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https://en.wikipedia.org/wiki/Statistical%20Office%20of%20the%20Republic%20of%20Serbia | The Statistical Office of the Republic of Serbia (; or RBS) is a specialized government agency of Serbia charged with collecting and disseminating official statistics.
History
Official statistics in the Republic of Serbia was established in 1862, when Prince Mihailo Obrenovic passed an act granting powers to the economic department of the Ministry of Finance concerning all statistical work. This was the beginning of state statistics in Serbia, but historic data suggest there was even earlier collecting of statistical data on tax payers, census of the cattle (in 1824) and regular population censuses (from 1834), as well as, since 1843, regular monitoring of statistical data on external trade, domestic trade, prices and wages.
Statistical work was performed even before the foundation of the National Statistical Office through participation of Serbian representatives at international congresses of statisticians held in the Hague in 1859, in Berlin in 1863 and in Florence in 1867.
The Law on the Organization of Statistics was enacted in 1881 and in 1882 the Ministry of National Economy assumed responsibility regarding national statistics.
State Statistics of Serbia has been a member of the International Statistical Institute since its foundation in 1885.
The State Statistics Directorate was founded in 1919 in the scope of the Ministry of Social Policy of the Kingdom of Serbs, Croats and Slovenes, but a separate Statistical Office of Serbia was opened only in 1945.
Regarding the publishing activity, the first State Statistics of Serbia was published in 1863 and the first results of Population Census in 1863. The first Statistical Yearbook of the Kingdom of Serbia was published in 1893 and in 1894 the State Statistics was published for the last time. The last Statistical Yearbook of the Kingdom of Serbia was published in 1910. In 1954 a special edition of the Statistical Yearbook of Serbia was re-published, as a complex statistical publication that encompassed the results of versatile statistical surveys.
The Statistical Office of the Republic of Serbia was founded in 1945.
In the period 1945-2006 the Statistical Office of the Republic of Serbia was inferior to the Federal Statistical Office regarding the process of conducting unique programs of statistical surveys and methodologies. Simultaneously, the Office has been completely independent regarding financial and human resources and other issues.
References
External links
Government of Serbia
Demographics of Serbia
Government agencies established in 1862
1860s establishments in Serbia |
https://en.wikipedia.org/wiki/Link%20distance | In computational geometry, the link distance between two points in a polygon is the minimum number of line segments of any polygonal chain within the polygon that has the two points as its endpoints. The link diameter of the polygon is the maximum link distance of any two of its points.
A polygon is a convex polygon if and only if its link diameter is one.
Every star-shaped polygon has link diameter at most two: every two points may be connected by a polygonal chain that bends once, inside the kernel of the polygon. However, this property does not characterize star-shaped polygons, as there also exist polygons with holes in which the link diameter is two.
References
.
Computational geometry |
https://en.wikipedia.org/wiki/%C3%9Eorsteinn%20%C3%9Eorsteinsson | Þorsteinn Þorsteinsson (also written Thorsteinn Thorsteinsson; April 5, 1880 – February 22, 1979) was an Icelandic economist, director of the Icelandic Bureau of Statistics, and also one of the first authorities on Esperanto in Iceland, author of the first Icelandic textbook on Esperanto.
Life and career
Þorsteinn Þorsteinsson was born at Brú in Biskupstungur, in Árnessýsla, the youngest of six children. The poet Tómas Guðmundsson was a cousin. He graduated in 1902 from Menntaskólinn í Reykjavík, then earned a Candid. Polit. degree in economics from the University of Copenhagen in 1906, the fourth Icelander to major in the field. He started work at the Icelandic Department of Industry and Transportation, transferred in 1909 to the Department of Finance, and then on January 1, 1914 became director of the newly created Bureau of Statistics, where he continued working until his retirement in 1950. He also taught economics part-time at the Commercial College of Iceland from 1916 to 1929 and was an examiner in the subject at the University of Iceland beginning in 1941.
He sat on several boards and was a founder and first president of the Icelandic Association of Economists (Félag hagfræðinga).
Þorsteinn was married to Guðrún Geirsdóttir, daughter of Geir T. Zoëga, the rector of Menntaskólinn í Reykjavík; she died in 1955. They had five children. He died in Reykjavík.
Esperanto
Þorsteinn learned Esperanto in 1899, and soon after started to publish articles making the case for Esperanto. He wrote the first Icelandic textbook of Esperanto, a translation of the book by Théophile Cart; it appeared in 1909 and was republished in 1927.
In 1927 he co-founded the first Icelandic Esperanto Society in Reykjavík, and served as its president until 1931, when the first Icelandic Esperanto Association, Samband íslenzkra esperantista, was founded and he became its president. He became acquainted with L. L. Zamenhof during the 3rd World Esperanto Congress in 1907, corresponded with him, and in 1977 was a guest at the 62nd World Esperanto Congress, held in Reykjavík. He was a member of the Esperantist Linguistic Committee and dean of the
Honors
He was awarded an honorary doctorate in economics by the University of Iceland on its 35th anniversary in 1946, became a fellow of the in 1919 and was an honorary fellow of the Icelandic Association of Economists, the Icelandic Literary Society, and the revived Icelandic Esperanto Association.
Publications
In his position as director of the Bureau of Statistics, Þorsteinn edited and wrote or co-wrote many publications, including a monthly bulletin, a multi-volume list of the names in the 1703 census, and the handbook of Iceland published four times between 1926 and 1946 under the auspices of Landsbanki. Other publications include:
Kenslubók í Esperantó: ásamt orðasafni með íslenskum þýðingum. Trans. of Cart, Théophile. L'Esperanto en dix leçons. Reykjavík: Bókaverslun Guðm. Gamalíelssonar, 1909. . (Icelandic and Espera |
https://en.wikipedia.org/wiki/Committee%20on%20Monetary%2C%20Financial%20and%20Balance%20of%20Payments%20Statistics | CMFB, in the context of European statistics, stands for Committee on Monetary, Financial and Balance of Payments Statistics. Originally established in 1991, the Committee is an advisory committee for the European Commission (Eurostat) and European Central Bank and a platform for cooperation between the statistical and central banking community in Europe (CMFB).
Main tasks
The Commission, on its own initiative, and, should the occasion arise, following a request from the Council or from the committees which assist them, shall consult the Committee on:
the establishment of multiannual Community programmes for monetary, financial and balance of payments statistics;
the measures which the Commission intends to undertake to achieve the objectives referred to in the multiannual programmes for monetary, financial and balance of payments statistics and the resources and timetables involved;
any other question, in particular questions of methodology, arising from the establishment or implementation of the Statistical Programme in the relevant fields.
The Committee may express opinions on its own initiative on any questions relating to the establishment or the implementation of statistical programmes in the monetary, financial and balance of payments fields.
CMFB opinions
The CMFB's main output is its opinion, adopted by a majority of its members, according to the applicable rules of procedure (special rules apply for adoption opinion in the context of the Excessive Deficit Procedure).
Below is a list of the most recent and relevant opinions that the Committee has concluded, upon the request of one or more EU Member States:
The CMFB's advisory role in the EU's Excessive Deficit Procedure (EDP)
The format of the questionnaires shall be defined by the Commission (Eurostat) after consultation of the Committee on Monetary, Financial and Balance of Payments Statistics (hereinafter referred to as CMFB).
The inventories shall be prepared in accordance with guidelines adopted by the Commission (Eurostat) after consultation of CMFB.
In the event of a doubt regarding the correct implementation of the ESA 95 [today: ESA 2010] accounting rules, the Member State concerned shall request clarification from the Commission (Eurostat). The Commission (Eurostat) shall promptly examine the issue and communicate its clarification to the Member State concerned and, when appropriate, to the CMFB.
For cases which are either complex or of general interest in the view of the Commission or the Member State concerned, the Commission (Eurostat) shall take a decision after consultation of the CMFB. The Commission (Eurostat) shall make decisions public, together with the opinion of the CMFB, without prejudice to the provisions relating to statistical confidentiality of Regulation (EC) No 322/97.
The CMFB's role in ensuring the quality of statistics underlying the EU's Macroeconomic Imbalance Procedure (MIP)
The (ECOFIN) Council of the European Union, in its 2015 conclusi |
https://en.wikipedia.org/wiki/Planning%20Ministry%20%28Bangladesh%29 | The Ministry of Planning (; Parikalpanā mantraṇālaẏa) oversees the financial policies of the Bangladeshi Government, responsible for socioeconomic planning and statistics management.
It contains three divisions:
Planning Division
Statistics and Informatics Division
Implementation Monitoring & Evaluation Division
Directorates
1. Planning Division
Bangladesh Institute of Development Studies
Planning Commission
National Academy for Planning and Development
2. Statistics and Informatics Division
Bangladesh Bureau of Statistics
3. Implementation Monitoring and Evaluation Division
Central Procurement Technical Unit
References
Planning
Bangladesh |
https://en.wikipedia.org/wiki/Clean%20ring | In mathematics, a clean ring is a ring in which every element can be written as the sum of a unit and an idempotent. A ring is a local ring if and only if it is clean and has no idempotents other than 0 and 1. The endomorphism ring of a continuous module is a clean ring. Every clean ring is an exchange ring. A matrix ring over a clean ring is itself clean.
References
Ring theory |
https://en.wikipedia.org/wiki/UEFA%20Euro%202016%20statistics | The following article outlines statistics for UEFA Euro 2016, which took place in France from 10 June to 10 July 2016. Goals scored during penalty shoot-outs are not counted, and matches decided by a penalty shoot-out are considered draws.
Goalscorers
Assists
Clean sheets
4 clean sheets
Manuel Neuer
Rui Patrício
3 clean sheets
Thibaut Courtois
Hugo Lloris
Gianluigi Buffon
2 clean sheets
Łukasz Fabiański
David de Gea
Yann Sommer
Wayne Hennessey
1 clean sheet
Etrit Berisha
Robert Almer
Danijel Subašić
Joe Hart
Gábor Király
Michael McGovern
Wojciech Szczęsny
Darren Randolph
Matúš Kozáčik
Volkan Babacan
Awards
Golden Boot
Antoine Griezmann of France received the Golden Boot award as the top scorer of the tournament with six goals, the most for a player at a single tournament since countryman Michel Platini scored nine in 1984.
Man of the Match
Scoring
Overview
Timing
Teams
Individual
Attendance
Overall attendance: 2,427,303
Average attendance per match:
Highest attendance: 76,833 – France vs Iceland
Lowest attendance: 28,840 – Russia vs Wales
Wins and losses
Discipline
Summary
Sanctions
By match
By referee
By team
By individual
Overall statistics
Notes
References
External links
UEFA Euro 2016 statistics at Union of European Football Associations
Statistics
2016 |
https://en.wikipedia.org/wiki/List%20of%20film%20scores%20by%20Ilaiyaraaja%201970s | This article lists the films composed by Ilaiyaraaja in the 1970s..
Ilaiyaraaja 1976
Ilaiyaraaja 1977
Ilaiyaraaja 1978
Ilaiyaraaja 1979
Decade-wise statistics
Bibliography
References
External links
Raaja.com: The official Internet website of Ilaiyaraaja
Discographies of Indian artists |
https://en.wikipedia.org/wiki/Aleksei%20Parshin | Aleksei Nikolaevich Parshin (; 7 November 1942 – 18 June 2022) was a Russian mathematician, specializing in arithmetic geometry. He is most well-known for his role in the proof of the Mordell conjecture.
Education and career
Parshin entered the Faculty of Mathematics and Mechanics of Moscow State University in 1959 and graduated in 1964. He then enrolled as a graduate student at the Steklov Institute of Mathematics, where he received his Kand. Nauk (Ph.D.) in 1968 under Igor Shafarevich. In 1983, he received his Doctor Nauk (doctorate of sciences) from Moscow State University.
Parshin became a junior research fellow at the Steklov Institute of Mathematics in Moscow in 1968, later becoming a senior and leading research fellow. He became the head of its Department of Algebra in 1995. He also taught at Moscow State University.
Research
In his 1968 thesis, Parshin proved that the Mordell conjecture is a logical consequence of Shafarevich's finiteness conjecture concerning isomorphism classes of abelian varieties via what is known as Parshin's trick, which gives an embedding of an algebraic curve into the Siegel modular variety. Shafarevich proved his finiteness conjecture for the case with genus g = 1. Parshin proved a special case (for = the empty set) of the following theorem: If is a smooth complex curve and is a finite subset of then there exist only finitely many families (up to isomorphism) of smooth curves of fixed genus g ≥ 2 over . The general case (for non-empty ) of the preceding theorem was proved by Suren Arakelov in 1971. At the same time, Parshin gave a new proof (without an application of the Shafarevich finiteness condition) of the Mordell conjecture in function fields (already proved by Yuri Manin in 1963 and by Hans Grauert in 1965). In 1983, Gerd Faltings completed the program and proved Shafarevich's finiteness conjecture, thereby proving the Mordell conjecture.
His other research dealt with generalizations of class field theory in higher dimensions, with integrable systems, and with the history of mathematics.
He was an editor for the Russian edition of the collected works of David Hilbert and was a co-editor, with V. I. Arnold, of selected works of Hermann Weyl.
Personal life
Parshin was born on 7 November 1942 in Sverdlovsk and died on 18 June 2022.
Parshin was longtime friends with Russian philosopher Aleksei Losev and started the Russian philosophy seminar at the Dom Loseva Library in Moscow. Parshin was Orthodox Christian and wrote about the relationship between Russian religious philosophy and the modern sciences.
Awards and honors
In 1971, Parshin received the Prize of the Moscow Mathematical Society for young mathematicians. He was awarded the Humboldt Prize in 1996. He received the Vinogradov Prize in 2004 and the Chebyshev Gold Medal in 2012 from the Russian Academy of Sciences.
The Université Paris-Nord granted Parshin an honorary doctorate in 2001. Parshin was elected a corresponding member of the Russi |
https://en.wikipedia.org/wiki/Iselilja%20%28given%20name%29 | Iselilja is a Norwegian feminine given name. In 2015, in Norway 17 people had the name as a first name and 15 people had it as a middle name, according to SSB's name statistics.
Origin
"Iselilja" is mentioned in the medieval Norwegian ballad , a song that has been recorded and released by Alf Cranner on the album Rosemalt Sound (1967), by the folk-rock band on (1978), and by Norwegian folk music band Gåte on their studio album Iselilja (2004) and their live album Liva (2006).
The name is, according to Norwegian historian Harald S. Næss in his eponymous Knut Hamsun biography (1984) and according to A Handbook of Scandinavian Names (2010), a probable influence for the later name Iselin known since the mid 18th century.
References
Norwegian feminine given names
Feminine given names |
https://en.wikipedia.org/wiki/Pullback%20%28cohomology%29 | In algebraic topology, given a continuous map f: X → Y of topological spaces and a ring R, the pullback along f on cohomology theory is a grade-preserving R-algebra homomorphism:
from the cohomology ring of Y with coefficients in R to that of X. The use of the superscript is meant to indicate its contravariant nature: it reverses the direction of the map. For example, if X, Y are manifolds, R the field of real numbers, and the cohomology is de Rham cohomology, then the pullback is induced by the pullback of differential forms.
The homotopy invariance of cohomology states that if two maps f, g: X → Y are homotopic to each other, then they determine the same pullback: f* = g*.
In contrast, a pushforward for de Rham cohomology for example is given by integration-along-fibers.
Definition from chain complexes
We first review the definition of the cohomology of the dual of a chain complex. Let R be a commutative ring, C a chain complex of R-modules and G an R-module. Just as one lets , one lets
where Hom is the special case of the Hom between a chain complex and a cochain complex, with G viewed as a cochain complex concentrated in degree zero. (To make this rigorous, one needs to choose signs in the way similar to the signs in the tensor product of complexes.) For example, if C is the singular chain complex associated to a topological space X, then this is the definition of the singular cohomology of X with coefficients in G.
Now, let f: C → C be a map of chain complexes (for example, it may be induced by a continuous map between topological spaces). Then there is
which in turn determines
If C, C are singular chain complexes of spaces X, Y, then this is the pullback for singular cohomology theory.
References
J. P. May (1999), A Concise Course in Algebraic Topology.
S. P. Novikov (1996), Topology I - General Survey.
Cohomology theories |
https://en.wikipedia.org/wiki/Alice%20Rogers | Frances Alice Rogers is a British mathematician and mathematical physicist. She is an emeritus professor of mathematics at King's College London.
Research
Rogers' research concerns mathematical physics and more particularly supermanifolds, generalizations of the manifold concept based on ideas coming from supersymmetry. She is the author of the book Supermanifolds: Theory and Applications (World Scientific, 2007).
Service
Rogers has been a member of the British government's Advisory Committee on Mathematics Education, is the education secretary of the London Mathematical Society (LMS), and represents the LMS on the Joint Mathematical Council of the UK.
Education
Rogers studied mathematics in New Hall, Cambridge, in the 1960s. Her mother had also studied mathematics at Cambridge in the 1930s and later became a wartime code-breaker at Bletchley Park. Rogers earned her Ph.D. in 1981 from Imperial College London.
Recognition
In 2016, she was appointed as an Officer of the Order of the British Empire "for services to Mathematics Education and Higher Education".
In 2018, Rogers was awarded the Kavli Education Medal for "her outstanding contributions to mathematics education" from The Royal Society.
References
External links
Home page
Year of birth missing (living people)
Living people
English mathematicians
Women mathematicians
Alumni of New Hall, Cambridge
Alumni of Imperial College London
Academics of King's College London
Officers of the Order of the British Empire
Fellows of King's College London |
https://en.wikipedia.org/wiki/Trace%20field%20of%20a%20representation | In mathematics, the trace field of a linear group is the field generated by the traces of its elements. It is mostly studied for Kleinian and Fuchsian groups, though related objects are used in the theory of lattices in Lie groups, often under the name field of definition.
Fuchsian and Kleinian groups
Trace field and invariant trace fields for Fuchsian groups
Fuchsian groups are discrete subgroups of . The trace of an element in is well-defined up to sign (by taking the trace of an arbitrary preimage in ) and the trace field of is the field generated over by the traces of all elements of (see for example in ).
The invariant trace field is equal to the trace field of the subgroup generated by all squares of elements of (a finite-index subgroup of ).
The invariant trace field of Fuchsian groups is stable under taking commensurable groups. This is not the case for the trace field; in particular the trace field is in general different from the invariant trace field.
Quaternion algebras for Fuchsian groups
Let be a Fuchsian group and its trace field. Let be the -subalgebra of the matrix algebra generated by the preimages of elements of . The algebra is then as simple as possible, more precisely:
If is of the first or second type then is a quaternion algebra over .
The algebra is called the quaternion algebra of . The quaternion algebra of is called the invariant quaternion algebra of , denoted by . As for trace fields, the former is not the same for all groups in the same commensurability class but the latter is.
If is an arithmetic Fuchsian group then and together are a number field and quaternion algebra from which a group commensurable to may be derived.
Kleinian groups
The theory for Kleinian groups (discrete subgroups of ) is mostly similar as that for Fuchsian groups. One big difference is that the trace field of a group of finite covolume is always a number field.
Trace fields and fields of definition for subgroups of Lie groups
Definition
When considering subgroups of general Lie groups (which are not necessarily defined as a matrix groups) one has to use a linear representation of the group to take traces of elements. The most natural one is the adjoint representation. It turns out that for applications it is better, even for groups which have a natural lower-dimensional linear representation (such as the special linear groups ), to always define the trace field using the adjoint representation. Thus we have the following definition, originally due to Ernest Vinberg, who used the terminology "field of definition".
