Note: Intro -- Preface -- Contents -- 1 Introduction -- 2 Waveguides. Radiation Principle. Scattering Matrices -- 2.1 Boundary Value Problem in a Cylinder -- 2.1.1 Statement of the Problem. Operator Pencil -- 2.1.2 The Solvability of the Problem in a Cylinder -- 2.1.3 Asymptotics of Solutions -- 2.2 Problem in a Domain G with Cylindrical Ends -- 2.2.1 Statement and Fredholm Property of the Problem -- 2.2.2 Asymptotics of Solutions -- 2.2.3 Properties of the Index Ind mathcalAβ(µ) and of the Spaces ker mathcalAβ(µ) and coker mathcalAβ(µ) -- 2.2.4 Calculation of the Coefficients in the Asymptotics -- 2.3 Waves and Scattering Matrices -- 2.3.1 Waves -- 2.3.2 Continuous Spectrum Eigenfunctions. The Scattering Matrix -- 2.3.3 The Intrinsic Radiation Principle -- 3 Properties of Scattering Matrices in a Vicinity of Thresholds -- 3.1 Augmented Space of Waves -- 3.1.1 Waves in a Cylinder -- 3.1.2 Waves in Domain G -- 3.2 Continuous Spectrum Eigenfunctions. Scattering Matrices -- 3.2.1 Intrinsic and Expanded Radiation Principles -- 3.2.2 Analyticity of Scattering Matrices with Respect to Spectral Parameter -- 3.3 Other Properties of the Scattering Matrices -- 3.3.1 The Connection Between mathcalS(µ) and S(µ) for τ'< -- µ< -- τ -- 3.3.2 The Connection Between mathcalS(µ) and S(µ) for τ< -- µ< -- τ'' -- 3.3.3 The Limits of S(µ) as µtoτpm0 -- 4 Method for Computing Scattering Matrices -- 4.1 A Method for Computing Scattering Matrices Outside Thresholds -- 4.1.1 Statement of the Method -- 4.1.2 The Problem in GR -- 4.1.3 Justification of the Method for Computing the Scattering Matrix -- 4.2 A Method for Computing Scattering Matrices in Vicinity of Thresholds -- 5 Asymptotic and Numerical Studies of Resonant Tunneling in 2D-Waveguides for Electrons of Small Energy -- 5.1 Statement of the Problem -- 5.2 Limit Problems -- 5.2.1 First Kind Limit Problems. , 5.2.2 Second Kind Limit Problems -- 5.3 Special Solutions to the First Kind Homogeneous Problems -- 5.4 Asymptotic Formulas -- 5.4.1 Asymptotics of the Wave Function -- 5.4.2 Formulas for widetildeS11, widetildeS12, and C1j -- 5.4.3 Formulas for Resonant Tunneling Characteristics -- 5.5 Justification of the Asymptotics -- 5.6 Comparison of Asymptotic and Numerical Results -- 5.6.1 Problems and Methods for Numerical Analysis -- 5.6.2 Comparison of Asymptotic and Numerical Results -- 6 Resonant Tunneling in 2D-Waveguides with Several Resonators -- 6.1 Statement of the Problem and Preliminaries -- 6.1.1 Waveguide and the Radiation Conditions -- 6.1.2 First Kind Limit Problems -- 6.1.3 Second Kind Limit Problems -- 6.2 Asymptotics of the Wave Function and the Scattering Matrix -- 6.2.1 Asymptotics of the Wave Function -- 6.2.2 Formulas for C0, …, C2n+1 -- 6.2.3 Asymptotics of the Scattering Matrix -- 6.3 Asymptotics of the Resonant Tunneling -- 6.3.1 Amplitude of the Transmitted Wave -- 6.3.2 Poles of the Scattering Matrix -- 6.3.3 Transmission Coefficient -- 6.4 Comparison of Asymptotic and Numerical Results -- 7 Resonant Tunneling of High-Energy Electrons in 2D-Waveguides -- 7.1 Introduction -- 7.2 Statement of the Problem -- 7.3 Limit Problems -- 7.3.1 Limit Problems of the First Kind -- 7.3.2 Limit Problems of the Second Kind -- 7.4 Asymptotic Formulas -- 7.4.1 Asymptotics of Wave Functions -- 7.4.2 Formulas for Cml -- 7.4.3 Asymptotics of Scattering Matrix -- 7.4.4 Asymptotics for Poles of Scattering Matrix -- 7.4.5 Asymptotics of Resonant Tunneling -- 7.5 Comparison of Asymptotic and Numerical Results … -- 7.5.1 Asymptotic Formulas -- 7.5.2 Calculation of the Scattering Matrix -- 7.5.3 Comparison of Asymptotics and Numerical Results -- 8 Numerical Simulation of High Energy Electron Transport. , 8.1 Numerical Simulation of Multichannel Resonant Tunneling -- 8.1.1 Closed Resonator -- 8.1.2 The Method for Computing Scattering Matrix -- 8.1.3 Discussion of Numerical Results -- 8.2 Fano Resonances -- 9 The Impact of a Finite Waveguide Work Function on Resonant Tunneling -- 9.1 Preliminaries -- 9.2 A Qualitative Analysis of a Finite Work Function Impact on Electron Transport -- 9.3 Numerical Simulation of Resonant Tunneling with Regard to the Waveguide Work Function -- 9.4 Impact of Finite Work Function on High Energy Electron Transport -- 10 Asymptotics of Resonant Tunneling in 3D Waveguides for Electrons of Small Energy -- 10.1 Statement of the Problem and Outline of the Results -- 10.2 Limit Problems -- 10.2.1 First Kind Limit Problems -- 10.2.2 Second Kind Limit Problems -- 10.3 Tunneling in a Waveguide with One Narrow -- 10.3.1 Special Solutions to the First Kind Homogeneous Problems -- 10.3.2 Passing Through the Narrow -- 10.3.3 Formal Asymptotics -- 10.3.4 The Estimate of the Remainder -- 10.4 Tunneling in a Waveguide with Two Narrows -- 10.4.1 Special Solutions to the Problem in the Resonator -- 10.4.2 Formal Asymptotics -- 10.4.3 The Estimate of the Remainder -- 11 Resonant Tunneling in 2D Waveguides in Magnetic Field -- 11.1 Statement of the Problem -- 11.2 The Limit Problems -- 11.2.1 First Kind Limit Problems -- 11.2.2 Second Kind Limit Problems -- 11.3 Special Solutions to Homogeneous First Kind Limit Problems -- 11.4 Asymptotic Formulas -- 11.4.1 Asymptotics of the Wave Function -- 11.4.2 Formulas for widetildeS11, widetildeS12, and C1j -- 11.4.3 Formulas for Resonant Tunneling Characteristics -- 11.5 Justification of the Asymptotics -- 11.6 Comparison of Asymptotic and Numerical Approaches -- 11.6.1 Problems and Methods for Numerical Analysis -- 11.6.2 Comparison of Asymptotic and Numerical Results. , 11.6.3 Dependence of Resonant Tunneling on the Magnetic Field Location in the Resonator -- 12 Effect of Magnetic Field on Resonant Tunneling in 3D Waveguides of Variable Cross-Section -- 12.1 Introduction -- 12.2 Statement of the Problem -- 12.3 Limit Problems -- 12.3.1 First Kind Limit Problems -- 12.3.2 Second Kind Limit Problems -- 12.4 Special Solutions of Limit Problems -- 12.5 Asymptotic Formulas -- 12.5.1 The Asymptotics of a Wave Function -- 12.5.2 Formulas for widetildeS11, widetildeS12, and C11,…,C14 -- 12.5.3 Asymptotics for Resonant Tunneling Characteristics -- 12.6 Justification of the Asymptotics -- 13 Asymptotic Analysis of Multichannel Resonant Tunneling -- 13.1 Statement of the Problem and Limit Problems -- 13.2 Tunneling in a Waveguide with One Narrow -- 13.2.1 Special Solutions to the First Kind Homogeneous Problems -- 13.2.2 Asymptotic Formulas -- 13.3 Tunneling in a Waveguide with Two Narrows -- 13.3.1 Formal Asymptotics -- 13.3.2 The Estimate of the Remainder -- 14 Electronics Devices Based on Resonant Tunneling -- 14.1 Magnetic Field Sensors Based on Quantum Waveguides -- 14.2 Transistors Based on Quantum Waveguides -- 14.3 Electron Flow Switch for Quantum Nets -- Appendix Bibliographical Sketch -- Appendix References.

Note: Includes bibliographical references (p. 281-299) and index

Note: Intro -- Preface -- Contents -- Contributors -- Part I Overview -- Co-development of Methodology, Applications, and Hardware in Computational Science and Artificial Intelligence -- 1 Simultaneous Development of Hardware and Software -- 2 Co-development Potential of Computational Science and Artificial Intelligence -- 3 Challenges in the Contemporary Field of Scientific Computing and Artificial Intelligence -- 4 Conclusions -- References -- Part II Methodology -- Novel Strategies for Data-Driven Evolutionary Optimization -- 1 Introduction -- 2 Algorithms -- 2.1 BioGP -- 2.2 EvoNN -- 2.3 EvoDN2 -- 2.4 cRVEA -- 3 Test Functions -- 4 Applications in Materials Research -- 5 Concluding Remarks -- References -- Artificial Intelligence and Computational Science -- 1 Classical Method of Scientific Knowledge -- 2 Genetic Algorithms -- 3 AI and New Methods of Scientific Analysis -- 4 Open Problems and Development Prospect -- 5 Conclusions -- References -- Supervised Learning and Applied Mathematics -- 1 Introduction -- 2 Applied Mathematics for Supervised Learning -- 3 Supervised Learning for Applied Mathematics -- 4 Illustration: Calibration of the Heston Model -- 4.1 Monte Carlo Solutions -- 4.2 Calibration -- 4.3 Numerical Tests -- 5 Discussion -- References -- Application of the Topological Gradient to Parsimonious Neural Networks -- 1 Introduction -- 2 Parsimonious Neural Networks -- 2.1 Topological Optimization Methods -- 2.2 Adaptation for Compression -- 3 Numerical Examples -- 3.1 NeurEco -- 3.2 Image Compression -- References -- Generation of Error Indicators for Partial Differential Equations by Machine Learning Methods -- 1 Introduction -- 2 Indicators of Computational Errors -- 2.1 Adaptive Numerical Methods and Error Indicators -- 2.2 Accuracy of Error Indicators -- 2.3 A Class of Boundary Value Problems -- 3 Network Error Indicator. , 3.1 Local Networks -- 4 Examples -- 5 Conclusions -- References -- Newton Method for Minimal Learning Machine -- 1 Introduction -- 2 MLM -- 2.1 Formulae -- 2.2 MLM Using the Newton Method -- 3 Experiments -- 3.1 Experimental Setup -- 3.2 Results -- 4 Discussion -- 5 Conclusions -- References -- Limited Memory Bundle Method for Clusterwise Linear Regression -- 1 Introduction -- 2 Clusterwise Linear Regression -- 3 LMBM-CLR -- 4 Numerical Experiments -- 4.1 Results on Small Data Sets with Known Solution -- 4.2 Results on Large Real-World Data Sets -- 5 Conclusions -- References -- Improving Clustering and Cluster Validation with Missing Data Using Distance Estimation Methods -- 1 Introduction -- 2 Methods -- 3 Experiments and Results -- 4 Discussion -- 5 Conclusions -- References -- Part III Medical Applications -- Kubelka-Munk Model and Stochastic Model Comparison in Skin Physical Parameter Retrieval -- 1 Introduction -- 2 Materials and Methods -- 2.1 Stochastic Model -- 2.2 Kubelka-Munk Model -- 2.3 Convolutional Neural Network -- 2.4 Model Inversion -- 3 Results and Discussion -- 3.1 Retrieval Results -- 3.2 Model Comparison -- 3.3 Discussion -- 4 Conclusion -- References -- Unsupervised Numerical Characterization in Determining the Borders of Malignant Skin Tumors from Spectral Imagery -- 1 Introduction -- 2 Mathematical Model of the Human Skin -- 3 Spectral Imaging -- 4 Computational Methods -- 4.1 Modified Standard Normal Variate Correction Algorithm -- 4.2 Linear Unmixing -- 4.3 Linear Unmixing of Estimated Single Scattering Albedo -- 4.4 Closed-Form Chromophore Specific Approximation for Estimated Single Scattering Albedo -- 5 Results -- 5.1 Simulated Spectral Cube -- 5.2 Basal Cell Carcinoma -- 5.3 In-situ Melanoma -- 6 Discussion -- 7 Conclusion -- References -- Validation of Knee KL-classifying Deep Neural Network with Finnish Patient Data. , 1 Introduction -- 2 Materials and Methods -- 3 Results -- 4 Discussion and Summary -- References -- Predicting Future Overweight and Obesity from Childhood Growth Data: A Case Study -- 1 Introduction -- 2 Materials and Methods -- 2.1 Data -- 2.2 Model Fitting -- 2.3 Performance Evaluation -- 3 Results -- 4 Discussion -- 5 Conclusion -- References -- Predicting