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https://en.wikipedia.org/wiki/S%C3%B8ren%20Galatius | Søren Galatius (born 1 August 1976) is a Danish mathematician who works as a professor of mathematics at the University of Copenhagen. He works in algebraic topology, where one of his most important results concerns the homology of the automorphisms of free groups. He is also known for his joint work with Oscar Randal-Williams on moduli spaces of manifolds, comprising several papers.
Life
Galatius was born in Randers, Denmark. He earned his PhD from Aarhus University in 2004 under the supervision of Ib Madsen. He then joined the Stanford University faculty, first with a temporary position as a Szegő Assistant Professor and then two years later with a tenure-track position, eventually becoming full professor in 2011. He relocated to the University of Copenhagen in 2016.
Recognition
In 2010, Galatius won the Silver Medal of the Royal Danish Academy of Sciences and Letters.
In 2012, he became one of the inaugural fellows of the American Mathematical Society.
He was an invited speaker at the 2014 International Congress of Mathematicians, speaking about his joint work with Oscar Randal-Williams. In 2017, he won an Elite Research Prize from the Danish Government for his work. In 2022 he was awarded the Clay Research Award jointly with Oscar Randal-Williams.
Selected publications
References
External links
1976 births
Living people
Danish mathematicians
21st-century American mathematicians
Aarhus University alumni
Stanford University Department of Mathematics faculty
Fellows of the American Mathematical Society
People from Randers
Topologists
Academic staff of the University of Copenhagen |
https://en.wikipedia.org/wiki/Mark%20Freidlin | Mark Iosifovich Freidlin (, born 1938) is a Russian-American probability theorist who works as a Distinguished University Professor of Mathematics at the University of Maryland, College Park. He is one of the namesakes of the Freidlin–Wentzell theory, which is an important part of the large deviations theory. Freidlin and Wentzell are the authors of the first monograph on the large deviations theory for stochastic processes (1979). The Freidlin-Wentzell theory describes, in particular, the long-time effects caused by random perturbations. The latest edition of the book was published by Springer in 2012. It contains not just the results on large deviations but also new results on other asymptotic problems, in particular, on the averaging principle for stochastic perturbations. Other works of Mark Freidlin concern perturbations of Hamiltonian systems, wave front propagation in reaction-diffusion equations, non-linear perturbations of partial differential equations. stochasticity in deterministic dynamical systems.
Friedlin was born in 1938 in Moscow.
He began studying mathematics at Moscow State University at the age of 16, and earned a candidate's degree there in 1962, under the supervision of Eugene Dynkin. In 1970 he completed a doctorate. However, growing anti-semitism in the Soviet Union prevented Friedlin from traveling and forced him to transfer from the Mechanics and Mathematics Department at Moscow State to the Bio-Physics Department (with the assistance of Andrey Kolmogorov in finding him this position). By 1979 he had decided to emigrate to the US, but was denied permission to leave Russia; despite having no permanent employment for the next eight years, he continued to work and publish in mathematics. Finally, in 1987, he was able to move to the University of Maryland.
Freidlin was an invited speaker at the 1998 International Congress of Mathematicians. He became a Distinguished Professor at Maryland in 2000.
In May 2003, a conference on "Asymptotic Problems in Stochastic Processes and PDE's" was held at the University of Maryland in honor of Freidlin's 65th birthday. In 2012, he became one of the inaugural fellows of the American Mathematical Society. His doctoral students include Jürgen Gärtner.
Selected publications
with Alexander D. Wentzell: ; 3rd edition 2012
with M. Weber: Random perturbations of nonlinear oscillators, Ann. Probability 26 (1998), no. 3, pp. 925–967.
with M. Weber: Random perturbations of dynamical systems and diffusion processes with conservation laws, Probability Theory Related Fields 128 (2004), pp. 441–466.
with A.D. Wentzell: On the Neumann problem for PDEs with a small parameter and corresponding diffusion processes, Probab. Theory Relat. Fields 152 (2012), no. 1-2, pp. 101–140.
with A.D. Wentzell: Diffusion approximation for noise-induced evolution of first integrals in multi-frequency systems, Journal of Statistical Physics, 182, Article number: 45 (2021).
with L. Koralov: Nonlinear stochastic pert |
https://en.wikipedia.org/wiki/Christiaan%20Heij | Christiaan Heij (born 1950s) is a Dutch mathematician, Assistant Professor in statistics and econometrics at the Econometric Institute at the Erasmus University Rotterdam, known for his work in the field of mathematical systems theory, and econometrics.
Life and work
Heij did his PhD research at the University of Groningen in the 1980s among other young system theorists, such as Hans Nieuwenhuis,
Pieter Otter, Jan Camiel Willems, and Dirk T. Tempelaar. In 1988 he graduated under Willems, Professor of Systems and Control and Nieuwenhuis with the thesis "Deterministic Identification of Dynamical Systems," which was published the next year by Springer in the "Lecture Notes in Control and Information Sciences" series.
In the 1990s Heij continued his research at the Econometric Institute of the Erasmus University Rotterdam, and wrote a series of books on systems theory, modelling, dynamics systems, and econometrics. With Jan Camiel Willems he supervised the promotion of Berend Roorda, who graduated in 1995 with the thesis, entitled "Deterministic Identification of Dynamical Systems."
Heij is credited extending "The behavioral approach to system theory put forward by Willems," and for presenting a new total least squares algorithms, specifically for system identification. His most cited work is the 2004 textbook "Econometric methods with applications in business and economics," co-authored with Philip Hans Franses, Teun Kloek, and Herman K. van Dijk, and published by the Oxford University Press.
In his later career he is well known for being the gatekeeper of the study Econometrics & Operational Research in Rotterdam, with an average passing percentage of 30% on the first course given to new students.
Selected publications
Heij C., Deterministic Identification of Dynamical Systems, Lecture Notes in Control and Information Sciences, vol. 127. PhD Thesis University of Groningen, New York: Springer, 1989.
Heij, C., Schumacher, J. M., Hanzon, B., & Praagman, C. System dynamics in economic and financial models. (1997).
Heij, C., De Boer, P., Franses, P. H., Kloek, T., & Van Dijk, H. K. (2004). Econometric methods with applications in business and economics. Oxford University Press.
Christiaan Heij, André C.M. Ran and F. van Schagen. Introduction to Mathematical Systems Theory: Linear Systems, Identification and Control. 2006
Articles, a selection:
Heij, Christiaan. "Exact modelling and identifiability of linear systems." Automatica 28.2 (1992): 325–344.
Roorda, Berend, and Christiaan Heij. "Global total least squares modeling of multivariable time series." Automatic Control, IEEE Transactions on 40.1 (1995): 50–63.
Heij, Christiaan, and Wolfgang Scherrer. "System identification by dynamic factor models." SIAM Journal on Control and Optimization 35.6 (1997): 1924–1951.
Heij, Christiaan, Patrick JF Groenen, and Dick van Dijk. "Forecast comparison of principal component regression and principal covariate regression." Computational statistics |
https://en.wikipedia.org/wiki/Christopher%20D.%20Sogge | Christopher Donald Sogge (; born July 14, 1960) is an American mathematician. He is the J. J. Sylvester Professor of Mathematics at Johns Hopkins University and the editor-in-chief of the American Journal of Mathematics. His research concerns Fourier analysis and partial differential equations.
Education and career
Sogge graduated from the University of Chicago in 1982, and earned a doctorate in mathematics from Princeton University in 1985 under the supervision of Elias M. Stein. He taught at the University of Chicago from 1985 to 1989 and the University of California, Los Angeles from 1989 to 1996 before moving to Johns Hopkins.
Personal life
In 1987, he married Elizabeth Lombardi. They had three children, Lewis, Susanna and William Sogge.
Awards and honors
In 2012, he became one of the inaugural fellows of the American Mathematical Society. He has fellowships from the National Science Foundation, Alfred P. Sloan Foundation, Guggenheim Foundation, and he received the Presidential Young Investigator Award. In 2007 he received the Diversity Recognition Award from Johns Hopkins University.
Books
Fourier integrals in classical analysis (Cambridge Tracts in Mathematics 105, Cambridge University Press, 1993)
Lectures on non-linear wave equations (International Press, 1995; 2nd ed., 2008)
Hangzhou lectures on eigenfunctions of the Laplacian, (Annals of Mathematical Studies 188, Princeton University Press, 2014)
References
External links
Home page
Google scholar profile
Living people
20th-century American mathematicians
21st-century American mathematicians
University of Chicago alumni
Princeton University alumni
University of Chicago faculty
University of California, Los Angeles faculty
Johns Hopkins University faculty
Fellows of the American Mathematical Society
1960 births |
https://en.wikipedia.org/wiki/Laver%20property | In mathematical set theory, the Laver property holds between two models if they are not "too dissimilar", in the following sense.
For and transitive models of set theory, is said to have the Laver property over if and only if for every function mapping to such that diverges to infinity, and every function mapping to and every function which bounds , there is a tree such that each branch of is bounded by and for every the level of has cardinality at most and is a branch of .
A forcing notion is said to have the Laver property if and only if the forcing extension has the Laver property over the ground model. Examples include Laver forcing.
The concept is named after Richard Laver.
Shelah proved that when proper forcings with the Laver property are iterated using countable supports, the resulting forcing notion will have the Laver property as well.
The conjunction of the Laver property and the -bounding property is equivalent to the Sacks property.
References
Forcing (mathematics) |
https://en.wikipedia.org/wiki/Teichm%C3%BCller%20cocycle | In mathematics, the Teichmüller cocycle is a certain 3-cocycle associated to a simple algebra A over a field L which is a finite Galois extension of a field K and which has the property that any automorphism of L over K extends to an automorphism of A. The Teichmüller cocycle, or rather its cohomology class, is the obstruction to the algebra A coming from a simple algebra over K. It was introduced by and named by .
Properties
If K is a finite normal extension of the global field k, then the Galois cohomology group H3(Gal(K/k,K*) is cyclic and generated by the Teichmüller cocycle. Its order is n/m where n is the degree of the extension K/k and m is the least common multiple of all the local degrees .
References
Class field theory |
https://en.wikipedia.org/wiki/Gaven%20Martin | Gaven John Martin FRSNZ FASL FAMS (born 8 October 1958) is a New Zealand mathematician. He is a Distinguished Professor of Mathematics at Massey University, the head of the New Zealand Institute for Advanced Study, the former president of the New Zealand Mathematical Society (from 2005 to 2007), and former editor-in-chief of the New Zealand Journal of Mathematics. He is a former Vice-President of the Royal Society of New Zealand [Mathematical, Physical Sciences Engineering and Technology. His research concerns quasiconformal mappings, regularity theory for partial differential equations, and connections between the theory of discrete groups and low-dimensional topology.
Education and career
Martin is originally from Rotorua, New Zealand. His family moved to Henderson when he was 11 years old, and he attended Henderson High School and the University of Auckland (as the first of his extended family to go to university), earning a BSc with first-class honours in 1980 and an MSc with distinction in 1981. He then went to the University of Michigan on a Fulbright scholarship, completing his doctorate in 1985 under the supervision of Frederick Gehring and earning the Sumner Byron Myers Prize for the best mathematics dissertation in his year and an A.P. Sloan Foundation Fellowship spent in T.U.B. Berlin and The University of Helsinki.
After short-term positions at the Mathematical Sciences Research Institute of the University of California, Berkeley and as a Gibbs Instructor at Yale University, Martin became a lecturer at the University of Auckland in 1989, but left after a year to research at the Mittag-Leffler Institute in Sweden and the Institut des Hautes Études Scientifiques in France.
Soon after his return, he was given a personal chair at Auckland; when he took it, he became (at age 32) the youngest full professor in New Zealand.
For the next several years, he split his time between Auckland and Australian National University, but by 1996, he gave up the Australian appointment and remained solely at Auckland. He moved to Massey as a distinguished professor in 2005, and in 2016--2020 served as elected as the academic staff representative on the Massey University Council, the University's topmost governing body. He currently is the Director of the NZ Mathematics Research Institute https://www.nzmri.org and a long serving board member of the Rotary Science Trust.
Awards and honours
Martin became a fellow of the Royal Society of New Zealand in 1997. In 2001, he won the James Cook Fellowship of the RSNZ; he also won the Hector Memorial Medal of the RSNZ in 2008. He was an invited speaker at the 2010 International Congress of Mathematicians.
In 2012, he became one of the inaugural fellows of the American Mathematical Society. He was made a Foreign Member of the Finnish Academy of Science and Letters in 2016.
He gave the Taft Memorial Lectures in 2010 https://www.artsci.uc.edu/content/dam/refresh/artsandsciences-62/departments/math/docs/taft-lectur |
https://en.wikipedia.org/wiki/Michael%20Wolf%20%28statistician%29 | Michael Wolf (born June 1, 1967) holds the Chair of Econometrics and Applied Statistics in the Department of Economics at the University of Zurich, Switzerland. He was previously Professor at UCLA, Charles III University of Madrid, and Pompeu Fabra University.
Biography
Wolf was born in Germany, where he obtained a bachelor's degree in mathematics from the University of Augsburg. From 1991 he studied statistics at Stanford University (M.Sc. 1995, Ph.D. 1996).
Wolf is known for his work on shrinkage estimation of large-dimensional covariance matrices. While originally motivated by Markowitz portfolio selection, the linear shrinkage estimator he developed in collaboration with Olivier Ledoit has been widely adopted by other researchers in a variety of scientific fields such as
cancer research,
chemistry,
civil engineering,
climatology,
electrical engineering,
genetics, geology,
neuroscience,
psychology,
speech recognition, etc. The common feature between these applications is that the dimension of the covariance matrix is not negligible with respect to the size of the sample. In this case the usual estimator, the sample covariance matrix, is inaccurate and ill-conditioned. By contrast, the Ledoit-Wolf estimator is more accurate and guaranteed to be well-conditioned, even in the difficult case where matrix dimension exceeds sample size.
Michael Wolf also co-wrote the book on Subsampling, a resampling method inspired by the jackknife that constitutes an alternative to the bootstrap. In the field of multiple testing, he introduced new procedures to control the family-wise error rate that are more powerful than previous methods, by taking into account the dependence between test statistics. He also worked on procedures to control generalized error rates, such as the generalized family-wise error rate, the false discovery proportion and the false discovery rate.
Michael Wolf served on the editorial board of the Annals of Statistics and Statistics and Probability Letters. In 2004, he won the Distinguished Researcher award from the Generalitat of Catalonia. He was invited to give the prestigious Gumbel Lecture at the Annual Meeting of the German Statistical Society in Cologne in 2008.
Selected publications
Books
Articles on Shrinkage Estimation of Covariance Matrices
Articles on Subsampling
Articles on Multiple Testing
References
External links
Official University of Zurich webpage
Google Scholar Citation page
1967 births
Living people
German statisticians
Econometricians
Academic staff of the University of Zurich
Stanford University School of Humanities and Sciences alumni
University of Augsburg alumni
Computational statisticians |
https://en.wikipedia.org/wiki/1998%E2%80%9399%20WNBL%20season | The 1998–99 WNBL season was the 19th season of competition since its establishment in 1981. A total of 8 teams contested the league.
Team standings
Finals
Season award winners
Statistics leaders
References
https://web.archive.org/web/20141227122005/http://www.wnbl.com.au/fileadmin/user_upload/Media_Guide/12284_BASKAUST_WNBL_MEDIA_GUIDE_2014-15_BACK.pdf
1998-99
1998–99 in Australian basketball
Aus
basketball
basketball |
https://en.wikipedia.org/wiki/2002%E2%80%9303%20WNBL%20season | The 2002–03 WNBL season was the 23rd season of competition since its establishment in 1981. A total of 8 teams contested the league.
Team standings
Finals
Season award winners
Statistics leaders
References
https://web.archive.org/web/20141227122005/http://www.wnbl.com.au/fileadmin/user_upload/Media_Guide/12284_BASKAUST_WNBL_MEDIA_GUIDE_2014-15_BACK.pdf
2002-03
2002–03 in Australian basketball
Aus
basketball
basketball |
https://en.wikipedia.org/wiki/1999%E2%80%932000%20WNBL%20season | The 1999–2000 WNBL season was the 20th season of competition since its establishment in 1981. A total of 8 teams contested the league.
Team standings
Finals
Season award winners
Statistics leaders
References
https://web.archive.org/web/20141227122005/http://www.wnbl.com.au/fileadmin/user_upload/Media_Guide/12284_BASKAUST_WNBL_MEDIA_GUIDE_2014-15_BACK.pdf
1999-2000
1999–2000 in Australian basketball
Aus
basketball
basketball |
https://en.wikipedia.org/wiki/2000%E2%80%9301%20WNBL%20season | The 2000–01 WNBL season was the 21st season of competition since its establishment in 1981. A total of 8 teams contested the league.
Team standings
Finals
Season award winners
Statistics leaders
References
https://web.archive.org/web/20141227122005/http://www.wnbl.com.au/fileadmin/user_upload/Media_Guide/12284_BASKAUST_WNBL_MEDIA_GUIDE_2014-15_BACK.pdf
2000-01
2000–01 in Australian basketball
Aus
basketball
basketball |
https://en.wikipedia.org/wiki/2001%E2%80%9302%20WNBL%20season | The 2001–02 WNBL season was the 22nd season of competition since its establishment in 1981. A total of 8 teams contested the league.
Team standings
Finals
Season award winners
Statistics leaders
References
https://web.archive.org/web/20141227122005/http://www.wnbl.com.au/fileadmin/user_upload/Media_Guide/12284_BASKAUST_WNBL_MEDIA_GUIDE_2014-15_BACK.pdf
2001-02
2001–02 in Australian basketball
Aus
basketball
basketball |
https://en.wikipedia.org/wiki/NUTS%20statistical%20regions%20of%20Albania | The Nomenclature of Territorial Units for Statistics (NUTS) is a geographical standard used by Albania in order to divide its territory into regions at three different levels of specified classes of its population codified by the Albanian Institute of Statistics (INSTAT). Albania is a recognised candidate country for membership of the European Union (EU) and thus part of the classification. The three hierarchical levels are known as NUTS-1, NUTS-2 and NUTS-3, moving from larger to smaller territorial divisions.
Overall
Regions
The NUTS codes are as follows:
References
Albania
Nuts |
https://en.wikipedia.org/wiki/Reflexive%20sheaf | In algebraic geometry, a reflexive sheaf is a coherent sheaf that is isomorphic to its second dual (as a sheaf of modules) via the canonical map. The second dual of a coherent sheaf is called the reflexive hull of the sheaf. A basic example of a reflexive sheaf is a locally free sheaf of finite rank and, in practice, a reflexive sheaf is thought of as a kind of a vector bundle modulo some singularity. The notion is important both in scheme theory and complex algebraic geometry.
For the theory of reflexive sheaves, one works over an integral noetherian scheme.
A reflexive sheaf is torsion-free. The dual of a coherent sheaf is reflexive. Usually, the product of reflexive sheaves is defined as the reflexive hull of their tensor products (so the result is reflexive.)
A coherent sheaf F is said to be "normal" in the sense of Barth if the restriction is bijective for every open subset U and a closed subset Y of U of codimension at least 2. With this terminology, a coherent sheaf on an integral normal scheme is reflexive if and only if it is torsion-free and normal in the sense of Barth. A reflexive sheaf of rank one on an integral locally factorial scheme is invertible.
A divisorial sheaf on a scheme X is a rank-one reflexive sheaf that is locally free at the generic points of the conductor DX of X. For example, a canonical sheaf (dualizing sheaf) on a normal projective variety is a divisorial sheaf.
See also
Torsionless module
Torsion sheaf
Twisted sheaf
Notes
References
Further reading
External links
Reflexive sheaves on singular surfaces
Push-forward of locally free sheaves
http://www-personal.umich.edu/~kschwede/GeneralizedDivisors.pdf
Sheaf theory |
https://en.wikipedia.org/wiki/Discrepancy%20%28algebraic%20geometry%29 | In algebraic geometry, given a pair (X, D) consisting of a normal variety X and a -divisor D on X (e.g., canonical divisor), the discrepancy of the pair (X, D) measures the degree of the singularity of the pair.