Let be a Lie group and a subgroup. Let be the adjoint representation of . The trace field of is the field:
If two Zariski-dense subgroups of are commensurable then they have the same trace field in this sense.
The trace field for lattices
Let be a semisimple Lie group and a lattice. Suppose further that either is irreducible and is not locally isomorphic to , or that has no facto |
https://en.wikipedia.org/wiki/Heptagonal%20triangle | In Euclidean geometry, a heptagonal triangle is an obtuse, scalene triangle whose vertices coincide with the first, second, and fourth vertices of a regular heptagon (from an arbitrary starting vertex). Thus its sides coincide with one side and the adjacent shorter and longer diagonals of the regular heptagon. All heptagonal triangles are similar (have the same shape), and so they are collectively known as the heptagonal triangle. Its angles have measures and and it is the only triangle with angles in the ratios 1:2:4. The heptagonal triangle has various remarkable properties.
Key points
The heptagonal triangle's nine-point center is also its first Brocard point.
The second Brocard point lies on the nine-point circle.
The circumcenter and the Fermat points of a heptagonal triangle form an equilateral triangle.
The distance between the circumcenter O and the orthocenter H is given by
where R is the circumradius. The squared distance from the incenter I to the orthocenter is
where r is the inradius.
The two tangents from the orthocenter to the circumcircle are mutually perpendicular.
Relations of distances
Sides
The heptagonal triangle's sides a < b < c coincide respectively with the regular heptagon's side, shorter diagonal, and longer diagonal. They satisfy
(the latter being the optic equation) and hence
and
Thus –b/c, c/a, and a/b all satisfy the cubic equation
However, no algebraic expressions with purely real terms exist for the solutions of this equation, because it is an example of casus irreducibilis.
The approximate relation of the sides is
We also have
satisfy the cubic equation
We also have
satisfy the cubic equation
We also have
satisfy the cubic equation
We also have
and
We also have
There are no other (m, n), m, n > 0, m, n < 2000 such that
Altitudes
The altitudes ha, hb, and hc satisfy
and
The altitude from side b (opposite angle B) is half the internal angle bisector of A:
Here angle A is the smallest angle, and B is the second smallest.
Internal angle bisectors
We have these properties of the internal angle bisectors and of angles A, B, and C respectively:
Circumradius, inradius, and exradius
The triangle's area is
where R is the triangle's circumradius.
We have
We also have
The ratio r /R of the inradius to the circumradius is the positive solution of the cubic equation
In addition,
We also have
In general for all integer n,
where
and
We also have
We also have
The exradius ra corresponding to side a equals the radius of the nine-point circle of the heptagonal triangle.
Orthic triangle
The heptagonal triangle's orthic triangle, with vertices at the feet of the altitudes, is similar to the heptagonal triangle, with similarity ratio 1:2. The heptagonal triangle is the only obtuse triangle that is similar to its orthic triangle (the equilateral triangle being the only acute one).
Trigonometric properties
Trigonometric identities
The various trigonometric |
https://en.wikipedia.org/wiki/G%C3%BCnter%20Harder | Günter Harder (born 14 March 1938 in Ratzeburg) is a German mathematician, specializing in arithmetic geometry and number theory.
Education and career
Harder studied mathematics and physics in Hamburg und Göttingen. Simultaneously with the Staatsexamen in 1964 in Hamburg, he received his doctoral degree (Dr. rer. nat.) under Ernst Witt with a thesis Über die Galoiskohomologie der Tori. Two years later he completed his habilitation. After a one-year postdoc position at Princeton University and a position as an assistant professor at the University of Heidelberg, he became a professor ordinarius at the University of Bonn. With the exception of a six-year stay at the former Universität-Gesamthochschule Wuppertal, Harder remained at the University of Bonn until his retirement in 2003. From 1995 to 2006 he was one of the directors of the Max-Planck-Institut für Mathematik in Bonn.
His research deals with arithmetic geometry, automorphic forms, Shimura varieties, motives, and algebraic number theory. He made foundational contributions to the Waldspurger formula.
He was a visiting professor at Harvard University, Yale University, at Princeton's Institute for Advanced Study (IAS) (for the academic years 1966–1967, 1972–1973, 1986–1987, autumn of 1983, autumn of 2006), at the Institut des Hautes Études Scientifiques (I.H.É.S.) in Paris, at the Tata Institute of Fundamental Research in Mumbai, and at the Mathematical Sciences Research Institute (MSRI) at the University of California, Berkeley. He was an Invited Speaker at the ICM in 1970 in Nice with talk Semisimple group schemes over curves and automorphic functions and in 1990 in Kyōto with talk Eisenstein cohomology of arithmetic groups and its applications to number theory. In 1988 he was awarded the Leibniz Prize by the Deutsche Forschungsgemeinschaft. In 2004 Harder received, with Friedhelm Waldhausen, the von Staudt Prize.
For decades, Harder was known to German mathematicians as the Spiritus Rector for a mathematical workshop held for one week in spring and one week in autumn; the workshop, sponsored by the Mathematical Research Institute of Oberwolfach, introduced young mathematicians and scientists to important new developments in pure mathematics and mathematical sciences.
With Ina Kersten, he is a co-editor of the collected works of Ernst Witt.
Harder's doctoral students include Kai Behrend, Maria Heep-Altiner and Jörg Bewersdorff.
Selected publications
(online).
(online)
(online).
(contains Harder's contribution: )
References
External links
Homepage of Günter Harder at the Hausdorff Center of the University of Bonn
Homepage of Günter Harder at the University of Bonn
1938 births
Living people
20th-century German mathematicians
21st-century German mathematicians
Algebraists
Number theory
University of Hamburg alumni
Academic staff of the University of Bonn
Academic staff of the University of Wuppertal
Institute for Advanced Study visiting scholars
People from Rat |
https://en.wikipedia.org/wiki/1955%20Campe%C3%B3n%20de%20Campeones | The 1955 Campeon de Campeones was the 14th Mexican Super Cup football one-leg match played on 3 March 1955.
League winners: Zacatepec
Cup winners: América
Match details
References
- Statistics of Mexican Super Cup. (RSSSF)
Campeón de Campeones
1955–56 in Mexican football
March 1955 sports events in Mexico |
https://en.wikipedia.org/wiki/1959%20Campe%C3%B3n%20de%20Campeones | The 1959 Campeon de Campeones was the 18th Mexican Super Cup football one-leg match played on May, 1959.
League winners: Guadalajara
Cup winners: Zacatepec
Match details
References
- Statistics of Mexican Super Cup. (RSSSF)
Campeón de Campeones
Campeón
May 1959 sports events in Mexico |
https://en.wikipedia.org/wiki/Probability%20of%20success | The probability of success (POS) is a statistics concept commonly used in the pharmaceutical industry including by health authorities to support decision making.
The probability of success is a concept closely related to conditional power and predictive power. Conditional power is the probability of observing statistical significance given the observed data assuming the treatment effect parameter equals a specific value. Conditional power is often criticized for this assumption. If we know the exact value of the treatment effect, there is no need to do the experiment. To address this issue, we can consider conditional power in a Bayesian setting by considering the treatment effect parameter to be a random variable. Taking the expected value of the conditional power with respect to the posterior distribution of the parameter gives the predictive power. Predictive power can also be calculated in a frequentist setting. No matter how it is calculated, predictive power is a random variable since it is a conditional probability conditioned on randomly observed data. Both conditional power and predictive power use statistical significance as the success criterion. However, statistical significance is often not sufficient to define success. For example, a health authority often requires the magnitude of the treatment effect to be bigger than an effect which is merely statistically significant in order to support successful registration. In order to address this issue, we can extend conditional power and predictive power to the concept of probability of success. For probability of success, the success criterion is not restricted to statistical significance. It can be something else such as a clinical meaningful result.
Types of POS
Conditional probability of success (CPOS): It is the probability of observing success (in terms of the observed result) in the future given the observed data and the treatment effect equaling a specific value. CPOS is an extension of conditional power. Its success criteria are not restricted to statistical significance. However when the success is defined as statistical significance, it becomes conditional power.
Predictive probability of success (PPOS): It is the probability of observing success in the future given the observed data. PPOS is an extension of predictive power. Its success criteria are not restricted to statistical significance. However when the success is defined as statistical significance, it becomes predictive power. Note that PPOS is a conditional probability conditioned on randomly observed data. Hence it is a random variable.
Posterior probability of success (OPOS): It is the probability of success (in terms of the treatment effect parameter) calculated using posterior probability. Note that OPOS is a conditional probability conditioned on randomly observed data. Hence it is a random variable.
Application in clinical trials design
Pilot trial design using PPOS
Traditional pilot trial design is t |
https://en.wikipedia.org/wiki/Vladimir%20Gerdt | Vladimir P. Gerdt (21 January 1947—January 5, 2021) was a Russian mathematician and a full professor at the Joint Institute for Nuclear Research (JINR) where he was the head of the Group of Algebraic and Quantum Computations. His research interests were concentrated in computer algebra, symbolic and algebraic computations, algebraic and numerical analysis of nonlinear differential equations, polynomial equations, applications to mathematics and physics, and quantum computation with over 210 published articles.
Biography
Gerdt, who was born in Engels, earned his MSc in theoretical physics from Saratov State University in 1971, his PhD in theoretical and mathematical physics from JINR in 1976, and his D.Sc. in mathematics and computer science from JINR in 1992. He also did graduate studies in theoretical physics at the Lomonosov Moscow State University (1969-1971). After his MSc he worked as an engineer-programmer (1971-1975) and as a junior researcher (1975-1977) at the JINR Department of Radiation Safety developing software for neutron spectroscopy. In 1977 he moved to the JINR Laboratory of Computing Techniques and Automation renamed in 2000 as Laboratory of Information Technologies for doing research in computer algebra. He worked as a researcher (1977-1980) and as a senior researcher (1980-1983), and since 1983 as the head of the research group on computer algebra, currently the Group of Algebraic and Quantum Computations.
Gerdt designed a number of original algorithms and software packages for the investigation of differential equations as well as for the transformation of polynomial and differential systems into the canonical involutive form that alleviates their analysis and the construction of their solutions. In the case of polynomial, differential, and difference systems their involutive form is a Gröbner basis.
He was a member of the editorial board of the Journal of Symbolic Computation, the leading international journal specialized in the area of symbolic and algebraic computation, since its foundation in 1985. In 1997 he co-founded the annual international conference Computer Algebra in Scientific Computing with Ernst W. Mayr and since that time was a general chair of this conference.
Gerdt was married to Evgenia Almazova and had two sons, Anton and Peter.
Gerdt died in 2020 of COVID-19.
Selected works
Gerdt, Vladimir P. Involutive algorithms for computing Gröbner bases. Computational Commutative and Non-Commutative Algebraic Geometry, Amsterdam, IOS Press, 2005.
Gerdt, Vladimir P., Yuri A. Blinkov, and Denis A. Yanovich. "Construction of Janet Bases I. Monomial Bases." Computer Algebra in Scientific Computing CASC 2001. Springer Berlin Heidelberg, 2001. 233–247.
Gerdt, Vladimir P., Aleksey Y.Zharkov. "Solution of Chew-Low Equations in the Quadratic Approximation", Sov. Theor. Math. Phys. (Teor. Mat. Fiz., 52, 3, 1982, 384–392), 52, 3, 1983, 868–874.
Gerdt, Vladimir P., Aleksey Y.Zharkov. "A REDUCE Package for Solving of Ordi |
https://en.wikipedia.org/wiki/Robert%20Megginson | Robert Eugene Megginson is an American mathematician, the Arthur F. Thurnau Professor of Mathematics at the University of Michigan. His research concerns functional analysis and Banach spaces; he is the author of the textbook An Introduction to Banach Space Theory (GTM 183, Springer, 1998).
Megginson was born in 1948 in Washington, Illinois, of Oglala Sioux heritage on his mother's side, and grew up in Sheldon, Illinois, where his father was mayor. He earned a degree in physics from the University of Illinois at Urbana–Champaign in 1969, and became a software specialist for the Roper Corporation until 1977, when he returned to graduate school. He earned a master's degree in statistics in 1983, He completed his Ph.D. in 1984 at the University of Illinois, with a thesis on normed vector spaces supervised by Mahlon M. Day.
This accomplishment made him one of only approximately 12 Native Americans to hold a doctorate in mathematics, and he has taken great interest in underrepresented minorities in mathematics.
Because his wife was employed nearby in Decatur, Illinois, Megginson took a teaching position in 1983, joining the faculty of Eastern Illinois University as an assistant professor, rather than doing postdoctoral research. He moved to the University of Michigan in 1992, was on leave as the deputy director of the Mathematical Sciences Research Institute in Berkeley, California from 2002 to 2004, and became the Thurnau Professor at Michigan in 2008.
Megginson won the U.S. Presidential Award for Excellence in Science, Mathematics, and Engineering Mentoring in 1997. The American Indian Science and Engineering Society gave him their Ely S. Parker Award for lifetime service to the Native American community in 1999. The American Association for the Advancement of Science elected him as a fellow in 2009, and in the same year the Mathematical Association of America gave him their Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service, for his work on underrepresented minorities. In 2012, Megginson became one of the inaugural fellows of the American Mathematical Society.
References
1948 births
Living people
20th-century American mathematicians
21st-century American mathematicians
20th-century Native Americans
Eastern Illinois University faculty
Fellows of the American Association for the Advancement of Science
Fellows of the American Mathematical Society
Oglala people
Mathematicians from Illinois
Native American scientists
People from Washington, Illinois
People from Iroquois County, Illinois
University of Illinois Urbana-Champaign alumni
University of Michigan faculty
21st-century Native American writers |
https://en.wikipedia.org/wiki/Monoid%20%28disambiguation%29 | A monoid is an algebraic structure.
Monoid may also refer to:
Monoid (category theory), a mathematical structure used in category theory
Monoid, a race of one-eyed creatures in the 1966 Doctor Who serial The Ark
See also |
https://en.wikipedia.org/wiki/Butler%20group | In mathematics, a Butler group is a group that is the image of a completely decomposable abelian group of finite rank. They were introduced by .
References
Abelian group theory |
https://en.wikipedia.org/wiki/Crossing%20number%20inequality | In the mathematics of graph drawing, the crossing number inequality or crossing lemma gives a lower bound on the minimum number of edge crossings in a plane drawing of a given graph, as a function of the number of edges and vertices of the graph. It states that, for graphs where the number of edges is sufficiently larger than the number of vertices, the crossing number is at least proportional to .
It has applications in VLSI design and combinatorial geometry,
and was discovered independently by Ajtai, Chvátal, Newborn, and Szemerédi
and by Leighton.
Statement and history
The crossing number inequality states that, for an undirected simple graph with vertices and edges such that , the crossing number obeys the inequality
The constant is the best known to date, and is due to Ackerman.
For earlier results with weaker constants see and .
The constant can be lowered to , but at the expense of replacing with the worse constant of .
It is important to distinguish between the crossing number and the pairwise crossing number . As noted by , the pairwise crossing number refers to the minimum number of pairs of edges that each determine one crossing, whereas the crossing number simply refers to the minimum number of crossings. (This distinction is necessary since some authors assume that in a proper drawing no two edges cross more than once.)
Applications
The motivation of Leighton in studying crossing numbers was for applications to VLSI design in theoretical computer science.
Later, realized that this inequality yielded very simple proofs of some important theorems in incidence geometry. For instance, the Szemerédi–Trotter theorem, an upper bound on the number of incidences that are possible between given numbers of points and lines in the plane,
follows by constructing a graph whose vertices are the points and whose edges are the segments of lines between incident points. If there were more incidences than the Szemerédi–Trotter bound, this graph would necessarily have more crossings than the total number of pairs of lines, an impossibility.
The inequality can also be used to prove Beck's theorem, that if a finite point set does not have a linear number of collinear points, then it determines a quadratic number of distinct lines.
Similarly, Tamal Dey used it to prove upper bounds on geometric k-sets.
Proof
We first give a preliminary estimate: for any graph with vertices and edges, we have
To prove this, consider a diagram of which has exactly crossings. Each of these crossings can be removed by removing an edge from . Thus we can find a graph with at least edges and vertices with no crossings, and is thus a planar graph. But from Euler's formula we must then have , and the claim follows. (In fact we have for ).
To obtain the actual crossing number inequality, we now use a probabilistic argument. We let be a probability parameter to be chosen later, and construct a random subgraph of by allowing each vertex of to li |
https://en.wikipedia.org/wiki/Kazimierz%20Urbanik | Kazimierz Urbanik (February 5, 1930 – May 29, 2005) was a prominent member of the Polish School of Mathematics. He founded the journal Probability and Mathematical Statistics and served as rector of the University of Wrocław.
Early life and education
Urbanik was born in Krzemieniec and studied at the lyceum there. During World War II the town came under Soviet control, and was annexed by Ukraine; after the war, Urbanik's family moved to Brzeg, which remained Polish. Beginning in 1948, Urbanik studied mathematics and physics at the University of Wrocław, where he was mentored by Hugo Steinhaus and Edward Marczewski. He completed a degree in 1952, and began teaching at the university while continuing his studies under Marczewski, researching general topology, measure theory, and probability theory. He completed his doctorate in 1956, and his habilitation in 1957.
Academic career
Urbanik began teaching at the University of Wrocław in 1956. By 1960,he was promoted to professor, and in 1965 he became a member of the Polish Academy of Sciences, becoming its youngest member. He was an invited speaker at the International Congress of Mathematicians in 1966. He directed the university's Institute of Mathematics for most of the years from 1967 to 1996, and was rector of the university from 1975 to 1981. In 1980, he founded the journal Probability and Mathematical Statistics, and became its first editor-in-chief.
Contributions
His research contributions include over 180 papers. His work in probability theory included work on random variables in compact groups, connections between measurability and connectivity, generalized convolutions, and decomposability semigroups. He also studied stochastic processes, information theory, universal algebra, and functional analysis. He was the doctoral advisor of 17 students.
References
20th-century Polish mathematicians
University of Wrocław alumni
Academic staff of the University of Wrocław
Members of the Polish Academy of Sciences
1930 births
2005 deaths
Polish statisticians
Probability theorists |
https://en.wikipedia.org/wiki/Sergei%20Petrovskii | Sergei Petrovskii is a Russian-born British mathematician who researches the modeling of natural phenomena. He is a professor of Applied Mathematics at the University of Leicester. In 2015, he led a study that found that if the ocean temperature were to increase by about six degrees Celsius due to global warming, phytoplankton might stop producing oxygen. This would lead to shortages of oxygen in the atmosphere, which could be very harmful to humans. Petrovskii said, "About two thirds of the planet's total atmospheric oxygen is produced by ocean phytoplankton - and therefore cessation would result in the depletion of atmospheric oxygen on a global scale. This would likely result in the mass mortality of animals and humans." Petrovskii's study appeared in the Bulletin of Mathematical Biology.
Another stream of his research is modelling of biological invasions where he discovered a new phenomenon called "patchy invasion". Contrary to a commonly used paradigm of alien species spread by a travelling population front, in the patchy invasion the invasive species spreads into new areas by creating individual patches not preceded by a front propagation. Patchy invasion has been observed in several invasions of insects and birds and has been studied theoretically using a variety of growth-dispersal models.
