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https://en.wikipedia.org/wiki/William%20B.%20Johnson | William B. Johnson may refer to:
William B. Johnson (mathematician) (born 1944), functional analyst and professor of mathematics at Ohio State University
William Brooks Johnson (1763–1830), English physician and botanist
William B. Johnson, president of the Illinois Central Railroad 1969–1972
William Bullein Johnson (1782–1862), president of the Southern Baptist Convention, 1845–1851
See also
William Johnson (disambiguation) |
https://en.wikipedia.org/wiki/Oka%20coherence%20theorem | In mathematics, the Oka coherence theorem, proved by , states that the sheaf of germs of holomorphic functions on over a complex manifold is coherent.
See also
Cartan's theorems A and B
Several complex variables
GAGA
Oka–Weil theorem
Weierstrass preparation theorem
Note
References
Theorems in complex analysis
Theorems in complex geometry |
https://en.wikipedia.org/wiki/Ryosuke%20Tone | is a Japanese football player currently playing for Oita Trinita.
Club statistics
Updated to 25 February 2019.
References
External links
Profile at Oita Trinita
Profile at Giravanz Kitakyushu
1991 births
Living people
Association football people from Fukuoka Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Oita Trinita players
Tokyo Verdy players
Nagoya Grampus players
V-Varen Nagasaki players
Giravanz Kitakyushu players
Men's association football defenders |
https://en.wikipedia.org/wiki/List%20of%20Parma%20Calcio%201913%20records%20and%20statistics | This list encompasses the major honours won by and records set by Parma Calcio 1913, their managers and their players, an Italian professional football club currently playing in Serie A and based in Parma, Emilia-Romagna. The player records section includes details of the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Parma players on the international stage, and the highest transfer fees paid and received by the club and details Parma's achievements in major competitions. Although Parma have never won a domestic league title, they have won three Italian Cups, one Supercoppa Italiana, as well as two UEFA Cups, one European Super Cup and one UEFA Cup Winners' Cup. The club won all eight of these trophies between 1992 and 2002, a period in which it is also achieved its best ever league finish as runners-up in the 1996–97 season.
Statistics accurate as of 28 May 2018
Honours
Parma have won eight major titles in their history, with all eight coming in the space of ten years between 1992 and 2002. The only two major honours that Parma are yet to win are the Serie A title and the UEFA Champions League, the most prestigious domestic and continental competitions, respectively. Perhaps reflecting this, Parma are one of just four clubs worldwide who have won a major European trophy without having also won a national league title, along with West Ham United, Real Zaragoza and Bayer Leverkusen. The club were also the only side to represent Italy in European competition for every year between 1991 and 2005.
National
Coppa Italia:
Winners (3): 1991–92, 1998–99, 2001–02
Runners-up (2): 1994–95, 2000–01
Supercoppa Italiana:
Winners (1): 1999
Runners-up (3): 1992, 1995, 2002
Serie A:
Runners-up (1): 1996–97
Serie B:
Runners-up (2): 2008–09, 2017–18
European
UEFA Cup:
Winners (2): 1994–95, 1998–99
European Super Cup:
Winners (1): 1993
European Cup Winners' Cup:
Winners (1): 1992–93
Runners-up (1): 1993–94
Minor
Prima Divisione:
Runners-up (1): 1928–29
Seconda Divisione:
Winners (1): 1924–25
Promozione:
Runners-up (1): 1919–20
Serie C:
Winners (4): 1953–54, 1972–73, 1983–84, 1985–86
Runners-up (2): 1942–43, 1978–79, 2016–17
Serie D:
Winners (1): 1969–70, 2015–16
Coppa delle Alpi:
Winners (1): 1960–61
Friendly Tournaments
Trofeo Ciudad de Zaragoza:
Winners (1): 1998
Runners-up (1): 2000
Trofeo Birra Moretti:
Winners (1): 1999
Orange Trophy:
Winners (2): 2000, 2007
Joan Gamper Trophy:
Runners-up (1): 2001
Ciutat de Barcelona Trophy:
Winners (1): 2003
Trofeo Costa del Sol:
Runners-up (1): 2010
Players
All current players are in bold.
Appearances
Antonio Benarrivo heads the all-time appearances list in Serie A and European competitions and is the only player who was at the club for all eight major trophy victories, but Alessandro Lucarelli holds the appearance record for all league competitions, playing through all four categories in the past decade.
Youngest pla |
https://en.wikipedia.org/wiki/Randall%20Dougherty | Randall Dougherty (born 1961) is an American mathematician. Dougherty has made contributions in widely varying areas of mathematics, including set theory,
logic, real analysis, discrete mathematics, computational geometry, information theory, and coding theory.
Dougherty is a three-time winner of the U.S.A. Mathematical Olympiad (1976, 1977, 1978) and a three-time medalist in the International Mathematical Olympiad. He is also a three-time Putnam Fellow (1978, 1979, 1980). Dougherty earned his Ph.D. in 1985 at University of California, Berkeley under the direction of Jack Silver.
With Matthew Foreman he showed that the Banach-Tarski decomposition is possible with pieces with the Baire property, solving a problem of Marczewski that remained unsolved for more than 60 years.
With Chris Freiling and Ken Zeger, he showed that linear codes are insufficient to gain the full advantages of network coding.
Selected publications
References
1961 births
Living people
20th-century American mathematicians
21st-century American mathematicians
University of California, Berkeley alumni
Ohio State University faculty
International Mathematical Olympiad participants
Putnam Fellows |
https://en.wikipedia.org/wiki/Open%20Mathematics | Open Mathematics is a peer-reviewed open access scientific journal covering all areas of mathematics. It is published by Walter de Gruyter and the editors-in-chief are Salvatore Angelo Marano (University of Catania) and Vincenzo Vespri (University of Florence).
Abstracting and indexing
The journal is abstracted and indexed in Science Citation Index Expanded, Current Contents/Physical, Chemical & Earth Sciences, Mathematical Reviews, Zentralblatt MATH, and Scopus. According to the Journal Citation Reports, the journal has a 2018 impact factor of 0.726.
History
The journal was established in 2003 as the Central European Journal of Mathematics and published by Versita, since 2012 part of Walter de Gruyter, in collaboration with Springer Science+Business Media. In 2014 it was moved to the Walter de Gruyter imprint and started charging article processing charges. In protest, the editor-in-chief and the quasi-totality of the editorial board resigned and, in August 2014, established a new journal, the European Journal of Mathematics.
Editors-in-chief
The following persons have been editors-in-chief of the journal:
Andrzej Białynicki-Birula (University of Warsaw; 2003–2004)
Grigory Margulis (Yale University; 2004–2009)
Fedor Bogomolov (Courant Institute of Mathematical Sciences; 2009–2014)
Ugo Gianazza (University of Pavia; 2014–2019)
Vincenzo Vespri (University of Florence; 2014–present)
Salvatore Angelo Marano (University of Catania; 2020–present)
References
External links
Academic journals established in 2003
Mathematics journals
English-language journals
De Gruyter academic journals
Creative Commons Attribution-licensed journals |
https://en.wikipedia.org/wiki/Special%20group%20%28algebraic%20group%20theory%29 | In the theory of algebraic groups, a special group is a linear algebraic group G with the property that every principal G-bundle is locally trivial in the Zariski topology. Special groups include the general linear group, the special linear group, and the symplectic group. Special groups are necessarily connected. Products of special groups are special. The projective linear group is not special because there exist Azumaya algebras, which are trivial over a finite separable extension, but not over the base field.
Special groups were defined in 1958 by Jean-Pierre Serre and classified soon thereafter by Alexander Grothendieck.
References
Linear algebraic groups |
https://en.wikipedia.org/wiki/Shotaro%20Ihata | is a former Japanese football player.
Club statistics
References
External links
1987 births
Living people
Shizuoka Sangyo University alumni
Association football people from Shizuoka Prefecture
Japanese men's footballers
J2 League players
Singapore Premier League players
Roasso Kumamoto players
Albirex Niigata Singapore FC players
Lion City Sailors FC players
Geylang International FC players
Expatriate men's footballers in Singapore
Men's association football forwards |
https://en.wikipedia.org/wiki/Achmad%20Jufriyanto | Achmad Jufriyanto Tohir (born 7 February 1987 in Tangerang, Banten) is an Indonesian professional footballer who plays as a centre-back for Liga 1 club Persib Bandung.
Career statistics
Club
International goals
Scores and results list Indonesia's goal tally first.
Honours
Club
Sriwijaya
Indonesia Super League: 2011–12
Indonesian Community Shield: 2010
Indonesian Inter Island Cup (2): 2010, 2012
Persib Bandung
Indonesia Super League: 2014
Indonesia President's Cup: 2015
References
External links
1987 births
Living people
Sportspeople from Tangerang
Footballers from Banten
Indonesian men's footballers
Persita Tangerang players
Arema F.C. players
Madura United F.C. players
Sriwijaya F.C. players
Persib Bandung players
Kuala Lumpur City F.C. players
Bhayangkara Presisi Indonesia F.C. players
Liga 1 (Indonesia) players
Malaysia Super League players
2007 AFC Asian Cup players
Indonesia men's international footballers
Indonesia men's youth international footballers
Indonesian expatriate men's footballers
Indonesian expatriate sportspeople in Malaysia
Expatriate men's footballers in Malaysia
Men's association football central defenders
Footballers at the 2014 Asian Games
Asian Games competitors for Indonesia |
https://en.wikipedia.org/wiki/Tam%C3%A1s%20Rubus | Tamás Rubus (born 13 July 1989) is a Hungarian football player who plays for Kisvárda II.
Club statistics
Updated to games played as of 15 May 2021.
External links
Player profile at HLSZ
1989 births
Living people
Footballers from Békéscsaba
Hungarian men's footballers
Men's association football defenders
Békéscsaba 1912 Előre footballers
Újpest FC players
Vasas SC players
Nyíregyháza Spartacus FC players
Kisvárda FC players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Nemzeti Bajnokság III players |
https://en.wikipedia.org/wiki/Acceptance%20set | In financial mathematics, acceptance set is a set of acceptable future net worth which is acceptable to the regulator. It is related to risk measures.
Mathematical Definition
Given a probability space , and letting be the Lp space in the scalar case and in d-dimensions, then we can define acceptance sets as below.
Scalar Case
An acceptance set is a set satisfying:
such that
Additionally if is convex then it is a convex acceptance set
And if is a positively homogeneous cone then it is a coherent acceptance set
Set-valued Case
An acceptance set (in a space with assets) is a set satisfying:
with denoting the random variable that is constantly 1 -a.s.
is directionally closed in with
Additionally, if is convex (a convex cone) then it is called a convex (coherent) acceptance set.
Note that where is a constant solvency cone and is the set of portfolios of the reference assets.
Relation to Risk Measures
An acceptance set is convex (coherent) if and only if the corresponding risk measure is convex (coherent). As defined below it can be shown that and .
Risk Measure to Acceptance Set
If is a (scalar) risk measure then is an acceptance set.
If is a set-valued risk measure then is an acceptance set.
Acceptance Set to Risk Measure
If is an acceptance set (in 1-d) then defines a (scalar) risk measure.
If is an acceptance set then is a set-valued risk measure.
Examples
Superhedging price
The acceptance set associated with the superhedging price is the negative of the set of values of a self-financing portfolio at the terminal time. That is
.
Entropic risk measure
The acceptance set associated with the entropic risk measure is the set of payoffs with positive expected utility. That is
where is the exponential utility function.
References
Financial risk modeling |
https://en.wikipedia.org/wiki/Saba%20Rajendran | Saba Rajendran is an Indian politician and an incumbent Member of legislative assembly of Tamil Nadu, Neyveli.
He was born in Sorathur on 18 June 1961. He holds a B.Sc. in Mathematics and a B.E. in mechanical engineering.
He was elected to the Tamil Nadu legislative assembly as a Dravida Munnetra Kazhagam candidate from Neyveli constituency in the 2016 elections. Previously he was elected to the Tamil Nadu legislative assembly as a Dravida Munnetra Kazhagam candidate from Nellikuppam constituency in the 2006 election. He again won the election in 2021 in Neyveli constituency.
Early life and education
Saba Rajendran, was born and brought up in Sorathur village, Cuddalore, Tamilnadu. Born in a family of leaders, he was naturally inclined towards social welfare, where his father was a panchayat leader and his mother was supportive of farming activities. Coming from a background of farmers, he has emphasized the need for proper ground water and natural farming. Prior to entering politics, he has actively voiced the struggles of the farmers and deployed various initiatives in support of these causes.
With Neyveli being the hub of electricity production in Tamilnadu, he was interested in Mechanical sciences and completed his Bachelor’s in JMIT, Chitradurga.
Through the work of Jawaharlal Nehru and Periyar, he found sincere passion towards political work and found integrity and need for social welfare through the work of M. Karunanidhi. The zeal to enter full time politics arrived when he found his political ideologies coinciding with that of Dravida Munnetra Kazhagam’s values.
Before actively contesting the Tamilnadu legislative assembly elections, he was appointed the Union Secretary of the DMK Panruti wing. He was also the director of the Lions Club, Neyveli, heading a group of established leaders. Owing to his interest in sports, he was the President of the football association, Cuddalore and aimed to promote a sport culture among the youth.
After assuming office as an MLA, he continues to work in his position at the DMK Panruti wing, while being a prominent member in major committees such as the Petitions Committee, Assurance Committee and Estimate Committee, continuing to serve people through any level of responsibility.
Political career
In the 2006 Tamil Nadu Legislative Assembly election,
Saba Rajendran contested the Nellikuppam constituency and won the election, under the leadership of Kalaignar.
In the 2011 Tamil Nadu Legislative Assembly election, he represented DMK and lost the election to a Desiya Murpokku Dravida Kazhagam candidate by a vote share difference of 6%.
Subsequently, in the 2016 and 2021 Tamil Nadu Legislative Assembly election, he won in the Neyveli constituency.
Throughout his career, he has achieved significant milestones, aimed at cohesive growth of the citizens and nurturing an entrepreneurship culture.
2016-Present
In Neyveli, the Kasambu lake was inaugurated by M. K. Stalin, which was preceded by efficient |
https://en.wikipedia.org/wiki/Subanalytic%20set | In mathematics, particularly in the subfield of real analytic geometry, a subanalytic set is a set of points (for example in Euclidean space) defined in a way broader than for semianalytic sets (roughly speaking, those satisfying conditions requiring certain real power series to be positive there). Subanalytic sets still have a reasonable local description in terms of submanifolds.
Formal definitions
A subset V of a given Euclidean space E is semianalytic if each point has a neighbourhood U in E such that the intersection of V and U lies in the Boolean algebra of sets generated by subsets defined by inequalities f > 0, where f is a real analytic function. There is no Tarski–Seidenberg theorem for semianalytic sets, and projections of semianalytic sets are in general not semianalytic.
A subset V of E is a subanalytic set if for each point there exists a relatively compact semianalytic set X in a Euclidean space F of dimension at least as great as E, and a neighbourhood U in E, such that the intersection of V and U is a linear projection of X into E from F.
In particular all semianalytic sets are subanalytic. On an open dense subset, subanalytic sets are submanifolds and so they have a definite dimension "at most points". Semianalytic sets are contained in a real-analytic subvariety of the same dimension. However, subanalytic sets are not in general contained in any subvariety of the same dimension. On the other hand, there is a theorem, to the effect that a subanalytic set A can be written as a locally finite union of submanifolds.
Subanalytic sets are not closed under projections, however, because a real-analytic subvariety that is not relatively compact can have a projection which is not a locally finite union of submanifolds, and hence is not subanalytic.
See also
Semialgebraic set
References
Edward Bierstone and Pierre D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ. Math. (1988), no. 67, 5–42.
External links
Real Algebraic and Analytic Geometry Preprint Server
Real algebraic geometry |
https://en.wikipedia.org/wiki/Real%20plane%20curve | In mathematics, a real plane curve is usually a real algebraic curve defined in the real projective plane.
Ovals
The field of real numbers is not algebraically closed, the geometry of even a plane curve C in the real projective plane. Assuming no singular points, the real points of C form a number of ovals, in other words submanifolds that are topologically circles. The real projective plane has a fundamental group that is a cyclic group with two elements. Such an oval may represent either group element; in other words we may or may not be able to contract it down in the plane. Taking out the line at infinity L, any oval that stays in the finite part of the affine plane will be contractible, and so represent the identity element of the fundamental group; the other type of oval must therefore intersect L.
There is still the question of how the various ovals are nested. This was the topic of Hilbert's sixteenth problem. See Harnack's curve theorem for a classical result.
See also
Real algebraic geometry
Ragsdale conjecture
References
Real algebraic geometry
Algebraic curves |
https://en.wikipedia.org/wiki/List%20of%20aperiodic%20sets%20of%20tiles | In geometry, a tiling is a partition of the plane (or any other geometric setting) into closed sets (called tiles), without gaps or overlaps (other than the boundaries of the tiles). A tiling is considered periodic if there exist translations in two independent directions which map the tiling onto itself. Such a tiling is composed of a single fundamental unit or primitive cell which repeats endlessly and regularly in two independent directions. An example of such a tiling is shown in the adjacent diagram (see the image description for more information). A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking it is the tiles themselves that are aperiodic. (The tiling itself is said to be "nonperiodic".)
The first table explains the abbreviations used in the second table. The second table contains all known aperiodic sets of tiles and gives some additional basic information about each set. This list of tiles is still incomplete.
Explanations
List
References
External links
Stephens P. W., Goldman A. I. The Structure of Quasicrystals
Levine D., Steinhardt P. J. Quasicrystals I Definition and structure
Tilings Encyclopedia
Mathematics-related lists |
https://en.wikipedia.org/wiki/Eichler%E2%80%93Shimura%20congruence%20relation | In number theory, the Eichler–Shimura congruence relation expresses the local L-function of a modular curve at a prime p in terms of the eigenvalues of Hecke operators. It was introduced by and generalized by . Roughly speaking, it says that the correspondence on the modular curve inducing the Hecke operator Tp is congruent mod p to the sum of the Frobenius map Frob and its transpose Ver. In other words,
Tp = Frob + Ver
as endomorphisms of the Jacobian J0(N)Fp of the modular curve X0N over the finite field Fp.
The Eichler–Shimura congruence relation and its generalizations to Shimura varieties play a pivotal role in the Langlands program, by identifying a part of the Hasse–Weil zeta function of a modular curve or a more general modular variety, with the product of Mellin transforms of weight 2 modular forms or a product of analogous automorphic L-functions.
