the Department of Geometry at Eötvös Loránd University in Budapest since 1978. In particular, he has been the chair of that department between 1999-2006 and a full professor between 1998–2012. During 1978–2003, while being on a number of special leaves from Eötvös Loránd University, he has held numerous visiting positions at research institutions in Canada, Germany, the Netherlands, and United States. This included a period of about 7 years at the Department of Mathematics of Cornell University in Ithaca, New York. Between 1998-2001 Bezdek was appointed a Széchenyi Professor of mathematics at Eötvös Loránd University, in Budapest, Hungary. From 2003 Károly Bezdek is the Canada Research Chair of computational and discrete geometry at the Department of Mathematics and Statistics of the University of Calgary and is the director of the Center for Computational and Discrete Geometry at the University of Calgary. Between 2006-2010 Bezdek was an associated member of the Alfréd Rényi Institute of Mathematics in Budapest, Hungary. From 2010 Bezdek is |
https://en.wikipedia.org/wiki/Rudolf%20Inzinger | Rudolf Inzinger (5 April 1907 – 26 August 1980) was an Austrian mathematician who made contributions to differential geometry, the theory of convex bodies, and inverse problems for sound waves.
Biography
Born in Vienna, he was a student at the Technische Hochschule in the same city. In 1933 he defended his PhD Die Liesche Abbildung and in 1936 he received his habilitation. After the Anschluss he had to leave. After his return from war captivity he started again working at the Technische Hochschule in Vienna in 1945 where he was appointed associated professor in 1946 and promoted to full professor one year later.
In 1946 he reestablished the Austrian Mathematical Society whose president he was until 1948. In 1968/69 he served as president of the Technische Hochschule in Vienna.
References
External links
1907 births
1980 deaths
Mathematicians from Vienna
20th-century Austrian mathematicians |
https://en.wikipedia.org/wiki/National%20Statistics%20Institute%20%28Chile%29 | The National Statistics Institute of Chile (, INE) is a state-run organization of the Government of Chile, created in the second half of the 19th century and tasked with performing a general census of population and housing, then collecting, producing and publishing official demographic statistics of people in Chile, in addition to other specific tasks entrusted to it by law.
Background
Its antecedents lie in the initiatives of president Manuel Bulnes and his minister, Manuel Rengifo, to draw up the second population census and obtain statistical data of the country. By Decree No. 18 March 27, 1843, the Office of Statistics was created, Ministry of the Interior to provide knowledge of the departments and provinces. It put the INE in charge of producing the national population census every 10 years, as required by the Census Act of July 12, 1843.
Law No. 187 of September 17, 1847 established the office as a permanent body of the state. By 1853, it was legally required that each section chief of the ministries collect and submit data to the Bureau of Statistics. Subsequently and by various legal modifications, it was called Dirección General de Estadísticas (1927–1953), Servicio Nacional de Estadísticas y Censos (1953–1960), Dirección de Estadísticas y Censos (1960–1970). It has called by its current name since 1970, and it has been under the Ministry of Economy since 1927.
Publications
The first official publication, National Repertoire (Repertorio Nacional), was released in 1850. It was followed by the Statistical Yearbook of the Republic of Chile (Anuario Estadístico de la República de Chile) published without interruption from 1837 to 1866.
In 1882 they published Statistical and Geographical Synopsis of Chile (Sinopsis Estadística y Geografía de Chile). In 1911, they began publishing independent volumes of statistics by subject.
References
External links
Chile
Government agencies of Chile
Demographics of Chile
Government agencies established in 1843
1843 establishments in Chile |
https://en.wikipedia.org/wiki/Latisha%20Chan%20career%20statistics | This is a list of the main career statistics of tennis player Latisha Chan.
Performance timelines
Singles
Doubles
Mixed doubles
Significant finals
Grand Slam finals
Doubles: 4 (1 title, 3 runner-ups)
Mixed doubles: 4 (3 titles, 1 runner-up)
WTA 1000 finals
Doubles: 13 (9 titles, 4 runner-ups)
WTA career finals
Singles: 1 (runner-up)
Doubles: 59 (33 titles, 26 runner-ups)
WTA Challenger finals
Singles: 1 (runner-up)
Doubles: 2 (2 titles)
ITF Circuit finals
Singles: 22 (16–6)
Doubles: 23 (16–7)
Notes
References
Chan, Latisha |
https://en.wikipedia.org/wiki/Christopher%20Hacon | Christopher Derek Hacon (born 14 February 1970) is a mathematician with British, Italian and US nationalities. He is currently distinguished professor of mathematics at the University of Utah where he holds a Presidential Endowed Chair. His research interests include algebraic geometry.
Hacon was born in Manchester, but grew up in Italy where he studied at the Scuola Normale Superiore and received a degree in mathematics at the University of Pisa in 1992. He received his doctorate from the University of California, Los Angeles in 1998, under supervision of Robert Lazarsfeld.
Awards and honors
In 2007, he was awarded a Clay Research Award for his work, joint with James McKernan, on "the birational geometry of algebraic varieties in dimension greater than three, in particular, for [an] inductive proof of the existence of flips."
In 2009, he was awarded the Cole Prize for outstanding contribution to algebra, along with McKernan.
He was an invited speaker at the International Congress of Mathematicians 2010 in Hyderabad, on the topic of "Algebraic Geometry."
In 2011, he was awarded the Antonio Feltrinelli Prize in Mathematics, Mechanics and Applications by Italy's prestigious Accademia Nazionale dei Lincei.
In 2012, he became a fellow of the American Mathematical Society.
In 2012, he became a Simons Investigator.
In 2015, he won the American Mathematical Society Moore Prize.
In 2017, he was elected to the American Academy of Arts and Sciences.
In 2017, he won the 2018 Breakthrough Prize in Mathematics (with James McKernan).
In 2018, he was elected to the National Academy of Sciences.
In 2019, he was elected to the Royal Society.
References
External links
Website of University of Utah
1970 births
Living people
Algebraic geometers
20th-century British mathematicians
21st-century British mathematicians
20th-century Italian mathematicians
21st-century Italian mathematicians
University of Utah faculty
Clay Research Award recipients
Fellows of the American Mathematical Society
University of Pisa alumni
Simons Investigator
University of California, Los Angeles alumni
Fellows of the Royal Society
Members of the United States National Academy of Sciences |
https://en.wikipedia.org/wiki/Aise%20Johan%20de%20Jong | Aise Johan de Jong (born 30 January 1966) is a Dutch mathematician born in Belgium. He currently is a professor of mathematics at Columbia University. His research interests include arithmetic geometry and algebraic geometry.
Education
De Jong attended high school in The Hague, obtained his master's degree at Leiden University and earned his doctorate at the Radboud University Nijmegen in 1992, under supervision of Frans Oort and Joseph H. M. Steenbrink.
Career
In 1996, de Jong developed his theory of alterations which was used by Fedor Bogomolov and Tony Pantev (1996) and Dan Abramovich and de Jong (1997) to prove resolution of singularities in characteristic 0 and to prove a weaker result for varieties of all dimensions in characteristic p which is strong enough to act as a substitute for resolution for many purposes.
In 2005, de Jong started the Stacks Project, "an open source textbook and reference work on algebraic stacks and the algebraic geometry needed to define them." The book that the project has generated currently runs to more than 7500 pages as of July 2022.
Awards and honors
In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. He won the Cole Prize in 2000 for his theory of alterations. In the same year, De Jong became a correspondent of the Royal Netherlands Academy of Arts and Sciences. In 2022 he received the Leroy P. Steele Prize for Mathematical Exposition.
Personal life
De Jong lives in New York City with his wife, Cathy O'Neil, and their three sons.
Selected works
The Stacks Project
References
External links
Website at Columbia University
The Stacks Project
1966 births
Living people
20th-century Dutch mathematicians
21st-century Dutch mathematicians
Leiden University alumni
Radboud University Nijmegen alumni
De Jong, Aise Johan
Members of the Royal Netherlands Academy of Arts and Sciences
De Jong, Aise Johan
De Jong, Aise Johan
Arithmetic geometers |
https://en.wikipedia.org/wiki/Mart%C3%ADn%20C%C3%A1rdenas%20%28motorcyclist%29 | Martín Cárdenas Ochoa (born 28 January 1982) is a Colombian professional motorcycle road racer.
Career statistics
All-time statistics
Grand Prix motorcycle racing
By season
By class
Races by year
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)
Supersport World Championship
Races by year
(key) (Races in bold indicate pole position) (Races in italics indicate fastest lap)
References
1982 births
Living people
Sportspeople from Medellín
Colombian motorcycle racers
AMA Superbike Championship riders
Moto2 World Championship riders
Supersport World Championship riders
250cc World Championship riders
21st-century Colombian people |
https://en.wikipedia.org/wiki/Alroey%20Cohen | Alroey Cohen is an Israeli former footballer who last played for Maccabi Petah Tikva.
Club career statistics
(correct as of November 2010)
Honours
Liga Leumit (1):
2009–10
Israel State Cup (2):
2011, 2012
References
1989 births
Israeli Jews
Living people
Israeli men's footballers
Israel men's international footballers
Hapoel Ironi Kiryat Shmona F.C. players
Hapoel Tel Aviv F.C. players
Maccabi Petah Tikva F.C. players
Israeli Premier League players
People from Katzrin
Men's association football forwards |
https://en.wikipedia.org/wiki/Mikhail%20Youzhny%20career%20statistics | Mikhail Youzhny is a Russian retired professional tennis player who has won ten ATP singles titles, and nine ATP doubles titles in his career to date.
During his junior career, Youzhny peaked at number 20 in the world junior rankings in early 2000, the year after reaching the boys' singles final at the 1999 Australian Open, losing to Kristian Pless of Denmark. He turned professional later in 1999, winning four futures tournaments to start his career. He started played on the ATP Challenger Circuit the same year, and won his first Challenger tournament in July 2000 against Jan Frode Andersen from Norway. While he debuted at the ATP World Tour in 1999, Youzhny won his first ATP title in July 2002 at the Mercedes Cup against Guillermo Cañas from Argentina.
Youzhny has reached the quarterfinals of all four Grand Slams, as of 2013 only 11 other active players have managed to do the same. He has reached a Grand Slam semifinal twice, both at the US Open, in 2006 and 2010. While chiefly a singles player, Youzhny has reached the quarterfinals of a grand slam in doubles twice, at the 2006 US Open and the 2014 Australian Open. He debuted within the top 10 in January 2008, but ended the year as a top 10 player for the only time in his career in 2010. As of 2020, Youzhny is second most successful Russian tennis player in history if considering match wins only, trailing behind Yevgeny Kafelnikov.
Keys
ATP career finals
Singles: 21 (10 titles, 11 runner-ups)
Doubles: 12 (9 titles, 3 runner-ups)
ATP Challenger Tour
Singles: 6 (5 title, 1 runner-up)
Doubles: 2 (1 title, 1 runner-up)
ITF Men's Circuit
Singles: 4 (4 titles)
Doubles 1 (1 title)
ITF Junior Circuit
Singles: 2 (1 title, 1 runner-up)
Doubles: 4 (3 titles, 1 runner-up)
Singles Grand Slam seedings
Performance timelines
Singles
Doubles
Top 10 wins
Singles
Doubles
National participation
Davis Cup
Wins: 2
Participations: 38 (21 wins, 17 losses)
indicates the result of the Davis Cup match followed by the score, date, place of event, the zonal classification and its phase, and the court surface.
Summer Olympics matches
Singles (5 wins, 3 losses)
Doubles (2 wins, 3 losses)
References
Notes
1. Russia did not participate in the World Group play-offs in those years.
General
Career finals, Grand Slam seedings, information for both the singles and doubles performance timelines, top 10 wins and national participation information have been taken from these sources:
Specific
Youzhny, Mikhail |
https://en.wikipedia.org/wiki/Zsolt%20Haraszti | Zsolt Haraszti (born 4 November 1991) is a Hungarian football player who plays for Paks.
Club statistics
References
Paksi FC Official Website
HLSZ
MLSZ
1991 births
Footballers from Budapest
Living people
Hungarian men's footballers
Hungary men's under-21 international footballers
Men's association football forwards
Paksi FC players
BFC Siófok players
Fehérvár FC players
Puskás Akadémia FC players
Ferencvárosi TC footballers
MTK Budapest FC players
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/Cameron%20Leigh%20Stewart | Cameron Leigh Stewart FRSC is a Canadian mathematician. He is a professor of pure mathematics at the University of Waterloo.
Contributions
He has made numerous contributions to number theory, in particular to work on the abc conjecture. In 1976 he obtained, with Alan Baker, an effective improvement to Liouville's Theorem. In 1991 he proved that the number of solutions to a Thue equation is at most , where is a pre-determined positive real number and is the number of distinct primes dividing a large divisor of . This improves on an earlier result of Enrico Bombieri and Wolfgang M. Schmidt and is close to the best possible result. In 1995 he obtained, along with Jaap Top, the existence of infinitely many quadratic, cubic, and sextic twists of elliptic curves of large rank. In 1991 and 2001 respectively, he obtained, along with Kunrui Yu, the best unconditional estimates for the abc conjecture. In 2013, he solved an old problem of Erdős (so his Erdős number is 1) involving Lucas and Lehmer numbers. In particular, he proved that the largest prime divisor of satisfies .
Education
Stewart completed a B.Sc. at the University of British Columbia in 1971 and a M.Sc in 1972 from McGill University. He earned his doctorate from the University of Cambridge in 1976, under the supervision of Alan Baker.
Recognition
In 1974, while at Cambridge, he was awarded the J.T. Knight Prize.
He was elected Fellow of the Royal Society of Canada in 1989. He was appointed Fellow of the Fields Institute in 2008. Since 2003 he has held a Canada Research Chair (tier 1). Since 2005 he has been appointed University Professor at the University of Waterloo. He was selected to give the annual Isidore and Hilda Dressler Lecture at Kansas State University in 2015.
He was elected as a fellow of the Canadian Mathematical Society in 2019.
Selected works
References
External links
Website at University of Waterloo
Year of birth missing (living people)
Living people
Fellows of the Canadian Mathematical Society
Fellows of the Royal Society of Canada
20th-century Canadian mathematicians
21st-century Canadian mathematicians
McGill University alumni
Alumni of the University of Cambridge
Academic staff of the University of Waterloo
University of British Columbia alumni
Canada Research Chairs |
https://en.wikipedia.org/wiki/Gustav%20von%20Escherich | Gustav Ritter von Escherich (1 June 1849 – 28 January 1935) was an Austrian mathematician.