Overweight and Obesity in Later Life from Childhood Data: A Review of Predictive Modeling Approaches -- 1 Introduction -- 2 Materials and Methods -- 3 Results -- 3.1 Surveys, Literature Reviews, and Meta-analyses -- 3.2 Predictive Modeling Approaches -- 4 Conclusions -- 5 Summary Points -- References -- Part IV Industrial and Technological Applications -- Applications of Industrial IoT and WSNs in O& -- M Programmes for Offshore Wind Farms -- 1 Introduction -- 1.1 Background and Overview -- 1.2 Remote Monitoring in Offshore Environments -- 2 Background-Practical Applications of WSNs in Offshore Environments -- 2.1 Structural and Condition Monitoring -- 2.2 WSNs for Environmental Monitoring -- 3 Technology Requirements and Challenges to Address -- 3.1 Power Requirements -- 3.2 Topology -- 3.3 Cyber Security -- 3.4 Machine Learning and Scientific Computing: Algorithms for Decision Systems -- 4 Case Study -- 5 Suggestions and Guidelines -- 6 Conclusions -- References -- Combined Model Order Reduction Techniques and Artificial Neural Network for Data Assimilation and Damage Detection in Structures -- 1 Introduction -- 2 Dataset Construction Through a Parametric Model Order Reduction (pMOR) Technique -- 3 Fully Convolutional Network -- 4 Numerical Benchmark -- 5 Conclusion -- References -- Using Wave Propagation Simulations and Convolutional Neural Networks to Retrieve Thin Film Thickness from Hyperspectral Images -- 1 Introduction -- 2 Materials and Methods. , 2.1 1D Wave Simulations with Discrete Exterior Calculus -- 2.2 Convolutional Neural Network -- 2.3 Measured Reference Samples -- 2.4 Hyperspectral Imaging -- 3 Results -- 4 Discussion and Conclusion -- References.

Note: Intro -- Preface -- Contents -- List of Contributors -- Index -- Scientifice Computation.

Note: Applied and Numerical Partial Differential Equations -- Roland Glowinski: The Unconventional and Unexpected Path of a Mathematician -- The Scientific Career of Roland Glowinski -- Books by Roland Glowinski -- On a Class of Partial Differential Equations with Nonlocal Dirichlet Boundary Conditions -- 1 Introduction -- 2 Setting of the Problem -- 2.1 Notation -- 2.2 The Problem -- 3 The Main Result -- 3.1 Boundary Conditions -- 3.2 A Priori Estimates -- 3.3 Further Regularity -- 4 Proof of Theorem 1 -- 4.1 Proof of Uniqueness -- 4.2 Approximation -- 4.3 Estimates -- 4.4 Proof of Existence -- References -- A Unified Discrete--Continuous Sensitivity Analysis Method for Shape Optimization -- 1 Introduction -- 2 A Potential Flow Model Problem -- 3 Sensitivity Analysis -- 3.1 Before Discretization -- 3.2 After Finite-Element Discretization -- 4 Shape and Material Derivatives of Functions -- 5 Rules for the Material Derivative -- 6 Sensitivity Analysis Using Material Derivatives -- References -- A Novel Approach to Modeling Coronary Stents Using a Slender Curved Rod Model: A Comparison Between Fractured Xience-Like and Palmaz-Like Stents -- 1 Motivation -- 2 The Model -- 2.1 Geometry: Parametrization of the Stent Frame -- 2.2 Mechanics: Stent as a Collection of Elastic Curved Rods -- 2.3 Numerical Implementation -- 3 Numerical Results -- 3.1 Xience-Like Stent (Stent X) (Non-Uniform Geometry) -- 3.2 Palmaz-Like Stent (Stent P) (Uniform Geometry) -- 4 Conclusions -- References -- On the Stochastic Modelling of Interacting Populations. A Multiscale Approach Leading to Hybrid Models -- 1 Introduction -- 2 Individuals, Interactions and Evolution -- 2.1 Direct Interaction and System Evolution -- 2.2 Indirect Interaction and System Evolution -- 3 Direct Interaction: an Aggregation--Repulsion Model -- 4 Interaction via Underlying Fields: A Birth and Growth Model. , 5 Hybrid Models: Large Population Behavior -- 5.1 The Aggregation--Repulsion Model -- 5.2 The Branching and Growth Process -- 6 Long Time Behavior -- 6.1 Interacting--Diffusing Particles -- 6.2 Complete System -- References -- Remarks on the Controllability of Some Parabolic Equations and Systems -- 1 Introduction: Controllability and Observability -- 2 The Classical Heat Equation: Observability and Carleman Estimates -- 3 Positive and Negative Controllability Results for the One-Dimensional Burgers