References
Year of birth missing (living people)
Living people
English mathematicians
Academics of the University of Leicester |
https://en.wikipedia.org/wiki/Hukukane%20Nikaido | was a Japanese economist.
Career
He received a B.S. in mathematics from the University of Tokyo and a D.Sc. in mathematics from the University of Tokyo in 1961.
honors
1962, Fellow, Econometric Society.
2000, Order of the Rising Sun, 3rd class.
Published works
Books
Journal articles
References
External links
1923 births
2001 deaths
20th-century Japanese economists
General equilibrium theorists
University of Tokyo alumni
Academic staff of Tokyo University of Science
Academic staff of Hitotsubashi University
University of Minnesota faculty
University of California, Berkeley faculty
University of Southern California faculty
Academic staff of the University of Tsukuba
Academic staff of Osaka University
Academic staff of Tokyo International University
Recipients of the Order of the Rising Sun, 3rd class
Fellows of the Econometric Society
Presidents of the Japanese Economic Association |
https://en.wikipedia.org/wiki/Shota%20Aoki | is a Japanese football player for Blaublitz Akita.
Club statistics
Updated to 7 December 2022.
References
External links
Profile at Azul Claro Numazu
1990 births
Living people
Toin University of Yokohama alumni
People from Atsugi, Kanagawa
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Yokohama FC players
AC Nagano Parceiro players
FC Ryukyu players
Azul Claro Numazu players
Thespakusatsu Gunma players
Blaublitz Akita players
Men's association football forwards |
https://en.wikipedia.org/wiki/Bill%20Mason%20%28footballer%29 | William Sidney Mason (31 October 1908 – 1995) was an English professional footballer who played in the Football League for Queens Park Rangers and Fulham as a goalkeeper.
Career statistics
References
English men's footballers
English Football League players
Brentford F.C. wartime guest players
1908 births
1995 deaths
People from Earlsfield
Footballers from the London Borough of Wandsworth
Men's association football goalkeepers
Wimbledon F.C. players
Fulham F.C. players
Queens Park Rangers F.C. players |
https://en.wikipedia.org/wiki/Th%C3%A9odore%20Olivier | Théodore Olivier (1793–1853) was a French mathematician.
Life and work
Olivier studied in the Licée Imperial of Lyon where he obtained in 1811 a degree in mathematics with high honours. After this, he went to the École Polytechnique. Olivier looked like Napoleon, but nobody could prove that Olivier was an illegitimate son of the Emperor.
In 1815, he was an adjunct professor in the Artillery School at Metz and, in 1819, he became a full professor. In 1821, at the request of the King of Sweden, Charles XIV John (Jean-Baptiste Bernadotte), he went to Sweden to organize the military school of Mariemberg.
Returning to France, Oliver criticized the pedagogical system in the École Polytechnique and in 1829, jointly with Alphonse Lavallée, Jean-Baptiste Dumas and Jean Claude Eugène Péclet, founded the École Centrale des Arts et Manufactures, where he was professor of geometry and mechanics for the rest of his life. He also was, between 1830 and 1844, a professor at the École Polytechnique and, from 1838, a professor at the École Nationale Supérieure des Arts et Métiers.
Olivier is mainly known for the construction of three-dimensional models of geometry for pedagogical purposes. Most of them were sold to North American institutions such as Union College, the University of Columbia and West Point, where they are preserved.
Olivier also studied the theory of gears, writing an extensive treatise on the subject, and constructing models, preserved in the Musée des Art et Offices in Paris.
Olivier had no children, but he was the uncle of the French explorer Aimé Olivier de Sanderval.
References
Bibliography
External links
Union College Permanent Collection, "Olivier Models".
19th-century French mathematicians
1793 births
1853 deaths |
https://en.wikipedia.org/wiki/Reinhardt%20Kiehl | Reinhardt Kiehl (born 31 May 1935 in Herne, North Rhine-Westphalia) is a German mathematician.
From 1955, Kiehl studied mathematics, physics and astronomy at the University of Göttingen and the University of Heidelberg. He received in 1965 his Ph.D. (promotion) under Friedrich Karl Schmidt at Heidelberg University with thesis Äquivalenzrelationen in analytischen Räumen. He was from 1966 to 1968 a research assistant and in 1968–1969 a docent at the University of Münster, where he received in 1968 his habilitation. From 1969 to 1972 he was a professor ordinarius at the Goethe-Universität Frankfurt am Main. From 1972 he was a professor ordinarius at the University of Mannheim, where he retired in 2003 as professor emeritus.
His research deals with algebraic and arithmetic geometry and non-archimedean function theory. He wrote with Eberhard Freitag a textbook on the Weil conjectures and étale cohomology. In 1970 Kiehl was an Invited Speaker at the ICM in Nice with talk Grauertsche Kohärenzsätze für stetige und differenzierbare Familien komplexer Räume.
Selected publications
with Eberhard Freitag: Etale Cohomology and the Weil Conjecture, Springer Verlag 1988
with Rainer Weissauer: Weil Conjectures, Perverse Sheaves and ℓ-adic Fourier Transform, Springer Verlag 2001
De Rham Kohomologie algebraischer Mannigfaltigkeiten über einem bewerteten Körper, Pub. Math. IHES, vol. 33, 1967, pp. 5–20, Online
Der Endlichkeitssatz für eigentliche Abbildungen in der nichtarchimedischen Funktionentheorie, Inventiones Mathematicae, vol. 2, 1967, pp. 191–214
Theorem A und B in der nichtarchimedischen Funktionentheorie, Inventiones Mathematicae, vol. 2, 1967, pp. 256–273
Ausgezeichnete Ringe in der nichtarchimedischen analytischen Geometrie, J. Reine Angewandte Mathematik, vol. 235, 1969, p. 89
mit Jean-Louis Verdier Ein einfacher Beweis des Kohärenzsatzes von Grauert, Mathematische Annalen, Band 195, 1971, pp. 24–50
Äquivalenzrelationen in analytischen Räumen, Mathematische Zeitschrift, vol. 105, 1968, pp. 1–20
Relativ analytische Räume, Inventiones Mathematicae, vol. 16, 1972, pp. 40–112
References
20th-century German mathematicians
21st-century German mathematicians
Algebraic geometers
People from Herne, North Rhine-Westphalia
Heidelberg University alumni
University of Münster alumni
Academic staff of the University of Mannheim
1935 births
Living people |
https://en.wikipedia.org/wiki/Dianne%20P.%20O%27Leary | Dianne Prost O'Leary (born 1951) is an American mathematician and computer scientist whose research concerns scientific computing, computational linear algebra, and the history of scientific computing. She is Distinguished University Professor Emerita of Computer Science at the University of Maryland, College Park, and is the author of the book Scientific Computing with Case Studies (SIAM, 2009).
Early life and education
O'Leary was born November 20, 1951, in Chicago.
She majored in mathematics at Purdue University, graduating in 1972,
and completed her Ph.D. in computer science at Stanford University in 1976. Her dissertation, Hybrid Conjugate Gradient Algorithms, was supervised by Gene H. Golub.
Career
After taking an assistant professorship in mathematics at the University of Michigan, she moved to Maryland in 1978, with a joint appointment in computer science and the Institute for Physical Science and Technology. She also became affiliated with Maryland's applied mathematics program in 1979, and became a member of Maryland's Institute for Advanced Computer Studies in 1985. She became Distinguished University Professor in 2014, the same year that she retired.
From 2009 to 2015 she was editor in chief of the SIAM Journal on Matrix Analysis and Applications.
Recognition
The University of Waterloo gave O'Leary an honorary doctorate in 2005. She was named a Fellow of the Association for Computing Machinery in 2006, "for mentoring activities and contributions to numerical algorithms", and became one of the inaugural Fellows of the Society for Industrial and Applied Mathematics (SIAM) in 2009. In 2008 she was the Sonia Kovalevsky Lecturer of SIAM and the Association for Women in Mathematics.
References
External links
Home page
Google scholar profile
1951 births
Living people
American computer scientists
20th-century American mathematicians
21st-century American mathematicians
American women computer scientists
American women mathematicians
Purdue University alumni
Stanford University alumni
University of Michigan faculty
University of Maryland, College Park faculty
Fellows of the Society for Industrial and Applied Mathematics
Fellows of the Association for Computing Machinery
20th-century women mathematicians
21st-century women mathematicians
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/Arithmetic%20Fuchsian%20group | Arithmetic Fuchsian groups are a special class of Fuchsian groups constructed using orders in quaternion algebras. They are particular instances of arithmetic groups. The prototypical example of an arithmetic Fuchsian group is the modular group . They, and the hyperbolic surface associated to their action on the hyperbolic plane often exhibit particularly regular behaviour among Fuchsian groups and hyperbolic surfaces.
Definition and examples
Quaternion algebras
A quaternion algebra over a field is a four-dimensional central simple -algebra. A quaternion algebra has a basis where and .
A quaternion algebra is said to be split over if it is isomorphic as an -algebra to the algebra of matrices .
If is an embedding of into a field we shall denote by the algebra obtained by extending scalars from to where we view as a subfield of via .
Arithmetic Fuchsian groups
A subgroup of is said to be derived from a quaternion algebra if it can be obtained through the following construction. Let be a totally real number field and a quaternion algebra over satisfying the following conditions. First there is a unique embedding such that is split over ; we denote by an isomorphism of -algebras. We also ask that for all other embeddings the algebra is not split (this is equivalent to its being isomorphic to the Hamilton quaternions). Next we need an order in . Let be the group of elements in of reduced norm 1 and let be its image in via . Then the image of is a subgroup of (since the reduced norm of a matrix algebra is just the determinant) and we can consider the Fuchsian group which is its image in .
The main fact about these groups is that they are discrete subgroups and they have finite covolume for the Haar measure on Moreover, the construction above yields a cocompact subgroup if and only if the algebra is not split over . The discreteness is a rather immediate consequence of the fact that is only split at one real embedding. The finiteness of covolume is harder to prove.
An arithmetic Fuchsian group is any subgroup of which is commensurable to a group derived from a quaternion algebra. It follows immediately from this definition that arithmetic Fuchsian groups are discrete and of finite covolume (this means that they are lattices in ).
Examples
The simplest example of an arithmetic Fuchsian group is the modular which is obtained by the construction above with and By taking Eichler orders in we obtain subgroups for of finite index in which can be explicitly written as follows:
Of course the arithmeticity of such subgroups follows from the fact that they are finite-index in the arithmetic group ; they belong to a more general class of finite-index subgroups, congruence subgroups.
Any order in a quaternion algebra over which is not split over but splits over yields a cocompact arithmetic Fuchsian group. There is a plentiful supply of such algebras.
More generally, all orders in quaternion algebras (sat |
https://en.wikipedia.org/wiki/Regular%20complex%20polygon | In geometry, a regular complex polygon is a generalization of a regular polygon in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. A regular polygon exists in 2 real dimensions, , while a complex polygon exists in two complex dimensions, , which can be given real representations in 4 dimensions, , which then must be projected down to 2 or 3 real dimensions to be visualized. A complex polygon is generalized as a complex polytope in .
A complex polygon may be understood as a collection of complex points, lines, planes, and so on, where every point is the junction of multiple lines, every line of multiple planes, and so on.
The regular complex polygons have been completely characterized, and can be described using a symbolic notation developed by Coxeter.
Regular complex polygons
While 1-polytopes can have unlimited p, finite regular complex polygons, excluding the double prism polygons p{4}2, are limited to 5-edge (pentagonal edges) elements, and infinite regular aperiogons also include 6-edge (hexagonal edges) elements.
Notations
Shephard's modified Schläfli notation
Shephard originally devised a modified form of Schläfli's notation for regular polytopes. For a polygon bounded by p1-edges, with a p2-set as vertex figure and overall symmetry group of order g, we denote the polygon as p1(g)p2.
The number of vertices V is then g/p2 and the number of edges E is g/p1.
The complex polygon illustrated above has eight square edges (p1=4) and sixteen vertices (p2=2). From this we can work out that g = 32, giving the modified Schläfli symbol 4(32)2.
Coxeter's revised modified Schläfli notation
A more modern notation p1{q}p2 is due to Coxeter, and is based on group theory. As a symmetry group, its symbol is p1[q]p2.
The symmetry group p1[q]p2 is represented by 2 generators R1, R2, where: R1p1 = R2p2 = I. If q is even, (R2R1)q/2 = (R1R2)q/2. If q is odd, (R2R1)(q−1)/2R2 = (R1R2)(q−1)/2R1. When q is odd, p1=p2.
For 4[4]2 has R14 = R22 = I, (R2R1)2 = (R1R2)2.
For 3[5]3 has R13 = R23 = I, (R2R1)2R2 = (R1R2)2R1.
Coxeter–Dynkin diagrams
Coxeter also generalised the use of Coxeter–Dynkin diagrams to complex polytopes, for example the complex polygon p{q}r is represented by and the equivalent symmetry group, p[q]r, is a ringless diagram . The nodes p and r represent mirrors producing p and r images in the plane. Unlabeled nodes in a diagram have implicit 2 labels. For example, a real regular polygon is 2{q}2 or {q} or .
One limitation, nodes connected by odd branch orders must have identical node orders. If they do not, the group will create "starry" polygons, with overlapping element. So and are ordinary, while is starry.
12 Irreducible Shephard groups
Coxeter enumerated this list of regular complex polygons in . A regular complex polygon, p{q}r or , has p-edges, and r-gonal vertex figures. p{q}r is a finite polytope if (p + r)q > pr(q − 2).
Its symmetry is written |
https://en.wikipedia.org/wiki/Abortion%20in%20Cameroon | Abortion in Cameroon is only legal if the abortion will save the woman's life, the pregnancy gravely endangers the woman's physical or mental health, or the pregnancy is a result of rape.
Statistics
In 1997, a survey in Yaoundé found 20 percent of women aged 20–29 had had at least one abortion. 80 percent of these procedures took place in a medical facility, but they were not always safe, and women often faced complications. The odds that a pregnant woman would seek an abortion were increased if they were educated or had children. Of women reporting past abortions, 40% had two or more. The survey found that 35% of all reported pregnancies in the capital city ended in abortion.
Abortion access
In 1990, the Cameroon government passed Act No. 90/035 to prohibit birth control education. Reports found that abortion and secretive reproductive health services were widespread and made up 40 percent of OB/GYN emergency admissions. However, most access to abortion clinics were limited to urban centers within the country.
References
Health in Cameroon
Cameroon
Cameroon
Sexuality in Cameroon |
https://en.wikipedia.org/wiki/Eberhard%20Freitag | Eberhard Freitag (born 19 May 1942, in Mühlacker) is a German mathematician, specializing in complex analysis and especially modular forms.
Education and career
Freitag studied from 1961 mathematics, physics and astronomy at Heidelberg University, where he received in 1964 his Diplom and in 1966 his Ph.D. (promotion), supervised by Hans Maaß (and also Albrecht Dold), with thesis Modulformen zweiten Grades zum rationalen und Gaußschen Zahlkörper, published in Sitzungsberichte Heidelberger Akad. Wiss. 1967. From 1964 he was a research assistant at the Mathematischen Institut in Heidelberg, where he received at the end of 1969 his habilitation and became there a Privatdozent and in 1970 a scientific advisor. In 1970–1971 he was a visiting professor at Johann-Wolfgang-Goethe-Universität Frankfurt am Main. In 1973 he became a professor ordinarius at the University of Mainz. In 1977 he became a professor ordinarius at Heidelberg University, where from 1991 to 1993 he was the dean of the Faculty of Mathematics.
Freitag's research (like that of his teacher Maaß) deals primarily with the theory of modular forms, but approaches modular forms via algebraic geometry. Among other work, Freitag described this theory in two monographs published by Springer Verlag in Grundlehren der mathematischen Wissenschaften. These two books and the first volume of his series on function theory are standard references. In 1974 in Vancouver he was an Invited Speaker of the ICM with talk Singularitäten von Modulmannigfaltigkeiten und Körper Automorpher Funktionen. In 1998 he proved with Rainer Weissauer and Richard Borcherds the existence of a Siegel cusp form of degree 12 and weight 12 using the theta series associated with the 24 Niemeier lattices of dimension 24. Freitag also demonstrated that the Siegel modular variety Ag is of general type when g = 8.
Selected publications
with Rolf Busam: Funktionentheorie 1. Springer-Verlag, 1993, 4th edition 2006, , Complex Analysis, 2006, Eng. trans. of 4th edition
Funktionentheorie 2: Riemannsche Flächen, Mehrere komplexe Variable, Abelsche Funktionen, Höhere Modulformen, Springer-Verlag, 2009
Hilbert Modular Forms. Springer-Verlag, Grundlehren der mathematischen Wissenschaften, 1990, 2013 pbk reprint
Singular Modular Forms and Theta Relations. In: Lecture Notes in Mathematics. vol. 1487, Springer-Verlag, 1991, ; 2006 pbk reprint
with Reinhardt Kiehl: Etale Cohomology and the Weil Conjecture, Springer Verlag, 1988,
Siegelsche Modulfunktionen. Springer-Verlag, Berlin 1983, Grundlehren der mathematischen Wissenschaften vol. 254,
Sources
Dagmar Drüll Heidelberger Gelehrtenlexikon 1933-1986, Springer 2009
References
External links
Freitag's homepage at the University of Heidelberg
List of reprints and preprints (with short descriptions) of some papers by Eberhard Freitag, University of Heidelberg
1942 births
Living people
20th-century German mathematicians
21st-century German mathematicians
Complex analysts
Heidelberg U |
https://en.wikipedia.org/wiki/2016%E2%80%9317%20PFC%20Levski%20Sofia%20season | The 2016–17 season was Levski Sofia's 96th season in the First League. This article shows player statistics and all matches (official and friendly) that the club has played during the season.
Transfers
In
Out
Loans out
Squad
Updated on 4 May 2017.
Fixtures
Performance overview
Friendlies
Summer
Mid-season
Winter
Parva Liga
Preliminary stage
League table
Results summary
Results by round
Matches
Championship stage
League table
Results summary
Results by round
Results
European play-off final
Bulgarian Cup
UEFA Europa League
Second qualifying round
Squad statistics
|-
|colspan="14"|Players away from the club on loan:
|-
|colspan="14"|Players who left Levski (Sofia) during the season:
|}
References
PFC Levski Sofia seasons
Levski Sofia |
https://en.wikipedia.org/wiki/VELCT | Velocity Energy-efficient and Link-aware Cluster-Tree (VELCT) is a cluster and tree-based topology management protocol for mobile wireless sensor networks (MWSNs).
See also
DCN
DCT
CIDT
References
Topology
Wireless networking |
https://en.wikipedia.org/wiki/Akramjon%20Komilov | Akramjon Komilov (born 14 March 1996 in Kokand, Uzbekistan) is an Uzbekistani footballer who currently plays for Pakhtakor Tashkent.
Career statistics
Club
International
Statistics accurate as of match played 7 June 2018
Honours
Club
Bunyodkor
Uzbekistan Super Cup: 2014
International
Uzbekistan U-23
AFC U-23 Championship (1): 2018
Uzbekistan U-16
AFC U-16 Championship (1): 2012
References
External links
Uzbekistani men's footballers
1996 births
Living people
FC Bunyodkor players
Pakhtakor Tashkent FK players
FC AGMK players
Men's association football defenders
Footballers at the 2018 Asian Games
Uzbekistan Super League players
Asian Games competitors for Uzbekistan
Uzbekistan men's international footballers |
https://en.wikipedia.org/wiki/CIDT | CIDT may refer to:
Cruel, inhuman or degrading treatment, a concept in international law and the laws of many countries
Mobile wireless sensor network#Topology |
https://en.wikipedia.org/wiki/Antonio%20Santucci | Antonio Santucci (?–1613) was an Italian astronomer, cosmographer, and scientific instrument maker.
