American mathematician
Edward James McShane (May 10, 1904 – June 1, 1989) was an Americanmathematician noted for his advancements of thecalculus of variations ,integration theory ,stochastic calculus , and exteriorballistics .[ 2] [ 3] [ 4] [ 5] McShane–Whitney extension theorem [ 6] McShane integral .McShane was professor of mathematics at theUniversity of Virginia ,[ 2] [ 4] American Mathematical Society ,[ 2] [ 3] [ 5] Mathematical Association of America ,[ 5] National Science Board [ 5] National Academy of Sciences and theAmerican Philosophical Society .[ 2] [ 3] [ 5] [ 7]
McShane was born and raised in New Orleans.He received his bachelor of engineering and Bachelor of Science degrees fromTulane University in 1925, following with a M.S. degree from Tulane in 1927. McShane received his Ph.D. in mathematics from theUniversity of Chicago .[ 2] [ 3] Victor Klee ,Billy James Pettis , and David Lowdenslager, who collaborated withHenry Helson . McShane died of congestive heart failure at the University of Virginia hospital.[ 3]
Selected publications [ edit ] McShane, E. J. (1931)."A remark concerning the necessary condition of Weierstrass" .Bulletin of the American Mathematical Society .37 (8):631– 632.doi :10.1090/S0002-9904-1931-05233-2 MR 1562210 . McShane, E. J. (1933)."Parametrizations of saddle surfaces, with application to the problem of plateau" Transactions of the American Mathematical Society .35 (3):716– 733.doi :10.1090/S0002-9947-1933-1501713-3 MR 1501713 . McShane, E. J. (1934)."On the minimizing property of the harmonic function" .Bulletin of the American Mathematical Society .40 (8):593– 598.doi :10.1090/S0002-9904-1934-05923-8 MR 1562913 . McShane, E. J. (1934)."Extension of range of functions" .Bulletin of the American Mathematical Society .40 (12):837– 842.doi :10.1090/S0002-9904-1934-05978-0 MR 1562984 . McShane, E. J. (1935)."Existence theorems for double integral problems of the calculus of variations" .Transactions of the American Mathematical Society .38 (3):549– 563.doi :10.1090/S0002-9947-1935-1501828-1 MR 1501828 . McShane, E. J. (1937)."Jensen's inequality" .Bulletin of the American Mathematical Society .43 (8):521– 527.doi :10.1090/S0002-9904-1937-06588-8 MR 1563579 . McShane, E. J. (1939)."On the uniqueness of the solutions of differential equations" .Bulletin of the American Mathematical Society .45 (10):755– 757.doi :10.1090/S0002-9904-1939-07076-6 MR 0000328 . McShane, E. J. (1940)."A remark concerning sufficiency theorems for the problem of Bolza" .Bull. Amer. Math. Soc .46 (8):698– 701.doi :10.1090/S0002-9904-1940-07284-2 McShane, E. J. (1942)."On Perron integration" .Bulletin of the American Mathematical Society .48 (10):718– 726.doi :10.1090/S0002-9904-1942-07766-4 MR 0007040 . McShane, E. J. (1950)."Linear functionals on certain Banach spaces" Proceedings of the American Mathematical Society .1 (3):402– 408.doi :10.1090/S0002-9939-1950-0036448-5 MR 0036448 . McShane, E. J. (1956)."On Stieltjes integration" Proceedings of the American Mathematical Society .7 :69– 74.doi :10.1090/S0002-9939-1956-0075280-9 MR 0075280 . McShane, E. J. (1962)."The Radius of Gyration of a Convex Body" Proceedings of the American Mathematical Society .13 (6):922– 926.doi :10.2307/2034088 .JSTOR 2034088 .S2CID 122564457 . McShane, E. J. (1963)."Integrals devised for special purposes" .Bulletin of the American Mathematical Society .69 (5):597– 627.doi :10.1090/S0002-9904-1963-10964-7 MR 0162905 . McShane, E. J. (1944).Integration . Princeton: Princeton University Press. [ 8] 2nd edition . 