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Author: Moshé Flato
Publisher: American Mathematical Soc.
ISBN: 0821806831
Category : Mathematics
Languages : en
Pages : 328
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Book Description
The purpose of this work is to present and give full proofs of new original research results concerning integration of and scattering for the classical Maxwell-Dirac equations.
Author: Moshé Flato
Publisher: American Mathematical Soc.
ISBN: 0821806831
Category : Mathematics
Languages : en
Pages : 328
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Book Description
The purpose of this work is to present and give full proofs of new original research results concerning integration of and scattering for the classical Maxwell-Dirac equations.
Author: Christopher Keil McCord
Publisher: American Mathematical Soc.
ISBN: 0821806920
Category : Mathematics
Languages : en
Pages : 106
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Book Description
The phase space of the spatial three-body problem is an open subset in R18. Holding the ten classical integrals of energu, center of mass, linear and angular momentum fixed defines an eight dimensional manifold. For fixed nonzero angular momentum, the topology of this manifold depends only on the energy. This volume computes the homology of this manifold for all energy values. This table of homology shows that for negative energy, the integral manifolds undergo seven bifurcations. Four of these are the well-known bifurcations due to central configurations, and three are due to "critical points at infinity". This disproves Birkhoffs conjecture that the bifurcations occur only at central configurations.
Author: Lawrence C. Evans
Publisher: American Mathematical Soc.
ISBN: 0821809385
Category : Mathematics
Languages : en
Pages : 81
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Book Description
In this volume, the authors demonstrate under some assumptions on $f $, $f $ that a solution to the classical Monge-Kantorovich problem of optimally rearranging the measure $\mu{ }=f dx$ onto $\mu =f dy$ can be constructed by studying the $p$-Laplacian equation $- \roman{div}(\vert DU_p\vert p-2}Du_p)=f -f $ in the limit as $p\rightarrow\infty$. The idea is to show $u_p\rightarrow u$, where $u$ satisfies $\vert Du\vert\leq 1, -\roman{div}(aDu)=f -f $ for some density $a\geq0$, and then to build a flow by solving a nonautonomous ODE involving $a, Du, f $ and $f $
Author: Russell Johnson
Publisher: American Mathematical Soc.
ISBN: 0821808656
Category : Computers
Languages : en
Pages : 63
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Book Description
This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness properties and which also preserves all the smoothness and recurrence properties of the coefficients. Finally, a general version of the local nonlinear feedback stabilization problem is solved.
Author: Weizhu Bao
Publisher: World Scientific
ISBN: 9812770224
Category : Mathematics
Languages : en
Pages : 307
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Book Description
The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on Nanoscale Material Interfaces: Experiment, Theory and Simulation'' from November 2004 to January 2005. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field. This invaluable volume collects the expanded lecture notes of four of those self-contained tutorials. The topics covered include dynamics in different models of domain coarsening and coagulation and their mathematical analysis in material sciences; a mathematical and computational study for quantized vortices in the celebrated GinzburgOCoLandau models of superconductivity and the mean field GrossOCoPitaevskii equations of superfluidity; the nonlinear SchrAdinger equation and applications in BoseOCoEinstein condensation and plasma physics as well as their efficient and accurate computation; and finally, an introduction to constitutive modeling of macromolecular fluids within the framework of the kinetic theory. This volume serves to inspire graduate students and researchers who will embark upon original research work in these fields."
Author: Adele Zucchi
Publisher: American Mathematical Soc.
ISBN: 0821806262
Category : Mathematics
Languages : en
Pages : 66
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Book Description
In the present paper the author studies the analogue of the class [italic capital]C0 within a class of operators having a functional calculus based on the algebra of bounded holomorphic functions in a finitely connected domain with an analytic boundary. The latter class consists of the operators having the closure of the domain as a spectral set and having no normal direct summands with spectra contained in the boundary of the domain. (If the domain is the disk the preceding class reduces to the class of completely nonunitary contractions.) The basic properties known for the case of the disk, including the model theory, are established. The extension, even the mere construction of the functional calculus, is not routine, in part because it is unknown whether the analogue of Sz.-Nagy's dilation theorem is true in the author's multiply connected setting.
Author: Moshé Flato
Publisher: Oxford University Press, USA
ISBN: 9781470401917
Category : MATHEMATICS
Languages : en
Pages : 328
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Book Description
The purpose of this work is to present and give full proofs of new original research results concerning integration of and scattering for the classical Maxwell-Dirac equations.
Author: Hasna Riahi
Publisher: American Mathematical Soc.
ISBN: 0821808737
Category : Mathematics
Languages : en
Pages : 127
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Book Description
In this work, the author examines the following: When the Hamiltonian system $m i \ddot{q} i + (\partial V/\partial q i) (t,q) =0$ with periodicity condition $q(t+T) = q(t),\; \forall t \in \germ R$ (where $q {i} \in \germ R{\ell}$, $\ell \ge 3$, $1 \le i \le n$, $q = (q {1},...,q {n})$ and $V = \sum V {ij}(t,q {i}-q {j})$ with $V {ij}(t,\xi)$ $T$-periodic in $t$ and singular in $\xi$ at $\xi = 0$) is posed as a variational problem, the corresponding functional does not satisfy the Palais-Smale condition and this leads to the notion of critical points at infinity. This volume is a study of these critical points at infinity and of the topology of their stable and unstable manifolds. The potential considered here satisfies the strong force hypothesis which eliminates collision orbits. The details are given for 4-body type problems then generalized to n-body type problems.
Author: Xingde Dai
Publisher: American Mathematical Soc.
ISBN: 0821808001
Category : Mathematics
Languages : en
Pages : 82
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Book Description
Investigates topological and structural properties of the set W(U) of all complete wandering vectors for a system U of unitary operators acting on a Hilbert space. The authors parameterize W(U) in terms of a fixed vector y and the set of all unitary operators which locally commute with U at y. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Author: David Ginzburg
Publisher: American Mathematical Soc.
ISBN: 0821805436
Category : Mathematics
Languages : en
Pages : 233
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Book Description
In this book, the authors establish global Rankin Selberg integrals which determine the standard [italic capital]L function for the group [italic capitals]GL[subscript italic]r x [italic capital]Gʹ, where [italic capital]Gʹ is an isometry group of a nondegenerate symmetric form. The class of automorphic representations considered here is for any pair [capital Greek]Pi1 [otimes/dyadic/Kronecker/tensor product symbol] [capital Greek]Pi2 where [capital Greek]Pi1 is generic cuspidal for [italic capitals]GL[subscript italic]r([italic capital]A) and [capital Greek]Pi2 is cuspidal for [italic capital]Gʹ([italic capital]A). The construction of these [italic capital]L functions involves the use of certain new "models" of local representations; these models generalize the usual generic models. The authors also computer local unramified factors in a new way using geometric ideas.