He was a reader in Mathematics at the University of Pisa during 1599–1612. Santucci was an astronomer and cosmographer to Grand Duke Ferdinand I (1549–1609) and later Cosimo II (1590–1621). An attentive observer of comets, most notably that of 1582, he published in 1611 the first edition of Trattato delle comete, in which he argued that, contrary to the prevailing scientific opinion, comets were not atmospheric phenomena. The following year, he wrote Breve discorso sopra il trattato galileiano sulle galleggianti (which survives in manuscript at the National Central Library). He also authored a treatise in 1593, commissioned by Ferdinand I, on the mathematical and surveying instruments in the Guardaroba Medicea collection. His monumental armillary spheres are famous. One sphere, made in 1582 for King Philip II of Spain, is now at the Escorial in Madrid; the other, the most famous Santucci's Armillary Sphere, built in 1588–1593 for the Sala delle Matematiche in the Uffizi, is now at the Museo Galileo of Florence.
References
External links
Italian scientific instrument makers
Academic staff of the University of Pisa
17th-century Italian astronomers
Italian astronomers
Astronomical instrument makers |
https://en.wikipedia.org/wiki/Peter%20Michorl | Peter Michorl (born 9 May 1995) is an Austrian professional footballer who plays as a midfielder for LASK.
Career statistics
Club
References
External links
Living people
1995 births
Austrian men's footballers
Men's association football midfielders
FK Austria Wien players
LASK players
Footballers from Vienna |
https://en.wikipedia.org/wiki/Felix%20Luckeneder | Felix Luckeneder (born 21 March 1994) is an Austrian footballer who plays for LASK.
Club career
On 31 August 2021, he returned to LASK on a three-year contract.
Career statistics
Club
References
External links
Austrian men's footballers
Men's association football defenders
LASK players
FC Juniors OÖ players
SC Rheindorf Altach players
TSV Hartberg players
Austrian Football Bundesliga players
2. Liga (Austria) players
Austrian Regionalliga players
1994 births
Living people
Footballers from Linz |
https://en.wikipedia.org/wiki/Zoel%20Garc%C3%ADa%20de%20Galdeano | Zoel García de Galdeano y Yanguas (5 July 1846 – 28 March 1924) was a Spanish mathematician. He was considered by Julio Rey Pastor as "The apostle of modern mathematics".
Biography
His father was a military man, and was killed in war action, so his maternal grandfather, the historian José Yanguas y Miranda (1782-1863), took care of Zoel. To continue his studies, in 1863, Zoel moved to Zaragoza, where he received the title of professor and expert surveyor. In 1869 he graduated as Bachelor. Later he began his studies of Philosophy and Letters, and Sciences at the University of Zaragoza. In 1871, he graduated from these two specialties.
Between 1872 and 1879, Zoel served as professor of mathematics at various schools and institutes in Spain. While he worked in the city of Toledo, he began to write mathematical works that introduced the modern concepts of the European Mathematical in Spain.
In 1889 he obtained the professorship of Analytic geometry at the University of Zaragoza, and in 1896, he was appointed to the professorship of Infinitesimal calculus. He worked at this university until his retirement in 1918.
In 1891, Zoel created El Progreso Matemático, the first strictly mathematical journal published in Spain. He was the principal editor in the two periods in which the journal was published (1891 – 1895 and 1899 – 1900). He was also the first contemporary Spanish mathematician to regularly participate in international congresses of mathematics.
He died in Zaragoza on 28 March 1924.
Notes
1846 births
1924 deaths
20th-century Spanish mathematicians
People from Pamplona
People from Zaragoza
19th-century Spanish mathematicians |
https://en.wikipedia.org/wiki/Renald%20Castillon | Renald Castillon (born in France is a French motorcycle racer. Castillon has also been a competitor in the European Junior Cup in 2013.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
References
External links
Living people
French motorcycle racers
Moto3 World Championship riders
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Joe%20Grice | Joseph William Grice (born 25 July 1952) is Chief Economist to the Office for National Statistics (ONS).
Early life
He was born in Tamworth in Staffordshire. He was educated at Worcester College, Oxford, receiving a BA in PPE in 1972.
Career
HM Treasury
In HM Treasury he was Director of Macroeconomic Policy, and also the Chief Economist to the Public Services Directorate from 2000-03.
Office for National Statistics
He has been Chief Economist at the ONS since 2007. He is responsible for the production of UK economic statistics such as GDP, inflation and labour market figures.
Note that as of November 2018, the ONS website no longer references Mr. Grice and lists Nick Vaughan as Chief Economist, suggesting that Mr. Grice has changed jobs.
Personal life
He has two sons and one daughter. He married Deborah Wicks in 1976 in Oxford.
References
External links
Green Growth Knowledge
Alumni of Worcester College, Oxford
British economists
Civil servants in the Office for National Statistics
People from Tamworth, Staffordshire
1952 births
Living people |
https://en.wikipedia.org/wiki/Center%20for%20Scientific%20Computation%20and%20Mathematical%20Modeling | The Center for Scientific Computation And Mathematical Modeling (CSCAMM) is a mathematics institute in the University of Maryland, College Park. CSCAMM is located on the UMD campus, in close proximity to UMD's Department of Mathematics and Department of Computer Science.
Mission
CSCAMM is a major research center in Applied Mathematics and Scientific Computation within the University of Maryland, College Park. The center is one of the three sponsors of the department of mathematics's AMSC program. The main mission of CSCAMM is to support and stimulate the interdisciplinary research activities using Applied Mathematics (in particular, scientific computation and mathematical modeling) as their main analysis, simulation, and computational tools.
Background
The center was created in 2001 by the University of Maryland, College Park as a major research project. Eitan Tadmor had been the center's first director from August 2002 to June 2016. Starting July 2016, Pierre-Emmanuel Jabin will be the center's second director. Agi Alipio is the center's director of administrative services. Beside the research funding from the university, CSCAMM works as the major hub of the research network, KI-Net; faculty members in CSCAMM receive funding from NSF, NIH, NOAA, and other research funding agencies.
Programs
CSCAMM maintains an active visitors program and helps organize international workshops and conferences in Applied Mathematics and its applications. During each school semester, CSCAMM also hosts weekly seminars which cover a wide range of mathematical subjects.
People
There are eight faculty members working in CSCAMM: Radu Balan, Jacob Bedrossian, Kayo Ide, Pierre-Emmanuel Jabin, Doron Levy, Dionisios Margetis, Eitan Tadmor, and Da-Lin Zhang. There are two visiting professors: Gil Ariel and Gadi Fibich. The student office usually seats five graduate students who are sponsored and advised by faculty members of CSCAMM. Those five graduate students come from various graduate programs in the university, in particular the AMSC program.
References
External links
CSCAMM home page
KI-Net home page
Research institutes in Maryland
Educational institutions established in 2000
2000 establishments in Maryland |
https://en.wikipedia.org/wiki/Copa%20Am%C3%A9rica%20Centenario%20statistics | The following article outlines statistics for Copa América Centenario, which took place in the United States from 3 to 26 June 2016.
Player statistics
Goalscorers
6 goals
Eduardo Vargas
5 goals
Lionel Messi
4 goals
Gonzalo Higuaín
3 goals
Philippe Coutinho
Alexis Sánchez
Clint Dempsey
2 goals
Ezequiel Lavezzi
Erik Lamela
Renato Augusto
José Pedro Fuenzalida
Edson Puch
Arturo Vidal
Carlos Bacca
James Rodríguez
Enner Valencia
Blas Pérez
Salomón Rondón
1 goal
Sergio Agüero
Éver Banega
Víctor Cuesta
Ángel Di María
Nicolás Otamendi
Juan Carlos Arce
Jhasmani Campos
Gabriel Barbosa
Lucas Lima
Charles Aránguiz
Frank Fabra
Marlos Moreno
Cristián Zapata
Celso Borges
Johan Venegas
Michael Arroyo
Jaime Ayoví
Miller Bolaños
Christian Noboa
Antonio Valencia
James Marcelin
Jesús Manuel Corona
Javier Hernández
Héctor Herrera
Rafael Márquez
Oribe Peralta
Abdiel Arroyo
Miguel Camargo
Víctor Ayala
Christian Cueva
Edison Flores
Paolo Guerrero
Raúl Ruidíaz
Jermaine Jones
Bobby Wood
Gyasi Zardes
Graham Zusi
Mathías Corujo
Diego Godín
Abel Hernández
Josef Martínez
José Manuel Velázquez
1 own goal
Frank Fabra (against Costa Rica)
Je-Vaughn Watson (against Uruguay)
Álvaro Pereira (against Mexico)
Source: CONMEBOL WorldFootball.net
Assists
4 assists
Lionel Messi
3 assists
Clint Dempsey
2 assists
Ángel Di María
Marcos Rojo
Dani Alves
Arturo Vidal
Edwin Cardona
Enner Valencia
Jefferson Montero
Raúl Jiménez
Paolo Guerrero
Alejandro Guerra
1 assist
Éver Banega
Nicolás Gaitán
Gonzalo Higuaín
Ezequiel Lavezzi
Elias
Filipe Luís
Gil
Jonas
Jean Beausejour
José Pedro Fuenzalida
Fabián Orellana
Mauricio Pinilla
Alexis Sánchez
Eduardo Vargas
Santiago Arias
Juan Cuadrado
Roger Martínez
James Rodríguez
Celso Borges
Bryan Oviedo
Walter Ayoví
Christian Noboa
Antonio Valencia
Jesús Manuel Corona
Héctor Herrera
Abdiel Arroyo
Gabriel Gómez
Alberto Quintero
Edison Flores
Andy Polo
Jermaine Jones
Bobby Wood
Gyasi Zardes
Nicolás Lodeiro
Carlos Sánchez
Christian Santos
Source: CONMEBOL WorldFootball.net
Clean sheets
4 clean sheets
Sergio Romero
3 clean sheets
Claudio Bravo
David Ospina
Pedro Gallese
2 clean sheets
Brad Guzan
Dani Hernández
1 clean sheet
Alisson
Patrick Pemberton
Alexander Domínguez
Esteban Dreer
Guillermo Ochoa
Justo Villar
Fernando Muslera
Scoring
Overview
Timing
Teams
Individual
Attendance
Overall attendance: 1,401,829
Average attendance per match:
Highest attendance: 83,263 – Mexico vs Jamaica
Lowest attendance: 11,937 – Ecuador vs Peru
Wins and losses
Discipline
Summary
Sanctions
By match
By referee
By team
By individual
Overall statistics
Notes
References
External links
Copa América Centenario statistics at CONMEBOL center
statistics
2016 |
https://en.wikipedia.org/wiki/Bernard%20Epstein | Bernard Epstein (10 August 1920, Harrison, New Jersey – 30 March 2005, Montgomery County, Maryland) was an American mathematician and physicist who wrote several widely used textbooks on mathematics.
Epstein was the son of Jewish immigrants from Lithuania and Romania, Yitzkhak Aharon Epstein and Sophie-Sarah née Goldenberg, and was the first person in his family to go to college. He received bachelor's and master's degrees in mathematics and physics from New York University and then in 1947 a Ph.D. in applied mathematics, with thesis advisor Maurice Heins, from Brown University with thesis Method for the Solution of the Dirichlet Problem for Certain Types of Domains.
In the early 1940s, he worked as a physicist at what is now the National Institute of Standards and Technology. During World War II, he was selected to join the Manhattan Project, which produced the first atomic bombs. After the war, he worked for two years at Harvard University as a research associate, taught mathematics as an associate professor at the University of Pennsylvania, Stanford University and NYU and as a professor at Yeshiva University and then spent 21 years on the faculty of the University of New Mexico as a professor of mathematics until his retirement in 1984.
Sabbaticals included Office of Naval Research, London; The Technion in Haifa, Israel; University of Maryland; and Air Force Office of Scientific Research. After retirement, he taught at George Mason University.
Epstein was dissertation advisor for the following Ph.D. students:
Anne Scheerer, University of Pennsylvania, 1953
William Trench, University of Pennsylvania, 1958
Jack Minker, University of Pennsylvania, 1959
Edwin Sherry, Yeshiva University, 1964
Darrell L. Hicks, University of New Mexico, 1969
Harvey Z. Senter, Yeshiva University
Upon his death at age 84, he was survived by his wife, five children, and 16 grandchildren. His sixth child, a daughter, predeceased him.
Selected publications
Articles
with S. Bergman:
with J. Lehner:
with A. Scheerer:
with David S. Greenstein and Jack Minker: "An extremal problem with infinitely many interpolation conditions". Annals of Finnish Academy of Science (Soumalainen Tiedaekatamia Tomituksia), Series A:1 Mathematics 250/10, 1958.
with F. Haber:
with I. J. Schoenberg:
with J. Minker:
with M. M. Schiffer:
with H. Senter:
with J. R. Blum:
Books
with Liang-shin Hahn:
References
1920 births
2005 deaths
20th-century American mathematicians
20th-century American physicists
American expatriates in the United Kingdom
American expatriates in Israel
American mathematicians
American people of Lithuanian-Jewish descent
American people of Romanian-Jewish descent
Brown University alumni
Jewish American scientists
Jewish physicists
Manhattan Project people
Mathematics writers
New York University alumni
People from Harrison, New Jersey
University of New Mexico faculty
University of Pennsylvania faculty |
https://en.wikipedia.org/wiki/Gon%C3%A7alo%20Sampaio | Gonçalo António da Silva Ferreira Sampaio (29 March 1865 in São Gens de Calvos – 28 July 1937 in Porto) was a Portuguese botanist.
He studied mathematics at the University of Coimbra and chemistry, mineralogy and botany at the Polytechnic Academy of Porto. From 1890 he served as an assistant naturalist at the Polytechnic Academy. From 1912 to 1935 he was a professor of botany at the faculty of sciences of the University of Porto.
As a taxonomist he described around 50 new species of vascular plants, five new species of desmids and about 70 new taxa of lichens that included the genus Carlosia (family Caliciaceae). The mycological genus Sampaioa (Gonz. Frag., 1923; syn. Mycoglaena) commemorates his name.
Selected works
Estudos sobre a flora dos arredores do Porto. Gen. Spergularia, 1904 – Studies on the flora in the vicinity of Porto; genus Spergularia.
"Rubus” portuguezes. Contribuções para o seu estudo, 1904 – Rubus native to Portugal.
Contribuções para o estudo da flora portugueza; Epilobiaceae, 1906 – Contributions for the study of the Portuguese flora; Epilobiaceae.
Notas criticas sobre a flora portugueza, 1906 – Critical notes involving Portuguese flora.
Flora vascular de Odemira, 1909 – Vascular plants of Odemira.
Manual da flora portugueza, 1909–14 – Manual of Portuguese flora.
Estudos botanicos. Especies novas e nomes novos, 1912 – Botanical studies, new species and new names.
Lista das espécies representadas no Herbário português, 1913 – List of species represented in the Portuguese Herbarium.
Apêndice à lista das espécies representadas no Herbário português, 1914 – Appendix to the list of species represented in the Portuguese Herbarium.
References
1865 births
1937 deaths
People from Póvoa de Lanhoso
University of Coimbra alumni
Academic staff of the University of Porto
19th-century Portuguese botanists
Lichenologists
Phycologists
University of Porto alumni
Portuguese taxonomists
20th-century Portuguese botanists |
https://en.wikipedia.org/wiki/Washington%20Valley%2C%20New%20Zealand | Washington Valley is a major inner suburb of Nelson, New Zealand. It lies to the west of Nelson city centre and south of Stepneyville and Beachville.
The equivalent Statistics New Zealand statistical area of Washington covers a land area of 1.12 km2.
The suburb has three local parks: Abraham Heights Reserve, Sequoia Reserve and Wolfe Reserve.
History
The estimated population of Washington reached 2,510 in 1996, before dropping to 2,450 in 2001.
It reached 2,526 in 2006, 2,469 in 2013, and 2,847 in 2018.
Demography
Washington statistical area covers and had an estimated population of as of with a population density of people per km2.
Washington had a population of 2,847 at the 2018 New Zealand census, an increase of 378 people (15.3%) since the 2013 census, and an increase of 321 people (12.7%) since the 2006 census. There were 1,011 households, comprising 1,437 males and 1,413 females, giving a sex ratio of 1.02 males per female. The median age was 33.4 years (compared with 37.4 years nationally), with 573 people (20.1%) aged under 15 years, 672 (23.6%) aged 15 to 29, 1,299 (45.6%) aged 30 to 64, and 303 (10.6%) aged 65 or older.
Ethnicities were 74.9% European/Pākehā, 14.3% Māori, 3.6% Pasifika, 15.0% Asian, and 3.5% other ethnicities. People may identify with more than one ethnicity.
The percentage of people born overseas was 29.9, compared with 27.1% nationally.
Although some people chose not to answer the census's question about religious affiliation, 53.7% had no religion, 29.7% were Christian, 0.3% had Māori religious beliefs, 1.9% were Hindu, 0.1% were Muslim, 2.8% were Buddhist and 3.3% had other religions.
Of those at least 15 years old, 507 (22.3%) people had a bachelor's or higher degree, and 396 (17.4%) people had no formal qualifications. The median income was $28,700, compared with $31,800 nationally. 258 people (11.3%) earned over $70,000 compared to 17.2% nationally. The employment status of those at least 15 was that 1,149 (50.5%) people were employed full-time, 435 (19.1%) were part-time, and 81 (3.6%) were unemployed.
Economy
In 2018, 11.5% worked in manufacturing, 7.6% worked in construction, 11.0% worked in hospitality, 3.4% worked in transport, 6.2% worked in education, and 11.2% worked in healthcare.
Transport
As of 2018, among those who commuted to work, 67.1% drove a car, 5.7% rode in a car, 4.7% use a bike, and 4.7% walk or run.
No one used public transport.
References
Suburbs of Nelson, New Zealand
Populated places in the Nelson Region |
https://en.wikipedia.org/wiki/Chenyang%20Xu | Chenyang Xu (; born 1981) is a Chinese mathematician in the area of algebraic geometry and a professor at Princeton University. Xu is known for his work in birational geometry, the minimal model program, and the K-stability of Fano varieties.
Career
After completing his PhD doctorate at Princeton under János Kollár's supervision, Xu joined MIT as a CLE Moore Instructor between 2008-2011. After a promotion to assistant professor at the University of Utah, Xu returned to Peking University in 2012 to join the Beijing International Center of Mathematical Research, subsequently promoted to professor in 2013.
In 2018, Xu joined the mathematics faculty at MIT as Professor.
In 2020, Xu moved to Princeton University as Professor.
Awards
In 2016, he was announced as a winner of the ICTP Ramanujan Prize for that year, "in recognition of Xu's outstanding works in algebraic geometry, notably in the area of birational geometry, including works both on log canonical pairs and on Q-Fano varieties, and on the topology of singularities and their dual complexes."
He is one of five winners of the 2019 New Horizons Prize for Early-Career Achievement in Mathematics, associated with the Breakthrough Prize in Mathematics for his research in the minimal model program and applications to the moduli of algebraic varieties.
He was elected as a Fellow of the American Mathematical Society in the 2020 Class, for "contributions to algebraic geometry, in particular the minimal model program and the K-stability of Fano varieties". In 2021, he received the Cole Prize in Algebra from the AMS.
