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  • 1
    Online Resource
    Online Resource
    Limit Theorems for Unions of Random Closed Sets (1993)
    Berlin, Heidelberg : Springer Berlin Heidelberg
    Details Availability
    Keywords: Distribution (Probability theory) ; Mathematics ; Probabilities. ; Probability Theory and Stochastic Processes ; Mathematics ; Zufällige Menge ; Grenzwertsatz
    Description / Table of Contents: The book concerns limit theorems and laws of large numbers for scaled unionsof independent identically distributed random sets. These results generalizewell-known facts from the theory of extreme values. Limiting distributions (called union-stable) are characterized and found explicitly for many examples of random closed sets. The speed of convergence in the limit theorems for unions is estimated by means of the probability metrics method.It includes the evaluation of distances between distributions of random sets constructed similarly to the well-known distances between distributions of random variables. The techniques include regularly varying functions, topological properties of the space of closed sets, Choquet capacities, convex analysis and multivalued functions. Moreover, the concept of regular variation is elaborated for multivalued (set-valued) functions. Applications of the limit theorems to simulation of random sets, statistical tests, polygonal approximations of compacts, limit theorems for pointwise maxima of random functions are considered. Several open problems are mentioned. Addressed primarily to researchers in the theory of random sets, stochastic geometry and extreme value theory, the book will also be of interest to applied mathematicians working on applications of extremal processes and their spatial counterparts. The book is self-contained, and no familiarity with the theory of random sets is assumed
    Type of Medium: Online Resource
    Pages: Online-Ressource (X, 158 p, online resource)
    ISBN: 9783540481119 , 9783540573937
    Series Statement: Lecture Notes in Mathematics 1561
    URL: https://doi.org/10.1007/BFb0073527
    URL: http://dx.doi.org/10.1007/BFb0073527
    URL: https://swbplus.bsz-bw.de/bsz404653332cov.jpg
    URL: https://zbmath.org/?q=an:0790.60015
    DOI: 10.1007/BFb0073527
    RVK:
    SI 850
    Language: English
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  • 2
    Online Resource
    Online Resource
    Singularity Theory and Equivariant Symplectic Maps (1993)
    Berlin, Heidelberg : Springer Berlin Heidelberg
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    Keywords: Global analysis (Mathematics) ; Cell aggregation Mathematics ; Mathematics ; Manifolds (Mathematics). ; Mathematical analysis. ; Manifolds and Cell Complexes (incl. Diff.Topology) ; Analysis ; Mathematics ; Symplektische Abbildung ; Äquivariante Abbildung ; Singularität
    Description / Table of Contents: The monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighborhood of a fixed point.The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits ofa symplectic map and critical points of an action functional. New results onsingularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is that a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points) is presented. Topics include: bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps. The monograph will appeal to researchers and graduate students in the areas of symplectic maps, Hamiltonian systems, singularity theory and equivariant bifurcation theory
    Type of Medium: Online Resource
    Pages: Online-Ressource (VI, 230 p, online resource)
    ISBN: 9783540480402 , 9783540572961
    Series Statement: Lecture Notes in Mathematics 1558
    URL: https://doi.org/10.1007/BFb0073471
    URL: http://dx.doi.org/10.1007/BFb0073471
    URL: https://swbplus.bsz-bw.de/bsz036607665cov.jpg
    URL: https://zbmath.org/?q=an:0799.58009
    URL: http://d-nb.info/931460301/04
    DOI: 10.1007/BFb0073471
    RVK:
    SI 850
    Language: English
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  • 3
    Online Resource
    Online Resource
    Difference Spaces and Invariant Linear Forms (1994)
    Berlin, Heidelberg : Springer Berlin Heidelberg
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    Keywords: Global analysis (Mathematics) ; Mathematics ; Topological Groups ; Mathematical analysis. ; Lie groups. ; Topological Groups, Lie Groups ; Analysis ; Mathematics ; Linearform ; Harmonische Analyse