See also
Canonical singularity
Crepant resolution
References
Algebraic geometry |
https://en.wikipedia.org/wiki/Rectangular%20mask%20short-time%20Fourier%20transform | In mathematics and Fourier analysis, a rectangular mask short-time Fourier transform (rec-STFT) has the simple form of short-time Fourier transform. Other types of the STFT may require more computation time than the rec-STFT.
The rectangular mask function can be defined for some bound (B) over time (t) as
We can change B for different tradeoffs between desired time resolution and frequency resolution.
Rec-STFT
Inverse form
Property
Rec-STFT has similar properties with Fourier transform
Integration
(a)
(b)
Shifting property (shift along x-axis)
Modulation property (shift along y-axis)
special input
When
When
Linearity property
If ,and are their rec-STFTs, then
Power integration property
Energy sum property (Parseval's theorem)
Example of tradeoff with different B
From the image, when B is smaller, the time resolution is better. Otherwise, when B is larger, the frequency resolution is better.
Advantage and disadvantage
Compared with the Fourier transform:
Advantage: The instantaneous frequency can be observed.
Disadvantage: Higher complexity of computation.
Compared with other types of time-frequency analysis:
Advantage: Least computation time for digital implementation.
Disadvantage: Quality is worse than other types of time-frequency analysis. The jump discontinuity of the edges of the rectangular mask results in Gibbs ringing artifacts in the frequency domain, which can be alleviated with smoother windows.
See also
Uncertainty principle
References
Jian-Jiun Ding (2014) Time-frequency analysis and wavelet transform
Fourier analysis
Time–frequency analysis
Transforms |
https://en.wikipedia.org/wiki/2014%20Moroccan%20census | The 2014 Moroccan census was held in Morocco between 1 September and 20 September 2014. The census was conducted by the High Planning Commission.
Modern techniques for statistics
This major national operation has mobilized the various technological, organizational and communication means available during the various stages of its implementation, and this census has been matched methodically, content and linearly with the standards adopted in this regard by the United Nations, which has given it a distinguished position compared to the rest of the previous national statistics in terms of its comprehensiveness to the population. Similar to the previous statistics, where modern techniques and methods are included, whether it comes to the stages of preparation or exploitation and dissemination of data, the same is true for the 2014 census, which has a special character due to its reliance on many developments, represented in particular in:
−The use of satellite images in cartographic works.
–A new approach to recruiting researchers and observers (submission of nominations via the Internet).
–Introducing new topics in the areas of demography, housing and disability.
References
External links
Population légale d'après les résultats du RGPH 2014 sur le Bulletin officiel N° 6354
Censuses in Morocco
2014 in Morocco
Morocco |
https://en.wikipedia.org/wiki/Raymond%20Flood%20%28mathematician%29 | Raymond Flood is Emeritus Fellow and a member of the Continuing Education Department at Kellogg College, Oxford, and has been a Professor of Geometry at Gresham College.
Education
Flood achieved a Bachelor of Science degree at Queens University, Belfast and a master's degree at Linacre College, Oxford. He obtained his PhD from University College, Dublin. Flood obtained his doctorate through part-time study, as he had already acquired a family and a job.
Career
In 1990, Flood was made a Founding Fellow of Kellogg College, Oxford, formally Rewley House. Kellogg College, Oxford was created to look after the interests of mature and part-time students. Flood primarily teaches those students who are either mature, or who study part-time. He has held numerous positions at the College and the University of Oxford, including Curator of the University Libraries and as a University lecturer at the University of Oxford.
Flood has dedicated much of his academic career promoting mathematics and computing to adult audiences. He has been President of the British Society for the History of Mathematics from 2006 until 2009, and also Research Associate in the School of Theoretical Physics, Dublin Institute for Advanced Studies. On Gresham College, Flood has said "Gresham College comes from a long tradition of liberal adult education. Allowing people from a variety of backgrounds... to get access to current thinking on the major issues of the day. Gresham College ethos is very similar to my own ethos"
In August 2012, Flood was appointed Gresham Professor of Geometry at Gresham College for a period of three years, replacing John D. Barrow. During his term at the College he delivered series of free public lectures on Shaping Modern Mathematics, Applying Modern Mathematics, and Great Mathematicians, Great Mathematics.
Other research work and publications
Aside from his academic work, Flood is active in communicating mathematics and its history to non-specialist audiences. He has appeared on BBC Radio 4's In Our Time and has lectured on transatlantic voyages with .
Flood has produced and co-produced many publications and books on Mathematics. Some of the most recent books with which he has been involved are James Clerk Maxwell: Perspectives on his Life and Work (Oxford University Press, 2014), The Great Mathematicians (Arcturus, 2011), which celebrates the achievements of the great mathematicians in their historical context, and Mathematics in Victorian Britain (Oxford University Press, 2011), which assembles in a single source, research on the history of mathematicians in Victorian Britain that would otherwise be out of reach of the general reader.
References
External links
Raymond G Flood, Kellogg College
Professor Raymond Flood, Gresham College
Raymond Flood's past Gresham College mathematics lectures
Professors of Gresham College
20th-century British mathematicians
21st-century British mathematicians
British historians of mathematics
Fellows of Kellogg Coll |
https://en.wikipedia.org/wiki/Israel%20Kleiner%20%28mathematician%29 | Israel Kleiner is a Canadian mathematician and historian of mathematics.
Kleiner earned an MA at Yale University (1963) and a PhD at McGill University (1967) under Joachim Lambek with a thesis Lie modules and rings of quotients. Before his retirement as professor emeritus, he spent his career as a mathematics professor at York University, where he was a member of the faculty since 1965 and where he coordinated the training program for mathematics teachers teaching at the secondary school level. He is noted for his work on the history of algebra and on the combination of the history of mathematics and mathematics education.
He received the Carl B. Allendoerfer Award in 1987 and again in 1992, the George Pólya Award in 1990, and the Lester Randolph Ford Award in 1995. He was in the mid 2000s vice-president of the Canadian Society for the History and Philosophy of Mathematics.
Selected works
Books
Turning Points in the History of Mathematics (with Hardy Grant), Birkhäuser 2016
Excursions in the History of Mathematics, Springer 2012
A History of Abstract Algebra, Birkhäuser 2007
Selected Papers in the History of Mathematics , in Hebrew, Maalot Academic Publishers, 1994.
A History of Abstract Algebra, in Korean, Kyung Moon Publ., 2012. (Translation of the 2007 Birkhäuser edition; see above)
A History of Abstract Algebra, in Japanese, The English Agency (Japan) Ltd., 2011. (Translation of the 2007 Birkhäuser edition; see above)
Articles
Abstract (modern) algebra in America (1870-1950): a brief account. In: A Century of Advancing Mathematics, Math. Assoc. of America, 2015, pp. 191–216
Intellectual courage and mathematical creativity (with N. Movshovitz-Hadar). In: Creativity in Mathematics and the Education of Gifted Students, ed. by R. Leiken, A. Berman, and B. Koichu, Sense Publishers, 2009, pp. 31–50
The roots of commutative algebra in algebraic number theory, Mathematics Magazine, Vol. 68, 1995, pp. 3–15
The principle of continuity: a brief history, Mathematical Intelligencer, Vol. 28, No. 4, 2006, pp. 49–57
Fermat: The founder of modern number theory, Mathematics Magazine, Vol. 78, 2005 , pp. 3–14
From Fermat to Wiles: Fermat's Last Theorem becomes a theorem, Elemente der Mathematik, Vol. 55, 2000, pp. 19–37
Field theory: from equations to axiomatization, Parts 1 and 2, American Mathematical Monthly, Vol. 106, 1999, pp. 677–684 and 859-863
A historically focused course on abstract algebra, Mathematics Magazine, Vol. 71, 1998, pp. 105–111
From numbers to rings: an early history of ring theory, Elemente der Mathematik, Vol. 53, 1998, pp. 18–35
Proof: a many-splendored thing (with N. Movshovitz-Hadar), The Mathematical Intelligencer, Vol. 19, No. 3, 1997, pp. 16–26
The genesis of the abstract ring concept, American Mathematical Monthly, Vol. 103, 1996, pp. 417–423
The role of paradoxes in the evolution of mathematics (with Nitsa Movshovitz-Hadar), The American Mathematical Monthly, Vol. 101, No. 10, 1994, pp. 963-974 (1995 Lester R. Ford Award) |
https://en.wikipedia.org/wiki/Joseph%20A.%20Thas | Joseph Adolphe François Thas (born 13 October 1944, Dilbeek, Belgium) is a Belgian mathematician, who works on combinatorics, incidence geometry and finite geometries.
Thas received in 1969 his PhD from Ghent University under Julien Bilo with thesis Een studie betreffende de projective rechte over de totale matrix algebra der 3x3-matrices met elementen in een algebraïsch afgesloten veld K. Thas showed how to extend projective geometry and cross-ratios with the concept of a projective line over a ring.
Thas is an emeritus professor at Ghent University.
Awards and honors
In 1994 Thas received the Euler medal. In 1998 he gave an invited address at the International Congress of Mathematicians in Berlin with lecture Finite geometries, varieties and codes. He received in 1969 the prize of the Royal Academy of Sciences, Letters and Fine Arts of Belgium, in 1970 the Scientific Louis Empain Award and in the same year the François Deruyts prize of the Royal Academy of Belgium.
In 1988 he became a member of the Royal Flemish Academy of Belgium for Science and the Arts; he was vice-director of the Class of Sciences in 1998 and director in 1999. In 1999 he was awarded an Erskine Fellowship of the University of Canterbury, New Zealand, in 2008 he was Platinum Jubilee Lecturer at the Indian Statistical Institute, and in 2012 he became one of the inaugural fellows of the American Mathematical Society.
Selected works
with Koen Thas, H. Van Maldeghem Translation generalized quadrangles, World Scientific 2006
with Stanley E. Payne Finite generalized quadrangles, Pitman 1984, 2nd edition, European Mathematical Society 2009
with J. W. P. Hirschfeld General Galois Geometries, Oxford University Press 1991
Projective geometry over a finite field and Generalized Polygons in F. Buekenhout Handbook of incidence geometry, North Holland 1995
with J. Bilo Enkele aspecten van de theorie der axiomatische projectieve vlakken, Simon Stevin, Supplement, Vol. 55, 1981
(For a complete list of papers see Homepage in Ghent.)
References
External links
Homepage in Ghent
search on author JA Thas from Google Scholar
1944 births
Living people
20th-century Belgian mathematicians
21st-century Belgian mathematicians
Combinatorialists
Fellows of the American Mathematical Society
People from Dilbeek |
https://en.wikipedia.org/wiki/Philippe%20Michel%20%28number%20theorist%29 | Philippe Gabriel Michel (born 23 January 1969) is a French mathematician who holds the chair in analytic number theory at the École Polytechnique Fédérale de Lausanne in Switzerland.
Early life, education and career
Michel was born in Lyon. He studied from 1989 to 1993 at the École normale supérieure de Cachan, and then moved to the University of Paris-Sud, where he earned a doctorate in 1995 under the supervision of Étienne Fouvry and then a habilitation in 1998. He was a professor at the University of Montpellier from 1998 to 2008, when he moved to EPFL.
Recognition
In 1999, Michel was awarded the Peccot-Vimont Prize and gave the Peccot Lecture at the Collège de France.
In 2006, he was an invited speaker at the International Congress of Mathematicians.
In 2011, he was elected to the Academia Europaea.
In 2012, he became one of the inaugural fellows of the American Mathematical Society.
References
External links
Home page
1969 births
Living people
Swiss mathematicians
20th-century French mathematicians
21st-century French mathematicians
Number theorists
Academic staff of the University of Montpellier
Academic staff of the École Polytechnique Fédérale de Lausanne
Members of Academia Europaea
Fellows of the American Mathematical Society
Institute for Advanced Study visiting scholars |
https://en.wikipedia.org/wiki/Philibert%20Nang | Philibert Nang (born 1967) is a Gabonese mathematician known for his work in algebra (D-modules, Riemann–Hilbert correspondence).
Nang won the 2011 ICTP Ramanujan Prize for his research in mathematics, and because he conducted it in Gabon the ICTP declared: "It is hoped that his example will inspire other young African mathematicians working at the highest levels while based in Africa." He was awarded the African Mathematics Millennium Science Initiative-Phillip Griffiths Prize in 2017.
He obtained his Ph.D. from the Pierre and Marie Curie University in 1996 under the supervision of Louis Boutet de Monvel.
Nang currently serves as president of the Gabon Mathematical Society.
He has been a visiting member at the Max Planck Institute for Mathematics and at the Tata Institute of Fundamental Research. Currently he is employed as associate professor at University of Pretoria in South Africa.
Selected publications
"On the classification of regular holonomic D-modules on skew-symmetric matrices", Journal of Algebra, Volume 356, Issue 1, 2012, pp. 115–132.
"D-modules associated to the determinantal singularities", Proc. Japan Acad. Ser. A Math. Sci., Volume 80, Number 5, 2004, pp. 74–78.
"D-modules associated to the group of similitudes", Publ. Res. I. Math. Sci., Volume 35, Number 2, 1999, pp. 223–247.
References
Gabonese mathematicians
Algebraists
1967 births
Living people
Pierre and Marie Curie University alumni
Academic staff of the University of Pretoria
21st-century Gabonese people
Gabonese academics |
https://en.wikipedia.org/wiki/1847%20in%20Chile | The following, lists events that happened during 1847 in Chile.
Incumbents
President of Chile: Manuel Bulnes
Events
September
17 September - The National Statistics Institute (Chile) is established.
Births
12 April - Aníbal Zañartu (d. 1902)
13 August - Luis Uribe (d. 1914)
Deaths
16 July - José Ignacio Zenteno (b. 1786)
8 November - José Ignacio Cienfuegos (b. 1762)
References
1840s in Chile
Chile
Chile |
https://en.wikipedia.org/wiki/James%20E.%20Humphreys | James Edward Humphreys (December 10, 1939 – August 27, 2020) was an American mathematician who worked in algebraic groups, Lie groups, and Lie algebras and applications of these mathematical structures. He is known as the author of several mathematical texts, such as Introduction to Lie Algebras and Representation Theory and Reflection Groups and Coxeter Groups.
After contracting COVID-19 weeks earlier during the COVID-19 pandemic in Massachusetts, Humphreys died on August 27, 2020, at the age of 80.
Education
Humphreys attended elementary and secondary school in Erie, Pennsylvania and then studied at Oberlin College (bachelor's degree 1961) and from 1961 philosophy and mathematics at Cornell University. At Yale University he earned his master's degree in 1964 and his PhD in 1966 under George Seligman with thesis Algebraic Lie Algebras over fields of prime characteristic.
Career
In 1966, he became an assistant professor at the University of Oregon and in 1970, an associate professor at New York University. At the University of Massachusetts Amherst he became in 1974 an associate professor and in 1976 a full professor; he retired there in 2003 as professor emeritus. In 1968/69 and in 1977, he was a visiting scholar at the Institute for Advanced Study and in 1969/70 at the Courant Institute of Mathematical Sciences of New York University. In 1985, he was a visiting professor at Rutgers University.
Works
Arithmetic Groups, Lecture Notes in Mathematics 789, Springer Verlag 1980 (from lectures at the Courant Institute 1971)
Conjugacy classes in semisimple algebraic groups, AMS 1995
Introduction to Lie Algebras and Representation Theory, Springer Verlag, Graduate Texts in Mathematics, 1972, 7th edition 1997 (also translated into Chinese and Russian)
Linear Algebraic Groups, Graduate Texts in Mathematics, Springer Verlag 1974, 1998 (also translated into Russian).
Ordinary and modular representations of Chevalley groups, Springer Verlag 1976.
Modular representations of finite groups of Lie type, London Mathematical Society Lecture Note Series 326, Cambridge University Press 2006
Reflection Groups and Coxeter Groups, Cambridge University Press 1990.
Representations of semisimple Lie algebras in the BGG category , AMS 2008
Modular representations of simple Lie algebras, Bull. Amer. Math. Soc. (N.S.), Vol. 35, 1998, pp. 105–122.
Modular representations of classical Lie algebras, Bull. Amer. Math. Soc., Vol. 76, 1970, 878–882
Algebraic groups and modular Lie algebras, Memoirs AMS 71, 1967
Hilbert's fourteenth problem, American Mathematical Monthly, Vol. 85, 1978, 341–353
Representations of , Amer. Math. Monthly, Vol. 82, 1975, 21–39
Highest weight modules for semisimple Lie algebras, in: Representation Theory I, Lecture Notes in Mathematics 831, Springer Verlag 1980, pp, 72–103
Awards
Humphreys received the Lester R. Ford Award for the publication Representations of in 1976.
References
External links
Homepage
1939 births
20th-century American m |
https://en.wikipedia.org/wiki/Cramer%E2%80%93Castillon%20problem | In geometry, the Cramer–Castillon problem is a problem stated by the Swiss mathematician Gabriel Cramer solved by the Italian mathematician, resident in Berlin, Jean de Castillon in 1776.
The problem consists of (see the image):
Given a circle and three points in the same plane and not on , to construct every possible triangle inscribed in whose sides (or their elongations) pass through respectively.
Centuries before, Pappus of Alexandria had solved a special case: when the three points are collinear. But the general case had the reputation of being very difficult.
After the geometrical construction of Castillon, Lagrange found an analytic solution, easier than Castillon's. In the beginning of the 19th century, Lazare Carnot generalized it to points.
References
Bibliography
External links
Geometry |
https://en.wikipedia.org/wiki/Chen%20Wen-chen | Chen Wen-chen (, sometimes romanized as Chen Wen-cheng) was a Taiwanese assistant professor of mathematics (specializing in probability and statistics) at Carnegie Mellon University who died on under mysterious circumstances. After the conclusion of his third year of teaching, he returned to his native Taiwan for a vacation. He was instructed not to leave Taiwan on his scheduled departure date. Members of Taiwan's secret police, the Garrison Command, detained and interrogated him for twelve hours on 2 July 1981, and his body was found on the campus of National Taiwan University the next day. The subsequent autopsy reported his death was due to a fall. Chen's death and the earlier massacre of Lin Yi-hsiung's family are cited as late examples of White Terror dissident suppression activities in Taiwan, although the case remains unsolved and the Garrison Command maintains it had nothing to do with his death. In 2020, the Transitional Justice Commission released a report concluding that Chen was most likely killed by state security agencies.
Personal life
Chen was one of eight children and was outspoken and straightforward, according to his brother. He was known to have criticized the Kuomintang (KMT)-led government in private conversations and advocated for Taiwan independence, raising funds to help those imprisoned in the wake of the Kaohsiung Incident as well as in support for Formosa Magazine, which opposed the KMT's one-party rule.
Academic career
Chen graduated with a B.S. in mathematics from National Taiwan University (NTU) in 1972 and served in the military, fulfilling his compulsory service. He left Taiwan for the United States in 1975, earning M.S. (1976) and Ph.D. (1978) degrees in statistics from the University of Michigan, with Professor Bruce Hill stating that he was "outstanding ... the best [student] that I'd seen in statistics in 21 years." Upon graduating from Michigan, he joined the faculty in the Department of Statistics of Carnegie Mellon University (CMU) in the fall of 1978. He published several papers in the area of statistics and probability.
Detainment and death
After his mother visited him in 1981 and assuaged his concerns about safely traveling to Taiwan, Chen returned to Taiwan for the first time since he had left in 1975, arriving on 20 May 1981 with his wife and son. He applied for the exit permit required to return to the US upon arrival, but it had not been granted by the time he was scheduled to depart on 1 July 1981. Typically, exit permits are granted within 48 hours.
