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Salomon Bochner
Salomon Bochner (20 August 1899 – 2 May 1982) was an Austrian mathematician, known for work in mathematical analysis, probability theory and differential geometry. Life He was born into a Jewish family in Podgórze (near Kraków), then Austria-Hungary, now Poland. Fearful of a Russian invasion in Galicia at the beginning of World War I in 1914, his family moved to Germany, seeking greater security. Bochner was educated at a Berlin gymnasium (secondary school), and then at the University of Berlin. There, he was a student of Erhard Schmidt, writing a dissertation involving what would later be called the Bergman kernel. Shortly after this, he left the academy to help his family during the escalating inflation. After returning to mathematical research, he lectured at the University of Munich from 1924 to 1933. His academic career in Germany ended after the Nazis came to power in 1933, and he left for a position at Princeton University. He was a visiting scholar at the Inst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Podgórze
Podgórze is a district of Kraków, Poland, situated on the right (southern) bank of the Vistula River, at the foot of Lasota Hill. The district was subdivided in 1990 into six new districts, see present-day districts of Kraków for more details. The name Podgórze roughly translates as ''the base of a hill''. Initially a small settlement, in the years following the First Partition of Poland the town's development was promoted by the Austria-Hungary Emperor Joseph II who in 1784 granted it the city status, as the Royal Free City of Podgórze. In the following years it was a self-governing administrative unit. After the Third Partition of Poland in 1795 and the takeover of the entire city by the Empire, Podgórze lost its political role of an independent suburb across the river from the Old Town. The administrative reform of 1810 which followed the expansion of the Duchy of Warsaw brought Podgórze together with the rest of the historic city. However, after the Congress of Vienna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigurdur Helgason (mathematician) (born 1940), Icelandic basketball player and coach
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Sigurdur Helgason may refer to: * Sigurdur Helgason (airline executive) (1921–2009), innovator in low-cost airlines * Sigurður Helgason (mathematician) (born 1927), Icelandic mathematician * Sigurður Helgason (basketball) Sigurður Már Helgason (born 29 April 1940) is an Icelandic former basketball player and businessman. He played several seasons in the Icelandic Basketball Tournament and was a member of the Icelandic national basketball team. Club career Sigu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bochner's Formula
In mathematics, Bochner's formula is a statement relating harmonic functions on a Riemannian manifold (M, g) to the Ricci curvature. The formula is named after the American mathematician Salomon Bochner. Formal statement If u \colon M \rightarrow \mathbb is a smooth function, then : \tfrac12 \Delta, \nabla u, ^2 = g(\nabla\Delta u,\nabla u) + , \nabla^2 u, ^2 + \mbox(\nabla u, \nabla u) , where \nabla u is the gradient of u with respect to g, \nabla^2 u is the Hessian of u with respect to g and \mbox is the Ricci curvature tensor.. If u is harmonic (i.e., \Delta u = 0 , where \Delta=\Delta_g is the Laplacian In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is ... with respect to the metric g ), Bochner's formula becomes : \tfrac12 \Delta, \nabla u, ^2 = , \nabla^2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernard Russell Gelbaum
Bernard Russell Gelbaum (died March 22, 2005 Laguna Beach, California) was a mathematician and academic administrator having served as a professor at the University of Minnesota, University of California, Irvine (where he was the first chair of the math department as well as acting dean and associate dean of physical sciences) and as well as emeritus professor in the Department of Mathematics, College of Arts and Sciences, University at Buffalo. When he arrived at Buffalo 1971, he served as vice president for academic affairs as well as being a math professor. Biography While still an undergraduate at Columbia University, Gelbaum served as a second lieutenant in the U.S. Signal Corps and was one of the first to liberate the Buchenwald concentration camp. He went on to get his doctorate at Princeton University in 1948. His dissertation, ''Expansions in Banach Spaces'', was supervised by Salomon Bochner Salomon Bochner (20 August 1899 – 2 May 1982) was an Austrian mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerard Washnitzer
Gerard Washnitzer (1926 in New York City – April 2, 2017) was an American mathematician specializing in algebraic geometry. Washnitzer studied at Princeton University under Emil Artin and in 1950 received a Ph.D. (''A Dirichlet Principle for analytic functions of several complex variables'') under the supervision of Salomon Bochner. In 1952 he was a C. L. E. Moore instructor at the Massachusetts Institute of Technology. After that, he was an associate professor at Johns Hopkins University and then a professor at Princeton University. From 1960 to 1961 and from 1967 to 1968 he was at the Institute for Advanced Study. In 1968, together with Paul Monsky, he introduced the Monsky–Washnitzer cohomology, which is a ''p''-adic cohomology theory In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William A
William is a masculine given name of Norman French origin.Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 276. It became very popular in the English language after the Norman conquest of England in 1066,All Things William"Meaning & Origin of the Name"/ref> and remained so throughout the Middle Ages and into the modern era. It is sometimes abbreviated "Wm." Shortened familiar versions in English include Will, Wills, Willy, Willie, Liam, Bill, and Billy. A common Irish form is Liam. Scottish diminutives include Wull, Willie or Wullie (as in Oor Wullie or the play ''Douglas''). Female forms are Willa, Willemina, Wilma and Wilhelmina. Etymology William is related to the German given name ''Wilhelm''. Both ultimately descend from Proto-Germanic ''*Wiljahelmaz'', with a direct cognate also in the Old Norse name ''Vilhjalmr'' and a West Germanic borrowing into Medieval Latin ''Willelmus''. The Proto-Germani ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herbert Scarf