Selected publications
C. D. Hacon, C. Xu (2013). "Existence of log canonical closures", Inventiones Mathematicae 192 (1), 161–195 49
C. D. Hacon, J. McKernan, C. Xu (2014). "ACC for log canonical thresholds", Annals of Mathematics 180 (2), 523–571 47
References
External links
Beijing International Center of Mathematics Research
1981 births
Living people
Algebraic geometers
Princeton University alumni
Massachusetts Institute of Technology School of Science faculty
Academic staff of Peking University
Peking University alumni
Mathematicians from Chongqing
Educators from Chongqing
Chinese science writers
Writers from Chongqing
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Ada%C3%ADlton%20%28footballer%2C%20born%201990%29 | Adaílton dos Santos da Silva (born 6 December 1990) is a Brazilian footballer who plays as Forward and Winger. He play for FC Tokyo of J1 League.
Club statistics
Updated to the start from 2023 season.
Honours
FC Tokyo
J.League Cup: 2020
References
External links
Profile at Júbilo Iwata
1990 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J1 League players
J2 League players
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Júbilo Iwata players
Fortaleza Esporte Clube players
Esporte Clube Vitória players
Club Athletico Paranaense players
Ituano FC players
Joinville Esporte Clube players
Associação Atlética Ponte Preta players
Paraná Clube players
FC Tokyo players
People from Camaçari
Men's association football midfielders
Brazilian expatriate sportspeople in Japan
Expatriate men's footballers in Japan
Footballers from Bahia |
https://en.wikipedia.org/wiki/Yaacov%20Schul | Yaacov Schul (born 1951) is an Israeli professor of cognitive and social psychology at the Hebrew University of Jerusalem.
Biography
Prof. Schul received his B.A. in Psychology and Mathematics in 1976 from the Hebrew University, and his Ph.D. in Social Psychology in 1981 from the University of Michigan.
He has been professor of social psychology at the Hebrew University since 1981, and held various positions at the Hebrew University, including vice rector.
He is married, a father of two and a grandfather of four.
Research contributions
Schul's theoretical orientation within Psychology is Social Cognition. His early research explored the process of impression formation in an attempt to characterize the operations involved according to their sensitivity to different features of the information, to investigate how each of these operations influence the representation in memory of the original information, and to explore how these representations influence different kinds of judgments. The early work evolved into two lines of research. The first explored the process by which people evaluate their own activity and the activity of others. The second line of studies examined the conditions under which people can successfully ignore invalid information. The research on discounting developed into the study of distrust, negation processing, and research on reliance on weak internal cues such as metacognitive experiences.
Processing of negations
In collaboration with Mayo, Schul studies the negation processes and their consequences, suggesting the existence of two basic negation models: One ("The Schema-Plus-Tag model") explains the possible failure of the negation process, while the other ("The Fusion model") proposes a successful negation. The work with Yaniv highlighted the implications of acceptance versus rejection to decision-making outcomes. Schul's recent studies concern the similarities and differences between negation processes that are triggered by communicated negations (e.g., “Honey is not made by butterflies”) and by false information (e.g., “Honey is made by butterflies”) in an attempt to understand people's sensitivity to misinformation.
Trust and Distrust and reliance on gut feelings
Past research highlighted many biases that stem from reliance on gut feelings. Schul's research suggests that such reliance is not ubiquitous. Schul, Mayo and Burnstein distinguished a mindset of trust from a mindset of distrust. In a series of studies they demonstrated that whereas a mindset of trust is associated with reliance on gut feelings and activation of congruent associations; a mindset of distrust, triggers thinking about incongruent associations and more willingness to consider alternative positions. The research with Yahalom further shows that suspicion in people's motivation weakens reliance on the metacognitive cues associated with ease of retrieval. The research with Shidlovski and Mayo explored a particularly important type of gut f |
https://en.wikipedia.org/wiki/Breaking%20Up%20Is%20Easy%20to%20Do | Breaking Up Is Easy to Do may refer to:
"Breaking Up Is Easy to Do", a season 11 episode of Married... with Children
"Breaking up is Easy to Do", a season 2 episode of Maths Mansion
See also
"Breaking Up Is Hard to Do", a song recorded by Neil Sedaka |
https://en.wikipedia.org/wiki/Cluster%20graph | In graph theory, a branch of mathematics, a cluster graph is a graph formed from the disjoint union of complete graphs.
Equivalently, a graph is a cluster graph if and only if it has no three-vertex induced path; for this reason, the cluster graphs are also called -free graphs. They are the complement graphs of the complete multipartite graphs and the 2-leaf powers. The cluster graphs are transitively closed, and every transitively closed undirected graph is a cluster graph.
The cluster graphs are the graphs for which adjacency is an equivalence relation, and their connected components are the equivalence classes for this relation.
Related graph classes
Every cluster graph is a block graph, a cograph, and a claw-free graph. Every maximal independent set in a cluster graph chooses a single vertex from each cluster, so the size of such a set always equals the number of clusters; because all maximal independent sets have the same size, cluster graphs are well-covered.
The Turán graphs are complement graphs of cluster graphs, with all complete subgraphs of equal or nearly-equal size. The locally clustered graph (graphs in which every neighborhood is a cluster graph) are the diamond-free graphs, another family of graphs that contains the cluster graphs.
When a cluster graph is formed from cliques that are all the same size, the overall graph is a homogeneous graph, meaning that every isomorphism between two of its induced subgraphs can be extended to an automorphism of the whole graph. With only two exceptions, the cluster graphs and their complements are the only finite homogeneous graphs, and infinite cluster graphs also form one of only a small number of different types of countably infinite homogeneous graphs.
Computational problems
A subcoloring of a graph is a partition of its vertices into induced cluster graphs. Thus, the cluster graphs are exactly the graphs of subchromatic number 1.
The computational problem of finding a small set of edges to add or remove from a graph to transform it into a cluster graph is called cluster editing. It is NP-complete but fixed-parameter tractable.
Given a complete graph with edge costs (positive and negative) the clique partitioning problem asks for a subgraph that is a cluster graph such that the sum of the costs of the edges of the cluster graph is minimal.
This problem is closely related to the correlation clustering problem.
References
Graph families
Perfect graphs |
https://en.wikipedia.org/wiki/Vyacheslav%20Vasilievich%20Sazonov | Vyacheslav Vasilievich Sazonov (Вячеслав Васильевич Сазонов, born August 25, 1935, Moscow – February 3, 2002, Moscow) was a Soviet-Russian mathematician, specializing in probability and measure theory. He is known for Sazonov's theorem.
Education and career
In 1958 he graduated from Moscow State University. There he received in 1961 his Ph.D. under Yuri Prokhorov with thesis "Распределения вероятностей и характеристические функционалы" (Probability distributions and characteristic functionals). Sazonov worked in the Steklov Institute of Mathematics from 1958 to 2002. In 1968 he received his Russian doctorate of sciences (Doctor Nauk) with thesis "Исследования по многомерным и бесконечномерным предельным теоремам теории вероятностей" (Investigations of multidimensional, infinite-dimensional and limit theorems of the theory of probabilities). In 1970 he was an Invited Speaker at the ICM in Nice. In 1971 he was awarded the academic title of Professor in Mathematics and became a member of the CPSU. From 1971 to 1999, he was a professor in the Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, Moscow State University. Professor Sazonov has been deputy editor-in-chief of the journal Theory of Probability and Its Applications for about two decades.
Awards
USSR State Prize (1979, jointly with Aleksandr A. Borovkov and V. Statulevičius) for a series of works on asymptotic methods in the theory of probability.
Selected publications
References
External links
Труды Сазонова (publication list in Russian)
Персональная страница на сайте Общероссийский математический портал (personal page on the site all-Russian mathematical portal mathnet.ru)
1935 births
2002 deaths
Moscow State University alumni
Probability theorists
Soviet mathematicians
20th-century Russian mathematicians |
https://en.wikipedia.org/wiki/Joseph%20Mugisha | Joseph Y.T. Mugisha is a Ugandan mathematician (specialising in biomathematics), academician and academic administrator. Currently he is a Professor of Mathematics and Principal of the College of Natural Sciences, a constituent college of Makerere University. Makerere University is the Oldest University in Uganda.
Background and education
He was born in 1960 in Bushenyi district, Western Uganda. Professor Mugisha received his PhD in Bio-mathematics in 2000 from Makerere university. Prior to that he was awarded a Masters of Science(Bio-mathematics) in 1992 and a Bachelors of Science in Education from Makerere University. He attended Mbarara High School for his Secondary Education; and Masheruka Primary School for foundation Education.
Career
Before his appointment as the Principal of the College of Natural Sciences (CONAS), he was the Dean-Faculty of Science from 2009 to 2010, in which position he led the process of conversion of the faculty to a college. He held the Principal post initially in acting capacity (2010 to 2011) before substantive appointment in 2012. He has also served as the Acting Deputy Vice Chancellor[Academic Affairs] at Makerere University.
Professor Mugisha joined Makerere University as a Teaching Assistant in 1987 rising through the ranks to Professorship in 2008. He has also served the University in various leadership and management capacities; Acting Director Institute of Computer Science - Makerere University from August to December 2003; Deputy Director Institute of Computer Science - Makerere university from 2003 to August 2005. He is also a member of the Makerere University Senate which is the highest academic decisions making body of the University, he has been appointed to several boards and committees within the University.
Professor Mugisha has taught courses at Undergraduate and Graduate level. He has supervised and mentored over 40 students at graduate level(both PhD and MSc.) in the region. He is an International Researcher and Examiner with strong links to several universities in Eastern, Central and Southern Africa. He has served as a Reviewer of several International Journals like Mathematical Biosciences, Southern Journal of Sciences, Mathematical Biosciences and Engineering, Mathematical Modelling and Analysis, Ecological Modelling, Computers and Mathematics with Application, Computational and Applied Mathematics, Mathematical and Computer Modelling, among others.
Professor Mugisha is a founder member and the current President of the African Society for Bio-mathematics since 2009. He has been a member of the American Mathematical Society, Ugandan Mathematical Society, Ugandan Biometric Society and is a Fellow of the Ugandan National Academy of Sciences [UNAS].
Professor Mugisha is widely published in over 50 articles in International Journals. His major research interest is in the application of mathematics in biology and biomedical processes with special emphasis on epidemiological and ecological mode |
https://en.wikipedia.org/wiki/Map%20graph | In graph theory, a branch of mathematics, a map graph is an undirected graph formed as the intersection graph of finitely many simply connected and internally disjoint regions of the Euclidean plane. The map graphs include the planar graphs, but are more general. Any number of regions can meet at a common corner (as in the Four Corners of the United States, where four states meet), and when they do the map graph will contain a clique connecting the corresponding vertices, unlike planar graphs in which the largest cliques have only four vertices. Another example of a map graph is the king's graph, a map graph of the squares of the chessboard connecting pairs of squares between which the chess king can move.
Combinatorial representation
Map graphs can be represented combinatorially as the "half-squares of planar bipartite graphs". That is, let be a planar bipartite graph, with bipartition . The square of is another graph on the same vertex set, in which two vertices are adjacent in the square when they are at most two steps apart in . The half-square or bipartite half is the induced subgraph of one side of the bipartition (say ) in the square graph: its vertex set is and it has an edge between each two vertices in that are two steps apart in . The half-square is a map graph. It can be represented geometrically by finding a planar embedding of , and expanding each vertex of and its adjacent edges into a star-shaped region, so that these regions touch at the vertices of . Conversely, every map graph can be represented as a half-square in this way.
Computational complexity
In 1998, Mikkel Thorup claimed that map graphs can be recognized in polynomial time. However, the high exponent of the algorithm that he sketched makes it impractical, and Thorup has not published the details of his method and its proof.
The maximum independent set problem has a polynomial-time approximation scheme for map graphs, and the chromatic number can be approximated to within a factor of two in polynomial time. The theory of bidimensionality leads to many other approximation algorithms and fixed-parameter tractable algorithms for optimization problems on map graphs.
Variations and related concepts
A -map graph is a map graph derived from a set of regions in which at most regions meet at any point. Equivalently, it is the half-square of a planar bipartite graph in which the vertex set (the side of the bipartition not used to induce the half-square) has maximum degree . A 3-map graph is a planar graph, and every planar graph can be represented as a 3-map graph. Every 4-map graph is a 1-planar graph, a graph that can be drawn with at most one crossing per edge, and every optimal 1-planar graph (a graph formed from a planar quadrangulation by adding two crossing diagonals to every quadrilateral face) is a 4-map graph. However, some other 1-planar graphs are not map graphs, because (unlike map graphs) they include crossing edges that are not part of a four-vertex com |
https://en.wikipedia.org/wiki/Janiszewski%27s%20theorem | In mathematics, Janiszewski's theorem, named after the Polish mathematician Zygmunt Janiszewski, is a result concerning the topology of the plane or extended plane. It states that if A and B are closed subsets of the extended plane with connected intersection, then any two points that can be connected by paths avoiding either A or B can be connected by a path avoiding both of them. The theorem has been used as a tool for proving the Jordan curve theorem and in complex function theory.
References
Theorems in topology |
https://en.wikipedia.org/wiki/Cyril%20Brown | Cyril Brown (25 May 1918 – 15 April 1990) was an English professional footballer who played as an inside forward in the Football League for Notts County and Rochdale.
Career statistics
References
1918 births
1990 deaths
Footballers from Ashington
Men's association football inside forwards
English men's footballers
English Football League players
Felixstowe & Walton United F.C. players
Brentford F.C. players
Sunderland A.F.C. players
Notts County F.C. players
Boston United F.C. players
Rochdale A.F.C. players
Midland Football League players
Peterborough United F.C. players |
https://en.wikipedia.org/wiki/Scott%20Easthope | Scott Easthope (born 15 October 1985) is a New Zealand football manager who manages the Samoa national team.
Managerial Statistics
References
1985 births
Living people
New Zealand association football managers
Samoa national football team managers |
https://en.wikipedia.org/wiki/Hessian%20polyhedron | In geometry, the Hessian polyhedron is a regular complex polyhedron 3{3}3{3}3, , in . It has 27 vertices, 72 3{} edges, and 27 3{3}3 faces. It is self-dual.
Coxeter named it after Ludwig Otto Hesse for sharing the Hessian configuration or (94123), 9 points lying by threes on twelve lines, with four lines through each point.
Its complex reflection group is 3[3]3[3]3 or , order 648, also called a Hessian group. It has 27 copies of , order 24, at each vertex. It has 24 order-3 reflections. Its Coxeter number is 12, with degrees of the fundamental invariants 3, 6, and 12, which can be seen in projective symmetry of the polytopes.
The Witting polytope, 3{3}3{3}3{3}3, contains the Hessian polyhedron as cells and vertex figures.
It has a real representation as the 221 polytope, , in 6-dimensional space, sharing the same 27 vertices. The 216 edges in 221 can be seen as the 72 3{} edges represented as 3 simple edges.
Coordinates
Its 27 vertices can be given coordinates in : for (λ, μ = 0,1,2).
(0,ωλ,−ωμ)
(−ωμ,0,ωλ)
(ωλ,−ωμ,0)
where .
As a Configuration
Its symmetry is given by 3[3]3[3]3 or , order 648.
The configuration matrix for 3{3}3{3}3 is:
The number of k-face elements (f-vectors) can be read down the diagonal. The number of elements of each k-face are in rows below the diagonal. The number of elements of each k-figure are in rows above the diagonal.
Images
These are 8 symmetric orthographic projections, some with overlapping vertices, shown by colors. Here the 72 triangular edges are drawn as 3-separate edges.
Related complex polyhedra
The Hessian polyhedron can be seen as an alternation of , = . This double Hessian polyhedron has 54 vertices, 216 simple edges, and 72 faces. Its vertices represent the union of the vertices and its dual .
Its complex reflection group is 3[3]3[4]2, or , order 1296. It has 54 copies of , order 24, at each vertex. It has 24 order-3 reflections and 9 order-2 reflections. Its coxeter number is 18, with degrees of the fundamental invariants 6, 12, and 18 which can be seen in projective symmetry of the polytopes.
Coxeter noted that the three complex polytopes , , resemble the real tetrahedron (), cube (), and octahedron (). The Hessian is analogous to the tetrahedron, like the cube is a double tetrahedron, and the octahedron as a rectified tetrahedron. In both sets the vertices of the first belong to two dual pairs of the second, and the vertices of the third are at the center of the edges of the second.
Its real representation 54 vertices are contained by two 221 polytopes in symmetric configurations: and . Its vertices can also be seen in the dual polytope of 122.
Construction
The elements can be seen in a configuration matrix:
Images
Rectified Hessian polyhedron
The rectification, doubles in symmetry as a regular complex polyhedron with 72 vertices, 216 3{} edges, 54 3{3}3 faces. Its vertex figure is 3{4}2, and van oss polygon 3{4}3. It is dual to the double Hessian polyhedron.
It |
https://en.wikipedia.org/wiki/Daniel%20Lightwing | Daniel James Lightwing is a former mathematics child prodigy and co-founder of the London-based Internet/gambling business Castella Research, which uses high-frequency trading inspired methods to place bets on sports exchanges. He was previously a web backend developer for the London offices of Google. In 2006, he represented the United Kingdom at the International Mathematical Olympiad (IMO) in Ljubljana, Slovenia, where he won a silver medal. His experience at the IMO was described in the 2007 BBC Two British television documentary Beautiful Young Minds and the 2014 film X+Y.
Lightwing started to gain more fame in China from 2016 onwards, particularly on the website Zhihu, where his articles written in Chinese, covering a broad range of topics had attracted over 170,000 followers within one year.
Early life and education
Lightwing was born in 1988 in Chesterfield, Derbyshire to David S. B. Lightwing and his wife Carolyn J. née Davidson. He grew up in the Lake District, and Warthill, Yorkshire. In 2015, he described that, before the age of nine, he "had no particular attraction to mathematics. I learnt to read very young, before attending primary school. And I did read all kinds of things—books aimed at children 5–10 years older. At primary school, I read the entire library."
As his education developed, his teachers "were a little perplexed what to do with me." He described how he wasn't learning anything he hadn't already learned and was bullied by one of his teachers who expected him to "sit under her desk and be ridiculed" for no apparent reason. The bullying increased after he "got extremely angry and jumped on top of the desk to denounce her."
After some intensive personal instruction within a special 'one-to-one' mathematics class with another teacher, he learned that he enjoyed those classes, and stated that, "before long, I had made my mind up that maths was what I wanted to do." He went through many gifted and talented programmes throughout his childhood.
At home, his mother, Carolyn, who was a maths and science teacher, had researched Asperger syndrome (AS) when he was 16 years of age after reading the 2003 mystery novel The Curious Incident of the Dog in the Night-Time, and, later, took him to a diagnostic consultation with University of Cambridge autism researcher and professor Simon Baron-Cohen FBA, who diagnosed Daniel with AS. Parts of the consultation were included in the 2007 BBC Two British television documentary, Beautiful Young Minds.
His interest in mathematics led him to being recruited as a member of the 2006 International Mathematical Olympiad (IMO) team, where he represented the United Kingdom and won a silver medal in Ljubljana, Slovenia.
He was the subject of Catalyst, an Australian television programme in 2008, as well as several Chinese television productions.