References
Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Publ. of Math. Soc. of Japan, 11, 1971
Modular forms
Zeta and L-functions
Theorems in number theory |
https://en.wikipedia.org/wiki/G%C3%A1bor%20J.%20Sz%C3%A9kely | Gábor J. Székely (; born February 4, 1947, in Budapest) is a Hungarian-American statistician/mathematician best known for introducing energy statistics (E-statistics). Examples include: the distance correlation, which is a bona fide dependence measure, equals zero exactly when the variables are independent; the distance skewness, which equals zero exactly when the probability distribution is diagonally symmetric; the E-statistic for normality test; and the E-statistic for clustering.
Other important discoveries include the Hungarian semigroups, the location testing for Gaussian scale mixture distributions, the uncertainty principle of game theory, the half-coin which involves negative probability, and the solution of an old open problem of lottery mathematics: in a 5-from-90 lotto the minimum number of tickets one needs to buy to guarantee that at least one of these tickets has (at least) 2 matches is exactly 100.
Life and career
Székely attended the Eötvös Loránd University, Hungary graduating in 1970. His first advisor was Alfréd Rényi. Székely received his Ph.D. in 1971 from Eötvös Loránd University, the Candidate Degree in 1976 under the direction of Paul Erdős and Andrey Kolmogorov, and the Doctor of Science degree from the Hungarian Academy of Sciences in 1986. During the years 1970-1995 he has worked as a Professor in Eötvös Loránd University at the Department of Probability Theory and Statistics.
Between 1985 and 1995 Székely was the first program manager of the Budapest Semesters in Mathematics. Between 1990 and 1997 he was the founding chair of the Department of Stochastics of the Budapest Institute of Technology (Technical University of Budapest) and editor-in-chief of Matematikai Lapok, the official journal of the János Bolyai Mathematical Society.
In 1989 Székely was visiting professor at Yale University, and in 1990-91 he was the first Lukacs Distinguished Professor in Ohio. Since 1995 he has been teaching at the Bowling Green State University at the Department of Mathematics and Statistics. Székely was academic advisor of Morgan Stanley, NY, and Bunge, Chicago, helped to establish the Morgan Stanley Mathematical Modeling Centre in Budapest (2005) and the Bunge Mathematical Institute (BMI) in Warsaw (2006) to provide quantitative analysis to support the firms' global business.
Since 2006 he is a Program Director of Statistics of the National Science Foundation, now retired. Székely is also Research Fellow of the Rényi Institute of Mathematics of the Hungarian Academy of Sciences.
For an informal biographical sketch see Conversations with Gábor J. Székely
Awards
Rollo Davidson Prize of Cambridge University (1988)
Elected Fellow of the International Statistical Institute (1996)
Elected Fellow of the American Statistical Association (2000)
Elected Fellow of the Institute of Mathematical Statistics (2010)
Books
Székely, G. J. (1986) Paradoxes in Probability Theory and Mathematical Statistics, Reidel.
Ruzsa, I. Z. and S |
https://en.wikipedia.org/wiki/Gorbea%2C%20Chile | Gorbea is a Chilean city and commune located in Cautín Province, Araucanía Region.
Demographics
According to the 2002 census of the National Statistics Institute, Gorbea spans an area of and has 15,222 inhabitants (7,609 men and 7,613 women). Of these, 9,413 (61.8%) lived in urban areas and 5,809 (38.2%) in rural areas. Between the 1992 and 2002 censuses, the population grew by 3.9% (570 persons).
The commune's largest settlements are Gorbea, Lastarria and Quitratué.
Administration
As a commune, Gorbea is a third-level administrative division of Chile administered by a municipal council, headed by an alcalde who is directly elected every four years. The 2016-2020 alcalde is Guido Siegmund González (UDI).
Within the electoral divisions of Chile, Gorbea is represented in the Chamber of Deputies by René Manuel García (RN) and Fernando Meza (PRSD) as part of the 52nd electoral district, together with Cunco, Pucón, Curarrehue, Villarrica, Loncoche and Toltén. The commune is represented in the Senate by José Garcia Ruminot (RN) and Eugenio Tuma Zedan (PPD) as part of the 15th senatorial constituency (Araucanía-South).
Education
Previously the area had a German school, Deutsche Schule Gorbea.
References
External links
Municipality of Gorbea
Communes of Chile
Populated places in Cautín Province
1887 establishments in Chile |
https://en.wikipedia.org/wiki/Labour%20market%20area | A labour market area is a spatially coherent area of cities and municipalities that enables meaningful statistics in terms of economic performance and jobs. The delimitation of the geographical area is based on statistical criteria and not on political organisation. A labour market area is defined as a region in which the majority of those employed there also live. The division of a country into labour market areas is widely used in statistical analyses and cartographic representations. The space is subdivided in such a way that spatial and temporal comparisons between units that are as similar as possible are possible. The method uses commuter flows between cities and municipalities as a characteristic. It thus enables uniform criteria for an entire country and is used in several European countries and by the Statistical Office of the European Union (Eurostat). Since settlement and land use of an area change considerably over time, the boundaries of the labour market areas must be revised regularly to ensure that they adequately reflect the current situation.
Germany
In Germany, labour market areas are defined and updated by the Federal Office for Building and Regional Planning. The division of Germany into labour market areas focuses on urban-suburban relations.
Switzerland
In 2018, the Swiss Federal Statistical Office (FSO) defined the labour market areas in Switzerland, a total of 101 labour market areas, which are grouped into 16 major labour market regions. In parallel, a total of ten cross-border labour market regions were designated.
See also
Metropolitan area
References
Metropolitan areas
Urban geography |
https://en.wikipedia.org/wiki/Wetland%20indicator%20status | Wetland indicator status denotes the probability of individual species of vascular plants occurring in freshwater, brackish and saltwater wetlands in the United States. The wetland status of 7,000 plants is determined upon information contained in a list compiled in the National Wetland Inventory undertaken by the U.S. Fish and Wildlife Service and developed in cooperation with a federal inter-agency review panel (Reed, 1988). The National List was compiled in 1988 with subsequent revisions in 1996 and 1998.
The wetland indicator status of a species is based upon the individual species occurrence in wetlands in 13 separate regions within the United States. In some instances the specified regions contain all or part of different floristic provinces and the tension zones which occur between them.
While many Obligate Wetland (OBL) species do occur in permanently or semi-permanently flooded wetlands, there are also a number of obligates that occur in temporary or seasonally flooded wetlands. A few species are restricted entirely to these transient-type wetland environments.
Plant species are general indicators of various degrees of environmental factors; they are however not precise. The presence of a plant species at a specific site depends on a variety of climatic, edaphic and biotic factors, and the effect of individual factors such as degree of substrate saturation and depth and duration of standing water is impossible to isolate.
A plant's indicator status is applied to the species as a whole however individual variations may exist within the species, referred to as "ecotypes"; individual plants which may have adapted to specific environments as may occur in a microhabitat, which isn't indicative of the species as a whole. The morphological differences between these ecotypes and the relevant species may or may not be easily discerned.
Indicator categories
Obligate wetland (OBL) - Almost always occurs in wetlands under natural conditions (estimated probability > 99%).
Facultative wetland (FACW) - Usually occurs in wetlands (estimated probability 67% – 99%), but occasionally found in non-wetlands (estimated probability 1% – 33%).
Facultative (FAC) - Equally likely to occur in wetlands and non-wetlands (estimated probability 34% – 66%).
Facultative upland (FACU) - Usually occurs in non-wetlands (estimated probability 67% – 99%), but occasionally found in wetlands (estimated probability 1% – 33%).
Obligate upland (UPL) - Almost always occurs in non-wetlands under natural conditions (estimated probability > 99%).
A positive (+) or negative (−) sign is used for the facultative categories. The (+) sign indicates a frequency towards the wetter end of the category (more frequently found in wetlands) and the (−) sign indicates a frequency towards the drier end of the category (less frequently found in wetlands).
Wetland regions
Corps wetland regions are defined as follows:
AGCP = Atlantic and Gulf Coastal Plain
AW = Arid West
CB = Caribbea |
https://en.wikipedia.org/wiki/Kenta%20Hiraishi | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Fukuoka University alumni
Association football people from Hiroshima Prefecture
Japanese men's footballers
J2 League players
Avispa Fukuoka players
Men's association football defenders |
https://en.wikipedia.org/wiki/Y%C5%8Dsuke%20Miyaji | is a Japanese football player and he is current manager Japan Football League club of Honda Lock.
Club statistics
References
External links
1987 births
Living people
Fukuoka University alumni
Association football people from Miyazaki Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Avispa Fukuoka players
Minebea Mitsumi FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Fabius%20function | In mathematics, the Fabius function is an example of an infinitely differentiable function that is nowhere analytic, found by . It was also written down as the Fourier transform of
by .
The Fabius function is defined on the unit interval, and is given by the cumulative distribution function of
where the are independent uniformly distributed random variables on the unit interval.
This function satisfies the initial condition , the symmetry condition for and the functional differential equation for It follows that is monotone increasing for with and
There is a unique extension of to the real numbers that satisfies the same differential equation for all x. This extension can be defined by for , for , and for with a positive integer. The sequence of intervals within which this function is positive or negative follows the same pattern as the Thue–Morse sequence.
Values
The Fabius function is constant zero for all non-positive arguments, and assumes rational values at positive dyadic rational arguments.
References
(an English translation of the author's paper published in Spanish in 1982)
Types of functions
Alkauskas, Giedrius (2001), "Dirichlet series associated with Thue-Morse sequence", preprint.
Rvachev, V. L., Rvachev, V. A., "Non-classical methods of the approximation theory in boundary value problems", Naukova Dumka, Kiev (1979) (in Russian). |
https://en.wikipedia.org/wiki/Major%20index | In mathematics (and particularly in combinatorics), the major index of a permutation is the sum of the positions of the descents of the permutation. In symbols, the major index of the permutation w is
For example, if w is given in one-line notation by w = 351624 (that is, w is the permutation of {1, 2, 3, 4, 5, 6} such that w(1) = 3, w(2) = 5, etc.) then w has descents at positions 2 (from 5 to 1) and 4 (from 6 to 2) and so maj(w) = 2 + 4 = 6.
This statistic is named after Major Percy Alexander MacMahon who showed in 1913 that the distribution of the major index on all permutations of a fixed length is the same as the distribution of inversions. That is, the number of permutations of length n with k inversions is the same as the number of permutations of length n with major index equal to k. (These numbers are known as Mahonian numbers, also in honor of MacMahon.) In fact, a stronger result is true: the number of permutations of length n with major index k and i inversions is the same as the number of permutations of length n with major index i and k inversions, that is, the two statistics are equidistributed. For example, the number of permutations of length 4 with given major index and number of inversions is given in the table below.
References
.
Permutations |
https://en.wikipedia.org/wiki/Tower%20of%20fields | In mathematics, a tower of fields is a sequence of field extensions
The name comes from such sequences often being written in the form
A tower of fields may be finite or infinite.
Examples
is a finite tower with rational, real and complex numbers.
The sequence obtained by letting F0 be the rational numbers Q, and letting
(i.e. Fn+1 is obtained from Fn by adjoining a 2n th root of 2) is an infinite tower.
If p is a prime number the p th cyclotomic tower of Q is obtained by letting F0 = Q and Fn be the field obtained by adjoining to Q the pn th roots of unity. This tower is of fundamental importance in Iwasawa theory.
The Golod–Shafarevich theorem shows that there are infinite towers obtained by iterating the Hilbert class field construction to a number field.
References
Section 4.1.4 of
Field extensions |
https://en.wikipedia.org/wiki/Qiang%20Du | Qiang Du (), the Fu Foundation Professor of Applied Mathematics at Columbia University, is a Chinese mathematician and computational scientist. Prior to moving to Columbia, he was the Verne M. Willaman Professor of Mathematics at Pennsylvania State University affiliated with the Pennsylvania State University Department of Mathematics and Materials Sciences.
Education
After completing his BS degree at University of Science and Technology of China in 1983, Du earned his Ph.D. degree from Carnegie Mellon University in 1988. His thesis was written under the direction of Max D. Gunzburger.
Selected publications
His two most often cited papers are
Students and post-doctorates
As of June 2018, 17 students had completed their Ph.D. degrees under Du's supervision. He had also supported 10 post-doctorates.
Recognition
Du was elected a fellow of the Society for Industrial and Applied Mathematics in 2013 for "contributions to applied and computational mathematics with applications in material science, computational geometry, and biology."
In 2017 he was elected as a Fellow of the American Association for the Advancement of Science.
He was elected as a Fellow of the American Mathematical Society in the 2020 Class, for "contributions to applied and computational mathematics with applications in materials science, computational geometry, and biology".
References
External links
Qiang Du's home page at Columbia University
Qiang Du's home page at Penn State
Chinese mathematicians
20th-century American mathematicians
21st-century American mathematicians
Numerical analysts
Living people
Pennsylvania State University faculty
Chinese emigrants to the United States
Fellows of the American Association for the Advancement of Science
Fellows of the American Mathematical Society
Fellows of the Society for Industrial and Applied Mathematics
Columbia University faculty
Columbia School of Engineering and Applied Science faculty
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Knut%20Syds%C3%A6ter | Knut Sydsæter (5 October 1937 – 29 September 2012) was a Norwegian mathematician.
Professor of Mathematics at the University of Oslo.
He is known for having written several books in mathematics for economic analysis, mainly in Norwegian and English.
However, his books have been released in several other languages such as Swedish, German, Italian, Chinese, Japanese, Portuguese, Spanish, Russian and Hungarian among others.
References
External links
Knut Sydsæter's Home Page (archived at web.archive.org)
Norwegian economists
Norwegian mathematicians
Academic staff of the University of Oslo
1937 births
2012 deaths |
https://en.wikipedia.org/wiki/Kazuki%20Yamaguchi%20%28footballer%2C%20born%201986%29 | is a former Japanese football player.
Club statistics
References
External links
1986 births
Living people
Fukuoka University alumni
Japanese men's footballers
J1 League players
J2 League players
Avispa Fukuoka players
Men's association football defenders
Association football people from Fukuoka (city) |
https://en.wikipedia.org/wiki/1996%E2%80%9397%20Real%20Madrid%20CF%20season | The 1996–97 season was the Real Madrid CF's 66th season in La Liga. This article shows player statistics and official matches that the club played during the 1996–97 season. For the first time since 1977–78, Real Madrid was not involved in any European competitions due to the previous season's lowest league finish in 19 years.
Summary
For the first time since the 1977–78 season, Real Madrid only played in the domestic competitions after having rejected the option to enter the 1996 Intertoto Cup. Madrid returned to domestic glory in the only season under the Fabio Capello's reign, who, after much conflict with club president Lorenzo Sanz, announced his exit already in mid-season, choosing to return to Italy (where he would eventually settle at his old club AC Milan). New signings Predrag Mijatović and Davor Šuker played alongside main striker Raúl González as well as Clarence Seedorf in midfield. Real Madrid was nearly on course to sign Newcastle United-bound Alan Shearer courtesy of his best form at Blackburn Rovers, but due to already featuring Raúl González as the club's main striker, Alan Shearer preferred to stay in England. Roberto Carlos, Carlos Secretário, Christian Panucci, and mid-season arrival Zé Roberto were also new signings in defense.
In May 1997, Real Madrid began to slip due to injuries of key players despite having won 3 of 5 matches in that month. However as rivals Barcelona also slipped in early June after a loss against Hércules, Real took an advantage by crushing CF Extremadura 5-0 in the same weekend. Real Madrid eventually won the La Liga title with a record 92 points, after a 3–1 victory against Atlético Madrid on the penultimate round of the season (five points ahead of Barcelona), and thus Fabio Capello became the first-ever Italian manager to win La Liga silverware. In the Copa del Rey, Madrid advanced to the round of 16 where they faced perennial rivals Barcelona, losing 4–3 on aggregate. The Catalans went on to win the tournament, setting up a Super Cup clash against Madrid.
Players
Squad information
Transfers
In
Total spending: €28,400,000
Out
Total income: €0
Competitions
La Liga
League table
Results by round
Matches
Copa del Rey
Second round
Third round
Round of 16
Statistics
Player statistics
References
External links
Real Madrid 96–97 bdfutbol.com
Spanish football clubs 1996–97 season
1996-97
1996-97 |
https://en.wikipedia.org/wiki/Tam%C3%A1s%20Egerszegi | Tamás Egerszegi (born 2 August 1991) is a Hungarian footballer who plays as a midfielder for Kozármisleny in Nemzeti Bajnokság II.
Honours
Diósgyőr
Hungarian League Cup (1): 2013–14
Club statistics
Updated to games played as of 24 June 2020.
References
External links
Player profile at HLSZ
1991 births
Living people
Hungarian men's footballers
Men's association football midfielders
Újpest FC players
BFC Siófok players
Sint-Truidense V.V. players
Gyirmót FC Győr players
Diósgyőri VTK players
Mezőkövesdi SE footballers
Miedź Legnica players
Vasas SC players
Paksi FC players
Budapest Honvéd FC players
Kozármisleny SE footballers
Nemzeti Bajnokság I players
I liga players
Nemzeti Bajnokság II players
Nemzeti Bajnokság III players
Hungarian expatriate men's footballers
Expatriate men's footballers in Belgium
Expatriate men's footballers in Poland
Hungarian expatriate sportspeople in Belgium
Hungarian expatriate sportspeople in Poland
Footballers from Pest County |
https://en.wikipedia.org/wiki/Signalizer%20functor | In mathematics, a signalizer functor gives the intersections of a potential subgroup of a finite group with the centralizers of nontrivial elements of an abelian group. The signalizer functor theorem gives conditions under which a signalizer functor comes from a subgroup. The idea is to try to construct a -subgroup of a finite group , which has a good chance of being normal in , by taking as generators certain -subgroups of the centralizers of nonidentity elements in one or several given noncyclic elementary abelian -subgroups of The technique has origins in the Feit–Thompson theorem, and was subsequently developed by many people including who defined signalizer functors, who proved the Solvable Signalizer Functor Theorem for solvable groups, and who proved it for all groups. This theorem is needed to prove the so-called "dichotomy" stating that a given nonabelian finite simple group either has local characteristic two, or is of component type. It thus plays a major role in the classification of finite simple groups.
Definition
Let A be a noncyclic elementary abelian p-subgroup of the finite group G. An A-signalizer functor on G or simply a signalizer functor when A and G are clear is a mapping θ from the set of nonidentity elements of A to the set of A-invariant p′-subgroups of G satisfying the following properties:
For every nonidentity , the group is contained in
For every nonidentity , we have
The second condition above is called the balance condition. If the subgroups are all solvable, then the signalizer functor itself is said to be solvable.