    Description / Table of Contents: Difference spaces arise by taking sums of finite or fractional differences. Linear forms which vanish identically on such a space are invariant in a corresponding sense. The difference spaces of L2 (Rn) are Hilbert spaces whose functions are characterized by the behaviour of their Fourier transforms near, e.g., the origin. One aim is to establish connections between these spaces and differential operators, singular integral operators and wavelets. Another aim is to discuss aspects of these ideas which emphasise invariant linear forms on locally compact groups. The work primarily presents new results, but does so from a clear, accessible and unified viewpoint, which emphasises connections with related work
    Type of Medium: Online Resource
    Pages: Online-Ressource (XII, 192 p, online resource)
    ISBN: 9783540486527 , 9783540583233
    Series Statement: Lecture Notes in Mathematics 1586
    URL: https://doi.org/10.1007/BFb0073511
    URL: http://dx.doi.org/10.1007/BFb0073511
    URL: https://swbplus.bsz-bw.de/bsz404653618cov.jpg
    URL: https://zbmath.org/?q=an:0830.43003
    URL: http://www.gbv.de/dms/bowker/toc/9783540583233.pdf
    DOI: 10.1007/BFb0073511
    RVK:
    SI 850
    Language: English
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  • 4
    Online Resource
    Online Resource
    Chaos and Quantum Chaos : Proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics Held at Blydepoort, Eastern Transvaal South Africa, 13-24 January 1992 (1992)
    Berlin, Heidelberg : Springer Berlin Heidelberg
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    Keywords: Physics ; Mathematics ; Statistical physics ; Dynamical systems ; Continuum mechanics ; Physics ; Mathematics ; Engineering ; Physics ; Complexity ; Mathematics, general
    Description / Table of Contents: Until now the important concept of quantum chaos has remained somewhat ill defined. This volume tackles the ubiquitous borderline between classical andquantum mechanics, studying in particular the semiclassical limit of chaotic systems. The effects of disorder from dynamics and their relation to stochastic systems, quantum coherence effects in mesoscopic systems, and the relevant theoretical approaches are fruitfully combined in this volume. The major paradigms of what is called quantum chaos, random matrix theory and applications to condensed matter and nuclear physics are presented. Detailed discussions of experimental work with particular emphasis on atomic physics are included. The book is highly recommended for graduate-student seminars
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (XIV, 330 p. 43 illus)
    Edition: Springer eBook Collection. Physics and Astronomy
    ISBN: 9783540474951 , 9783540562535
    Series Statement: Lecture Notes in Physics 411
    URL: http://dx.doi.org/10.1007/3-540-56253-2
    DOI: 10.1007/3-540-56253-2
    Language: English
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  • 5
    Online Resource
    Online Resource
    Classical Diophantine Equations (1993)
    Berlin, Heidelberg : Springer Berlin Heidelberg
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    Keywords: Mathematics ; Number theory ; Number Theory ; Mathematics ; Diophantische Gleichung
    Description / Table of Contents: The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, now that the book appears in English, close studyand emulation. In particular those emphases allow him to devote the eighth chapter to an analysis of the interrelationship of the class number of algebraic number fields involved and the bounds on the heights of thesolutions of the diophantine equations. Those ideas warrant further development. The final chapter deals with effective aspects of the Hilbert Irreducibility Theorem, harkening back to earlier work of the author. There is no other congenial entry point to the ideas of the last two chapters in the literature
    Type of Medium: Online Resource
    Pages: Online-Ressource (XII, 236 p, online resource)
    ISBN: 9783540480839 , 9783540573593
    Series Statement: Lecture Notes in Mathematics 1559
    URL: https://doi.org/10.1007/BFb0073786
    URL: http://dx.doi.org/10.1007/BFb0073786
    URL: https://swbplus.bsz-bw.de/bsz404653375cov.jpg
    URL: https://zbmath.org/?q=an:0787.11008
    DOI: 10.1007/BFb0073786
    RVK:
    SI 850
    Language: English
