Numerical analysis Books

Book SynopsisThis book constitutes the refereed proceedings of the 16th International Conference on Learning and Intelligent Optimization, LION 16, which took place in Milos Island, Greece, in June 2022.The 36 full papers and 3 short papers presented in this volume were carefully reviewed and selected from 60 submissions. LION deals with automatic solver configuration, parallel methods, intelligent optimization, nature-inspired algorithms, hard combinatorial optimization problems, DC learning, computational intelligence, and others. The contributions were organized in topical sections as follows: Invited Papers; Contributed Papers.Table of Contents​Invited Papers.- Optimal Scheduling of the Leaves of a Tree and the SVO Frequencies of Languages.- From Design of Experiments to Combinatorics of Disasters: A Conceptual Framework for Disaster Exercises.- Separating two polyhedra utilizing alternative theorems and penalty function.- Contributed Papers. -A Composite Index Method for Optimization Benchmarking.- Optimal Energy Management of Microgrid Using Multi-objective Optimisation Approach.- A Stochastic Alternating Balance k-Means Algorithm for Fair Clustering.- Binary Black Widow Optimization Algorithm for Feature Selection Problems.- Learning to Solve a Stochastic Orienteering Problem with Time Windows.- ML-based approach for accelerating global search algorithm for solving multicriteria problems .- The Skewed Kruskal algorithm.- Bounds for sparse solutions of K-SVCR multi-class classification model.- Integer Linear Programming in Solving an Optimization Problem at the Mixing Department of the Metallurgical Production.- Realtime Gray-Box Algorithm Configuration.- Dynamic urban solid waste management system for smart cities.- Single MCMC Chain Parallelisation on Decision Trees.- Single MCMC Chain Parallelisation on Decision Trees.- Competitive supply allocation in a distribution network under overproduction.- Safe-exploration of control policies from safe-experience via Gaussian Processes.- Bayesian Optimization in Wasserstein Spaces.- Network Vulnerability Analysis in Wasserstein Spaces.- BERT Self-Learning Approach with Limited Labels for Document Classification.- Autonomous Learning Optimization for Deep Learning.- Optimizing Data Augmentation Policy through Random Unidimensional Search.- Evaluating Student Behaviour on the MathE Platform - Clustering Algorithms Approaches.- Unsupervised Training for Neural TSP Solver.- Comparing surrogate models for tuning optimization algorithms.- Search and Score-based Waterfall Auction Optimization.- Survey on KNN Methods in Data Science.- Constrained Shortest Path and Hierarchical Structures.- Investigation of Graph Neural Networks for Instance Segmentation of Industrial Point Cloud Data.- Fitness landscape ruggedness impact on PSO in dealing with three variants of the travelling salesman problem.- A Multi-UAVs’ Provider Model for the provision of 5G Service Chains: a game theoretic approach.- Metabolic Syndrome Risk Forecasting on Elderly with ML Techniques.- Airport Digital Twins for Resilient Disaster Management Response.- Strategies for Surviving Aggressive Multiparty Repeated Standoffs.- A Hybridization of GRASP and UTASTAR for Solving the Vehicle Routing Problem with Pickups and Deliveries and 3D Loading Constraints.- Packing hypertrees and the k-cut problem in Hypergraphs.- Maximizing the Eigenvalue-Gap and Promoting Sparsity of Doubly Stochastic Matrices with PSO.- Value of Information in the Mean-Square Case and its Application to the Analysis of Financial Time-Series Forecast.