Solvable signalizer functor theorem
Given certain additional, relatively mild, assumptions allow one to prove that the subgroup of generated by the subgroups is in fact a -subgroup. The Solvable Signalizer Functor Theorem proved by Glauberman and mentioned above says that this will be the case if is solvable and has at least three generators. The theorem also states that under these assumptions, itself will be solvable.
Several earlier versions of the theorem were proven: proved this under the stronger assumption that had rank at least 5. proved this under the assumption that had rank at least 4 or was a 2-group of rank at least 3. gave a simple proof for 2-groups using the ZJ theorem, and a proof in a similar spirit has been given for all primes by . gave the definitive result for solvable signalizer functors. Using the classification of finite simple groups, showed that is a -group without the assumption that is solvable.
Completeness
The terminology of completeness is often used in discussions of signalizer functors. Let be a signalizer functor as above, and consider the set И of all -invariant -subgroups of satisfying the following condition:
for all nonidentity
For example, the subgroups belong to И by the balance condition. The signalizer functor is said to be complete if И has a unique maximal element when ordered by containment. In this case, the unique |
https://en.wikipedia.org/wiki/Soft%20set | Soft set theory is a generalization of fuzzy set theory, that was proposed by Molodtsov in 1999 to deal with uncertainty in a parametric manner. A soft set is a parameterised family of sets - intuitively, this is "soft" because the boundary of the set depends on the parameters. Formally, a soft set, over a universal set X and set of parameters E is a pair (f, A) where A is a subset of E, and f is a function from A to the power set of X. For each e in A, the set f(e) is called the value set of e in (f, A).
One of the most important steps for the new theory of soft sets was to define mappings on soft sets, which was achieved in 2009 by the mathematicians Athar Kharal and Bashir Ahmad, with the results published in 2011. Soft sets have also been applied to the problem of medical diagnosis for use in medical expert systems.
Fuzzy soft sets have also been introduced. Mappings on fuzzy soft sets were defined and studied by Kharal and Ahmad.
Notes
References
Molodtsov D. A. A theory of soft sets. Moscow: Editorial URSS, 2004.
Matsievsky S. V. Sets, multisets, fuzzy and soft sets without universe. Vestnik IKSUR, 2007, N. 10, pp. 44–52.
Ahmad, B., Kharal, A.On Fuzzy Soft Sets. Advances in Fuzzy Systems Volume 2009 (2009), Article ID 586507, 6 pages .
Set theory |
https://en.wikipedia.org/wiki/Tango%20bundle | In algebraic geometry, a Tango bundle is one of the indecomposable vector bundles of rank n − 1 constructed on n-dimensional projective space Pn by
References
Algebraic geometry
Vector bundles |
https://en.wikipedia.org/wiki/Transversality | Transversality may refer to:
Transversality (mathematics), a notion in mathematics
Transversality theorem, a theorem in differential topology
See also
Transverse (disambiguation)
Transversal (disambiguation)
Longitudinal (disambiguation) |
https://en.wikipedia.org/wiki/Distance%20correlation | In statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension. The population distance correlation coefficient is zero if and only if the random vectors are independent. Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson's correlation, which can only detect linear association between two random variables.
Distance correlation can be used to perform a statistical test of dependence with a permutation test. One first computes the distance correlation (involving the re-centering of Euclidean distance matrices) between two random vectors, and then compares this value to the distance correlations of many shuffles of the data.
Background
The classical measure of dependence, the Pearson correlation coefficient, is mainly sensitive to a linear relationship between two variables. Distance correlation was introduced in 2005 by Gábor J. Székely in several lectures to address this deficiency of Pearson's correlation, namely that it can easily be zero for dependent variables. Correlation = 0 (uncorrelatedness) does not imply independence while distance correlation = 0 does imply independence. The first results on distance correlation were published in 2007 and 2009. It was proved that distance covariance is the same as the Brownian covariance. These measures are examples of energy distances.
The distance correlation is derived from a number of other quantities that are used in its specification, specifically: distance variance, distance standard deviation, and distance covariance. These quantities take the same roles as the ordinary moments with corresponding names in the specification of the Pearson product-moment correlation coefficient.
Definitions
Distance covariance
Let us start with the definition of the sample distance covariance. Let (Xk, Yk), k = 1, 2, ..., n be a statistical sample from a pair of real valued or vector valued random variables (X, Y). First, compute the n by n distance matrices (aj, k) and (bj, k) containing all pairwise distances
where ||⋅ ||denotes Euclidean norm. Then take all doubly centered distances
where is the -th row mean, is the -th column mean, and is the grand mean of the distance matrix of the sample. The notation is similar for the values. (In the matrices of centered distances (Aj, k) and (Bj,k) all rows and all columns sum to zero.) The squared sample distance covariance (a scalar) is simply the arithmetic average of the products Aj, k Bj, k:
The statistic Tn = n dCov2n(X, Y) determines a consistent multivariate test of independence of random vectors in arbitrary dimensions. For an implementation see dcov.test function in the energy package for R.
The population value of distance covariance can be defined along the same lines. Let X be a random variable that takes value |
https://en.wikipedia.org/wiki/Kneser%E2%80%93Tits%20conjecture | In mathematics, the Kneser–Tits problem, introduced by based on a suggestion by Martin Kneser, asks whether the Whitehead group W(G,K) of a semisimple simply connected isotropic algebraic group G over a field K is trivial. The Whitehead group is the quotient of the rational points of G by the normal subgroup generated by K-subgroups isomorphic to the additive group.
Fields for which the Whitehead group vanishes
A special case of the Kneser–Tits problem asks for which fields the Whitehead group of a semisimple almost simple simply connected isotropic algebraic group is always trivial.
showed that this Whitehead group is trivial for local fields K, and gave examples of fields for which it is not always trivial. For global fields the combined work of several authors shows that this Whitehead group is always trivial .
References
External links
Algebraic groups
Conjectures |
https://en.wikipedia.org/wiki/UNESCO%20Institute%20for%20Statistics | The UNESCO Institute for Statistics (UIS) is the statistical office of UNESCO and is the UN depository for cross-nationally comparable statistics on education, science and technology, culture, and communication.
The UIS was established in 1999. Based in Montreal, Quebec, Canada, it was created to provide statistics for the UN.
The institute serves member states of UNESCO as well as intergovernmental and nongovernmental organisations, research institutes, universities, and citizens. All data is available for free.
The institute provides education data to many global reports and databases, such as the SDG global database of the UN Stats Division, the Global Education Monitoring Report, World Development Indicators and World Development Report (World Bank), Human Development Report (UNDP), and State of the World's Children (UNICEF).
Sex-disaggregated indicators are systematically integrated into all UIS data collections.
Services
Collecting, processing, verifying, analysing, and disseminating high-quality, relevant, cross-nationally comparable data about education, science, culture, and communication
Developing and maintaining appropriate methodologies and standards that reflect the challenges faced by countries at all stages of development
Reinforcing the capacities of national statistical offices and line ministries to produce and use high-quality statistics
Responding to the statistical needs of stakeholders while providing access to UIS data to a wide range of users
Providing open access to UIS data and other products to different types of users, such as governments, international and nongovernmental organisations, foundations, researchers, journalists, and the public
Areas of work
Program highlights
Largest repository of education data: The UIS is the repository of the world's most comprehensive education database. More than 200 countries and territories participate in the UIS annual education survey, which is the basis for calculating a wide range of indicators, from female enrollment in primary education to the mobility of higher education students. The UIS is the official data source for Sustainable Development Goal 4 – Education 2030.
Technical Co-operation Group for SDG 4 – Education 2030 builds consensus on the SDG 4 measurement agenda and provides the opportunity for member states, multilateral agencies, and civil society groups to make recommendations to the UIS, which is responsible for coordinating the technical work needed to define and implement the global and thematic indicators.
Global Alliance to Monitor Learning provides concrete solutions to develop new indicators and set standards in learning assessment, aiming to produce the first internationally comparable measures of learning for youth and adults. It brings together technical experts from countries, partner agencies, assessment organisations, donors, and civil society groups from around the world.
Inter-Agency Group on Education Inequality Indicators sets |
https://en.wikipedia.org/wiki/Baseball%20Almanac | Baseball Almanac is an interactive baseball encyclopedia with over 500,000 pages of baseball facts, research, awards, records, feats, lists, notable quotations, baseball movie ratings, and statistics. Its goal is to preserve the history of baseball.
It serves, in turn, as a source for a number of books and publications about baseball, and/or is mentioned by them as a reference, such as Baseball Digest, Understanding Sabermetrics: An Introduction to the Science of Baseball Statistics, and Baseball's Top 100: The Game's Greatest Records. Dan Zachofsky described it in Collecting Baseball Memorabilia: A Handbook as having the most current information regarding members of the Hall of Fame.
David Maraniss, author of Clemente, the Passion and Grace of Baseball's Last Hero, described it as "an absolutely reliable and first-rate bountiful source, that supplied accurate schedules and box scores". Glenn Guzo, in The New Ballgame: Baseball Statistics for the Casual Fan, described it as having "a rich supply of contemporary and historic information". Film critic Richard Roeper described it in Sox and the City: A Fan's Love Affair with the White Sox from the Heartbreak of '67 to the Wizards of Oz as "one of the beauteous wonders of the Internet". Harvey Frommer, Dartmouth College Professor and sports author, said of Baseball Almanac: "Definitive, vast in its reach and scope, Baseball Almanac is a mother lode of facts, figures, anecdotes, quotations and essays focused on the national pastime.... It has been an indispensable research tool for me."
References
External links
Baseball Almanac
Baseball statistics
Fantasy sports
Almanacs
Internet properties established in 1999
1999 establishments in the United States
Baseball websites |
https://en.wikipedia.org/wiki/Apex%20graph | In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called an apex of the graph. It is an apex, not the apex because an apex graph may have more than one apex; for example, in the minimal nonplanar graphs or , every vertex is an apex. The apex graphs include graphs that are themselves planar, in which case again every vertex is an apex. The null graph is also counted as an apex graph even though it has no vertex to remove.
Apex graphs are closed under the operation of taking minors and play a role in several other aspects of graph minor theory: linkless embedding, Hadwiger's conjecture, YΔY-reducible graphs, and relations between treewidth and graph diameter.
Characterization and recognition
Apex graphs are closed under the operation of taking minors: contracting any edge, or removing any edge or vertex, leads to another apex graph. For, if is an apex graph with apex , then any contraction or removal that does not involve preserves the planarity of the remaining graph, as does any edge removal of an edge incident to . If an edge incident to is contracted, the effect on the remaining graph is equivalent to the removal of the other endpoint of the edge. And if itself is removed, any other vertex may be chosen as the apex.
By the Robertson–Seymour theorem, because they form a minor-closed family of graphs, the apex graphs have a forbidden graph characterization.
There are only finitely many graphs that are neither apex graphs nor have another non-apex graph as a minor.
These graphs are forbidden minors for the property of being an apex graph.
Any other graph is an apex graph if and only if none of the forbidden minors is a minor of .
These forbidden minors include the seven graphs of the Petersen family, three disconnected graphs formed from the disjoint unions of two of and , and many other graphs. However, a complete description of them remains unknown.
Despite the complete set of forbidden minors remaining unknown, it is possible to test whether a given graph is an apex graph, and if so, to find an apex for the graph, in linear time. More generally, for any fixed constant , it is possible to recognize in linear time the -apex graphs, the graphs in which the removal of some carefully chosen set of at most vertices leads to a planar graph. If is variable, however, the problem is NP-complete.
Chromatic number
Every apex graph has chromatic number at most five: the underlying planar graph requires at most four colors by the four color theorem, and the remaining vertex needs at most one additional color. used this fact in their proof of the case of the Hadwiger conjecture, the statement that every 6-chromatic graph has the complete graph as a minor: they showed that any minimal counterexample to the conjecture would have to be an apex graph, but since there are no 6-chromatic apex graphs such a counterexample cannot exist.
conjectured tha |
https://en.wikipedia.org/wiki/Yudai%20Nakashima | is a former Japanese football player.
Club statistics
References
External links
1984 births
Living people
University of Teacher Education Fukuoka alumni
Association football people from Kumamoto Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Giravanz Kitakyushu players
Verspah Oita players
Men's association football forwards |
https://en.wikipedia.org/wiki/Takaki%20Shigemitsu | is a former Japanese football player.
Club statistics
References
External links
1983 births
Living people
Momoyama Gakuin University alumni
Association football people from Fukuoka Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Tokyo Verdy players
Fagiano Okayama players
Giravanz Kitakyushu players
Men's association football defenders |
https://en.wikipedia.org/wiki/Pinched%20torus | In mathematics, and especially topology and differential geometry, a pinched torus (or croissant surface) is a kind of two-dimensional surface. It gets its name from its resemblance to a torus that has been pinched at a single point. A pinched torus is an example of an orientable, compact 2-dimensional pseudomanifold.
Parametrisation
A pinched torus is easily parametrisable. Let us write . An example of such a parametrisation − which was used to plot the picture − is given by where:
Topology
Topologically, the pinched torus is homotopy equivalent to the wedge of a sphere and a circle. It is homeomorphic to a sphere with two distinct points being identified.
Homology
Let P denote the pinched torus. The homology groups of P over the integers can be calculated. They are given by:
Cohomology
The cohomology groups of P over the integers can be calculated. They are given by:
References
Surfaces |
https://en.wikipedia.org/wiki/2010%E2%80%9311%20Kitchee%20SC%20season | The 2010–11 season is the 32nd season of Kitchee SC in Hong Kong First Division League. The team is coached by Spain coach Josep Gombau.
Key events
Squad statistics
Statistics accurate as of match played 16 September 2010
Matches
Competitive
Hong Kong First Division League
Hong Kong Senior Challenge Shield
Singapore Cup
Quarter-final
References
Kitchee
Kitchee SC seasons |
https://en.wikipedia.org/wiki/Tomoki%20Hidaka | is a former Japanese football player.
Club statistics
References
External links
1980 births
Living people
University of Teacher Education Fukuoka alumni
Association football people from Miyazaki Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Giravanz Kitakyushu players
Men's association football midfielders
People from Miyazaki (city) |
https://en.wikipedia.org/wiki/Local%20feature%20size | Local feature size refers to several related concepts in computer graphics and computational geometry for measuring the size of a geometric object near a particular point.
Given a smooth manifold , the local feature size at any point is the distance between and the medial axis of .
Given a planar straight-line graph, the local feature size at any point is the radius of the smallest closed ball centered at which intersects any two disjoint features (vertices or edges) of the graph.
See also
Nearest neighbour function
References
Geometric algorithms |
https://en.wikipedia.org/wiki/Shinya%20Sato%20%28footballer%29 | is a former Japanese football player.
Club statistics
References
External links
1978 births
Living people
Saga University alumni
Japanese men's footballers
J2 League players
Japan Football League players
FC Ryukyu players
Giravanz Kitakyushu players
Men's association football midfielders
Association football people from Kumamoto |
https://en.wikipedia.org/wiki/Pseudomanifold | In mathematics, a pseudomanifold is a special type of topological space. It looks like a manifold at most of its points, but it may contain singularities. For example, the cone of solutions of forms a pseudomanifold.
A pseudomanifold can be regarded as a combinatorial realisation of the general idea of a manifold with singularities. The concepts of orientability, orientation and degree of a mapping make sense for pseudomanifolds and moreover, within the combinatorial approach, pseudomanifolds form the natural domain of definition for these concepts.
Definition
A topological space X endowed with a triangulation K is an n-dimensional pseudomanifold if the following conditions hold:
(pure) is the union of all n-simplices.
Every is a face of exactly one or two n-simplices for n > 1.
For every pair of n-simplices σ and σ' in K, there is a sequence of n-simplices such that the intersection is an for all i = 0, ..., k−1.
Implications of the definition
Condition 2 means that X is a non-branching simplicial complex.
Condition 3 means that X is a strongly connected simplicial complex.
If we require Condition 2 to hold only for in sequences of in Condition 3, we obtain an equivalent definition only for n=2. For n≥3 there are examples of combinatorial non-pseudomanifolds that are strongly connected through sequences of satisfying Condition 2.
Decomposition
Strongly connected n-complexes can always be assembled from gluing just two of them at . However, in general, construction by gluing can lead to non-pseudomanifoldness (see Figure 2).
Nevertheless it is always possible to decompose a non-pseudomanifold surface into manifold parts cutting only at singular edges and vertices (see Figure 2 in blue). For some surfaces several non-equivalent options are possible (see Figure 3).
On the other hand, in higher dimension, for n>2, the situation becomes rather tricky.
In general, for n≥3, n-pseudomanifolds cannot be decomposed into manifold parts only by cutting at singularities (see Figure 4).
For n≥3, there are n-complexes that cannot be decomposed, even into pseudomanifold parts, only by cutting at singularities.
Related definitions
A pseudomanifold is called normal if the link of each simplex with codimension ≥ 2 is a pseudomanifold.
Examples
A pinched torus (see Figure 1) is an example of an orientable, compact 2-dimensional pseudomanifold.
(Note that a pinched torus is not a normal pseudomanifold, since the link of a vertex is not connected.)
Complex algebraic varieties (even with singularities) are examples of pseudomanifolds.
(Note that real algebraic varieties aren't always pseudomanifolds, since their singularities can be of codimension 1, take xy=0 for example.)
Thom spaces of vector bundles over triangulable compact manifolds are examples of pseudomanifolds.
Triangulable, compact, connected, homology manifolds over Z are examples of pseudomanifolds.
Complexes obtained gluing two 4-simplices at a common tetrahed |
https://en.wikipedia.org/wiki/Steve%20Thompson%20%28writer%29 | Stephen Thompson (born 1967) is a British playwright and screenwriter.
Background
Thompson studied at the University of Warwick. He gained a maths degree but also did some English studies in his third year. Thompson worked as a maths teacher for twelve years at Tiffin School, and was head of maths.
Thompson left teaching in 2000 and became a full-time dad and house husband to his children. He has stated this was because his wife was earning much more money than him.
Career
In an interview, Thompson said "I took a sudden left turn and became a scriptwriter.” He trained on the RADA playwrights' course, and his first play, Damages, was performed at the Bush Theatre in 2004, winning the Meyer-Whitworth Award for new writing.
In 2005, he was made Pearson writer in residence at the Bush Theatre where his next play Whipping It Up was also performed. Roaring Trade was performed by Paines Plough at the Soho Theatre. His most recent play No Naughty Bits was performed at Hampstead Theatre in September 2011.
His first credit for television came on the medical soap Doctors in 2005. Since then, he has contributed scripts for several popular shows, including Silk, Upstairs Downstairs, Doctor Who, and the first three series of Sherlock (the latter two both in collaboration with Steven Moffat). In 2016, he created the period drama series Jericho, which re-imagines the building of the Ribblehead Viaduct. In April 2016, ITV confirmed that a second series of Jericho was not going to be commissioned.