Herbert Eli "Herb" Scarf (July 25, 1930 – November 15, 2015) was an American mathematical economist and Sterling Professor of Economics at Yale University. Education and career Scarf was born in Philadelphia, the son of Jewish emigrants from Ukraine and Russia, Lene (Elkman) and Louis Scarf. During his undergraduate work he finished in the top 10 of the 1950 William Lowell Putnam Mathematical Competition, the major mathematics competition between universities across the United States and Canada. He received his PhD from Princeton in 1954, supervised by Salomon Bochner. Contributions Among his notable works is a seminal paper in cooperative game in which he showed sufficiency for a core (economics) in general balanced games. Sufficiency and necessity had been previously shown by Lloyd Shapley for games where players were allowed to transfer utility between themselves freely. Necessity is shown to be lost in the generalization. Recognition Scarf received the 1973 Frederi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joseph H
Joseph is a common male given name, derived from the Hebrew Yosef (יוֹסֵף). "Joseph" is used, along with "Josef", mostly in English, French and partially German languages. This spelling is also found as a variant in the languages of the modern-day Nordic countries. In Portuguese and Spanish, the name is "José". In Arabic, including in the Quran, the name is spelled ''Yūsuf''. In Persian, the name is "Yousef". The name has enjoyed significant popularity in its many forms in numerous countries, and ''Joseph'' was one of the two names, along with ''Robert'', to have remained in the top 10 boys' names list in the US from 1925 to 1972. It is especially common in contemporary Israel, as either "Yossi" or "Yossef", and in Italy, where the name "Giuseppe" was the most common male name in the 20th century. In the first century CE, Joseph was the second most popular male name for Palestine Jews. In the Book of Genesis Joseph is Jacob's eleventh son and Rachel's first son, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harry Rauch
Harry Ernest Rauch (November 9, 1925 – June 18, 1979) was an American mathematician, who worked on complex analysis and differential geometry. He was born in Trenton, New Jersey, and died in White Plains, New York. Rauch earned his PhD in 1948 from Princeton University under Salomon Bochner with thesis ''Generalizations of Some Classic Theorems to the Case of Functions of Several Variables''. From 1949 to 1951 he was a visiting member of the Institute for Advanced Study. He was in the 1960s a professor at Yeshiva University and from the mid-1970s a professor at the City University of New York. His research was on differential geometry (especially geodesics on ''n''-dimensional manifolds), Riemann surfaces, and theta functions. In the early 1950s Rauch made fundamental progress on the ''quarter-pinched sphere conjecture'' in differential geometry. In the case of positive sectional curvature and simply connected differential manifolds, Rauch proved that, under the co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lynn Harold Loomis
__NOTOC__ Lynn Harold Loomis (25 April 1915 – 9 June 1994) was an American mathematician working on analysis. Together with Hassler Whitney, he discovered the Loomis–Whitney inequality. Loomis received his PhD in 1942 from Harvard University under Salomon Bochner with thesis ''Some Studies on Simply-Connected Riemann Surfaces: I. The Problem of Imbedding II. Mapping on the Boundary for Two Classes of Surfaces''. After completing his PhD, Loomis was a professor at Radcliffe College and from 1949 at Harvard. From 1956, he was a member of the American Academy of Arts and Sciences. Selected works Articles * * * * * *with Hassler Whitney Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, characteristic classes, and geometric integrati ...: Books *''Introduction to Abstract Harmonic Analysis'', Van Nostrand 1953 *with Shlomo St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paco Lagerstrom
Paco Axel Lagerstrom (February 24, 1914 – February 16, 1989) was an applied mathematician and aeronautical engineer. He was trained formally in mathematics, but worked for much of his career in aeronautical applications. He was known for work in applying the method of asymptotic expansion to fluid mechanics problems.Narasimha, R. (2004''Divide, conquer and unify'' Nature 432(7019), 807. Several of his works have become classics, including "Matched Asymptotic Expansions: Ideas And Techniques".Lagerstrom, P. A. (1988) Matched Asymptotic Expansions: Ideas And Techniques, Springer. Biography He was born on February 24, 1914, in Oskarshamn, Sweden. Lagerstrom earned bachelor's and master's degrees, in 1935 and 1939 respectively, at the University of Stockholm. He then came to America as a graduate student at Princeton University, earning a PhD in 1942 in mathematics under Salomon Bochner with a dissertation entitled "Measure and Integral in Partially Ordered Spaces". During thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anthony Knapp
Anthony W. Knapp (born 2 December 1941, Morristown, New Jersey) is an American mathematician at the State University of New York, Stony Brook working on representation theory, who classified the tempered representations of a semisimple Lie group. He won the Leroy P. Steele Prize for Mathematical Exposition in 1997. In 2012 he became a fellow of the American Mathematical Society. Selected publications *Book review *Book review''Elliptic curves''.nbsp;– Princeton, 1992 (Mathematical notes; 40)Zbl.0804.14013*''Representation theory of semisimple groups : An overview based on examples'', (Originally publ. 1986) Princeton: University Press, 2001. (Princeton Landmarks in Mathematics) . * Lie Groups: Beyond an Introduction, (Originally publ. 1996) Second Edition, Progress in Mathematics, Vol. 140, Birkhäuser, Boston, 2002. . *(with David A. Vogan) Cohomological Induction and Unitary Representations, Princeton Mathematical Series 45, Princeton University Press, Princeton, New Jersey, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |