Anmerkung: Intro -- Title Page -- Contents -- About the Authors -- About the Contributors -- Acknowledgements -- Acronyms -- Chapter 1 Introduction -- 1.1 Background -- 1.1.1 Anechoic Chambers -- 1.1.2 Reverberation Chambers -- 1.1.3 Relationship between Anechoic Chambers and Reverberation Chambers -- 1.2 Organisation of this Book -- References -- Chapter 2 Theory for Anechoic Chamber Design -- 2.1 Introduction -- 2.2 Absorbing Material Basics -- 2.2.1 General Knowledge -- 2.2.2 Absorbing Material Simulation -- 2.2.3 Absorbing Material Measurement -- 2.3 CEM Algorithms Overview -- 2.4 GO Theory -- 2.4.1 GO from Maxwell Equations -- 2.4.2 Analytical Expression of a Reflected Field from a Curved Surface -- 2.4.3 Alternative GO Form -- 2.5 GO-FEM Hybrid Method -- 2.6 Summary -- References -- Chapter 3 Computer-aided Anechoic Chamber Design -- 3.1 Introduction -- 3.2 Framework -- 3.3 Software Implementation -- 3.3.1 3D Model Description -- 3.3.2 Algorithm Complexities -- 3.3.3 Far-Field Data -- 3.3.4 Boundary Conditions -- 3.3.5 RAM Description -- 3.3.6 Forward Algorithm -- 3.3.7 Inverse Algorithm -- 3.3.8 Post Processing -- 3.4 Summary -- References -- Chapter 4 Anechoic Chamber Design Examples and Verifications -- 4.1 Introduction -- 4.2 Normalised Site Attenuation -- 4.2.1 NSA Definition -- 4.2.2 NSA Simulation and Measurement -- 4.3 Site Voltage Standing Wave Ratio -- 4.3.1 SVSWR Definition -- 4.3.2 SVSWR Simulation and Measurement -- 4.4 Field Uniformity -- 4.4.1 FU Definition -- 4.4.2 FU Simulation and Measurement -- 4.5 Design Margin -- 4.6 Summary -- References -- Chapter 5 Fundamentals of the Reverberation Chamber -- 5.1 Introduction -- 5.2 Resonant Cavity Model -- 5.3 Ray Model -- 5.4 Statistical Electromagnetics -- 5.4.1 Plane-Wave Spectrum Model -- 5.4.2 Field Correlations -- 5.4.3 Boundary Fields -- 5.4.4 Enhanced Backscattering Effect. , 5.4.5 Loss Mechanism -- 5.4.6 Probability Distribution Functions -- 5.5 Figures of Merit -- 5.5.1 Field Uniformity -- 5.5.2 Lowest Usable Frequency -- 5.5.3 Correlation Coefficient and Independent Sample Number -- 5.5.4 Field Anisotropy Coefficients and Inhomogeneity Coefficients -- 5.5.5 Stirring Ratio -- 5.5.6 K-Factor -- 5.6 Summary -- References -- Chapter 6 The Design of a Reverberation Chamber -- 6.1 Introduction -- 6.2 Design Guidelines -- 6.2.1 The Shape of the RC -- 6.2.2 The Lowest Usable Frequency -- 6.2.3 The Working Volume -- 6.2.4 The Q Factor -- 6.2.5 The Stirrer Design -- 6.3 Simulation of the RC -- 6.3.1 Monte Carlo Method -- 6.3.2 Time Domain Simulation -- 6.3.3 Frequency Domain Simulation -- 6.4 Time Domain Characterisation of the RC -- 6.4.1 Statistical Behaviour in the Time Domain -- 6.4.2 Stirrer Efficiency Based on Total Scattering Cross Section -- 6.4.3 Time-Gating Technique -- 6.5 Duality Principle in the RC -- 6.6 The Limit of ACS and TSCS -- 6.7 Design Example -- 6.8 Summary -- References -- Chapter 7 Applications in the Reverberation Chamber -- 7.1 Introduction -- 7.2 Q Factor and Decay Constant -- 7.3 Radiated Immunity Test -- 7.4 Radiated Emission Measurement -- 7.5 Free-Space Antenna S-Parameter Measurement -- 7.6 Antenna Radiation Efficiency Measurement -- 7.6.1 Reference Antenna Method -- 7.6.2 Non-reference Antenna Method -- 7.7 MIMO Antenna and