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  • 6
    Online Resource
    Online Resource
    Basic Analysis of Regularized Series and Products (1993)
    Berlin, Heidelberg : Springer Berlin Heidelberg
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    Keywords: Global analysis (Mathematics) ; Global differential geometry ; Mathematics ; Number theory ; Mathematical analysis. ; Geometry, Differential. ; Analysis ; Number Theory ; Differential Geometry ; Mathematics ; Regularisierte Reihe ; Regularisiertes Produkt
    Description / Table of Contents: Analytic number theory and part of the spectral theory of operators (differential, pseudo-differential, elliptic, etc.) are being merged under amore general analytic theory of regularized products of certain sequences satisfying a few basic axioms. The most basic examples consist of the sequence of natural numbers, the sequence of zeros with positive imaginary part of the Riemann zeta function, and the sequence of eigenvalues, say of a positive Laplacian on a compact or certain cases of non-compact manifolds. The resulting theory is applicable to ergodic theory and dynamical systems; to the zeta and L-functions of number theory or representation theory and modular forms; to Selberg-like zeta functions; andto the theory of regularized determinants familiar in physics and other parts of mathematics. Aside from presenting a systematic account of widely scattered results, the theory also provides new results. One part of the theory deals with complex analytic properties, and another part deals with Fourier analysis. Typical examples are given. This LNM provides basic results which are and will be used in further papers, starting with a general formulation of Cram r's theorem and explicit formulas. The exposition is self-contained (except for far-reaching examples), requiring only standard knowledge of analysis
    Type of Medium: Online Resource
    Pages: Online-Ressource (X, 130 p, online resource)
    ISBN: 9783540481935 , 9783540574880
    Series Statement: Lecture Notes in Mathematics 1564
    URL: https://doi.org/10.1007/BFb0077194
    URL: http://dx.doi.org/10.1007/BFb0077194
    URL: https://swbplus.bsz-bw.de/bsz036607487cov.jpg
    URL: https://zbmath.org/?q=an:0788.30003
    URL: http://d-nb.info/931557550/04
    DOI: 10.1007/BFb0077194
    RVK:
    SI 850
    Language: English
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  • 7
    Online Resource
    Online Resource
    Complex Fluids : Proceedings of the XII Sitges Conference Sitges, Barcelona, Spain, 1-5 June 1992 (1993)
    Berlin, Heidelberg : Springer Berlin Heidelberg
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    Keywords: Physics ; Physical chemistry ; Atoms ; Physics ; Chemistry, Physical organic ; Plasma (Ionized gases) ; Physics ; Physical Chemistry ; Atoms, Molecules, Clusters and Plasmas
    Description / Table of Contents: This set of survey talks presented to graduate students serves as a thorough exposition of the subject. The study of complex fluids (with internal structure) is important for theoretical purposes but also, and maybe even more so, for applied research. The reader will find papers on colloid mixtures, the structure of DNA mesophases, ferrofluids, chain dynamics, liquid crystals, computer simulations of macromolecules, fluidization, emulsions, relaxations and many other related topics
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (XIII, 416 p. 83 illus)
    Edition: Springer eBook Collection. Physics and Astronomy
    ISBN: 9783540475521 , 9783540563969
    Series Statement: Lecture Notes in Physics 415
    URL: http://dx.doi.org/10.1007/3-540-56396-2
    URL: https://zbmath.org/?q=an:0782.76005
    DOI: 10.1007/3-540-56396-2
    Language: English
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  • 8
    Online Resource
    Online Resource
    Dirichlet Forms : Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Varenna, Italy, June 8–19, 1992 (1993)
    Berlin, Heidelberg : Springer Berlin Heidelberg
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    Keywords: Global analysis (Mathematics) ; Distribution (Probability theory) ; Mathematics ; Probabilities. ; Mathematical analysis. ; Analysis ; Probability Theory and Stochastic Processes ; Mathematics ; Konferenzschrift 1992 ; Dirichletsche Form