Equation -- 4 The Navier--Stokes and Boussinesq Systems -- 5 Some Other Nonlinear Systems from Mechanics -- References -- Goal Oriented Mesh Adaptivity for Mixed Control-State Constrained Elliptic Optimal Control Problems -- 1 Introduction -- 2 The Mixed Control-State Elliptic Optimal Control Problem and Its Finite Element Approximation -- 3 Error Representation in the Quantity of Interest -- 4 Weighted Primal--Dual A Posteriori Error Estimator -- 5 Numerical Results -- References -- Feedback Solution and Receding Horizon Control Synthesis for a Class of Quantum Control Problems -- 1 Introduction -- 2 Control Formulation -- 3 Operator Splitting Method -- 4 Receding Horizon Control Synthesis -- 4.1 Time-Discretization -- 5 Numerical Tests -- References -- Fluid Dynamics of Mixtures of Incompressible Miscible Liquids -- 1 Introduction -- 2 Simple Mixtures and the Law of Additive Volume -- 3 Mass Transport Equations for Simple Mixtures of Incompressible Miscible Liquids -- 4 Volume Transport Equations for Simple Mixtures of Incompressible Miscible Liquids -- 5 Boundary Conditions at a Solid Wall -- 6 Korteweg Stresses -- 7 Relaxation Effects -- 8 Relaxation Effects in the Modeling of Gradient Stresses -- 9 Transient Interfacial Tension -- 10 Discussion -- References. , Demand Forecasting Method Based on Stochastic Processes and Its Validation Using Real-World Data -- 1 Introduction -- 2 Outline of the Newsboy Problem -- 3 Black--Scholes Models -- 4 Validation Data -- 4.1 Original Data -- 4.2 Calculation and Loss Evaluation -- 5 Numerical Experiments and Result -- 5.1 Aspects of the Techniques -- 5.2 Selection of Parameters -- 5.3 Result of Case 1 -- 5.4 Result of Case 2 -- 6 Conclusion -- References -- Analytic Bounds for Diagonal Elements of Functions of Matrices -- 1 Introduction -- 2 Quadratic Forms and Gauss Quadrature Rules -- 3 Analytic Bounds for the Diagonal Elements of the Inverse -- 4 Analytic Bounds for Elements of Other Functions -- References -- Numerical Methods for Ferromagnetic Plates -- 1 Introduction -- 2 Modeling of Ferromagnetism -- 2.1 A Scalar Potential Model -- 3 Two Formulations of the Scalar Potential Problem -- 3.1 Boundary Integral Formulation of the Scalar Potential Model -- 3.2 A Domain Decomposition Formulation for the Scalar Potential Problem -- 4 Discretization and Numerical Methods -- 4.1 Boundary Integral Method for the Scalar Potential Model -- 4.2 Scalar Potential Problem with Poisson Formula Boundary Condition -- 5 Numerical Results -- 5.1 A Thin Steel Plate Placed in Front of a Conductor -- 5.2 Screen Effect Behind the Plate -- 5.3 Magnetization in the Plate -- 5.4 An Industrial Application -- 6 Conclusion and Remarks -- References -- Two-Sided Estimates of the Solution Set for the Reaction--Diffusion Problem with Uncertain Data -- 1 Introduction -- 2 Lower Bound of rS -- 3 Upper Bound of rS -- 3.1 Error Majorant -- 3.2 Upper Bound -- References -- Guaranteed Error Bounds for Conforming Approximations of a Maxwell Type Problem -- 1 Introduction -- 2 Notation and Basic Relations -- 3 A Posteriori Error Estimates of the First Type -- 3.1 Upper Bound of the Error. , 3.2 Lower Bound of the Error -- 3.3 Practical Implementation -- 4 A Posteriori Error Estimate of the Second Type -- 5 A Posteriori Estimate of the Third Type -- 5.1 An Advanced Form of the Error Majorant -- 5.2 Optimal Form of -- References -- A Componentwise Splitting Method for Pricing American Options Under the Bates Model -- 1 Introduction -- 2 Option Pricing Model -- 2.1 Bates Model -- 2.2 Linear Complementarity Problem for American Options -- 3 Discretization -- 3.1 Discretization of Spatial Differential Operator -- 3.2 Discretization of Integral Term -- 3.3 Semidiscrete LCP -- 3.4 Time Discretization -- 4 Componentwise Splitting Method -- 4.1 Solution of One-Dimensional LCPs -- 5 Numerical Experiments -- 6 Conclusions -- References -- Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach -- 1 Introduction -- 2 Main Results -- 3 Bicharacteristic Rays and Group Velocity -- 4 A Key Identity via Multipliers -- 5 Filtering and Uniform Observability -- 6 Further Comments and Open Problems -- References -- Index.