Channel Emulation -- 7.7.1 Diversity Gain Measurement -- 7.7.2 Total Isotropic Sensitivity Measurement -- 7.7.3 Channel Capacity Measurement -- 7.7.4 Doppler Effect -- 7.8 Antenna Radiation Pattern Measurement -- 7.8.1 Theory -- 7.8.2 Simulations and Measurements -- 7.8.3 Discussion and Error Analysis -- 7.9 Material Measurements -- 7.9.1 Absorption Cross Section -- 7.9.2 Average Absorption Coefficient -- 7.9.3 Permittivity -- 7.9.4 Material Shielding Effectiveness. , 7.10 Cavity Shielding Effectiveness Measurement -- 7.11 Volume Measurement -- 7.12 Summary -- References -- Chapter 8 Measurement Uncertainty in the Reverberation Chamber -- 8.1 Introduction -- 8.2 Procedure for Uncertainty Characterisation -- 8.3 Uncertainty Model -- 8.3.1 ACF Method -- 8.3.2 DoF Method -- 8.3.3 Comparison of ACF and DoF Methods -- 8.3.4 Semi-empirical Model -- 8.4 Measurement Uncertainty of Antenna Efficiency -- 8.5 Summary -- References -- Chapter 9 Inter-Comparison Between Antenna Radiation Efficiency Measurements Performed in an Anechoic Chamber and in a Reverberatio... -- 9.1 Introduction -- 9.2 Measurement Facilities and Setups -- 9.2.1 Anechoic Chamber -- 9.2.2 Reverberation Chamber -- 9.3 Antenna Efficiency Measurements -- 9.3.1 Theory -- 9.3.1.1 Radiation Efficiency Using the Anechoic Chamber -- 9.3.1.2 Radiation Efficiency Using the Reverberation Chamber -- 9.3.2 Comparison Between the AC and the RC -- 9.3.2.1 Biconical Antenna -- 9.3.2.2 Horn Antenna -- 9.3.2.3 MIMO Antenna -- 9.4 Summary -- Acknowledgement -- References -- Chapter 10 Discussion on Future Applications -- 10.1 Introduction -- 10.2 Anechoic Chambers -- 10.3 Reverberation Chambers -- References -- Appendix A Code Snippets -- A.1 Import STL File into Matlab -- A.2 Possible Intersection Check Between a Triangle and a Hexahedron -- A.3 Intersection Check Between a Ray and a Hexahedron in the Octree -- A.4 Intersection Check Between a Ray and a Triangle -- A.5 Field Uniformity Extraction -- A.6 Mean and Standard Deviation of the Maximum Received Power with N Independent Samples -- A.7 Mean and Standard Deviation of the Maximum Rectangular E-Field with N Independent Samples -- A.8 Monte Carlo Simulation in the RC -- A.9 The Plot of Theoretical Rayleigh CDF -- Appendix B Reference NSA Values -- Reference -- Appendix C Test Report Template -- C.1 Summary. , C.2 Date and Place of Measurements -- C.3 Description of the Test Site -- C.4 Measurements and Results -- C.4.1 Normalised Site Attenuation (NSA) -- C.4.1.1 Test Description -- C.4.1.2 Measurement Equipment -- C.4.1.3 Results -- C.4.2 Site VSWR -- C.4.2.1 Test Description -- C.4.2.2 Measurement Equipment -- C.4.2.3 Results -- C.4.3 Field Uniformity (FU) Measurements -- C.4.3.1 Test Description -- C.4.3.2 Measurement Equipment -- C.4.3.3 Results -- Reference -- Appendix D Typical Bandpass Filters -- References -- Appendix E Compact Reverberation Chamber at NUAA -- E.1 Design Guidelines -- E.2 Measurements -- E.2.1 Field Uniformity -- E.2.2 The Ratio of Standard Deviation and Mean Value -- E.2.3 Q Factor -- E.2.4 Enhanced Backscatter Coefficient -- E.3 Summary -- References -- Appendix F Relevant Statistics -- F.1 Propagation of Uncertainty -- F.2 Parameter Estimation -- F.3 Useful Laws and Theorems -- References -- Index -- EULA.

