LEADER 06367nam 2200709 450 001 9910139627403321 005 20211109143510.0 010 $a1-283-17590-8 010 $a9786613175908 010 $a1-118-05791-0 010 $a1-118-05790-2 024 7 $a10.1002/9781118057926 035 $a(CKB)2550000000041747 035 $a(EBL)697723 035 $a(OCoLC)748245080 035 $a(SSID)ssj0000522052 035 $a(PQKBManifestationID)12209857 035 $a(PQKBTitleCode)TC0000522052 035 $a(PQKBWorkID)10527728 035 $a(PQKB)11766111 035 $a(MiAaPQ)EBC697723 035 $a(CaBNVSL)mat06047602 035 $a(IDAMS)0b00006481692aa4 035 $a(IEEE)6047602 035 $a(EXLCZ)992550000000041747 100 $a20151221d2011 uy 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDiscontinuities in the electromagnetic field /$fM. Mithat Idemen 210 1$aHoboken, New Jersey :$cWiley-IEEE Press,$dc2011. 210 2$a[Piscataqay, New Jersey] :$cIEEE Xplore,$d[2011] 215 $a1 online resource (240 p.) 225 1 $aIEEE Press series on electromagnetic wave theory ;$v40 300 $aDescription based upon print version of record. 311 $a1-118-05792-9 311 $a1-118-03415-5 320 $aIncludes bibliographical references and index. 327 $aPreface ix -- 1. Introduction 1 -- 2. Distributions and Derivatives in the Sense of Distribution 7 -- 2.1 Functions and Distributions, 7 -- 2.2 Test Functions. The Space C∞ 0 , 9 -- 2.3 Convergence in D, 14 -- 2.4 Distribution, 16 -- 2.5 Some Simple Operations in D, 21 -- 2.5.1 Multiplication by a Real Number or a Function, 21 -- 2.5.2 Translation and Rescaling, 21 -- 2.5.3 Derivation of a Distribution, 22 -- 2.6 Order of a Distribution, 26 -- 2.7 The Support of a Distribution, 31 -- 2.8 Some Generalizations, 33 -- 2.8.1 Distributions on Multidimensional Spaces, 33 -- 2.8.2 Vector-Valued Distributions, 38 -- 3. Maxwell Equations in the Sense of Distribution 49 -- 3.1 Maxwell Equations Reduced into the Vacuum, 49 -- 3.1.1 Some Simple Examples, 53 -- 3.2 Universal Boundary Conditions and Compatibility Relations, 54 -- 3.2.1 An Example. Discontinuities on a Combined Sheet, 57 -- 3.3 The Concept of Material Sheet, 59 -- 3.4 The Case of Monochromatic Fields, 62 -- 3.4.1 Discontinuities on the Interface Between Two -- Simple Media that Are at Rest, 64 -- 4. Boundary Conditions on Material Sheets at Rest 67 -- 4.1 Universal Boundary Conditions and Compatibility Relations for a Fixed Material Sheet, 67 -- 4.2 Some General Results, 69 -- 4.3 Some Particular Cases, 70 -- 4.3.1 Planar Material Sheet Between Two Simple Media, 70 -- 4.3.2 Cylindrically or Spherically Curved Material Sheet Located Between Two Simple Media, 91 -- 4.3.3 Conical Material Sheet Located Between Two Simple Media, 93 -- 5. Discontinuities on a Moving Sheet 109 -- 5.1 Special Theory of Relativity, 110 -- 5.1.1 The Field Created by a Uniformly Moving Point Charge, 112 -- 5.1.2 The Expressions of the Field in a Reference System Attached to the Charged Particle, 114 -- 5.1.3 Lorentz Transformation Formulas, 115 -- 5.1.4 Transformation of the Electromagnetic Field, 118 -- 5.2 Discontinuities on a Uniformly Moving Surface, 120 -- 5.2.1 Transformation of the Universal Boundary Conditions, 123 -- 5.2.2 Transformation of the Compatibility Relations, 126. 327 $a5.2.3 Some Simple Examples, 126 -- 5.3 Discontinuities on a Nonuniformly Moving Sheet, 138 -- 5.3.1 Boundary Conditions on a Plane that Moves in a Direction Normal to Itself, 139 -- 5.3.2 Boundary Conditions on the Interface of Two Simple Media, 143 -- 6. Edge Singularities on Material Wedges Bounded by Plane Boundaries 149 -- 6.1 Introduction, 149 -- 6.2 Singularities at the Edges of Material Wedges, 153 -- 6.3 The Wedge with Penetrable Boundaries, 154 -- 6.3.1 The H Case, 156 -- 6.3.2 The E Case, 171 -- 6.4 The Wedge with Impenetrable Boundaries, 174 -- 6.5 Examples. Application to Half-Planes, 175 -- 6.6 Edge Conditions for the Induced Surface Currents, 176 -- 7. Tip Singularities at the Apex of a Material Cone 179 -- 7.1 Introduction, 179 -- 7.2 Algebraic Singularities of an H-Type Field, 185 -- 7.2.1 Contribution of the Energy Restriction, 185 -- 7.2.2 Contribution of the Boundary Conditions, 186 -- 7.3 Algebraic Singularities of an E-Type Field, 191 -- 7.4 The Case of Impenetrable Cones, 193 -- 7.5 Confluence and Logarithmic Singularities, 195 -- 7.6 Application to some Widely used Actual Boundary Conditions, 197 -- 7.7 Numerical Solutions of the Transcendental Equations Satisfied by the Minimal Index, 200 -- 7.7.1 The Case of Very Sharp Tip, 200 -- 7.7.2 The Case of Real-Valued Minimal v, 201 -- 7.7.3 A Function-Theoretic Method to Determine Numerically the Minimal v, 203 -- 8. Temporal Discontinuities 209 -- 8.1 Universal Initial Conditions, 209 -- 8.2 Linear Mediums in the Generalized Sense, 211 -- 8.3 An Illustrative Example, 212 -- References 215 -- Index 219 -- IEEE Press Series on Electromagnetic Wave Theory. 330 $a"This book presents some new approaches and basic results connected with the discontinuities of the electromagnetic field. The discontinuities in question may be (1) the bounded jump discontinuities on the interfaces between two media or on the material sheets which model very thin layers or (2) unbounded values at the edge of wedge type structures or (3) unbounded values at the tips of conical structures. The book involves may examples as well as problems (exercises) to be solved by the readers"--$cProvided by publisher. 410 0$aIEEE Press series on electromagnetic wave theory ;$v40 606 $aElectromagnetic fields$xMathematics 606 $aMaxwell equations 606 $aElectromagnetic waves 608 $aElectronic books. 615 0$aElectromagnetic fields$xMathematics. 615 0$aMaxwell equations. 615 0$aElectromagnetic waves. 676 $a530.14/1 676 $a621.3 686 $aSCI022000$2bisacsh 700 $aIdemen$b M. Mithat$0845330 801 0$bCaBNVSL 801 1$bCaBNVSL 801 2$bCaBNVSL 906 $aBOOK 912 $a9910139627403321 996 $aDiscontinuities in the electromagnetic field$91886533 997 $aUNINA