Eigenvalue Problems Problems of Nonhomogenous Strings
Eigenvalue Problems Problems of Nonhomogenous Strings

Author: Binyamin Schwarz

Publisher:

Published: 1960

Total Pages: 12

ISBN-13:

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This research was divided into two parts which were contained in two Technical (Scientific) notes: (1) Technical Note No. 1. "Bounds for sums of reciprocals of eigenvalues". July, 1959. (2) Technical Note No. 2. "On the extrema of the frequencies of nonhomogeneous strings which equimeasurable density". December, 1959.

Control of Distributed Parameter Systems
Control of Distributed Parameter Systems

Author: S. P. Banks

Publisher: Elsevier

Published: 2014-05-18

Total Pages: 554

ISBN-13: 1483151123

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Control of Distributed Parameter Systems covers the proceedings of the Second IFAC Symposium, Coventry, held in Great Britain from June 28 to July 1, 1977. The book focuses on the methodologies, processes, and techniques in the control of distributed parameter systems, including boundary value control, digital transfer matrix, and differential equations. The selection first discusses the asymptotic methods in the optimal control of distributed systems; applications of distributed parameter control theory of a survey; and dual variational inequalities for external eigenvalue problems. The book also ponders on stochastic differential equations in Hilbert space and their application to delay systems and linear quadratic optimal control problem over an infinite time horizon for a class of distributed parameter systems. The manuscript investigates the semigroup approach to boundary value control and stability of nonlinear distributed parameter systems. Topics include boundary control action implemented through a dynamical system; classical boundary value controls; stability of nonlinear systems; and feedback control on the boundary. The text also focuses on the functional analysis interpretation of Lyapunov stability; method of multipliers for a class distributed parameter systems; and digital transfer matrix approach to distributed system simulation. The selection is a dependable source of data for readers interested in the control of distributed parameter systems.

Inequalities
Inequalities

Author: Edwin F. Beckenbach

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 210

ISBN-13: 3642649718

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Since the elassie work on inequalities by HARDY, LITTLEWOOD, and P6LYA in 1934, an enonnous amount of effort has been devoted to the sharpening and extension of the elassieal inequalities, to the discovery of new types of inequalities, and to the application of inqualities in many parts of analysis. As examples, let us eite the fields of ordinary and partial differential equations, whieh are dominated by inequalities and variational prineiples involving functions and their derivatives; the many applications of linear inequalities to game theory and mathe matieal economics, which have triggered a renewed interest in con vexity and moment-space theory; and the growing uses of digital com puters, which have given impetus to a systematie study of error esti mates involving much sophisticated matrix theory and operator theory. The results presented in the following pages reflect to some extent these ramifications of inequalities into contiguous regions of analysis, but to a greater extent our concem is with inequalities in their native habitat. Since it is elearly impossible to give a connected account of the burst of analytic activity of the last twenty-five years centering about inequalities, we have d. eeided to limit our attention to those topies that have particularly delighted and intrigued us, and to the study of whieh we have contributed.

Real and Complex Differential Systems
Real and Complex Differential Systems

Author: Binyamin Schwarz

Publisher:

Published: 1961

Total Pages: 66

ISBN-13:

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This final report is divided into two independent parts. No results on complex differential systems were obtained. The research on integral equations is a natural continuation of former work on real differential systems.

Inequalities Involving Functions and Their Integrals and Derivatives
Inequalities Involving Functions and Their Integrals and Derivatives

Author: Dragoslav S. Mitrinovic

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 602

ISBN-13: 9401135622

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One service mathematics has rendered the ~l moil ..., Ii j'avait su comment en revenir, je n'y serais point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'(ftre of this series.