Instead, Chen was questioned by Garrison Command for two hours about his United States activities on 30 June 1981, with one question about a personal visit revealing that he had been spied upon. After the first interview, Chen was told he should receive the exit permit the next day. Chen's wife, Chen Su-jen (), received a phone call late in the afternoon of 1 July 1981 asking that Chen remain at home early the next morning to await another phone c |
https://en.wikipedia.org/wiki/Isaac%20Namioka | Isaac Namioka (April 25, 1928 – September 25, 2019) was a Japanese-American mathematician who worked in general topology and functional analysis. He was a professor emeritus of mathematics at the University of Washington. He died at home in Seattle on September 25, 2019.
Early life and education
Namioka was born in Tōno, not far from Namioka in the north of Honshu, Japan. When he was young his parents moved farther south, to Himeji.
He attended graduate school at the University of California, Berkeley, earning a doctorate in 1956 under the supervision of John L. Kelley. As a graduate student, Namioka married Chinese-American mathematics student Lensey Namioka, later to become a well-known novelist who used Namioka's Japanese heritage in some of her novels.
Career
Namioka taught at Cornell University until 1963, when he moved to the University of Washington. There he was the doctoral advisor to four students. He has over 20 academic descendants, largely through his student Joseph Rosenblatt, who became a professor at the University of Illinois at Urbana–Champaign.
Contributions
Namioka's book Linear Topological Spaces with Kelley has become a "standard text". Although his doctoral work and this book both concerned general topology, his interests later shifted to functional analysis.
With Asplund in 1967, Namioka gave one of the first complete proofs of the Ryll-Nardzewski fixed-point theorem.
Following his 1974 paper "separate continuity and joint continuity", a Namioka space has come to mean a topological space X with the property that whenever Y is a compact space and function f from the Cartesian product of X and Y to Z is separately continuous in X and Y, there must exist a dense Gδ set within X whose Cartesian product with Y is a subset of the set of points of continuity of f. The result of the 1974 paper, a proof of this property for a specific class of topological spaces, has come to be known as Namioka's theorem.
In 1975, Namioka and Phelps established one side of the theorem that a space is an Asplund space if and only if its dual space has the Radon–Nikodým property. The other side was completed in 1978 by Stegall.
Awards and honors
A special issue of the Journal of Mathematical Analysis and Applications was dedicated to Namioka to honor his 80th birthday.
In 2012, he became one of the inaugural fellows of the American Mathematical Society.
Selected publications
Books
Partially Ordered Linear Topological Spaces (Memoirs of the American Mathematical Society 14, 1957)
Linear Topological Spaces (with John L. Kelley, Van Nostrand, 1963; Graduate Texts in Mathematics 36, Springer-Verlag, 1976)
Research papers
.
.
.
References
1928 births
2019 deaths
People from Iwate Prefecture
Japanese mathematicians
Japanese emigrants to the United States
20th-century American mathematicians
21st-century American mathematicians
Topologists
Functional analysts
University of California, Berkeley alumni
Cornell University faculty
University of Washi |
https://en.wikipedia.org/wiki/Daniel%20K.%20Nakano | Daniel Ken Nakano (born July 30, 1964) is an American mathematician. Nakano is a Distinguished Research Professor of Mathematics at the University of Georgia; he specializes in representation theory.
Nakano graduated from the University of California, Berkeley in 1986, and earned a doctorate in mathematics from Yale University in 1990 under the supervision of George B. Seligman with thesis Projective Modules over Lie Algebras of Cartan Type. After temporary positions at Auburn University and Northwestern University, he became an assistant professor at Utah State University in 1994 and moved to the University of Georgia in 2001.
In 2010, Nakano was named Distinguished Research Professor.
In 2012, he became one of the inaugural fellows of the American Mathematical Society.
In 2016, he received the Lamar Dodd Award Creative Research Award.
Publications
Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics, American Mathematical Society, (2016)
References
1964 births
Living people
20th-century American mathematicians
21st-century American mathematicians
University of California, Berkeley alumni
Yale University alumni
Utah State University faculty
University of Georgia faculty
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/1984%E2%80%9385%20VfL%20Bochum%20season | The 1984–85 VfL Bochum season was the 47th season in club history.
Review and events
Matches
Legend
Bundesliga
DFB-Pokal
Squad
Squad and statistics
Squad, appearances and goals scored
Transfers
Summer
In:
Out:
Winter
In:
Out:
Sources
External links
1984–85 VfL Bochum season at Weltfussball.de
1984–85 VfL Bochum season at kicker.de
1984–85 VfL Bochum season at Fussballdaten.de
Bochum
VfL Bochum seasons |
https://en.wikipedia.org/wiki/Bernd%20Kr%C3%A4mer | Bernd Johann Krämer (born 22 July 1947, in Berlin) is a German computer scientist and professor emeritus of the Faculty of Mathematics and Informatics.
Biography
Bernd Krämer studied electrical engineering and computer science at the Technical University of Berlin where he also obtained his doctorate in engineering. From 1975 to 1989 and again from 1990 to 1992 he was a scientist and project leader at the Gesellschaft für Mathematik und Datenverarbeitung, the German National Research Center of Computer Science, which later became part of the Fraunhofer Society. From 1989 to mid 1990 he was an adjunct professor in the Computer Science department at the Naval Postgraduate School in Monterey, California.
In April 1992 he was appointed full professor at FernUniversität in Hagen. He is a co-founder, past president, fellow, and Board Member of the Society for Design & Process Science (SDPS). From 2008 to 2013 he was a member of the first University Council of FernUniversität in Hagen.
He has been a visiting professor at a number of prestigious international universities, including the Queensland University of Technology, in Brisbane and Monash University in Melbourne, both in Australia, McGill University in Montreal, the University of California, Berkeley and Shanghai Jiao Tong University.
He is a co-founder of two non-profit research associations, the Scientific Academy for Service Technology and edu-sharing.net. ServTech conducts EU-funded research projects in the areas ofSmart Manufacturing, Product Customization,’’ and Smart Healthcare and is the main sponsor of the annual International Conference on Service Oriented Computing (ICSOC). Since mid-2009, the association edu-sharing.net has been developing one of the first distributed repositories for digital learning content, which was developed by the DFG-funded project CampusContent, under the new name edu-sharing. It forms the basis of several repositories for Open Educational Resources and has been rolled out in several German states as an infrastructure for networking schools to provide them with broad access to digital learning materials and codified methodological knowledge through a single portal and to enable the exchange and joint development of such content.
Krämer co-founded the open access journal e-learning and education and was its first editor-in-chief.
He received the C. V. Ramamoorthy Distinguished Scholar Award In 2003 and the Raymond T. Yeh Life Time Achievement Award in 2006, both from the SDPS.
Selected books
Software Service and Application Engineering - Festschrift Dedicated to Bernd Krämer on the Occasion of His 65th Birthday, Lecture Notes in Computer ScienceAdvances in Collective Intelligence (Advances in Intelligent and Soft Computing, Vol. 113) by Jörn Altmann, Ulrike Baumöl, Bernd Krämer (2012)On Collective Intelligence (Advances in Intelligent and Soft Computing, Vol. 76) by Theo J. Bastiaens, Ulrike Baumöl, Bernd Krämer (2011) Contributions to Ubiquitous Comp |
https://en.wikipedia.org/wiki/W.%20Dale%20Brownawell | Woodrow Dale Brownawell (born April 21, 1942) is an American mathematician who has performed research in number theory and algebraic geometry. He is a Distinguished Professor emeritus at Pennsylvania State University, and is particularly known for his proof of explicit degree bounds that can be used to turn Hilbert's Nullstellensatz into an effective algorithm.
Brownawell was born in Grundy County, Missouri; his father was a farmer and train inspector. He earned a double baccalaureate in German and mathematics (with highest distinction) in 1964 from the University of Kansas, and after studying for a year at the University of Hamburg (at which he met Eva, the woman he later married) he returned to the US for graduate study at Cornell University. His graduate advisor, Stephen Schanuel, moved to Stony Brook University in 1969, and Brownawell followed him there for a year, but earned his Ph.D. from Cornell in 1970. That year, he joined the Penn State faculty, and he remained there until his retirement in 2013.
Brownawell and Michel Waldschmidt shared the 1986 Hardy–Ramanujan Prize for their independent proofs that at least one of the two numbers and is a transcendental number; here denotes Euler's number, approximately 2.718.
In 2004, a conference at the University of Waterloo was held in honor of Brownawell's 60th birthday.
In 2012, he became one of the inaugural fellows of the American Mathematical Society.
References
External links
Home page
1942 births
Living people
20th-century American mathematicians
Number theorists
University of Kansas alumni
Cornell University alumni
Pennsylvania State University faculty
Fellows of the American Mathematical Society
Mathematicians from Missouri
People from Grundy County, Missouri |
https://en.wikipedia.org/wiki/Michael%20Shulman%20%28mathematician%29 | Michael "Mike" Shulman (; born 1980) is an American associate professor of mathematics at the University of San Diego who works in category theory and higher category theory, homotopy theory, logic as applied to set theory, and computer science.
Work
Shulman did his undergraduate work at the California Institute of Technology and his postgraduate work at the University of Cambridge and the University of Chicago, where he received his Ph.D. in 2009.
His doctoral thesis and subsequent work dealt with applications of category theory to homotopy theory.
In 2009, he received a National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship.
In 2012–13, he was a visiting scholar at the Institute for Advanced Study, where he was one of the official participants in the Special Year on Univalent Foundations of Mathematics. Shulman was one of the principal authors of the book Homotopy type theory: Univalent foundations of mathematics, an informal exposition on the basics of univalent foundations and homotopy type theory. In 2014, Shulman was part of a team headed by Steve Awodey that was awarded a $7.5M grant from the Air Force Research Laboratory for homotopy type theory.
Blogs
Shulman is a supporter of using web-based software systems, such as GitHub, to promote collaborative work by mathematicians—the six-hundred-page Homotopy type theory book being a notable example. He is a prolific contributor to the nLab (and a member of its steering committee), and a co-host of the homotopy type theory blog and of the n-Category Cafe, a blog focusing on higher category theory.
Selected publications
Michael Shulman; Synthetic Differential Geometry. May 31, 2006.
Daniel Licata and Michael Shulman; Calculating the fundamental group of the circle in homotopy type theory. January 15, 2013.
Benedikt Ahrens, Chris Kapulkin, and Michael Shulman; Univalent categories and the Rezk completion. March 4, 2013.
Michael Shulman – In Cambridge Journals Special Issue: From type theory and homotopy theory to Univalent Foundations of Mathematics; Univalence for inverse diagrams and homotopy canonicity. November 23, 2013.
John C. Baez and Michael Shulman; Lectures on -categories and cohomology In .
References
External links
Shulman's home page at University of San Diego
Michael Shulman: Papers
Shulman postings to Homotopy Type Theory blog
21st-century American mathematicians
Category theorists
University of San Diego faculty
University of Chicago alumni
Institute for Advanced Study visiting scholars
California Institute of Technology alumni
Living people
1980 births |
https://en.wikipedia.org/wiki/Jill%20Chapman | Jill Chapman-Daily (born November 4, 1979) is a former professional basketball player. She played 19 games for the Detroit Shock.
Indiana statistics
Source
Professional statistics
|-
|2002
|Detroit
|19
|0
|6.3
|.370
|.000
|.667
|1.4
|0.0
|0.2
|0.1
|0.4
|1.2
After Basketball
Jill Chapman ended her basketball career in 2003 shortly after the birth of her first daughter.
References
External links
WNBA.com: Jill Chapman Player Info
1979 births
Living people
American women's basketball players
Detroit Shock players
Indiana Hoosiers women's basketball players
Centers (basketball) |
https://en.wikipedia.org/wiki/Chris%20Stevens%20%28mathematician%29 | Terrie Christine Stevens, also known as T. Christine Stevens, is an American mathematician whose research concerns topological groups, the history of mathematics, and mathematics education. She is also known as the co-founder of Project NExT, a mentorship program for recent doctorates in mathematics, which she directed from 1994 until 2009.
Education and career
Stevens graduated from Smith College in 1970, and completed her doctorate in 1978 at Harvard University under the supervision of Andrew M. Gleason. Her dissertation was Weakened Topologies for Lie Groups.
She held teaching positions at the University of Massachusetts Lowell, at Mount Holyoke College and at Arkansas State University before joining Saint Louis University, where for 25 years she was a professor of mathematics and computer science.
She was also a Congressional Science Fellow assisting congressman Theodore S. Weiss in 1984–1985, and was a program officer at the National Science Foundation in 1987–1989. After retiring from SLU, she became Associate Executive Director for Meetings and Professional Services of the American Mathematical Society. She also served as an AMS Council member at large from 2011 to 2013.
Recognition
In 2004 Stevens won the Gung and Hu Award for
Distinguished Service to Mathematics of the Mathematical Association of America for her work on Project NExT.
In 2010 Stevens was awarded the Smith College Medal by her alma mater.
She has been a fellow of the American Association for the Advancement of Science since 2005,
and in 2012, she became one of the inaugural fellows of the American Mathematical Society. She was the 2015 winner of the Louise Hay Award of the Association for Women in Mathematics.
References
External links
Home page
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
Group theorists
Mathematics educators
American historians of mathematics
Smith College alumni
Harvard University alumni
University of Massachusetts Lowell faculty
Mount Holyoke College faculty
Arkansas State University faculty
Saint Louis University faculty
Saint Louis University mathematicians
Fellows of the American Association for the Advancement of Science
Fellows of the American Mathematical Society
20th-century women mathematicians
21st-century women mathematicians
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/Eduard%20Looijenga | Eduard Jacob Neven Looijenga (born 30 September 1948, Zaandam) is a Dutch mathematician who works in algebraic geometry and the theory of algebraic groups. He was a professor of mathematics at Utrecht University until his retirement in 2013.
Looijenga studied mathematics at the University of Amsterdam beginning in 1965, and earned a master's degree there in 1971. He obtained a Dutch fellowship for two years of study at the Institut des Hautes Études Scientifiques in France, and then returned to the University of Amsterdam, earning a Ph.D. in 1974 under the supervision of Nicolaas Kuiper. After postdoctoral research at the University of Liverpool, he took a faculty position at the University of Nijmegen in 1975, returned as a professor to the University of Amsterdam in 1987, and moved again to Utrecht in 1991. Since his 2013 retirement, he has also held a professorship at Tsinghua University.
In 1978, Looijenga was an invited speaker at the International Congress of Mathematicians. He became a member of the Royal Netherlands Academy of Arts and Sciences in 1995, and in 2012 he became one of the inaugural fellows of the American Mathematical Society. In 2013, a conference in honor of his retirement was held at Utrecht University.
Publications
References
External links
Home page
1948 births
Living people
20th-century Dutch mathematicians
21st-century Dutch mathematicians
University of Amsterdam alumni
Academic staff of Radboud University Nijmegen
Academic staff of Utrecht University
Academic staff of the University of Amsterdam
Academic staff of Tsinghua University
Fellows of the American Mathematical Society
Members of the Royal Netherlands Academy of Arts and Sciences
People from Zaanstad
Topologists
Algebraic geometers |
https://en.wikipedia.org/wiki/Michael%20Loss | Michael Loss (born 1954) is a mathematician and mathematical physicist who works as a professor of mathematics at the Georgia Institute of Technology.
Loss obtained his Ph.D. in 1982 from ETH Zurich, with a dissertation on the three-body problem jointly supervised by Walter Hunziker and Israel Michael Sigal.
With Elliott H. Lieb he is the author of the textbook Analysis (Graduate Studies in Mathematics 14. American Mathematical Society, 1997; 2nd ed., 2001).
In 2012, he became one of the inaugural fellows of the American Mathematical Society, and was elected as a Foreign Corresponding Member of the Chilean Academy of Sciences. He is one of the 2015 winners of the Humboldt Prize.
References
External links
Google scholar profile
1954 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Mathematical physicists
Georgia Tech faculty
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Ray%20Kunze | Ray Alden Kunze (March 7, 1928 – May 21, 2014) was an American mathematician who chaired the mathematics departments at the University of California, Irvine and the University of Georgia. His mathematical research concerned the representation theory of groups and noncommutative harmonic analysis.
Kunze was born in Des Moines, Iowa and grew up near Milwaukee, Wisconsin. He began his undergraduate studies at Denison University but transferred to the University of Chicago after two years, and earned bachelor's and master's degrees in mathematics. After working as a military mathematical analyst, he returned to the University of Chicago, and earned his Ph.D. in 1957 with a dissertation on Fourier transformations supervised by Irving Segal. As well as his positions at UCI and Georgia, he also worked at the Institute for Advanced Study, Massachusetts Institute of Technology, Brandeis University, and Washington University in St. Louis. He has over 50 academic descendants, many of them through his students Paul Sally at Brandeis and Edward N. Wilson at Washington University.
With his advisor Irving Segal, Kunze was the author of the textbook Integrals and Operators (McGraw-Hill, 1968; 2nd ed., Grundlehren der Mathematischen Wissenschaften 228, Springer, 1978). With Kenneth M. Hoffman he was the author of Linear Algebra (Prentice-Hall, 1961; 2nd ed., Pearson, 1971).
In 1994, a special session on representation theory and harmonic analysis was held in honor of Kunze as part of the 889th meeting of the American Mathematical Society, and the papers from the session were published as a festschrift.
In 2012, Kunze was recognized as one of the inaugural fellows of the American Mathematical Society.
References
1928 births
2014 deaths
20th-century American mathematicians
21st-century American mathematicians
Group theorists
University of Chicago alumni
Massachusetts Institute of Technology faculty
Brandeis University faculty
Washington University in St. Louis faculty
Washington University in St. Louis mathematicians
University of California, Irvine faculty
University of Georgia faculty
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/True%20Mathematics | Kenny Houston aka True Mathematics is a rapper from Hempstead, New York. He released an album called "Greatest Hits" as a collaboration with Hank Shocklee (Public Enemy), Eric Sadler, Carl Ryder (aka Chuck D), and spawned four singles: "After Dark", which charted at #92 on the UK Singles Chart; For the Lover in You; I Don't Love You Anymore; For the Money/KAOss, which also charted at #92 on the UK Singles Chart. He also contributed to the Public Enemy song "Get the Fuck Outta Dodge", which was the B-Side to their single "Can't Do Nuttin' For Ya Man" from their album Fear of a Black Planet and also appeared on their album Apocalypse '91...The Enemy Strikes Black.
References
Rappers from New York (state) |
https://en.wikipedia.org/wiki/M%C3%A1t%C3%A9%20Schmid | Máté Schmid (born 8 July 1996) is a Hungarian professional footballer who plays for Lombard-Pápa TFC.
Club statistics
Updated to games played as of 30 November 2014.
References
External links
MLSZ
HLSZ
1996 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football forwards
Pápai FC footballers
Nemzeti Bajnokság I players |
https://en.wikipedia.org/wiki/Martin%20Iv%C3%A1nyi | Martin Iványi (born 16 August 1995 in Pápa) is a Hungarian professional footballer who plays for Lombard-Pápa TFC.
Club statistics
Updated to games played as of 6 December 2014.
External links
MLSZ
HLSZ
1995 births
Living people
People from Pápa
Hungarian men's footballers
Men's association football midfielders
Pápai FC footballers
Nemzeti Bajnokság I players
Footballers from Veszprém County |
https://en.wikipedia.org/wiki/NUST%20School%20of%20Natural%20Sciences | The School of Natural Sciences (SNS), formerly Centre for Advanced Mathematics and Physics (CAMP), is a department and research center of the National University of Sciences and Technology (Pakistan). Established in May 2004, SNS offers the Bachelor of Science (BS), Master of Science (MS)/Master of Philosophy (MPhil) and Doctor of Philosophy (PhD) in natural science subjects; Physics, Chemistry and Mathematics.