Note: Structural Optimization with Uncertainties -- Part I Prototype Problems -- 1 Guaranteed Approaches -- 1.1 Prototype Problem 1 -- 1.2 Prototype Problem 2 Illustrating Nonexistenceof a Worst Load -- 2 Probabilistic Uncertainties -- 2.1 Prototype Problem 3: Moment Constraints -- 2.2 Prototype Problem 4: Optimization with Direct Probabilistic Constraints -- Part II Optimization in Frame of Guaranteed Approach -- 3 Uncertainties and Worst Case Scenarios -- 3.1 Transformation Schemes -- 3.2 Uncertainties in Loading Conditions -- 3.3 Some Optimal Solutions -- 3.4 Optimal Design with Uncertainties Versus Optimal Multipurpose Design -- 4 Optimal Design of Beams and Plates with Uncertainties -- 4.1 Beams Having the Smallest Weight with Constraints on Strength -- 4.2 Some Rigidity Optimization Problems for Elastic Beams and Plates -- 4.2.1 Minimization of Elastic Deflection -- 4.2.2 Rigidity Estimation for Thin-Walled Elastic Structures and Worst Case Loading -- 5 Uncertainties in Fracture Mechanics and Optimal Design Formulations -- 5.1 Basic Relations of Fracture Mechanics -- 5.2 Model Assumptions and Optimization Problems -- 6 Beams and Plates with Brittle-Fracture Constraints -- 6.1 Optimization of Beams -- 6.2 Optimum Shapes of Holes in Elastic Plates -- 6.3 Optimal Design of Bimaterial Layered Beams -- 7 Optimization of Axisymmetric Shells Against Brittle Fracture -- 7.1 Basic Relations of the Membrane Shell Model -- 7.2 Some Problems of Optimal Thickness Distribution -- 7.2.1 Thickness Distribution for Toroidal Shell -- 7.2.2 Thickness Distribution for Conical Shell -- 7.2.3 Thickness Distribution for Spherical Shell -- 7.3 Some Examples with Prescribed Middle Surfaces -- 8 Shape and Thickness Distribution of Pressure Vessels -- 8.1 Optimizing the Shape of a Shell of Revolution. , 8.2 The Search for the Shape and Thickness Distribution of an Optimal Shell -- 8.3 Some Properties of the Optimal Solution -- 9 Brittle and Quasi-Brittle Materials -- 9.1 Mass Effectiveness and Its Maximization -- 9.2 Analytical Solution and Convexity Properties -- 10 Gravity Forces and Snow Loading -- 10.1 Equilibrium of Shells Under Gravity Forces -- 10.2 Weight Minimization -- 10.3 Shape and Thickness Optimization by Genetic Algorithm -- 11 Damage Characteristics and Longevity Constraints -- 11.1 Transformations of the Longevity Constraint -- 11.2 Investigation of Optimal Design -- 11.3 Loader Crane Optimization with Longevity Constraints -- 11.3.1 First Example -- 11.3.2 Second Example -- 11.3.3 Third Example -- 12 Optimization of Shells Under Cyclic Crack Growth -- 12.1 Basic Relations and Optimization Modeling -- 12.2 Optimal Thickness Distribution for Shells of Given Geometry -- 12.3 Shape Optimization of Axisymmetric Shells -- 12.4 Simultaneous Optimization of the Meridian Shape and the Thickness Distribution of the Shell -- 12.4.1 Optimum Shells of Positive Gaussian Curvature -- 12.4.2 Optimum Shells of Negative Gaussian Curvature -- 12.4.3 Some Properties of Optimal Solution -- 13 Uncertainties in Material Characteristics -- 13.1 Discrete Sets of Materials with Uncertain Properties -- 13.1.1 Basic Representations -- 13.1.2 Minimization of Reaction Force -- 13.2 Uncertainties in Elastic Moduli -- Part III Probabilistic and Mixed Probabilistic - GuaranteedApproaches -- 14 Some Basic Notions of Probability Theory -- 14.1 Random Variables -- 14.2 Some Continuous Distributions -- 14.3 Functions of Random Variables -- 15 Probabilistic Approaches for Incomplete Information -- 15.1 Probabilistic Problems with Fracture Mechanics Constraints -- 15.2 Beams with Random Crack Length -- 15.3 Beams with Randomly Placed Cracks. , 15.4 The Probabilistic Approach with Constrainton the Stress Intensity Factor -- 15.5 Conclusions -- 16 Optimization Under Longevity Constraint -- 16.1 Basic Assumptions and Relations -- 16.2 Probabilistic Optimization -- 16.3 Examples of Probabilistic Problems -- 16.3.1 Simply Supported Beam -- 16.3.2 Cantilever Beam -- 16.3.3 Optimal Design of a Frame -- 16.3.4 Clamped-Simply Supported Beam -- 16.4 Moment Constraints -- 17 Mixed Probabilistic-Guaranteed Optimal Design -- 17.1 Probabilistic-Guaranteed Optimization -- 17.2 Analytic Solution -- 17.3 A Toroidal Shell -- 17.4 A Shell Loaded by Forces at the Free Ends -- References -- Index.