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Book SynopsisIn this book, well-known scientists discuss modern aspects of generalized continua, in order to better understand modern materials and advanced structures. They possess complicated internal structure, and it requires the development of new approaches to model such structures and new effects caused by it. This book combines fundamental contributions in honor of Victor Eremeyev and his 60th birthday.Table of Contents1 Effects of 3-D Printing Infill Density Parameter on the Mechanical Properties of PLA Polymer Reza Afshar, Simon Jeanne, and Bilen Emek Abali1.1 Introduction 1.2 Additive Manufacturing 1.3 Materials and Methods 1.3.1 Fused Deposition Modeling (FDM) 1.3.2 Unidirectional Tensile Tests 1.3.3 Digital Image Correlation Method 1.4 Results and Discussions 1.5 Conclusions References 2 Advance Approximate Analytical Solutions of the Contact Problem for an Inhomogeneous Layer Sergei M. Aizikovich, Polina A. Lapina, and Sergei S. Volkov2.1 Introduction 2.2 Statement of the Problem of a Shear of the Surface of an Inhomogeneous Layer 2.3 Integral Equations of Contact Problems 2.4 Numerical Analysis 2.5 Closure References 3 The Direct Approach for Plates Considering Hygrothermal Loading and Residual Kinetics Marcus Aßmus, Zia Javanbakht, and Holm Altenbach3.1 Introduction 3.2 Frame of Reference 3.3 Thermal Effects and Hygroscopic Impact 3.4 Residual Kinetics 3.5 Conclusion References 4 A Technique for Determining True Deformation Diagrams Under Dynamic Tension Using DIC Artem V. Basalin, Anatoly M. Bragov, Aleksandr Yu. Konstantinov,and Andrey R. Filippov4.1 Introduction 4.2 Pneumatic Dynamic Installation for Testing Materials at a Deformation Rate of the Order of 10-100 s−1 4.2.1 Installation Scheme 4.2.2 Methods of Obtaining and Processing Information in the Experiment 4.3 Test Results of Sheet (3 mm) Steel 09G2S in a Wide Range of Strain Rates 4.4 Conclusion References 5 Strain Gradient Elasticity and Dual Internal Variables Arkadi Berezovski5.1 Introduction 5.2 Dual Internal Variables 5.2.1 Evolution Equations 5.2.2 Quadratic Free Energy 5.3 Concluding Remarks References 6 On the Coercivity of Strain Energy Functions in Generalized Models of 6-Parameter Shells Mircea Bîrsan and Patrizio Neff6.1 Introduction 6.2 General 6-Parameter Elastic Shells. Governing Equations 6.3 The Order ℎ3 Model of 6-Parameter Shells made of Cosserat Material 6.3.1 Coercivity Results for the Model of Order ����(ℎ3) 6.3.2 Existence of Minimizers 6.4 The Higher Order Model of Cosserat 6-Parameter Shells References 7 Solving the Equations of Nonlinear Model of Crystalline Media with Complex Lattice and Some Structures of Plane Deformation Anatolii N. Bulygin and Yuri V. Pavlov7.1 Introduction 7.2 Nonlinear Model of Deformation of Crystal Media 7.3 General Solution of Dynamic Equations of Plane Deformation of the Nonlinear Model 7.4 Solving the Micro-Field Equations 7.5 Conclusion References 8 Modal Analysis of a Second-Gradient Annular Plate made of an Orthogonal Network of Logarithmic Spiral Fibers Alessandro Ciallella, Francesco D’Annibale, Francesco dell’Isola,Dionisio Del Vescovo, and Ivan Giorgio8.1 Introduction 8.2 The Model for a Fiber Net Arranged in Logarithmic Spirals 8.3 Modal Analysis 8.4 