On 3 October 2018, it was announced that Thompson would be teaming with Frank Spotnitz to develop a drama about Leonardo da Vinci. On 17 February 2019, it was revealed that Thompson was developing an adaptation of Runestaff for BBC. On 16 August 2019, the BBC announced they would broadcast Thompson's adaptation of the popular Liebermann novels by Frank Tallis, Vienna Blood. On 6 July 2020, Endor Productions and MR Film announced that a second series had been jointly recommissioned by ORF, ZDF, BBC and PBS. On 22 February 2022, a third series was commissioned.
Bibliography
Damages, Josef Weinberger Plays, 2004.
Whipping It Up, Nick Hern Books, 2006.
Roaring Trade, Nick Hern Books, 2009.
No Naughty Bits, Nick Hern Books, 2011.
Television writing credits
Personal life
Thompson is married to the media barrister Lorna Skinner and they have five children.
References
External links
Living people
1967 births
Date of birth missing (living people)
Place of birth missing (living people)
English male dramatists and playwrights
English dramatists and playwrights
English television writers
British science fiction writers
English screenwriters
English male screenwriters
British male television writers |
https://en.wikipedia.org/wiki/List%20of%20Cruzeiro%20Esporte%20Clube%20records%20and%20statistics | Records of Brazilian football club Cruzeiro Esporte Clube.
Records and statistics
Campeonato Brasileiro Série A record
italic = ongoing
Campeonato Brasileiro Série B record
italic = ongoing
Top appearances
stats updated as of January 5, 2022
italic = active player
Top scorers
Notable season statistics
2003 Serie A Title Campaign
In 2003 Cruzeiro won the National Triple Crown, winning national cup and both the state and national championships. The stats below regard the historical, record breaking Serie A title achieved that year, with 100 points and breaking the 100 goal mark. To this day, no team has won the title with a higher point percentage. That year, Cruzeiro also set a record for the most consecutive wins in the Campeonato Brasileiro Série A. On two occasions, the team won 8 games in a row, a record which is still unbeaten.
The team that year was led by coach Vanderlei Luxemburgo and captain/midfielder Alex, with many other notable players in the squad, such as 1994 FIFA World Cup winner Zinho, along with Colombia national football team legend Aristizábal, Brazil national football team regulars Gomes, Cris, Luisão, Maicon and Felipe Melo, as well as big name players such as Claudio Maldonado, Deivid de Souza, Maurinho and Edu Dracena.
Cruzeiro and defending champions Santos FC fought hard for the lead for most of the championship, until on round 29, Cruzeiro took the lead for good. The two teams were tied on points until round 31, when Cruzeiro, with a brace from Aristizábal, took a major 3-0 home win against second placed Santos, who boasted of national greats such as Robinho, Diego Ribas, Elano and Ricardo Oliveira. From then on, Cruzeiro only increased its lead until being confirmed champions with 2 rounds advance.
Having led the team to the domestic treble and scored 23 goals on the 2003 Campeonato Brasileiro Série A, Alex won the 2003 Bola de Ouro award and racked up all the years best player awards. Defender Maurinho and Chilean midfielder Claudio Maldonado also received individual awards.
2013 Serie A Title Campaign
After losing the 2009 Copa Libertadores final, Cruzeiro struggled for a couple of seasons, undergoing major changes in its squad and director board and unable to play in its home, Mineirão, while the stadium was being prepared for the 2014 FIFA World Cup.
In 2013 Cruzeiro was back to its revamped home stadium and was finally able to direct higher investments to its football department. President Gilvan Tavares, along with director Alexandre Mattos signed coach Marcelo Oliveira and over 20 players during the 2012-2013 off-season.
The team quickly started showing what it was capable of, barely missing out on the regional championship title and starting the 2013 Campeonato Brasileiro Série A with a stunning 5-0 victory over Goiás. After alternating with Botafogo on 1st place for many rounds, the team reached a definitive lead on the 16th round, which was carried on until reaching the title, before even p |
https://en.wikipedia.org/wiki/Location%20testing%20for%20Gaussian%20scale%20mixture%20distributions | In statistics, the topic of location testing for Gaussian scale mixture distributions arises in some particular types of situations where the more standard Student's t-test is inapplicable. Specifically, these cases allow tests of location to be made where the assumption that sample observations arise from populations having a normal distribution can be replaced by the assumption that they arise from a Gaussian scale mixture distribution. The class of Gaussian scale mixture distributions contains all symmetric stable distributions, Laplace distributions, logistic distributions, and exponential power distributions, etc.
Introduce
tGn(x),
the counterpart of Student's t-distribution for Gaussian scale mixtures. This means that if we test the null hypothesis that the center of a Gaussian scale mixture distribution is 0, say, then tnG(x) (x ≥ 0) is the infimum of all monotone nondecreasing functions u(x) ≥ 1/2, x ≥ 0 such that if the critical values of the test are u−1(1 − α), then the significance level is at most α ≥ 1/2 for all Gaussian scale mixture distributions [tGn(x) = 1 − tGn(−x),for x < 0]. An explicit formula for tGn(x), is given in the papers in the references in terms of Student’s t-distributions, tk, k = 1, 2, …, n. Introduce
ΦG(x):= limn → ∞ tGn(x),
the Gaussian scale mixture counterpart of the standard normal cumulative distribution function, Φ(x).
Theorem. ΦG(x) = 1/2 for 0 ≤ x < 1, ΦG(1) = 3/4, ΦG(x) = C(x/(2 − x2)1/2) for quantiles between 1/2 and 0.875, where C(x) is the standard Cauchy cumulative distribution function. This is the convex part of the curve ΦG(x), x ≥ 0 which is followed by a linear section ΦG(x) = x/(2) + 1/2 for 1.3136… < x < 1.4282... Thus the 90% quantile is exactly 4/5. Most importantly,
ΦG(x) = Φ(x) for x ≥ .
Note that Φ() = 0.958…, thus the classical 95% confidence interval for the unknown expected value of Gaussian distributions covers the center of symmetry with at least 95% probability for Gaussian scale mixture distributions. On the other hand, the 90% quantile of ΦG(x) is 4/5 = 1.385… > Φ−1(0.9) = 1.282… The following critical values are important in applications: 0.95 = Φ(1.645) = ΦG(1.651), and 0.9 = Φ(1.282) = ΦG(1.386).
For the extension of the Theorem to all symmetric unimodal distributions one can start with a classical result of Aleksandr Khinchin: namely that all symmetric unimodal distributions are scale mixtures of symmetric uniform
distributions.
Open problem
The counterpart of the Theorem above for the class of all symmetric distributions, or equivalently, for the class of scale mixtures of coin flipping random variables, leads to the following problem:
How many vertices of an n-dimensional unit cube can be covered by a sphere with given radius r (and varying center)? Answer this question for all positive integers n and all positive real numbers r. (Certain special cases can be easy to compute.)
References
Statistical tests |
https://en.wikipedia.org/wiki/Fussballdaten.de | fussballdaten.de is a German-language website that predominantly collects comprehensive statistics on the top five tiers of German football.
The website offers statistics on every Bundesliga, 2. Bundesliga and 3. Liga match and team since the leagues' foundation in 1963, 1974 and 2008, respectively.
References
External links
Online databases
German sport websites
Football mass media in Germany |
https://en.wikipedia.org/wiki/Eli%20Maor | Eli Maor (born 1937), an historian of mathematics, is the author of several books about the history of mathematics. Eli Maor received his PhD at the Technion – Israel Institute of Technology. He teaches the history of mathematics at Loyola University Chicago. Maor was the editor of the article on trigonometry for the Encyclopædia Britannica.
Asteroid 226861 Elimaor, discovered at the Jarnac Observatory in 2004, was named in his honor. The official was published by the Minor Planet Center on 22 July 2013 ().
Selected works
To Infinity and Beyond: A Cultural History of the Infinite, 1991, Princeton University Press.
e:The story of a Number, by Eli Maor, Princeton University Press (Princeton, New Jersey) (1994)
Venus in Transit, 2000, Princeton University Press.
Trigonometric Delights, Princeton University Press, 2002 . Ebook version, in PDF format, full text presented.
The Pythagorean Theorem: A 4,000-Year History, 2007, Princeton University Press,
The Facts on File Calculus Handbook (Facts on File, 2003), 2005, Checkmark Books, an encyclopedia of calculus concepts geared for high school and college students
References
Israeli mathematicians
Israeli historians
Historians of mathematics
Living people
Loyola University Chicago faculty
Technion – Israel Institute of Technology alumni
1937 births |
https://en.wikipedia.org/wiki/Categorical%20quantum%20mechanics | Categorical quantum mechanics is the study of quantum foundations and quantum information using paradigms from mathematics and computer science, notably monoidal category theory. The primitive objects of study are physical processes, and the different ways that these can be composed. It was pioneered in 2004 by Samson Abramsky and Bob Coecke. Categorical quantum mechanics is entry 18M40 in MSC2020.
Mathematical setup
Mathematically, the basic setup is captured by a dagger symmetric monoidal category: composition of morphisms models sequential composition of processes, and the tensor product describes parallel composition of processes. The role of the dagger is to assign to each state a corresponding test. These can then be adorned with more structure to study various aspects. For instance:
A dagger compact category allows one to distinguish between an "input" and "output" of a process. In the diagrammatic calculus, it allows wires to be bent, allowing for a less restricted transfer of information. In particular, it allows entangled states and measurements, and gives elegant descriptions of protocols such as quantum teleportation. In quantum theory, it being compact closed is related to the Choi-Jamiołkowski isomorphism (also known as process-state duality), while the dagger structure captures the ability to take adjoints of linear maps.
Considering only the morphisms that are completely positive maps, one can also handle mixed states, allowing the study of quantum channels categorically.
Wires are always two-ended (and can never be split into a Y), reflecting the no-cloning and no-deleting theorems of quantum mechanics.
Special commutative dagger Frobenius algebras model the fact that certain processes yield classical information, that can be cloned or deleted, thus capturing classical communication.
In early works, dagger biproducts were used to study both classical communication and the superposition principle. Later, these two features have been separated.
Complementary Frobenius algebras embody the principle of complementarity, which is used to great effect in quantum computation, as in the ZX-calculus.
A substantial portion of the mathematical backbone to this approach is drawn from 'Australian category theory', most notably from work by Max Kelly and M. L. Laplaza, Andre Joyal and Ross Street, A. Carboni and R. F. C. Walters, and
Steve Lack.
Modern textbooks include Categories for quantum theory and Picturing quantum processes.
Diagrammatic calculus
One of the most notable features of categorical quantum mechanics is that the compositional structure can be faithfully captured by string diagrams.
These diagrammatic languages can be traced back to Penrose graphical notation, developed in the early 1970s. Diagrammatic reasoning has been used before in quantum information science in the quantum circuit model, however, in categorical quantum mechanics primitive gates like the CNOT-gate arise as composites of more basic algebr |
https://en.wikipedia.org/wiki/Memory%20geometry | In the design of modern computers, memory geometry describes the internal structure of random-access memory. Memory geometry is of concern to consumers upgrading their computers, since older memory controllers may not be compatible with later products. Memory geometry terminology can be confusing because of the number of overlapping terms.
The geometry of a memory system can be thought of as a multi-dimensional array. Each dimension has its own characteristics and physical realization. For example, the number of data pins on a memory module is one dimension.
Physical features
Memory geometry describes the logical configuration of a RAM module, but consumers will always find it easiest to grasp the physical configuration. Much of the confusion surrounding memory geometry occurs when the physical configuration obfuscates the logical configuration. The first defining feature of RAM is form factor. RAM modules can be in compact SO-DIMM form for space constrained applications like laptops, printers, embedded computers, and small form factor computers, and in DIMM format, which is used in most desktops.
The other physical characteristics, determined by physical examination, are the number of memory chips, and whether both sides of the memory "stick" are populated. Modules with the number of RAM chips equal to some power of two do not support memory error detection or correction. If there are extra RAM chips (between powers of two), these are used for ECC.
RAM modules are 'keyed' by indentations on the sides, and along the bottom of the module. This designates the technology, and classification of the modules, for instance whether it is DDR2, or DDR3, and whether it is suitable for desktops, or for servers. Keying was designed to make it difficult to install incorrect modules in a system (but there are more requirements than are embodied in keys). It is important to make sure that the keying of the module matches the key of the slot it is intended to occupy.
Additional, non-memory chips on the module may be an indication that it was designed for high capacity memory systems for servers, and that the module may be incompatible with mass-market systems.
As the next section of this article will cover the logical architecture, which covers the logical structure spanning every populated slot in a system, the physical features of the slots themselves become important. By consulting the documentation of your motherboard, or reading the labels on the board itself, you can determine the underlying logical structure of the slots. When there is more than one slot, they are numbered, and when there is more than one channel, the different slots are separated in that way as well – usually color-coded.
Logical features
In the 1990s, specialized computers were released where two computers that each had their own memory controller could be networked at such a low level that the software run could use the memory, or CPU of either computer as if they wer |
https://en.wikipedia.org/wiki/Poincar%C3%A9%20complex | In mathematics, and especially topology, a Poincaré complex (named after the mathematician Henri Poincaré) is an abstraction of the singular chain complex of a closed, orientable manifold.
The singular homology and cohomology groups of a closed, orientable manifold are related by Poincaré duality. Poincaré duality is an isomorphism between homology and cohomology groups. A chain complex is called a Poincaré complex if its homology groups and cohomology groups have the abstract properties of Poincaré duality.
A Poincaré space is a topological space whose singular chain complex is a Poincaré complex. These are used in surgery theory to analyze manifold algebraically.
Definition
Let be a chain complex of abelian groups, and assume that the homology groups of are finitely generated. Assume that there exists a map , called a chain-diagonal, with the property that . Here the map denotes the ring homomorphism known as the augmentation map, which is defined as follows: if , then .
Using the diagonal as defined above, we are able to form pairings, namely:
,
where denotes the cap product.
A chain complex C is called geometric if a chain-homotopy exists between and , where is the transposition/flip given by .
A geometric chain complex is called an algebraic Poincaré complex, of dimension n, if there exists an infinite-ordered element of the n-dimensional homology group, say , such that the maps given by
are group isomorphisms for all . These isomorphisms are the isomorphisms of Poincaré duality.
Example
The singular chain complex of an orientable, closed n-dimensional manifold is an example of a Poincaré complex, where the duality isomorphisms are given by capping with the fundamental class .
See also
Poincaré space
References
– especially Chapter 2
External links
Classifying Poincaré complexes via fundamental triples on the Manifold Atlas
Algebraic topology
Homology theory
Duality theories |
https://en.wikipedia.org/wiki/Copa%20Sudamericana%20records%20and%20statistics | This page details the records and statistics of the Copa Sudamericana football tournament. The Copa Sudamericana is an international club tournament played annually in South America. It includes 3-8 teams from all ten CONMEBOL members. It is typically held from August to December and it consists of six stages. The all-time leader in titles won are Argentina's Boca Juniors and Independiente, Ecuadorian's Independiente del Valle and LDU Quito and Brazilian Athletico Paranaense.
General performances
By club
By nation
Number of participating clubs by country
Updated until 2023 edition.
Teams in bold: winner of the edition.
Teams in italics: runner-up of the edition.
Clubs
By semifinal appearances
In bold, teams that were finalists that year.
By country
By quarterfinal appearances
By country
Specific group stage records
Best group stage
Worst group stage
Unbeaten sides
Five clubs have won the Copa Sudamericana unbeaten:
Universidad de Chile had 10 wins and 2 draws in 2011
São Paulo had 5 wins and 5 draws in 2012
River Plate had 8 wins and 2 draws in 2014
Defensa y Justicia had 6 wins and 3 draws in 2020
Independiente del Valle had 6 wins and 1 draw in 2023
Finals success rate
Four clubs has appeared in the finals of the Copa Sudamericana more than once with a 100% success rate:
Boca Juniors (2004, 2005)
Independiente (2010, 2017)
Athletico Paranaense (2018, 2021)
Independiente del Valle (2019, 2022)
Eleven clubs have appeared in the final once, being victorious on that occasion:
San Lorenzo (2002)
Cienciano (2003)
Pachuca (2006)
Arsenal (2007)
Internacional (2008)
Universidad de Chile (2011)
Santa Fe (2015)
Chapecoense (2016)
Defensa y Justicia (2020)
On the other end, fifteen clubs have appeared in the finals and have never won the tournament. One of those clubs has appeared in the finals more than once, losing on each occasion:
Atlético Nacional (2002, 2014, 2016)
Consecutive participations
Emelec have the record number of consecutive participations with 8 from 2009 to 2016.
Goals
Biggest wins
Oriente Petrolero 1–10 Fluminense (May 26, 2022, also largest away win)
Defensor Sporting 9–0 Sport Huancayo (September 16, 2010)
Biggest two leg win
Alajuelense 2–11 Colo-Colo (2006 Copa Sudamericana)
Consecutive finals
One team has appeared in a record of two consecutive finals:
Boca Juniors (2004, 2005)
Successful defending
Only one club have successfully defended the trophy: Boca Juniors (2005)
References |
https://en.wikipedia.org/wiki/Steenrod%20problem | In mathematics, and particularly homology theory, Steenrod's Problem (named after mathematician Norman Steenrod) is a problem concerning the realisation of homology classes by singular manifolds.
Formulation
Let be a closed, oriented manifold of dimension , and let be its orientation class. Here denotes the integral, -dimensional homology group of . Any continuous map defines an induced homomorphism . A homology class of is called realisable if it is of the form where . The Steenrod problem is concerned with describing the realisable homology classes of .
Results
All elements of are realisable by smooth manifolds provided . Moreover, any cycle can be realized by the mapping of a pseudo-manifold.
The assumption that M be orientable can be relaxed. In the case of non-orientable manifolds, every homology class of , where denotes the integers modulo 2, can be realized by a non-oriented manifold, .
Conclusions
For smooth manifolds M the problem reduces to finding the form of the homomorphism , where is the oriented bordism group of X. The connection between the bordism groups and the Thom spaces MSO(k) clarified the Steenrod problem by reducing it to the study of the homomorphisms . In his landmark paper from 1954, René Thom produced an example of a non-realisable class, , where M is the Eilenberg–MacLane space .
See also
Singular homology
Pontryagin-Thom construction
Cobordism
References
External links
Thom construction and the Steenrod problem on MathOverflow
Explanation for the Pontryagin-Thom construction
Homology theory
Manifolds
Geometric topology |
https://en.wikipedia.org/wiki/Cubas | Cubas is a Brazilian district of the mining city of Ferros, in the state of Minas Gerais. According to the Brazilian Institute of Geography and Statistics (IBGE), its population in 2010 was 1,385 inhabitants, 687 men and 698 women, with a total of 540 private households.
