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Jean Leray is one of the great French mathematicians of this century. His life's work divides into 3 major areas, reflected in these 3 volumes. Vol. 1, to which an Introduction in English has been contributed by A. Borel, covers Leray's seminal work in algebraic topology, where he created sheaf theory and discovered the spectral sequences. Vol. 2, with an introduction by P. Lax, covers fluid mechanics and PDE: Leray demonstrated the existence of the infinite-time extension of weak solutions of the Navier-Stokes equations; 60 years later this profound work has retained all its impact. Vol. 3, on the theory of several complex variables, has a long introduction by G. Henkin. Leray's work on the ramified Cauchy problem will stand for centuries alongside the Cauchy-Kovalevska theorem for the unramified case. ... Read more

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This volume contains papers presented at the first conference held to honor the memory of, arguably, the greatest mathematician of the twentieth century, Jean Leray. Contributors from all over the world have submitted their work to be included in this unique collection, and it reflects the esteem in which Jean Leray was, and still is held.
The book is divided into five parts: hyperbolic systems and equations; symplectic mechanics and geometry; sheaves and spectral sequences; elliptic operators and index theory; and mathematical physics.
This volume will appeal to all those who acknowledge the value of Jean Leray's work in general, and students and researchers interested in analysis, topology and geometry, mathematical physics, classical mechanics and fluid mechanics and dynamics in particular. ... Read more

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This work might have been entitled The Introduction of Planck's Constant into Mathematics, in that it introduces quantum conditions in a purely mathematical way in order to remove the singularities that arise in obtaining approximations to solutions of complex differential equations.

The book's first chapter develops the necessary mathematical apparatus: Fourier transforms, metaplectic and symplectic groups, the Maslov index, and lagrangian varieties. The second chapter orders Maslov's conceptions in a manner that avoids contraditions and creates step by step an essentially new structure-the lagrangian ayalysis.

Unexpectedly and strangely the last step requires the datum of a constant, which in applications to quantum mechanics is identified with Planck's constant. The final two chapters apply lagrangian analysis directly to the Schrödinger, the Klein-Gordon, and the Dirac equations. Magnetic field effects and even the Paschen-Back effect are taken into account.

Jean Leray-who has been professor at the Collège de France for the past thirty years-has made fundamental contributions to theoretical hydrodynamics, to the study of elliptic, hyperbolic, and analytic linear and nonlinear equations, and to algebraic topology and its applications to analysis. His motivations always had their origin in physical problems, except during World War II: As a prisoner of war in Germany for five years, he concealed his interest in mathematical applications by making fruitful investigations in the field of pure algebraic topology. ... Read more

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Most articles contain complete proofs and excellent bibliographies. For graduate students and mathematical physicists as well as mathematicians in analysis and PDEs.

The 17 invited research articles in this volume, all written by leading experts in their respective fields, are dedicated to the great French mathematician Jean Leray. A wide range of topics with significant new results---detailed proofs - are presented in the areas of partial differential equations, complex analysis, and mathematical physics.

Key subjects are treated from the mathematical physics viewpoint:

nonlinear stability of an expanding universethe compressible Euler equationspin groups and the Leray-Maslov indexLinked to the Cauchy problem: an intermediate case between effective hyperbolicity and the Levi condition, global Cauchy--Kowalewski theorem in some Gevrey classes, the analytic continuation of the solution, necessary conditions for hyperbolic systems, well posedness in the Gevrey class, uniformly diagonalizable systems and reduced dimension, and monodromy of ramified Cauchy problem.