Conclusions and Future Perspectives References 9 Non-Linear Simplest Reduced Kelvin’s Medium in the Vicinity of the Spherical Stress State: Waves and Instabilities Mikhail A. Drepin and Elena F. Grekova9.1 Introduction and Notation9.2 Basic Equations for the Isotropic Elastic Reduced Kelvin’s Medium in the Vicinity of a Preliminary Stress State 9.2.1 Dynamic Laws of a Nonlinear Reduced Kelvin Medium 9.2.2 Constitutive Relations for a Nonlinear Reduced Kelvin Medium9.2.3 The Simplest Nonlinear Reduced Kelvin Medium. Strain Energy9.2.4 Medium in the Vicinity of a Homogeneous Nonlinear Spherical Deformation State 9.3 Dispersion Relations of the Simplest Elastic Reduced Kelvin Medium in the Vicinity of Preliminary Spherical Strain State for Special Directions of Perturbation Propagation. Waves and Stability9.3.1 Harmonic Waves 9.3.2 Propagation of Harmonic Waves Along the Body Point Axis (ˆ������������ = ±������������0) 9.3.3 Propagation of Harmonic Waves in the Direction Orthogonal to the Body Point Axis (ˆ������������⊥������������0) 9.4 Conclusion References 10 On the Spectrum of Relaxation Times of Coupled Diffusion and Rheological Processes in Media with Microstructure Dmitrii S. Dudin and Ilya E. Keller10.1 Introduction 10.2 Deformations 10.3 Balance Equations 10.4 The Helmholtz Free Energy 10.5 Thermodynamic Inequality 10.6 Constitutive Equations 10.7 Model Problem and its Equations 10.8 Diffusion Coefficients in Coupled System 10.9 Conclusion References 11 Representative Volume Element Size and Length Scale Identification in Generalised Magneto-Elasticity Sinan Eraslan, Inna M. Gitman, Mingxiu Xu, Harm Askes, and René de Borst11.1 Introduction 11.2 Formulation 11.2.1 Homogenisation and Macroscopic Characteristic Length Scale Parameters11.2.2 Determination of RVE Sizes and Identification of Characteristic Length Scale Parameters 11.3 Numerical Results and Discussion11.4 Conclusions References 12 Rayleigh Waves in the Cosserat Half-Space (Reduced Model) and Half-Space of Damaged Material Vladimir Erofeev, Artem Antonov, Anna Leonteva, and Alexey Malkhanov12.1 Introduction 12.2 Rayleigh Waves in the Cosserat Half-space (Reduced Model) 12.3 Rayleigh Waves in the Half-space of Damaged Material 12.4 Conclusion References 13 Validation of a Hemi-Variational Block-Based Approach to the Modelling of Common In-plane Failures in Masonry Structures José Manuel Torres Espino, Jaime Heman Espinoza Sandoval, Chuong Anthony Tran, Roberto Fedele, Emilio Turco, Francesco dell’Isola, LucaPlacidi, Anil Misra, Francisco James León Trujillo, and Emilio Barchiesi13.1 Introduction 13.2 Mathematical Formulation 13.2.1 Vertex Springs and Stiffnesses 13.2.2 Deformation Energy and Impenetrability Potential 13.2.3 Damage Laws 13.2.4 Principle of Minimum Potential Energy 13.2.5 Numerical Model 13.2.6 Stiffness Matrix13.2.7 Algorithm 13.3 Results 13.3.1 Comparative Result 13.3.2 Influence of Mortar Thickness on Masonry Performance 13.3.3 Bending and Shear Sliding 13.3.4 Rocking 13.4 Conclusions and Future Challenges References 14 Size Effects in Cosserat Crystal Plasticity Samuel Forest and Flavien Ghiglione14.1 Introduction 14.2 Problem Setting 14.2.1 Field Equations 14.2.2 Constitutive Equations14.2.3 Studied Boundary Value Problem 14.3 Cosserat Elastoplasticity Based on a Quadratic Potential14.3.1 Simple Glide in Isotropic Elasticity 14.3.2 Crystal Plasticity Based on the Full Stress Tensor 14.3.3 Schmid Law Limited to the