Equations of mathematical diffraction theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall
2005
|
| Series: | Differential and integral equations and their applications
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. [281]-286) and index |
| Physical Description: | XIII, 291 S. graph. Darst. |
| ISBN: | 0415308496 |
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| 245 | 1 | 0 | |a Equations of mathematical diffraction theory |c Mezhlum A. Sumbatyan, Antonio Scalia |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall |c 2005 | |
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| 650 | 4 | |a Diffraction |x Mathematics | |
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Record in the Search Index
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| adam_text | EQUATIONS OF MATHEMATICAL DIFFRACTION THEORY MEZHLUM A. SUMBATYAN
ANTONIO SCALIA CHAPMAN & HALL/CRC A CRC PRESS COMPANY BOCA RATON LONDON
NEW YORK WASHINGTON, D.C. CONTENTS PREFACE V AUTHORS IX CONTENTS XI 1.
SOME PRELIMINARIES FROM ANALYSIS AND THE THEORY OF WAVE PROCESSES 1 1.1.
FOURIER TRANSFORM, LINE INTEGRALS OF COMPLEX-VALUED INTEGRANDS, AND
SERIES IN RESIDUES 1 1.2. CONVOLUTION INTEGRAL EQUATIONS AND THE
WIENER-HOPF METHOD 6 1.3. SUMMATION OF DIVERGENT SERIES AND INTEGRALS 9
1.4. ASYMPTOTIC ESTIMATES OF INTEGRALS 12 1.5. FREDHOLM THEORY FOR
INTEGRAL EQUATIONS OF THE SECOND KIND 21 1.6. FREDHOLM INTEGRAL
EQUATIONS OF THE FIRST KIND 24 1.7. SINGULAR INTEGRAL EQUATIONS WITH A
CAUCHY-TYPE SINGULARITY IN THE KERNEL 29 1.8. HYPER-SINGULAR INTEGRALS
AND INTEGRAL EQUATIONS 35 1.9. GOVERNING EQUATIONS OF
HYDROAEROACOUSTICS, ELECTROMAGNETIC THEORY, AND DYNAMIC ELASTICITY 38 2.
INTEGRAL EQUATIONS OF DIFFRACTION THEORY FOR OBSTACLES IN UNBOUNDED
MEDIUM 45 2.1. PROPERTIES OF THE POTENTIALS OF SINGLE AND DOUBLE LAYERS
45 2.2. BASIC INTEGRAL EQUATIONS OF THE DIFFRACTION THEORY 52 2.3.
PROPERTIES OF INTEGRAL OPERATORS OF DIFFRACTION THEORY: GENERAL CASE AND
LOW FREQUENCIES 57 2.4. FULL LOW-FREQUENCY SOLUTION FOR SPHERICAL
OBSTACLE 61 2.5. APPLICATION: SCATTERING DIAGRAM FOR OBSTACLES OF
CANONICAL SHAPE 65 2.6. ASYMPTOTIC CHARACTER OF THE KIRCHHOFF PHYSICAL
DIFFRACTION THEORY 68 3. WAVE FIELDS IN A LAYER OF CONSTANT THICKNESS 73
3.1. WAVE OPERATOR IN ACOUSTIC LAYER: MODE EXPANSION, HOMOGENEOUS AND
INHOMOGENEOUS WAVES 73 3.2. PRINCIPLES OF SELECTION OF UNIQUE SOLUTION
IN UNBOUNDED DOMAIN 76 3.3. WAVES IN ELASTIC LAYER 82 3.4. GENERALIZED
RIEMANN S ZETA FUNCTION AND SUMMATION OF SOME OSCILLATING SERIES 87 3.5.
APPLICATION: EFFICIENT CALCULATION OF WAVE FIELDS IN A LAYER OF CONSTANT
THICKNESS 91 3.6. WAVES IN THE STRATIFIED HALF-PLANE 94 XII CONTENTS 4.
ANALYTICAL METHODS FOR SIMPLY CONNECTED BOUNDED DOMAINS 101 4.1. GENERAL
SPECTRAL PROPERTIES OF THE INTERIOR PROBLEM FOR LAPLACIAN 101 4.2.
