Andrew Komech's Books

Principles of Partial Differential Equations

By: Alexander Komech,Andrew Komech

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Principles of Partial Differential Equations

By: Alexander Komech,Andrew Komech

This concise book covers the classical tools of Partial Differential Equations Theory in today’s science and engineering. The rigorous theoretical presentation includes many hints, and the book contains many illustrative applications from physics.

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165

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441910956

ISBN 13

9781441910950

Probability and Mathematical Physics

A Volume in Honor of Stanislav Molchanov

By: Donald Andrew Dawson

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Probability and Mathematical Physics

A Volume in Honor of Stanislav Molchanov

By: Donald Andrew Dawson

A collection of survey and research papers that gives a glance of the profound consequences of Molchanov's contributions in stochastic differential equations, spectral theory for deterministic and random operators, localization and intermittency, mathematical physics and optics, and other topics.

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Page Count

490

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821840894

ISBN 13

9780821840894

Application of Geometric Algebra to Electromagnetic Scattering

The Clifford-Cauchy-Dirac Technique

By: Andrew Seagar

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Application of Geometric Algebra to Electromagnetic Scattering

The Clifford-Cauchy-Dirac Technique

By: Andrew Seagar

This work presents the Clifford-Cauchy-Dirac (CCD) technique for solving problems involving the scattering of electromagnetic radiation from materials of all kinds. It allows anyone who is interested to master techniques that lead to simpler and more efficient solutions to problems of electromagnetic scattering than are currently in use. The technique is formulated in terms of the Cauchy kernel, single integrals, Clifford algebra and a whole-field approach. This is in contrast to many conventional techniques that are formulated in terms of Green's functions, double integrals, vector calculus and the combined field integral equation (CFIE). Whereas these conventional techniques lead to an implementation using the method of moments (MoM), the CCD technique is implemented as alternating projections onto convex sets in a Banach space. The ultimate outcome is an integral formulation that lends itself to a more direct and efficient solution than conventionally is the case, and applies without exception to all types of materials. On any particular machine, it results in either a faster solution for a given problem or the ability to solve problems of greater complexity. The Clifford-Cauchy-Dirac technique offers very real and significant advantages in uniformity, complexity, speed, storage, stability, consistency and accuracy.

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Page Count

187

Publisher

Springer

Published Date

ISBN 10

9811000891

ISBN 13

9789811000898

Nonlinear Dirac Equation: Spectral Stability of Solitary Waves

By: Nabile Boussaïd,Andrew Comech

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Nonlinear Dirac Equation: Spectral Stability of Solitary Waves

By: Nabile Boussaïd,Andrew Comech

This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.

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Page Count

306

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470443953

ISBN 13

9781470443955

Principles of Partial Differential Equations

By: Alexander Komech,Andrew Komech

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Principles of Partial Differential Equations

By: Alexander Komech,Andrew Komech

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Solve jigsaw puzzle

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Page Count

165

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441910956

ISBN 13

9781441910950

Nonlinear Dirac Equation: Spectral Stability of Solitary Waves

By: Nabile Boussaïd,Andrew Comech

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Nonlinear Dirac Equation: Spectral Stability of Solitary Waves

By: Nabile Boussaïd,Andrew Comech

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N/A

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Solve jigsaw puzzle

Age

Page Count

306

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470443953

ISBN 13

9781470443955

Book's by Andrew Komech

Principles of Partial Differential Equations

Principles of Partial Differential Equations

Probability and Mathematical Physics

Probability and Mathematical Physics

Application of Geometric Algebra to Electromagnetic Scattering

Application of Geometric Algebra to Electromagnetic Scattering

Nonlinear Dirac Equation: Spectral Stability of Solitary Waves

Nonlinear Dirac Equation: Spectral Stability of Solitary Waves

Principles of Partial Differential Equations

Principles of Partial Differential Equations

Nonlinear Dirac Equation: Spectral Stability of Solitary Waves

Nonlinear Dirac Equation: Spectral Stability of Solitary Waves

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