Populated places in Minas Gerais |
https://en.wikipedia.org/wiki/2010%E2%80%9311%20FK%20Partizan%20season | The 2010–11 season was FK Partizan's 5th season in Serbian SuperLiga. This article shows player statistics and all matches (official and friendly) that the club had and who played during the 2010–11 season.
Tournaments
Players
Squad information
Top scorers
Includes all competitive matches. The list is sorted by shirt number when total goals are equal.
Squad statistics
Competitions
Serbian SuperLiga
Overview
League table
Matches
Serbian Cup
Final
1 The match was abandoned in the 83rd minute with Partizan leading 2-1 when Vojvodina walked off to protest the quality of the officiating. Originally, this was declared the final score and the Cup was awarded to Partizan, but on May 16, 2011, after further investigation from Serbian FA concerning the match, the result was officially registered as a 3–0 win to Partizan.
UEFA Champions League
Second qualifying round
Third qualifying round
Play-off round
Group stage
Friendlies
Transfers
In
Out
Sponsors
External links
Official website
Partizanopedia 2010-11 (in Serbian)
FK Partizan seasons
Partizan
Partizan
Serbian football championship-winning seasons |
https://en.wikipedia.org/wiki/Quasi-separated%20morphism | In algebraic geometry, a morphism of schemes from to is called quasi-separated if the diagonal map from to is quasi-compact (meaning that the inverse image of any quasi-compact open set is quasi-compact). A scheme is called quasi-separated if the morphism to Spec is quasi-separated. Quasi-separated algebraic spaces and algebraic stacks and morphisms between them are defined in a similar way, though some authors include the condition that is quasi-separated as part of the definition of an algebraic space or algebraic stack . Quasi-separated morphisms were introduced by as a generalization of separated morphisms.
All separated morphisms (and all morphisms of Noetherian schemes) are automatically quasi-separated. Quasi-separated morphisms are important for algebraic spaces and algebraic stacks, where many natural morphisms are quasi-separated but not separated.
The condition that a morphism is quasi-separated often occurs together with the condition that it is quasi-compact.
Examples
If is a locally Noetherian scheme then any morphism from to any scheme is quasi-separated, and in particular is a quasi-separated scheme.
Any separated scheme or morphism is quasi-separated.
The line with two origins over a field is quasi-separated over the field but not separated.
If is an "infinite dimensional vector space with two origins" over a field then the morphism from to spec is not quasi-separated. More precisely consists of two copies of Spec glued together by identifying the nonzero points in each copy.
The quotient of an algebraic space by an infinite discrete group acting freely is often not quasi-separated. For example, if is a field of characteristic then the quotient of the affine line by the group of integers is an algebraic space that is not quasi-separated. This algebraic space is also an example of a group object in the category of algebraic spaces that is not a scheme; quasi-separated algebraic spaces that are group objects are always group schemes. There are similar examples given by taking the quotient of the group scheme by an infinite subgroup, or the quotient of the complex numbers by a lattice.
References
Algebraic geometry |
https://en.wikipedia.org/wiki/List%20of%20localities%20in%20Waikato | This is a list of localities in Waikato as defined by government agency Statistics New Zealand in 2013, listed by the territorial authorities to which each locality belongs. Waikato is a region of New Zealand in the central North Island which reaches from coast to coast and from Coromandel Peninsula in the north to Lake Taupō and King Country in the south. Many boundaries and names were changed in the 2018 census. It is bordered by Auckland to the north, Bay of Plenty to the east, and Taranaki, Manawatū-Whanganui and Hawke's Bay to the south.
Thames-Coromandel District
The Thames-Coromandel District is located in the area around the Firth of Thames and Coromandel Peninsula, to the southeast of Auckland. At the 2006 Census, Thames-Coromandel had 25,941 people (including 4,020 self-identified Māori) and 22,704 occupied dwellings. The district council is seated in the district's largest town, Thames, and was constituted before any other district council in 1975. Thames is located in the southwest of the district; the other major settlements are Whitianga in the northeast and Whangamatā in the southeast.
Hauraki District
Waikato District
Matamata-Piako District
Hamilton City
Waipa District
Ōtorohanga District
South Waikato District
Waitomo District
Taupō District
Rotorua District
Area outside territorial authority
References |
https://en.wikipedia.org/wiki/Whitney%20topologies | In mathematics, and especially differential topology, functional analysis and singularity theory, the Whitney topologies are a countably infinite family of topologies defined on the set of smooth mappings between two smooth manifolds. They are named after the American mathematician Hassler Whitney.
Construction
Let M and N be two real, smooth manifolds. Furthermore, let C∞(M,N) denote the space of smooth mappings between M and N. The notation C∞ means that the mappings are infinitely differentiable, i.e. partial derivatives of all orders exist and are continuous.
Whitney Ck-topology
For some integer , let Jk(M,N) denote the k-jet space of mappings between M and N. The jet space can be endowed with a smooth structure (i.e. a structure as a C∞ manifold) which make it into a topological space. This topology is used to define a topology on C∞(M,N).
For a fixed integer consider an open subset and denote by Sk(U) the following:
The sets Sk(U) form a basis for the Whitney Ck-topology on C∞(M,N).
Whitney C∞-topology
For each choice of , the Whitney Ck-topology gives a topology for C∞(M,N); in other words the Whitney Ck-topology tells us which subsets of C∞(M,N) are open sets. Let us denote by Wk the set of open subsets of C∞(M,N) with respect to the Whitney Ck-topology. Then the Whitney C∞-topology is defined to be the topology whose basis is given by W, where:
Dimensionality
Notice that C∞(M,N) has infinite dimension, whereas Jk(M,N) has finite dimension. In fact, Jk(M,N) is a real, finite-dimensional manifold. To see this, let denote the space of polynomials, with real coefficients, in m variables of order at most k and with zero as the constant term. This is a real vector space with dimension
Writing } then, by the standard theory of vector spaces and so is a real, finite-dimensional manifold. Next, define:
Using b to denote the dimension Bkm,n, we see that , and so is a real, finite-dimensional manifold.
In fact, if M and N have dimension m and n respectively then:
Topology
Given the Whitney C∞-topology, the space C∞(M,N) is a Baire space, i.e. every residual set is dense.
References
Differential topology
Singularity theory |
https://en.wikipedia.org/wiki/H%20topology | In algebraic geometry, the h topology is a Grothendieck topology introduced by Vladimir Voevodsky to study the homology of schemes. It combines several good properties possessed by its related "sub"topologies, such as the qfh and cdh topologies. It has subsequently been used by Beilinson to study p-adic Hodge theory, in Bhatt and Scholze's work on projectivity of the affine Grassmanian, Huber and Jörder's study of differential forms, etc.
Definition
Voevodsky defined the h topology to be the topology associated to finite families of morphisms of finite type such that is a universal topological epimorphism (i.e., a set of points in the target is an open subset if and only if its preimage is open, and any base change also has this property). Voevodsky worked with this topology exclusively on categories of schemes of finite type over a Noetherian base scheme S.
Bhatt-Scholze define the h topology on the category of schemes of finite presentation over a qcqs base scheme to be generated by -covers of finite presentation. They show (generalising results of Voevodsky) that the h topology is generated by:
fppf-coverings, and
families of the form where
is a proper morphism of finite presentation,
is a closed immersion of finite presentation, and
is an isomorphism over .
Note that is allowed in an abstract blowup, in which case Z is a nilimmersion of finite presentation.
Examples
The h-topology is not subcanonical, so representable presheaves are almost never h-sheaves. However, the h-sheafification of representable sheaves are interesting and useful objects; while presheaves of relative cycles are not representable, their associated h-sheaves are representable in the sense that there exists a disjoint union of quasi-projective schemes whose h-sheafifications agree with these h-sheaves of relative cycles.
Any h-sheaf in positive characteristic satisfies where we interpret as the colimit over the Frobenii (if the Frobenius is of finite presentation, and if not, use an analogous colimit consisting of morphisms of finite presentation). In fact, (in positive characteristic) the h-sheafification of the structure sheaf is given by . So the structure sheaf "is an h-sheaf on the category of perfect schemes" (although this sentence doesn't really make sense mathematically since morphisms between perfect schemes are almost never of finite presentation). In characteristic zero similar results hold with perfection replaced by semi-normalisation.
Huber-Jörder study the h-sheafification of the presheaf of Kähler differentials on categories of schemes of finite type over a characteristic zero base field . They show that if X is smooth, then , and for various nice non-smooth X, the sheaf recovers objects such as reflexive differentials and torsion-free differentials. Since the Frobenius is an h-covering, in positive characteristic we get for , but analogous results are true if we replace the h-topology with the cdh-topology.
By the Nu |
https://en.wikipedia.org/wiki/List%20of%20topologies%20on%20the%20category%20of%20schemes | The most fundamental item of study in modern algebraic geometry is the category of schemes. This category admits many different Grothendieck topologies, each of which is well-suited for a different purpose. This is a list of some of the topologies on the category of schemes.
cdh topology A variation of the h topology
Étale topology Uses etale morphisms.
fppf topology Faithfully flat of finite presentation
fpqc topology Faithfully flat quasicompact
h topology Coverings are universal topological epimorphisms
v-topology (also called universally subtrusive topology): coverings are maps which admit liftings for extensions of valuation rings
topology A variation of the Nisnevich topology
Nisnevich topology Uses etale morphisms, but has an extra condition about isomorphisms between residue fields.
qfh topology Similar to the h topology with a quasifiniteness condition.
Zariski topology Essentially equivalent to the "ordinary" Zariski topology.
Smooth topology Uses smooth morphisms, but is usually equivalent to the etale topology (at least for schemes).
Canonical topology The finest such that all representable functors are sheaves.
See also
References
Belmans, Pieter. Grothendieck topologies and étale cohomology
Algebraic geometry |
https://en.wikipedia.org/wiki/Multiplier%20ideal | In commutative algebra, the multiplier ideal associated to a sheaf of ideals over a complex variety and a real number c consists (locally) of the functions h such that
is locally integrable, where the fi are a finite set of local generators of the ideal. Multiplier ideals were independently introduced by (who worked with sheaves over complex manifolds rather than ideals) and , who called them adjoint ideals.
Multiplier ideals are discussed in the survey articles , , and .
Algebraic geometry
In algebraic geometry, the multiplier ideal of an effective -divisor measures singularities coming from the fractional parts of D. Multiplier ideals are often applied in tandem with vanishing theorems such as the Kodaira vanishing theorem and the Kawamata–Viehweg vanishing theorem.
Let X be a smooth complex variety and D an effective -divisor on it. Let be a log resolution of D (e.g., Hironaka's resolution). The multiplier ideal of D is
where is the relative canonical divisor: . It is an ideal sheaf of . If D is integral, then .
See also
Canonical singularity
Test ideal
Nadel vanishing theorem
References
Commutative algebra
Algebraic geometry |
https://en.wikipedia.org/wiki/Maryam%20Mirzakhani%20Prize%20in%20Mathematics | The Maryam Mirzakhani Prize in Mathematics (ex-NAS Award in Mathematics until 2012) is awarded by the U.S. National Academy of Sciences "for excellence of research in the mathematical sciences published within the past ten years." Named after the Iranian mathematician Maryam Mirzakhani, the prize has been awarded every four years since 1988.
Award winners
Source:
2022: Camillo De Lellis "for his fundamental contributions to the study of dissipative solutions to the incompressible Euler equations and to the regularity theory of minimal surfaces."
2020: Larry Guth "for developing surprising, original, and deep connections between geometry, analysis, topology, and combinatorics, which have led to the solution of, or major advances on, many outstanding problems in these fields."
2012: Michael J. Hopkins "For his leading role in the development of homotopy theory, which has both reinvigorated algebraic topology as a central field in mathematics and led to the resolution of the Kervaire invariant problem for framed manifolds."
2008: Clifford H. Taubes "For groundbreaking work relating to Seiberg-Witten and Gromov-Witten invariants of symplectic 4-manifolds, and his proof of Weinstein conjecture for all contact 3-manifolds."
2004: Dan-Virgil Voiculescu "For the theory of free probability, in particular, using random matrices and a new concept of entropy to solve several hitherto intractable problems in von Neumann algebras."
2000: Ingrid Daubechies "For fundamental discoveries on wavelets and wavelet expansions and for her role in making wavelet methods a practical basic tool of applied mathematics."
1996: Andrew J. Wiles "For his proof of Fermat's Last Theorem by discovering a beautiful strategy to establish a major portion of the Shimura-Taniyama conjecture, and for his courage and technical power in bringing his idea to completion."
1992: Robert MacPherson "For his role in the introduction and application of radically new approaches to the topology of singular spaces, including characteristics classes, intersection homology, perverse sheaves, and stratified Morse theory."
1988: Robert P. Langlands "For his extraordinary vision, which has brought the theory of group representations into a revolutionary new relationship with the theory of automorphic forms and number theory."
See also
List of mathematics awards
References
Awards established in 1988
Mathematics awards
Awards of the United States National Academy of Sciences |
https://en.wikipedia.org/wiki/Rich%C3%A1rd%20Frank | Richárd Frank (born 28 August 1990) is a Hungarian striker who plays for Pécsi Mecsek FC.
Career statistics
References
External links
Player profile at HLSZ
1990 births
Living people
Footballers from Pécs
Hungarian men's footballers
Men's association football forwards
Újpest FC players
MTK Budapest FC players
Tatabányai SC players
Pécsi MFC players
Nemzeti Bajnokság I players
Men's association football midfielders
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/Zigzag%20stitch | A zigzag stitch is variant geometry of the lockstitch. It is a back-and-forth stitch used where a straight stitch will not suffice, such as in reinforcing buttonholes, in stitching stretchable fabrics, and in temporarily joining two work pieces edge-to-edge.
When creating a zigzag stitch, the side to side motion of the sewing machine's needle is controlled by a cam. As the cam rotates, a fingerlike follower, connected to the needle bar, rides along the cam and tracks its indentations. As the follower moves in and out, the needle bar is moved from side to side. Sewing machines made before the mid-1950s mostly lack this hardware and so cannot natively produce a zigzag stitch. However there are often shank-driven attachments available which enable them to achieve a similar effect by moving the fabric from side to side instead of the needle bar.
Helen Blanchard is said to have invented and patented the first zigzag stitch sewing machine in 1873. The first dedicated zigzag machine for the consumer market, whilst many assume was the Singer 206K, introduced in 1936, was in fact the Necchi BU, introduced in Italy in 1932.
Zigzagger attachments
Older sewing machines designed to sew only a straight stitch can be adapted to sew a zigzag by means of an attachment. The attachment replaces the machine's presser foot with its own, and draws mechanical power from the machine's needle clamp (which requires the needle clamp to have a side-facing thumbscrew). It creates a zigzag by mechanically moving the fabric side to side as the machine runs.
The zigzagger's foot has longitudinal grooves on its underside, facing the material, which confer traction only sideways. This allows the zigzagger to move the material side to side while the machine's feed dogs are simultaneously moving the material forward or backward in the usual manner.
Singer zigzaggers
Singer produced a variety of "Singer Automatic Zigzagger" attachments over the years, including part numbers 160985 and 161102. These zigzaggers are equipped with pop-in cams (called "Stitch Patterns") for making four different zigzag stitches, as well as a bight control for choosing the zigzag width.
Four cams are included. There are also sets of additional different cams, four cams per set, sold as "Singer Stitch Patterns for Automatic Zigzagger". All cam sets are Singer part number 161008, and contain the following cams:
* The #2 red set is included with the 160985 and 161102 zigzaggers.
** Older #2 white sets have red-colored cams.
"YS Star" zigzagger
"YS Star" is a brand of Japanese sewing accessories that once included a zigzagger, model YS-7. Like the Singer zigzagger, it fits almost any low-shank sewing machine and draws mechanical power via an arm connected to the machine's needle clamp. Its stitch pattern is controlled by small flat rectangular metal templates, seven of which are included.
Two versions were made:
White zigzagger
The White Sewing Machine Company produced a zigzag attachme |
https://en.wikipedia.org/wiki/Demolinguistic%20descriptors%20used%20in%20Canada | A number of demolinguistic descriptors are used by Canadian federal and provincial government agencies, including Statistics Canada, the Commissioner of Official Languages, the Office québécois de la langue française to assist in accurately measuring the status of the country’s two official languages and its many non-official languages. This page provides definitions of these descriptors, and also records where and for how long each descriptor has been in use.
Descriptors used in the census (primary descriptors)
"First official language spoken"
This measure is based on: first, knowledge of the two official languages: second, mother tongue; and third, the home language (i.e., the language spoken most often at home). The first official language spoken may be: English only, French only, both English and French, or neither English nor French. Data for this descriptor were first collected in the census of 1986.
"Home language"
Home language is the language most often spoken at home at the time of the census. Because some couples have different mother tongues, the census allows individuals to indicate that they speak more than one language at home. Persons who live alone may not speak at all in the privacy of their own homes, so the census asks such individuals to identify the language in which they feel most comfortable. Data for this descriptor were first collected in the census of 1971.
Inclusion of a question along these lines was recommended in the report of the Royal Commission on Bilingualism and Biculturalism, which highlighted the shortcomings of the mother tongue measure:
On this basis, the commissioners made the following additional statement: "If a question on the language generally used is added to the census—and if the data gained from the responses to this question are considered valid—we think this should be used as a basis for future calculations [as to where services ought to be offered in which language]."
"Knowledge of Official Languages"
This measure describes which of the two official languages of Canada a person can speak. In Canada, knowledge of both official languages is referred to as "bilingualism", even though bilingualism can technically mean a knowledge of any two languages. This descriptor relies on the census respondent’s own evaluation of his/her linguistic competence. Some people claim that this reliance on each Canadian’s subjective opinion leads to over-reporting of bilingualism, because many people with only a limited ability to speak the other official language record themselves as having a knowledge of both official languages. As well, levels of knowledge have been shown to change dramatically within the same age cohort over time. (For example, there is a significant decline in knowledge of French among English-speaking Canadians in the decade after they graduate from high school.) Data for this descriptor were first collected in the census of 1931.
"Language used most often at work"
This is the languag |
https://en.wikipedia.org/wiki/J%C4%81nis%20Andersons | Jānis Andersons (born October 7, 1986) is a Latvian ice hockey defenceman, currently playing for Indian Žiar nad Hronom of the Slovak Hockey League.