EXPLICIT FORMULAS FOR EIGENFREQUENCIES OF ROUND DISC 107 4.3. SOME
VARIATIONAL PRINCIPLES FOR EIGENVALUES 110 4.4. WEYL-CARLEMAN THEORY OF
ASYMPTOTIC DISTRIBUTION OF LARGE EIGENVALUES 115 4.5. EXACT EXPLICIT
RESULTS FOR SOME POLYGONS 119 4.6. EXPLICIT ANALYTICAL RESULTS FOR SOME
POLYHEDRA 125 5. INTEGRAL EQUATIONS IN DIFFRACTION BY LINEAR OBSTACLES
133 5.1. INTEGRAL OPERATORS IN DIFFRACTION BY LINEAR SCREEN AND BY A GAP
IN THE SCREEN . 133 5.2. OPERATOR EQUATION IN DIFFRACTION PROBLEM ON A
CRACK IN UNBOUNDED ELASTIC MEDIUM 138 5.3. HIGH-FREQUENCY ASYMPTOTICS IN
DIFFRACTION BY LINEAR OBSTACLES IN UNBOUNDED MEDIUM 142 5.4.
HIGH-FREQUENCY ASYMPTOTICS FOR DIFFRACTION BY LINEAR OBSTACLES IN OPEN
WAVEGUIDES 145 5.5. HIGH-FREQUENCY DIFFRACTION BY A LINEAR DISCONTINUITY
IN THE WAVEGUIDE 151 5.6. WAVES IN ELASTIC HALF-SPACE. FACTORIZATION OF
THE RAYLEIGH FUNCTION 157 5.7. INTEGRAL EQUATION OF THE MIXED BOUNDARY
VALUE PROBLEM FOR ELASTIC LAYER 160 6. SHORT-WAVE ASYMPTOTIC METHODS ON
THE BASIS OF MULTIPLE INTEGRALS 165 6.1. SCHOCH S METHOD: EXACT
REPRESENTATION OF 3D WAVE FIELDS BY ONE-DIMENSIONAL QUADRATURES 165 6.2.
HIGH-FREQUENCY WAVE FIELDS IN ELASTIC HALF-SPACE 169 6.3. ASYMPTOTIC
NATURE OF THE GEOMETRICAL DIFFRACTION THEORY 171 6.4. HIGH-FREQUENCY
DIFFRACTION WITH RE-REFLECTIONS 175 6.5. APPLICATION: EXAMPLES OF
HIGH-FREQUENCY MULTIPLE DIFFRACTION 180 6.6. APPLICATION: PHYSICAL
DIFFRACTION THEORY FOR NONCONVEX OBSTACLES 184 6.7. SHORT-WAVE INTEGRAL
OPERATOR IN DIFFRACTION BY A FLAW IN ELASTIC MEDIUM .... 186 6.8.
HIGH-FREQUENCY ASYMPTOTICS OF INTEGRAL OPERATOR IN A THREE-DIMENSIONAL
DIFFRACTION THEORY 190 7. INVERSE PROBLEMS OF THE SHORT-WAVE DIFFRACTION
195 7.1. SOME BASIC RESULTS IN A LOCAL DIFFERENTIAL GEOMETRY OF SMOOTH
CONVEX SURFACES 195 7.2. REDUCING INVERSE PROBLEM OF THE SHORT-WAVE
DIFFRACTION TO MINKOWSKI PROBLEM 199 7.3. EXPLICIT RESULTS FOR A
DIFFERENTIAL OPERATOR OF THE 2D INVERSE PROBLEM 201 7.4. EXACT EXPLICIT
INVERSION OF THE BASIC OPERATOR IN THE CASE OF AXIAL SYMMETRY 203 7.5.
NONLINEAR DIFFERENTIAL OPERATOR OF THE THREE-DIMENSIONAL INVERSE PROBLEM
... 205 7.6. RECONSTRUCTION OF NONCONVEX OBSTACLES IN THE HIGH-FREQUENCY
RANGE: 2D CASE 208 7.7. RECONSTRUCTION OF NONCONVEX OBSTACLES IN THE
HIGH-FREQUENCY RANGE: 3D CASE 213 CONTENTS XIII 8. ILL-POSED EQUATIONS
OF INVERSE DIFFRACTION PROBLEMS FOR ARBITRARY BOUNDARY 219 8.1.