Biography
Born in Mantua, he studied mathematics and physics at the University of Vienna. From 1876 to 1879 he was professor at the University of Graz. In 1882 he went to the Graz University of Technology and in 1884 he went to the University of Vienna, where he also was president of the university in 1903/04.
Together with Emil Weyr he founded the journal Monatshefte für Mathematik und Physik and together with Ludwig Boltzmann and Emil Müller he founded the Austrian Mathematical Society.
Escherich died in Vienna.
Work on hyperbolic geometry
Following Eugenio Beltrami's (1868) discussion of hyperbolic geometry, Escherich in 1874 published a paper named "The geometry on surfaces of constant negative curvature". He used coordinates initially introduced by Christoph Gudermann (1830) for spherical geometry, which were adapted by Escherich using hyperbolic functions. For the case of translation of points on this surface of negative curvature, Escherich gave the following transformation on page 510:
and
which is identical with the relativistic velocity addition formula by interpreting the coordinates as velocities and by using the rapidity:
or with a Lorentz boost by using homogeneous coordinates:
These are in fact the relations between the coordinates of Gudermann/Escherich in terms of the Beltrami–Klein model and the Weierstrass coordinates of the hyperboloid model - this relation was pointed out by Homersham Cox (1882, p. 186),.
References
External links
1849 births
1935 deaths
Mathematicians from Austria-Hungary
19th-century Austrian mathematicians
20th-century Austrian mathematicians
Scientists from Mantua
University of Vienna alumni
Academic staff of the University of Vienna
Academic staff of the University of Graz
Academic staff of Chernivtsi University
Mathematicians from Austria-Hungary |
https://en.wikipedia.org/wiki/Asian%20Journal%20of%20Mathematics | The Asian Journal of Mathematics is a peer-reviewed scientific journal covering all areas of pure and theoretical applied mathematics. It is published by International Press.
English-language journals
Quarterly journals
Mathematics journals
Academic journals established in 1997
International Press academic journals |
https://en.wikipedia.org/wiki/Barbara%20Bag%C3%B3csi | Barbara Bagócsi (born 18 May 1988 in Budapest) is a retired Hungarian handball player.
References
External links
Player Profile on Handball.hu
Barbara Bagócsi career statistics at Worldhandball
1988 births
Living people
Hungarian female handball players
Handball players from Budapest
Expatriate handball players
Hungarian expatriate sportspeople in Italy
Hungarian expatriate sportspeople in Germany |
https://en.wikipedia.org/wiki/Emil%20M%C3%BCller%20%28mathematician%29 | Emil Adalbert Müller (22 April 1861 – 1 September 1927) was an Austrian mathematician.
Biography
Born in Lanškroun, he studied mathematics and physics at the University of Vienna and Vienna University of Technology. In 1898 he defended his dissertation (Die Geometrie orientierter Kugeln nach Grassmann’schen Methoden) at the University of Königsberg with Wilhelm Franz Meyer. One year later he received his habilitation at the same university. Since 1902 he was professor for descriptive geometry at the Vienna University of Technology and founder of the Vienna school of descriptive geometry. He also served as dean and president (1912–13). In 1903 he founded the Austrian Mathematical Society together with Ludwig Boltzmann and Gustav von Escherich. In 1904 Müller was an Invited Speaker of the ICM in Heidelberg.
He was a member of the Austrian Academy of Sciences and the German Academy of Sciences Leopoldina.
References
External links
1861 births
1927 deaths
20th-century Austrian mathematicians
Academic staff of TU Wien
Mathematicians from Austria-Hungary
Rectors of universities in Austria |
https://en.wikipedia.org/wiki/Interlocking%20interval%20topology | In mathematics, and especially general topology, the interlocking interval topology is an example of a topology on the set , i.e. the set of all positive real numbers that are not positive whole numbers. To give the set S a topology means to say which subsets of S are "open", and to do so in a way that the following axioms are met:
The union of open sets is an open set.
The finite intersection of open sets is an open set.
S and the empty set ∅ are open sets.
Construction
The open sets in this topology are taken to be the whole set S, the empty set ∅, and the sets generated by
The sets generated by Xn will be formed by all possible unions of finite intersections of the Xn.
See also
List of topologies
References
General topology
Topological spaces |
https://en.wikipedia.org/wiki/Lexicographic%20order%20topology%20on%20the%20unit%20square | In general topology, the lexicographic ordering on the unit square (sometimes the dictionary order on the unit square) is a topology on the unit square S, i.e. on the set of points (x,y) in the plane such that and
Construction
The lexicographical ordering gives a total ordering on the points in the unit square: if (x,y) and (u,v) are two points in the square, if and only if either or both and . Stated symbolically,
The lexicographic order topology on the unit square is the order topology induced by this ordering.
Properties
The order topology makes S into a completely normal Hausdorff space. Since the lexicographical order on S can be proven to be complete, this topology makes S into a compact space. At the same time, S contains an uncountable number of pairwise disjoint open intervals, each homeomorphic to the real line, for example the intervals for . So S is not separable, since any dense subset has to contain at least one point in each . Hence S is not metrizable (since any compact metric space is separable); however, it is first countable. Also, S is connected and locally connected, but not path connected and not locally path connected. Its fundamental group is trivial.
See also
List of topologies
Long line
Notes
References
General topology
Topological spaces |
https://en.wikipedia.org/wiki/Kaimri%2C%20Hisar | Kaimri is a village in Hisar tehsil and district in the Indian state of Haryana.
History
According to the data maintained by the Government of India's Department of Statistics, the Govt Primary School Kaimri was established in 1943, which was upgraded to a high school in 1967 and to senior secondary school in 1997.
Occupation
Main occupation of people is agriculture and government/private jobs. Some villagers are employed in government services and many people are doing private jobs.
Transport
Kaimri is connected to nearby villages through the road network with presence of State Transport Service and Private Bus Services which link it to Amardeep colony and beyond to Hisar.
Geography
Kaimri is located at Hisar-Kaimri road.
Demographics
Demographics as per 2001 census
India Census, Kaimri had a population of 7204. Male population is 3853, while female population is 3351.
Demographics as per 2011 census
As of 2011 India census, Kaimri had a population of 8399 in 1584 households. Males (4443) constitute 52.89% of the population and females (3956) 47.1%. Kaimri has an average literacy (4968) rate of 59.14%, more than the national average of 74%: male literacy (3018) is 60.74%, and female literacy (1950) is 39.25%. In Kaimri, 11.31% of the population is under 6 years of age (950).
Facilities
Kaimri village has government school, dispensary, etc. It is also the home of Shri Krishan Pranami Bal Sewa Ashram, Kaimri charitable orphanage and free school.
It also contain a Sankatmochan Kaimridham balaji mandir where peoples come from different cities of India.
See also
Kaimri (disambiguation)
Bidhwan
Dhillon
Hansi City and Tehsil
Haryana
Hissar
Hisar division
Hisar (Lok Sabha constituency)
Hisar Urban Agglomeration
India
Jat
Siwani
Tosham
References
Villages in Hisar district |
https://en.wikipedia.org/wiki/Appert%20topology | In general topology, a branch of mathematics, the Appert topology, named for , is a topology on the set } of positive integers.
In the Appert topology, the open sets are those that do not contain 1, and those that asymptotically contain almost every positive integer. The space X with the Appert topology is called the Appert space.
Construction
For a subset S of X, let denote the number of elements of S which are less than or equal to n:
S is defined to be open in the Appert topology if either it does not contain 1 or if it has asymptotic density equal to 1, i.e., it satisfies
.
The empty set is open because it does not contain 1, and the whole set X is open since
for all n.
Related topologies
The Appert topology is closely related to the Fort space topology that arises from giving the set of integers greater than one the discrete topology, and then taking the point 1 as the point at infinity in a one point compactification of the space. The Appert topology is finer than the Fort space topology, as any cofinite subset of X has asymptotic density equal to 1.
Properties
The closed subsets S of X are those that either contain 1 or that have zero asymptotic density, namely .
Every point of X has a local basis of clopen sets, i.e., X is a zero-dimensional space.Proof: Every open neighborhood of 1 is also closed. For any , is both closed and open.
X is Hausdorff and perfectly normal (T6).Proof: X is T1. Given any two disjoint closed sets A and B, at least one of them, say A, does not contain 1. A is then clopen and A and its complement are disjoint respective neighborhoods of A and B, which shows that X is normal and Hausdorff. Finally, any subset, in particular any closed subset, in a countable T1 space is a Gδ, so X is perfectly normal.
X is countable, but not first countable, and hence not second countable and not metrizable.
A subset of X is compact if and only if it is finite. In particular, X is not locally compact, since there is no compact neighborhood of 1.
X is not countably compact.Proof: The infinite set has zero asymptotic density, hence is closed in X. Each of its points is isolated. Since X contains an infinite closed discrete subset, it is not limit point compact, and therefore it is not countably compact.
See also
Notes
References
.
.
General topology
Topological spaces |
https://en.wikipedia.org/wiki/Jean-Baptiste%20de%20La%20Chapelle | Jean-Baptiste de La Chapelle (c.1710–1792, Paris) was a French priest, mathematician and inventor.
He contributed 270 articles to the Encyclopédie in the subjects of arithmetic and geometry. In June 1747 he was elected a Fellow of the Royal Society of London.
He was the inventor of a primitive diving suit in 1775, which he called a "scaphandre" from the Greek words skaphe (boat) and andros (man) in his book Traité de la construction théorique et pratique du scaphandre ou du bateau de l'homme (Treatise on the theoretical and practical construction of the "Scaphandre" or human boat). The invention of the Abbé de la Chapelle consisted of a suit made of cork which allowed soldiers to float and swim in water. As the name and description suggest, it was more of a flotation suit than a diving suit.
Publications
Discours sur l’Étude des Mathématiques, Paris, 1743.
Institutions de Géométrie, enrichies de notes critiques et philosophiques sur la nature et des développements de l’esprit humain; précédées d’un Discours sur l’Étude des Mathématiques, 2 vol., Paris 1746, 1757.
Traité des sections coniques et autres courbes anciennes, appliquées et appliquables à la pratique des differens arts, 1750.
L’Art de communiquer ses idées, enrichi de notes historiques et philosophiques, London, 1763.
Le Ventriloque, ou l’Engastrimythe, London & Paris, 1772 (sur Google Books).
Traité de la Construction théorique et pratique du Scaphandre ou du bateau de l’homme, approuvé par l’Académie des Sciences (Paris 1774) ; réédité sous le titre Traité de la construction théorique et pratique du scaphandre ou bateau de l’homme… par M. de La Chapelle. Nouvelle édition… Précédé du Projet de formation d’une légion nautique ou d’éclaireurs des côtes, destinée à opérer tels débarquemens qu’on avisera sans le secours de vaisseaux… par… La Reynie… [Jean-Baptiste-Marie-Louis de La Reynie de La Bruyère] (Paris an XIII – 1805)
Sources
Frank Arthur Kafker, The encyclopedists as individuals: a biographical dictionary of the authors of the Encyclopédie, Oxford, Studies on Voltaire and the eighteenth Century, 1988, p. 181-4, .
1710 births
1792 deaths
18th-century French mathematicians
Fellows of the Royal Society
Contributors to the Encyclopédie (1751–1772)
18th-century French inventors |
https://en.wikipedia.org/wiki/Rectified%209-orthoplexes | In nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-orthoplex.
There are 9 rectifications of the 9-orthoplex. Vertices of the rectified 9-orthoplex are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 9-orthoplex are located in the triangular face centers of the 9-orthoplex. Vertices of the trirectified 9-orthoplex are located in the tetrahedral cell centers of the 9-orthoplex.
These polytopes are part of a family 511 uniform 9-polytopes with BC9 symmetry.
Rectified 9-orthoplex
The rectified 9-orthoplex is the vertex figure for the demienneractic honeycomb.
or
Alternate names
rectified enneacross (Acronym riv) (Jonathan Bowers)
Construction
There are two Coxeter groups associated with the rectified 9-orthoplex, one with the C9 or [4,37] Coxeter group, and a lower symmetry with two copies of 8-orthoplex facets, alternating, with the D9 or [36,1,1] Coxeter group.
Cartesian coordinates
Cartesian coordinates for the vertices of a rectified 9-orthoplex, centered at the origin, edge length are all permutations of:
(±1,±1,0,0,0,0,0,0,0)
Root vectors
Its 144 vertices represent the root vectors of the simple Lie group D9. The vertices can be seen in 3 hyperplanes, with the 36 vertices rectified 8-simplexs cells on opposite sides, and 72 vertices of an expanded 8-simplex passing through the center. When combined with the 18 vertices of the 9-orthoplex, these vertices represent the 162 root vectors of the B9 and C9 simple Lie groups.
Images
Birectified 9-orthoplex
Alternate names
Rectified 9-demicube
Birectified enneacross (Acronym brav) (Jonathan Bowers)
Images
Trirectified 9-orthoplex
Alternate names
trirectified enneacross (Acronym tarv) (Jonathan Bowers)
Images
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966)
x3o3o3o3o3o3o3o4o - vee, o3x3o3o3o3o3o3o4o - riv, o3o3x3o3o3o3o3o4o - brav, o3o3o3x3o3o3o3o4o - tarv, o3o3o3o3x3o3o3o4o - nav, o3o3o3o3o3x3o3o4o - tarn, o3o3o3o3o3o3x3o4o - barn, o3o3o3o3o3o3o3x4o - ren, o3o3o3o3o3o3o3o4x - enne
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
9-polytopes |
https://en.wikipedia.org/wiki/Rectified%2010-orthoplexes | In ten-dimensional geometry, a rectified 10-orthoplex is a convex uniform 10-polytope, being a rectification of the regular 10-orthoplex.
There are 10 rectifications of the 10-orthoplex. Vertices of the rectified 10-orthoplex are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 10-orthoplex are located in the triangular face centers of the 10-orthoplex. Vertices of the trirectified 10-orthoplex are located in the tetrahedral cell centers of the 10-orthoplex.
These polytopes are part of a family 1023 uniform 10-polytopes with BC10 symmetry.
Rectified 10-orthoplex
In ten-dimensional geometry, a rectified 10-orthoplex is a 10-polytope, being a rectification of the regular 10-orthoplex.
Rectified 10-orthoplex
The rectified 10-orthoplex is the vertex figure for the demidekeractic honeycomb.
or
Alternate names
rectified decacross (Acronym rake) (Jonathan Bowers)
Construction
There are two Coxeter groups associated with the rectified 10-orthoplex, one with the C10 or [4,38] Coxeter group, and a lower symmetry with two copies of 9-orthoplex facets, alternating, with the D10 or [37,1,1] Coxeter group.