Career statistics
Regular season and playoffs
International
External links
1986 births
Living people
AIK IF players
Almtuna IS players
HC 07 Detva players
HC Dukla Jihlava players
HK Dukla Trenčín players
HC Havířov players
Heilbronner EC players
Hokej Šumperk 2003 players
Kompanion Kiev players
LHK Jestřábi Prostějov players
Latvian ice hockey defencemen
HK Liepājas Metalurgs players
HC Nové Zámky players
HC Oceláři Třinec players
Dinamo Riga players
HK Riga 2000 players
Prizma Riga players
Ice hockey people from Riga
VHK Vsetín players
MsHK Žilina players
HKM Zvolen players
HK MŠK Indian Žiar nad Hronom players
Slovak Hockey League players
Slovak Extraliga players
Expatriate ice hockey players in Slovakia
Expatriate ice hockey players in the Czech Republic
Expatriate ice hockey players in Sweden
Expatriate ice hockey players in Ukraine
Expatriate ice hockey players in Germany
Latvian expatriate sportspeople in Germany
Latvian expatriate sportspeople in Ukraine
Latvian expatriate sportspeople in Sweden
Latvian expatriate sportspeople in the Czech Republic
Latvian expatriate sportspeople in Slovakia
Latvian expatriate ice hockey people |
https://en.wikipedia.org/wiki/Continuum%20structure%20function | In mathematics, a continuum structure function (CSF) is defined by Laurence Baxter as a nondecreasing mapping from the unit hypercube to the unit interval. It is used by Baxter to help in the Mathematical modelling of the level of performance of a system in terms of the performance levels of its components.
References
Kim, C., Baxter. L. A. (1987) "Axiomatic characterizations of continuum structure functions", Operations Research Letters, 6 (6), 297–300, .
Probabilistic models
Survival analysis |
https://en.wikipedia.org/wiki/List%20of%20genetic%20algorithm%20applications | This is a list of genetic algorithm (GA) applications.
Natural Sciences, Mathematics and Computer Science
Bayesian inference links to particle methods in Bayesian statistics and hidden Markov chain models
Artificial creativity
Chemical kinetics (gas and solid phases)
Calculation of bound states and local-density approximations
Code-breaking, using the GA to search large solution spaces of ciphers for the one correct decryption.
Computer architecture: using GA to find out weak links in approximate computing such as lookahead.
Configuration applications, particularly physics applications of optimal molecule configurations for particular systems like C60 (buckyballs)
Construction of facial composites of suspects by eyewitnesses in forensic science.
Data Center/Server Farm.
Distributed computer network topologies
Electronic circuit design, known as evolvable hardware
Feature selection for Machine Learning
Feynman-Kac models
File allocation for a distributed system
Filtering and signal processing
Finding hardware bugs.
Game theory equilibrium resolution
Genetic Algorithm for Rule Set Production
Scheduling applications, including job-shop scheduling and scheduling in printed circuit board assembly. The objective being to schedule jobs in a sequence-dependent or non-sequence-dependent setup environment in order to maximize the volume of production while minimizing penalties such as tardiness. Satellite communication scheduling for the NASA Deep Space Network was shown to benefit from genetic algorithms.
Learning robot behavior using genetic algorithms
Image processing: Dense pixel matching
Learning fuzzy rule base using genetic algorithms
Molecular structure optimization (chemistry)
Optimisation of data compression systems, for example using wavelets.
Power electronics design.
Traveling salesman problem and its applications
Earth Sciences
Climatology: Estimation of heat flux between the atmosphere and sea ice
Climatology: Modelling global temperature changes
Design of water resource systems
Groundwater monitoring networks
Finance and Economics
Financial mathematics
Real options valuation
Portfolio optimization
Genetic algorithm in economics
Representing rational agents in economic models such as the cobweb model
the same, in Agent-based computational economics generally, and in artificial financial markets
Social Sciences
Design of anti-terrorism systems
Linguistic analysis, including grammar induction and other aspects of Natural language processing (NLP) such as word-sense disambiguation.
Industry, Management and Engineering
Audio watermark insertion/detection
Airlines revenue management
Automated design of mechatronic systems using bond graphs and genetic programming (NSF)
Automated design of industrial equipment using catalogs of exemplar lever patterns
Automated design, including research on composite material design and multi-objective design of automotive components for crashworthiness, weight sa |
https://en.wikipedia.org/wiki/Oliver%20Byrne%20%28mathematician%29 | Oliver Byrne (; 31 July 1810 – 9 December 1880) was a civil engineer and prolific author of works on subjects including mathematics, geometry, and engineering. He is best known for his 'coloured' book of Euclid's Elements. He was also a large contributor to Spon's Dictionary of Engineering.
Family and early life
Byrne reports the Vale of Avoca, County Wicklow, Ireland as his birthplace. The son of Lawrence Oliver Byrne and Mary Byrne, he had a younger brother John who co-authored a book with him. Little is known about his childhood. He emerges in Dublin at age 20 with his first publication. By the age of 29, Byrne was noted as the "principal support of an aged mother and sisters in Ireland." Later in England, he was appointed Professor of Mathematics in the College for Civil Engineers at Putney.
Marriage
His wife Eleanor (née Rugg), was 12 years younger than Oliver and published meteorological articles and books. She is featured on a token struck to commemorate Oliver Byrne's invention of Byneore.
Byrne's Euclid
His most innovative educational work was a version of the first six books of Euclid's Elements that used coloured graphic explanations of each geometric principle. It was published by William Pickering in 1847.
The book has become the subject of renewed interest in recent years for its innovative graphic conception and its style which prefigures the modernist experiments of the Bauhaus and De Stijl movements. Information design writer Edward Tufte refers to the book in his work on graphic design and McLean in his Victorian book design of 1963. In 2010 Taschen republished the work in a facsimile edition and in 2017 a project was launched to extend the work to the remaining works of Euclid.
Byrne described himself as a mathematician, civil engineer, military engineer, and mechanical engineer and indicates on the title pages of one of his books that he was surveyor of Queen Victoria's settlement in the Falkland Islands. Evidence shows Byrne never traveled to the Falkland Islands.
The U.S. Library of Congress has a steel-engraved portrait of Oliver Byrne.
Engineering and inventions
Byrne engaged in numerous railroad projects and invented mechanical devices including the following:
The Byrnegraph
The Gauger's Patent Calculating Instruments.
In 1842, Oliver Byrne and Henry William Hull (BA, CE) made a proposal for a School of Mathematics, Engineering, Classics, and General Literature at Surrey Villa, near Lambeth Palace.
Byrne was an anti-phrenologist, and wrote a book on the fallacy of phrenology.
Irish independence
In 1853 while residing in the US, Oliver Byrne wrote a book titled Freedom to Ireland, published in Boston. The book advocates Irish revolt against British rule and outlining house and street fighting, handling of small arms, etc. Oliver toured the United States providing lessons in the use of small arms, field fortifications, pike exercises and street fighting. Freedom to Ireland was dedicated 'To the memory of Wi |
https://en.wikipedia.org/wiki/Troposkein | In physics and geometry, the troposkein is the curve an idealized rope assumes when anchored at its ends and spun around its long axis at a constant angular velocity. This shape is similar to the shape assumed by a skipping rope, and is independent of rotational speed in the absence of gravity, but varies with respect to rotational speed in the presence of gravity. The troposkein does not have a closed-form representation; in the absence of gravity, though, it can be approximated by a pair of line segments spanned by a circular arc (tangential to the line segments at its endpoints). The form of a troposkein can be approximated for a given gravitational acceleration, rope density and angular velocity by iterative approximation. This shape is also useful for decreasing the stress experienced by the blades of a Darrieus vertical axis wind turbine.
References
Ashwill, T., Leonard, T. (1986). "Developments in Blade Shape Design for a Darrieus Vertical Axis Wind Turbine", Sandia Report, 86(1085).
Plane curves |
https://en.wikipedia.org/wiki/Borwein%20integral | In mathematics, a Borwein integral is an integral whose unusual properties were first presented by mathematicians David Borwein and Jonathan Borwein in 2001. Borwein integrals involve products of , where the sinc function is given by for not equal to 0, and .
These integrals are remarkable for exhibiting apparent patterns that eventually break down. The following is an example.
This pattern continues up to
At the next step the pattern fails,
In general, similar integrals have value whenever the numbers are replaced by positive real numbers such that the sum of their reciprocals is less than 1.
In the example above, but
With the inclusion of the additional factor , the pattern holds up over a longer series,
but
In this case, but . The exact answer can be calculated using the general formula provided in the next section, and a representation of it is shown below. Fully expanded, this value turns into a fraction that involves two 2736 digit integers.
The reason the original and the extended series break down has been demonstrated with an intuitive mathematical explanation. In particular, a random walk reformulation with a causality argument sheds light on the pattern breaking and opens the way for a number of generalizations.
General formula
Given a sequence of nonzero real numbers, , a general formula for the integral
can be given. To state the formula, one will need to consider sums involving the . In particular, if is an -tuple where each entry is , then we write , which is a kind of alternating sum of the first few , and we set , which is either . With this notation, the value for the above integral is
where
In the case when , we have .
Furthermore, if there is an such that for each we have and , which means that is the first value when the partial sum of the first elements of the sequence exceed , then for each but
The first example is the case when .
Note that if then and but , so because , we get that
which remains true if we remove any of the products, but that
which is equal to the value given previously.
/* This is a sample program to demonstrate for Computer Algebra System "maxima". */
f(n) := if n=1 then sin(x)/x else f(n-2) * (sin(x/n)/(x/n));
for n from 1 thru 15 step 2 do (
print("f(", n, ")=", f(n) ),
print("integral of f for n=", n, " is ", integrate(f(n), x, 0, inf)) );
/* This is also sample program of another problem. */
f(n) := if n=1 then sin(x)/x else f(n-2) * (sin(x/n)/(x/n)); g(n) := 2*cos(x) * f(n);
for n from 1 thru 19 step 2 do (
print("g(", n, ")=", g(n) ),
print("integral of g for n=", n, " is ", integrate(g(n), x, 0, inf)) );
Method to solve Borwein integrals
An exact integration method that is efficient for evaluating Borwein-like integrals is discussed here. This integration method works by reformulating integration in terms of a series of differentiations and it yields intuition into the unusual behavior of the Borwein integrals. The Integratio |
https://en.wikipedia.org/wiki/Osborn%20High%20School | Osborn High School, also known as Osborn Academy of Mathematics is a public high school in the Detroit Public Schools Community District (DPSCD), located in Northeast Detroit.
Currently, the school has over 20 course offerings some of which are: Engineering, Finance, Spanish, Dual Enrollment through WCCCD, Honors and AP Classes, Reading, Web-Based Academic Tutoring, Extended Day Program, Credit Recovery Program, Internship Programs, Community Service Opportunities, Band, ROTC, Robotics Team, Literacy Circles, Chess, DAPCEP, Media Club, Book Club, Recycling Program, Finance, Technology & Engineering Club, Alternative Energy Greenhouse, Drama, Cheer-leading, Student Government, Basketball, Football, Softball, Baseball, Volleyball, Track and Field, and Cross Country.
Mildred Gaddis of WCHB said that Osborn "is considered the glue to the community."
History
Laura F. Osborn High School was opened in February 1957. It was named after Laura Freele Osborn, the first female president of the Detroit Board of Education. When opened it had no auditorium, gym or pool, no facilities for vocational courses such as automotive. It took the Board of Education over four years to develop these, although the funds had been appropriated before January 1957. On the northwest side, Osborn's 'sister' school, Henry Ford had these facilities built by the end of 1959. Parents of Osborn students inquired and made visits to the Board offices and never received positive answers regarding the delay. The first student newspaper was called The Lance, the masthead designed by Gregg T. Trendowski (Class of June 1960). The teams were named the Knights, a name suggested by Gregg Trendowski (a member of the first student council and member of a special committee for name selections). Mr. Trendowski also designed the team logos and the yearbook (The Acolyte) logo in February 1957.
In 2006 Kimberly Chou of The Michigan Daily said that the school was "often criticized for its lack of resources and tension among students."
The school complex was divided into three separate schools occupying the same campus in 2009.
In 2010 Robert Bobb, the emergency financial manager of the school district, announced that Osborn was closing. In July 2010 Osborn High School was closed; it reopened in August of that year. DPS officials planned to keep the facility open for two years.
An April 2011 report from the office of Mayor of Detroit Dave Bing stated that gangs have caused problems at Osborn High.
Jeff Siedel of Detroit Free Press said that in the northern hemisphere summer of 2011 "as a wave of violence swirled around" Osborn as several students died in violent incidents. On August 24, 2011, Osborn High star football player, Allantae Powell, was murdered in western Detroit.
2012 Osborn High School was divided into four separate entities. Osborn College Preparatory Academy, Osborn Collegiate Academy of Mathematics, Science and Technology (Osborn MST), and Osborn Evergreen Academy of Des |
https://en.wikipedia.org/wiki/Nested%20interval%20topology | In mathematics, more specifically general topology, the nested interval topology is an example of a topology given to the open interval (0,1), i.e. the set of all real numbers x such that . The open interval (0,1) is the set of all real numbers between 0 and 1; but not including either 0 or 1.
To give the set (0,1) a topology means to say which subsets of (0,1) 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 (0,1) and the empty set ∅ are open sets.
Construction
The set (0,1) and the empty set ∅ are required to be open sets, and so we define (0,1) and ∅ to be open sets in this topology. The other open sets in this topology are all of the form where n is a positive whole number greater than or equal to two i.e. .
Properties
The nested interval topology is neither Hausdorff nor T1. In fact, if x is an element of (0,1), then the closure of the singleton set {x} is the half-open interval , where n is maximal such that .
The nested interval topology is not compact. It is, however, strongly Lindelöf since there are only countably many open sets.
The nested interval topology is hyperconnected and hence connected.
The nested interval topology is Alexandrov.
References
General topology |
https://en.wikipedia.org/wiki/Balbis | In geometry, a balbis is a geometric shape that can be colloquially defined as a single (primary) line that is terminated by a (secondary) line at one endpoint and by a (secondary) line at the other endpoint. The terminating secondary lines are at right angles to the primary line. Its parallel sides are of indefinite lengths and can be infinitely long. The word "balbis" comes from the ancient Greek word βαλβίς, meaning a rope between two posts used to indicate the start and finish of a race.
The most common example of a balbis is the capital letter 'H', the eighth letter in the ISO basic Latin alphabet. It can also be seen in, for example, rugby posts and old-fashioned television antenna.
Another type of balbis is the rectangular balbis, that may be loosely described as a rectangle with one side missing. A rectangular balbis was used in the Olympic Games, as a throwing area and is described by Philostratus II.
In his book about the balbis (see References below), the Rev. P. H. Francis describes the balbis as "the commonest geometrical figure, more in evidence than the triangle, circle, ellipse, or other geometrical figure that has been studied from ancient times" and goes on to state that it "was known to but not studied by the ancient Greeks; and this geometrical figure has been neglected." His memorial illustrates a balbis and can be seen in St. Mary's Church, Stoughton, West Sussex.
References
The Rev. Francis was sometime vicar of Stoughton, West Sussex.
Geometric shapes |
https://en.wikipedia.org/wiki/Asplund%20space | In mathematics — specifically, in functional analysis — an Asplund space or strong differentiability space is a type of well-behaved Banach space. Asplund spaces were introduced in 1968 by the mathematician Edgar Asplund, who was interested in the Fréchet differentiability properties of Lipschitz functions on Banach spaces.
Equivalent definitions
There are many equivalent definitions of what it means for a Banach space X to be an Asplund space:
X is Asplund if, and only if, every separable subspace Y of X has separable continuous dual space Y∗.
X is Asplund if, and only if, every continuous convex function on any open convex subset U of X is Fréchet differentiable at the points of a dense Gδ-subset of U.
X is Asplund if, and only if, its dual space X∗ has the Radon–Nikodým property. This property was established by Namioka & Phelps in 1975 and Stegall in 1978.
X is Asplund if, and only if, every non-empty bounded subset of its dual space X∗ has weak-∗-slices of arbitrarily small diameter.
X is Asplund if and only if every non-empty weakly-∗ compact convex subset of the dual space X∗ is the weakly-∗ closed convex hull of its weakly-∗ strongly exposed points. In 1975, Huff & Morris showed that this property is equivalent to the statement that every bounded, closed and convex subset of the dual space X∗ is closed convex hull of its extreme points.
Properties of Asplund spaces
The class of Asplund spaces is closed under topological isomorphisms: that is, if X and Y are Banach spaces, X is Asplund, and X is homeomorphic to Y, then Y is also an Asplund space.
Every closed linear subspace of an Asplund space is an Asplund space.
Every quotient space of an Asplund space is an Asplund space.
The class of Asplund spaces is closed under extensions: if X is a Banach space and Y is an Asplund subspace of X for which the quotient space X ⁄ Y is Asplund, then X is Asplund.
Every locally Lipschitz function on an open subset of an Asplund space is Fréchet differentiable at the points of some dense subset of its domain. This result was established by Preiss in 1990 and has applications in optimization theory.
The following theorem from Asplund's original 1968 paper is a good example of why non-Asplund spaces are badly behaved: if X is not an Asplund space, then there exists an equivalent norm on X that fails to be Fréchet differentiable at every point of X.
In 1976, Ekeland & Lebourg showed that if X is a Banach space that has an equivalent norm that is Fréchet differentiable away from the origin, then X is an Asplund space. However, in 1990, Haydon gave an example of an Asplund space that does not have an equivalent norm that is Gateaux differentiable away from the origin.
References
Banach spaces
Functional analysis |
https://en.wikipedia.org/wiki/Giulio%20Giorello | Giulio Giorello (; 14 May 1945 – 15 June 2020) was an Italian philosopher, mathematician, and epistemologist.
Biography
Giorello graduated with a degree in philosophy in 1968 and in mathematics in 1971 at the University of Milan. While there, he studied under the philosopher Ludovico Geymonat. He then taught physics and natural sciences at the University of Pavia, University of Catania, University of Insubria and the University of Milan. Giorello was a professor of philosophy of science at the University of Milan; he was also President of SILFS (Italian Society of Logic and Philosophy of Science). He directed the "Scienza e idee" series by Raffaello Cortina Editore and collaborated on the cultural pages of the newspaper Corriere della Sera.
In 2010, Giorello expressed his atheistic thought with work Senza Dio. Del buon uso dell'ateismo, but in the last years of his life he expressed an agnostic thought.
In March 2012 he was a speaker at the national congress of the Grand Orient of Italy in Rimini. Giorello won the 4th edition of the 2012 Frascati Philosophy National Award.