See also
National University of Sciences and Technology (Pakistan)
References
External links
SNS official website
NUST official website
National University of Sciences & Technology
Universities and colleges in Islamabad |
https://en.wikipedia.org/wiki/Coskewness | In probability theory and statistics, coskewness is a measure of how much three random variables change together. Coskewness is the third standardized cross central moment, related to skewness as covariance is related to variance. In 1976, Krauss and Litzenberger used it to examine risk in stock market investments. The application to risk was extended by Harvey and Siddique in 2000.
If three random variables exhibit positive coskewness they will tend to undergo extreme deviations at the same time, an odd number of which are in the positive direction (so all three random variables undergoing extreme positive deviations, or one undergoing an extreme positive deviation while the other two undergo extreme negative deviations). Similarly, if three random variables exhibit negative coskewness they will tend to undergo extreme deviations at the same time, an even number of which are in the positive direction (so all three random variables undergoing extreme negative deviations, or one undergoing an extreme negative deviation while the other two undergo extreme positive deviations).
Types
There are two different measures for the degree of coskewness in data.
Coskewness
For three random variables X, Y and Z, the non-trivial coskewness statistic is defined as:
where E[X] is the expected value of X, also known as the mean of X, and is the standard deviation of X.
Standardized rank coskewness
Bernard, Chen, Rüschendorf and Vanduffel defined the standardized rank coskewness of three random variables X, Y and Z as:
where FX (X), FY (Y) and FZ (Z) are the cumulative distribution functions of X, Y and Z, respectively.
Properties
Skewness is a special case of the coskewness when the three random variables are identical:
For two random variables, X and Y, the skewness of the sum, X + Y, is
where SX is the skewness of X and is the standard deviation of X. It follows that the sum of two random variables can be skewed (SX+Y ≠ 0) even if both random variables have zero skew in isolation (SX = 0 and SY = 0).
The coskewness between variables X and Y does not depend on the scale on which the variables are expressed. If we are analyzing the relationship between X and Y, the coskewness between X and Y will be the same as the coskewness between a + bX and c + dY, where a, b, c, and d are constants.
The standardized rank coskewness RS(X, Y, Z) satisfies the following properties:
(1) −1 ≤ RS(X, Y, Z) ≤ 1.
(2) The upper bound of 1 is obtained by the copula given in (3.3) in Bernard, Chen, Rüschendorf and Vanduffel (2023). The lower bound of −1 is obtained by the copula (3.5) in the same paper.
(3) It is invariant under strictly increasing transformations, i.e., when fi, i = 1, 2, 3, are arbitrary strictly increasing functions, RS(X, Y, Z) = RS(f1 (X), f2 (Y), f3 (Z)).
(4) RS(X, Y, Z) = 0 if X, Y and Z are independent.
Example
Let X be standard normally distributed and Y be the distribution obtained by setting X=Y whenever X<0 and drawing Y |
https://en.wikipedia.org/wiki/Stephen%20Gelbart | Stephen Samuel Gelbart (born June 12, 1946) is an American-Israeli mathematician who holds the Nicki and J. Ira Harris Professorial Chair in mathematics at the Weizmann Institute of Science in Israel. He was named a fellow of the American Mathematical Society in 2013 "for contributions to the development and dissemination of the Langlands program."
Biography
Gelbart was born in Syracuse, New York. He graduated from Cornell University in 1967, and earned a Ph.D. from Princeton University in 1970, with a dissertation on Fourier analysis supervised by Elias M. Stein. He returned to Cornell as an assistant professor in 1971, was promoted to full professor in 1980, moved to the Weizmann Institute in 1984, and was given his named chair in 1998. He was president of the Israel Mathematical Union from 1994 to 1996. His doctoral students include Erez Lapid.
Selected publications
Articles
Harmonics on Stiefel manifolds and generalized Hankel transforms. Bull. Amer. Math. Soc. 78 (1972) 451–455.
A theory of Stiefel harmonics. Trans. Amer. Math. Soc. 192 (1974) 29–50.
An elementary introduction to the Langlands program. Bull. Amer. Math. Soc. 10 (1984) 177–219.
with Freydoon Shahidi: Boundedness of automorphic L-functions in vertical strips. J. Amer. Math. Soc. 14 (2001) 79–107.
with Stephen D. Miller: Riemann's zeta function and beyond. Bull. Amer. Math. Soc. 41 (2004) 59–112.
Books
with Ilya Piatetski-Shapiro and Stephen Rallis:
with Freydoon Shahidi:
as editor
with Joseph Bernstein as editor and 6 contributing authors:
References
External links
Home page
1946 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Israeli mathematicians
Cornell University alumni
Princeton University alumni
Cornell University faculty
Academic staff of Weizmann Institute of Science
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Straight-line%20program | In mathematics, more specifically in computational algebra, a straight-line program (SLP) for a finite group G = 〈S〉 is a finite sequence L of elements of G such that every element of L either belongs to S, is the inverse of a preceding element, or the product of two preceding elements. An SLP L is said to compute a group element g ∈ G if g ∈ L, where g is encoded by a word in S and its inverses.
Intuitively, an SLP computing some g ∈ G is an efficient way of storing g as a group word over S; observe that if g is constructed in i steps, the word length of g may be exponential in i, but the length of the corresponding SLP is linear in i. This has important applications in computational group theory, by using SLPs to efficiently encode group elements as words over a given generating set.
Straight-line programs were introduced by Babai and Szemerédi in 1984 as a tool for studying the computational complexity of certain matrix group properties. Babai and Szemerédi prove that every element of a finite group G has an SLP of length O(log2|G|) in every generating set.
An efficient solution to the constructive membership problem is crucial to many group-theoretic algorithms. It can be stated in terms of SLPs as follows. Given a finite group G = 〈S〉 and g ∈ G, find a straight-line program computing g over S. The constructive membership problem is often studied in the setting of black box groups. The elements are encoded by bit strings of a fixed length. Three oracles are provided for the group-theoretic functions of multiplication, inversion, and checking for equality with the identity. A black box algorithm is one which uses only these oracles. Hence, straight-line programs for black box groups are black box algorithms.
Explicit straight-line programs are given for a wealth of finite simple groups in the online ATLAS of Finite Groups.
Definition
Informal definition
Let G be a finite group and let S be a subset of G. A sequence L = (g1,…,gm) of elements of G is a straight-line program over S if each gi can be obtained by one of the following three rules:
gi ∈ S
gi = gj gk for some j,k < i
gi = g for some j < i.
The straight-line cost c(g|S) of an element g ∈ G is the length of a shortest straight-line program over S computing g. The cost is infinite if g is not in the subgroup generated by S.
A straight-line program is similar to a derivation in predicate logic. The elements of S correspond to axioms and the group operations correspond to the rules of inference.
Formal definition
Let G be a finite group and let S be a subset of G. A straight-line program of length m over S computing some g ∈ G is a sequence of expressions (w1,…,wm) such that for each i, wi is a symbol for some element of S, or wi = (wj,-1) for some j < i, or wi = (wj,wk) for some j,k < i, such that wm takes upon the value g when evaluated in G in the obvious manner.
The original definition appearing in requires that G =〈S〉. The definition presented above is a common g |
https://en.wikipedia.org/wiki/List%20of%20people%20executed%20in%20India | The number of people executed in India since independence in 1947 is a matter of dispute; official government statistics claim that only 57 people had been executed since independence. However, available information from other sources indicates that the official government figures are false, and the actual number of executions in India may run to several thousand.
Research by the People's Union for Democratic Rights (PUDR) has located government records of 1,422 executions in 16 states in the decade from 1953 to 1963 alone. PUDR located this information in an appendix of the 35th report of the Fourth Law Commission in 1967. The National Law University Delhi compiled a list of persons executed in India since 1947 and found that at least 752 individuals had been executed, including the period from 1 January to 15 August 1947. Their report was compiled "as per responses received from Central prisons in India. Certain prisons have either provided information only for a limited period or refused to provide any information or did not have any records available." Therefore, the actual number of persons would be much more than 752. While information about the number of executions should be available with individual prison departments within each state, the government has been reluctant to share such information. For example, authorities in Kerala claimed that all records of executions had been destroyed by termites. Andhra Pradesh gave the same reason for not furnishing post-1968 records. Bihar claimed that the state did not maintain records of executions, while Tamil Nadu's Additional Director General of Police (Prisons) refused to provide any records at all. According to Alexander Jacob, Additional Director General of Police (Prisons) of Kerala, "nearly 50 people had been executed in Kerala in the post-Independence period".
Rasha alias Raghuraj Singh, executed on 9 September 1947 at Jabalpur Central Jail, is presumed to be the first person executed in independent India. Akshay Thakur, Mukesh Singh, Pawan Gupta and Vinay Sharma, who were hanged on 20 March 2020, were the last persons to be executed in India. Rattan Bai Jain, executed on 3 January 1955 at Tihar Jail, is presumed to be the first woman executed in independent India.
List
This is not an exhaustive list of prisoners executed in independent India, and is not meant to be a reference for the total number of prisoners who have been executed in India since independence. There are no official collated figures available for executions in India, and this list has been compiled from multiple sources. Unless otherwise noted, all persons were executed by hanging.
See also
Capital punishment in India
References
External links
Death Penalty Research Project's list of prisoners executed in India since 1947
Executed people
India
Lists
Executed people |
https://en.wikipedia.org/wiki/Rigo%20Nova | Rigo Nova (born December 12, 1979), born Rigoberto Nova Matute, is a Honduran-born American actor and writer. His background is Engineering, Mathematics, and Acting. He and his mother (Amanda Matute) founded "Light for Honduras" - a non-profit organization geared to help those of need in Honduras.
References
External links
Living people
1979 births |
https://en.wikipedia.org/wiki/Talinoc%20i%20Muhaxhir%C3%ABve | Talinoc i Muhaxhirëve, also known as Talinovce or Muhadžer Talinovac, is a village in Ferizaj Municipality, Kosovo. According to the Kosovo Agency of Statistics (KAS) estimate from the 2011 census, there were 1,961 people residing in Gaçkë, with Albanians constituting the majority of the population.
History
Talinoc i Muhaxhirëve was founded by Albanian muhajirs in the second half of the 19th century, hence the name. After the war, the population structure shifted with increasing number of Albanians, so that in the 1990s, there were roughly twice the number of Albanians than Serbs. After the Kachak movement in Kosovo between 1918–1924, the Yugoslav government disarmed the village, which was administratively part of the Nerodimlje srez.
Demography
Serb refugees
Before the Kosovo War, the village was ethnically mixed, with ca. 300 Serbs. In 1999, all Serbs were expelled. In 2006, 30 Serbs returned to the village. Until the murders, 18 Serbs lived in the village.
A married Serb couple, war refugees who had returned to the village, were murdered in their house on 6 July 2012. After the murders, the village Serbs asked the government to secure their relocation to either Strpce or Gracanica, or else they were to leave for Central Serbia.
References
Villages in Ferizaj |
https://en.wikipedia.org/wiki/Camille%20Cooper | Camille Kaye Cooper (born February 5, 1979) is a former professional basketball player. She played for the New York Liberty in 2001 and 2002. She played a total of 2 games.
Purdue statistics
Source
Statistics leaders
Personal life
After basketball, Cooper became an attorney.
References
External links
Purdue bio
1979 births
Living people
American lawyers
American women's basketball players
Basketball players from Kentucky
Centers (basketball)
Duke University School of Law alumni
Kentucky women in law
Los Angeles Sparks draft picks
New York Liberty players
People from Georgetown, Kentucky
Purdue Boilermakers women's basketball players
Sportswomen from Kentucky |
https://en.wikipedia.org/wiki/Bangladesh%E2%80%93Israel%20relations | Bangladesh and Israel do not maintain diplomatic relations. Bangladesh said that it will not recognize Israel until there is an independent Palestine. Some reports and statistics revealed that Bangladesh and Israel maintain some trade relations indirectly and sometimes secretly, although the government always denies these allegations.
Country comparison
Diplomacy
Bangladesh is one of 28 UN member states that does not recognize the state of Israel. It is one of several countries that officially bans its citizens from traveling to Israel and does not accept Israeli passports. In November 2003, Bangladeshi journalist Salah Choudhury was arrested for attempting to fly to Tel Aviv, arraigned for "sedition, treason, and blasphemy", and sentenced to a seven-year prison term. Bangladesh officially supports a sovereign Palestinian state and "an end to Israel's illegal occupation of Palestine".
In a September 2011 statement published in The Jerusalem Post, an Israeli government spokesperson said, "We have no conflict with Bangladesh. We want dialogue. We want people-to-people relations. We welcome the religious-minded people of Bangladesh to visit the holy land of Jerusalem". Israel fruitlessly "sought a relationship with Bangladesh" after they had established "full diplomatic relations with China and India in 1992". Bangladeshi Prime Minister Sheikh Hasina said in 2014, "We have been continuing our support to the Palestinians and occupation of their land by the Israelis is never acceptable".
In late May 2021, Bangladesh removed "except Israel" from their passport to meet the "international standard" from an earlier version which said "This passport is valid for all countries of the world except Israel". The removal was only from their e-passport and removal from machine readable passports (MRP) is on process. Though the term was removed from the passport, Bangladesh did not remove the ban on traveling to Israel with Bangladeshi passport.
Trade
Bangladesh maintains a ban on trade with Israel even though both countries are members of the World Trade Organization. In 2014, it was found from the official statistics of the Bangladesh Export Promotion Bureau that Bangladesh had exported a small amount of merchandise goods worth about to Israel in 2013–14 fiscal year. In recent years however, it is found that Bangladeshi products are exported to Israel through the United States, the European Union or other third countries.
Israel imported ready-made garments, apparel and textile products from Bangladesh worth $333.74 million in the fiscal year 2022. Most imported Bangladeshi goods came via Turkey, Malaysia, the United Arab Emirates and Singapore. Ready-made garments brokerage based in Singapore made payments to Bangladeshi banks from Singapore and Turkey as there is no direct diplomatic and economic relationship between both countries.
Indian company Adani Group’s take-over plan of Israeli Haifa port would allow Muslim countries, including Bangladesh and |
https://en.wikipedia.org/wiki/Cokurtosis | In probability theory and statistics, cokurtosis is a measure of how much two random variables change together. Cokurtosis is the fourth standardized cross central moment. If two random variables exhibit a high level of cokurtosis they will tend to undergo extreme positive and negative deviations at the same time.
Definition
For two random variables X and Y there are three non-trivial cokurtosis statistics
and
where E[X] is the expected value of X, also known as the mean of X, and is the standard deviation of X.
Properties
Kurtosis is a special case of the cokurtosis when the two random variables are identical:
For two random variables, X and Y, the kurtosis of the sum, X + Y, is
where is the kurtosis of X and is the standard deviation of X.
It follows that the sum of two random variables can have kurtosis different from 3 () even if both random variables have kurtosis of 3 in isolation ( and ).
The cokurtosis between variables X and Y does not depend on the scale on which the variables are expressed. If we are analyzing the relationship between X and Y, the cokurtosis between X and Y will be the same as the cokurtosis between a + bX and c + dY, where a, b, c and d are constants.
Examples
Bivariate normal distribution
Let X and Y each be normally distributed with correlation coefficient ρ. The cokurtosis terms are
Since the cokurtosis depends only on ρ, which is already completely determined by the lower-degree covariance matrix, the cokurtosis of the bivariate normal distribution contains no new information about the distribution. It is a convenient reference, however, for comparing to other distributions.
Nonlinearly correlated normal distributions
Let X be standard normally distributed and Y be the distribution obtained by setting X=Y whenever X<0 and drawing Y independently from a standard half-normal distribution whenever X>0. In other words, X and Y are both standard normally distributed with the property that they are completely correlated for negative values and uncorrelated apart from sign for positive values. The joint probability density function is
where H(x) is the Heaviside step function and δ(x) is the Dirac delta function. The fourth moments are easily calculated by integrating with respect to this density:
It is useful to compare this result to what would have been obtained for an ordinary bivariate normal distribution with the usual linear correlation. From integration with respect to density, we find that the linear correlation coefficient of X and Y is
A bivariate normal distribution with this value of ρ would have and . Therefore, all of the cokurtosis terms of this distribution with this nonlinear correlation are smaller than what would have been expected from a bivariate normal distribution with ρ=0.818.
Note that although X and Y are individually standard normally distributed, the distribution of the sum X+Y is platykurtic. The standard deviation of the sum is
Inserting that and t |
https://en.wikipedia.org/wiki/Kuratowski%E2%80%93Ulam%20theorem | In mathematics, the Kuratowski–Ulam theorem, introduced by , called also the Fubini theorem for category, is an analog of Fubini's theorem for arbitrary second countable Baire spaces.
Let X and Y be second countable Baire spaces (or, in particular, Polish spaces), and let . Then the following are equivalent if A has the Baire property:
A is meager (respectively comeager).
The set is comeager in X, where , where is the projection onto Y.
Even if A does not have the Baire property, 2. follows from 1.
Note that the theorem still holds (perhaps vacuously) for X an arbitrary Hausdorff space and Y a Hausdorff space with countable π-base.
The theorem is analogous to the regular Fubini's theorem for the case where the considered function is a characteristic function of a subset in a product space, with the usual correspondences, namely, meagre set with a set of measure zero, comeagre set with one of full measure, and a set with the Baire property with a measurable set.
References
General topology
Descriptive set theory
Theorems in topology |
https://en.wikipedia.org/wiki/Simultaneous%20algebraic%20reconstruction%20technique | Simultaneous algebraic reconstruction technique (SART) is a computerized tomography (CT) imaging algorithm useful in cases when the projection data is limited; it was proposed by Anders Andersen and Avinash Kak in 1984.
It generates a good reconstruction in just one iteration and it is superior to standard algebraic reconstruction technique (ART).
As a measure of its popularity, researchers have proposed various extensions to
SART: OS-SART, FA-SART, VW-OS-SART, SARTF, etc. Researchers have also studied how SART can best be implemented on different parallel processing architectures. SART and its proposed extensions are used in emission CT in nuclear medicine, dynamic CT, and holographic tomography, and other reconstruction applications. Convergence
of the SART algorithm was theoretically established in 2004 by Jiang and Wang. Further convergence analysis was done by Yan.
An application of SART to ionosphere was presented by Hobiger et al. Their method does not use matrix algebra and therefore it can be implemented in a low-level programming language. Its convergence speed is significantly higher than that of classical SART. A discrete version of SART called DART was developed by Batenburg and Sijbers.
References
Radiology
Medical imaging
Inverse problems |
https://en.wikipedia.org/wiki/Semi-simplicity | In mathematics, semi-simplicity is a widespread concept in disciplines such as linear algebra, abstract algebra, representation theory, category theory, and algebraic geometry. A semi-simple object is one that can be decomposed into a sum of simple objects, and simple objects are those that do not contain non-trivial proper sub-objects. The precise definitions of these words depends on the context.
For example, if G is a finite group, then a nontrivial finite-dimensional representation V over a field is said to be simple if the only subrepresentations it contains are either {0} or V (these are also called irreducible representations). Now Maschke's theorem says that any finite-dimensional representation of a finite group is a direct sum of simple representations (provided the characteristic of the base field does not divide the order of the group). So in the case of finite groups with this condition, every finite-dimensional representation is semi-simple. Especially in algebra and representation theory, "semi-simplicity" is also called complete reducibility. For example, Weyl's theorem on complete reducibility says a finite-dimensional representation of a semisimple compact Lie group is semisimple.
A square matrix (in other words a linear operator with V finite dimensional vector space) is said to be simple if its only invariant subspaces under T are {0} and V. If the field is algebraically closed (such as the complex numbers), then the only simple matrices are of size 1 by 1. A semi-simple matrix is one that is similar to a direct sum of simple matrices; if the field is algebraically closed, this is the same as being diagonalizable.
These notions of semi-simplicity can be unified using the language of semi-simple modules, and generalized to semi-simple categories.