Cartesian coordinates
Cartesian coordinates for the vertices of a rectified 10-orthoplex, centered at the origin, edge length are all permutations of:
(±1,±1,0,0,0,0,0,0,0,0)
Root vectors
Its 180 vertices represent the root vectors of the simple Lie group D10. The vertices can be seen in 3 hyperplanes, with the 45 vertices rectified 9-simplices facets on opposite sides, and 90 vertices of an expanded 9-simplex passing through the center. When combined with the 20 vertices of the 9-orthoplex, these vertices represent the 200 root vectors of the simple Lie group B10.
Images
Birectified 10-orthoplex
Alternate names
Birectified decacross
Cartesian coordinates
Cartesian coordinates for the vertices of a birectified 10-orthoplex, centered at the origin, edge length are all permutations of:
(±1,±1,±1,0,0,0,0,0,0,0)
Images
Trirectified 10-orthoplex
Alternate names
Trirectified decacross (Acronym trake) (Jonathan Bowers)
Cartesian coordinates
Cartesian coordinates for the vertices of a trirectified 10-orthoplex, centered at the origin, edge length are all permutations of:
(±1,±1,±1,±1,0,0,0,0,0,0)
Images
Quadrirectified 10-orthoplex
Alternate names
Quadrirectified decacross (Acronym brake) (Jonthan Bowers)
Cartesian coordinates
Cartesian coordinates for the vertices of a quadrirectified 10-orthoplex, centered at the origin, edge length are all permutations of:
(±1,±1,±1,±1,±1,0,0,0,0,0)
Images
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M |
https://en.wikipedia.org/wiki/Helly%20space | In mathematics, and particularly functional analysis, the Helly space, named after Eduard Helly, consists of all monotonically increasing functions , where [0,1] denotes the closed interval given by the set of all x such that In other words, for all we have and also if then
Let the closed interval [0,1] be denoted simply by I. We can form the space II by taking the uncountable Cartesian product of closed intervals:
The space II is exactly the space of functions . For each point x in [0,1] we assign the point ƒ(x) in
Topology
The Helly space is a subset of II. The space II has its own topology, namely the product topology. The Helly space has a topology; namely the induced topology as a subset of II. It is normal Haudsdorff, compact, separable, and first-countable but not second-countable.
References
Functional analysis
Gelfand–Shilov space |
https://en.wikipedia.org/wiki/Truncated%208-orthoplexes | In eight-dimensional geometry, a truncated 8-orthoplex is a convex uniform 8-polytope, being a truncation of the regular 8-orthoplex.
There are 7 truncation for the 8-orthoplex. Vertices of the truncation 8-orthoplex are located as pairs on the edge of the 8-orthoplex. Vertices of the bitruncated 8-orthoplex are located on the triangular faces of the 8-orthoplex. Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 8-orthoplex. The final truncations are best expressed relative to the 8-cube.
Truncated 8-orthoplex
Alternate names
Truncated octacross (acronym tek) (Jonthan Bowers)
Construction
There are two Coxeter groups associated with the truncated 8-orthoplex, one with the C8 or [4,3,3,3,3,3,3] Coxeter group, and a lower symmetry with the D8 or [35,1,1] Coxeter group.
Coordinates
Cartesian coordinates for the vertices of a truncated 8-orthoplex, centered at the origin, are all 224 vertices are sign (4) and coordinate (56) permutations of
(±2,±1,0,0,0,0,0,0)
Images
Bitruncated 8-orthoplex
Alternate names
Bitruncated octacross (acronym batek) (Jonthan Bowers)
Coordinates
Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of
(±2,±2,±1,0,0,0,0,0)
Images
Tritruncated 8-orthoplex
Alternate names
Tritruncated octacross (acronym tatek) (Jonthan Bowers)
Coordinates
Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of
(±2,±2,±2,±1,0,0,0,0)
Images
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. (1966)
x3x3o3o3o3o3o4o - tek, o3x3x3o3o3o3o4o - batek, o3o3x3x3o3o3o4o - tatek
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
8-polytopes |
https://en.wikipedia.org/wiki/Ernest%20Corominas | Ernest Corominas i Vigneaux (1913 – 24 January 1992) was a Spanish-French mathematician.
Born in Barcelona, he studied architecture and mathematics at the University of Barcelona, graduating in 1936. He served as in officer of engineering in the Spanish Republican Army during the Spanish Civil War. In 1939 he fled to France, before moving to South America in 1940. After working six months as an architect in Chile, he moved to Argentina, where Julio Rey Pastor offered him a lecturer position at the University of Buenos Aires.
Corominas returned to Europe, where he attained his doctorate at the University of Paris in 1952, under the supervision of Arnaud Denjoy. He then lectured in Barcelona, Princeton, and Caracas, before settling in France at the University of Lyon. In 1966, Corominas became a French citizen.
He was awarded a Guggenheim Fellowship in 1953.
References
External links
1913 births
1992 deaths
20th-century French mathematicians
20th-century Spanish mathematicians
University of Paris alumni
Academic staff of the University of Lyon
Spanish emigrants to France |
https://en.wikipedia.org/wiki/Pitch%20interval | In musical set theory, there are four kinds of interval:
Ordered pitch interval
Unordered pitch interval
Ordered pitch-class interval
Unordered pitch-class interval
Pitch Intervals
Ordered Pitch Interval
The ordered pitch interval. is the number of semitones that separates one pitch from another, upward or downward. It is thus more specific than the unordered pitch interval in that it represents the directionality of the interval. An ordered pitch interval always includes a plus or minus sign. Thus this interval type can describe a melodic as well as a harmonic interval.
Unordered Pitch Interval
The unordered pitch interval does not include directionality information and is thus less specific than the ordered pitch interval. It is still the distance between two pitches measured in semitones, but that distance is not qualified by a positive (+) or negative symbol. (-). An unordered pitch interval can describe a harmonic interval but not a melodic interval.
Both types of pitch intervals describe octave information in that they do not treat all octaves as being equivalent. Pitch intervals, both ordered and unordered, may therefore be larger than 12.
Comparison to Pitch-Class Intervals
By treating all octaves as being equivalent, pitch-classes contain less information (ex 'C') than pitches (ex: C3). Pitch-class intervals (below) are therefore never larger than 12 semitones.
Pitch-Class Intervals
In musical set theory, pitch-class intervals do not distinguish between octaves since pitch-classes themselves treat all octaves as being equivalent.
There are two kinds of pitch-class intervals:
ordered pitch-class interval (also called a pitch-interval class - PIC)
unordered pitch-class interval (also called an 'interval class')
Ordered pitch-class intervals ('pitch interval class; PIC')
The ordered pitch-class interval describes the number of ascending semitones from one pitch-class to the next, ordered from lowest to highest.
Since pitch-classes have octave equivalence, the ordered pitch -class interval can be computed mathematically as "the absolute value of the difference between the two pitch-classes modulo 12". See Equations, below. A more visual way to do this calculation is to place the pitch-classes on a clockface and measure the difference, always going clockwise (i.e. always ascending).
Unordered pitch-class intervals ('interval class; IC')
Unlike the ordered, the unordered pitch-class interval (often called the 'Interval class') does not require the two pitch-classes to be ordered from lowest to highest. Rather, this type of interval measures in semitones whichever interval is smallest.
Because of symmetry, the smallest semitone interval between any two pitch-classes can only be an integer between 0 and 6. (hence the seven 'interval classes') The tonal interval names 'minor 2nd' and 'major 7th' both correspond to "interval class 1" for example, This is because both are composed of one semitone and directional order is |
https://en.wikipedia.org/wiki/Mil%C3%A1n%20N%C3%A9meth | Milán Németh (born 29 May 1988 in Szombathely) is a retired Hungarian football player.
Club statistics
Updated to games played as of 19 May 2019.
External links
HLSZ
MLSZ
1988 births
Living people
Footballers from Szombathely
Hungarian men's footballers
Men's association football defenders
Pápai FC footballers
Diósgyőri VTK players
Soproni VSE players
Szombathelyi Haladás footballers
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/Probable%20error | In statistics, probable error defines the half-range of an interval about a central point for the distribution, such that half of the values from the distribution will lie within the interval and half outside.
Thus for a symmetric distribution it is equivalent to half the interquartile range, or the median absolute deviation. One such use of the term probable error in this sense is as the name for the scale parameter of the Cauchy distribution, which does not have a standard deviation.
The probable error can also be expressed as a multiple of the standard deviation σ, which requires that at least the second statistical moment of the distribution should exist, whereas the other definition does not. For a normal distribution this is
(see details)
See also
Average absolute deviation
Circular error probable
Confidence interval
Standard error
References
Theory of probability distributions
Errors and residuals
Statistical deviation and dispersion
ru:Срединное отклонение |
https://en.wikipedia.org/wiki/Alexandrov%27s%20uniqueness%20theorem | The Alexandrov uniqueness theorem is a rigidity theorem in mathematics, describing three-dimensional convex polyhedra in terms of the distances between points on their surfaces. It implies that convex polyhedra with distinct shapes from each other also have distinct metric spaces of surface distances, and it characterizes the metric spaces that come from the surface distances on polyhedra. It is named after Soviet mathematician Aleksandr Danilovich Aleksandrov, who published it in the 1940s.
Statement of the theorem
The surface of any convex polyhedron in Euclidean space forms a metric space, in which the distance between two points is measured by the length of the shortest path from one point to the other along the surface. Within a single shortest path, distances between pairs of points equal the distances between corresponding points of a line segment of the same length; a path with this property is known as a geodesic.
This property of polyhedral surfaces, that every pair of points is connected by a geodesic, is not true of many other metric spaces, and when it is true the space is called a geodesic space. The geodesic space formed from the surface of a polyhedron is called its development.
The polyhedron can be thought of as being folded from a sheet of paper (a net for the polyhedron) and it inherits the same geometry as the paper: for every point p within a face of the polyhedron, a sufficiently small open neighborhood of p will have the same distances as a subset of the Euclidean plane. The same thing is true even for points on the edges of the polyhedron: they can be modeled locally as a Euclidean plane folded along a line and embedded into three-dimensional space, but the fold does not change the structure of shortest paths along the surface. However, the vertices of the polyhedron have a different distance structure: the local geometry of a polyhedron vertex is the same as the local geometry at the apex of a cone. Any cone can be formed from a flat sheet of paper with a wedge removed from it by gluing together the cut edges where the wedge was removed. The angle of the wedge that was removed is called the angular defect of the vertex; it is a positive number less than 2. The defect of a polyhedron vertex can be measured by subtracting the face angles at that vertex from 2. For instance, in a regular tetrahedron, each face angle is /3, and there are three of them at each vertex, so subtracting them from 2 leaves a defect of at each of the four vertices.
Similarly, a cube has a defect of /2 at each of its eight vertices. Descartes' theorem on total angular defect (a form of the Gauss–Bonnet theorem) states that the sum of the angular defects of all the vertices is always exactly 4. In summary, the development of a convex polyhedron is geodesic, homeomorphic (topologically equivalent) to a sphere, and locally Euclidean except for a finite number of cone points whose angular defect sums to 4.
Alexandrov's theorem gives a converse to |
https://en.wikipedia.org/wiki/Block%20graph | In graph theory, a branch of combinatorial mathematics, a block graph or clique tree
is a type of undirected graph in which every biconnected component (block) is a clique.
Block graphs are sometimes erroneously called Husimi trees (after Kôdi Husimi), but that name more properly refers to cactus graphs, graphs in which every nontrivial biconnected component is a cycle.
Block graphs may be characterized as the intersection graphs of the blocks of arbitrary undirected graphs.
Characterization
Block graphs are exactly the graphs for which, for every four vertices , , , and , the largest two of the three distances ,
,
and are always equal.
They also have a forbidden graph characterization as the graphs that do not have the diamond graph or a cycle of four or more vertices as an induced subgraph; that is, they are the diamond-free chordal graphs. They are also the Ptolemaic graphs (chordal distance-hereditary graphs) in which every two nodes at distance two from each other are connected by a unique shortest path, and the chordal graphs in which every two maximal cliques have at most one vertex in common.
A graph is a block graph if and only if the intersection of every two connected subsets of vertices of is empty or connected. Therefore, the connected subsets of vertices in a connected block graph form a convex geometry, a property that is not true of any graphs that are not block graphs. Because of this property, in a connected block graph, every set of vertices has a unique minimal connected superset, its closure in the convex geometry. The connected block graphs are exactly the graphs in which there is a unique induced path connecting every pair of vertices.
Related graph classes
Block graphs are chordal, distance-hereditary, and geodetic. The distance-hereditary graphs are the graphs in which every two induced paths between the same two vertices have the same length, a weakening of the characterization of block graphs as having at most one induced path between every two vertices. Because both the chordal graphs and the distance-hereditary graphs are subclasses of the perfect graphs, block graphs are perfect.
Every tree, cluster graph, or windmill graph is a block graph.
Every block graph has boxicity at most two.
Block graphs are examples of pseudo-median graphs: for every three vertices, either there exists a unique vertex that belongs to shortest paths between all three vertices, or there exists a unique triangle whose edges lie on these three shortest paths.
The line graphs of trees are exactly the block graphs in which every cut vertex is incident to at most two blocks, or equivalently the claw-free block graphs. Line graphs of trees have been used to find graphs with a given number of edges and vertices in which the largest induced subgraph that is a tree is as small as possible.
The block graphs in which every block has size at most three are a special type of cactus graph, a triangular cactus. The largest triangular cactu |
https://en.wikipedia.org/wiki/Rimhak%20Ree | Rimhak Ree (; December 18, 1922 – January 9, 2005), alternatively Im-hak Ree, was a Korean Canadian mathematician. He contributed in the field of group theory, most notably with the concept of the Ree group in .
Early life
Ree received his early education in Hamhung, South Hamgyong, Korea, Empire of Japan. His birthplace is now in North Korea. He attended the Hamhung #1 Public Ordinary School (), and in 1934 entered the Hamhung Public High School (). He went onto Keijō Imperial University, where he studied physics, which was an unusual choice for Koreans at the time. Ree graduated in 1944 with a physics degree; he then went to Fengtian, Manchukuo (today Shenyang, Liaoning in the People's Republic of China) to work for an aircraft company.
Career
After the surrender of Japan in 1945 and the end of Japanese rule in Korea, Ree returned to his home country and in 1947 took up a teaching position in the mathematics department at Seoul National University as an assistant professor. Later that year, in Namdaemun Market, Ree found an issue of the Bulletin of the American Mathematical Society, which proposedly was left by an American soldier. On the Bulletin was the paper 'Note on power series', in which Max Zorn solved a problem about the convergence of certain power series with complex coefficients. In the paper, Zorn posed a question of whether the same result held for power series with real coefficients. Ree solved the problem and sent the solution to Max Zorn. When Zorn received Ree's solution, it was sent to the Bulletin of the American Mathematical Society to be published in 1949 with the title 'On a problem of Max Zorn' and become the first mathematical paper published by a Korean in an international journal.