Symmetric Part of the Stress Tensor 14.3.4 Comparison with the Curl ���� ���� Model 14.4 Rank One Energy Potential 14.4.1 Elasticity Solution14.4.2 Crystal Plasticity 14.4.3 Comparison with the Curl ���� ���� Model14.5 Combined Potential 14.6 Application to Grain Boundary Behaviour 14.6.1 Cosserat-Phase Field Model of Grain Boundaries 14.6.2 Analytical Solution of a Single Flat Grain Boundary 14.6.3 Grain Boundary Energy References 15. On the Influence of Poisson’s Ratio on Phase Transformations Limiting Surfaces Alexander B. Freidin and Leah L. Sharipova15.1 Introduction15.2 Phase Equilibrium and Phase Transition Zones for Phases with Positive and Negative Poisson’s Ratios15.3 Optimal Laminates and Phase Transformations Limiting Surfaces15.4 Results 15.5 Conclusions References 16. Application of Nonlocal Fick’s Law Within Micropolar Approach Ksenia Frolova, Nikolay Bessonov, and Elena Vilchevskaya16.1 Introduction 16.2 Diffusion in Media Modeled by Micropolar Continuum 16.3 Axially Symmetric Problem 16.4 Results and Discussion 16.5 Conclusions Appendix. Some Remarks on Numerical Approximation References 17 Geometrically Nonlinear Cosserat Elasticity with Chiral Effects Based upon Granular Micromechanics Ivan Giorgio, Anil Misra, and Luca Placidi17.1 Introduction 17.2 Discrete and Continuous Models for Granular Systems 17.2.1 Identification via Piola’s Ansatz 17.2.2 Relative Intergranular Displacement and Related Continuum Deformation Measures 17.2.3 On the Objective (Macro and Micro-macro)Displacement Vectors 17.2.4 On the Objective Tensor 17.2.5 The Objective Scalar Deformation Measures17.3 Elastic Energy Function 17.4 Identification of the Undamaged Isotropic Case 17.4.1 Characterization of the Undamaged Isotropic Case 17.4.2 Macroscopic Isotropic Stiffness Matrices 17.4.3 Identification of the Macroscopic Isotropic Stiffness Matrices 17.5 Conclusion References 18 Study of the Dynamic Properties of Reinforced Concrete Under High-Speed Compression Mikhail E. Gonov, Vladimir V. Balandin, Anatoly M. Bragov,and Aleksandr Yu. Konstantinov18.1 Introduction 18.2 Test Method 18.3 Characteristics of the Tested Materials 18.4 Results of Dynamic Tests for Uniaxial Compression 18.5 Conclusion References19 Multistability of Convective Flows in a Porous Enclosure Vasily Govorukhin, Mezhlum Sumbatyan, and Vyacheslav Tsybulin19.1 Introduction 19.2 Mathematical Formulation of the Problem19.3 Numerical Methods and Extreme Multistability 19.3.1 Spectral Global Galerkin Method 19.3.2 Cosymmetry Preserving Finite-Difference Approximations19.3.3 Continuation on the Hidden Parameter Method 19.4 Multistability References 20 Hydrogen Transport in Framework of Linear Non-Equilibrium Thermodynamics Approach Polina M. Grigoreva and Vladimir A. Polyanskiy20.1 Introduction 20.2 Problem Statement and Governing Equations 20.3 Plane Boundary Value Problem 20.4 ConclusionReferences 21 Classical and Non-Classical Models of Changes in the Young Modulus of Geomaterials Under Alternating Loads Mikhail A. Guzev, Evgenii P. Riabokon, Mikhail S. Turbakov,Vladimir V. Poplygin, Evgenii V. Kozhevnikov, and Evgenii A. Gladkikh21.1 Introduction 21.2 Experimental Studies 21.3 Classical Model of Changes in the Young Modulus Under an Alternating Load 21.4 Non-classical Model of Change in the Young Modulus Under the Alternating Load 21.4.1 Formulation of the Non-classical Model 21.4.2 Building the Solution 21.5 Conclusion References22 Two Approaches