Anmerkung: Intro -- Conformal Field Theories and Tensor Categories -- Preface -- Contents -- From Hopf Algebras to Tensor Categories -- 1 Introduction -- 2 Preliminaries -- 2.1 Notations -- 2.2 Tensor Categories -- 2.3 Hopf Algebras -- 2.4 Nichols Algebras -- 3 Spherical Hopf Algebras -- 3.1 Spherical Hopf Algebras -- 3.2 Spherical Categories -- 3.3 Quantum Dimensions -- 3.3.1 Some Properties of Quantum Dimension -- 3.3.2 Computing the Quantum Dimension -- 3.3.3 Projective Objects Have Null Quantum Dimension -- 3.4 The Non-degenerate Quotient -- 3.5 Pointed or Copointed Pivotal Hopf Algebras -- 3.5.1 Pivots in the Pointed Case -- 3.5.2 Pivots in the Copointed Case -- 3.6 Spherical Hopf Algebras with Involutory Pivot -- 3.6.1 The Pointed Abelian Case -- 3.6.2 The Pointed Nonabelian Case -- 3.6.3 The Copointed Case -- 3.6.4 Fusion subcategories of RepH, Involutory Pivot -- 3.7 Ribbon Hopf Algebras -- 3.8 Cospherical Hopf Algebras -- 4 Tilting Modules -- 4.1 Quasi-hereditary Algebras and Tilting Modules -- 4.2 Induced and Produced -- 4.2.1 De nition and General Properties -- 4.2.2 The Finite Case -- 4.2.3 Further Properties for Inclusions of Hopf Algebras -- 4.2.4 Quantum Groups -- 4.3 Finite-Dimensional Nichols Algebras of Diagonal Type -- 4.3.1 Weights -- 4.3.2 Nichols Algebras of Diagonal Type -- 4.3.3 Pre-Nichols Algebras -- 4.3.4 Lusztig Algebras -- 4.4 The Small Quantum Groups -- 4.5 Generalized Quantum Groups -- References -- Pattern-of-Zeros Approach to Fractional Quantum Hall States and a Classi cation of Symmetric Polynomial of In nite Variables -- 1 Introduction -- 1.1 What Is a Quantum Many-Boson System -- 1.2 What Are Quantum Phases -- 1.3 How to Classify Quantum Phases of Matter -- 2 Examples of Fractional Quantum Hall States -- 2.1 The Hamiltonian for FQH Systems -- 2.2 Three Ideal FQH States: The Exact Zero-Energy Ground States. , 3 The Universal Properties of FQH Phases -- 3.1 The Filling Fractions of FQH Phases -- 3.1.1 Why nu=1 for State Psi1=i< -- j (zi-zj) e-|zi|2/4 -- 3.1.2 Why nu=1/m for the Laughlin State Psi1/m=i< -- j (zi-zj)m e-|zi|2/4 -- 3.2 Quasiparticle and Fractional Charge in nu=1/m Laughlin States -- 3.3 The Concept of Quasiparticle Type -- 3.4 Fractional Statistics in Laughlin States -- 3.5 Quasi-holes in the nu=1 Pfaf an State -- 3.5.1 Charge-1 and Charge-1/2 Quasi-holes -- 3.5.2 How Many States with Four Charge-1/2 Quasi-holes? -- 3.6 Edge Excitations and Conformal Field Theory -- 4 Pattern-of-Zeros Approach to FQH States and Symmetric Polynomials -- 4.1 What Is In nite-Variable Symmetric Polynomial -- 4.1.1 What Is Pattern of Zeros? -- 4.1.2 The Unique Fusion Condition -- 4.1.3 Different Encodings of Pattern of Zeros Sa -- 4.1.4 The Cluster Condition -- 4.1.5 A De nition of In nite-Variable Symmetric Polynomial -- 4.2 A Classi cation of In nite-Variable Symmetric Polynomials -- 4.2.1 Derived Polynomials -- 4.2.2 The Concave Conditions on Pattern of Zeros -- 4.2.3 Some Additional Conditions -- 4.2.4 Primitive Solutions for Pattern of Zeros -- 4.2.5 How Good Is the Pattern-of-Zeros Classi cation? -- 4.3 Topological Properties from Pattern of Zeros -- 4.3.1 Pattern of Zeros of Quasiparticle Excitations -- 4.3.2 Conditions on Quasiparticle Pattern of Zeros Sgamma -- a -- 4.3.3 The Solutions for the Quasiparticle Patterns of Zeros -- 4.3.4 Quasiparticle Fusion Algebra: gamma1 gamma2=gamma3 Ngamma3gamma1gamma2 gamma3 -- 5 The Vertex-Algebra + Pattern-of-Zeros Approach -- 5.1 Z-Graded Vertex Algebra -- 5.2 Zn-Vertex Algebra -- 6 Summary -- References -- Virasoro Central Charges for Nichols Algebras -- 1 Introduction -- 1.1 From Virasoro to Extended Algebras -- 1.2 Points to Note -- 1.3 Notation -- 2 The List, Item 1 -- 3 The List, Items 2.