During the Korean War, he fled south to Busan, and in 1953 he was awarded a Canadian scholarship to allow him to study for a Ph.D. degree at the University of British Columbia in Vancouver, Canada. He completed his dissertation on Witt algebras in 1955. His thesis advisor was Stephen Arthur Jennings. Following the award of his doctorate, Ree was appointed as a lecturer at Montana State University, despite facing several problems regarding his labour permission and nationality.
In mid-1955, Ree received a grant from the National Research Council of Canada and he worked with Jennings on Lie algebras. In 1958, he published a solution to a problem of Paul Erdős regarding a certain class of irrational numbers. Ree's two most renowned papers were written from 1960 to 1961, in which he suggested a Lie type group over a finite field now named after him. In 1962 after being promoted to an assistant professor in mathematics at University of British Columbia, he was granted an academic year which he spent in Yale. He was elected a member of Royal Society of Canada in 1964.
Personal life
Family
Ree had two daughters Erran and Hiran from his first marriage. He later married Rhoda Mah, a doctor and the daughter of John Ming Mah, who owned Northwest |
https://en.wikipedia.org/wiki/George%20Johnston%20Allman | George Johnston Allman (28 September 1824 – 9 May 1904) was an Irish professor, mathematician, classical scholar, and historian of ancient Greek mathematics. His fame rests mainly upon his authorship of Greek Geometry from Thales to Euclid, first published in Dublin in 1889, and republished several times subsequently.
Life
He was born in Dublin the son of William Allman MD, also a botanist.
He held the position of Professor of Mathematics at Queen's University of Ireland for forty years, from 1853 until reaching retirement age in 1893.
He died at Finglass, Dublin on 9 May, 1904. He had married in 1853 Louisa, the daughter of John Smith Taylor of Dublin.
Recognition
He was elected a Fellow of the Royal Society in June, 1884. His candidacy citation read: "Member of the Senate of the Queen's University of Ireland, – Appointed by Charter one of the original Senators of the Royal University of Ireland – Member of Standing Committee of the said University. Author of the following papers, amongst others: "Method of deriving the Polar Equations of Dynamics & Hydrodynamics from direct physical considerations" – Dublin University Phil Transactions 1848. "On certain Curves traced on the Surface of an Ellipsoid", Camb & Dub Math Journal. 1848. "On the Attraction of Ellipsoids, with a new demonstration of Clairaut's Theorem, being an account of the late Prof MacCullagh's lectures", Trans RI Academy 1855. "On some properties of Paraboloids". Quarterly Journal Maths 1874. "Greek Geometry from Thales to Euclid, Part 1" Hermathena 1877. Do "Part 2" Hermathena, 1881"
References
External links
About George Johnston Allman
1824 births
1904 deaths
19th-century Irish mathematicians
Irish classical scholars
Historians of mathematics
Alumni of Trinity College Dublin
Fellows of the Royal Society
Scientists from County Dublin |
https://en.wikipedia.org/wiki/Robert%20Minlos | Robert Adol'fovich Minlos (; 28 February 1931 – 9 January 2018) was a Soviet and Russian mathematician who has made important contributions to probability theory and mathematical physics. His theorem on the extension of cylindrical measures to Radon measures on the continuous dual of a nuclear space is of fundamental importance in the theory of generalized random processes.
He died on 9 January 2018 at the age of 86.
References
External links
List of publications on mathnet.ru
1931 births
2018 deaths
Mathematicians from Moscow
Soviet mathematicians
Moscow State University alumni
Academic staff of Moscow State University |
https://en.wikipedia.org/wiki/Escaping%20set | In mathematics, and particularly complex dynamics, the escaping set of an entire function ƒ consists of all points that tend to infinity under the repeated application of ƒ.
That is, a complex number belongs to the escaping set if and only if the sequence defined by converges to infinity as gets large. The escaping set of is denoted by .
For example, for , the origin belongs to the escaping set, since the sequence
tends to infinity.
History
The iteration of transcendental entire functions was first studied by Pierre Fatou in 1926
The escaping set occurs implicitly in his study of the explicit entire functions and .
The first study of the escaping set for a general transcendental entire function is due to Alexandre Eremenko who used Wiman-Valiron theory.
He conjectured that every connected component of the escaping set of a transcendental entire function is unbounded. This has become known
as Eremenko's conjecture. There are many partial results
on this problem but as of 2013 the conjecture is still open.
Eremenko also asked whether every escaping point can be connected to infinity by a curve in the escaping set; it was later shown that this is not the case. Indeed,
there exist entire functions whose escaping sets do not contain any curves at all.
Properties
The following properties are known to hold for the escaping set of any non-constant and non-linear entire function. (Here nonlinear means that the function is not of the form .)
The escaping set contains at least one point.
The boundary of the escaping set is exactly the Julia set. In particular, the escaping set is never closed.
For a transcendental entire function, the escaping set always intersects the Julia set. In particular, the escaping set is open if and only if is a polynomial.
Every connected component of the closure of the escaping set is unbounded.
The escaping set always has at least one unbounded connected component.
The escaping set is connected or has infinitely many components.
The set is connected.
Note that the final statement does not imply Eremenko's Conjecture. (Indeed, there exist connected spaces in which the removal of a single dispersion point leaves the remaining space totally disconnected.)
Examples
Polynomials
A polynomial of degree 2 extends to an analytic self-map of the Riemann sphere, having a super-attracting fixed point at infinity. The escaping set is precisely the basin of attraction of this fixed point, and hence usually referred to as the **basin of infinity**. In this case, is an open and connected subset of the complex plane, and the Julia set is the boundary of this basin.
For instance the escaping set of the complex quadratic polynomial consists precisely of the complement of the closed unit disc:
Transcendental entire functions
For transcendental entire functions, the escaping set is much more complicated than for polynomials: in the simplest cases like the one illustrated in the picture it consists of uncountably ma |
https://en.wikipedia.org/wiki/Lithuania%20national%20football%20team%20records%20and%20statistics | The following is a list of the Lithuania national football team's competitive records and statistics.
Individual records
Player records
Players in bold are still active, at least at club level.
Most capped players
Top goalscorers
Manager records
Team records
Competition records
FIFA World Cup
UEFA European Championship
UEFA Nations League
*Draws include knockout matches decided via penalty shoot-out.
**Group stage played home and away. Flag shown represents host nation for the finals stage.
Head-to-head record
This list attempts to list every official and friendly game played by the Lithuania national football team since 1990. Although it has played a number of countries around the world, some repeatedly, Lithuania has played the most games (19) against neighbouring Latvia.
Notes
References
Lithuania national football team
National association football team records and statistics |
https://en.wikipedia.org/wiki/Egyptian%20geometry | Egyptian geometry refers to geometry as it was developed and used in Ancient Egypt. Their geometry was a necessary outgrowth of surveying to preserve the layout and ownership of farmland, which was flooded annually by the Nile river.
We only have a limited number of problems from ancient Egypt that concern geometry. Geometric problems appear in both the Moscow Mathematical Papyrus (MMP) and in the Rhind Mathematical Papyrus (RMP). The examples demonstrate that the ancient Egyptians knew how to compute areas of several geometric shapes and the volumes of cylinders and pyramids.
Area
The ancient Egyptians wrote out their problems in multiple parts. They gave the title and the data for the given problem, in some of the texts they would show how to solve the problem, and as the last step they verified that the problem was correct. The scribes did not use any variables and the problems were written in prose form. The solutions were written out in steps, outlining the process.
Egyptian units of length are attested from the Early Dynastic Period. Although it dates to the 5th dynasty, the Palermo stone recorded the level of the Nile River during the reign of the Early Dynastic pharaoh Djer, when the height of the Nile was recorded as 6 cubits and 1 palm (about ). A Third Dynasty diagram shows how to construct a circular vault using body measures along an arc. If the area of the Square is 434 units. The area of the circle is 433.7.
The ostracon depicting this diagram was found near the Step Pyramid of Saqqara. A curve is divided into five sections and the height of the curve is given in cubits, palms, and digits in each of the sections.
At some point, lengths were standardized by cubit rods. Examples have been found in the tombs of officials, noting lengths up to remen. Royal cubits were used for land measures such as roads and fields. Fourteen rods, including one double-cubit rod, were described and compared by Lepsius. Two examples are known from the Saqqara tomb of Maya, the treasurer of Tutankhamun.
Another was found in the tomb of Kha (TT8) in Thebes. These cubits are long and are divided into palms and hands: each palm is divided into four fingers from left to right and the fingers are further subdivided into ro from right to left. The rules are also divided into hands so that for example one foot is given as three hands and fifteen fingers and also as four palms and sixteen fingers.
Surveying and itinerant measurement were undertaken using rods, poles, and knotted cords of rope. A scene in the tomb of Menna in Thebes shows surveyors measuring a plot of land using rope with knots tied at regular intervals. Similar scenes can be found in the tombs of Amenhotep-Sesi, Khaemhat and Djeserkareseneb. The balls of rope are also shown in New Kingdom statues of officials such as Senenmut, Amenemhet-Surer, and Penanhor.
Triangles:
The ancient Egyptians knew that the area of a triangle is where b = base and h = height. Calculations of the area of a |
https://en.wikipedia.org/wiki/Cartesian%20oval | In geometry, a Cartesian oval is a plane curve consisting of points that have the same linear combination of distances from two fixed points (foci). These curves are named after French mathematician René Descartes, who used them in optics.
Definition
Let and be fixed points in the plane, and let and denote the Euclidean distances from these points to a third variable point . Let and be arbitrary real numbers. Then the Cartesian oval is the locus of points S satisfying . The two ovals formed by the four equations and are closely related; together they form a quartic plane curve called the ovals of Descartes.
Special cases
In the equation , when and the resulting shape is an ellipse. In the limiting case in which P and Q coincide, the ellipse becomes a circle. When it is a limaçon of Pascal. If and the equation gives a branch of a hyperbola and thus is not a closed oval.
Polynomial equation
The set of points satisfying the quartic polynomial equation
where is the distance between the two fixed foci and , forms two ovals, the sets of points satisfying the two of the following four equations
that have real solutions. The two ovals are generally disjoint, except in the case that or belongs to them. At least one of the two perpendiculars to through points and cuts this quartic curve in four real points; it follows from this that they are necessarily nested, with at least one of the two points and contained in the interiors of both of them. For a different parametrization and resulting quartic, see Lawrence.
Applications in optics
As Descartes discovered, Cartesian ovals may be used in lens design. By choosing the ratio of distances from and to match the ratio of sines in Snell's law, and using the
surface of revolution of one of these ovals, it is possible to design a so-called aplanatic lens, that has no spherical aberration.
Additionally, if a spherical wavefront is refracted through a spherical lens, or reflected from a concave spherical surface, the refracted or reflected wavefront takes on the shape of a Cartesian oval. The caustic formed by spherical aberration in this case may therefore be described as the evolute of a Cartesian oval.
History
The ovals of Descartes were first studied by René Descartes in 1637, in connection with their applications in optics.
These curves were also studied by Newton beginning in 1664. One method of drawing certain specific Cartesian ovals, already used by Descartes, is analogous to a standard construction of an ellipse by a pinned thread. If one stretches a thread from a pin at one focus to wrap around a pin at a second focus, and ties the free end of the thread to a pen, the path taken by the pen, when the thread is stretched tight, forms a Cartesian oval with a 2:1 ratio between the distances from the two foci. However, Newton rejected such constructions as insufficiently rigorous. He defined the oval as the solution to a differential equation, constructed its subn |
https://en.wikipedia.org/wiki/Rational%20sequence%20topology | In mathematics, more specifically general topology, the rational sequence topology is an example of a topology given to the set R of real numbers.
Construction
For each irrational number x take a sequence of rational numbers {xk} with the property that {xk} converges to x with respect to the Euclidean topology.
The rational sequence topology is specified by letting each rational number singleton to be open, and using as a neighborhood base for each irrational number x, the sets
References
Topological spaces |
https://en.wikipedia.org/wiki/Freydoon%20Shahidi | Freydoon Shahidi (born June 19, 1947) is an Iranian American mathematician who is a Distinguished Professor of Mathematics at Purdue University in the U.S. He is known for a method of automorphic L-functions which is now known as the Langlands–Shahidi method.
Education and career
Shahidi graduated from the University of Tehran with a bachelor's degree in 1969. He received his Ph.D. in 1975 from Johns Hopkins University with dissertation On Gauss Sums Attached to the Pairs and the Exterior Powers of the Representations of the General Linear Groups over Finite and Local Fields with advisor Joseph Shalika. As a postdoc Shahidi was for the academic year 1975–1976 at the Institute for Advanced Study and for the academic year 1976–1977 a visiting assistant professor at Indiana University in Bloomington. At Purdue University he became in 1977 an assistant professor, in 1982 an associate professor, and 1986 a full professor. There he since 2001 is a Distinguished Professor.
He returned to the Institute for Advanced Study in 1983–1984, in 1990–1991, in October–November 1999, and in several other brief visits. He has held visiting positions from 1981 to 1982 at the University of Toronto, in June 1990 at the University of Paris VII, in May 1993 and again in February 1997 as a Fellow of the Japan Society for the Promotion of Science at Kyōto University, in June–July 1993 at the Catholic University of Eichstätt-Ingolstadt, in May–June 1995 at the École normale supérieure, and at several other institutions.
Shahidi was a Guggenheim Fellow for the academic year 2001–2002. He as in 2002 an Invited Speaker at the International Congress of Mathematicians in Beijing with talk Automorphic L-functions and functoriality. He is a member of the American Academy of Arts and Sciences since 2010. In 2012 he became a fellow of the American Mathematical Society. He is a member of the editorial board of the American Journal of Mathematics.
Selected publications
Eisenstein Series and Automorphic L-Functions, AMS Colloquium Publications 58, 2010
Functional Equation Satisfied by Certain L-Functions, Compositio Math., vol. 37, 1978, 171–208.
On certain L-functions, American Journal of Mathematics, vol. 103, 1981, 297–355.
A proof of Langlands conjecture on Plancherel measures; Complementary series for p-adic groups, Annals of Mathematics, Band 132, 1990, 273–330
Local coefficients as Artin L-factors for real groups, Duke Math. J., vol. 52, 1985, 973–1007
with Stephen Gelbart: Boundedness of automorphic L-functions in vertical strips, Journal of the American Mathematical Society, vol. 14, 2001, 79–107.
mit H. H. Kim: Functorial products for GL(2) × GL(3) and the symmetric cube for GL(2), Annals of Mathematics, vol. 155, 2002, 837–893.