to Modeling Viscoelastic Cosserat Continua Elena A. Ivanova22.1 Introduction 22.2 Kinematics and Balance Equations 22.3 Differential Equations Relating the Strain Tensors to the Velocity Vector and the Angular Velocity Vector 22.4 The Reduced Energy Balance Equation and the Heat Conduction Equation: Zhilin’s Method 22.5 Integral Equations Relating the Strain Tensors to the Velocity Vector and the Angular Velocity Vector 22.6 Source Terms in the Strain Balance Equations22.7 The Reduced Energy Balance Equation and the Heat Conduction Equation: A new Method 22.8 A Comparison of two Approaches 22.9 Discussion References 23 Porous Media Models Based on Generalized State Equations with Simple Examples Anna Knyazeva and Nelli Nazarenko23.1 Introduction 23.2 Definitions and General Relationships 23.3 Thermodynamical Relations 23.4 Examples of Particular Problems 23.4.1 Compressible Nonviscous Gas 23.4.2 Compressible Fluid with Bulk Viscosity 23.4.3 Non-ideal Gas Under Non-isothermal Conditions 23.4.4 Binary Non-viscous Imperfect Mixture 23.4.5 Diffusion and Filtration in Media with Double Porosity 23.4.6 Viscous Two-component Fluid in Media with DoublePorosity23.4.7 Nonviscous Two-component Fluid in Porous media with Nano- and Micro-pores 23.5 Conclusion References 24 Ball Indentation of Perforated Circular Hyperelastic Membranes Alexey M. Kolesnikov24.1 Introduction 24.2 Mathematical Model 24.2.1 Axisymmetric Problem of Non-linear Elastic Membranes 24.2.2 Ball Indentation of Perforated Circular Hyperelastic Membranes 24.3 Numerical Results 24.4 Conclusions References25 Integrated Asymptotic Approach to the Structural Mechanics Models Alexander G. Kolpakov and Sergey I. Rakin25.1 Motivation of the Research 25.2 Modern State of Structural Mechanics 25.2.1 Deformation of the “Main” Part of Frame 25.2.2 Deformation of Connecting Units of Frame 25.2.3 “Infinite Rigidity” of Connecting Units 25.2.4 Structural Mechanics Achievements and Limitations 25.3 Integrated Approach to the Computation of Thin-walled Structures 25.3.1 Displacements in the “Main” Part of the Beams 25.3.2 “Rigid” Displacements of the Connecting Unit 25.3.3 Conjugation of the Displacements in the Main Part of a Beam with the “Rigid Body” Displacements of the Connecting Unit 25.3.4 Assembling the Single-beam Domain Functions into the Function in 2-D Frame 25.3.5 Supplement of the Functions (25.5) with the Local Perturbations 25.4 Local Stress-strain State in the Connecting Units 25.5 Representative Fragment of Joint 25.6 Integrated Procedure for Computation of Framework 25.7 Actual Problems 25.8 Conclusions References 26 The Homogenized Delamination Criterion for Fiber-reinforced Plate Alexander G. Kolpakov, Sergey I. Rakin, and Igor V. Andrianov26.1 Introduction 26.2 Boundary Layer 26.3 Numerical Computation Results 26.3.1 Extension Along ��������- or ��������-axis 26.3.2 Shift in ��������2����3-plane 26.4 The Asymptotic Homogenized Strength Criterion of the Interface Zone 26.5 Constructing the Delaminating Strength Criterion26.6 Conclusions References 27 Lightly Loaded Hydrodynamic Thrust Bearing Lubricated by a Non-Newtonian Fluid Ilya I. Kudish, Sergei S. Volkov, and Andrey S. Vasiliev27.1 Introduction 27.2 Formulation of the Lubrication Problem 27.3 Asymptotic Analysis of the Rheological and Motion Equations 27.4 Examples of Some Specific Lubrication Problem Solutions and Discussion 27.5 Closure References 28 The Idea of Using Adhesive