Introductory example of vector spaces
If one considers all vector spaces (over a field, such as the real numbers), the simple vector spaces are those that contain no proper nontrivial subspaces. Therefore, the one-dimensional vector spaces are the simple ones. So it is a basic result of linear algebra that any finite-dimensional vector space is the direct sum of simple vector spaces; in other words, all finite-dimensional vector spaces are semi-simple.
Semi-simple matrices
A square matrix or, equivalently, a linear operator T on a finite-dimensional vector space V is called semi-simple if every T-invariant subspace has a complementary T-invariant subspace. This is equivalent to the minimal polynomial of T being square-free.
For vector spaces over an algebraically closed field F, semi-simplicity of a matrix is equivalent to diagonalizability. This is because such an operator always has an eigenvector; if it is, in addition, semi-simple, then it has a complementary invariant hyperplane, which itself has an eigenvector, and thus by induction is diagonalizable. Conversely, diagonalizable operators are easily seen to be semi-simple, as invariant subspaces are direct sums of eigensp |
https://en.wikipedia.org/wiki/List%20of%20Brentford%20F.C.%20records%20and%20statistics | Brentford Football Club is an English professional football club based in Brentford, Hounslow, London. Between 1897 and 1920, the first team competed in the London League, Southern League and Western League. Since 1920, the first team has competed in the Football League, the Premier League and other nationally and internationally organised competitions.
The list encompasses the major honours won by Brentford, records set by the club, its managers and its players. "League" constitutes records and statistics from the 1920–21 season until the present day, during which the club has competed in League football.
Club honours and best performances
Major domestic competitions
Leagues
First Division / Premier League (level 1)
Best performance: 5th – 1935–36
Second Division / First Division / Championship (level 2)
Winners (1): 1934–35
Play-off winners (1): 2021
Third Division / Third Division South / Second Division / League One (level 3)
Winners (2): 1932–33, 1991–92
Runners-up (4): 1929–30, 1957–58, 1994–95, 2013–14
Fourth Division / Third Division / League Two (level 4)
Winners (3): 1962–63, 1998–99, 2008–09
Third-place promotion (1): 1971–72
Fourth-place promotion (1): 1977–78
Cups
FA Cup
Best performance: Sixth round/quarter-final – 1937–38, 1945–46, 1948–49, 1988–89
EFL Cup
Best performance: Semi-final – 2020–21
EFL Trophy
Best performance: Finalists – 1984–85, 2000–01, 2010–11
European competitions
Anglo-Italian Cup
Best performance: Semi-final – 1992–93
Minor domestic competitions
Leagues
Southern League First Division / Premier Division
Best performance: 9th – 1905–06
Southern League Second Division
Winners: 1900–01
United League
Winners: 1907–08
Western League First Division / Premier Division
Best performance: 2nd – 1904–05
London League First Division
Best performance: 2nd – 1897–98
London League Second Division
Best performance: 2nd – 1896–97
Cups
Middlesex Junior Cup
Winners (1): 1893–94
West Middlesex Cup
Winners (1): 1894–95
London Senior Cup
Winners (1): 1897–98
Middlesex Senior Cup
Winners (1): 1897–98
Southern Professional Charity Cup
Winners (1): 1908–09
Ealing Hospital Cup
Winners (1): 1910–11
London Challenge Cup
Winners (3): 1934–35, 1964–65, 1966–67
Supporters Direct Cup
Winners (2): 2004, 2008
Empire Exhibition Trophy
Best performance: First round – 1938
FA Amateur Cup
Best performance: First round – 1898–99
Southern Professional Floodlit Cup
Best performance: Semi-final – 1955–56, 1956–57
First Alliance Cup
Best performance: First round – 1988
Kent Challenge Cup
Best performance: Runners-up – 1975–76
Player records
Appearances
Youngest debutant (all competitions): Paul Walker – 15 years, 7 months, 28 days (versus Watford, Football League Cup first round, August 1976)
Youngest League debutant: Danis Salman – 15 years, 8 months, 3 days (versus Watford, Fourth Division, 15 November 1975)
Oldest player: Jimmy Hodson – 40 years, 8 months, 2 days (versus Plymouth Argyle, T |
https://en.wikipedia.org/wiki/Davalyn%20Cunningham | Davalyn Cunningham is a former professional basketball player who played for the Orlando Miracle.
Rutgers statistics
Source
Personal life
Cunningham has a younger brother, Dante, who also played in the NBA
References
External links
WNBA.com: Davalyn Cunningham Player Info
1980 births
Living people
American women's basketball players
Basketball players from Washington, D.C.
Orlando Miracle players
Rutgers Scarlet Knights women's basketball players
Forwards (basketball) |
https://en.wikipedia.org/wiki/Mu-Tao%20Wang | Mu-Tao Wang () is a Taiwanese mathematician and current Professor of Mathematics at Columbia University.
Education
He entered National Taiwan University in 1984, originally for international business, but after a year he switched to mathematics. He earned his BS in Mathematics at National Taiwan University in 1988 and his MS from the same institution in 1992. He received a PhD in Mathematics in 1998 from Harvard University with a thesis entitled "Generalized harmonic maps and representations of discrete groups." His thesis adviser at Harvard was Chinese Fields Medalist and differential geometer Shing-Tung Yau.
Career
Wang joined the Columbia faculty as an assistant professor in 2001, and was appointed full professor in 2009. Before joining the faculty at Columbia, Wang was Szego Assistant Professor at Stanford University.
He was a Sloan Research Fellow from 2003–2005. In 2007, he was named a Kavli Fellow of the National Academy of Sciences and was awarded the Chern Prize. Wang is a Fellow of the American Mathematical Society and won the Morningside Gold Medal of Mathematics in 2010.
In 2010, Wang delivered the plenary address at the International Congress of Chinese Mathematicians, and was plenary speaker at the International Congress on Mathematical Physics. In addition, he was also plenary speaker at the International Conference on Differential Geometry in 2011.
After winning the Morningside Medal, Wang told interviewers that he did not consider himself a particularly good student and did not consistently make good grades. He struggled with studying topics which did not interest him just for the grade, but spends a lot of time on subjects which interested him. He credits his career in mathematics to two people: his mother and his thesis adviser Shing-Tung Yau. He cites his mother's support and understanding of his decision to switch to mathematics in university despite it being a much less lucrative field, and describes meeting Yau in 1992 as the pivotal point in his life when he decided to make mathematics research his primary focus.
Work
Wang's research is focused in the fields of differential geometry and mathematical physics, specifically general relativity. He has studied higher co-dimensional mean curvature flow extensively, leading to criteria relating to the flow's existence, regularity, and convergence. In the field of general relativity, he is especially known for his work on quasilocal mass–energy; the Wang-Yau quasi-local mass is named in his honor.
Selected bibliography
"A fixed point theorem of isometry action on Riemannian manifolds", Journal of Differential Geometry 50 (1998), no. 2, 249-267
"Mean curvature flow of surfaces in Einstein four-manifolds", Journal of Differential Geometry 57 (2001), no. 2, 301-338
"Long-time existence and convergence of graphic mean curvature flow in arbitrary codimension", Inventiones Mathematicae 148 (2002), no. 3, 525-543
(with Knut Smoczyk) "Mean curvature flows of Lagrangian submanifold |
https://en.wikipedia.org/wiki/Ivar%20Kristianslund | Ivar Kristianslund (1 January 1934 – 20 April 2023) was a Norwegian preacher, former professor of statistics, agronomist, farmer and politician. He was active as a Christian fundamentalist preacher in the self-proclaimed "Church of Norway in Exile", and was active in the leadership of several minor Christian right political parties from the late 1990s.
Career and personal life
Kristianslund was educated as an agronomist from the Norwegian College of Agriculture (NLH) in 1959, and as cand.oecon. from the University of Oslo in 1962. He has two doctorates, dr. scient. from NLH in 1963, and dr. philos. in agricultural economics from the Michigan State University in 1972. He also completed a master's degree in theology at KNOX theological seminary in 2015. He worked most of his career at the NLH writing numerous books and dissertations, and was leader of the institute of social economics at the Oslo Business School from 1989 to 1992. He was rector of BI Østfold from 1994 to 1995, and professor of statistics at the BI Norwegian Business School between 1993 and 1997.
He resided in Greåker, Østfold where he also worked as a farmer. He was married and had eight children. Kristianslund died on 20 April 2023.
Politics and activism
Kristianslund became the leader of the New Future Coalition Party in 1998, which merged into the Christian Unity Party the same year. He was leader of the new party until 2001, when he was dismissed after a court ruled against his leadership of the party, following an internal conflict since the party's national convention. He founded the more fundamentalist party Christian Future later the same year, which only allowed men and those confessing to Lutheran faith to hold formal posts. He left the party to join the Abortion Opponents' List for the 2005 and 2009 elections, from 2008 as party secretary, alongside figures such as Ludvig Nessa, Børre Knudsen and Per Kørner.
In 1998 he criticised a sex-information film from the Department of Health as "solicitating to adultery", and filed charges against Christian Democratic cabinet minister Jon Lilletun. He also filed charges against a children's program by state broadcaster NRK that had arranged a "kissing school" for children. In 1999 he gathered 6,000 signatures demanding the government dismiss bishop Rosemarie Köhn and capellan Siri Sunde from their positions due to their liberal positions on homosexual relations. The same year he also filed charges of blasphemy against the art exhibition "Ecce Homo", which displayed photographs by Swedish artist Elisabeth Ohlson imaging Jesus surrounded by gays and lesbians. He participated in the demonstration against Muslim prayer calling in Oslo in 2000, and has expressed fears of a coming "religious war" in Norway because of increasing numbers of Muslims.
Kristianslund appeared in the first season of Fredrik Skavlan's talk-show Først & sist in 1998. In 2002 he was portrayed with his then-new party in the NRK-documentary "Norwegian fundam |
https://en.wikipedia.org/wiki/Kamil%20Dankowski | Kamil Dankowski (born 22 July 1996) is a Polish professional footballer who plays as a right-back for ŁKS Łódź.
Club career
On 1 September 2020, he joined ŁKS Łódź.
Career statistics
Club
Honours
ŁKS Łódź
I liga: 2022–23
References
External links
1996 births
People from Duszniki-Zdrój
Footballers from Lower Silesian Voivodeship
Living people
Polish men's footballers
Poland men's youth international footballers
Poland men's under-21 international footballers
Men's association football midfielders
Śląsk Wrocław players
ŁKS Łódź players
Ekstraklasa players
I liga players
III liga players |
https://en.wikipedia.org/wiki/Sigmundur%20Gudmundsson | Sigmundur Gudmundsson (born 1960) is an Icelandic-Swedish mathematician working at Lund University in the fields of differential geometry and global analysis. He is mainly interested in the geometric aspects of harmonic maps and their derivatives, such as harmonic morphisms and p-harmonic functions. His work is partially devoted to the existence theory of complex-valued harmonic morphisms and p-harmonic functions from Riemannian homogeneous spaces of various types, such as symmetric spaces and semisimple, solvable and nilpotent Lie groups.
Gudmundsson earned his Ph.D. from the University of Leeds in 1992, under the supervision of John C. Wood.
Gudmundsson is the founder of the website Nordic-Math-Job advertising vacant academic positions in the Nordic university departments of Mathematics and Statistics. This started off in 1997 as a one-man show, but is now supported by the mathematical societies in the Nordic countries and the National Committee for Mathematics of
The Royal Swedish Academy of Sciences.
Publications
Introduction to Gaussian Geometry, Lund University (2021).
Introduction to Riemannian Geometry, Lund University (2021).
Research Papers
References
External links
Home Page at Lund University
Profile at Zentralblatt MATH
Profile at Google Scholar
Nordic-Math-Job - Established on the 14th of February 1997
Sigmundur Gudmundsson
20th-century Swedish mathematicians
21st-century Swedish mathematicians
Alumni of the University of Leeds
Academic staff of Lund University
1960 births
Living people |
https://en.wikipedia.org/wiki/Harmonic%20morphism | In mathematics, a harmonic morphism is a (smooth) map between Riemannian manifolds that pulls back real-valued harmonic functions on the codomain to harmonic functions on the domain. Harmonic morphisms form a special class of harmonic maps i.e. those that are horizontally (weakly) conformal.
In local coordinates, on and on , the harmonicity of is expressed by the non-linear system
where and are the Christoffel symbols on and , respectively. The horizontal conformality is given by
where the conformal factor is a continuous function called the dilation. Harmonic morphisms are therefore solutions to non-linear over-determined systems of partial differential equations, determined by the geometric data of the manifolds involved. For this reason, they are difficult to find and have no general existence theory, not even locally.
Complex analysis
When the codomain of is a surface, the system of partial differential equations that we are dealing with, is invariant under conformal changes of the metric . This means that, at least for local studies, the codomain can be chosen to be the complex plane with its standard flat metric. In this situation a complex-valued function is a harmonic morphisms if and only if
and
This means that we look for two real-valued harmonic functions with gradients that are orthogonal and of the same norm at each point. This shows that complex-valued harmonic morphisms from Riemannian manifolds generalise holomorphic functions from Kähler manifolds and possess many of their highly interesting properties. The theory of harmonic morphisms can therefore be seen as a generalisation of complex analysis.
Minimal surfaces
In differential geometry, one is interested in constructing minimal submanifolds of a given ambient space . Harmonic morphisms are useful tools for this purpose. This is due to the fact that every regular fibre of such a map with values in a surface is a minimal submanifold of the domain with codimension 2. This gives an attractive method for manufacturing whole families of minimal surfaces in 4-dimensional manifolds , in particular, homogeneous spaces, such as Lie groups and symmetric spaces.
Examples
Identity and constant maps are harmonic morphisms.
Holomorphic functions in the complex plane are harmonic morphisms.
Holomorphic functions in the complex vector space are harmonic morphisms.
Holomorphic maps from Kähler manifolds with values in a Riemann surface are harmonic morphisms.
The Hopf maps , and are harmonic morphisms.
For compact Lie groups the standard Riemannian fibration is a harmonic morphism.
Riemannian submersions with minimal fibres are harmonic morphisms.
References
External links
The Bibliography of Harmonic Morphisms, offered by Sigmundur Gudmundsson
Riemannian geometry
Harmonic functions
Analytic functions |
https://en.wikipedia.org/wiki/Maria-Carme%20Calderer | Maria-Carme T. Calderer (Berga, 1951) is a professor of mathematics at University of Minnesota. Her research concerns applied mathematics.
Career
Calderer received her Ph.D. from Heriot-Watt University in 1980. She was a postdoctoral researcher at the Institute for Mathematics and its Applications from 1984 to 1987, first as a postdoctoral researcher, and then as a visiting professor. She worked at Penn State from 1989 until 2001, when she joined the faculty of University of Minnesota.
Awards and honors
In 2000 Calderer received the Teresa Cohen Service Award from Penn State University.
In 2012 she became a fellow of the American Mathematical Society.
In 2022 she will become a fellow of the Association for Women in Mathematics, "For being a role model nationally and internationally due to her outstanding research contributions in the mathematics of materials; for her long record of mentoring, advising, and supervising women in applied mathematics; and for her leadership role in the mathematics community by organizing conferences, workshops, and thematic years."
Personal life
Calderer was raised in Berga, Spain. She is married to Douglas Arnold, one of her fellow professors of mathematics at University of Minnesota.
Selected publications
Bauman, Patricia; Calderer, M. Carme; Liu, Chun; Phillips, Daniel The phase transition between chiral nematic and smectic A∗ liquid crystals. Arch. Ration. Mech. Anal. 165 (2002), no. 2, 161–186.
Calderer, M. Carme; Liu, Chun Liquid crystal flow: dynamic and static configurations. SIAM J. Appl. Math. 60 (2000), no. 6, 1925–1949.
References
Living people
American women mathematicians
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Mathematical Society
Alumni of Heriot-Watt University
Pennsylvania State University faculty
University of Minnesota faculty
20th-century women mathematicians
21st-century women mathematicians
Year of birth missing (living people)
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/M%C3%B3nica%20Clapp | Mónica Alicia Clapp Jiménez Labora is a mathematician at the Universidad Nacional Autónoma de México (UNAM) known for her work in nonlinear partial differential equations and algebraic topology.
Life and work
Clapp was born in Mexico City. She graduated from UNAM in 1974. Clapp then graduated with her Ph.D from Heidelberg University in 1979, and has been a faculty member at UNAM since that time.
Clapp has been an editor of the journals Boletín de la Sociedad Matemática Mexicana and Aportaciones Matemáticas.
Awards and honors
In 2012, Clapp became a fellow of the American Mathematical Society. She is also a member of the Mexican Academy of Sciences.
Selected publications
Clapp, Mónica; Puppe, Dieter Invariants of the Lusternik-Schnirelmann type and the topology of critical sets. Transactions of the American Mathematical Society 298 (1986), no. 2, 603–620.
Clapp, Mónica; Puppe, Dieter Critical point theory with symmetries. Journal für die reine und angewandte Mathematik 418 (1991), 1–29.
Bartsch, Thomas; Clapp, Mónica Critical point theory for indefinite functionals with symmetries. Journal of Functional Analysis 138 (1996), no. 1, 107–136.
Castro, Alfonso; Clapp, Mónica The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domain. Nonlinearity 16 (2003), no. 2, 579–590.
References
20th-century Mexican mathematicians
21st-century Mexican mathematicians
Mexican women mathematicians
Fellows of the American Mathematical Society
Living people
National Autonomous University of Mexico alumni
Heidelberg University alumni
Academic staff of the National Autonomous University of Mexico
20th-century women mathematicians
21st-century women mathematicians
Year of birth missing (living people)
Mexican expatriates in Germany
Members of the Mexican Academy of Sciences |
https://en.wikipedia.org/wiki/Symbol%20%28number%20theory%29 | In number theory, a symbol is any of many different generalizations of the Legendre symbol. This article describes the relations between these various generalizations.
The symbols below are arranged roughly in order of the date they were introduced, which is usually (but not always) in order of increasing generality.
Legendre symbol defined for p a prime, a an integer, and takes values 0, 1, or −1.
Jacobi symbol defined for b a positive odd integer, a an integer, and takes values 0, 1, or −1. An extension of the Legendre symbol to more general values of b.
Kronecker symbol defined for b any integer, a an integer, and takes values 0, 1, or −1. An extension of the Jacobi and Legendre symbols to more general values of b.
Power residue symbol is defined for a in some global field containing the mth roots of 1 ( for some m), b a fractional ideal of K built from prime ideals coprime to m. The symbol takes values in the m roots of 1. When m = 2 and the global field is the rationals this is more or less the same as the Jacobi symbol.
Hilbert symbol The local Hilbert symbol (a,b) = is defined for a and b in some local field containing the m roots of 1 (for some m) and takes values in the m roots of 1. The power residue symbol can be written in terms of the Hilbert symbol. The global Hilbert symbol is defined for a and b in some global field K, for p a finite or infinite place of K, and is equal to the local Hilbert symbol in the completion of K at the place p.
Artin symbol The local Artin symbol or norm residue symbol is defined for L a finite extension of the local field K, α an element of K, and takes values in the abelianization of the Galois group Gal(L/K). The global Artin symbol is defined for α in a ray class group or idele (class) group of a global field K, and takes values in the abelianization of Gal(L/K) for L an abelian extension of K. When α is in the idele group the symbol is sometimes called a Chevalley symbol or Artin–Chevalley symbol. The local Hilbert symbol of K can be written in terms of the Artin symbol for Kummer extensions L/K, where the roots of unity can be identified with elements of the Galois group.
The Frobenius symbol is the same as the Frobenius element of the prime P of the Galois extension L of K.
"Chevalley symbol" has several slightly different meanings. It is sometimes used for the Artin symbol for ideles. A variation of this is the Chevalley symbol for p a prime ideal of K, a an element of K, and χ a homomorphism of the Galois group of K to R/Z. The value of the symbol is then the value of the character χ on the usual Artin symbol.