ILL-POSED PROBLEMS FOR OPERATOR EQUATIONS OF THE FIRST KIND: GENERAL
PROPERTIES 219 8.2. REGULARIZATION OF ILL-POSED PROBLEMS WITH THE HELP
OF SMOOTHING FUNCTIONAL . 222 8.3. ITERATIVE METHODS FOR OPERATOR
EQUATIONS OF THE FIRST KIND 226 8.4. COMPARISON OF VARIOUS METHODS FOR
RECONSTRUCTION OF THE SCATTERER GEOMETRY 231 8.5. GENERAL INVERSE
DIFFRACTION PROBLEM: COMBINATION OF ITERATIONS AND SMOOTHING 235 8.6. A
CORRECT TREATMENT OF ILL-POSED BOUNDARY EQUATIONS IN ACOUSTICS OF CLOSED
REGIONS 242 8.7. ILL-POSED METHOD OF AUXILIARY SOURCES IN DIFFRACTION
THEORY 248 8.8. A METHOD OF GLOBAL RANDOM SEARCH IN INVERSE PROBLEMS 251
8.9. ILL-POSED PROBLEM ON RECONSTRUCTION OF CONVEX HULL OF THE OBSTACLE
IN ACOUSTIC MEDIUM 253 9. NUMERICAL METHODS FOR IRREGULAR OPERATOR
EQUATIONS 259 9.1. STEEPEST DESCENT METHOD: STABILITY AND IMPROVEMENT OF
THE CONVERGENCE 259 9.2. GALERKIN METHODS FOR INTEGRAL EQUATIONS OF THE
FIRST KIND WITH WEAKLY SINGULAR KERNELS 263 9.3. INTEGRAL EQUATIONS OF
THE PHYSICAL DIFFRACTION THEORY IN THE CASE OF NONCONVEX OBSTACLES 268
9.4. NUMERICAL METHODS IN SINGULAR INTEGRAL EQUATIONS WITH THE
CAUCHY-TYPE KERNEL 272 9.5. NUMERICAL METHODS FOR HYPER-SINGULAR
INTEGRAL EQUATIONS 276 REFERENCES 281 INDEX 287
|
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| indexdate | 2024-07-09T20:05:18Z |
| institution | BVB |
| isbn | 0415308496 |
| language | English |
| lccn | 2004051957 |
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| physical | XIII, 291 S. graph. Darst. |
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| publisher | Chapman & Hall |
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| series | Differential and integral equations and their applications |
| series2 | Differential and integral equations and their applications |
| spelling | Sumbatyan, Mezhlum, A. Verfasser aut Equations of mathematical diffraction theory Mezhlum A. Sumbatyan, Antonio Scalia Boca Raton [u.a.] Chapman & Hall 2005 XIII, 291 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differential and integral equations and their applications 5 Includes bibliographical references (p. [281]-286) and index Mathematik Diffraction Mathematics Lichtbeugung (DE-588)4195853-6 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Lichtbeugung (DE-588)4195853-6 s Mathematische Methode (DE-588)4155620-3 s DE-604 Scalia, Antonio Sonstige oth Differential and integral equations and their applications 5 (DE-604)BV014412675 5 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013078178&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sumbatyan, Mezhlum, A. Equations of mathematical diffraction theory Differential and integral equations and their applications Mathematik Diffraction Mathematics Lichtbeugung (DE-588)4195853-6 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4195853-6 (DE-588)4155620-3 |
| title | Equations of mathematical diffraction theory |
| title_auth | Equations of mathematical diffraction theory |
| title_exact_search | Equations of mathematical diffraction theory |
| title_full | Equations of mathematical diffraction theory Mezhlum A. Sumbatyan, Antonio Scalia |
| title_fullStr | Equations of mathematical diffraction theory Mezhlum A. Sumbatyan, Antonio Scalia |
| title_full_unstemmed | Equations of mathematical diffraction theory Mezhlum A. Sumbatyan, Antonio Scalia |
| title_short | Equations of mathematical diffraction theory |
| title_sort | equations of mathematical diffraction theory |
| topic | Mathematik Diffraction Mathematics Lichtbeugung (DE-588)4195853-6 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Mathematik Diffraction Mathematics Lichtbeugung Mathematische Methode |
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