Bonds in Shaping of Cold-formed Thin-walled Beam-columnsMarcin Kujawa, Antonio Cazzani, Lukasz Smakosz, ViolettaKonopińska-Zmysłowska, Karol Winkelmann, Faizullah Jan, andCzesław Szymczak28.1 Introduction 28.2 State of the Art28.2.1 Static, Dynamics, and Stability Analysis of Thin-walled Members 28.2.2 Influence of Imperfections 28.2.3 Failure Analysis with Attention to Creep in Adhesive Bonded Metal Members/Structures 28.3 The Rationale for Addressing the Research Problem 28.4 Conclusions References 29 Dissipative Mechano-Electro-Magnetism Simulations in Electronic Components Yiming Liu, Wolfgang H. Müller, and Bilen Emek Abali29.1 Introduction29.2 Governing Equations 29.3 Constitutive Equations 29.4 Generating Weak Forms 29.5 Implementation and Results 29.6 Conclusion References 30 On Possible Reduction of Gradient Theories of Elasticity Sergey A. Lurie, Petr A. Belov, and Yury O. Solyaev30.1 Introduction30.2 Variational Formulation of Gradient Theories 30.3 Structure of Sixth Rank Tensors 30.4 Special Structure of Gradient Part of Potential Energy. Hypothesis on Absence of Divergent Terms30.5 Features of Variational Formulation of Vector-Type Gradient Models 30.6 System of Governing Equilibrium Equations 30.7 On Uniqueness of Reduced Vector-Type Models 30.8 Conclusions References 31 Dynamics of a Rectangular Rigid Body on a Movable Base Vladimir S. Metrikin, Leonid A. Igumnov, and Elena I. Komarova31.1 Introduction 31.2 Mathematical Model31.3 Construction of a Point Mapping of the Poincaré Surface 31.3.1 The Coordinates of the Fixed Point Corresponding to the Symmetrical Periodic Motion. Sustainability 31.3.2 Equations for Determining the Coordinates of a Fixed Point Corresponding to Asymmetric Periodic Motions.Sustainability 31.4 Numerical Results for ¥����(����) = ����sin(��������) 31.5 Numerical Results 31.6 Conclusion References 32 Asymptotically Correct Analytical Model for Flexural Response of a Two-Layer Strip with Contrast Elastic Constants Gennadi Mikhasev and Nguyen Le32.1 Introduction 32.2 Statement of the Problem 32.3 Bernoulli-Euler Type Model for Strip Consisting of Layers with Close Material Constants 32.4 Timoshenko-Reissner Type Model for Strip Consisting of Layers with High-Contrast Elastic Properties 32.4.1 Leading Approximation 32.4.2 First-Order Approximation 32.4.3 One-Dimensional Governing Equation32.5 Free Vibrations 32.6 ConclusionsReferences 33 On Analytical Modeling of Tension-Assisted Winding of Flexible Sheets Aleksandr Morozov, Wilhelm Rickert, and Sergei Shubin33.1 Introduction 33.2 General Assumptions for the Winding Problem 33.3 Winding the First Layer 33.4 Winding the Subsequent Layers 33.5 Conclusions References 34 On Using Rotations as Primary Variables in the Nonlinear Theory of Thin Elastic Shells Wojciech Pietraszkiewicz34.1 Introduction 34.2 Geometry and Deformation of the Reference Surface 34.3 Equilibrium Conditions 34.4 Boundary Value Problem with Independent Rotations 34.5 Constitutive Equations of Rubber-Like Shells References 35 Continuum Description of Extended Mass-in-Mass Metamaterial Models Alexey V. Porubov35.1 Introduction 35.2 Classic Mass-in-Mass Chain 35.3 Chain with Extra Attached Masses35.4 Chain with Extra Internal Attached Masses 35.5 Attached Masses Through one Element of the Main Chain 35.6 Conclusions References 36 Multi-Element Metamaterial’s Design Through the Relaxed Micromorphic Model Leonardo A. Perez Ramirez, Gianluca Rizzi, and