Norm residue symbol This name is for several different closely related symbols, such as the Artin symbol or the Hilbert symbol or Hasse's norm residue symbol. The Hasse norm residue symbol is defined if p is a place of K and α an element of K. It is essentially the same as the local Artin symbol for the localization of K at p. The Hilbert symbol is a special cas |
https://en.wikipedia.org/wiki/Edward%20W.%20Formanek | Edward William Formanek (born May 6, 1942) is an American mathematician and chess player. He is a professor emeritus of mathematics at Pennsylvania State University, and a FIDE International Master in chess.
Mathematical career
Formanek earned his Ph.D. in 1970 from Rice University, under the supervision of Stephen M. Gersten. He joined the Penn State faculty in 1978, and retired in 2009.
In 1972, Formanek was one of two mathematicians to independently discover the central polynomials, which have applications to polynomial identity rings. With Vesselin Drensky, Formanek is the author of the book Polynomial Identity Rings (Birkhäuser, 2004).
In 2012, he became one of the inaugural fellows of the American Mathematical Society.
Chess career
Formanek became a FIDE International Master in 1977.
He has won the Pennsylvania State Championship five times, in 1984, 1993, 1997, 1998, and 2004. However, his most famous result from this series may be in 1988, when he led the tournament going into the last round but was defeated by computer program HiTech, becoming the first IM to lose a game to a computer. Later the same year HiTech would also defeat grandmaster Arnold Denker.
References
1942 births
Living people
20th-century American mathematicians
21st-century American mathematicians
American chess players
Chess International Masters
Rice University alumni
Pennsylvania State University faculty
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Stanley%20Wasserman | Stanley Wasserman (born August 29, 1951) is an American statistician and prior to retirement was the Rudy Professor of Statistics, Psychology, and Sociology at Indiana University Bloomington and the Academic Supervisor of the International laboratory for Applied Network Research at Moscow's National Research University – Higher School of Economics (since 2014). He is known for his work on social network analysis, mathematical sociology, network science and multidimensional network. In 2017 Wasserman launched the Master's program 'Applied statistics with Network Analysis' at National Research University – Higher School of Economics.
Biography
Born in Louisville, Kentucky, Wasserman obtained his BSc in economics from the University of Pennsylvania in 1973, as well as his MA in Business & Applied Economics. He then moved to Harvard University, where he obtained his MA in Statistics in 1974, and his PhD in Statistics in 1977 with the thesis, entitled "Stochastic Models for Directed Graphs" under supervision of Frederick Mosteller.
Wasserman started his career in 1974 at the National Bureau of Economics Research as Research Assistant and System Consultant in Statistics. After a year as an instructor at Harvard University, and as a Visiting Instructor at Carnegie-Mellon University, he started in 1977 as assistant professor at the University of Minnesota. In 1982 he moved to the University of Illinois at Urbana–Champaign, where he was appointed associate professor and in 1988 Professor of Psychology, Statistics, and Sociology. Beginning in 2004 he served as the James H. Rudy Professor of Statistics, Psychology, and Sociology at Indiana University in Bloomington.
Wasserman was awarded the J. Parker Bursk Memorial Award in 1973 while at the University of Pennsylvania. He was elected Fellow of the American Statistical Association in 1991, and Fellow of the American Association for the Advancement of Science in 1996.
Work
Social network analysis
In their 1994 "Advances in social network analysis," Wasserman and Joseph Galaskiewicz address:
... the issue of how effectively to apply the latest developments in social network analysis to behavioural and social science disciplines. Topics examined include: ways to specify the network contents to be studied; how to select the method for representing network structures; how social network analysis has been used to study interorganizational relations via the resource dependence model; how to use a contact matrix for studying the spread of disease in epidemiology; and how cohesion and structural equivalence network theories relate to studying social influence. The book also offers some statistical models for social support networks.
Books
Wasserman, Stanley, and Faust, Katherine, Social Network Analysis: Methods and Applications (Structural Analysis in the Social Sciences), (First Edition 1994) Cambridge University Press, Cambridge, UK, West 20th St., New York, USA, Melbourne, Madrid,
Wasserman, Stanley, & |
https://en.wikipedia.org/wiki/Cramer%27s%20theorem%20%28algebraic%20curves%29 | In algebraic geometry, Cramer's theorem on algebraic curves gives the necessary and sufficient number of points in the real plane falling on an algebraic curve to uniquely determine the curve in non-degenerate cases. This number is
where is the degree of the curve. The theorem is due to Gabriel Cramer, who published it in 1750.
For example, a line (of degree 1) is determined by 2 distinct points on it: one and only one line goes through those two points. Likewise, a non-degenerate conic (polynomial equation in and with the sum of their powers in any term not exceeding 2, hence with degree 2) is uniquely determined by 5 points in general position (no three of which are on a straight line).
The intuition of the conic case is this: Suppose the given points fall on, specifically, an ellipse. Then five pieces of information are necessary and sufficient to identify the ellipse—the horizontal location of the ellipse's center, the vertical location of the center, the major axis (the length of the longest chord), the minor axis (the length of the shortest chord through the center, perpendicular to the major axis), and the ellipse's rotational orientation (the extent to which the major axis departs from the horizontal). Five points in general position suffice to provide these five pieces of information, while four points do not.
Derivation of the formula
The number of distinct terms (including those with a zero coefficient) in an n-th degree equation in two variables is (n + 1)(n + 2) / 2. This is because the n-th degree terms are numbering n + 1 in total; the (n − 1) degree terms are numbering n in total; and so on through the first degree terms and numbering 2 in total, and the single zero degree term (the constant). The sum of these is (n + 1) + n + (n – 1) + ... + 2 + 1 = (n + 1)(n + 2) / 2 terms, each with its own coefficient. However, one of these coefficients is redundant in determining the curve, because we can always divide through the polynomial equation by any one of the coefficients, giving an equivalent equation with one coefficient fixed at 1, and thus [(n + 1)(n + 2) / 2] − 1 = n(n + 3) / 2 remaining coefficients.
For example, a fourth degree equation has the general form
with 4(4+3)/2 = 14 coefficients.
Determining an algebraic curve through a set of points consists of determining values for these coefficients in the algebraic equation such that each of the points satisfies the equation. Given n(n + 3) / 2 points (xi, yi), each of these points can be used to create a separate equation by substituting it into the general polynomial equation of degree n, giving n(n + 3) / 2 equations linear in the n(n + 3) / 2 unknown coefficients. If this system is non-degenerate in the sense of having a non-zero determinant, the unknown coefficients are uniquely determined and hence the polynomial equation and its curve are uniquely determined. More than this number of points would be redundant, and fewer would be insufficient to solve the |
https://en.wikipedia.org/wiki/William%20J.%20Ellison | William John Ellison (1943 - 16 March 2022) was a British mathematician who worked on number theory.
Ellison studied at the University of Cambridge, where he earned his bachelor's degree and then, after spending the academic year 1969/70 at the University of Michigan, his PhD in 1970 under John Cassels with thesis Waring's and Hilbert's 17th Problems. Subsequently, he became a postdoc at the University of Bordeaux. In 1972 he received the Leroy P. Steele Prize and a Lester Randolph Ford Award for his article "Waring's Problem“, an exposition of Waring's problem
Selected works
with Fern Ellison: Prime Numbers (Les nombres premiers, 1975). Wiley, New York 1985,
with Fern Ellison: Zahlentheorie In: Jean Dieudonné (ed.): Geschichte der Mathematik 1700 bis 1900 (Abrege d'histoire des mathematiques 1700–1900, 1978). Vieweg, Braunschweig 1985, online at archive.org, pp. 171–358,
References
1943 births
Living people
Number theorists
Alumni of the University of Cambridge
British mathematicians
20th-century British mathematicians
21st-century British mathematicians
University of Michigan alumni |
https://en.wikipedia.org/wiki/Tara%20S.%20Holm | Tara Suzanne Holm is a mathematician at Cornell University specializing in algebraic geometry and symplectic geometry.
Life and career
Holm graduated summa cum laude from Dartmouth College. Holm received her Ph.D. from the Massachusetts Institute of Technology in 2002 under the supervision of Victor Guillemin. She went on to a three-year postdoc at the University of California, Berkeley, before eventually joining the faculty at Cornell.
Awards and honors
In 2012, Holm became a fellow of the American Mathematical Society.
In 2013, Holm was awarded a Simons Fellowship.
In 2019, Holm was awarded the Sze/Hernandez Teaching prize at Cornell.
In 2019, Holm was the AWM/MAA Falconer Lecturer at MAA MathFest.
From 2011-2013, Holm was an AMS Council member at large.
Selected publications
References
Living people
American women mathematicians
Cornell University faculty
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Mathematical Society
20th-century women mathematicians
21st-century women mathematicians
Year of birth missing (living people)
20th-century American women
21st-century American women
Massachusetts Institute of Technology alumni |
https://en.wikipedia.org/wiki/Polygram%20%28geometry%29 | In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but can also include disconnected sets of edges, called a compound polygon. For example, a regular pentagram, {5/2}, has 5 sides, and the regular hexagram, {6/2} or 2{3}, has 6 sides divided into two triangles.
A regular polygram {p/q} can either be in a set of regular star polygons (for gcd(p,q) = 1, q > 1) or in a set of regular polygon compounds (if gcd(p,q) > 1).
Etymology
The polygram names combine a numeral prefix, such as penta-, with the Greek suffix -gram (in this case generating the word pentagram). The prefix is normally a Greek cardinal, but synonyms using other prefixes exist. The -gram suffix derives from γραμμῆς (grammos) meaning a line.
Generalized regular polygons
A regular polygram, as a general regular polygon, is denoted by its Schläfli symbol {p/q}, where p and q are relatively prime (they share no factors) and q ≥ 2. For integers p and q, it can be considered as being constructed by connecting every qth point out of p points regularly spaced in a circular placement.
Regular compound polygons
In other cases where n and m have a common factor, a polygram is interpreted as a lower polygon, {n/k, m/k}, with k = gcd(n,m), and rotated copies are combined as a compound polygon. These figures are called regular compound polygons.
See also
References
Cromwell, P.; Polyhedra, CUP, Hbk. 1997, . Pbk. (1999), . p. 175
Grünbaum, B. and G.C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), .
Grünbaum, B.; Polyhedra with Hollow Faces, Proc of NATO-ASI Conference on Polytopes ... etc. (Toronto 1993), ed T. Bisztriczky et al., Kluwer Academic (1994) pp. 43–70.
John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, (Chapter 26. pp. 404: Regular star-polytopes Dimension 2)
Robert Lachlan, An Elementary Treatise on Modern Pure Geometry. London: Macmillan, 1893, p. 83 polygrams.
Branko Grünbaum, Metamorphoses of polygons, published in The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History, (1994)
Types of polygons
Star symbols |
https://en.wikipedia.org/wiki/Suicide%20in%20the%20military | Suicide in the military is the act of ending one's life during or after a career in the armed forces.
While suicide rates in military organisations vary internationally, official statistics in several countries show a consistently higher risk in certain subgroups.
In the United Kingdom (UK), young serving personnel are markedly more likely than older personnel and same-age civilians to end their lives.
The risk among former military personnel is higher than among either serving personnel or the general population, according to research in Australia, Canada, the UK, and the United States (US). The risk is particularly marked among veterans who joined up at a young age.
Contrary to popular belief, deployment to a war zone has not been associated with an increased risk of suicide overall, according to research in Canada, Denmark, the UK, and the US. Participating in, or witnessing killing and wounding, however, can increase the risk.
A study of the US army found that the career stage carrying the greatest suicide risk was not deployment, but initial military training, as a time of disorientation and stress.
Individuals most at risk of suicide during or after a military career include those who: had a troubled childhood; are of low rank; have close-combat roles in war; and/or leave service soon after joining. Certain other known risk factors for suicide are common in military life, including depression, posttraumatic stress disorder, alcohol misuse, bullying and sexual harassment.
Variations in the suicide rate in military populations may also signify changes in the prevalence of related mental health problems, such as anxiety, depression, and histories of self-harm.
Incidence
Research from Australia, Canada, the UK, and the US indicates that suicide is a pervasive problem in military life, particularly after personnel leave, and that the youngest are most affected.
Serving personnel
In countries where data are collected, the rate of suicide among serving armed forces personnel varies widely. The table below presents rates among serving male personnel in the regular armed forces (i.e. excluding reserve forces) of four countries, with comparisons to the general population.
Since most military personnel are male and suicide is a rare event, it is not usually possible to calculate a statistically significant rate among female personnel. The large military of the US is an exception, where the suicide rate among serving female personnel in 2020 was 12 per 100,000.
Former personnel
Typically, former personnel are more likely than serving personnel to end their lives. The table below shows suicide rates among ex-armed forces personnel for three countries.
(The UK Ministry of Defence has announced that it will begin collecting and publishing official statistics on suicides in the ex-armed forces population from 2023.)
Research suggests that the period of maximum risk for those leaving the armed forces is in the years shortly following discha |
https://en.wikipedia.org/wiki/Consistent%20and%20inconsistent%20equations | In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity. In contrast, a linear or non linear equation system is called inconsistent if there is no set of values for the unknowns that satisfies all of the equations.
If a system of equations is inconsistent, then it is possible to manipulate and combine the equations in such a way as to obtain contradictory information, such as , or and (which implies ).
Both types of equation system, consistent and inconsistent, can be any of overdetermined (having more equations than unknowns), underdetermined (having fewer equations than unknowns), or exactly determined.
Simple examples
Underdetermined and consistent
The system
has an infinite number of solutions, all of them having (as can be seen by subtracting the first equation from the second), and all of them therefore having for any values of and .
The nonlinear system
has an infinitude of solutions, all involving
Since each of these systems has more than one solution, it is an indeterminate system.
Underdetermined and inconsistent
The system
has no solutions, as can be seen by subtracting the first equation from the second to obtain the impossible .
The non-linear system
has no solutions, because if one equation is subtracted from the other we obtain the impossible .
Exactly determined and consistent
The system
has exactly one solution: .
The nonlinear system
has the two solutions and , while
has an infinite number of solutions because the third equation is the first equation plus twice the second one and hence contains no independent information; thus any value of can be chosen and values of and can be found to satisfy the first two (and hence the third) equations.
Exactly determined and inconsistent
The system
has no solutions; the inconsistency can be seen by multiplying the first equation by 4 and subtracting the second equation to obtain the impossible .
Likewise,
is an inconsistent system because the first equation plus twice the second minus the third contains the contradiction .
Overdetermined and consistent
The system
has a solution, , because the first two equations do not contradict each other and the third equation is redundant (since it contains the same information as can be obtained from the first two equations by multiplying each through by 2 and summing them).
The system
has an infinitude of solutions since all three equations give the same information as each other (as can be seen by multiplying through the first equation by either 3 or 7). Any value of is part of a solution, with the corresponding value of being .
The nonlinear system
has the three solutions .
Overdetermined and inconsistent
The system
is inconsisten |
https://en.wikipedia.org/wiki/Plethystic%20substitution | Plethystic substitution is a shorthand notation for a common kind of substitution in the algebra of symmetric functions and that of symmetric polynomials. It is essentially basic substitution of variables, but allows for a change in the number of variables used.
Definition
The formal definition of plethystic substitution relies on the fact that the ring of symmetric functions is generated as an R-algebra by the power sum symmetric functions
For any symmetric function and any formal sum of monomials , the plethystic substitution f[A] is the formal series obtained by making the substitutions
in the decomposition of as a polynomial in the pk's.
Examples
If denotes the formal sum , then .
One can write to denote the formal sum , and so the plethystic substitution is simply the result of setting for each i. That is,
.
Plethystic substitution can also be used to change the number of variables: if , then is the corresponding symmetric function in the ring of symmetric functions in n variables.
Several other common substitutions are listed below. In all of the following examples, and are formal sums.
If is a homogeneous symmetric function of degree , then
If is a homogeneous symmetric function of degree , then
,
where is the well-known involution on symmetric functions that sends a Schur function to the conjugate Schur function .
The substitution is the antipode for the Hopf algebra structure on the Ring of symmetric functions.
The map is the coproduct for the Hopf algebra structure on the ring of symmetric functions.
is the alternating Frobenius series for the exterior algebra of the defining representation of the symmetric group, where denotes the complete homogeneous symmetric function of degree .
is the Frobenius series for the symmetric algebra of the defining representation of the symmetric group.
External links
Combinatorics, Symmetric Functions, and Hilbert Schemes (Haiman, 2002)
References
M. Haiman, Combinatorics, Symmetric Functions, and Hilbert Schemes, Current Developments in Mathematics 2002, no. 1 (2002), pp. 39–111.
Combinatorics
Symmetric functions |
https://en.wikipedia.org/wiki/List%20of%20Juventud%20Independiente%20records%20and%20statistics | This article lists various statistics related to Juventud Independiente.
All stats accurate as of 17 December 2014.
Honours
As of 6 February 2015 Juventud Independiente have won 2 Segunda División trophies.
Domestic competitions
League
Segunda División de El Salvador
Winners (2): 2008 Clausura, 2011 Clausura
Cup
CONCACAF competitions
Official titles
Individual awards
Award winners
Top Goalscorer (1)
The following players have won the Goalscorer while playing for Santa Tecla:
Jesús Toscanini (13) – Apertura 2013
Goalscorers
Most goals scored : 29 - Irvin Valdez
Most League goals: 29 - Irvin Valdez
Most League goals in a season: 14 - Jesús Toscanini, Primera Division, Apertura 2013
Most goals scored by a Juventud player in a match:
Most goals scored by a Juventud player in an International match:
Most goals scored in CONCACAF competition:
All-time top goalscorers
Note: Players in bold text are still active with Santa Tecla F.C.
Historical goals
Players
Appearances
Other appearances records
Youngest first-team player:
Oldest first-team player:
Most appearances in Primera Division:
Most appearances in International competitions:
Most appearances in CONCACAF competitions:
Most appearances in CONCACAF Champions League:
Most appearances as a foreign player in all competitions:
Most appearances as a foreign player in Primera Division:
Most consecutive League appearances:
Shortest appearance: –
Records
Scorelines
Record League victory: 6–0 v Alianza, Primera division, 27 October 2013
Record League Defeat: 0-10 v C.D. Aguila, Primera division, August 24, 2008
Record Cup victory:
Record CONCACAF Champions League Victory:
Record CONCACAF Champions League Defeat:
Sequences
Most wins in a row:
Most home wins in a row (all competitions):
Most home league wins in a row:
Most away wins in a row:
Most draws in a row:
Most home draws in a row:
Most away draws in a row:
Most defeats in a row:
Most home defeats in a row:
Most away defeats in a row:
Longest unbeaten run: 18, 2003 Season
Longest unbeaten run at home:
Longest unbeaten run away:
Longest winless run:
Longest winless run at home:
Longest winless run away:
Seasonal
Most goals in all competitions in a season: 40 goals - Apertura 2013
Most League goals scored in a season (Apertura/Clausura): 40 goals - Apertura 2013
Fewest league goals conceded in a season (Apertura/Clausura): 20 goals - Clausura 2013
Most points in a season (Apertura/Clausura): 30 points - Apertura 2013
Most League wins in a season (Apertura/Clausura): 8 wins – Clausura 2013, Apertura 2013, Clausura 2014
Most League losses in a season (Apertura/Clausura): 12 losses – Clausura 2009
Most home League wins in a season:
Most away League wins in a season:
Internationals
Most international caps (total while at club): 6 caps - Oscar Ceren - El Salvador
Attendances
Highest home attendance: v A.D. Isidro Metapan, 1,647 (May 11, 2014)
Highest away attendance:
Other
Internationals
The following players rep |
https://en.wikipedia.org/wiki/Furstenberg%20boundary | In potential theory, a discipline within applied mathematics, the Furstenberg boundary is a notion of boundary associated with a group. It is named for Harry Furstenberg, who introduced it in a series of papers beginning in 1963 (in the case of semisimple Lie groups). The Furstenberg boundary, roughly speaking, is a universal moduli space for the Poisson integral, expressing a harmonic function on a group in terms of its boundary values.