He attended Trinity College, Cambridge, where he received a Master of Arts degree in mathematics in 2009, as well as Peking University, where he studi |
https://en.wikipedia.org/wiki/Charlie%20Briggs%20%28footballer%29 | Charles Edward Briggs (4 April 1911 – 29 January 1993) was an English professional footballer who played as a goalkeeper in the Football League for Halifax Town and Rochdale.
Career statistics
References
1911 births
1993 deaths
People from Liphook
English men's footballers
Men's association football goalkeepers
Haywards Sports F.C. players
Guildford City F.C. players
Fulham F.C. players
Tottenham Hotspur F.C. players
Crystal Palace F.C. players
Bradford (Park Avenue) A.F.C. players
Halifax Town A.F.C. players
Clyde F.C. players
Rochdale A.F.C. players
Chesterfield F.C. players
Southern Football League players
English Football League players
Brentford F.C. wartime guest players
Ransome & Marles F.C. players
Ilkeston Town F.C. (1945) players
Aldershot F.C. wartime guest players
Halifax Town A.F.C. wartime guest players
Fulham F.C. wartime guest players
Footballers from Hampshire |
https://en.wikipedia.org/wiki/Pablo%20Ferrari | Pablo Augusto Ferrari (September 11, 1949) is an Argentine mathematician, member of the Bernoulli Society, the Institute for Mathematical Statistics, the Brazilian Academy of Sciences, and the International Statistical Institute. He is also co-principal investigator at the Brazilian research center NeuroMat. Ferrari investigates probabilistic models of microscopic phenomena and macroscopic counterpart. He is the son of the contemporary conceptual artist León Ferrari.
Biography
Pablo Ferrari was born in 1949. He got a degree in mathematics from the University of Buenos Aires (UBA) in 1974 and PhD in Statistics from the University of Sao Paulo (USP) in 1982. Ferrari was Professor at the USP from 1978 to 2008 and a visiting professor at Rutgers, Paris, Rome, Santiago de Chile and Cambridge. He is a UBA Professor and Researcher of CONICET from 2009 and a member of the Group Probability of Buenos Aires. He received a Guggenheim Fellowship in 1999, the Consecration Award of the Academy of Exact, Physical and Natural Sciences in Buenos Aires in 2011 and was named a fellow of the International Statistical Institute in 2013.
References
Academic staff of the University of São Paulo
1949 births
Living people
Members of the Brazilian Academy of Sciences
Argentine mathematicians |
https://en.wikipedia.org/wiki/Al-Funduq | Al-Funduq () was a Palestinian village in the Qalqilya Governorate in the northeastern West Bank, located east of Qalqilya. According to the Palestinian Central Bureau of Statistics, the village had a population of 1,125 in 2017. The village took its name from one Arabic word for "inn."
In 2012 it was decided that Jinsafut and Al-Funduq should be merged under one local council.
Location
Al-Funduq and Jinsafut are located east of Qalqiliya. It is bordered by Immatin to the east, Deir Istiya to the south, Wadi Qana (in Salfit Governorate) to the west and Hajja to the north.
History
Byzantine period
Ceramics from the Byzantine era have been found here, and it has been suggested that this was the place Fondeka, once inhabited by Samaritans.
Crusader period
During the Crusader period the village was inhabited by Muslims, according to the historian Diya al-Din al-Maqdisi. A Hanbali scholar named Ahmad ibn Abd al-Daim al-Maqaddasi al-Hanbali was born in the village in 575 AH/1180 CE, dying there in 668 AH/March 1270 CE. Followers of the Hanbali scholar Ibn Qudamah (1146/47-1223) also lived in the village, and during this period al-Funduq was home to a well-known Muslim sheikh named Abd Allah.
Ottoman period
The place appeared in 1596 Ottoman tax registers as Funduq, being in the Nahiya of Bani Sa'b of the Liwa of Nablus. It had a population of 86 households, all Muslim. They paid a fixed tax-rate of 33.3% on agricultural products, including wheat, barley, summer crops, olives, goats and beehives, and a press for olives or grapes, in addition to occasional revenues and a fixed sum for people of the Nablus area; a total of 10,500 akçe.
A map from Napoleon's invasion of 1799 by Pierre Jacotin named it Fondouk, as a village by the road from Jaffa to Nablus.
In 1838 Robinson noted el-Funduk as a village in Beni Sa'ab district, west of Nablus.
In 1870 Victor Guérin noted El-Fondouk from Fara'ata, but did not visit it.
In 1870/1871 (1288 AH), an Ottoman census listed the village in the nahiya (sub-district) of Bani Sa'b.
In 1882, the PEF's Survey of Western Palestine described the village as "a small poor village by the main road, with wells to the north and two sacred places; it stands on high ground," and located in the Beni Sab district.
British Mandate
In the 1922 census of Palestine conducted by the British Mandate authorities, Funduq had a population of 66 inhabitants, all Muslims, increasing in the 1931 census to 72 Muslims, with 21 houses.
In the 1945 census El Funduq had a population was 100 Muslims, with 1,619 dunams of land, according to an official land and population survey. Of this, 43 dunams were for plantations or irrigated land, 1,026 for cereals, while 14 dunams were built-up (urban) land.
Jordanian period
In the wake of the 1948 Arab–Israeli War, and after the 1949 Armistice Agreements, Al-Funduq came under Jordanian rule.
The Jordanian census of 1961 found 137 inhabitants in Al-Funduq.
Post-1967
Since the Six-Day War in 196 |
https://en.wikipedia.org/wiki/Ilie%20N%C4%83stase%20career%20statistics | These are the main career statistics of Romanian former professional tennis player Ilie Năstase, whose playing career lasted from 1969 through 1985.
Grand Slam finals
Singles: 5 (2 titles, 3 runner-ups)
Doubles: 5 (3 titles, 2 runner-ups)
Mixed doubles: 3 (2 titles, 1 runner-up)
Grand Prix year-end championships finals
Singles: 5 (4 titles, 1 runner-up)
ATP Career finals
Singles: 104 (64 titles, 40 runner-ups)
Sources
Michel Sutter, Vainqueurs Winners 1946–2003, Paris, 2003. Sutter has attempted to list all tournaments meeting his criteria for selection beginning with 1946 and ending in the fall of 1991. For each tournament, he has indicated the city, the date of the final, the winner, the runner-up, and the score of the final. A tournament is included in his list if: (1) the draw for the tournament included at least eight players (with a few exceptions, such as the Pepsi Grand Slam tournaments in the second half of the 1970s); and (2) the level of the tournaments was at least equal to the present day challenger tournaments. Later, Sutter issued a second edition of his book, with only the players, their wins, and years from 1946 to 27 April 2003, period.
John Barrett, editor, World of Tennis Yearbooks, London, from 1976 to 1983.
Joe McCauley in Mr Nastase: The Autobiography, by Ilie Năstase with Debbie Beckerman, 2004.
1982 WCT Yearbook
ATP Official Guide to Professional Tennis 2004 (page G18).
Doubles (45 titles )
Singles performance timeline
Qualifying matches and walkovers are neither official match wins nor losses.
Other titles (24)
Here are Năstase's tournament wins that are not included in the statistics on the Association of Tennis Professionals (ATP) website. The website is incomplete from 1968 to 1970 and has some omissions for tournaments held since 1968.
Năstase won several tournaments during the early years of his career that were equivalent to the present day "challenger" tournaments. Because the term "challenger" started to be applied to second-rank tournaments in 1978, those tournaments are termed "minor tournaments" in the following list.
1967 – Cannes (minor tournament), Travemünde (minor tournament)
1968 – Viareggio, Bucharest (minor tournament)
1969 – Madras (minor tournament), New Delhi (minor tournament), Gauhati (minor tournament), Travemünde, La Corogne, Budapest, Denver
1970 – Napoli, Ancona
1971 – Istanbul
1973 – Istanbul
1974 – Portland
1975 – Helsinki, Dutch Round Robin (Utrecht Netherlands), Graz, Uppsala
1976 – Caracas (a four-man invitation tournament in October, not to be confused with the Caracas WCT in March that was won by Raúl Ramírez), Argentine Round Robin (invitational tournament)
1977 – Rotterdam World Star (invitational tournament)
1978 – Frankfurt (invitational tournament)
Records
These records were attained in the Open Era of tennis.
References
External links
Năstase |
https://en.wikipedia.org/wiki/Nicolas%20Fizes | Nicolas Fizes (27 October 1648 in Frontignan – 1718) was a French professor of mathematics and hydrography, who lived under the reign of Louis XIV. He is especially known as the librettist who wrote L'Opéra de Frontignan (1670), a play in Occitan, dealing with a slight love intrigue, and an idyllic poem on the fountain of Frontignan.
Career
Nicolas Fizes's parents were carpenters in the French Navy. He studied with the Jesuits, and became engineer to armies and a doctor of law. In 1682 he held the first professorship of mathematics and hydrography in Montpellier.
From 1689, he headed a school of hydrography in Frontignan. In the hall of the Town Hall, he taught a few young sailors the concepts of mathematics and astrology. But this school was previously free, and Fizes asked for a salary of 150 pounds a year, which led to a conflict with the consuls of Frontignan. The school only survived 7 years, and closed its doors in 1696.
Bibliography
Lucien Albagnac, Contribution à l'Histoire de Frontignan (no ISBN)
André Cablat, René Michel, Maurice Nougaret, Jean Valette, La Petite Encyclopédie de Frontignan la Peyrade (no ISBN)
See also
Occitan literature
1648 births
People from Hérault
1718 deaths
French mathematicians
Mathematics educators
French hydrographers
French opera librettists |
https://en.wikipedia.org/wiki/P-curvature | In algebraic geometry, -curvature is an invariant of a connection on a coherent sheaf for schemes of characteristic . It is a construction similar to a usual curvature, but only exists in finite characteristic.
Definition
Suppose X/S is a smooth morphism of schemes of finite characteristic , E a vector bundle on X, and a connection on E. The -curvature of is a map defined by
for any derivation D of over S. Here we use that the pth power of a derivation is still a derivation over schemes of characteristic .
By the definition -curvature measures the failure of the map to be a homomorphism of restricted Lie algebras, just like the usual curvature in differential geometry measures how far this map is from being a homomorphism of Lie algebras.
See also
Grothendieck–Katz p-curvature conjecture
Restricted Lie algebra
References
Katz, N., "Nilpotent connections and the monodromy theorem", IHES Publ. Math. 39 (1970) 175–232.
Ogus, A., "Higgs cohomology, -curvature, and the Cartier isomorphism", Compositio Mathematica, 140.1 (Jan 2004): 145–164.
Connection (mathematics)
Algebraic geometry |
https://en.wikipedia.org/wiki/Thomas%20Lynch%20%28footballer%29 | Thomas John Lynch (31 August 1907 – 1976) was a Welsh professional footballer who played in the Football League for Rochdale, Barnsley, Barrow and Watford as a goalkeeper.
Career statistics
References
Welsh men's footballers
English Football League players
1907 births
1976 deaths
Sportspeople from Tredegar
Men's association football goalkeepers
Southern Football League players
Rochdale A.F.C. players
Colwyn Bay F.C. players
Barnsley F.C. players
Barrow A.F.C. players
Yeovil Town F.C. players
Watford F.C. players
Gloucester City A.F.C. players
Bangor City F.C. players |
https://en.wikipedia.org/wiki/Planar%20Riemann%20surface | In mathematics, a planar Riemann surface (or schlichtartig Riemann surface) is a Riemann surface sharing the topological properties of a connected open subset of the Riemann sphere. They are characterized by the topological property that the complement of every closed Jordan curve in the Riemann surface has two connected components. An equivalent characterization is the differential geometric property that every closed differential 1-form of compact support is exact. Every simply connected Riemann surface is planar. The class of planar Riemann surfaces was studied by Koebe who proved in 1910, as a generalization of the uniformization theorem, that every such surface is conformally equivalent to either the Riemann sphere or the complex plane with slits parallel to the real axis removed.
Elementary properties
A closed 1-form ω is exact if and only if ∫γ ω = 0 for every closed Jordan curve γ.
This follows from the Poincaré lemma for 1-forms and the fact that ∫δ df = f(δ(b)) – f(δ(a)) for a path δ parametrized by [a, b] and f a smooth function defined on an open neighbourhood of δ([a, b]). This formula for ∫δ df extends by continuity to continuous paths, and hence vanishes for a closed path. Conversely if ∫γ ω = 0 for every closed Jordan curve γ, then a function f(z) can be defined on X by fixing a point w and taking any piecewise smooth path δ from w to z and set f(z) = ∫δ ω. The assumption implies that f is independent of the path. To check that df = ω, it suffices to check this locally. Fix z0 and take a path δ1 from w to z0. Near z0 the Poincaré lemma implies ω = dg for some smooth function g defined in a neighbourhood of z0. If δ2 is a path from z0 to z, then f(z) = ∫δ1 ω + ∫δ2 ω = ∫δ1 ω + g(z) − g(z0), so f differs from g by a constant near z0. Hence df = dg = ω near z0.
A closed Jordan curve γ on a Riemann surface separates the surface into two disjoint connected regions if and only if ∫γ ω = 0 for every closed 1-form ω of compact support.
If the closed Jordan curve γ separates the surface, it is homotopic to a smooth Jordan curve δ (with non-vanishing derivative) that separates the surface into two halves. The integral of dω over each half equals ± ∫δ ω by Stokes' theorem. Since dω = 0, it follows that ∫δ ω = 0. Hence ∫γ ω = 0.
Conversely suppose γ is a Jordan curve that does not separate the Riemann surface. Replacing γ by a homotopic curve, it may be assumed that γ is a smooth Jordan curve δ with non-vanishing derivative. Since γ does not separate the surface, there is a smooth Jordan curve δ (with non-vanishing derivative) which cuts γ transversely at only one point. An open neighbourhood of γ ∪ δ is diffeomorphic to an open neighbourhood of corresponding Jordan curves in a torus. A model for this can be taken as the square [−π,π]×[−π,π] in R2 with opposite sides identified; the transverse Jordan curves γ and δ correspond to the x and y axes. Let ω = a(x) dx with a ≥ 0 supported near 0 with ∫ a = 1. Thus ω is a closed 1-form supp |
https://en.wikipedia.org/wiki/Archie%20Reay | Albert Frederick Reay (15 September 1901 – 31 December 1962) was an English professional footballer who played as a left back in the Football League for Gillingham and Norwich City.
Career statistics
References
1901 births
1962 deaths
People from West Derby
Men's association football fullbacks
English men's footballers
Gnome Athletic F.C. players
Brentford F.C. players
Gillingham F.C. players
Norwich City F.C. players
Sheppey United F.C. players
Guildford City F.C. players
English Football League players
Footballers from Liverpool |
https://en.wikipedia.org/wiki/Inscriptions%20of%20Bhoja | {
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Bhoja was an Indian king from the Paramara dynasty, whose kingdom was centered around the Malwa region in present-day Madhya Pradesh. By 2003, 12 inscriptions dated to Bhoja's region had been discovered at Banswara, Betma, Bhojpur, Depalpur, Dhar, Kalwan, Mahaudi, Kokapur (in Modasa taluka), Piploda, Tilakwada and Ujjain.
Some of these inscriptions, including those issued by Bhoja himself, are described below. All the inscriptions issued by Bhoja are in Sanskrit language and Nagari script, although some inscriptions feature a few Prakrit words. They are usually in form of copper plates that record land grants. They begin with the auspicious Siddham symbol, and verses praising Shiva. They contain a brief genealogy, naming Bhoja's predecessors as Sindhuraja-deva, Vakpatiraja-deva and Siyaka-deva. Bhoja himself is mentioned as Bhoja-deva, and his titles are given as Parama-bhattaraka, Maharajadhiraja and Parameshvara. All of Bhoja's own inscriptions feature the Paramara emblem of a flying Garuda (with a bird's head and a man's body). The Garuda is shown holding a cobra snake in its left hand, about to strike it with his right hand. The grant records are usually followed by benedictive and imprecatory verses (the latter curse the person who does not honour the gran |
https://en.wikipedia.org/wiki/Barbara%20Niethammer | Barbara Niethammer (born 1967) is a German mathematician and materials scientist who works as a professor at the Hausdorff Center for Mathematics at the University of Bonn. Her research concerns partial differential equations for physical materials, and in particular the phenomenon of Ostwald ripening by which particles in liquids grow over time.
Education and career
Niethammer completed her PhD in 1996 at the University of Bonn, under the supervision of Hans Wilhelm Alt. Her dissertation was Approximation of Coarsening Madels by Homogenization of a Stefan Problem.
After postdoctoral research at the Courant Institute, she returned to Bonn for her habilitation in 2002, after which she became in 2003 a professor at the Humboldt University of Berlin. She moved to the University of Oxford in 2007, where she was a fellow of St Edmund Hall. In 2012 she returned as a professor to the University of Bonn.
Recognition
Niethammer won the Richard von Mises Prize of the Gesellschaft für Angewandte Mathematik und Mechanik in 2003 for her work on Ostwald ripening, and the Whitehead Prize of the London Mathematical Society in 2011 "for her deep and rigorous contributions to material science, especially on the Lifshitz–Slyozov–Wagner and Becker–Doering equations".
She was an invited speaker at the International Congress of Mathematicians in 2014.
References
1967 births
Living people
20th-century German mathematicians
German materials scientists
Women mathematicians
Women materials scientists and engineers
University of Bonn alumni
Academic staff of the Humboldt University of Berlin
Fellows of St Edmund Hall, Oxford
Academic staff of the University of Bonn
21st-century German mathematicians |
https://en.wikipedia.org/wiki/Jimmy%20Hindson | James Bell Hindson (15 July 1908 – 1950) was an English professional footballer who made over 100 appearances as a full back in the Football League for Fulham.
Career statistics
References
1908 births
1950 deaths
Footballers from Sunderland
English men's footballers
Men's association football fullbacks
Hylton Colliery Welfare F.C. players
Sunderland A.F.C. players
Spennymoor United A.F.C. players
Fulham F.C. players
Middlesbrough F.C. players
English Football League players |
https://en.wikipedia.org/wiki/List%20of%20Guidances%20for%20Statistics%20in%20Regulatory%20Affairs | This List presents a comprehensive source of references for statistical guidance documents and related articles that are relevant to regulatory affairs for those statisticians that work on clinical studies. The List is associated with the Wikipedia page Guidances for statistics in regulatory affairs that aims to address the various topics of the listed guidances. Regulatory guidances (draft and/or final ) are subject to revisions. Therefore, users of the guidances are advised to consult the original website to check for the latest version. Users are also encouraged to update the Wikipedia List.
References classified by statistical topic
Good clinical practice
ICH E6(R2): Good clinical practice is an international ethical and scientific quality standard for designing, conducting, recording and reporting trials that involve the participation of human subjects.
FDA: Good Review Practice: Clinical Review of Investigational New Drug Applications. This good review practice (GRP) document was prepared to assist FDA clinical review staff in reviewing clinical submissions to an investigational new drug application (IND) from the pre-IND phase to the time of the pre-new drug application/biologics license application meeting.
Data monitoring committees
CHMP/EWP/5872/03: Data monitoring committees (EMA) deals with independent data monitoring committees. It highlights the key issues involved when sponsors include data monitoring committees as a part of their trial management.
FDA: Establishment and Operation of Clinical Trial Data Monitoring Committees. This guidance discusses the roles, responsibilities and operating procedures of Data Monitoring Committees (DMCs) (also known as Data and Safety Monitoring Boards (DSMBs) or Data and Safety Monitoring Committees (DSMCs)) that may carry out important aspects of clinical trial monitoring.