Additional articles examine results on:

Local solvability for a system of partial differential operators, The hypoellipticity of second order operators Differential forms and Hodge theory on analytic spaces Subelliptic operators and subriemannian geometry.Contributors: R. Beals, Y. Choquet-Bruhat, F. Colombini, M. De Gosson, B. Gaveau, D. Gourdin, P. Greiner, Y. Hamada, K. Mizohata, T. Nishitani, T. Okaji, S. Ouchi, Y. Ohya, S. Spagnolo, J. Vaillant, C. Wagschal, S. Wakabayashi

The book is suitable as a reference text for graduate students and active researchers. ... Read more

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Chapters: Louison Bobet, Louis de Montfort, Jean Boucher, Henri Pinault, Francis Xavier Leray, Jeanne de Fougères, Countess of La Marche and of Angouleme, Colin Clive, Jeanne Jugan, Frédéric Guesdon, Joseph-François Lambert, Morvan Marchal, Charles de Sévigné, Jeanne Coroller-Danio, Louis de Beaupoil de Saint-Aulaire, Raffig Tullou, Jacky Duguépéroux, Marcel Loncle, Pierre Méhaignerie, Louis Tiercelin, Arthur Bernède. Source: Wikipedia. Pages: 91. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Louis ("Louison") Bobet (born Saint-Méen-le-Grand, Brittany, France, 12 March, 1925, died 13 March, 1983) was a French professional road cyclist. He was the first great French rider of the post-war period and the first rider to win the Tour de France in three successive years, from 1953 to 1955. His career included the national road championship (1950 and 1951), Milan-Sanremo (1951), Giro di Lombardia (1951), Critérium International (1951 ... Read more

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"The road stretched in a pale, straight streak, narrowing to a mere thread at the limit of vision--the only living thing in the wild darkness. All was very still. It had been raining; the wet heather and the pines gave forth scent, and little gusty shivers shook the dripping birch trees. In the pools of sky, between broken clouds, a few stars shone, and half of a thin moon was seen from time to time, like the fragment of a silver horn held up there in an invisible hand, waiting to be blown." ... Read more

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The road stretched in a pale, straight streak, narrowing to a mere thread at the limit of vision--the only living thing in the wild darkness. All was very still. It had been raining; the wet heather and the pines gave forth scent, and little gusty shivers shook the dripping birch trees. In the pools of sky, between broken clouds, a few stars shone, and half of a thin moon was seen from time to time, like the fragment of a silver horn held up there in an invisible hand, waiting to be blown. ... Read more

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Chapters: Jean-Marie Odin, James Blenk, the Church of Jesus Christ of Latter-Day Saints in Louisiana, Francis Xavier Leray, Francis Janssens, Robert William Muench, Southern District, Valeria of Milan, Episcopal Diocese of Louisiana, Augustus Marie Martin, Roman Catholic Diocese of Lafayette in Louisiana, Leo-Raymond de Neckere, Cyril of Barcelona, Orthodox Church in America Diocese of the South, Louisiana Baptist Convention, Monastery of Mary, Mother of Grace. Source: Wikipedia. Pages: 64. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Jean-Marie Odin, C.M. (February 25, 1800May 25, 1870) was a French Roman Catholic missionary, first Bishop of Galveston (1847-1861), and second Archbishop of New Orleans (1861-1870). The seventh of ten children, Jean-Marie Odin was born in Hauteville, Ambierle, to Jean and Claudine Marie (née Seyrol) Odin. He showed a strong inclination toward religion from an early age, and was sent at age 9 to study Latin under his uncle, the pastor of Noailly, whose death soon ended this period of instruction. After two years at home, he studied the classics at Roanne and Verrières before beginning his studies in philosophy at L'Argentière and Alix. Odin, while attending the Sulpician seminary in Lyon, accepted an appeal from Bishop Louis Dubourg in 1822 to join the missions in Louisiana, United States. After arriving in New Orleans in July 1822, he was sent to complete his theological studies at St. Mary's of the Barrens Seminary in Perryville, Missouri, on the outskirts of St. Louis. He entered the Congregation of the Mission (also known as the Lazarists or Vincentians) on November 8, 1822, and was later ordained to the priesthood by Bishop Dubourg on May 4, 1823. Odin then did missionary work in New Madrid and among the Native Americans along the Arkansas River, al...More: http://booksllc.net/?id=23862525 ... Read more