Motivation
A model for the Furstenberg boundary is the hyperbolic disc . The classical Poisson formula for a bounded harmonic function on the disc has the form
where P is the Poisson kernel. Any function f on the disc determines a function on the group of Möbius transformations of the disc by setting . Then the Poisson formula has the form
where m is the Haar measure on the boundary. This function is then harmonic in the sense that it satisfies the mean-value property with respect to a measure on the Möbius group induced from the usual Lebesgue measure of the disc, suitably normalized. The association of a bounded harmonic function to an (essentially) bounded function on the boundary is one-to-one.
Construction for semi-simple groups
In general, let G be a semi-simple Lie group and μ a probability measure on G that is absolutely continuous. A function f on G is μ-harmonic if it satisfies the mean value property with respect to the measure μ:
There is then a compact space Π, with a G action and measure ν, such that any bounded harmonic function on G is given by
for some bounded function on Π.
The space Π and measure ν depend on the measure μ (and so, what precisely constitutes a harmonic function). However, it turns out that although there are many possibilities for the measure ν (which always depends genuinely on μ), there are only a finite number of spaces Π (up to isomorphism): these are homogeneous spaces of G that are quotients of G by some parabolic subgroup, which can be described completely in terms of root data and a given Iwasawa decomposition. Moreover, there is a maximal such space, with quotient maps going down to all of the other spaces, that is called the Furstenberg boundary.
References
Potential theory |
https://en.wikipedia.org/wiki/Taishang | Taishang () are Taiwanese businesspeople who do business in mainland China. The term literally translates into English as "Taiwan Business." There are no official statistics on the number of Taishang working in mainland China. Unofficial estimates circulating in 2011 suggested that between 1 million and 3 million Republic of China nationals (including family members) lived in mainland China.
Economic impact
The more Taiwanese capital is invested in the mainland, the more it becomes part and parcel of China's growing economy. Therefore, the Taishang are a major force in the economic integration of China with the larger world-economy.
After the economic reform escalated, China has attracted a huge amount of direct investments from Taiwan and concomitantly a large number of Taiwanese entrepreneurs, managers, and professionals moved to China. China has replaced the US as Taiwan's top importer in 2003.
The change of government in Taiwan in May 2008 and the economic crisis that took hold of coastal China in late 2008 and continued throughout 2009, forced many factories in Taiwan to close down or relocate to other countries. This led to a large increase in the number of Taishang in Mainland China.
As of the end of 2008, China's Ministry of Commerce (MOC) reported Taiwanese direct investment (TDI) in China to be US$47.7 billion; Taiwan's Ministry of Economic Affairs (MOEA) Investment Commission (hereafter, Investment Commission) announced a total investment value of US$75.6 billion; Taiwan's Mainland Affairs Council (MAC) estimated the amount at between US$100 billion and US$150 billion; many private sectors in Taiwan estimated the amount to be between US$100 billion and US$200 billion.
Political impact
Collectively, the Taishang are seen as an important group in Taiwanese politics and are widely perceived to be supportive of deeper economic integration between Taiwan and mainland China. Taishang as a group are widely assumed to support Taiwan's pro-Chinese-Nationalist KMT party. Prior to the 2012 Taiwanese legislative and presidential elections, an organization controlled by the Chinese government's Taiwan Affairs Office, (ATIEM), organized discounted flights to Taiwan for Taishang to vote in Taiwanese elections.
Most Taishang are not interested in Chinese media journalism or television programmes. This is because the perception of being superior to the PRC Chinese discourages them from becoming involved in Chinese society and politics.
References
Cross-Strait relations
Politics of Taiwan |
https://en.wikipedia.org/wiki/Carole%20Lacampagne | Carole Baker Lacampagne is a retired mathematician formerly of George Washington University. She is known for her work in mathematics education and gender equality.
Career
Lacampagne received her Ed.D. from Teachers College, Columbia University in 1964. She then worked at Northern Illinois University and the National Science Foundation before moving to the Department of Education in 1991, becoming Director of the National Institute on Postsecondary Education, Libraries, and Lifelong Learning (PLLI). She then became Director of the Mathematical Sciences Education Board at the National Academies of Science before her partial retirement as an adjunct at George Washington University.
Work for gender equality
Lacampagne was actively involved in supporting women in mathematics, and became head of the Women and Mathematic's program of the Mathematical Association of America. She wrote about women and mathematics throughout her career, including her 1979 dissertation.
Awards and honors
In 2012, Lacampagne became a fellow of the American Mathematical Society.
Selected publications
Lacampagne, Carole B., et al. "Gender equity in mathematics." Handbook for achieving gender equity through education (2007): 235–253.
Lacampagne, Carole B. State of the Art: Transforming Ideas for Teaching and Learning Mathematics. US Dept. of Education, OERI Education Information, 555 New Jersey Avenue, NW, Washington, DC 20208-5641
References
Living people
American women mathematicians
20th-century American mathematicians
21st-century American mathematicians
Teachers College, Columbia University alumni
Northern Illinois University faculty
George Washington University faculty
Fellows of the American Mathematical Society
20th-century women mathematicians
21st-century women mathematicians
Year of birth missing (living people)
21st-century American women academics |
https://en.wikipedia.org/wiki/Jason%20Behrstock | Jason Alan Behrstock is a mathematician at City University of New York known for his work in geometric group theory and low-dimensional topology.
Life and career
Behrstock was born in California and was educated in California's public school system. He received his Ph.D. from State University of New York at Stony Brook in 2004. He went to work at Columbia University and the University of Utah before his time at Lehman College, City University of New York.
Awards and honors
In 2009, Behrstock was award the Feliks Gross Endowment Award by the CUNY Graduate Center, a research award for young faculty.
In 2010, Behrstock was awarded the Alfred P. Sloan Fellowship.
In 2012, Behrstock became a fellow of the American Mathematical Society.
Behrstock became a Simons Fellow in 2014.
Selected publications
Behrstock, Jason A. "Asymptotic geometry of the mapping class group and Teichmüller space". Geom. Topol. 10 (2006), 1523–1578.
Behrstock, Jason; Druţu, Cornelia; Mosher, Lee. "Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity". Math. Ann. 344 (2009), no. 3, 543–595.
Behrstock, Jason A.; Minsky, Yair N. "Dimension and rank for mapping class groups". Ann. of Math. (2) 167 (2008), no. 3, 1055–1077.
References
Living people
20th-century American mathematicians
21st-century American mathematicians
Fellows of the American Mathematical Society
Stony Brook University alumni
Columbia University faculty
University of Utah faculty
Lehman College faculty
CUNY Graduate Center faculty
City University of New York faculty
Sloan Research Fellows
Mathematicians from California
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Michael%20Dorff | Michael John Dorff is a mathematician at Brigham Young University known for his work in undergraduate research, promoting careers in math, popularizing mathematics, and harmonic mappings.
Life and career
Michael Dorff received his BA in Mathematics Education from Brigham Young University in 1986. He then taught High School math at Palos Verdes High, California, and Nurnberg High, Germany from 1986–1990. He received his MS from University of New Hampshire in 1992 followed by a Ph.D. in Mathematics from University of Kentucky in 1997. He taught at University of Missouri-Rolla as an assistant professor in the Department of Math and Statistics from 1997-2000 when he was hired by Brigham Young University as an assistant professor in the Department of Mathematics. Dorff became a full professor at BYU in 2011. He was the Chair of the Department of Mathematics at BYU from 2015–2019. Dorff visited Purdue University as an assistant professor in the Spring of 2003, Uniwersytet Marii Curie-Sklodowskiej as a U.S. Fulbright Scholar in Poland from 2005–2006, and Mathematical Association of America as a mathematician in Washington D.C. in 2012.
Dorff founded the NSF-funded Center for Undergraduate Research in Mathematics CURM and directed it from 2006–2017. He co-founded and co-directed the NSF-funded PIC (Preparation of Industrial Careers) Math program with Dr. Suzanne Weekes. He has served on several international and national advisory boards including the East African Centre of Mathematical Research in Kampala Uganda, the Mathematical Association of America (MAA), and the Council of Undergraduate Research (CUR).
His research interests include geometric function theory, complex analysis, minimal surfaces, data analytics, and preparing students for non-academic careers. In 2018, He was asked to be part of a compilation of videos about beauty at BYU. For his video, he discussed his work with soap bubbles. https://www.youtube.com/watch?v=m0jxX67ghPA
He married Sarah Watts Dorff; together they had 5 daughters. They are members of the Church of Jesus Christ of Latter-day Saints. While working at BYU, Michael was invited to give a devotional on campus on April 3, 2018. https://www.youtube.com/watch?v=E0wFmKn0KO8&feature=emb_logo
Awards and honors
2020, Council on Undergraduate Research (CUR) Fellows Award.
2019–2020, President of the Mathematical Association of America.
In 2015, The "Mathematics Programs that Make a Difference" from the AMS for CURM.
2012–2015, The Lawrence K. Egbert Teaching and Learning Faculty Fellowship at Brigham Young University.
2012, Fellow of the American Mathematical Society.
2010, The Karl G. Maeser Excellence in Teaching Award at Brigham Young University.
2010, The Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics.
Selected publications
Books:
M. Dorff, A. Henrich, and L. Pudwell. A Mathematician's Practical Guide to Mentoring Undergraduate Research. MAA Press: An Impri |
https://en.wikipedia.org/wiki/Shreveport%20Grays | The Shreveport Grays were a minor-league baseball team based from Shreveport, Louisiana. The team played in 1895 in the Texas-Southern League.
See also
Historical Minor League Statistics
References
Defunct minor league baseball teams
Baseball teams established in 1895
Grays
Professional baseball teams in Louisiana
1895 establishments in Louisiana
Defunct baseball teams in Louisiana
Baseball teams disestablished in 1895
1895 disestablishments in Louisiana
Texas-Southern League teams |
https://en.wikipedia.org/wiki/Congruence-permutable%20algebra | In universal algebra, a congruence-permutable algebra is an algebra whose congruences commute under composition. This symmetry has several equivalent characterizations, which lend to the analysis of such algebras. Many familiar varieties of algebras, such as the variety of groups, consist of congruence-permutable algebras, but some, like the variety of lattices, have members that are not congruence-permutable.
Definition
Given an algebra , a pair of congruences are said to permute when . An algebra is called congruence-permutable when each pair of congruences of permute. A variety of algebras is referred to as congruence-permutable when every algebra in is congruence-permutable.
Properties
In 1954 Maltsev gave two other conditions that are equivalent to the one given above defining a congruence-permutable variety of algebras. This initiated the study of congruence-permutable varieties.
Theorem (Maltsev, 1954)
Suppose that is a variety of algebras. The following are equivalent:
Such a term is called a Maltsev term and congruence-permutable varieties are also known as Maltsev varieties in his honor.
Examples
Most classical varieties in abstract algebra, such as groups, rings, and Lie algebras are congruence-permutable. Any variety that contains a group operation is congruence-permutable, and the Maltsev term is .
Nonexamples
Viewed as a lattice the chain with three elements is not congruence-permutable and hence neither is the variety of lattices.
References
Universal algebra |
https://en.wikipedia.org/wiki/Jurimetrics | Jurimetrics is the application of quantitative methods, and often especially probability and statistics, to law. In the United States, the journal Jurimetrics is published by the American Bar Association and Arizona State University. The Journal of Empirical Legal Studies is another publication that emphasizes the statistical analysis of law.
The term was coined in 1949 by Lee Loevinger in his article "Jurimetrics: The Next Step Forward". Showing the influence of Oliver Wendell Holmes Jr., Loevinger quoted Holmes' celebrated phrase that:
The first work on this topic is attributed to Nicolaus I Bernoulli in his doctoral dissertation De Usu Artis Conjectandi in Jure, written in 1709.
Common methods
Bayesian inference
Causal inference
Instrumental variables
Design of experiments
Vital for epidemiological studies
Generalized linear models
Ordinary least squares, logistic regression, Poisson regression
Meta-analysis
Probability distributions
Binomial distribution, hypergeometric distribution, normal distribution
Survival analysis
Kaplan-Meier estimator, proportional hazards model, Weibull distribution
Applications
Accounting fraud detection (Benford's law)
Airline deregulation
Analysis of police stops (Negative binomial regression)
Ban the Box legislation and subsequent impact on job applications
Statistical discrimination (economics)
Calorie labeling mandates and food consumption
Risk compensation
Challenging election results (Hypergeometric distribution)
Condorcet's jury theorem
Cost-benefit analysis of renewable portfolio standards for greenhouse gas abatement
Effect of compulsory schooling on future earnings
Effect of corporate board size on firm performance
Effect of damage caps on medical malpractice claims
Effect of a fiduciary standard on financial advice
False conviction rate of inmates sentenced to death
Legal evidence (Bayesian network)
Impact of "pattern-or-practice" investigations on crime
Legal informatics
Ogden tables
Optimal stopping of clinical trials
Peremptory challenges in jury selection
Personality predictors of antisocial behavior
Predictive policing
Predictors of criminal recidivism
Prevalence of Caesarean delivery and malpractice claims risk
Prosecutor's fallacy (People v. Collins)
Reference class problem
Gender quotas on corporate boards
In 2018, California's legislature passed Senate Bill 826, which requires all publicly held corporations based in the state to have a minimum number of women on their board of directors. Boards with five or fewer members must have at least two women, while boards with six or more members must have at least three women.
Using the binomial distribution, we may compute what the probability is of violating the rule laid out in Senate Bill 826 by the number of board members. The probability mass function for the binomial distribution is:where is the probability of getting successes in trials, and is the binomial coefficient. For this computation, is the probability that a perso |
https://en.wikipedia.org/wiki/List%20of%20sums%20of%20reciprocals | In mathematics and especially number theory, the sum of reciprocals generally is computed for the reciprocals of some or all of the positive integers (counting numbers)—that is, it is generally the sum of unit fractions. If infinitely many numbers have their reciprocals summed, generally the terms are given in a certain sequence and the first n of them are summed, then one more is included to give the sum of the first n+1 of them, etc.
If only finitely many numbers are included, the key issue is usually to find a simple expression for the value of the sum, or to require the sum to be less than a certain value, or to determine whether the sum is ever an integer.
For an infinite series of reciprocals, the issues are twofold: First, does the sequence of sums diverge—that is, does it eventually exceed any given number—or does it converge, meaning there is some number that it gets arbitrarily close to without ever exceeding it? (A set of positive integers is said to be large if the sum of its reciprocals diverges, and small if it converges.) Second, if it converges, what is a simple expression for the value it converges to, is that value rational or irrational, and is that value algebraic or transcendental?
Finitely many terms
The harmonic mean of a set of positive integers is the number of numbers times the reciprocal of the sum of their reciprocals.
The optic equation requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c. All solutions are given by a = mn + m2, b = mn + n2, c = mn. This equation appears in various contexts in elementary geometry.
The Fermat–Catalan conjecture concerns a certain Diophantine equation, equating the sum of two terms, each a positive integer raised to a positive integer power, to a third term that is also a positive integer raised to a positive integer power (with the base integers having no prime factor in common). The conjecture asks whether the equation has an infinitude of solutions in which the sum of the reciprocals of the three exponents in the equation must be less than 1. The purpose of this restriction is to preclude the known infinitude of solutions in which two exponents are 2 and the other exponent is any even number.
The n-th harmonic number, which is the sum of the reciprocals of the first n positive integers, is never an integer except for the case n = 1.
Moreover, József Kürschák proved in 1918 that the sum of the reciprocals of consecutive natural numbers (whether starting from 1 or not) is never an integer.
The sum of the reciprocals of the first n primes is not an integer for any n.
There are 14 distinct combinations of four integers such that the sum of their reciprocals is 1, of which six use four distinct integers and eight repeat at least one integer.
An Egyptian fraction is the sum of a finite number of reciprocals of positive integers. According to the proof of the Erdős–Graham problem, if the set of integers greater than |
https://en.wikipedia.org/wiki/Newton%E2%80%93Okounkov%20body | In algebraic geometry, a Newton–Okounkov body, also called an Okounkov body, is a convex body in Euclidean space associated to a divisor (or more generally a linear system) on a variety. The convex geometry of a Newton–Okounkov body encodes (asymptotic) information about the geometry of the variety and the divisor. It is a large generalization of the notion of the Newton polytope of a projective toric variety.
It was introduced (in passing) by Andrei Okounkov in his papers in the late 1990s and early 2000s. Okounkov's construction relies on an earlier result of Askold Khovanskii on semigroups of lattice points. Later, Okounkov's construction was generalized and systematically developed in the papers of Robert Lazarsfeld and Mircea Mustață as well as Kiumars Kaveh and Khovanskii.
Beside Newton polytopes of toric varieties, several polytopes appearing in representation theory (such as the Gelfand–Zetlin polytopes and the string polytopes of Peter Littelmann and Arkady Berenstein–Andrei Zelevinsky) can be realized as special cases of Newton–Okounkov bodies.
References
External links
Oberwolfach workshop "Okounkov bodies and applications"
BIRS workshop "Positivity of linear series and vector bundles"
BIRS workshop "Convex bodies and representation theory"
Oberwolfach workshop "New developments in Newton–Okounkov bodies"
Algebraic geometry
Multi-dimensional geometry |
https://en.wikipedia.org/wiki/Hughes-Hallett | Hughes-Hallett may refer to several people with the surname:
Charles Hughes-Hallett (1898-1985), British Royal Navy officer.
Deborah Hughes Hallett, mathematics education reformer
Francis Hughes-Hallett (1838–1903), British politician.
James Hughes-Hallett (1949-2019), British businessman and investor.
John Hughes-Hallett (1901-1972), British politician.
Kathleen Hughes-Hallett (1918-2002), Canadian fencer.
Lucy Hughes-Hallett (born 1951), British cultural historian and biographer.
Norton Hughes-Hallett (1895–1985), British army officer and cricket player.
Sir Thomas Hughes-Hallett (born 1954), British barrister, investment banker and philanthropy executive. |
https://en.wikipedia.org/wiki/Christelle%20N%27Garsanet | Christelle N'Garsanet (born June 23, 1983) is an Ivorian female professional basketball player.
Missouri statistics
Source
References
External links
Profile at eurobasket.com
Southern Illinois Salukis coaching bio
1983 births
Living people
Centers (basketball)
Illinois Central Cougars women's basketball coaches
Illinois Central Cougars women's basketball players
Ivorian women's basketball players
Missouri Tigers women's basketball players
New York Liberty draft picks
New York Liberty players
Southern Illinois Salukis women's basketball coaches
Sportspeople from Abidjan |
https://en.wikipedia.org/wiki/Optic%20equation | In number theory, the optic equation is an equation that requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c:
Multiplying both sides by abc shows that the optic equation is equivalent to a Diophantine equation (a polynomial equation in multiple integer variables).
Solution
All solutions in integers a, b, c are given in terms of positive integer parameters m, n, k by
where m and n are coprime.
Appearances in geometry
The optic equation, permitting but not requiring integer solutions, appears in several contexts in geometry.
In a bicentric quadrilateral, the inradius r, the circumradius R, and the distance x between the incenter and the circumcenter are related by Fuss' theorem according to
and the distances of the incenter I from the vertices A, B, C, D are related to the inradius according to
In the crossed ladders problem, two ladders braced at the bottoms of vertical walls cross at the height h and lean against the opposite walls at heights of A and B. We have Moreover, the formula continues to hold if the walls are slanted and all three measurements are made parallel to the walls.
Let P be a point on the circumcircle of an equilateral triangle ABC, on the minor arc AB. Let a be the distance from P to A and b be the distance from P to B. On a line passing through P and the far vertex C, let c be the distance from P to the triangle side AB. Then
In a trapezoid, draw a segment parallel to the two parallel sides, passing through the intersection of the diagonals and having endpoints on the non-parallel sides. Then if we denote the lengths of the parallel sides as a and b and half the length of the segment through the diagonal intersection as c, the sum of the reciprocals of a and b equals the reciprocal of c.
