T Rk Solu
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Almost Periodic Solutions Of Differential Equations In Banach Spaces
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Author : Yoshiyuki Hino
language : en
Publisher: CRC Press
Release Date : 2001-10-25
Almost Periodic Solutions Of Differential Equations In Banach Spaces written by Yoshiyuki Hino and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-25 with Mathematics categories.
This monograph presents recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces. Many of the results represent significant advances in this area. In particular, the authors systematically present a new approach based on the so-called evolution semigroups with
Fast Solution Of Discretized Optimization Problems
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Author : Karl-Heinz Hoffmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Fast Solution Of Discretized Optimization Problems written by Karl-Heinz Hoffmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. This welcome reference for many new results and recent methods is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory.
Mathematical Questions And Solutions In Continuation Of The Mathematical Columns Of The Educational Times
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Author :
language : en
Publisher:
Release Date : 1896
Mathematical Questions And Solutions In Continuation Of The Mathematical Columns Of The Educational Times written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1896 with categories.
Linear Ordinary Differential Equations
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Author : Earl A. Coddington
language : en
Publisher: SIAM
Release Date : 1997-01-01
Linear Ordinary Differential Equations written by Earl A. Coddington and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
Linear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering. Three recurrent themes run through the book. The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions. The use of power series, beginning with the matrix exponential function leads to the special functions solving classical equations. Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions.
Mathematical Questions And Solutions
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Author :
language : en
Publisher:
Release Date : 1896
Mathematical Questions And Solutions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1896 with Mathematics categories.
Periodic Solutions Of Nonlinear Dynamical Systems
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Author : Eduard Reithmeier
language : en
Publisher: Springer
Release Date : 2006-11-14
Periodic Solutions Of Nonlinear Dynamical Systems written by Eduard Reithmeier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions by means of parameter variations plays an important role in transition to chaos, so numerical algorithms are necessary to compute periodic solutions and investigate their stability on a numerical basis. From the technical point of view, dynamical systems with discontinuities are of special interest. The discontinuities may occur with respect to the variables describing the configuration space manifold or/and with respect to the variables of the vector-field of the dynamical system. The multiple shooting method is employed in computing limit cycles numerically, and is modified for systems with discontinuities. The theory is supported by numerous examples, mainly from the field of nonlinear vibrations. The text addresses mathematicians interested in engineering problems as well as engineers working with nonlinear dynamics.
Mathematical Questions And Solutions From The Educational Times With Many Papers And Solutions In Addition To Those Published In The Educational Times
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Author :
language : en
Publisher:
Release Date : 1896
Mathematical Questions And Solutions From The Educational Times With Many Papers And Solutions In Addition To Those Published In The Educational Times written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1896 with Mathematics categories.
Almost Global Solutions Of Capillary Gravity Water Waves Equations On The Circle
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Author : Massimiliano Berti
language : en
Publisher: Springer
Release Date : 2018-11-02
Almost Global Solutions Of Capillary Gravity Water Waves Equations On The Circle written by Massimiliano Berti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-02 with Mathematics categories.
The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.
A Course On Plasticity Theory
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Author : David Steigmann
language : en
Publisher: Oxford University Press
Release Date : 2023-01-20
A Course On Plasticity Theory written by David Steigmann and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-20 with Continuum mechanics categories.
Plasticity Theory is characterized by many competing and often incompatible points of view. This book seeks to strengthen the foundations of continuum plasticity theory, emphasizing a unifying perspective grounded in the fundamental notion of material symmetry. Steigmann's book offers a systematic framework for the proper understanding of established models of plasticity and for their modern extensions and generalizations. Particular emphasis is placed on the differential-geometric aspects of the subject and their role in illuminating the conceptual foundations of plasticity theory. Classical models, together with several subjects of interest in contemporary research, are developed in a unified format. The book is addressed to graduate students and academics working in the field of continuum mechanics.
Time Parallel Methods For Accelerating The Solution Of Structural Dynamics Problems
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Author : Julien Remi Cortial
language : en
Publisher: Stanford University
Release Date : 2011
Time Parallel Methods For Accelerating The Solution Of Structural Dynamics Problems written by Julien Remi Cortial and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
The classical approach for solving evolution Partial Differential Equations (PDEs) using a parallel computer consists in first partitioning the spatial domain and assigning each subdomain to a processor to achieve space-parallelism, then advancing the solution sequentially. However, enabling parallelism along the time dimension, despite its intrinsic difficulty, can be of paramount importance to fast computations when space-parallelism is unfeasible, cannot fully exploit a massively parallel machine or when near-real-time prediction is desired. The aforementioned objective can be achieved by applying classical domain decomposition principles to the time axis. The latter is first partitioned into time-slices to be processed independently. Starting with approximate seed information that provides a set of initial conditions, the response is then advanced in parallel in each time-slice using a standard time-stepping integrator. This decomposed solution exhibits discontinuities or jumps at the time-slice boundaries if the initial guess is not accurate. Applying a Newton-like approach to the time-dependent system, a correction function is then computed to improve the accuracy of the seed values and the process is repeated until convergence is reached. Methods based on the above concept have been successfully applied to various problems but none was found to be competitive for even for the simplest of second-order hyperbolic PDEs, a class of equations that covers the field of structural dynamics among others. To overcome this difficulty, a key idea is to improve the sequential propagator used for correcting the seed values, observing that the original evolution problem and the derived corrective one are closely related. The present work first demonstrates how this insight can be brought to fruition in the context of linear oscillators, with numerical examples featuring structural models ranging from academic to more challenging large-scale ones. An extension of this method to nonlinear equations is then developed and its concrete application to geometrically nonlinear transient dynamics is presented. Finally, it is shown how the time-reversibility property that characterizes some of the above problems can be exploited to develop a new framework that provides an increased speed-up factor.