Note: Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Resonance Structures -- 1.2 Scattering Matrix -- 1.3 Method for Approximate Computation of Scattering Matrices -- 1.4 Asymptotic and Numerical Studies of Resonant Tunneling -- 1.5 The Impact of a Finite Waveguide Work Function on Resonant Tunneling -- 1.6 Asymptotic Study of Resonant Tunneling in 3D Waveguides for Electrons of Small Energy -- 1.7 Electron Resonant Tunneling in the Presence of Magnetic Fields -- 1.8 Numerical Simulation of High Energy Electron Resonant Tunneling, the Fano Resonances -- 1.9 Asymptotic Analysis of Multichannel Resonant Tunneling -- 1.10 Electronics Devices Based on Resonant Tunneling in Waveguides of Variable Cross-Sections -- 2 Waveguides. Radiation Principle. Scattering Matrices -- 2.1 Boundary Value Problem in a Cylinder -- 2.1.1 Statement of the Problem. Operator Pencil -- 2.1.2 The Solvability of the Problem in a Cylinder -- 2.1.3 Asymptotics of Solutions -- 2.2 Problem in a Domain G with Cylindrical Ends -- 2.2.1 Statement and Fredholm Property of the Problem -- 2.2.2 Asymptotics of Solutions -- 2.2.3 Properties of the Index Ind mathcalAβ(μ) and of the Spaces ker mathcalAβ(μ) and coker mathcalAβ(μ) -- 2.2.4 Calculation of the Coefficients in the Asymptotics -- 2.3 Waves and Scattering Matrices -- 2.3.1 Waves -- 2.3.2 Continuous Spectrum Eigenfunctions. The Scattering Matrix -- 2.3.3 The Intrinsic Radiation Principle -- 3 Properties of Scattering Matrices in a Vicinity of Thresholds -- 3.1 Augmented Space of Waves -- 3.1.1 Waves in a Cylinder -- 3.1.2 Waves in Domain G -- 3.2 Continuous Spectrum Eigenfunctions. Scattering Matrices -- 3.2.1 Intrinsic and Expanded Radiation Principles -- 3.2.2 Analyticity of Scattering Matrices with Respect to Spectral Parameter -- 3.3 Other Properties of the Scattering Matrices. , 3.3.1 The Connection Between mathcalS(μ) and S(μ) for τ'< -- μ< -- τ -- 3.3.2 The Connection Between mathcalS(μ) and S(μ) for τ< -- μ< -- τ'' -- 3.3.3 The Limits of S(μ) as μtoτpm0 -- 4 Method for Computing Scattering Matrices -- 4.1 A Method for Computing Scattering Matrices Outside Thresholds -- 4.1.1 Statement of the Method -- 4.1.2 The Problem in GR -- 4.1.3 Justification of the Method for Computing the Scattering Matrix -- 4.2 A Method for Computing Scattering Matrices in Vicinity of Thresholds -- 5 Asymptotic and Numerical Studies of Resonant Tunneling in 2D-Waveguides for Electrons of Small Energy -- 5.1 Statement of the Problem -- 5.2 Limit Problems -- 5.2.1 First Kind Limit Problems -- 5.2.2 Second Kind Limit Problems -- 5.3 Special Solutions to the First Kind Homogeneous Problems -- 5.4 Asymptotic Formulas -- 5.4.1 Asymptotics of the Wave Function -- 5.4.2 Formulas for widetildeS11, widetildeS12, and C1j -- 5.4.3 Formulas for Resonant Tunneling Characteristics -- 5.5 Justification of the Asymptotics -- 5.6 Comparison of Asymptotic and Numerical Results -- 5.6.1 Problems and Methods for Numerical Analysis -- 5.6.2 Comparison of Asymptotic and Numerical Results -- 5.7 The