*. , 4 The List, Items 3.* -- 5 The List, Items 4.* -- 6 The List, Items 5.* -- 7 Conclusions -- Appendix A: Virasoro Algebra -- Appendix B: W3 Logarithmic Octuplet Algebras -- References -- Logarithmic Bulk and Boundary Conformal Field Theory and the Full Centre Construction -- 1 Introduction -- 2 Bulk and Boundary Correlators -- 2.1 Consistency Conditions for CFT on the Complex Plane -- 2.2 Background States, Non-degeneracy, and Ideals -- 2.3 Modular Invariant Partition Functions -- 2.4 Consistency Conditions for CFT on the Upper Half Plane -- 2.5 From Boundary to Bulk -- 3 Algebraic Reformulation -- 3.1 Conjugates -- 3.2 Deligne Product -- 3.3 Braiding -- 3.4 Algebras -- 3.5 The Full Centre in CCrev -- 3.6 The Right Adjoint R of T -- 3.7 Left Centre and Full Centre -- 4 The W2,3-Model with c=0 -- 4.1 The W-Algebra and Some of Its Representations -- 4.2 Computation of R(W(0)) -- 4.3 Computation of R(W*) -- 4.4 Modular Invariance -- 4.5 Correlators and OPEs in R(W*) -- 4.5.1 Some OPEs -- 4.5.2 Some Correlators -- Appendix A: Conditions B1-B5 -- Appendix B: Further Details on the Algebraic Reformulation -- B.1 Proof of Theorem 3.5 -- B.2 Idempotent Absolutely Simple Objects Are Algebras -- B.3 Proof of Theorem 3.16 -- B.4 Proofs for Theorems 3.17 and 3.18 -- B.5 Adjoint to the Tensor Product -- B.6 More Details on Centres -- Appendix C: OPEs in R(W*) -- C.1 OPEs Involving Omega -- C.2 OPEs Involving the Holomorphic Field T -- C.3 OPEs of Generalised Weight Zero Fields -- References -- Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and Their Generalized Modules -- 1 Introduction -- 1.1 Tensor Category Theory for Finitely Reductive Vertex Operator Algebras -- 1.2 Logarithmic Tensor Category Theory -- 1.3 The Lie Algebra Case -- 1.4 The Vertex Algebra Case. , 1.5 Some Recent Applications and Related Literature -- 1.6 Main Results of the Present Work -- 2 The Setting: Strongly Graded Conformal and Möbius Vertex Algebras and Their Generalized Modules -- References -- C2-Co nite W-Algebras and Their Logarithmic Representations -- 1 Introduction: Irrational C2-Co nite Vertex Algebras -- 2 Preliminaries -- 3 Quantum W-Algebras from Integral Lattices -- 3.1 Af ne W-Algebras -- 3.2 Further Extended Af ne W-Algebras -- 3.3 Maximally Extended W-Algebras: A Conjecture -- 3.4 Triplet Vertex Algebra W(p) -- 4 W-Algebra Extensions of Minimal Models -- 4.1 The Triplet Vertex Algebra Wp,2 -- 5 Construction of Logarithmic Modules and Related Problems -- 5.1 Progenerator and Logarithmic Modules -- 5.2 Screenings and Logarithmic Modules -- 6 Some Logarithmic Modules for W(p)Q -- 7 Conclusion -- References -- C1-Co niteness and Fusion Products for Vertex Operator Algebras -- 1 Introduction -- 2 Proof of Key Theorem -- 3 On Fusion Products -- 4 Proof of Main Theorem -- 5 Discussion -- References.