Giorello died in Milan on 15 June 2020 due to COVID-19 during the COVID-19 pandemic in Italy. Three days before his death, he married his partner Roberta Pelachin.
Personal life
Giorello was a "comic book expert"; he wrote essays about Tex Willer and Topolino, and he also wrote the prefaces to Logicomix and Rat-Man: Superstorie di un supernessuno. In 2014, he co-created the comic "The philosophy of Donald Duck".
Works
Saggi di storia della matematica, Milan, FER, 1974.
Il pensiero matematico e l'infinito, Milan, UNICOPLI, 1982. .
Lo spettro e il libertino. Teologia, matematica, libero pensiero, Milan, A. Mondadori, 1985.
Le ragioni della scienza, with Ludovico Geymonat and Fabio Minazzi, Rome-Bari, Laterza, 1986. .
Filosofia della scienza, Milan, Jaca Book, 1992. .
Le stanze della ricerca, Milan, Mazzotta, 1992. .
Europa universitas. Tre saggi sull'impresa scientifica europea, with Tullio Regge and Salvatore Veca, Milan, Feltrinelli, 1993. .
Introduzione alla filosofia della scienza, Milan, R.C.S. libri & grandi opere, 1994. .
Quale Dio per la sinistra? Note su democrazia e violenza, with Pietro Adamo, Milan, UNICOPLI, 1994. .
La filosofia della scienza nel XX secolo, with Donald Gillies, Rome-Bari, Laterza, 1995.
Lo specchio del reame. Riflessioni su potere e comunicazione, with Roberto Esposito, Carlo Sini and Danilo Zolo, Ravenna, Longo, 1997. .
Epistemologia applicata. Percorsi filosofici, with Michele Di Francesco, Milan, CUEM, 1999. .
I volti del tempo,with Elio Sindoni, Corrado Sinigaglia, Milan, Bompiani, 2001. .
Prometeo, Ulisse, Gilgameš. Figure del mito, Milan, Raffaello Cortina Editore, 2004. .
Di nessuna chiesa. La libertà del laico, Milan, Raffaello Cortina Editore, 2005. .
Dove fede e ragione si incontrano?, with Bruno Forte, Cinisello Balsamo, San Paolo, 2006. .
La libertà della vita, with Umberto Veronesi, Milan, Raffaello Cortina Edit |
https://en.wikipedia.org/wiki/Divisor%20topology | In mathematics, more specifically general topology, the divisor topology is a specific topology on the set of positive integers greater than or equal to two. The divisor topology is the poset topology for the partial order relation of divisibility of integers on .
Construction
The sets for form a basis for the divisor topology on , where the notation means is a divisor of .
The open sets in this topology are the lower sets for the partial order defined by if . The closed sets are the upper sets for this partial order.
Properties
All the properties below are proved in or follow directly from the definitions.
The closure of a point is the set of all multiples of .
Given a point , there is a smallest neighborhood of , namely the basic open set of divisors of . So the divisor topology is an Alexandrov topology.
is a T0 space. Indeed, given two points and with , the open neighborhood of does not contain .
is a not a T1 space, as no point is closed. Consequently, is not Hausdorff.
The isolated points of are the prime numbers.
The set of prime numbers is dense in . In fact, every dense open set must include every prime, and therefore is a Baire space.
is second-countable.
is ultraconnected, since the closures of the singletons and contain the product as a common element.
Hence is a normal space. But is not completely normal. For example, the singletons and are separated sets (6 is not a multiple of 4 and 4 is not a multiple of 6), but have no disjoint open neighborhoods, as their smallest respective open neighborhoods meet non-trivially in .
is not a regular space, as a basic neighborhood is finite, but the closure of a point is infinite.
is connected, locally connected, path connected and locally path connected.
is a scattered space, as each nonempty subset has a first element, which is an isolated element of the set.
The compact subsets of are the finite subsets, since any set is covered by the collection of all basic open sets , which are each finite, and if is covered by only finitely many of them, it must itself be finite. In particular, is not compact.
is locally compact in the sense that each point has a compact neighborhood ( is finite). But points don't have closed compact neighborhoods ( is not locally relatively compact.)
References
Topological spaces |
https://en.wikipedia.org/wiki/First-pitch%20strike | In baseball, a first-pitch strike is when the pitcher throws a strike to the batter during the first pitch of the at bat. Statistics indicate that throwing a strike on the first pitch allows the pitcher to gain an advantage in the at bat, limiting the hitter's chance of getting on base.
Importance
With the continued interest and development of statistics in the game of baseball, first-pitch strikes have been under the microscope of many fans and sabermetricians (those who study the game based on evidence, mainly stats that measure game activity). Many studies have proven that the first pitch in the at bat is the most important one. And according to Craig Burley's 2004 study in The Hardball Times, throwing a strike on a 0-0 count could potentially save over 12,000 runs scored in a single Major League Baseball season.
In Burley's study, he used stats from the 2003 MLB season. He found that when a pitcher throws a strike on the first pitch of the at bat, hitters collected a .261 batting average. But if the first pitch was a ball, their batting average jumped to .280, a substantial difference.
From Burley, "Let's imagine that we have two pitchers, both of whom are otherwise perfectly average but one of whom always throws a strike on the first pitch, while the other always throws a ball. The first pitcher, the "strike one" pitcher, has an expected ERA (earned run average) of about 3.60. The second one, the otherwise perfectly average one who always throws a ball on pitch one, has an expected ERA of about 5.50. He'll also pitch about 12% fewer innings (without taking into account the higher pitch counts that would result from starting 1-0)."
While there are some players in the game who are notorious for swinging at the first pitch, Burley's study proved that there is little risk in jumping ahead early in the count. Less than 8 percent of first-pitch strikes turn into base hits.
After that it becomes even more difficult for the hitter. Once a pitcher gets to a 0-1 count, hitters hit just .239 against him from there on out.
Minnesota Twins
The Minnesota Twins franchise has taken the idea of command and first-pitch strikes to a new level. Considered a small-market team, the Twins needed to find any advantage they could to keep pace with the larger franchises.
Twins pitchers are taught from the very beginning to get ahead in the count, throwing first-pitch strikes as often as possible. In training camp, pitchers who collect the most first-pitch strikes are given free dinner or other rewards.
The scouts and coaches throughout the organization are trained to look for pitchers with consistent arm slots and deliveries, allowing them to spot young players who will harness the command that the franchise looks for.
As a team, the Twins haven’t ranked outside the top five in fewest walks allowed since 1996, and they’ve been first or second in that category in nine of the past 13 seasons.
Former Minnesota pitcher Brad Radke became the poster boy for first |
https://en.wikipedia.org/wiki/Plantation%2C%20Lexington | Plantation is a neighborhood in southwestern Lexington, Kentucky, United States. It is bounded by Man O War Boulevard, Harrodsburg Road, and Old Higbee Mill Road.
Neighborhood statistics
Area:
Population: 1,322
Population density: 3,466 people per square mile
Median household income: $85,047
External links
http://www.city-data.com/neighborhood/Plantation-Lexington-KY.html
Neighborhoods in Lexington, Kentucky |
https://en.wikipedia.org/wiki/Gras%20conjecture | In algebraic number theory, the Gras conjecture relates the p-parts of the Galois eigenspaces of an ideal class group to the group of global units modulo cyclotomic units. It was proved by as a corollary of their work on the main conjecture of Iwasawa theory. later gave a simpler proof using Euler systems.
References
Theorems in algebraic number theory
Conjectures that have been proved |
https://en.wikipedia.org/wiki/Gregory%20Kriegsmann | Gregory Anthony Kriegsmann (1946–2018) was Distinguished Professor of Mathematics and Foundation Chair at New Jersey Institute of Technology’s department of Mathematical Sciences.
Education
Gregory received his BS in Electrical Engineering (1969) from Marquette University, MS in Electrical Engineering (1970), MA in Mathematics (1972) and PhD in Applied Mathematics (1974) from University of California at Los Angeles.
Research interests
Gregory's research focuses include applied mathematics, asymptotic methods, differential equations, bifurcation theory, wave propagation, acoustics, electromagnetic fields, circuit theory and more.
Honors
Gregory was elected as a (first batch) Fellow of the Society for Industrial and Applied Mathematics (SIAM) in 2009.
Doctoral students
According to the Mathematics Genealogy Project, Gregory mentored a total 10 doctoral students (total of 17 descendants) at Northwestern University and New Jersey Institute of Technology including John Pelesko.
Others
He was an Associate Editor of Analysis and Applications, Journal of Engineering Mathematics (JEMA), IMA Journal of Applied Mathematics (IMA) and European Journal of Applied Mathematics.
References
External links
'New Jersey Institute of Technology : NJIT Mathematicians Named First Fellows of Math Society'
'NJIT Department of Mathematical Sciences : Gregory A Kriegsmann'
1946 births
2018 deaths
20th-century American mathematicians
21st-century American mathematicians
New Jersey Institute of Technology faculty |
https://en.wikipedia.org/wiki/Listing%20number | In mathematics, a Listing number of a topological space is one of several topological invariants introduced by the 19th-century mathematician Johann Benedict Listing and later given this name by Charles Sanders Peirce. Unlike the later invariants given by Bernhard Riemann, the Listing numbers do not form a complete set of invariants: two different two-dimensional manifolds may have the same Listing numbers as each other.
There are four Listing numbers associated with a space. The smallest Listing number counts the number of connected components of a space, and is thus equivalent to the zeroth Betti number.
References
Topology
Charles Sanders Peirce |
https://en.wikipedia.org/wiki/Fritz%20Gesztesy | Friedrich "Fritz" Gesztesy (born 5 November 1953 in Austria) is a well-known Austrian-American mathematical physicist and Professor of Mathematics at Baylor University, known for his important contributions in spectral theory, functional analysis, nonrelativistic quantum mechanics (particularly, Schrödinger operators), ordinary and partial differential operators, and completely integrable systems (soliton equations). He has authored more than 300 publications on mathematics and physics.
Career
After studying physics at the University of Graz, he continued with his PhD in theoretical physics. The title of his dissertation 1976 with Heimo Latal and Ludwig Streit was Renormalization, Nelson's symmetry and energy densities in a field theory with quadratic interaction. After working at the Institut for Theoretical Physics of the University of Graz (1977–82) and several stays abroad at the Bielefeld University (Alexander von Humboldt Scholarship 1980–81 and 1983–84) and at the California Institute of Technology (Max Kade Scholarship 1987–88) he was appointed to Professor at the University of Missouri in 1988 and as Houchins Distinguished Professor in 2002. In 2016 he joined the faculty of Baylor University as Storm Professor of Mathematics.
In 1983 he got the Austrian Theodor Körner Award in Natural Sciences, in 1987 the Ludwig Boltzmann Prize of the Austrian Physical Society. In 2002 he was elected to the Royal Norwegian Society of Sciences and Letters. In 2013 he became a Fellow of the American Mathematical Society. 2022 he received an honorary doctorate from the Graz University of Technology.
Among his students are Gerald Teschl, Karl Unterkofler , Selim Sukhtaiev , and Maxim Zinchenko .
Selected publications
with Sergio Albeverio, Raphael Høegh-Krohn and Helge Holden: " Solvable Models in Quantum Mechanics", 2nd edition, AMS-Chelsea Series, Amer. Math. Soc., 2005
with Helge Holden: Soliton Equations and their Algebro-Geometric Solutions, Bd.1 (1+1 dimensional continuous models), Cambridge Studies in Advanced Mathematics Bd.79, Cambridge University Press 2003
with Helge Holden, Johanna Michor, and Gerald Teschl: Soliton Equations and their Algebro-Geometric Solutions, Bd.2 (1+1 dimensional discrete models), Cambridge Studies in Advanced Mathematics Bd.114, Cambridge University Press 2008
with Barry Simon, The xi function, Acta Math. 176 (1996), 49–71
with Rudi Weikard, Picard potentials and Hill's equation on a torus, Acta Math. 176 (1996), 73–107
with Rudi Weikard, A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy, Acta Math. 181 (1998), 63–108
with Barry Simon, A new approach to inverse spectral theory. II. General real potentials and the connection to the spectral measure, Ann. of Math. 2 152 (2000), 593–643
Literature
Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday, H. Holden, B. Simon and G. Teschl (eds), Proceedings of Symposi |
https://en.wikipedia.org/wiki/Mark%20Yee | Mark Yee (born January 4, 1982) is a Filipino professional basketball player for Bacoor City Strikers of the Maharlika Pilipinas Basketball League (MPBL).
PBA career statistics
Correct as of September 24, 2016
Season-by-season averages
|-
| align=left |
| align=left | Burger King
| 15 || 19.5 || .483 || .387 || .800 || 3.9 || 1.4 || .1 || .4 || 8.8
|-
| align=left |
| align=left | Burger King / Talk 'N Text
| 42 || 14.1 || .392 || .343 || .627 || 2.5 || .7 || .3 || .4 || 5.2
|-
| align=left |
| align=left | Talk 'N Text
| 23 || 5.0 || .469 || .273 || .750 || .7 || .4 || .0 || .0 || 2.7
|-
| align=left |
| align=left | Meralco
| 18 || 11.4 || .377 || .231 || .875 || 1.4 || .7 || .1 || .2 || 3.3
|-
| align=left |
| align=left | GlobalPort
| 31 || 14.7 || .420 || .250 || .727 || 3.1 || .5 || .2 || .1 || 4.2
|-
| align=left |
| align=left | GlobalPort
| 19 || 13.6 || .397 || .333 || .909 || 2.5 || .6 || .2 || .2 || 3.2
|-
| align=left |
| align=left | Kia
| 20 || 16.9 || .500 || .286 || .684 || 4.3 || .6 || .2 || .1 || 5.0
|-
| align=left |
| align=left | Mahindra
| 35 || 16.1 || .442 || .231 || .831 || 4.9 || .7 || .7 || .6 || 6.7
|-class="sortbottom"
| align=center colspan=2 | Career
| 203 || 13.9 || .432 || .301 || .759 || 3.0 || .7 || .3 || .3 || 4.9
References
External links
Yee PBA.ph profile
1982 births
Living people
Barako Bull Energy players
Basketball players from Negros Occidental
Terrafirma Dyip players
Filipino men's basketball players
NorthPort Batang Pier players
Meralco Bolts players
Power forwards (basketball)
Small forwards
TNT Tropang Giga players
College basketball players in the Philippines
Maharlika Pilipinas Basketball League players |
https://en.wikipedia.org/wiki/Time%20evolution%20of%20integrals | Within differential calculus, in many applications, one needs to calculate the rate of change of a volume or surface integral whose domain of integration, as well as the integrand, are functions of a particular parameter. In physical applications, that parameter is frequently time t.
Introduction
The rate of change of one-dimensional integrals with sufficiently smooth integrands, is governed by this extension of the fundamental theorem of calculus:
The calculus of moving surfaces provides analogous formulas for volume integrals over Euclidean domains, and surface integrals over differential geometry of surfaces, curved surfaces, including integrals over curved surfaces with moving contour boundaries.
Volume integrals
Let t be a time-like parameter and consider a time-dependent domain Ω with a smooth surface boundary S. Let F be a time-dependent invariant field defined in the interior of Ω. Then the rate of change of the integral
is governed by the following law:
where C is the velocity of the interface. The velocity of the interface C is the fundamental concept in the calculus of moving surfaces. In the above equation, C must be expressed with respect to the exterior normal. This law can be considered as the generalization of the fundamental theorem of calculus.
Surface integrals
A related law governs the rate of change of the surface integral
The law reads
where the -derivative is the fundamental operator in the calculus of moving surfaces, originally proposed by Jacques Hadamard. is the trace of the mean curvature tensor. In this law, C need not be expression with respect to the exterior normal, as long as the choice of the normal is consistent for C and . The first term in the above equation captures the rate of change in F while the second corrects for expanding or shrinking area. The fact that mean curvature represents the rate of change in area follows from applying the above equation to since is area:
The above equation shows that mean curvature can be appropriately called the shape gradient of area. An evolution governed by
is the popular mean curvature flow and represents steepest descent with respect to area. Note that for a sphere of radius R,
, and for a circle of radius R,
with respect to the exterior normal.
Surface integrals with moving contour boundaries
Suppose that S is a moving surface with a moving contour γ. Suppose that the velocity of the contour γ with respect to S is c. Then the rate of change of the time dependent integral:
is
The last term captures the change in area due to annexation, as the figure on the right illustrates.
References
Differential calculus
Integral calculus |
https://en.wikipedia.org/wiki/Remarks%20on%20the%20Foundations%20of%20Mathematics | Remarks on the Foundations of Mathematics () is a book of Ludwig Wittgenstein's notes on the philosophy of mathematics. It has been translated from German to English by G.E.M. Anscombe, edited by G.H. von Wright and Rush Rhees, and published first in 1956. The text has been produced from passages in various sources by selection and editing. The notes have been written during the years 1937–1944 and a few passages are incorporated in the Philosophical Investigations which were composed later. When the book appeared it received many negative reviews mostly from working logicians and mathematicians, among them Michael Dummett, Paul Bernays, and Georg Kreisel. Today Remarks on the Foundations of Mathematics is read mostly by philosophers sympathetic to Wittgenstein and they tend to adopt a more positive stance.
Wittgenstein's philosophy of mathematics is exposed chiefly by simple examples on which further skeptical comments are made. The text offers an extended analysis of the concept of mathematical proof and an exploration of Wittgenstein's contention that philosophical considerations introduce false problems in mathematics. Wittgenstein in the Remarks adopts an attitude of doubt in opposition to much orthodoxy in the philosophy of mathematics.
Particularly controversial in the Remarks was Wittgenstein's "notorious paragraph", which contained an unusual commentary on Gödel's incompleteness theorems. Multiple commentators read Wittgenstein as misunderstanding Gödel. In 2000 Juliet Floyd and Hilary Putnam suggested that the majority of commentary misunderstands
Wittgenstein but their interpretation has not been met with approval.
Wittgenstein wrote
The debate has been running around the so-called Key Claim: If one assumes that P is provable in PM, then one should give up the "translation" of P by the English sentence "P is not provable".
Wittgenstein does not mention the name of Kurt Gödel who was a member of the Vienna Circle during the period in which Wittgenstein's early ideal language philosophy and Tractatus Logico-Philosophicus dominated the circle's thinking; multiple writings of Gödel in his Nachlass contain his own antipathy for Wittgenstein, and belief that Wittgenstein wilfully misread the theorems. Some commentators, such as Rebecca Goldstein, have hypothesized that Gödel developed his logical theorems in opposition to Wittgenstein.