On nonvanishing of L-functions, Bull. Amer. Math. Soc. (N.S.), vol. 2, 1980, 462–464.
On the Ramanujan conjecture and finiteness of poles of certain L-functions, Annals of Mathematics, vol. 127, 1988, 547–584
The notion of norm and |
https://en.wikipedia.org/wiki/Board%20puzzles%20with%20algebra%20of%20binary%20variables | Board puzzles with algebra of binary variables ask players to locate the hidden objects based on a set of clue cells and their neighbors marked as variables (unknowns). A variable with value of 1 corresponds to a cell with an object. Contrary, a variable with value of 0 corresponds to an empty cell—no hidden object.
Overview
These puzzles are based on algebra with binary variables taking a pair of values, for example, (no, yes), (false, true), (not exists, exists), (0, 1). It invites the player quickly establish some equations, and inequalities for the solution. The partitioning can be used to reduce the complexity of the problem. Moreover, if the puzzle is prepared in a way that there exists a unique solution only, this fact can be used to eliminate some variables without calculation.
The problem can be modeled as binary integer linear programming which is a special case of integer linear programming.
History
Minesweeper, along with its variants, is the most notable example of this type of puzzle.
Algebra with binary variables
Below the letters in the mathematical statements are used as variables where each can take the value either 0 or 1 only. A simple example of an equation with binary variables is given below:
a + b = 0
Here there are two variables a and b but one equation. The solution is constrained by the fact that a and b can take only values 0 or 1. There is only one solution here, both a = 0, and b = 0. Another simple example is given below:
a + b = 2
The solution is straightforward: a and b must be 1 to make a + b equal to 2.
Another interesting case is shown below:
a + b + c = 2
a + b ≤ 1
Here, the first statement is an equation and the second statement is an inequality indicating the three possible cases:
a = 1 and b = 0,
a = 0 and b = 1, and
a = 0 and b = 0,
The last case causes a contradiction on c by forcing c = 2, which is not possible. Therefore, either first or second case is correct. This leads to the fact that c must be 1.
The modification of a large equation into smaller form is not difficult. However, an equation set with binary variables cannot be always solved by applying linear algebra. The following is an example for applying the subtraction of two equations:
a + b + c + d = 3
c + d = 1
The first statement has four variables whereas the second statement has only two variables. The latter one means that the sum of c and d is 1. Using this fact on the first statement, the equations above can be reduced to
a + b = 2
c + d = 1
The algebra on a board
A game based on the algebra with binary variables can be visualized in many different ways. One generic way is to represent the right side of an equation as a clue in a cell (clue cell), and the neighbors of a clue cell as variables. A simple case is shown in Figure 1. The neighbors can be assumed to be the up/down, left/right, and corner cells that are sharing an edge or a corner. The white cells may contain a hidden object or nothing. In other words, t |
https://en.wikipedia.org/wiki/Stationary%20subspace%20analysis | Stationary Subspace Analysis (SSA) in statistics is a blind source separation algorithm which factorizes a multivariate time series into stationary and non-stationary components.
Introduction
In many settings, the measured time series contains contributions from various underlying sources that cannot be measured directly. For instance, in EEG analysis, the electrodes on the scalp record the activity of a large number of sources located inside the brain. These sources can be stationary or non-stationary, but they are not discernible in the electrode signals, which are a mixture of these sources. SSA allows the separation of the stationary from the non-stationary sources in an observed time series.
According to the SSA model, the observed multivariate time series is assumed to be generated as a linear superposition of stationary sources and non-stationary sources ,
where is an unknown but time-constant mixing matrix; and are the basis of the stationary and non-stationary subspace respectively.
Given samples from the time series , the aim of Stationary Subspace Analysis is to estimate the inverse mixing matrix separating the stationary from non-stationary sources in the mixture .
Identifiability of the solution
The true stationary sources are identifiable (up to a linear transformation) and the true non-stationary subspace is identifiable. The true non-stationary sources and the true stationary subspace cannot be identified, because arbitrary contributions from the stationary sources do not change the non-stationary nature of a non-stationary source.
Applications and extensions
Stationary subspace analysis has been successfully applied to Brain-computer interfacing, computer vision and temporal segmentation. There are variants of the SSA problem that can be solved analytically in closed form, without numerical optimization.
See also
Blind signal separation (BSS)
Factor analysis
Independent component analysis
Cointegration
References
Multivariate time series |
https://en.wikipedia.org/wiki/Egyptian%20algebra | In the history of mathematics, Egyptian algebra, as that term is used in this article, refers to algebra as it was developed and used in ancient Egypt. Ancient Egyptian mathematics as discussed here spans a time period ranging from 3000 BCE to 300 BCE.
There are limited surviving examples of ancient Egyptian algebraic problems. They appear in the Moscow Mathematical Papyrus (MMP) and in the Rhind Mathematical Papyrus (RMP), among others.
Fractions
Known mathematical texts show that scribes used (least) common multiples to turn problems with fractions into problems using integers. The multiplicative factors were often recorded in red ink and are referred to as Red auxiliary numbers.
Aha problems, linear equations and false position
Aha problems involve finding unknown quantities (referred to as Aha) if the sum of the quantity and part(s) of it are given. The Rhind Mathematical Papyrus also contains four of these type of problems. Problems 1, 19, and 25 of the Moscow Papyrus are Aha problems. Problem 19 asks one to calculate a quantity taken 1 and ½ times and added to 4 to make 10. In modern mathematical notation, this linear equation is represented:
Solving these Aha problems involves a technique called method of false position. The technique is also called the method of false assumption. The scribe would substitute an initial guess of the answer into the problem. The solution using the false assumption would be proportional to the actual answer, and the scribe would find the answer by using this ratio.
Pefsu problems
10 of the 25 problems of the practical problems contained in the Moscow Mathematical Papyrus are pefsu problems. A pefsu measures the strength of the beer made from a heqat of grain.
A higher pefsu number means weaker bread or beer. The pefsu number is mentioned in many offering lists. For example, problem 8 translates as:
(1) Example of calculating 100 loaves of bread of pefsu 20
(2) If someone says to you: “You have 100 loaves of bread of pefsu 20
(3) to be exchanged for beer of pefsu 4
(4) like 1/2 1/4 malt-date beer
(5) First calculate the grain required for the 100 loaves of the bread of pefsu 20
(6) The result is 5 heqat. Then reckon what you need for a des-jug of beer like the beer called 1/2 1/4 malt-date beer
(7) The result is 1/2 of the heqat measure needed for des-jug of beer made from Upper-Egyptian grain.
(8) Calculate 1/2 of 5 heqat, the result will be 2
(9) Take this 2 four times
(10) The result is 10. Then you say to him:
(11) Behold! The beer quantity is found to be correct.
Geometrical progressions
The use of the Horus eye fractions shows some (rudimentary) knowledge of geometrical progression. One unit was written as 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/64. But the last copy of 1/64 was written as 5 ro, thereby writing 1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + (5 ro). These fractions were further used to write fractions in terms of terms plus a remainder specified in terms of ro |
https://en.wikipedia.org/wiki/Regenerative%20process | In applied probability, a regenerative process is a class of stochastic process with the property that certain portions of the process can be treated as being statistically independent of each other. This property can be used in the derivation of theoretical properties of such processes.
History
Regenerative processes were first defined by Walter L. Smith in Proceedings of the Royal Society A in 1955.
Definition
A regenerative process is a stochastic process with time points at which, from a probabilistic point of view, the process restarts itself. These time point may themselves be determined by the evolution of the process. That is to say, the process {X(t), t ≥ 0} is a regenerative process if there exist time points 0 ≤ T0 < T1 < T2 < ... such that the post-Tk process {X(Tk + t) : t ≥ 0}
has the same distribution as the post-T0 process {X(T0 + t) : t ≥ 0}
is independent of the pre-Tk process {X(t) : 0 ≤ t < Tk}
for k ≥ 1. Intuitively this means a regenerative process can be split into i.i.d. cycles.
When T0 = 0, X(t) is called a nondelayed regenerative process. Else, the process is called a delayed regenerative process.
Examples
Renewal processes are regenerative processes, with T1 being the first renewal.
Alternating renewal processes, where a system alternates between an 'on' state and an 'off' state.
A recurrent Markov chain is a regenerative process, with T1 being the time of first recurrence. This includes Harris chains.
Reflected Brownian motion is a regenerative process (where one measures the time it takes particles to leave and come back).
Properties
By the renewal reward theorem, with probability 1,
where is the length of the first cycle and is the value over the first cycle.
A measurable function of a regenerative process is a regenerative process with the same regeneration time
References
Stochastic processes |
https://en.wikipedia.org/wiki/Half-disk%20topology | In mathematics, and particularly general topology, the half-disk topology is an example of a topology given to the set , given by all points in the plane such that . The set can be termed the closed upper half plane.
To give the set a topology means to say which subsets of are "open", and to do so in a way that the following axioms are met:
The union of open sets is an open set.
The finite intersection of open sets is an open set.
The set and the empty set are open sets.
Construction
We consider to consist of the open upper half plane , given by all points in the plane such that ; and the x-axis , given by all points in the plane such that . Clearly is given by the union . The open upper half plane has a topology given by the Euclidean metric topology. We extend the topology on to a topology on by adding some additional open sets. These extra sets are of the form , where is a point on the line and is a neighbourhood of in the plane, open with respect to the Euclidean metric (defining the disk radius).
See also
List of topologies
References
General topology
Topological spaces |
https://en.wikipedia.org/wiki/Bob%20Bryan%20career%20statistics | This is a list of the main career statistics of tennis player Bob Bryan.
Major finals
Grand Slam finals
Doubles: 30 (16–14)
By winning the 2006 Wimbledon title, Bryan completed the men's doubles Career Grand Slam. He became the 19th individual player and, with Mike Bryan, the 7th doubles pair to achieve this.
Mixed doubles: 9 (7–2)
Summer Olympics finals
Doubles: 1 (1–0)
ATP Masters 1000 finals
Doubles: 59 (39 titles, 20 Losses)
Performance timelines
Doubles
Mixed doubles
ATP Tour career earnings
See also
Bob and Mike Bryan
List of twins
Notes
References
Bryan, Bob |
https://en.wikipedia.org/wiki/Marilyn%20Tremaine | Marilyn Mantei Tremaine is an American computer scientist. She is an expert in human–computer interaction and considered a pioneer of the field.
Education
Tremaine received a BS in mathematics, physics and French from the University of Wisconsin, and later in 1982 obtained a PhD in communication theory at the University of Southern California - with the last two years of her PhD spent at Carnegie Mellon University under the direction of Professor Allen Newell.
Awards
Marilyn Tremaine received the ACM SIGCHI Lifetime Service Award in 2005, the Canadian Human Computer Communications Society 2010 Achievement Award, the Usability Professionals Association 2010 Lifetime Achievement Award. In 2022, Tremaine was elected into the ACM CHI Academy.
Professional career
Tremaine's academic career started as a lecturer and later assistant professor in the University of Michigan Business School, then in 1988 she became associate professor in the Computer Science Department of the University of Toronto, Canada, and a part of the Dynamic Graphics Project. In 1997, she returned to the US. She joined Drexel University as Professor of Computer and Information Systems. In 2001, she joined the New Jersey Institute of Technology where she was a professor and chair of the Information Systems Department. In 2008, she was a research professor at Rutgers University with joint appointments in the College of Communication and Information and the Department of Electrical and Computer Engineering. She is currently teaching as an adjunct professor at the University of Toronto.
Tremaine is a distinguished alumni of the University of Toronto Knowledge Media Design Institute. Tremaine has also been vice president of product development for three software startup companies and a senior research scientist at the EDS Center for Applied Research.
Tremaine co-founded ACM SIGCHI. She was the president of SIGCHI from 1999 to 2002, and served as SIGCHI's vice-president of communications, finance, and conference planning. Tremaine served on six editorial boards for journals and received two university teaching awards.
Tremaine is known for psychology studies of early interactive user interfaces, collaborative software, and for developing a framework for cost-justifying usability engineering. Other research interests include auditory and multimodal interface design, global software development, and the development of interfaces for the blind and visually impaired, people with Aphasia, or in rehabilitation following a stroke.
Tremaine has developed educational programs in HCI and related fields, such as the Master of Business and Science on User Experience Design at Rudgers University. In addition, she helped develop SIGCHI's Human-Computer Interaction curriculum resources.
Personal life
Marilyn Tremaine resides in Toronto, Canada, and is married to the astrophysicist Scott Tremaine.
Marilyn Tremaine enjoys cooking and catering formal dinners.
Bibliography
Mantei, M. a |
https://en.wikipedia.org/wiki/Partial%20group%20algebra | In mathematics, a partial group algebra is an associative algebra related to the partial representations of a group.
Examples
The partial group algebra is isomorphic to the direct sum:
See also
Group ring
Group representation
Notes
References
Algebras
Representation theory of groups |
https://en.wikipedia.org/wiki/Carlos%20Saa | Carlos Alfredo Saa Posso (born December 4, 1983) is a Colombian football defender, who currently plays for Millonarios in Categoría Primera A.
Statistics (Official games/Colombian Ligue and Colombian Cup)
(As of November 14, 2010)
References
External links
1983 births
Living people
Colombian men's footballers
América de Cali footballers
Deportivo Pasto footballers
Botafogo Futebol Clube (SP) players
Grêmio Esportivo Juventus players
Millonarios F.C. players
Colombian expatriate men's footballers
Expatriate men's footballers in Brazil
Men's association football defenders
Footballers from Valle del Cauca Department |
https://en.wikipedia.org/wiki/Cantellated%206-orthoplexes | In six-dimensional geometry, a cantellated 6-orthoplex is a convex uniform 6-polytope, being a cantellation of the regular 6-orthoplex.
There are 8 cantellation for the 6-orthoplex including truncations. Half of them are more easily constructed from the dual 5-cube
Cantellated 6-orthoplex
Alternate names
Cantellated hexacross
Small rhombated hexacontatetrapeton (acronym: srog) (Jonathan Bowers)
Construction
There are two Coxeter groups associated with the cantellated 6-orthoplex, one with the B6 or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D6 or [33,1,1] Coxeter group.
Coordinates
Cartesian coordinates for the 480 vertices of a cantellated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of
(2,1,1,0,0,0)
Images
Bicantellated 6-orthoplex
Alternate names
Bicantellated hexacross, bicantellated hexacontatetrapeton
Small birhombated hexacontatetrapeton (acronym: siborg) (Jonathan Bowers)
Construction
There are two Coxeter groups associated with the bicantellated 6-orthoplex, one with the B6 or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D6 or [33,1,1] Coxeter group.
