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P-adic deterministic and random dynamics / par Khrennikov,, Andrei Y. Publication : [S.l.] : Springer, 2004 . 270 p. ; , This is the first monograph in the theory of p-adic (and more general non-Archimedean) dynamical systems. The theory of such systems is a new intensively developing discipline on the boundary between the theory of dynamical systems, theoretical physics, number theory, algebraic geometry and non-Archimedean analysis. Investigations on p-adic dynamical systems are motivated by physical applications (p-adic string theory, p-adic quantum mechanics and field theory, spin glasses) as well as natural inclination of mathematicians to generalize any theory as much as possible (e.g., to consider dynamics not only in the fields of real and complex numbers, but also in the fields of p-adic numbers). The main part of the book is devoted to discrete dynamical systems: cyclic behavior (especially when p goes to infinity), ergodicity, fuzzy cycles, dynamics in algebraic extensions, conjugate maps, small denominators. There are also studied p-adic random dynamical system, especially Markovian behavior (depending on p). In 1997 one of the authors proposed to apply p-adic dynamical systems for modeling of cognitive processes. In applications to cognitive science the crucial role is played not by the algebraic structure of fields of p-adic numbers, but by their tree-like hierarchical structures. In this book there is presented a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. There are also studied p-adic neural network and their applications to cognitive sciences: learning algorithms, memory recalling. Finally, there are considered wavelets on general ultrametric spaces, developed corresponding calculus of pseudo-differential operators and considered cognitive applications. Audience: This book will be of interest to mathematicians working in the theory of dynamical systems, number theory, algebraic geometry, non-Archimedean analysis as well as general functional analysis, theory of pseudo-differential operators; physicists working in string theory, quantum mechanics, field theory, spin glasses; psychologists and other scientists working in cognitive sciences and even mathematically oriented philosophers. 25 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Positivity in algebraic geometry I : classical setting : line bundles and linear series / par Lazarsfeld, R. K. Publication : [S.l.] : Springer, 2004 . 387 p. ; , This two volume work on. 24 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Positivity in algebraic geometry ii : positivity for vector bundles, and multiplier ideals / par Lazarsfeld, R. K. Publication : [S.l.] : Springer, 2004 . 385 p. ; , This two volume work on. 23 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Riemann surfaces / par Farkas, Hershel M. Publication : [S.l.] : Springer, 1991 . 388 p. ; , This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case. Basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the Abelian varities associated with these surfaces. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented. Alternate proofs for the most important results are included, showing the diversity of approaches to the subject. For this new edition, the material has been brought up-to-date, and erros have been corrected. The book should be of interest no only to pure mathematicians, but also to physicists interested in string theory and related topics. 25 cm. Date : 1991 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Serre's problem on projective modules / par Lam,, T. Y. Publication : Berlin ; | New York : Springer, 2006 . xxi, 401 p. : , Revised reissue of author's "Serre's conjecture," 1978. 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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SHEAVES ON MANIFOLDS : WITH A SHORT HISTORY "LES DEBUTS DE LA THEORIE DES FAISCEAUX" BY CHRISTIAN HOUZEL / par Kashiwara, Masaki. Publication : [S.l.] : Springer, 1990 . 512 p. ; , From the reviews: This book is devoted to the study of sheaves by microlocal methods..(it) may serve as a reference source as well as a textbook on this new subject. Houzel's historical overview of the development of sheaf theory will identify important landmarks for students and will be a pleasure to read for specialists. Math. Reviews 92a (1992). The book is clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics.(...)The book can be strongly recommended to a younger mathematician enthusiastic to assimilate a new range of techniques allowing flexible application to a wide variety of problems. Bull. L.M.S. (1992) 24 cm. Date : 1990 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Splitting deformations of degenerations of complex curves : towards the classification of atoms of degenerations, iii / par Takamura, Shigeru. Publication : [S.l.] : Springer, 2006 . 594 p. ; , The author develops a deformation theory for degenerations of complex curves; specifically, he treats deformations which induce splittings of the singular fiber of a degeneration. He constructs a deformation of the degeneration in such a way that a subdivisor is "barked" (peeled) off from the singular fiber. These "barking deformations" are related to deformations of surface singularities (in particular, cyclic quotient singularities) as well as the mapping class groups of Riemann surfaces (complex curves) via monodromies. Important applications, such as the classification of atomic degenerations, are also explained. 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Strings and geometry : proceedings of the clay mathematics institute 2002 summer school on strings and geometry, isaac newton institute, cambridge   Publication : [S.l.] Amer Mathematical Society 2004 . 376 p. , This volume is the proceedings of the 2002 Clay Mathematics Institute School on Geometry and String Theory. This month-long program was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England, and was organized by both mathematicians and physicists: A. Corti, R. Dijkgraaf, M. Douglas, J. Gauntlett, M. Gross, C. Hull, A. Jaffe and M. Reid. The early part of the school had many lectures that introduced various concepts of algebraic geometry and string theory with a focus on improving communication between these two fields. During the latter part of the program there were also a number of research level talks. This volume contains a selection of expository and research articles by lecturers at the school and highlights some of the current interests of researchers working at the interface between string theory and algebraic geometry. The topics covered include manifolds of special holonomy, supergravity, supersymmetry, D-branes, the McKay correspondence and the Fourier-Mukai transform. The book is suitable for graduate students and research mathematicians interested in relations between mathematical physics and algebraic geometry. 25 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Topological methods in algebraic geometry / par Hirzebruch,, Friedrich. Publication : Berlin ; | New York : Springer, 1995 . ix, 234 p. ; , "Reprint of the 1978 edition." | "Originally published as vol. 131 of the Grundlehren der mathematischen Wissenschaften"--T.p. verso. 24 cm. Date : 1995 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Using algebraic geometry par Cox, David A. Publication : New York Springer 2005 . xii-572 p. , The discovery of new algorithms for dealing with polynomial equations, and their implementation on fast, inexpensive computers, has revolutionized algebraic geometry and led to exciting new applications in the field. This book details many uses of algebraic geometry and highlights recent applications of Grobner bases and resultants. This edition contains two new sections, a new chapter, updated references and many minor improvements throughout. 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Combinatorial convexity and algebraic geometry / par Ewald, Günter, Publication : New York : Springer, 1996 . xiv, 372 pages : 24 cm. Date : 1996 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Geometric algebra for computer science : an object-oriented approach to geometry / par Dorst, Leo, Publication : . 1 online resource (xxxv, 626 pages) : Disponibilité :  http://www.sciencedirect.com/science/book/9780123694652,

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Unstable singularities and randomness : their importance in the complexity of physical, biological, and social sciences / par Zbilut, Joseph P., Publication : . 1 online resource (xiv, 237 pages) : Disponibilité :  http://www.sciencedirect.com/science/book/9780444516138,

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Introduction to algebraic geometry and algebraic groups / par Demazure, Michel. Publication : . 1 online resource (xiv, 357 pages) , Translation of Groupes algébrigues, volume 1, chapters 1-2. | Includes indexes. Disponibilité :  http://www.sciencedirect.com/science/book/9780444854438,  http://www.sciencedirect.com/science/publication?issn=03040208&volume=39,

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