1947.McShane, E. J. (1953).Order-preserving maps and integration processes ISBN 0691095825 {{cite book }}:ISBN / Date incompatibility (help ) McShane, E. J.;Kelley, John L. ; Reno, Franklin V. (1953).Exterior ballistics . The University of Denver Press. [ 9] McShane, E. J.; Botts, Truman Arthur (1959).Real analysis . Princeton: Van Nostrand.Bibcode :1959rean.book.....M . [ 10] McShane, Edward James; Botts, Truman Arthur (2013).Dover reprint ISBN 9780486165677 McShane, E. J. (1969).A Riemann-type integral that includes Lebesgue-Stieltjes, Bochner and stochastic integrals ISBN 9780821812884 {{cite book }}: CS1 maint: postscript (link )[ 11] McShane, E. J. (1974).Stochastic calculus and stochastic models ISBN 9781483218779 [ 12] McShane, E. J. (1983).Unified integration . Orlando: Academic Press. [ 13] Courant, R. (1937),Differential and Integral Calculus , vol. I, translated by McShane, E. J. (2nd ed.), New York: Interscience,ISBN 978-4-87187-838-8 {{citation }}:ISBN / Date incompatibility (help ) Courant, R. (1936),Differential and Integral Calculus , vol. II, translated by McShane, E. J., New York: Interscience,ISBN 978-4-87187-835-7 {{citation }}:ISBN / Date incompatibility (help ) ^ McShane, E. J. (1952)."Partial Orderings and Moore-Smith Limits" Amer. Math. Monthly .59 (1):1– 11.doi :10.2307/2307181 .JSTOR 2307181 . ^a b c d e National Academies Press: Biographical Memoirs: Edward James McShane, By Leonard D. Berkovitz and Wendell H. Fleming ^a b c d e New York Times:Edward McShane, 85, Mathematician, Dies; June 06, 1989 ^a b New York Times:4 New Members Named To National Science Boards;July 17, 1962 ^a b c d e Proceedings of the American Philosophical Society, vol 140, no. 4, Dec 1996, pp. 572–578 ^ Chen, Li (2010). "Smoothness and Smooth Extensions (I): Generalization of MWK Functions and Gradually Varied Functions".arXiv :1005.3727 math.NA ]. ^ "E. J. McShane" .www.nasonline.org . Retrieved2022-12-07 .^ Agnew, R. P. (1945)."Review ofIntegration by E. J. McShane" .Bull. Amer. Math. Soc .51 :51– 53.doi :10.1090/S0002-9904-1945-08285-8 ^ Howarth, L. (1954)."Review:Exterior ballistics by E. J. McShane, J. L. Kelley, and F. V. Reno" (PDF) .Bull. Amer. Math. Soc .60 (3):274– 276.doi :10.1090/s0002-9904-1954-09802-6 ^ Olmsted, John M. H. (1961)."Review ofReal analysis by E. J. McShane and T. A. Botts" .Bull. Amer. Math. Soc .67 :86– 89.doi :10.1090/S0002-9904-1961-10506-5 ^ Henstock, R. (March 1971)."Book Review:A Riemann-type integral that includes Lebesgues-Stieltjes Bochner and stochastic integrals by E. J. Shane" Bulletin of the London Mathematical Society .3 (1): 105.doi :10.1112/blms/3.1.105a .^ Stroock, D. W. (1976)."joint review ofThe theory of stochastic processes , vol. I by I. I. Gihman and A. V. Skorohod;Stochastic calculus and stochastic models by E. J. McShane;Mesures cylindriques, espaces de Wiener, et fonctions aléatoires Gaussiennes by Albert Badrikian and Simone Chevet;Almost sure convergence by William F. Stout;Integration in Hilbert space by A. V. Skorohod" .Bull. Amer. Math. Soc .82 :227– 232.doi :10.1090/S0002-9904-1976-13996-1 MR 1566848 .^ Saab, Elias (1985)."Review ofUnified integration by E. J. McShane" .Bull. Amer. Math. Soc .13 :68– 70.doi :10.1090/S0273-0979-1985-15369-8
1888–1900 1901–1924 1925–1950 1951–1974 1975–2000 2001–present
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