    Description / Table of Contents: The theory of Dirichlet forms has witnessed recently some very important developments both in theoretical foundations and in applications (stochasticprocesses, quantum field theory, composite materials,..). It was therefore felt timely to have on this subject a CIME school, in which leading experts in the field would present both the basic foundations of the theory and some of the recent applications. The six courses covered the basic theory and applications to: - Stochastic processes and potential theory (M. Fukushima and M. Roeckner) - Regularity problems for solutions to elliptic equations in general domains (E. Fabes and C. Kenig) - Hypercontractivity of semigroups, logarithmic Sobolev inequalities and relation to statistical mechanics (L. Gross and D. Stroock). The School had a constant and active participation of young researchers, both from Italy and abroad
    Type of Medium: Online Resource
    Pages: Online-Ressource (VIII, 252 p, online resource)
    ISBN: 9783540481515 , 9783540574217
    Series Statement: Lecture Notes in Mathematics 1563
    URL: https://doi.org/10.1007/BFb0074088
    URL: http://dx.doi.org/10.1007/BFb0074088
    URL: https://swbplus.bsz-bw.de/bsz036768200cov.jpg
    URL: https://zbmath.org/?q=an:0782.00060
    DOI: 10.1007/BFb0074088
    RVK:
    SI 850
    Language: English
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  • 9
    Online Resource
    Online Resource
    The Space of Dynamical Systems with the C0-Topology (1994)
    Berlin, Heidelberg : Springer Berlin Heidelberg
    Details Availability
    Keywords: Global analysis (Mathematics) ; Global differential geometry ; Mathematics ; Mathematical analysis. ; Geometry, Differential. ; Analysis ; Differential Geometry ; Mathematics ; Glatte Mannigfaltigkeit ; Dynamisches System ; Stabilität
    Description / Table of Contents: This book is an introduction to main methods and principal results in the theory of Co(remark: o is upper index!!)-small perturbations of dynamical systems. It is the first comprehensive treatment of this topic. In particular, Co(upper index!)-generic properties of dynamical systems, topological stability, perturbations of attractors, limit sets of domains are discussed. The book contains some new results (Lipschitz shadowing of pseudotrajectories in structurally stable diffeomorphisms for instance). The aim of the author was to simplify and to "visualize" some basic proofs, so the main part of the book is accessible to graduate students in pure and applied mathematics. The book will also be a basic reference for researchers in various fields of dynamical systems and their applications, especially for those who study attractors or pseudotrajectories generated by numerical methods
    Type of Medium: Online Resource
    Pages: Online-Ressource (CCIV, 194 p, online resource)
    ISBN: 9783540483144 , 9783540577027
    Series Statement: Lecture Notes in Mathematics 1571
    URL: https://doi.org/10.1007/BFb0073519
    URL: http://dx.doi.org/10.1007/BFb0073519
    URL: https://swbplus.bsz-bw.de/bsz404653448cov.jpg
    URL: https://zbmath.org/?q=an:0812.54043
    DOI: 10.1007/BFb0073519
    RVK:
    SI 850
    Language: English
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  • 10
    Online Resource
    Online Resource
    Topological methods for variational problems with symmetries (1993)
    Berlin, Heidelberg : Springer Berlin Heidelberg
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    Keywords: Global analysis (Mathematics) ; Cell aggregation Mathematics ; Mathematics ; Algebraic topology ; Mathematical analysis. ; Manifolds (Mathematics). ; Manifolds and Cell Complexes (incl. Diff.Topology) ; Algebraic Topology ; Analysis ; Mathematics ; Variationsproblem ; Symmetrie ; Kritischer Punkt ; Morse-Theorie
    Description / Table of Contents: Symmetry has a strong impact on the number and shape of solutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for "special" solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic algebraic topology is assumed
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (X, 158 Seiten)
    ISBN: 9783540480990 , 9783540573784
    Series Statement: Lecture Notes in Mathematics 1560
    URL: https://doi.org/10.1007/BFb0073859
    URL: http://dx.doi.org/10.1007/BFb0073859
    URL: https://swbplus.bsz-bw.de/bsz036642541cov.jpg
    URL: https://zbmath.org/?q=an:0789.58001
    DOI: 10.1007/BFb0073859
    RVK:
    SI 850
    RVK:
    SK 660
    Language: English
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