Coordinates
Cartesian coordinates for the 1440 vertices of a bicantellated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of
(2,2,1,1,0,0)
Images
Cantitruncated 6-orthoplex
Alternate names
Cantitruncated hexacross, cantitruncated hexacontatetrapeton
Great rhombihexacontatetrapeton (acronym: grog) (Jonathan Bowers)
Construction
There are two Coxeter groups associated with the cantitruncated 6-orthoplex, one with the B6 or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D6 or [33,1,1] Coxeter group.
Coordinates
Cartesian coordinates for the 960 vertices of a cantitruncated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of
(3,2,1,0,0,0)
Images
Bicantitruncated 6-orthoplex
Alternate names
Bicantitruncated hexacross, bicantitruncated hexacontatetrapeton
Great birhombihexacontatetrapeton (acronym: gaborg) (Jonathan Bowers)
Construction
There are two Coxeter groups associated with the bicantitruncated 6-orthoplex, one with the B6 or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D6 or [33,1,1] Coxeter group.
Coordinates
Cartesian coordinates for the 2880 vertices of a bicantitruncated 6-orthoplex, centered at the origin, are all the sign and coordinate permutations of
(3,3,2,1,0,0)
Images
Related polytopes
These polytopes are part of a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) |
https://en.wikipedia.org/wiki/Koml%C3%B3s%E2%80%93Major%E2%80%93Tusn%C3%A1dy%20approximation | In probability theory, the Komlós–Major–Tusnády approximation (also known as the KMT approximation, the KMT embedding, or the Hungarian embedding) refers to one of the two strong embedding theorems: 1) approximation of random walk by a standard Brownian motion constructed on the same probability space, and 2) an approximation of the empirical process by a Brownian bridge constructed on the same probability space. It is named after Hungarian mathematicians János Komlós, Gábor Tusnády, and Péter Major, who proved it in 1975.
Theory
Let be independent uniform (0,1) random variables. Define a uniform empirical distribution function as
Define a uniform empirical process as
The Donsker theorem (1952) shows that converges in law to a Brownian bridge Komlós, Major and Tusnády established a sharp bound for the speed of this weak convergence.
Theorem (KMT, 1975) On a suitable probability space for independent uniform (0,1) r.v. the empirical process can be approximated by a sequence of Brownian bridges such that
for all positive integers n and all , where a, b, and c are positive constants.
Corollary
A corollary of that theorem is that for any real iid r.v. with cdf it is possible to construct a probability space where independent sequences of empirical processes and Gaussian processes exist such that
almost surely.
References
Komlos, J., Major, P. and Tusnady, G. (1975) An approximation of partial sums of independent rv’s and the sample df. I, Wahrsch verw Gebiete/Probability Theory and Related Fields, 32, 111–131.
Komlos, J., Major, P. and Tusnady, G. (1976) An approximation of partial sums of independent rv’s and the sample df. II, Wahrsch verw Gebiete/Probability Theory and Related Fields, 34, 33–58.
Empirical process |
https://en.wikipedia.org/wiki/Ylli%20Pango | Ylli Pango (born in, Tirana, Albania) is an Albanian psychologist, academic, writer, and politician.
Education
Pango completed studies in mathematics at the University of Tirana, and later completed a postgraduate in psychology at the same university. He later completed graduate studies in education administration at Boston University through the Fulbright Program in 1994–1995.
Career and Controversy
Pango became the Deputy Minister of Education for Albania from 1992–1994, as well as Vice president of Higher Commission of Scientific Qualification of Albania and Vice president of National Committee of UNICEF of Albania.
He then lectured at the University of Tirana from 1997–1999, also serving as Head of Leading Committee of Albanian State Radio Television. He became dean of the university's Faculty of Social Sciences from 1999–2005, as well as serving as Political Counselor to the Albanian president from 2002 onwards.
He served as the Elected Depute of District nr.38 Tirana, Member of the Albanian Parliament-Deputy Head of Media and Education Committee from 2005–2009, and in 2007 became the Minister of Tourism, Culture, Youth and Sports of Albania.
As of 2010 Pango is the General Executive Director of Albanian Agency of Research, Technology and Innovation.
Publications
Psychology of Child think, (1987)
Statistic methods on Psychology(1985)
Secrets of memory(1990)
America(1996)
Social Psychology(1998)
The ruin(1994)
Civic education –education for democracy
Prostitution- an open wound of Albanian society(2002)
Problems of organization and methodology of sociology and psychology research.
Psychology of school youngsters (Articles, studies, presentations).
Mid term Plan for education sector (Research director).(1993)
High education in Europe. 1994.(Coauthor and author of the chapter "High Education in Albania"). Publication of Council of Europe.(1992–1993)
Crime-Articles and Essays-2003 (130 pages)
Psychotherapy-A diagnostic and treatment Manual for Psychological Disorders (870 pages) (2004)
Scandal (2010)-Essays on Albanian moral. (2010) (120 pages)
Vip –Essays (2010) (170 pages)
Additionally, Pango has written about 500 editorials and studies on psychology, social work, sociology and education.
Prof. Dr. Ylli Pango - Official site - Faqe zyrtare
References
Government ministers of Albania
Tourism ministers of Albania
1952 births
Living people
University of Tirana alumni
Boston University School of Education alumni
Academic staff of the University of Tirana
Albanian psychologists |
https://en.wikipedia.org/wiki/Topological%20category | In category theory, a discipline in mathematics, the notion of topological category has a number of different, inequivalent definitions.
In one approach, a topological category is a category that is enriched over the category of compactly generated Hausdorff spaces. They can be used as a foundation for higher category theory, where they can play the role of (,1)-categories. An important example of a topological category in this sense is given by the category of CW complexes, where each set Hom(X,Y) of continuous maps from X to Y is equipped with the compact-open topology.
In another approach, a topological category is defined as a category along with a forgetful functor that maps to the category of sets and has the following three properties:
admits initial (also known as weak) structures with respect to
Constant functions in lift to -morphisms
Fibers are small (they are sets and not proper classes).
An example of a topological category in this sense is the category of all topological spaces with continuous maps, where one uses the standard forgetful functor.
See also
Infinity category
Simplicial category
References
Category theory |
https://en.wikipedia.org/wiki/Simplicially%20enriched%20category | In mathematics, a simplicially enriched category, is a category enriched over the category of simplicial sets. Simplicially enriched categories are often also called, more ambiguously, simplicial categories; the latter term however also applies to simplicial objects in Cat (the category of small categories). Simplicially enriched categories can, however, be identified with simplicial objects in Cat whose object part is constant, or more precisely, whose all face and degeneracy maps are bijective on objects. Simplicially enriched categories can model (∞, 1)-categories, but the dictionary has to be carefully built. Namely many notions, limits for example, are different from the limits in the sense of enriched category theory.
References
External links
Category theory |
https://en.wikipedia.org/wiki/Segal%20category | In mathematics, a Segal category is a model of an infinity category introduced by , based on work of Graeme Segal in 1974.
References
External links
Category theory |
https://en.wikipedia.org/wiki/John%20Ulloque | John Jairo Ulloque Pérez (born May 11, 1986) is a Colombian football midfield, who currently plays for Millonarios in Categoría Primera A.
Statistics (Official games/Colombian Ligue and Colombian Cup)
(As of November 14, 2010)
External links
1986 births
Living people
Colombian men's footballers
Atlético Bucaramanga footballers
Millonarios F.C. players
Men's association football midfielders
Sportspeople from Santander Department |
https://en.wikipedia.org/wiki/MPIR%20%28mathematics%20software%29 | Multiple Precision Integers and Rationals (MPIR) is an open-source software multiprecision integer library forked from the GNU Multiple Precision Arithmetic Library (GMP) project. It consists of much code from past GMP releases, and some original contributed code.
According to the MPIR-devel mailing list, "MPIR is no longer maintained", except for building the old code on Windows using new versions of Microsoft Visual Studio.
According to the MPIR developers, some of the main goals of the MPIR project were:
Maintaining compatibility with GMP – so that MPIR can be used as a replacement for GMP.
Providing build support for Linux, Mac OS, Solaris and Windows systems.
Supporting building MPIR using Microsoft based build tools for use in 32- and 64-bit versions of Windows.
MPIR is optimized for many processors (CPUs). Assembly language code exists for these : ARM, DEC Alpha 21064, 21164, and 21264, AMD K6, K6-2, Athlon, K8 and K10, Intel Pentium, Pentium Pro-II-III, Pentium 4, generic x86, Intel IA-64, Core 2, i7, Atom, Motorola-IBM PowerPC 32 and 64, MIPS R3000, R4000, SPARCv7, SuperSPARC, generic SPARCv8, UltraSPARC.
Language bindings
See also
Arbitrary-precision arithmetic, data type: bignum
GNU Multiple Precision Arithmetic Library
GNU Multiple Precision Floating-Point Reliably (MPFR)
Class Library for Numbers supporting GiNaC
References
External links
GMP — official site of GNU Multiple Precision Arithmetic Library
MPFR — official site of GNU Multiple Precision Floating-Point Reliably
C (programming language) libraries
Computer arithmetic
Computer arithmetic algorithms
Free software programmed in C
Numerical software |
https://en.wikipedia.org/wiki/Mana%20Nakao | is a Japanese football player who plays for AS Laranja Kyoto. His mother is Japanese and his father is Tanzanian.
Club statistics
References
External links
Sanfrecce profile
1983 births
Living people
Association football people from Kyoto Prefecture
Japanese men's footballers
Japanese people of Tanzanian descent
J1 League players
Sanfrecce Hiroshima players
Zweigen Kanazawa players
Men's association football defenders |
https://en.wikipedia.org/wiki/Simplicial%20category | In mathematics, simplicial category may refer to:
Simplex category, the category of finite ordinals and order-preserving functions
Simplicially enriched category, a category enriched over the category of simplicial sets
Simplicial object in the category of categories |
https://en.wikipedia.org/wiki/Dendroidal%20set | In mathematics, a dendroidal set is a generalization of simplicial sets introduced by .
They have the same relation to (colored symmetric) operads, also called symmetric multicategories, that simplicial sets have to categories.
Definition
A dendroidal set is a contravariant functor from Ω to sets, where Ω is the tree category consisting of finite rooted trees considered as operads, whose morphisms are operad morphisms. The trees are allowed to have some edges with a vertex on only one side; these are called outer edges, and the root is one of the outer edges.
References
Simplicial sets |
https://en.wikipedia.org/wiki/International%20Journal%20of%20Mathematics%20and%20Computer%20Science | The International Journal of Mathematics and Computer Science (online: , print: ) is a quarterly peer-reviewed scientific journal which was established in 2006 and publishes original papers in the broad subjects of mathematics and computer science. It is abstracted and indexed by Clarivate Analytics (Thomson Reuters previously), Scopus, Zentralblatt Math, and Mathematical Reviews. The editor-in-chief is Professor Badih Ghusayni.
External links
Mathematics journals
Academic journals established in 2006
English-language journals |
https://en.wikipedia.org/wiki/Ji%C5%99%C3%AD%20Jech | Jiří Jech (born December 22, 1975) is a Czech football referee. He was a full international for FIFA from 2007 to 2010, and served as a referee in 2010 World Cup qualifiers.
Career statistics
Statistics for Gambrinus liga matches only.
References
External links
Jiří Jech at WorldReferee.com
Jiří Jech at WorldFootball.net
1975 births
Living people
Czech football referees |
https://en.wikipedia.org/wiki/Segal%20space | In mathematics, a Segal space is a simplicial space satisfying some pullback conditions, making it look like a homotopical version of a category. More precisely, a simplicial set, considered as a simplicial discrete space, satisfies the Segal conditions iff it is the nerve of a category. The condition for Segal spaces is a homotopical version of this.
Complete Segal spaces were introduced by as models for (∞, 1)-categories.
References
External links
Category theory
Simplicial sets |
https://en.wikipedia.org/wiki/Simon%20B.%20Kochen | Simon Bernhard Kochen (; born 14 August 1934) is a Canadian mathematician, working in the fields of model theory, number theory and quantum mechanics.
Biography
Kochen received his Ph.D. (Ultrafiltered Products and Arithmetical Extensions) from Princeton University in 1958 under the direction of Alonzo Church. Since 1967 he has been a member of Princeton's Department of Mathematics. He chaired the department from 1989 to 1992 and became the Henry Burchard Fine Professor in mathematics in 1994. During 1966–1967 and 1978–1979, Kochen was at the Institute for Advanced Study.
In 1967 he was awarded, together with James Ax, the seventh Frank Nelson Cole Prize in Number Theory for a series of three joint papers on Diophantine problems involving p-adic techniques. Kochen and Ax also co-authored the Ax–Kochen theorem, an application of model theory to algebra.
In 1967 Kochen and Ernst Specker proved the Kochen–Specker theorem in quantum mechanics and quantum contextuality. In 2004 Kochen and John Horton Conway proved the free will theorem. The theorem states that if we have a certain amount of free will, then, subject to certain assumptions, so must some elementary particles.
See also
Borel–Cantelli lemma
References
External links
Living people
Model theorists
1934 births
Scientists from Antwerp
Institute for Advanced Study visiting scholars |
https://en.wikipedia.org/wiki/Mihail%20Zervos | Mihail Zervos is a Greek financial mathematician. He is Professor of Financial Mathematics at the London School of Economics.
Curriculum
Zervos received his MSc and PhD degrees from Imperial College London in 1995. After completing his PhD, he was a lecturer at the Department of Statistics, University of Newcastle, where he stayed until 2000. He then joined King's College London, initially as a lecturer and then as a reader in the Department of Mathematics. In 2006 he was appointed to the Chair in Financial Mathematics at the London School of Economics where he was tasked with founding a new Research Group in Financial Mathematics within the Departement of Mathematics.
References
D. Brody, J. Syroka and M. Zervos: "Dynamical pricing of weather derivatives". Quantitative Finance 2 (2002), 189–198.
K. Duckworth, M. Zervos: "A model for investment decisions with switching costs", Annals of Applied Probability, vol.11, 1, 2001, pp. 239–260
Davis, M. H. A. and Zervos, M. (1994) "A problem of singular stochastic control with discretionary stopping". Annals of Applied Probability 4, 226–240.