Adjustment by covariates
EMA/CHMP/295050/2013: Adjustment for baseline covariates in clinical trials (EMA) provides advice on how to address important baseline covariates in designing, analysing and reporting clinical trials. It mainly focuses on confirmatory randomised trials.
Small populations / rare diseases
CHMP/EWP/83561/05: Clinical trials in small populations (EMA) addresses problems associated with clinical trials when there are limited numbers of patients available to study.
FDA Rare diseases: Common issues in drug development. Guidance for industry.
see also the subgroup analysis section
Extrapolation / bridging
EMA/199678/2016: Reflection paper on extrapolation of efficacy and safety in paediatric medicine development.
EMA/189724/2018: Reflection paper on the use of extrapolation in the development of medicines for paediatrics.
EMA/129698/2012: Concept paper on extrapolation of efficacy and safety in medicine development.
FDA-2015-D-1376: Leveraging existing clinical data for extrapolation to pediatric uses of medical devices. Guidance for Industry and Food and Drug Administration Staff.
ICH E5 ( |
https://en.wikipedia.org/wiki/Fichera%27s%20existence%20principle | In mathematics, and particularly in functional analysis, Fichera's existence principle is an existence and uniqueness theorem for solution of functional equations, proved by Gaetano Fichera in 1954. More precisely, given a general vector space and two linear maps from it onto two Banach spaces, the principle states necessary and sufficient conditions for a linear transformation between the two dual Banach spaces to be invertible for every vector in .
See also
Notes
References
. A survey of Gaetano Fichera's contributions to the theory of partial differential equations, written by two of his pupils.
.
.
: for a review of the book, see .
. The paper Some recent developments of the theory of boundary value problems for linear partial differential equations describes Fichera's approach to a general theory of boundary value problems for linear partial differential equations through a theorem similar in spirit to the Lax–Milgram theorem.
. A monograph based on lecture notes, taken by Lucilla Bassotti and Luciano De Vito of a course held by Gaetano Fichera at the INdAM: for a review of the book, see .
.
, reviewed also by , and by
.
.
. An expository paper detailing the contributions of Gaetano Fichera and his school on the problem of numerical calculation of eigenvalues for general differential operators.
Banach spaces
Normed spaces
Partial differential equations
Theorems in functional analysis |
https://en.wikipedia.org/wiki/Yvette%20Amice | Yvette Amice (June 4, 1936 – July 4, 1993) was a French mathematician whose research concerned number theory and -adic analysis. She was president of the Société mathématique de France.
Education
Amice studied mathematics at the École normale supérieure de jeunes filles in Sèvres, beginnining in 1956 and earning her agrégation in 1959. She became an assistant at the Faculté des sciences de Paris until 1964, when she completed a state doctorate under the supervision of Charles Pisot. Her dissertation was Interpolation p-adique [p-adic interpolation].
Career
On completing her doctorate, she became maître de conférences at the University of Poitiers and then, in 1966, professor at the University of Bordeaux. She returned to Poitiers in 1968 but then in 1970 became one of the founding professors of Paris Diderot University, where she was vice president from 1978 to 1981.
In 1975 she became president of the Société mathématique de France.
Textbook
Amice was the author of a textbook on the p-adic number system, Les nombres p-adiques (Presses Universitaires de France, 1975).
References
1936 births
1993 deaths
20th-century French mathematicians
French women mathematicians
20th-century French women
Academic staff of the University of Bordeaux
Academic staff of Paris Diderot University |
https://en.wikipedia.org/wiki/Jaszczak%20phantom | A Jaszczak phantom (pronounced "JAY-zak") aka Data Spectrum ECT phantom is an imaging phantom used for validating scanner geometry, 3D contrast, uniformity, resolution, attenuation and scatter correction or alignment tasks in nuclear medicine. It is commonly used in academic centers and hospitals to characterize a SPECT or some gamma camera systems for quality control purposes. It is used for accreditation by clinical and academic facilities for the American College of Radiology.
The phantom was developed by Ronald J. Jaszczak of Duke University, and was filed for a patent in 1982. It is a cylinder containing fillable inserts that is often used with a radionuclide such as Technetium-99m or Fluorine-18.
Although the phantom can be used for acceptance testing, the National Electrical Manufacturers Association recommends a 30 million count acquisition and section reconstruction of the phantom be performed quarterly.
In 1981 Ronald J. Jaszczak founded Data Spectrum Corporation which manufactures the Jaszczak phantom and several other nuclear imaging tools, such as the Hoffman Brain phantom.
Structure and composition
Jaszczak phantoms consist of a main cylinder or tank made of acrylic plastic with several inserts. The circular phantom comes in two varieties: flanged and flangeless. The latter is recommended by the American College of Radiology for accreditation of nuclear medicine departments. All Jaszczak phantoms have six solid spheres and six sets of 'cold' rods. In flanged models, the sizes of the spheres vary. The number of rods in each set depends on the size of the rod in that set as different models of the phantom have rods of different sizes. In flangeless models, the diameters of the spheres are 9.5, 12.7, 15.9, 19.1, 25.4 and 31.8 mm, while the rod diameters are 4.8, 6.4, 7.9, 9.5, 11.1 and 12.7 mm. Both solid spheres and rod inserts mimic cold lesions in a hot background. Spheres are used to measure the image contrast while the rods are used to investigate the image resolution in SPECT systems.
References
External links
ACR Accreditation of Nuclear Medicine and PET Imaging Departments
Nuclear medicine
Quality control tools
Positron emission tomography |
https://en.wikipedia.org/wiki/Decomposition%20theorem%20of%20Beilinson%2C%20Bernstein%20and%20Deligne | In mathematics, especially algebraic geometry, the decomposition theorem of Beilinson, Bernstein and Deligne or BBD decomposition theorem is a set of results concerning the cohomology of algebraic varieties. It was originally conjectured by Gelfand and MacPherson.
Statement
Decomposition for smooth proper maps
The first case of the decomposition theorem arises via the hard Lefschetz theorem which gives isomorphisms, for a smooth proper map of relative dimension d between two projective varieties
Here is the fundamental class of a hyperplane section, is the direct image (pushforward) and is the n-th derived functor of the direct image. This derived functor measures the n-th cohomologies of , for .
In fact, the particular case when Y is a point, amounts to the isomorphism
This hard Lefschetz isomorphism induces canonical isomorphisms
Moreover, the sheaves appearing in this decomposition are local systems, i.e., locally free sheaves of Q-vector spaces, which are moreover semisimple, i.e., a direct sum of local systems without nontrivial local subsystems.
Decomposition for proper maps
The decomposition theorem generalizes this fact to the case of a proper, but not necessarily smooth map between varieties. In a nutshell, the results above remain true when the notion of local systems is replaced by perverse sheaves.
The hard Lefschetz theorem above takes the following form: there is an isomorphism in the derived category of sheaves on Y:
where is the total derived functor of and is the i-th truncation with respect to the perverse t-structure.
Moreover, there is an isomorphism
where the summands are semi-simple perverse-sheaves, meaning they are direct sums of push-forwards of intersection cohomology sheaves.
If X is not smooth, then the above results remain true when is replaced by the intersection cohomology complex .
Proofs
The decomposition theorem was first proved by Beilinson, Bernstein, and Deligne. Their proof is based on the usage of weights on l-adic sheaves in positive characteristic. A different proof using mixed Hodge modules was given by Saito. A more geometric proof, based on the notion of semismall maps was given by de Cataldo and Migliorini.
For semismall maps, the decomposition theorem also applies to Chow motives.
Applications of the theorem
Cohomology of a Rational Lefschetz Pencil
Consider a rational morphism from a smooth quasi-projective variety given by . If we set the vanishing locus of as then there is an induced morphism . We can compute the cohomology of from the intersection cohomology of and subtracting off the cohomology from the blowup along . This can be done using the perverse spectral sequence
Local invariant cycle theorem
Let be a proper morphism between complex algebraic varieties such that is smooth. Also, let be a regular value of that is in an open ball B centered at . Then the restriction map
is surjective, where is the fundamental group of the intersection of with the set |
https://en.wikipedia.org/wiki/Wu-Chung%20Hsiang | Wu-Chung Hsiang (; born 12 June 1935 in Zhejiang) is a Chinese-American mathematician, specializing in topology. Hsiang served as chairman of the Department of Mathematics at Princeton University from 1982 to 1985 and was one of the most influential topologists of the second half of the 20th century.
Biography
Hsiang hails from Wenzhou, Zhejiang. He received in 1957 his bachelor's degree from the National Taiwan University and in 1963 his Ph.D. under Norman Steenrod from Princeton University with thesis Obstructions to sectioning fibre bundles. At Yale University he became in 1962 a lecturer, in 1963 an assistant professor, and in 1968 a full professor. At Princeton University he was a full professor from 1972 until retiring in 2006 as professor emeritus and was the department chair from 1982 to 1985. He was a visiting scholar at the Institute for Advanced Study for the academic years 1965–1966, 1971–1972, and 1979–1980. He was a visiting professor at the University of Warwick in 1966, the University of Amsterdam in 1969, the University of Bonn in 1971, the University of California, Berkeley in 1976, and the Mathematical Sciences Research Institute and Stanford University in 1980.
Hsiang has made important contributions to algebraic and differential topology. Works by Hsiang, Julius Shaneson, C. T. C. Wall, Robion Kirby, Laurent Siebenmann and Andrew Casson led in the 1960s to the proof of the annulus theorem (previously known as the annulus conjecture). The annulus theorem is important in the theory of triangulation of manifolds.
With F. Thomas Farrell he worked on a program to prove the Novikov conjecture and the Borel conjecture with methods from geometric topology and gave proofs for special cases. For example, they gave a proof of the integral Novikov conjecture for compact Riemannian manifolds with non-positive sectional curvature. Hsiang also made contributions to the topological study of simply-connected 4-manifolds.
From 1967 to 1969 he was a Sloan Fellow and for the academic year 1975–1976 a Guggenheim Fellow. In 1980 he was elected a member of Academia Sinica. He was an Invited Speaker at the International Congress of Mathematicians in 1970 in Nice, with a talk on Differentiable actions of compact connected Lie groups on and a Plenary Speaker in 1983 in Warsaw, with a talk on Geometric applications of algebraic K-theory. In 2005 there was a conference at Stanford University in honor of his 70th birthday.
His doctoral students include Ruth Charney, F. Thomas Farrell, Thomas Goodwillie, Michael W. Davis, and Lowell E. Jones.
References
1935 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Chinese emigrants to the United States
Topologists
Institute for Advanced Study visiting scholars
Members of Academia Sinica
National Taiwan University alumni
Yale University faculty
Princeton University faculty
University of California, Berkeley faculty
Educators from Wenzhou
Scientists from Wenzhou |
https://en.wikipedia.org/wiki/Chahamanas%20of%20Ranastambhapura | {
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The Chahamanas of Ranastambhapura were a 13th-century Indian dynasty. They ruled the area around their capital Ranastambhapura (Ranthambore) in present-day Rajasthan, initially as vassals of the Delhi Sultanate, and later gained independence. They belonged to the Chahamana (Chauhan) clan of the Rajputs, and are also known as Chauhans of Ranthambore in vernacular Rajasthani bardic literature.
The Chahamana line of Ranastambhapura was established by Govindaraja, who agreed to rule as a vassal of the Ghurids in 1192, after they defeated his father, the Shakambhari Chahamana king Prithviraja III. Govindaraja's descendants gained and lost their independence to the Delhi Sultanate multiple times during the 13th century. Hammira, the last king of the dynasty, adopted an expansionist policy, and raided several neighbouring kingdoms. The dynasty ended with his defeat against the Delhi Sultan Alauddin Khalji at the Siege of Ranthambore in 1301.
History
The Chahamana dynasty of Ranastambhapura was established by Govinda-raja, a member of the Shakambhari Chahamana family (also known as the Chauhans of Ajmer). Govinda was the son of Prithviraja III, who was defeated and killed in a battle with the Ghurids, in 1192 CE. The Ghurid ruler Muhammad of Ghor appointed Govinda as his vassal at Ajmer. However, Prithviraja's brother Hari-raja de-throned him, and himself became the ruler of Ajmer. Govinda then established a new kingdom with its capital at Ranastambhapura (modern Ranthambor). After the Muslim conquest of Ajmer, he granted asylum to Hari.
Balhana, the son of Govindaraja, is recorded as a vassal of the Delhi Sultan Iltumish in 1215 CE, but declared independence in the later years. Balhana's elder son Prahlada succeeded him, and died in a lion-hunt. Prahlada's son Viranarayana was invited to Delhi by Iltumish, but was poisoned to death there. Iltumish captured the fort in 1226 CE. Balhana's younger son Vagabhata then ascended the throne. He recaptured Ranthambore during the reign of the Delhi ruler Razia (r. 1236-1240). He successfully defended the fort against the Delhi Sultanate's invasions in 1248 and 1253 CE.
Vagbhata's son Jaitrasimha achieved military successes against Paramaras of Malwa and other chiefs. He, however, lost his sovereignty to Nasir-ud-din, and ended up paying tribute to the Delhi Sultanate.
Hammira-Deva, the last ruler of the dynasty, was also its most powerful ruler. He ascended the throne sometime between 1283 and 1289 CE. Hammira Mahakavya, his biography by Nayachandra, is one of the few non-Muslim sources for the region's history from that period, and enables the historians to verify the accounts of the Muslim chronicles. The Balvan inscription of 1288 CE mentions that Hammira captured the elephan |
https://en.wikipedia.org/wiki/Zo%C3%A9%20Chatzidakis | Zoé Maria Chatzidakis is a mathematician who works as a director of research at the École Normale Supérieure in Paris, France. Her research concerns model theory and difference algebra. She was invited to give the Tarski Lectures in 2020, though the lectures were postponed due to the COVID-19 pandemic.
Education and employment
Chatzidakis earned her Ph.D. in 1984 from Yale University, under the supervision of Angus Macintyre, with a dissertation on the model theory of profinite groups. She is Senior researcher and team director in Algebra and Geometry in the Département de mathématiques et applications de l'École Normale Supérieure.
Honors and awards
She was the 2013 winner of the Leconte Prize, and was an invited speaker at the International Congress of Mathematicians in 2014. She was named MSRI Chern Professor for Fall 2020.
References
External links
Home page
Year of birth missing (living people)
Living people
Model theorists
French mathematicians
French women mathematicians
Yale Graduate School of Arts and Sciences alumni |
https://en.wikipedia.org/wiki/Prior-independent%20mechanism | A Prior-independent mechanism (PIM) is a mechanism in which the designer knows that the agents' valuations are drawn from some probability distribution, but does not know the distribution.
A typical application is a seller who wants to sell some items to potential buyers. The seller wants to price the items in a way that will maximize his profit. The optimal prices depend on the amount that each buyer is willing to pay for each item. The seller does not know these values, but he assumes that the values are random variables with some unknown probability distribution.
A PIM usually involves a random sampling process. The seller samples some valuations from the unknown distribution, and based on the samples, constructs an auction that yields approximately-optimal profits. The major research question in PIM design is: what is the sample complexity of the mechanism? I.e, how many agents it needs to sample in order to attain a reasonable approximation of the optimal welfare?
Single-item auctions
The results in imply several bounds on the sample-complexity of revenue-maximization of single-item auctions:
For a -approximation of the optimal expected revenue, the sample-complexity is - a single sample suffices. This is true even when the bidders are not i.i.d.
For a -approximation of the optimal expected revenue, when the bidders are i.i.d OR when there is an unlimited supply of items (digital goods), the sample-complexity is when the agents' distributions have monotone hazard rate, and when the agents' distributions are regular but do not have monotone-hazard-rate.
The situation becomes more complicated when the agents are not i.i.d (each agent's value is drawn from a different regular distribution) and the goods have limited supply. When the agents come from different distributions, the sample complexity of -approximation of the optimal expected revenue in single-item auctions is:
at most - using a variant of the empirical Myerson auction.
at least (for monotone-hazard-rate regular valuations) and at least (for arbitrary regular valuations).
Single-parametric agents
discuss arbitrary auctions with single-parameter utility agents (not only single-item auctions), and arbitrary auction-mechanisms (not only specific auctions). Based on known results about sample complexity, they show that the number of samples required to approximate the maximum-revenue auction from a given class of auctions is:
where:
the agents' valuations are bounded in ,
the pseudo-VC dimension of the class of auctions is at most ,
the required approximation factor is ,
the required success probability is .
In particular, they consider a class of simple auctions called -level auctions: auctions with reserve prices (a Vickrey auction with a single reserve price is a 1-level auction). They prove that the pseudo-VC-dimension of this class is , which immediately translates to a bound on their generalization error and sample-complexity. They also prove bounds on th |
https://en.wikipedia.org/wiki/Clyde%20Martin%20%28mathematician%29 | Clyde Martin is an American mathematician and Professor of Statistics. He is best known for his work collaborating with scientists, engineers, and health care professionals developing applications of statistics.
Biography
Martin received his B.A. in mathematics education from Emporia State University. He completed a M.S., and he received his Ph.D. in 1971 from the University of Wyoming. After receiving his Ph.D. in mathematics, Martin worked as a National Research Council Research Associate at NASA from 1971 to 1973 and later in '76 and '77. He was coauthor with Robert Hermann of Algebro-geometric and Lie theoretic Techniques in Systems Theory (1977).
Since 1983, Martin has been on the faculty of Texas Tech University, and is currently an emeritus professor. From 1991 to 2014, he held the Paul Whitfield Horn Professorship of Mathematics.
Martin is a Fellow of the Institute of Electrical and Electronics Engineers and the American Statistical Association. In 2012, he served as Jefferson Science Fellow in the Secretary's Office of Global Food Security at the United States Department of State.
Recently, Martin has focused his research on studying improvements in crop insurance for farmers in Sub Saharan Africa. He also serves on the Science Advisory Board of the United States Environmental Protection Agency.
Martin has an Erdos number of 3.
References
Living people
Emporia State University alumni
University of Wyoming alumni
Texas Tech University faculty
Jefferson Science Fellows
Year of birth missing (living people)
Fellows of the American Statistical Association
Fellow Members of the IEEE |
https://en.wikipedia.org/wiki/Kim%20Yun-ho%20%28footballer%29 | Kim Yun-ho (; born 21 September 1990) is a South Korean footballer who plays as defender for Busan IPark.
Career
He was selected by Gangwon FC in 2013 K League draft.
Club career statistics
As of 4 December 2016
References
External links
1990 births
Living people
Men's association football defenders
South Korean men's footballers
Gangwon FC players
Busan IPark players
K League 1 players
K League 2 players |
https://en.wikipedia.org/wiki/CricHQ | CricHQ is a digital platform for sport which combines competition management and administration software with live scoring and statistics for cricket clubs. It is based in Wellington, New Zealand, and was set up by CEO Simon Baker and former New Zealand cricketers Stephen Fleming and Brendon McCullum. It manages the administration of cricket test countries New Zealand, Sri Lanka, South Africa and Zimbabwe. A number of other national governing bodies also use its services from club level upwards (see National Governing Bodies section below).
The company provides a range of digital services to cricket organisations that typically use paper-based administration and scoring. The services include instant updates for fans, performance insights for coaches and the ability to set up cricket-related social networks. It also makes it easier to register players, organise competition draws and analyse demographics of sport participants.
When the app was launched it was briefly one of the world's most downloaded sporting apps and since then it has amassed over 1 million Facebook fans.