References
External links
Sorin Bangu, Ludwig Wittgenstein: Later Philosophy of Mathematics, IEP
Victor Rodych, Wittgenstein's Philosophy of Mathematics, The Stanford Encyclopedia of Philosophy
1953 non-fiction books
Books by Ludwig Wittgenstein
Philosophy of mathematics literature
Logic literature |
https://en.wikipedia.org/wiki/Calculus%20of%20moving%20surfaces | The calculus of moving surfaces (CMS) is an extension of the classical tensor calculus to deforming manifolds. Central to the CMS is the Tensorial Time Derivative whose original definition was put forth by Jacques Hadamard. It plays the role analogous to that of the covariant derivative on differential manifolds in that it produces a tensor when applied to a tensor.
Suppose that is the evolution of the surface indexed by a time-like parameter . The definitions of the surface velocity and the operator are the geometric foundations of the CMS. The velocity C is the rate of deformation of the surface in the instantaneous normal direction. The value of at a point is defined as the limit
where is the point on that lies on the straight line perpendicular to at point P. This definition is illustrated in the first geometric figure below. The velocity is a signed quantity: it is positive when points in the direction of the chosen normal, and negative otherwise. The relationship between and is analogous to the relationship between location and velocity in elementary calculus: knowing either quantity allows one to construct the other by differentiation or integration.
The Tensorial Time Derivative for a scalar field F defined on is the rate of change in in the instantaneously normal direction:
This definition is also illustrated in second geometric figure.
The above definitions are geometric. In analytical settings, direct application of these definitions may not be possible. The CMS gives analytical definitions of C and in terms of elementary operations from calculus and differential geometry.
Analytical definitions
For analytical definitions of and , consider the evolution of given by
where are general curvilinear space coordinates and are the surface coordinates. By convention, tensor indices of function arguments are dropped. Thus the above equations contains rather than . The velocity object is defined as the partial derivative
The velocity can be computed most directly by the formula
where are the covariant components of the normal vector .
Also, defining the shift tensor representation of the Surface's Tangent Space and the Tangent Velocity as , then the definition of the derivative for an invariant F reads
where is the covariant derivative on S.
For tensors, an appropriate generalization is needed. The proper definition for a representative tensor reads
where are Christoffel symbols and is the surface's appropriate temporal symbols ( is a matrix representation of the surface's curvature shape operator)
Properties of the -derivative
The -derivative commutes with contraction, satisfies the product rule for any collection of indices
and obeys a chain rule for surface restrictions of spatial tensors:
Chain rule shows that the -derivatives of spatial "metrics" vanishes
where and are covariant and contravariant metric tensors, is the Kronecker delta symbol, and and |
https://en.wikipedia.org/wiki/Pavel%20Grinfeld | Pavel Grinfeld (also known as Greenfield) is an American mathematician and associate professor of Applied Mathematics at Drexel University working on problems in moving surfaces in applied mathematics (particularly calculus of variations), geometry, physics, and engineering.
Biography
Grinfeld received his PhD in Applied Mathematics from MIT in 2003; followed by two years as a postdoctoral fellow at the MIT Department of Earth, Atmosphere and Planetary Sciences, conducting research in geodynamics. He joined the Department of Mathematics at Drexel University in 2005; currently teaching Linear Algebra, Differential Equations, and Tensor calculus.
Grinfeld is the author of the dynamic fluid film equations. Grinfeld co-authored with Haruo Kojima of Rutgers University on the instability of the 2S electron bubbles.
He is the author of a textbook on Tensor Calculus (2013) as well as an e-workbook on Linear Algebra. He has recorded hundreds of video lectures; several dozen on Tensors (in a video course which may accompany his textbook) as well as over a hundred shorter videos on linear algebra. Many of these are available on YouTube as well as other sites.
Research interests
Hydrodynamics and fluid films dynamics, thermodynamics and phase transformations, minimal surfaces and calculus of variations.
Other Activities
Grinfeld is the founder of Lemma, Inc. which has developed the online learning system also called Lemma (https://www.lem.ma)
Bibliography
References
External links
Grinfeld's site at Drexel University
Grinfeld's Lemma site with videos, practice problems, and textbooks
1974 births
Living people
21st-century American mathematicians
Massachusetts Institute of Technology School of Science alumni
Drexel University faculty |
https://en.wikipedia.org/wiki/Ludwig%20Wittgenstein%27s%20philosophy%20of%20mathematics | Ludwig Wittgenstein considered his chief contribution to be in the philosophy of mathematics, a topic to which he devoted much of his work between 1929 and 1944. As with his philosophy of language, Wittgenstein's views on mathematics evolved from the period of the Tractatus Logico-Philosophicus: with him changing from logicism (which was endorsed by his mentor Bertrand Russell) towards a general anti-foundationalism and constructivism that was not readily accepted by the mathematical community. The success of Wittgenstein's general philosophy has tended to displace the real debates on more technical issues.
His Remarks on the Foundations of Mathematics contains his compiled views, notably a controversial repudiation of Gödel's incompleteness theorems.
Tractatus
Wittgenstein's initial conception of mathematics was logicist and even formalist. The Tractatus described the propositions of logic as a series of tautologies derived from syntactic manipulation, and without the pictorial force of elementary propositions depicting states of affairs obtaining in the world.
Wittgenstein asserted that “[t]he logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics” (6.22) and further that “Mathematics is a method of logic” (6.234).
Philosophy of mathematics, post-1929
During the 1920s Wittgenstein turned away from philosophical matters but his interest in mathematics was rekindled when he attended in Vienna a lecture by the intuitionist L. E. J. Brouwer. After 1929, his primary mathematical preoccupation entailed resolving the account of logical necessity he had articulated in the Tractatus Logico-Philosophicus—an issue which had been fiercely pressed by Frank P. Ramsey. Wittgenstein's initial response, Some Remarks on Logical Form, was the only academic paper he published during his lifetime, and marked the beginnings of a departure from the ideal language philosophy and correspondence theory of truth of the Tractatus.
The Lectures on the Foundations of mathematics
During the two terms of 1938/9 Wittgenstein lectured without any notes before students for two hours twice a week. From four sets of notes made during the lectures a text has been created, presenting Wittgenstein's views at that time.
The Remarks on the Foundations of mathematics (1937–44)
An editorial team prepared the edition of Wittgenstein's Remarks on the Foundations of mathematics from the manuscript notes he made during the years 1937–44. The material has been arranged in chronological order, allowing to observe some changes of emphasis or interest in Wittgenstein's views over the years.
References
Crispin Wright, 1980, Wittgenstein on the Foundations of Mathematics, Harvard University Press,
Pasquale Frascolla, 1994, Wittgenstein's Philosophy of Mathematics, Routledge
External links
Sorin Bangu, Ludwig Wittgenstein: Later Philosophy of Mathematics , IEP
Victor Rodych, Wittgenstein's Philosophy of Mathematics, The Stan |
https://en.wikipedia.org/wiki/Some%20Remarks%20on%20Logical%20Form | "Some Remarks on Logical Form" (1929) was the only academic paper ever published by Ludwig Wittgenstein, and contained Wittgenstein's thinking on logic and the philosophy of mathematics immediately before the rupture that divided the early Wittgenstein of the Tractatus Logico-Philosophicus from the late Wittgenstein. The approach to logical form in the paper reflected Frank P. Ramsey's critique of Wittgenstein's account of color in the Tractatus, and has been analyzed by G. E. M. Anscombe and Jaakko Hintikka, among others.
References
External links
Full text of Some Remarks on Logical Form at the Ludwig Wittgenstein Project
Books by Ludwig Wittgenstein
Philosophy of mathematics literature
Logic literature |
https://en.wikipedia.org/wiki/Witting%20polytope | In 4-dimensional complex geometry, the Witting polytope is a regular complex polytope, named as: 3{3}3{3}3{3}3, and Coxeter diagram . It has 240 vertices, 2160 3{} edges, 2160 3{3}3 faces, and 240 3{3}3{3}3 cells. It is self-dual. Each vertex belongs to 27 edges, 72 faces, and 27 cells, corresponding to the Hessian polyhedron vertex figure.
Symmetry
Its symmetry by 3[3]3[3]3[3]3 or , order 155,520. It has 240 copies of , order 648 at each cell.
Structure
The configuration matrix is:
The number of vertices, edges, faces, and cells are seen in the diagonal of the matrix. These are computed by the order of the group divided by the order of the subgroup, by removing certain complex reflections, shown with X below. The number of elements of the k-faces are seen in rows below the diagonal. The number of elements in the vertex figure, etc., are given in rows above the digonal.
Coordinates
Its 240 vertices are given coordinates in :
where .
The last 6 points form hexagonal holes on one of its 40 diameters. There are 40 hyperplanes contain central 3{3}3{4}2, figures, with 72 vertices.
Witting configuration
Coxeter named it after Alexander Witting for being a Witting configuration in complex projective 3-space:
or
The Witting configuration is related to the finite space PG(3,22), consisting of 85 points, 357 lines, and 85 planes.
Related real polytope
Its 240 vertices are shared with the real 8-dimensional polytope 421, . Its 2160 3-edges are sometimes drawn as 6480 simple edges, slightly less than the 6720 edges of 421. The 240 difference is accounted by 40 central hexagons in 421 whose edges are not included in 3{3}3{3}3{3}3.
The honeycomb of Witting polytopes
The regular Witting polytope has one further stage as a 4-dimensional honeycomb, . It has the Witting polytope as both its facets, and vertex figure. It is self-dual, and its dual coincides with itself.
Hyperplane sections of this honeycomb include 3-dimensional honeycombs .
The honeycomb of Witting polytopes has a real representation as the 8-dimensional polytope 521, .
Its f-vector element counts are in proportion: 1, 80, 270, 80, 1. The configuration matrix for the honeycomb is:
Notes
References
Coxeter, H. S. M. and Moser, W. O. J.; Generators and Relations for Discrete Groups (1965), esp pp 67–80.
Coxeter, H. S. M.; Regular Complex Polytopes, Cambridge University Press, second edition (1991). pp. 132–5, 143, 146, 152.
Coxeter, H. S. M. and Shephard, G.C.; Portraits of a family of complex polytopes, Leonardo Vol 25, No 3/4, (1992), pp 239–244
Polytopes
Complex analysis |
https://en.wikipedia.org/wiki/Runcinated%205-simplexes | In six-dimensional geometry, a runcinated 5-simplex is a convex uniform 5-polytope with 3rd order truncations (Runcination) of the regular 5-simplex.
There are 4 unique runcinations of the 5-simplex with permutations of truncations, and cantellations.
Runcinated 5-simplex
Alternate names
Runcinated hexateron
Small prismated hexateron (Acronym: spix) (Jonathan Bowers)
Coordinates
The vertices of the runcinated 5-simplex can be most simply constructed on a hyperplane in 6-space as permutations of (0,0,1,1,1,2) or of (0,1,1,1,2,2), seen as facets of a runcinated 6-orthoplex, or a biruncinated 6-cube respectively.
Images
Runcitruncated 5-simplex
Alternate names
Runcitruncated hexateron
Prismatotruncated hexateron (Acronym: pattix) (Jonathan Bowers)
Coordinates
The coordinates can be made in 6-space, as 180 permutations of:
(0,0,1,1,2,3)
This construction exists as one of 64 orthant facets of the runcitruncated 6-orthoplex.
Images
Runcicantellated 5-simplex
Alternate names
Runcicantellated hexateron
Biruncitruncated 5-simplex/hexateron
Prismatorhombated hexateron (Acronym: pirx) (Jonathan Bowers)
Coordinates
The coordinates can be made in 6-space, as 180 permutations of:
(0,0,1,2,2,3)
This construction exists as one of 64 orthant facets of the runcicantellated 6-orthoplex.
Images
Runcicantitruncated 5-simplex
Alternate names
Runcicantitruncated hexateron
Great prismated hexateron (Acronym: gippix) (Jonathan Bowers)
Coordinates
The coordinates can be made in 6-space, as 360 permutations of:
(0,0,1,2,3,4)
This construction exists as one of 64 orthant facets of the runcicantitruncated 6-orthoplex.
Images
Related uniform 5-polytopes
These polytopes are in a set of 19 uniform 5-polytopes based on the [3,3,3,3] Coxeter group, all shown here in A5 Coxeter plane orthographic projections. (Vertices are colored by projection overlap order, red, orange, yellow, green, cyan, blue, purple having progressively more vertices)
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.
x3o3o3x3o - spidtix, x3x3o3x3o - pattix, x3o3x3x3o - pirx, x3x3x3x3o - gippix
External links
Polytopes of Various Dimensions, Jonathan Bowers
Runcinated uniform polytera (spid), Jonathan Bowers
Multi-dimensional Glossary
5-polytopes |
https://en.wikipedia.org/wiki/Portezuelo%2C%20Chile | Portezuelo () is a Chilean town and commune located in the Itata Province, Ñuble Region.
Demographics
According to the 2002 census of the National Statistics Institute, Portezuelo spans an area of and has 5,470 inhabitants (2,825 men and 2,645 women). Of these, 1,750 (32%) lived in urban areas and 3,720 (68%) in rural areas. The population fell by 8.4% (500 persons) between the 1992 and 2002 censuses.
Localities
Quitento
Administration
As a commune, Portezuelo is a third-level administrative division of Chile administered by a communal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is Modesto Sepúlveda Andrade (PDC). The communal council has the following members:
Paulina Zamudio (Ind./Pro-PDC)
Daniel Pastén (UDI)
Pedro Fernández (Ind./PDC)
Flavio Barrientos (Ind./RN)
Marcelo Cortés (PRI)
Melitón Aravena (PDC)
Within the electoral divisions of Chile, Portezuel belongs to the 42nd electoral district and 12th senatorial constituency.
See also
List of towns in Chile
References
External links
Municipality of Portezuelo
Communes of Chile
Populated places in Itata Province |
https://en.wikipedia.org/wiki/Florida%2C%20Chile | Florida () is a Chilean town and commune located in the Concepción Province, Biobío Region.
Demographics
According to the 2002 census of the National Statistics Institute, Florida spans an area of and has 10,177 inhabitants (5,231 men and 4,946 women). Of these, 3,875 (38.1%) lived in urban areas and 6,302 (61.9%) in rural areas. Between the 1992 and 2002 censuses, the population fell by 2.5% (260 persons).
Administration
As a commune, Florida is a third-level administrative division of Chile administered by a communal council, headed by an alcalde who is directly elected every four years. The 2008-2012 alcalde is Juan Vergara Reyes. The communal council has the following members:
Aureliano Illanes (PRI)
Jorge Roa (PDC)
Juan Contreras (PS)
Agustin Montero (RN)
José Lizama (UDI)
Renán Arriagada (Ind.)
Within the electoral divisions of Chile, Florida is represented in the Chamber of Deputies by Sergio Bobadilla (UDI) and Clemira Pacheco (PS) as part of the 45th electoral district, (together with Tomé, Penco, Hualqui, Coronel and Santa Juana). The commune is represented in the Senate by Alejandro Navarro Brain (MAS) and Hosain Sabag Castillo (PDC) as part of the 12th senatorial constituency (Biobío-Cordillera).
References
External links
Municipality of Florida
Communes of Chile
Populated places in Concepción Province |
https://en.wikipedia.org/wiki/Uzma%20Aslam%20Khan | Uzma Aslam Khan is a Pakistani American writer. Her five novels include Trespassing (2003), The Geometry of God (2008), Thinner Than Skin (2012) and The Miraculous True History of Nomi Ali (2019).
Personal life
Khan was born in Lahore and raised largely in Karachi, though her earliest years were spent in Manila, Tokyo, and London. She describes her childhood as "forcibly uprooted and happily nomadic." Her family resettled in Pakistan shortly before the country's military dictator, General Zia, declared martial law—she has said that these changes, personal and political, were her "transition from childhood to adulthood." She received a scholarship to study at Hobart and William Smith Colleges, New York, from where she obtained a BA in Comparative Literature, and obtained an MFA from the University of Arizona, Tucson, US.
Career
Novelist
Khan's first novel, The Story of Noble Rot, was published by Penguin Books India in 2001, and reissued by Rupa & Co. in 2009.
Her second novel, Trespassing, was published simultaneously by Flamingo/HarperCollins in the UK and Penguin Books India in 2003. It has been translated into fourteen languages in eighteen countries. Set in the 1990s during the aftermaths of the Afghan War and Gulf War and completed a few months before 9/11, the book has been called "prescient" for how it illustrates the dark and troubled context of the west's involvement in the east and a precursor to the post-9/11 fiction from Pakistan that was to come. As Khan puts it "So much of this book is about history coming back to haunt you." Writing for Outlook magazine, Nilanjana S. Roy wrote that "While Khan's prose may be subtle, her style is as forceful as any of the great storytellers... Khan is creating a tradition and style of her own as a writer." Trespassing was shortlisted for the 2003 Commonwealth Writers' Prize, Eurasia region.
Khan's third novel, The Geometry of God, was printed by Rupa & Co. India in 2008. It tells the story of Amal, who, as a child, accidentally discovers the fossil of the ear of the first whale – or 'dog-whale', as she calls it – while on a dig with her paleontologist grandfather. Despite the pressures imposed on her by her family, and by society, Amal goes on to become the first woman paleontologist to work with men in the mountains of Pakistan to look for fossils of ancient whales. The novel was praised for boldly charting new territory, and for its characters. Khan was becoming recognized for her frank exploration of sexuality, unique in Pakistani English-language writing.
Following its release in India, The Geometry of God was published in Spain, Italy, France, the US, the UK, and Pakistan. It won the Bronze Award for multicultural fiction in the Independent Publisher Book Awards, 2010; was selected as one of Kirkus Reviews Best Books of 2009; and was a finalist of Foreword magazine's Best Books of 2009.
Khan's fourth novel, Thinner than Skin, was published in 2012 in the US, and subsequently in Canada, I |
https://en.wikipedia.org/wiki/Ba%C5%9Far | Başar is a Turkish male given name and surname.
Name statistics
Başar is the 1020th most popular name in Turkey. 1/9,816 of all Turks are named Başar, so its popularity is 0.1 in a thousand. If this is compared to Turkey's population statistics, there are 7,423 Başars and 119 are born each year.
Given name
Başar Sabuncu, Turkish film director, screenwriter, cinematographer and occasional actor
Başar Oktar, Turkish Figure Skater
Surname
Günseli Başar (1932–2013), Turkish beauty contestant and Miss Europe 1952
Kemal Başar, Turkish theatre director, drama teacher and translator
Metehan Başar (born 1991), Turkish wrestler
Şükûfe Nihal Başar (1896–1973), Turkish school teacher, poet, novelist and women's right activist
Tamer Başar, Turkish control theorist
References
Turkish masculine given names
Masculine given names
Turkish-language surnames |
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