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Morris Hirsch
Morris William Hirsch (born June 28, 1933) is an American mathematician, formerly at the University of California, Berkeley. A native of Chicago, Illinois, Hirsch attained his doctorate from the University of Chicago in 1958, under supervision of Edwin Spanier and Stephen Smale. His thesis was entitled ''Immersions of Manifolds''. In 2012 he became a fellow of the American Mathematical Society. Hirsch had 23 doctoral students, including William Thurston, William Goldman, and Mary Lou Zeeman. Selected works *with Stephen Smale and Robert L. Devaney: ''Differential equations, dynamical systems and an introduction to chaos'', Academic Press 2004 (2nd edition3rd edition, 2013*with Stephen Smale: ''Differential equations, dynamical systems and linear algebra'', Academic Press 1974 *Differential Topology, Springer 1976, 1997 *with Barry MazurSmoothings of piecewise linear manifolds Princeton University Press 1974 *with Charles C. Pugh, Michael Shub: Invariant Manifolds, Springer 1977 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chicago, Illinois
(''City in a Garden''); I Will , image_map = , map_caption = Interactive Map of Chicago , coordinates = , coordinates_footnotes = , subdivision_type = Country , subdivision_name = United States , subdivision_type1 = State , subdivision_type2 = Counties , subdivision_name1 = Illinois , subdivision_name2 = Cook and DuPage , established_title = Settled , established_date = , established_title2 = Incorporated (city) , established_date2 = , founder = Jean Baptiste Point du Sable , government_type = Mayor–council , governing_body = Chicago City Council , leader_title = Mayor , leader_name = Lori Lightfoot ( D) , leader_title1 = City Clerk , leader_name1 = Anna Valencia ( D) , unit_pref = Imperial , area_footnotes = , area_tot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, ''The Daily Princetonian'', and later added book publishing to it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Chicago
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1933 Births
Events January * January 11 – Sir Charles Kingsford Smith makes the first commercial flight between Australia and New Zealand. * January 17 – The United States Congress votes in favour of Philippines independence, against the wishes of U.S. President Herbert Hoover. * January 28 – "Pakistan Declaration": Choudhry Rahmat Ali publishes (in Cambridge, UK) a pamphlet entitled ''Now or Never; Are We to Live or Perish Forever?'', in which he calls for the creation of a Muslim state in northwest India that he calls " Pakstan"; this influences the Pakistan Movement. * January 30 ** National Socialist German Workers Party leader Adolf Hitler is appointed Chancellor of Germany by President of Germany Paul von Hindenburg. ** Édouard Daladier forms a government in France in succession to Joseph Paul-Boncour. He is succeeded on October 26 by Albert Sarraut and on November 26 by Camille Chautemps. February * February 1 – Adolf Hitler gives his "Proclamation to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Google Scholar
Google Scholar is a freely accessible web search engine that indexes the full text or metadata of scholarly literature across an array of publishing formats and disciplines. Released in beta in November 2004, the Google Scholar index includes peer-reviewed online academic journals and books, conference papers, theses and dissertations, preprints, abstracts, technical reports, and other scholarly literature, including court opinions and patents. Google Scholar uses a web crawler, or web robot, to identify files for inclusion in the search results. For content to be indexed in Google Scholar, it must meet certain specified criteria. An earlier statistical estimate published in PLOS One using a mark and recapture method estimated approximately 80–90% coverage of all articles published in English with an estimate of 100 million.''Trend Watch'' (2014) Nature 509(7501), 405 – discussing Madian Khabsa and C Lee Giles (2014''The Number of Scholarly Documents on the Public Web'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Whitney Embedding Theorem
In mathematics, particularly in differential topology, there are two Whitney embedding theorems, named after Hassler Whitney: *The strong Whitney embedding theorem states that any differentiable manifold, smooth real numbers, real -dimension (mathematics), dimensional manifold (required also to be Hausdorff space, Hausdorff and second-countable) can be smooth map, smoothly embedding, embedded in the real coordinate space, real -space (), if . This is the best linear bound on the smallest-dimensional Euclidean space that all -dimensional manifolds embed in, as the real projective spaces of dimension cannot be embedded into real -space if is a power of two (as can be seen from a characteristic class argument, also due to Whitney). *The weak Whitney embedding theorem states that any continuous function from an -dimensional manifold to an -dimensional manifold may be approximated by a smooth embedding provided . Whitney similarly proved that such a map could be approximated by an imm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Immersion (mathematics)