Impact of a Finite Waveguide Work Function on Resonant Tunneling -- 5.7.1 Preliminaries -- 5.7.2 A Qualitative Analysis of a Finite Work Function Impact on Electron Transport -- 5.7.3 Numerical Simulation of Resonant Tunneling with Regard to the Waveguide Work Function -- 6 Asymptotics of Resonant Tunneling in 3D Waveguides for Electrons of Small Energy -- 6.1 Statement of the Problem and Outline of the Results -- 6.2 Limit Problems -- 6.2.1 First Kind Limit Problems -- 6.2.2 Second Kind Limit Problems -- 6.3 Tunneling in a Waveguide with One Narrow -- 6.3.1 Special Solutions to the First Kind Homogeneous Problems -- 6.3.2 Passing Through the Narrow. , 6.3.3 Formal Asymptotics -- 6.3.4 The Estimate of the Remainder -- 6.4 Tunneling in a Waveguide with Two Narrows -- 6.4.1 Special Solutions to the Problem in the Resonator -- 6.4.2 Formal Asymptotics -- 6.4.3 The Estimate of the Remainder -- 7 Resonant Tunneling in 2D Waveguides in Magnetic Field -- 7.1 Statement of the Problem -- 7.2 The Limit Problems -- 7.2.1 First Kind Limit Problems -- 7.2.2 Second Kind Limit Problems -- 7.3 Special Solutions to Homogeneous First Kind Limit Problems -- 7.4 Asymptotic Formulas -- 7.4.1 Asymptotics of the Wave Function -- 7.4.2 Formulas for widetildeS11, widetildeS12, and C1j -- 7.4.3 Formulas for Resonant Tunneling Characteristics -- 7.5 Justification of the Asymptotics -- 7.6 Comparison of Asymptotic and Numerical Approaches -- 7.6.1 Problems and Methods for Numerical Analysis -- 7.6.2 Comparison of Asymptotic and Numerical Results -- 7.6.3 Dependence of Resonant Tunneling on the Magnetic Field Location in the Resonator -- 8 Effect of Magnetic Field on Resonant Tunneling in 3D Waveguides of Variable Cross-Section -- 8.1 Introduction -- 8.2 Statement of the Problem -- 8.3 Limit Problems -- 8.3.1 First Kind Limit Problems -- 8.3.2 Second Kind Limit Problems -- 8.4 Special Solutions of Limit Problems -- 8.5 Asymptotic Formulas -- 8.5.1 The Asymptotics of a Wave Function -- 8.5.2 Formulas for widetildeS11, widetildeS12, and C11,,C14 -- 8.5.3 Asymptotics for Resonant Tunneling Characteristics -- 8.6 Justification of the Asymtotics -- 9 Numerical Simulation of High Energy Electron Transport -- 9.1 Numerical Simulation of Multichannel Resonant Tunneling -- 9.1.1 Closed Resonator -- 9.1.2 The Method for Computing Scattering Matrix -- 9.1.3 Discussion of Numerical Results -- 9.2 Fano Resonances -- 10 Asymptotic Analysis of Multichannel Resonant Tunneling -- 10.1 Statement of the Problem and Limit Problems. , 10.2 Tunneling in a Waveguide with One Narrow -- 10.2.1 Special Solutions to the First Kind Homogeneous Problems -- 10.2.2 Asymptotic Formulas -- 10.3 Tunneling in a Waveguide with Two Narrows -- 10.3.1 Formal Asymptotics -- 10.3.2 The Estimate of the Remainder -- 11 Electronics Devices Based on Resonant Tunneling -- 11.1 Magnetic Field Sensors Based on Quantum Waveguides -- 11.2 Transistors Based on Quantum Waveguides -- 11.3 Electron Flow Switch for Quantum Nets -- Bibliographical Sketch -- Bibliography.