The special case in which the integers whose reciprocals are taken must be square numbers appears in two ways in the context of right triangles. First, the sum of the reciprocals of the squares of the altitudes from the legs (equivalently, of the squares of the legs themselves) equals the reciprocal of the square of the altitude from the hypotenuse. This holds whether or not the numbers are integers; there is a formula (see here) that generates all integer cases. Second, also in a right triangle the sum of the squared reciprocal of the side of one of the two inscribed squares and the squared reciprocal of the hypotenuse equals the squared reciprocal of the side of the other inscribed square.
The sides of a heptagonal triangle, which shares its vertices with a regular heptagon, satisfy the optic equation.
Other appearances
Thin lens equation
For a lens of negligible thickness and focal length f, the distances from the lens to an object, S1, and from the lens to its image, S2, are related by the thin lens formula:
.
Electrical engineering
Components of an electrical circuit or electronic circuit can be connected in what is called a series or parallel c |
https://en.wikipedia.org/wiki/Eastern%20Kings | Eastern Kings is a municipality that holds community status in Prince Edward Island, Canada. It was incorporated in 1974.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Eastern Kings had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
See also
List of communities in Prince Edward Island
References
Communities in Kings County, Prince Edward Island
Rural municipalities in Prince Edward Island |
https://en.wikipedia.org/wiki/List%20of%20Associa%C3%A7%C3%A3o%20Portuguesa%20de%20Desportos%20statistics | Associação Portuguesa de Desportos, simply known as Portuguesa, is a football team based in São Paulo, Brazil. It was founded on 14 August 1920, and is one of the five biggest clubs of the São Paulo state.
Honours
Major titles
Campeonato Brasileiro Série B: Winners (1)
2011
Campeonato Paulista: Winners (3)
1935
1936
1973
Torneio Rio – São Paulo: Winners (2)
1952
1955
Campeonato Paulista Série A2: Winners (2)
2007
2013
Minor titles
Fita Azul: Winners (3)
Torneio Sócrates: Winners (1)
1–0 Corinthians (18/01/2012)
Other titles
Taça San Izidro: 1951
Torneio Quadrangular de Istambul: 1972
Torneio Internacional do Estádio do Canindé (Torneio dos Refletores): 1981
Torneio Quadrangular de Salvador: 1951
Torneio de Belo Horizonte: 1951
Torneio Oswaldo Teixeira Duarte (Goiás): 1971
Taça Governador do Estado de São Paulo: 1976
Taça Estado de São Paulo: 1973
Torneio Início Paulista: 1935, 1947, 1996
Taça Mário Soares: 1987
Taça dos Invictos: 1955, 1974
Youth team honours
Copa São Paulo de Futebol Júnior: 1991, 2002
Campeonato Paulista sub-20: 1990, 2010
Campeonato Paulista sub-15: 2002, 2004
Rankings
Campeonato Brasileiro Série A historical ranking:
Campeonato Brasileiro Série B historical ranking:
Campeonato Paulista appearances: 92
Campeonato Paulista Série A2 appearances: 7
Copa do Brasil appearances: 15
Torneio Rio – São Paulo appearances: 19
Copa CONMEBOL appearances: 1
Copa Sudamericana appearances: 1
Landmarks
1920: Foundation;
1935: APEA's Campeonato Paulista winners;
1936: APEA's Campeonato Paulista winners;
1951: Fita Azul winners;
1952: Torneio Rio – São Paulo winners;
1953: Fita Azul winners;
1954: Fita Azul winners;
1955: Torneio Rio – São Paulo winners;
1973: Campeonato Paulista winners;
1981: Campeonato Brasileiro Série A relegation;
1983: Campeonato Brasileiro Série B promotion;
2002: Campeonato Brasileiro Série A relegation;
2006: Campeonato Paulista relegation;
2006: Campeonato Brasileiro Série B promotion;
2007: Campeonato Paulista Série A2 winners (promotion);
2008: Campeonato Brasileiro Série A relegation;
2011: Campeonato Brasileiro Série B winners (promotion);
2012: Campeonato Paulista relegation;
2013: Campeonato Paulista Série A2 winners (promotion);
2013: Campeonato Brasileiro Série A relegation;
2014: Campeonato Brasileiro Série B relegation;
2015: Campeonato Paulista relegation;
2016: Campeonato Brasileiro Série C relegation;
2017: Campeonato Brasileiro Série D relegation (no division status for the following year).
Notes
References
External links
Official website
Alma Lusa - History and statistics
Associação Portuguesa de Desportos
Brazilian football club statistics |
https://en.wikipedia.org/wiki/Niky%20Kamran | Niky Kamran (born May 22, 1959) is a Belgian-Canadian mathematician whose research concerns geometric analysis, differential geometry, and mathematical physics. He is a James McGill Professor in the Department of Mathematics and Statistics at McGill University.
Early life and education
Kamran was born in Brussels, Belgium. He earned a licentiate in mathematics from the Université libre de Bruxelles in 1980. He moved to Canada for graduate studies, earning a Ph.D. in 1984 from the University of Waterloo; his dissertation, titled Contributions to the Study of the Separation of Variables and Symmetry Operators for Relativistic Wave Equations on Curved Spacetime, was jointly supervised by Raymond G. McLenaghan and Robert Debever.
Career
In 1986 he became an assistant professor at Waterloo but then, after spending a year as a member of the Institute for Advanced Study, Princeton, New Jersey, he moved to McGill in 1989. He was promoted to full professor in 1995 and given the James McGill Professorship in 2003.
Kamran won the Aisenstadt Prize in 1992. He was elected a Fellow of the Royal Society of Canada in 2002 and was awarded a Killam Fellowship from 2006 to 2008. In 2012, he became one of the inaugural Fellows of the American Mathematical Society. In 2014, Kamran was the winner of the CRM-Fields-PIMS prize, and in 2019 he was elected a member of the Royal Academy of Science, Letters and Fine Arts of Belgium. That same academy had awarded him in 1988 the mathematics prize of its annual competition for a memoir on the equivalence problem of Élie Cartan and its applications.
References
External links
Home page
1959 births
Living people
20th-century Belgian mathematicians
21st-century Canadian mathematicians
Mathematical physicists
Differential geometers
Université libre de Bruxelles alumni
University of Waterloo alumni
Academic staff of the University of Waterloo
Academic staff of McGill University
Fellows of the American Mathematical Society
Fellows of the Royal Society of Canada |
https://en.wikipedia.org/wiki/Miltonvale%20Park | Miltonvale Park is a municipality that holds community status in Prince Edward Island, Canada. It was incorporated in 1974.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Miltonvale Park had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
See also
List of communities in Prince Edward Island
References
Communities in Queens County, Prince Edward Island
Rural municipalities in Prince Edward Island |
https://en.wikipedia.org/wiki/Tasso%20J.%20Kaper | Tasso Joost Kaper (born June 25, 1964) is an American mathematician at Boston University, where he chairs the Department of Mathematics and Statistics. His research concerns dynamical systems and applied mathematics.
Kaper's father is Hans G. Kaper, a Dutch-born retired mathematician at Argonne National Laboratory.
Tasso Kaper did his undergraduate studies at the University of Chicago, graduating in 1986. He earned a Ph.D. in 1992 from the California Institute of Technology, under the supervision of Stephen Wiggins. On finishing his doctorate, he joined the faculty at Boston University, where he has remained. He was editor-in-chief of SIAM Journal on Applied Dynamical Systems from 2005 to 2011, when he became department chair.
In 2009, both Tasso and Hans Kaper were simultaneously honored as fellows of the Society for Industrial and Applied Mathematics. In 2012, Kaper became one of the inaugural fellows of the American Mathematical Society.
References
External links
Home page
1964 births
Living people
American people of Dutch descent
20th-century American mathematicians
21st-century American mathematicians
University of Chicago alumni
California Institute of Technology alumni
Boston University faculty
Fellows of the Society for Industrial and Applied Mathematics
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/Warren%20Grove | Warren Grove is a municipality that holds community status in Prince Edward Island, Canada. It was incorporated in 1985.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Warren Grove had a population of living in of its total private dwellings, a change of from its 2016 population of . With a land area of , it had a population density of in 2021.
See also
List of communities in Prince Edward Island
References
Communities in Queens County, Prince Edward Island
Rural municipalities in Prince Edward Island |
https://en.wikipedia.org/wiki/Bangladesh%20National%20Film%20Award%20for%20Best%20Lyrics | The Bangladesh National Film Award for Best Lyrics is the highest award for lyrics of film music in Bangladesh.
List of winners
Records and statistics
Multiple wins and nominations
The following individuals received two or more Best Lyricist awards:
See also
Bangladesh National Film Award for Best Music Director
Bangladesh National Film Award for Best Music Composer
Bangladesh National Film Award for Best Male Playback Singer
Bangladesh National Film Award for Best Female Playback Singer
References
Lyrics |
https://en.wikipedia.org/wiki/Summa%20de%20arithmetica | (Summary of arithmetic, geometry, proportions and proportionality) is a book on mathematics written by Luca Pacioli and first published in 1494. It contains a comprehensive summary of Renaissance mathematics, including practical arithmetic, basic algebra, basic geometry and accounting, written for use as a textbook and reference work.
Written in vernacular Italian, the Summa is the first printed work on algebra, and it contains the first published description of the double-entry bookkeeping system. It set a new standard for writing and argumentation about algebra, and its impact upon the subsequent development and standardization of professional accounting methods was so great that Pacioli is sometimes referred to as the "father of accounting".
Contents
The Summa de arithmetica as originally printed consists of ten chapters on a series of mathematical topics, collectively covering essentially all of Renaissance mathematics. The first seven chapters form a summary of arithmetic in 222 pages. The eighth chapter explains contemporary algebra in 78 pages. The ninth chapter discusses various topics relevant to business and trade, including barter, bills of exchange, weights and measures and bookkeeping, in 150 pages. The tenth and final chapter describes practical geometry (including basic trigonometry) in 151 pages.
The book's mathematical content draws heavily on the traditions of the abacus schools of contemporary northern Italy, where the children of merchants and the middle class studied arithmetic on the model established by Fibonacci's Liber Abaci. The emphasis of this tradition was on facility with computation, using the Hindu–Arabic numeral system, developed through exposure to numerous example problems and case studies drawn principally from business and trade. Pacioli's work likewise teaches through examples, but it also develops arguments for the validity of its solutions through reference to general principles, axioms and logical proof. In this way the Summa begins to reintegrate the logical methods of classical Greek geometry into the medieval discipline of algebra.
Bookkeeping and finance
Within the chapter on business, a section entitled (Details of calculation and recording) describes the accounting methods then in use among northern-Italian merchants, including double-entry bookkeeping, trial balances, balance sheets and various other tools still employed by professional accountants. The business chapter also introduces the rule of 72 for predicting an investment's future value, anticipating the development of the logarithm by more than century. These techniques did not originate with Pacioli, who merely recorded and explained the established best practices of contemporary businesspeople in his region.
Plagiarism controversy
Pacioli explicitly states in the Summa that he contributed no original mathematical content to the work, but he also does not specifically attribute any of the material to other sources. Subsequent scholars |
https://en.wikipedia.org/wiki/Emma%20Previato | Emma Previato (November 29, 1952 – June 29, 2022) was a professor of mathematics at Boston University. Her research concerned algebraic geometry and partial differential equations.
Career
Previato received her Ph.D. from Harvard University in 1983 under David Mumford. She was a faculty member at Boston University.
Previato founded Boston University's chapters of the Mathematical Association of America and of the Association for Women in Mathematics.
Awards and honors
In 2003, she received the Mathematical Association of America Northeastern Section's Award for Distinguished College or University Teaching of Mathematics for her work in and out of the classroom, especially her mentoring of students.
In 2012, Previato became a fellow of the American Mathematical Society.
Selected publications
Previato, Emma. Hyperelliptic quasiperiodic and soliton solutions of the nonlinear Schrödinger equation. Duke Mathematical Journal 52 (1985), no. 2, 329–377.
Adams, M. R.; Harnad, J.; Previato, E. Isospectral Hamiltonian flows in finite and infinite dimensions. I. Generalized Moser systems and moment maps into loop algebras. Communications in Mathematical Physics 117 (1988), no. 3, 451–500.
Eilbeck, J. C.; Enolski, V. Z.; Matsutani, S.; Ônishi, Y.; Previato, E. Abelian functions for trigonal curves of genus three. International Mathematics Research Notices 2008, no. 1, Art. ID rnm 140, 38 pp.
References
1952 births
2022 deaths
American women mathematicians
20th-century American mathematicians
21st-century American mathematicians
Algebraic geometers
Harvard University alumni
Boston University faculty
Fellows of the American Mathematical Society
20th-century women mathematicians
21st-century women mathematicians
20th-century American women
21st-century American women
Italian emigrants to the United States
People from the Province of Rovigo |
https://en.wikipedia.org/wiki/Mei-Chi%20Shaw | Mei-Chi Shaw (; born 1955) is a professor of mathematics at the University of Notre Dame. Her research concerns partial differential equations.
Life and career
Shaw was born in Taipei, Taiwan in 1955. She graduated with an undergraduate degree in mathematics from National Taiwan University in 1977. Shaw received her PhD from Princeton University four years later in 1981, working with Joseph Kohn. She then took a postdoctoral position at Purdue University During this time, she married her husband, Hsueh-Chia Chang. In 1983, Shaw took a tenure-track position at Texas A&M University, moving to University of Houston in 1986 and finally relocating to the University of Notre Dame in 1987, first as an associate professor and then as full professor.
Awards and honors
In 2012, Shaw became a fellow of the American Mathematical Society. For 2019 she received the Stefan Bergman Prize.
Selected publications
Chen, So-Chin; Shaw, Mei-Chi. Partial differential equations in several complex variables. AMS/IP Studies in Advanced Mathematics, 19. American Mathematical Society, Providence, RI; International Press, Boston, MA, 2001. xii+380 pp.
Shaw, Mei-Chi. L2-estimates and existence theorems for the tangential Cauchy-Riemann complex. Invent. Math. 82 (1985), no. 1, 133–150.
Boas, Harold P.; Shaw, Mei-Chi Sobolev estimates for the Lewy operator on weakly pseudoconvex boundaries. Math. Ann. 274 (1986), no. 2, 221–231.
References
1955 births
Living people
American women mathematicians
20th-century American mathematicians
21st-century American mathematicians
National Taiwan University alumni
Texas A&M University faculty
University of Houston faculty
University of Notre Dame faculty
Fellows of the American Mathematical Society
20th-century Taiwanese mathematicians
Scientists from Taipei
Taiwanese emigrants to the United States
20th-century women mathematicians
21st-century women mathematicians
20th-century American women scientists
21st-century American women scientists |
https://en.wikipedia.org/wiki/Kenneth%20Millett | Kenneth C. Millett (born 1941) is a professor of mathematics at the University of California, Santa Barbara. His research concerns low-dimensional topology, knot theory, and the applications of knot theory to DNA structure; his initial is the "M" in the name of the HOMFLY polynomial.
Millett graduated from the Massachusetts Institute of Technology in 1963 with a bachelor's degree in mathematics. He earned his Ph.D. in 1967 from the University of Wisconsin under the supervision of Edward R. Fadell. After short-term instructor positions at the University of California, Los Angeles and MIT, he joined the UCSB faculty in 1969 and was promoted to professor in 1979.
Millett won the Carl B. Allendoerfer Award of the Mathematical Association of America in 1989 and the Chauvenet Prize in 1991 for a paper on knot theory with W. B. R. Lickorish.
He became a fellow of the American Association for the Advancement of Science in 2000. In 2012, he became one of the inaugural fellows of the American Mathematical Society.
Selected publications
with Eric J. Rawdon, Andrzej Stasiak:
with Michal Jamroz, Wanda Niemyska, Eric J. Rawdon, Andrzej Stasiak, Piotr Sułkowski, Joanna I. Sulkowska:
with Joanna I. Sułkowska, Eric J. Rawdon, Jose N. Onuchic, Andrzej Stasiak:
with D. Jonish:
with P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish and A. Ocneanu:
References
External links
Home page
Google scholar profile
1941 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Topologists
Massachusetts Institute of Technology School of Science alumni
University of California, Santa Barbara faculty
Fellows of the American Association for the Advancement of Science
Fellows of the American Mathematical Society |
https://en.wikipedia.org/wiki/A4%20polytope | {{DISPLAYTITLE:A4 polytope}}
In 4-dimensional geometry, there are 9 uniform polytopes with A4 symmetry. There is one self-dual regular form, the 5-cell with 5 vertices.
Symmetry
A4 symmetry, or [3,3,3] is order 120, with Conway quaternion notation +1/60[I×].21. Its abstract structure is the symmetric group S5. Three forms with symmetric Coxeter diagrams have extended symmetry, [[3,3,3]] of order 240, and Conway notation ±1/60[I×].2, and abstract structure S5×C2.
Visualizations
Each can be visualized as symmetric orthographic projections in Coxeter planes of the A4 Coxeter group, and other subgroups. Three Coxeter plane 2D projections are given, for the A4, A3, A2 Coxeter groups, showing symmetry order 5,4,3, and doubled on even Ak orders to 10,4,6 for symmetric Coxeter diagrams.
The 3D picture are drawn as Schlegel diagram projections, centered on the cell at pos. 3, with a consistent orientation, and the 5 cells at position 0 are shown solid.
Coordinates
The coordinates of uniform 4-polytopes with pentachoric symmetry can be generated as permutations of simple integers in 5-space, all in hyperplanes with normal vector (1,1,1,1,1). The A4 Coxeter group is palindromic, so repeated polytopes exist in pairs of dual configurations. There are 3 symmetric positions, and 6 pairs making the total 15 permutations of one or more rings. All 15 are listed here in order of binary arithmetic for clarity of the coordinate generation from the rings in each corresponding Coxeter diagram.
The number of vertices can be deduced here from the permutations of the number of coordinates, peaking at 5 factorial for the omnitruncated form with 5 unique coordinate values.
References
J.H. Conway and M.J.T. Guy: Four-Dimensional Archimedean Polytopes, Proceedings of the Colloquium on Convexity at Copenhagen, page 38 und 39, 1965
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 26)
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
External links
Uniform, convex polytopes in four dimensions:, Marco Möller
4-polytopes |
https://en.wikipedia.org/wiki/B4%20polytope | {{DISPLAYTITLE:B4 polytope}}
In 4-dimensional geometry, there are 15 uniform 4-polytopes with B4 symmetry. There are two regular forms, the tesseract and 16-cell, with 16 and 8 vertices respectively.
Visualizations
They can be visualized as symmetric orthographic projections in Coxeter planes of the B5 Coxeter group, and other subgroups.
Symmetric orthographic projections of these 32 polytopes can be made in the B5, B4, B3, B2, A3, Coxeter planes. Ak has [k+1] symmetry, and Bk has [2k] symmetry.
These 32 polytopes are each shown in these 5 symmetry planes, with vertices and edges drawn, and vertices colored by the number of overlapping vertices in each projective position.
The pictures are drawn as Schlegel diagram perspective projections, centered on the cell at pos. 3, with a consistent orientation, and the 16 cells at position 0 are shown solid, alternately colored.
Coordinates
The tesseractic family of 4-polytopes are given by the convex hulls of the base points listed in the following table, with all permutations of coordinates and sign taken. Each base point generates a distinct uniform 4-polytopes. All coordinates correspond with uniform 4-polytopes of edge length 2.
References
J.H. Conway and M.J.T. Guy: Four-Dimensional Archimedean Polytopes, Proceedings of the Colloquium on Convexity at Copenhagen, page 38 und 39, 1965
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 26)
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, Wiley::Kaleidoscopes: Selected Writings of H.S.M. Coxeter
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966
External links
Uniform, convex polytopes in four dimensions:, Marco Möller
4-polytopes |
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