In mathematics, an immersion is a differentiable function between differentiable manifolds whose differential (or pushforward) is everywhere injective. Explicitly, is an immersion if :D_pf : T_p M \to T_N\, is an injective function at every point ''p'' of ''M'' (where ''TpX'' denotes the tangent space of a manifold ''X'' at a point ''p'' in ''X''). Equivalently, ''f'' is an immersion if its derivative has constant rank equal to the dimension of ''M'': :\operatorname\,D_p f = \dim M. The function ''f'' itself need not be injective, only its derivative must be. A related concept is that of an embedding. A smooth embedding is an injective immersion that is also a topological embedding, so that ''M'' is diffeomorphic to its image in ''N''. An immersion is precisely a local embedding – that is, for any point there is a neighbourhood, , of ''x'' such that is an embedding, and conversely a local embedding is an immersion. For infinite dimensional manifolds, this is sometimes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homotopy Principle
In mathematics, the homotopy principle (or h-principle) is a very general way to solve partial differential equations (PDEs), and more generally partial differential relations (PDRs). The h-principle is good for underdetermined PDEs or PDRs, such as the immersion problem, isometric immersion problem, fluid dynamics, and other areas. The theory was started by Yakov Eliashberg, Mikhail Gromov and Anthony V. Phillips. It was based on earlier results that reduced partial differential relations to homotopy, particularly for immersions. The first evidence of h-principle appeared in the Whitney–Graustein theorem. This was followed by the Nash–Kuiper isometric ''C''1 embedding theorem and the Smale–Hirsch immersion theorem. Rough idea Assume we want to find a function ''ƒ'' on R''m'' which satisfies a partial differential equation of degree ''k'', in co-ordinates (u_1,u_2,\dots,u_m). One can rewrite it as :\Psi(u_1,u_2,\dots,u_m, J^k_f)=0 where J^k_f stands for all parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Structure
In mathematics, an ''n''-dimensional differential structure (or differentiable structure) on a set ''M'' makes ''M'' into an ''n''-dimensional differential manifold, which is a topological manifold with some additional structure that allows for differential calculus on the manifold. If ''M'' is already a topological manifold, it is required that the new topology be identical to the existing one. Definition For a natural number ''n'' and some ''k'' which may be a non-negative integer or infinity, an ''n''-dimensional ''C''''k'' differential structure is defined using a ''C''''k''-atlas, which is a set of bijections called charts between a collection of subsets of ''M'' (whose union is the whole of ''M''), and a set of open subsets of \mathbb^: :\varphi_:M\supset W_\rightarrow U_\subset\mathbb^ which are ''C''''k''-compatible (in the sense defined below): Each such map provides a way in which certain subsets of the manifold may be viewed as being like open subsets of \mathbb^ but th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chern's Conjecture (affine Geometry)
Chern's conjecture for affinely flat manifolds was proposed by Shiing-Shen Chern in 1955 in the field of affine geometry. As of 2018, it remains an unsolved mathematical problem. Chern's conjecture states that the Euler characteristic of a compact affine manifold vanishes. Details In case the connection ∇ is the Levi-Civita connection of a Riemannian metric, the Chern–Gauss–Bonnet formula: : \chi(M) = \left ( \frac \right )^n \int_M \operatorname(K) implies that the Euler characteristic is zero. However, not all flat torsion-free connections on T M admit a compatible metric, and therefore, Chern–Weil theory cannot be used in general to write down the Euler class in terms of the curvature. History The conjecture is known to hold in several special cases: * when a compact affine manifold is 2-dimensional (as shown by Jean-Paul Benzécri in 1955, and later by John Milnor in 1957) * when a compact affine manifold is complete (i.e., affinely diffeomorphic to a quotien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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