External links
Professor Zervos
Prof Mihail Zervos on ATACD
Appointment of New Chair in Financial Maths (September 2006)
Academics of the London School of Economics
Greek mathematicians
Greek engineers
National Technical University of Athens alumni
Living people
Greek emigrants to the United Kingdom
Academics of King's College London
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Ph%E1%BA%A1m%20Minh%20Ho%C3%A0ng | Phạm Minh Hoàng (born 1955) is a French-Vietnamese blogger and lecturer in applied mathematics at the Ho Chi Minh City University of Technology, who was arrested in Vietnam for his political writing and activism on August 13, 2010. Phạm Minh Hoàng, who writes with the pen name Phan Kien Quoc, was convicted on August 10, 2011 for writing “33 articles that distort the policies and guidelines of the Party and the State.” He was sentenced to three years in jail and three years of probation under Article 79, “subversion of administration”—one of many penal codes defined vaguely and used to detain and arrest political activists but served only 17 months and spend another three years under house arrest. Phạm Minh Hoàng was based in Ho Chi Minh City, Vietnam where he used to lecture at the university and offered free classes for Vietnamese youth on leadership skills. In June 2017, he published a call for help on his Facebook page upon receiving the news that he is likely to lose his Vietnamese citizenship and be deported to France. Hoang was detained by local authorities on June 23 before being forcibly exiled to France the following day.
Background
Phạm Minh Hoàng was born on August 8, 1955 in Vung Tau, what is now Ba Ria-Vung Tau Province. In 1973, Hoàng left to study in France. Hoàng lived, studied, and worked in France for 28 years, during which time he officially joined the political party, Viet Tan. Hoang returned to Vietnam in 2000, and worked as a lecturer at the Ho Chi Minh City Polytechnic University. Before his arrest on August 13, 2010, Hoàng wrote articles about political and social issues in Vietnam, which were published on his blog under pseudonym Phan Kien Quoc. To empower young Vietnamese to become leaders and serve the community, Hoàng also started teaching free classes on leadership skills. Hoàng's political articles and leadership classes were the basis for his arrest in 2010.
2010 Arrest
When Phạm Minh Hoàng as arrested on August 13, 2010, he was detained in secret and unlawfully. His arrest was unconfirmed by Vietnamese authorities until September 9, 2010, when Viet Tan published the details online. At the time, Hoàng was 55 years old and lecturing at the Ho Chi Minh City Polytechnic Institute. According to Hoàng's lawyer, Tran Vu Hai, Hoàng admitted to writing the essays, but did not believe he committed any crime against the state.
Revocation of Vietnamese citizenship and forced exile
On June 1, 2017, the French Consulate in Ho Chi Minh City invited Hoàng to inform him of the Vietnamese government's decision to revoke his Vietnamese citizenship on May 17, 2017. Phạm Minh Hoàng stated he would be separated from his wife due to his family's situation if he were to be deported. Hoàng received the official letter from authorities on June 10, 2017 on the decision to revoke his Vietnamese citizenship which was signed by the President of Vietnam Trần Đại Quang. Reporters Without Borders said this was the first incident Hanoi has st |
https://en.wikipedia.org/wiki/Matilde%20Marcolli | Matilde Marcolli is an Italian and American mathematical physicist. She has conducted research work in areas of mathematics and theoretical physics; obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft, and the Sofia Kovalevskaya Award of the Alexander von Humboldt Foundation. Marcolli has authored and edited numerous books in the field. She is currently the Robert F. Christy Professor of Mathematics and Computing and Mathematical Sciences at the California Institute of Technology.
Career
Marcolli obtained her Laurea in Physics in 1993 summa cum laude from the University of Milan under the supervision of Renzo Piccinini, with a thesis on Classes of self equivalences of fibre bundles. She moved to the USA in 1994, where she obtained a master's degree (1994) and a PhD (1997) in Mathematics from the University of Chicago, under the supervision of Melvin Rothenberg, with a thesis on Three dimensional aspects of Seiberg-Witten Gauge Theory. Between 1997 and 2000 she worked at the Massachusetts Institute of Technology (MIT) as a C.L.E. Moore instructor in the Department of Mathematics.
Between 2000 and 2010 she held a C3 position (German equivalent of associate professor) at the Max Planck Institute for Mathematics in Bonn and held an associate professor position (courtesy) at Florida State University in Tallahassee. She also held an honorary professorship at the University of Bonn. From 2008 to 2017 she was a full professor of Mathematics in the Division of Physics, Mathematics and Astronomy of the California Institute of Technology. Between 2018 and 2020 she was a professor in the mathematics department of the University of Toronto and a member of the Perimeter Institute. She is currently the Robert F. Christy Professor of Mathematics and Computing and Mathematical Sciences at the California Institute of Technology.
She held visiting positions at the Tata Institute of Fundamental Research in Mumbai, the Kavli Institute for Theoretical Physics in Santa Barbara, the Mittag-Leffler Institute in Stockholm, the Isaac Newton Institute in Cambridge, and the Mathematical Sciences Research Institute in Berkeley, California.
Research
Marcolli's research work has covered different areas of mathematics and theoretical physics: gauge theory and low-dimensional topology, algebraic-geometric structures in quantum field theory, noncommutative geometry with applications to number theory and to physics models, especially related to particle physics, quantum gravity and cosmology, and to the quantum Hall effect.
She also worked in linguistics.
She has collaborated with several other mathematicians, physicists, and linguists, among them Yuri I. Manin, Alain Connes, Michael Atiyah, Roger Penrose, Noam Chomsky.
Twenty six graduate students obtained their PhD under her supervision between 2006 and 2022.
Honors and awards
In 2001 she obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft (DFG) and in 2002 th |
https://en.wikipedia.org/wiki/Yoon%20Soung-min | Yoon Soung-Min (born May 22, 1985 in South Korea) is a South Korean former footballer who plays as a midfielder.
Career statistics
References
External links
Profile at Liga Indonesia Official Site
South Korean men's footballers
South Korean expatriate men's footballers
South Korean expatriate sportspeople in Indonesia
Living people
Expatriate men's footballers in Azerbaijan
Expatriate men's footballers in Indonesia
1985 births
Azerbaijan Premier League players
Liga 1 (Indonesia) players
FK Genclerbirliyi Sumqayit players
Persijap Jepara players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Frobenius%20manifold | In the mathematical field of differential geometry, a Frobenius manifold, introduced by Dubrovin, is a flat Riemannian manifold with a certain compatible multiplicative structure on the tangent space. The concept generalizes the notion of Frobenius algebra to tangent bundles.
Frobenius manifolds occur naturally in the subject of symplectic topology, more specifically quantum cohomology. The broadest definition is in the category of Riemannian supermanifolds. We will limit the discussion here to smooth (real) manifolds. A restriction to complex manifolds is also possible.
Definition
Let M be a smooth manifold. An affine flat structure on M is a sheaf Tf of vector spaces that pointwisely span TM the tangent bundle and the tangent bracket of pairs of its sections vanishes.
As a local example consider the coordinate vectorfields over a chart of M. A manifold admits an affine flat structure if one can glue together such vectorfields for a covering family of charts.
Let further be given a Riemannian metric g on M. It is compatible to the flat structure if g(X, Y) is locally constant for all flat vector fields X and Y.
A Riemannian manifold admits a compatible affine flat structure if and only if its curvature tensor vanishes everywhere.
A family of commutative products * on TM is equivalent to a section A of S2(T*M) ⊗ TM via
We require in addition the property
Therefore, the composition g#∘A is a symmetric 3-tensor.
This implies in particular that a linear Frobenius manifold (M, g, *) with constant product is a Frobenius algebra M.
Given (g, Tf, A), a local potential Φ is a local smooth function such that
for all flat vector fields X, Y, and Z.
A Frobenius manifold (M, g, *) is now a flat Riemannian manifold (M, g) with symmetric 3-tensor A that admits everywhere a local potential and is associative.
Elementary properties
The associativity of the product * is equivalent to the following quadratic PDE in the local potential Φ
where Einstein's sum convention is implied, Φ,a denotes the partial derivative of the function Φ by the coordinate vectorfield ∂/∂xa which are all assumed to be flat. gef are the coefficients of the inverse of the metric.
The equation is therefore called associativity equation or Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equation.
Examples
Beside Frobenius algebras, examples arise from quantum cohomology. Namely, given a semipositive symplectic manifold (M, ω) then there exists an open neighborhood U of 0 in its even quantum cohomology QHeven(M, ω) with Novikov ring over C such that the big quantum product *a for a in U is analytic. Now U together with the intersection form g = <·,·> is a (complex) Frobenius manifold.
The second large class of examples of Frobenius manifolds come from the singularity theory. Namely, the space of miniversal deformations of an isolated singularity has a Frobenius manifold structure. This Frobenius manifold structure also relates to Kyoji Saito's primitive forms.
Referen |
https://en.wikipedia.org/wiki/Laplace%20functional | In probability theory, a Laplace functional refers to one of two possible mathematical functions of functions or, more precisely, functionals that serve as mathematical tools for studying either point processes or concentration of measure properties of metric spaces. One type of Laplace functional, also known as a characteristic functional is defined in relation to a point process, which can be interpreted as random counting measures, and has applications in characterizing and deriving results on point processes. Its definition is analogous to a characteristic function for a random variable.
The other Laplace functional is for probability spaces equipped with metrics and is used to study the concentration of measure properties of the space.
Definition for point processes
For a general point process defined on , the Laplace functional is defined as:
where is any measurable non-negative function on and
where the notation interprets the point process as a random counting measure; see Point process notation.
Applications
The Laplace functional characterizes a point process, and if it is known for a point process, it can be used to prove various results.
Definition for probability measures
For some metric probability space (X, d, μ), where (X, d) is a metric space and μ is a probability measure on the Borel sets of (X, d), the Laplace functional:
The Laplace functional maps from the positive real line to the positive (extended) real line, or in mathematical notation:
Applications
The Laplace functional of (X, d, μ) can be used to bound the concentration function of (X, d, μ), which is defined for r > 0 by
where
The Laplace functional of (X, d, μ) then gives leads to the upper bound:
Notes
References
Point processes
Metric geometry |
https://en.wikipedia.org/wiki/Newton%27s%20theorem%20about%20ovals | In mathematics, Newton's theorem about ovals states that the area cut off by a secant of a smooth convex oval is not an algebraic function of the secant.
Isaac Newton stated it as lemma 28 of section VI of book 1 of Newton's Principia, and used it to show that the position of a planet moving in an orbit is not an algebraic function of time. There has been some controversy about whether or not this theorem is correct because Newton did not state exactly what he meant by an oval, and for some interpretations of the word oval the theorem is correct, while for others it is false. If "oval" means merely a continuous closed convex curve, then there are counterexamples, such as triangles or one of the lobes of Huygens lemniscate y2 = x2 − x4, while pointed that if "oval" an infinitely differentiable convex curve then Newton's claim is correct and his argument has the essential steps of a rigorous proof.
generalized Newton's theorem to higher dimensions.
Statement
An English translation Newton's original statement is:
"There is no oval figure whose area, cut off by right lines at pleasure, can be universally found by means of equations of any number of finite terms and dimensions."
In modern mathematical language, Newton essentially proved the following theorem:
There is no convex smooth (meaning infinitely differentiable) curve such that the area cut off by a line ax + by = c is an algebraic function of a, b, and c.
In other words, "oval" in Newton's statement should mean "convex smooth curve". The infinite differentiability at all points is necessary: For any positive integer n there are algebraic curves that are smooth at all but one point and differentiable n times at the remaining point for which the area cut off by a secant is algebraic.
Newton observed that a similar argument shows that the arclength of a (smooth convex) oval between two points is not given by an algebraic function of the points.
Newton's proof
Newton took the origin P inside the oval, and considered the spiral of points (r, θ) in polar coordinates whose distance r from P is the area cut off by the lines from P with angles 0 and θ. He then observed that this spiral cannot be algebraic as it has an infinite number of intersections with a line through P, so the area cut off by a secant cannot be an algebraic function of the secant.
This proof requires that the oval and therefore the spiral be smooth; otherwise the spiral might be an infinite union of pieces of different algebraic curves. This is what happens in the various "counterexamples" to Newton's theorem for non-smooth ovals.
References
Alternative translation of earlier (2nd) edition of Newton's Principia.
Theorems about curves
Isaac Newton
Theorems in plane geometry |
https://en.wikipedia.org/wiki/List%20of%20VFL%20debuts%20in%201944 | This is a listing of Australian rules footballers who made their senior debut for a Victorian Football League (VFL) club in 1944.
Debuts
References
Australian rules football records and statistics
Australian rules football-related lists
1944 in Australian rules football |
https://en.wikipedia.org/wiki/The%20Fractal%20Geometry%20of%20Nature | The Fractal Geometry of Nature is a 1982 book by the Franco-American mathematician Benoît Mandelbrot.
Overview
The Fractal Geometry of Nature is a revised and enlarged version of his 1977 book entitled Fractals: Form, Chance and Dimension, which in turn was a revised, enlarged, and translated version of his 1975 French book, Les Objets Fractals: Forme, Hasard et Dimension. American Scientist put the book in its one hundred books of 20th century science.
As technology has improved, mathematically accurate, computer-drawn fractals have become more detailed. Early drawings were low-resolution black and white; later drawings were higher resolution and in color. Many examples were created by programmers working with Mandelbrot, primarily at IBM Research. These visualizations have added to persuasiveness of the books and their impact on the scientific community.
See also
Chaos theory
References
1982 non-fiction books
Mathematics books
Fractals |
https://en.wikipedia.org/wiki/Uniform%20limit%20theorem | In mathematics, the uniform limit theorem states that the uniform limit of any sequence of continuous functions is continuous.
Statement
More precisely, let X be a topological space, let Y be a metric space, and let ƒn : X → Y be a sequence of functions converging uniformly to a function ƒ : X → Y. According to the uniform limit theorem, if each of the functions ƒn is continuous, then the limit ƒ must be continuous as well.
This theorem does not hold if uniform convergence is replaced by pointwise convergence. For example, let ƒn : [0, 1] → R be the sequence of functions ƒn(x) = xn. Then each function ƒn is continuous, but the sequence converges pointwise to the discontinuous function ƒ that is zero on [0, 1) but has ƒ(1) = 1. Another example is shown in the adjacent image.
In terms of function spaces, the uniform limit theorem says that the space C(X, Y) of all continuous functions from a topological space X to a metric space Y is a closed subset of YX under the uniform metric. In the case where Y is complete, it follows that C(X, Y) is itself a complete metric space. In particular, if Y is a Banach space, then C(X, Y) is itself a Banach space under the uniform norm.
The uniform limit theorem also holds if continuity is replaced by uniform continuity. That is, if X and Y are metric spaces and ƒn : X → Y is a sequence of uniformly continuous functions converging uniformly to a function ƒ, then ƒ must be uniformly continuous.