The company has been described as "one of New Zealand’s largely unsung tech success stories" by one of New Zealand's leading technology journalists.
In October 2016, CricHQ's then-Executive Chair, Mike Loftus, was invited to visit India with New Zealand's Prime Minister, John Key, as part of a trade delegation.
In December 2016, former Saatchi & Saatchi Chair and CEO Kevin Roberts was appointed as Chair of CricHQ's board.
In October 2017, CricHQ was put in voluntary receivership by majority shareholders Tembusu Partners who appointed insolvency experts KordaMentha to sell the business. CricHQ was purchased by a group of private investors and continues to trade.
Video content
In 2017, CricHQ acquired My Action Replay, a sportstech company based in Bristol. My Action Replay provides cameras and the capability for sports teams to livestream their games and to package up highlights to be hosted online. With CricHQ's customer base, the acquisition of My Action Replay could make CricHQ the largest broadcaster of cricket in the world.
Investment
In June 2015 CricHQ raised US$10m from Singapore private equity firm Tembusu Partners to expand globally including a doubling of staff in India, the world's largest cricketing nation.
In September 2016 it was revealed that CricHQ was seeking further investment of US$10M and was in discussions with investment bankers in the United States and United Kingdom. It also stated that the company was valued at US$70M while forecast to make a loss of more than US$4m in the 2016/17 financial year.
Incoming Chair Kevin Roberts (businessman) revealed that he had invested a "seven figure" sum in the company in December 2016.
National Governing Bodies
As well as having a partnership with the International Cricket Council, CricHQ signed Hong Kong as its 50th cricketing National Governing Body in August 2016. As of May 2017, 54 National Governin |
https://en.wikipedia.org/wiki/Martin%20Wirsing | Martin Wirsing (born 24 December 1948 in Bayreuth) is a German computer scientist, and Professor at the Ludwig-Maximilians-Universität München, Germany.
Biography
Wirsing studied Mathematics at Ludwig-Maximilians-Universität München (LMU) and at Université Paris 7, obtaining the Diplom in Mathematics from LMU and the Mâitrise-ès-Sciences Mathématiques at the Université Paris 7. Supervised by Kurt Schütte, he received his PhD from LMU in 1976, with a thesis on a topic in mathematical logic (Das Entscheidungsproblem der Prädikatenlogik mit Identität und Funktionszeichen). In 1975-1983 he was a research assistant at the chair of F.L. Bauer at Technical University of Munich where in 1984 he completed his Habilitation in Informatics; in 1985 Wirsing became full professor and Chair of Informatics at the University of Passau and in 1992 he returned to LMU as the Chair of Programming and Software Engineering. Several years he served as Dean, Head of Department and Vice President of the Senat of LMU. Since 2010 he is Vice President for Teaching and Studies of LMU. In July 2016, he was awarded a Degree of Doctor of Science (Honoris Causa) by Royal Holloway, University of London.
His research interests comprise software engineering and its formal foundations, autonomous self-aware systems, and digitisation of universities. In 2006-2015 he was coordinating the European IP projects SENSORIA (2006-2010) on software engineering for service-oriented systems and ASCENS (2010-2015) on engineering collective autonomic systems. In 2007-2010 Martin Wirsing was the chairman of the Scientific Board of INRIA and in 2014-2017 a member of the scientific committee of Institut Mines-Télécom. Currently, he is a member of the board of trustees of Max Planck Institute of Psychiatry and of the scientific committees of the University of Bordeaux and IMDEA Software Institute. He is a member of the editorial board of several scientific journals and book series including Theoretical Computer Science (journal), International Journal of Software and Informatics, and Electronic Proceedings in Theoretical Computer Science.
Selected papers and books
Martin Wirsing: Algebraic Specification. In: J. van Leeuwen (ed.): Handbook of Theoretical Computer Science, Amsterdam, North-Holland, 1990, pp. 675–788 ()
Pietro Cenciarelli, Alexander Knapp, Bernhard Reus, and Martin Wirsing. An Event-Based Structural Operational Semantics of Multi-Threaded Java. In: Jim Alves-Foss (ed.): Formal Syntax and Semantics of Java, Lect. Notes Comp. Sci. 1523, Berlin: Springer, 1999, pp. 157–200 ()
Iman Poernomo, John Crossley, Martin Wirsing: Adapting Proofs-as-Programs: The Curry—Howard Protocol. Springer Monographs in Computer Science, 2005, 420 pages ()
Martin Wirsing, Jean-Pierre Banatre, Matthias Hölzl, Axel Rauschmayer (Eds.): Software-Intensive Systems and New Computing Paradigms. Lecture Notes in Computer Science 5380, Springer-Verlag, 2008, 265 pages ()
Martin Wirsing, Matthias Hölzl (Ed |
https://en.wikipedia.org/wiki/Mileva%20Prvanovi%C4%87 | Mileva Prvanović (born July 16, 1929 - 2016) was a Serbian differential geometer. She is a retired professor of mathematics at the University of Novi Sad and a member of the Serbian Academy of Sciences and Arts.
Education and career
Prvanović was born in Knjaževac on July 16, 1929, the daughter of mathematics professor Stanko Prvanović (1904–1982). After studying at the University of Belgrade, she earned a doctorate in 1955 from the University of Zagreb under the supervision of Danilo Blanuša, with a dissertation concerning differential geometry. In doing so, she became the first student in Serbia to earn a doctorate in geometry.
While completing her doctorate, she worked as a teaching assistant at the Serbian Academy of Sciences. Then, she joined the mathematics department at Novi Sad as an assistant professor. She was promoted to docent in 1957, associate professor in 1962, and full professor in 1967. She retired in 1993. As well as her professorial duties, she also served as editor in chief of the journal Publications de l'Institut Mathématique of the Mathematical Institute of the Serbian Academy of Sciences and Arts.
Recognition
Prvanović was elected to the Serbian Academy of Sciences and Arts in 1981.
A seminar in Vrnjačka Banja was held in 2014 in honor of her 85th birthday.
References
1929 births
2016 deaths
Serbian mathematicians
Women mathematicians
Differential geometers
University of Belgrade alumni
University of Zagreb alumni
Academic staff of the University of Novi Sad
Members of the Serbian Academy of Sciences and Arts |
https://en.wikipedia.org/wiki/Alexander%20Novikov%20%28disambiguation%29 | Alexander Novikov (1900–1976) was a Soviet Air Force marshal.
Alexander or Aleksandr Novikov may also refer to:
Alexander Novikov (mathematician), professor of mathematics
Aleksandr Novikov (singer) (born 1953), Soviet and Russian author and performer of songs
Aleksandr Novikov (footballer, born 1955), Soviet and Russian football manager and former defender
Aleksandr Novikov (footballer, born 1958) (1958–1991), Soviet Russian football goalkeeper
Aleksandr Novikov (footballer, born 1984), Russian football centre-back
Aleksandr Novikov (rower) (born 1985), Belarusian Olympic rower
Aleksandr Novikov (footballer, born 2002), Russian football midfielder |
https://en.wikipedia.org/wiki/Suresh%20Appusamy | Suresh Appusamy is a Tamil Nadu born Singapore cricketer. He was born in Namakkal, Tamil Nadu on June 16, 1987. He is a right arm batsman and right-arm medium pace bowler.
Statistics
He plays for Singapore national cricket team. He played for the team in the 2014 ICC World Cricket League Division Three. His best bowling figures are 4/16 vs Maldives national cricket team and 4/35 vs Sinhalese.
Recent matches
Suresh Appusamy scored 6* and 2/12 vs Bhutan national cricket team. He took 1 wicket giving 21 runs against Kuwait national cricket team on 25 January 2015 and the same against Malaysia national cricket team on 30 January 2015 both at Sharjah.
References
1987 births
Living people
Singaporean cricketers
Indian emigrants to Singapore
Singaporean people of Tamil descent |
https://en.wikipedia.org/wiki/Casa%20Branca%2C%20Sousel | Casa Branca () is a civil parish in the municipality of Sousel.
Location and statistics
References
Parishes of Sousel |
https://en.wikipedia.org/wiki/Bioctonion | In mathematics, a bioctonion, or complex octonion, is a pair (p,q) where p and q are biquaternions.
The product of two bioctonions is defined using biquaternion multiplication and the biconjugate p → p*:
The bioctonion z = (p,q) has conjugate z* = (p*, – q).
Then norm N(z) of bioctonion z is z z* = p p* + q q*, which is a complex quadratic form with eight terms.
The bioctonion algebra is sometimes introduced as simply the complexification of real octonions, but in abstract algebra it is the result of the Cayley–Dickson construction that begins with the field of complex numbers, the trivial involution, and quadratic form z2. The algebra of bioctonions is an example of an octonion algebra.
For any pair of bioctonions y and z,
showing that N is a quadratic form admitting composition, and hence the bioctonions form a composition algebra.
Guy Roos explained how bioctonions are used to present the exceptional symmetric domains:
Complex octonions have been used to describe the generations of quarks and leptons.
References
J. D. Edmonds (1978) Nine-vectors, complex octonion/quaternion hypercomplex numbers, Lie groups and the ‘real’ world, Foundations of Physics 8(3-4): 303–11, link from PhilPapers.
J. Koeplinger & V. Dzhunushaliev (2008) "Nonassociative decomposition of angular momentum operator using complex octonions", presentation at a meeting of the American Physical Society
D.G. Kabe (1984) "Hypercomplex Multivariate Normal Distribution", Metrika 31(2):63−76
A.A. Eliovich & V.I. Sanyuk (2010) "Polynorms", Theoretical and Mathematics Physics 162(2) 135−48
Composition algebras
Octonions |
https://en.wikipedia.org/wiki/1966%E2%80%9367%20Galatasaray%20S.K.%20season | The 1966–67 season was Galatasaray's 63rd in existence and the 9th consecutive season in the 1. Lig. This article shows statistics of the club's players in the season, and also lists all matches that the club have played in the season.
Squad statistics
Players in / out
In
Out
1.Lig
Standings
Matches
Türkiye Kupası
Kick-off listed in local time (EET)
1/4 final
Süper Kupa
Kick-off listed in local time (EET)
European Cup Winners' Cup
First round
Friendly Matches
TSYD Kupası
Spor Toto Kupası
Attendance
References
Tuncay, Bülent (2002). Galatasaray Tarihi. Yapı Kredi Yayınları
External links
Galatasaray Sports Club Official Website
Turkish Football Federation – Galatasaray A.Ş.
uefa.com – Galatasaray AŞ
Galatasaray S.K. (football) seasons
Turkish football clubs 1966–67 season
1960s in Istanbul |
https://en.wikipedia.org/wiki/Worldwide%20Center%20of%20Mathematics | The Worldwide Center of Mathematics (or Center of Math) is an American education technology company that publishes mathematics textbooks and produces educational videos and mathematical research. Since 2010, it has published the Journal of Singularities.
History
The Center of Math was founded in 2008 by David B. Massey and is based in Cambridge, Massachusetts. It publishes textbooks, and additionally offers open textbooks.
References
Mathematical Sciences Publishers academic journals
2008 establishments in Massachusetts |
https://en.wikipedia.org/wiki/Bozenna%20Pasik-Duncan | Bozenna Janina Pasik-Duncan (born 1947) is a Polish-American mathematician who works as a professor of mathematics at the University of Kansas.
Research
Pasik-Duncan's research concerns stochastic control and its applications in communications, economics, and health science. She is also interested in mathematics education, particularly for women in STEM fields.
Education and career
Pasik-Duncan attended high school in Radom. She earned a master's degree in mathematics from the University of Warsaw in 1970. She completed a Ph.D. at the Warsaw School of Economics in 1978, and earned a habilitation there in 1986.
She moved to the University of Kansas mathematics department in 1984, joining there her husband Tyrone Duncan (also a University of Kansas mathematician).
Recognition
She was a recipient of the IEEE's Third Millennium Medal in 2000, and became a Fellow of the IEEE in 2001. She was the 2004 AWM/MAA Falconer Lecturer, and the 2004 winner of the Louise Hay Award for Contributions to Mathematics Education of the Association for Women in Mathematics. She was named a Fellow of the International Federation of Automatic Control in 2014. Pasik-Duncan was selected as a Fellow of the Association for Women in Mathematics in the Class of 2021 "for her decades of contributions: as a founder and sustainer of the Women in Control Committee of the IEEE Control Systems Society; as the chair of IFAC’s Task Force on Diversity and Inclusion; and via other programs and activities to support and encourage women and girls in mathematics and engineering".
References
1947 births
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
Polish women mathematicians
20th-century Polish mathematicians
21st-century Polish mathematicians
Control theorists
University of Warsaw alumni
SGH Warsaw School of Economics alumni
University of Kansas faculty
Fellow Members of the IEEE
Fellows of the International Federation of Automatic Control
20th-century women mathematicians
21st-century women mathematicians
Fellows of the Association for Women in Mathematics
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/Sergei%20Chernikov | Sergei Nikolaevich Chernikov (11 May 1912 – 23 January 1987; ) was a Russian mathematician who contributed significantly to the development of infinite group theory and linear inequalities.
Biography
Chernikov was born on 11 May 1912 in Sergiyev Posad, in Moscow Oblast, Russia, to Nikolai Nikolaevich, a priest, and Anna Alekseevna, a housewife.
After graduating from secondary school, he worked as a labourer, as a driver, as a book-keeper and as an accountant. Until November 1931 he taught mathematics in a school for workers. From 1930 he was an external student of the Pedagogic Institute of Saratov State University, where he graduated in 1933. He began graduate studies at the Ural Industrial Institute under the outside tutelage of Alexandr G. Kurosh (of the University of Moscow). A remarkable student, Chernikov was made head of the Ural Mathematics department (1939–1946) immediately after earning his PhD in 1938, even before defending his DSc in 1940. He went on to be head of mathematical departments at Ural State University (1946–1951), Perm State University (1951–1961), the Steklov Institute of Mathematics (1961–1964), and finally the National Academy of Sciences of Ukraine from 1964 until days before his death in 1987. During his career, he trained more than 40 PhD and 7 DSc students, and published dozens of papers that remained influential 100 years after his birth.
Contributions
Chernikov is credited with introducing a number of fundamental concepts to group theory, including the locally finite group, and nilpotent group. As with many of his other contributions, these allow infinite groups to be partially or locally solved, establishing important early links between finite and infinite group theories. Later in his career, he was hailed as "one of the pioneers of linear programming", for his breakthrough algebraic theory of linear inequalities.
Published works
Chernikov S.N. (1939) Infinite special groups. Mat. Sbornik 6, 199–214
Chernikov S.N. (1940) Infinite locally soluble groups. Mat. Sbornik 7, 35–61
Chernikov S.N. (1940) To theory of infinite special groups. Mat. Sbornik 7, 539–548.
Chernikov S.N. (1940) On groups with Sylow sets. Mat. Sbornik 8, 377–394.
Chernikov S.N. (1943) To theory of locally soluble groups. Mat. Sbornik 13, 317–333.
Chernikov S.N. (1946) Divisible groups possesses an ascending central series. Mat. Sbornik 18, 397–422.
Chernikov S.N. (1947) To the theory of finite p – extensions of abelian p – groups. Doklady AN USSR, 58, 1287–1289. Journal Algebra Discrete Math. M.
Kurosh A.G., Chernikov S.N. (1947) Soluble and nilpotent groups. Uspekhi Math. Nauk 2, number 3, 18 – 59.
Chernikov S.N. (1948) Infinite layer – finite groups. Mat. Sbornik 22, 101–133.
Chernikov S.N. (1948) To the theory of divisible groups. Mat. Sbornik 22, 319–348.
Chernikov S.N. (1948) A complement to the paper “To the theory of divisible groups”. Mat. Sbornik 22, 455–456.
Chernikov S.N. (1949) To the theory of torsion – free groups |
https://en.wikipedia.org/wiki/Differential%20forms%20on%20a%20Riemann%20surface | In mathematics, differential forms on a Riemann surface are an important special case of the general theory of differential forms on smooth manifolds, distinguished by the fact that the conformal structure on the Riemann surface intrinsically defines a Hodge star operator on 1-forms (or differentials) without specifying a Riemannian metric. This allows the use of Hilbert space techniques for studying function theory on the Riemann surface and in particular for the construction of harmonic and holomorphic differentials with prescribed singularities. These methods were first used by in his variational approach to the Dirichlet principle, making rigorous the arguments proposed by Riemann. Later found a direct approach using his method of orthogonal projection, a precursor of the modern theory of elliptic differential operators and Sobolev spaces. These techniques were originally applied to prove the uniformization theorem and its generalization to planar Riemann surfaces. Later they supplied the analytic foundations for the harmonic integrals of . This article covers general results on differential forms on a Riemann surface that do not rely on any choice of Riemannian structure.
Hodge star on 1-forms
On a Riemann surface the Hodge star is defined on 1-forms by the local formula
It is well-defined because it is invariant under holomorphic changes of coordinate.
Indeed, if is holomorphic as a function of ,
then by the Cauchy–Riemann equations and . In the new coordinates
so that
proving the claimed invariance.
Note that for 1-forms and
In particular if then
Note that in standard coordinates
Recall also that
so that
The decomposition is independent of the choice of local coordinate. The 1-forms with only a component are called (1,0) forms; those with only a component are called (0,1) forms. The operators and are called the Dolbeault operators.
It follows that
The Dolbeault operators can similarly be defined on 1-forms and as zero on 2-forms. They have the properties
Poincaré lemma
On a Riemann surface the Poincaré lemma states that every closed 1-form or 2-form is locally exact. Thus if ω is a smooth 1-form with then in some open neighbourhood of a given point there is a smooth function f such that in that neighbourhood; and for any smooth 2-form Ω there is a smooth 1-form ω defined in some open neighbourhood of a given point such that in that neighbourhood.
If is a closed 1-form on , then . If then and . Set
so that . Then must satisfy and . The right hand side here is independent of x since its partial derivative with respect to x is 0. So
and hence
Similarly, if then with . Thus a solution is given by and
Comment on differential forms with compact support. Note that if ω has compact support, so vanishes outside some smaller rectangle with and , then the same is true for the solution f(x,y). So the Poincaré lemma for 1-forms holds with this additional conditions of compact support.
A similar stateme |
https://en.wikipedia.org/wiki/Angelina%20Cabras | Angelina Cabras (23 December 1898 – 19 June 1993) was an Italian mathematician and physicist. She earned degrees in mathematics from the University of Turin in 1924 and in physics from the University of Cagliari in 1927. She obtained a position in mathematical physics at Cagliari, later moving to the institute of theoretical mechanics there. Her research concerned higher dimensional rigid body dynamics, the theory of relativity, and inductance.
She was an invited speaker at the International Congress of Mathematicians in 1928.
She died in Cagliari in 1993.
References
1898 births
1993 deaths
20th-century Italian mathematicians
20th-century women mathematicians
20th-century Italian women scientists
Italian women mathematicians
20th-century Italian physicists
Italian women physicists
University of Turin alumni
University of Cagliari alumni
Academic staff of the University of Cagliari |
https://en.wikipedia.org/wiki/Football%20at%20the%201927%20Far%20Eastern%20Championship%20Games | The football sporting event at the 1927 Far Eastern Championship Games featured matches between China, Japan and the Philippines.
Results
Winner
Statistics
Goalscorers
References
Football at the Far Eastern Championship Games
International association football competitions hosted by China
1927 in Asian football
1927 in Chinese sport |
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