Proof
In order to prove the continuity of f, we have to show that for every ε > 0, there exists a neighbourhood U of any point x of X such that:
Consider an arbitrary ε > 0. Since the sequence of functions (fn) converges uniformly to f by hypothesis, there exists a natural number N such that:
Moreover, since fN is continuous on X by hypothesis, for every x there exists a neighbourhood U such that:
In the final step, we apply the triangle inequality in the following way:
Hence, we have shown that the first inequality in the proof holds, so by definition f is continuous everywhere on X.
Uniform limit theorem in complex analysis
There are also variants of the uniform limit theorem that are used in complex analysis, albeit with modified assumptions.
Theorem.
Let be an open and connected subset of the complex numbers. Suppose that is a sequence of holomorphic functions that converges uniformly to a function on every compact subset of . Then is holomorphic in , and moreover, the sequence of derivatives converges uniformly to on every compact subset of .
Theorem.
Let be an open and connected subset of the complex numbers. Suppose that is a sequence of univalent functions that converges uniformly to a function . Then is holomorphic, and moreover, is either univalent or constant in .
Notes
References
E. M. Stein, R. Shakarachi (2003). Complex Analysis (Princeton Lectures in Analysis, No. 2), Princeton University Press, pp.53-54.
E. C. Titchmarsh (1939). The Theory of Functions, 2002 Reprint, Ox |
https://en.wikipedia.org/wiki/Artists%20View%20Park%20West%2C%20Alberta | Artists View Park West is an unincorporated community in Alberta, Canada within Rocky View County that is recognized as a designated place by Statistics Canada. It is located on the north side of Highway 563 (Old Banff Coach Road), south of Highway 1. It is adjacent to the City of Calgary to the northeast.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Artists View Park West had a population of 205 living in 72 of its 73 total private dwellings, a change of from its 2016 population of 219. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Artists View Park West had a population of 98 living in 32 of its 32 total private dwellings, a change of from its 2011 population of 77. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Rocky View County |
https://en.wikipedia.org/wiki/Shapley%E2%80%93Folkman%20lemma | The Shapley–Folkman lemma is a result in convex geometry that describes the Minkowski addition of sets in a vector space. It is named after mathematicians Lloyd Shapley and Jon Folkman, but was first published by the economist Ross M. Starr.
The lemma may be intuitively understood as saying that, if the number of summed sets exceeds the dimension of the vector space, then their Minkowski sum is approximately convex.
Related results provide more refined statements about how close the approximation is. For example, the Shapley–Folkman theorem provides an upper bound on the distance between any point in the Minkowski sum and its convex hull. This upper bound is sharpened by the Shapley–Folkman–Starr theorem (alternatively, Starr's corollary).
The Shapley–Folkman lemma has applications in economics, optimization and probability theory. In economics, it can be used to extend results proved for convex preferences to non-convex preferences. In optimization theory, it can be used to explain the successful solution of minimization problems that are sums of many functions. In probability, it can be used to prove a law of large numbers for random sets.
Introductory example
A set is convex if every line segment joining two of its points is a subset in the set: For example, the solid disk is a convex set but the circle is not, because the line segment joining two distinct points is not a subset of the circle.
The convex hull of a set Q is the smallest convex set that contains Q. This distance is zero if and only if the sum is convex.
Minkowski addition is the addition of the set members. For example, adding the set consisting of the integers zero and one to itself yields the set consisting of zero, one, and two:
The subset of the integers {0, 1, 2} is contained in the interval of real numbers [0, 2], which is convex. The Shapley–Folkman lemma implies that every point in [0, 2] is the sum of an integer from {0, 1} and a real number from [0, 1].
The distance between the convex interval [0, 2] and the non-convex set {0, 1, 2} equals one-half
1/2 = |1 − 1/2| = |0 − 1/2| = |2 − 3/2| = |1 − 3/2|.
However, the distance between the average Minkowski sum
1/2 ( {0, 1} + {0, 1} ) = {0, 1/2, 1}
and its convex hull [0, 1] is only 1/4, which is half the distance (1/2) between its summand {0, 1} and [0, 1]. As more sets are added together, the average of their sum "fills out" its convex hull: The maximum distance between the average and its convex hull approaches zero as the average includes more summands.
Preliminaries
The Shapley–Folkman lemma depends upon the following definitions and results from convex geometry.
Real vector spaces
A real vector space of two dimensions can be given a Cartesian coordinate system in which every point is identified by an ordered pair of real numbers, called "coordinates", which are conventionally denoted by x and y. Two points in the Cartesian plane can be added coordinate-wise
(x1, y1) + (x2, y2) = (x1+x2, y1+y2);
further |
https://en.wikipedia.org/wiki/Hawk%20Hills%2C%20Alberta%20%28designated%20place%29 | Hawk Hills is an unincorporated community in Alberta, Canada within Red Deer County that is recognized as a designated place by Statistics Canada. It is located on the east side of Range Road 270, north of Highway 11. Prior to the 2021 census, Statistics Canada referred to Hawk Hills as Balmoral NW.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Hawk Hills had a population of 52 living in 13 of its 13 total private dwellings, a change of from its 2016 population of 42. With a land area of , it had a population density of in 2021.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Red Deer County |
https://en.wikipedia.org/wiki/Balmoral%20Heights%2C%20Alberta | Balmoral Heights is an unincorporated community in Alberta, Canada within Red Deer County that is recognized as a designated place by Statistics Canada. It is located on the north side of Highway 11, east of Red Deer. It is adjacent to the designated place of Herder to the southwest. Prior to the 2021 census, Statistics Canada referred to Balmoral Heights as Balmoral SE.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Balmoral Heights had a population of 196 living in 66 of its 68 total private dwellings, a change of from its 2016 population of 193. With a land area of , it had a population density of in 2021.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Red Deer County |
https://en.wikipedia.org/wiki/Birch%20Hill%20Park%2C%20Alberta | Birch Hill Park is an unincorporated community in Alberta, Canada within Parkland County that is recognized as a designated place by Statistics Canada. It is located on the west side of Range Road 262, south of Highway 627. It is adjacent to the designated place of Sunset View Acres to the north.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Birch Hill Park had a population of 112 living in 39 of its 40 total private dwellings, a change of from its 2016 population of 107. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Birch Hill Park had a population of 107 living in 39 of its 39 total private dwellings, a change of from its 2011 population of 115. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Parkland County |
https://en.wikipedia.org/wiki/Bone%20Town%2C%20Alberta | Bone Town is an unincorporated community in Alberta, Canada within Lac La Biche County that is recognized as a designated place by Statistics Canada. It is located on the east side of Highway 36, south of Lac La Biche.
Demographics
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Bone Town recorded a population of 58 living in 21 of its 25 total private dwellings, a change of from its 2011 population of 88. With a land area of , it had a population density of in 2016.
As a designated place in the 2011 Census, Bone Town had a population of 88 living in 27 of its 34 total dwellings, a 31.3% change from its 2006 population of 67. With a land area of , it had a population density of in 2011.
See also
List of communities in Alberta
References
Former designated places in Alberta
Localities in Lac La Biche County |
https://en.wikipedia.org/wiki/Braim%2C%20Alberta | Braim is an unincorporated community in Alberta, Canada within Camrose County that is recognized as a designated place by Statistics Canada. It is located on the east side of Highway 833, north of Highway 13. It is adjacent to the City of Camrose to the south and the Camrose Airport to the east.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Braim had a population of 85 living in 32 of its 33 total private dwellings, a change of from its 2016 population of 93. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Braim had a population of 78 living in 31 of its 32 total private dwellings, a change of from its 2011 population of 84. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Camrose County |
https://en.wikipedia.org/wiki/Bristol%20Oakes%2C%20Alberta | Bristol Oakes is an unincorporated community in Alberta, Canada within Sturgeon County that is recognized as a designated place by Statistics Canada. It is located on the east side of Range Road 251 (Starkey Road), south of Highway 37. It is adjacent to the designated places of Lower Manor Estates to the east, Upper and Lower Viscount Estates to the south, and Upper Manor Estates to the northwest.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Bristol Oakes had a population of 240 living in 82 of its 83 total private dwellings, a change of from its 2016 population of 242. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Bristol Oakes had a population of 242 living in 76 of its 77 total private dwellings, a change of from its 2011 population of 292. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta |
https://en.wikipedia.org/wiki/Canyon%20Heights%2C%20Alberta | Canyon Heights is an unincorporated community in Alberta, Canada within Red Deer County that is recognized as a designated place by Statistics Canada. It is located on the north side of Township Road 384, north of Highway 11.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Canyon Heights had a population of 33 living in 15 of its 15 total private dwellings, a change of from its 2016 population of 93. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Canyon Heights had a population of 93 living in 31 of its 32 total private dwellings, a change of from its 2011 population of 92. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Red Deer County |
https://en.wikipedia.org/wiki/Central%20Park%2C%20Alberta | Central Park is an unincorporated community in Alberta, Canada within Red Deer County that is recognized as a designated place by Statistics Canada. It is located on the south side of Township Road 391, west of Highway 2A.
Demographics
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Central Park recorded a population of 80 living in 27 of its 28 total private dwellings, a change of from its 2011 population of 79. With a land area of , it had a population density of in 2016.
As a designated place in the 2011 Census, Central Park had a population of 79 living in 28 of its 28 total dwellings, a -7.1% change from its 2006 population of 85. With a land area of , it had a population density of in 2011.
See also
List of communities in Alberta
References
Former designated places in Alberta
Localities in Red Deer County |
https://en.wikipedia.org/wiki/Clearwater%20Estates%2C%20Alberta | Clearwater Estates is an unincorporated community in Alberta, Canada within Parkland County that is recognized as a designated place by Statistics Canada. It is located on the west side of Range Road 264, south of Highway 16.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Clearwater Estates had a population of 41 living in 17 of its 18 total private dwellings, a change of from its 2016 population of 76. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Clearwater Estates had a population of 76 living in 31 of its 33 total private dwellings, a change of from its 2011 population of 69. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Parkland County |
https://en.wikipedia.org/wiki/Crystal%20Meadows%2C%20Alberta | Crystal Meadows is an unincorporated community in Alberta, Canada within Parkland County that is recognized as a designated place by Statistics Canada. It is located on the east side of Range Road 21, south of Highway 16.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Crystal Meadows had a population of 123 living in 43 of its 45 total private dwellings, a change of from its 2016 population of 121. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Crystal Meadows had a population of 121 living in 43 of its 44 total private dwellings, a change of from its 2011 population of 127. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Parkland County |
https://en.wikipedia.org/wiki/Dawn%20Valley%2C%20Alberta | Dawn Valley is an unincorporated community in Alberta, Canada within Parkland County that is recognized as a designated place by Statistics Canada. It is located on the south side of Township Road 540, west of Highway 779.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Dawn Valley had a population of 173 living in 57 of its 58 total private dwellings, a change of from its 2016 population of 185. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Dawn Valley had a population of 185 living in 58 of its 58 total private dwellings, a change of from its 2011 population of 202. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Parkland County |
https://en.wikipedia.org/wiki/Devonshire%20Meadows%2C%20Alberta | Devonshire Meadows is an unincorporated community in Alberta, Canada within Parkland County that is recognized as a designated place by Statistics Canada. It is located on the north side of Township Road 511, west of Highway 60.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Devonshire Meadows had a population of 137 living in 52 of its 52 total private dwellings, a change of from its 2016 population of 136. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Devonshire Meadows had a population of 136 living in 48 of its 50 total private dwellings, a change of from its 2011 population of 147. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Parkland County |
https://en.wikipedia.org/wiki/Eastview%20Acres%2C%20Alberta | Eastview Acres is an unincorporated community in Alberta, Canada within the Lethbridge County that is recognized as a designated place by Statistics Canada. It is located on the east side of Highway 3, east of Highway 23.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Eastview Acres had a population of 45 living in 15 of its 15 total private dwellings, a change of from its 2016 population of 38. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Eastview Acres had a population of 38 living in 14 of its 14 total private dwellings, a change of from its 2011 population of 15. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Lethbridge County |
https://en.wikipedia.org/wiki/Erin%20Estates%2C%20Alberta | Erin Estates is an unincorporated community in Alberta, Canada within Parkland County that is recognized as a designated place by Statistics Canada. It is located on the west side of Range Road 274, south of Highway 633. It is adjacent to the designated place of Panorama Heights to the south.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Erin Estates had a population of 75 living in 27 of its 28 total private dwellings, a change of from its 2016 population of 122. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Erin Estates had a population of 44 living in 15 of its 17 total private dwellings, a change of from its 2011 population of 78. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Parkland County |
https://en.wikipedia.org/wiki/Ferrier%2C%20Alberta | Ferrier, or Ferrier Acres is an unincorporated community in Alberta, Canada within Clearwater County that is recognized as a designated place by Statistics Canada. It is located on the south side of Township Road 393A, west of Highway 11A.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Ferrier Acres Trailer Court had a population of 258 living in 103 of its 112 total private dwellings, a change of from its 2016 population of 421. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Ferrier Acres Trailer Court had a population of 395 living in 149 of its 153 total private dwellings, a change of from its 2011 population of 239. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Clearwater County, Alberta
Populated places on the North Saskatchewan River |
https://en.wikipedia.org/wiki/Fleming%20Park%2C%20Alberta | Fleming Park is an unincorporated community in Alberta, Canada within Parkland County that is recognized as a designated place by Statistics Canada. It is located on the west side of Range Road 261, south of Highway 627.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Fleming Park had a population of 103 living in 39 of its 39 total private dwellings, a change of from its 2016 population of 110. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Fleming Park had a population of 110 living in 39 of its 39 total private dwellings, a change of from its 2011 population of 121. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
References
Designated places in Alberta
Localities in Parkland County |
https://en.wikipedia.org/wiki/Flyingshot%20Lake%2C%20Alberta | Flyingshot Lake, or Flyingshot Lake Settlement, is an unincorporated community in Alberta, Canada within the County of Grande Prairie No. 1 that is recognized as a designated place by Statistics Canada. It is located approximately west of Highway 40, and south of Highway 43. It surrounds a lake of the same name, and is adjacent to the City of Grande Prairie to the northeast.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Flyingshot Lake had a population of 237 living in 88 of its 106 total private dwellings, a change of from its 2016 population of 269. With a land area of , it had a population density of in 2021.
As a designated place in the 2016 Census of Population conducted by Statistics Canada, Flyingshot Lake had a population of 269 living in 96 of its 96 total private dwellings, a change of from its 2011 population of 263. With a land area of , it had a population density of in 2016.
See also
List of communities in Alberta
List of designated places in Alberta
List of settlements in Alberta
References
Designated places in Alberta
Localities in the County of Grande Prairie No. 1
Settlements in Alberta |
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