Angela Madeo36.1 Introduction 36.2 The Relaxed Micromorphic Model: Constitutive laws,Equilibrium Equations, and Boundary Conditions 36.2.1 Equilibrium Equations 36.2.2 Boundary and Interface Conditions 36.2.3 Numerical Results 36.3 Parametric Study on the Thickness of a Shielding Device: Capability Limit for the Relaxed Micromorphic Model 36.4 Design of a Double Shield Device 36.5 Multiple-Shields Optimization 36.6 Conclusions References37 On Magnetically Induced Motion of Micropolar FerrofluidsWilhelm Rickert, Margarita Dementeva, Gregor Ganzosch, Elena N.Vilchevskaya, and Wolfgang H. Müller37.1 Introduction 37.2 A Flow Problem Coupled to Electromagnetism 37.3 Simplifications and Normalization 37.4 Electromagnetic Force Density 37.5 Initial Values, Boundary Conditions and Implementation 37.6 Results 37.6.1 Slip 37.6.2 No Slip 37.6.3 Homogeneous Magnetic Field 37.7 Summary References 38 Manufacturing Quality Evaluation of Photopolymer Resin 3D-Printed Scaffolds Using Microtomography Evgeniy V. Sadyrin, Andrey L. Nikolaev, Sergei V. Chapek, Dmitry V.Nazarenko, Sergei M. Aizikovich, and Yun-Che Wang38.1 Introduction 38.2 Materials and Methods 38.3 Results and Discussion 38.4 Conclusion References 39 Comparison of Homogenization Techniques in Strain Gradient Elasticity for Determining Material Parameters Bekir Cagri Sarar, M. Erden Yildizdag, and Bilen Emek Abali39.1 Introduction 39.2 Determining Strain Gradient Parameters 39.3 Microscale Structure 39.4 Results and Discussion 39.5 Conclusion References 40 Buckling of Rectangular Micropolar Plate with Prestressed Coatings Denis N. Sheydakov40.1 Introduction 40.2 Micropolar Plate with Prestressed Coatings40.3 Equations of Neutral Equilibrium 40.4 Micropolar Plate with Identical Coatings 40.5 Conclusion References 41 A Cosserat Model for Fiber-Reinforced Elastic Plates David J. Steigmann, Mircea Bîrsan, and Milad Shirani41.1 Introduction 41.2 The Three-Dimensional Cosserat Model for Fiber-Reinforced Elastic Solids 41.2.1 Kinematical Variables and Strain Measures in Cosserat Elasticity 41.2.2 Fiber-Reinforced Materials 41.2.3 Equilibrium and Constitutive Equations 41.3 Plate Theory for Fiber-Reinforced Laminae41.4 Specific Constitutive Assumptions 41.4.1 Coercivity 41.4.2 Minimum Property Appendix References 42 On the Structure of Solutions in the Vicinity of Discontinuity of Boundary Conditions for Gradient ModelsAlexander O. Vatulyan, Sergey A. Nesterov, Victor O. Yurov, and OksanaV. Yavruyan42.1 Introduction 42.2 Constitutive Relations of the Gradient Theory of Elasticity and Electroelasticity 42.3 Problem for a Strip with Delamination 42.4 Problem for an Electroelastic Strip with a Surface Electrode42.5 Conclusion References 43 A Damaged Medium Model for Assessing Life Characteristics of Polycrystalline Structural Alloys with Joint Mechanical Fatigue and Long-Term Strength of Material Ivan A. Volkov, Leonid A. Igumnov, Aleksandr A. Belov, and Andrey I.Volkov43.1 Introduction43.2 Constitutive Relations of the Mathematical Model of Mechanics of Damaged Medium 43.2.1 Constitutive Relations of Thermoviscoplasticity 43.2.2 Evolutionary Equations for Damage Accumulation43.3 Numerical Results 43.4 ConclusionReferences44 Bandgap Properties of a Class of Chiral and Achiral Metamaterials Yun-Che Wang, Tse-Chun Liao, Kai-Wen Tan, and Sergey M. Aizikovich44.1 Introduction 44.2 Theoretical Considerations 44.3 Numerical Considerations 44.4 Results and Discussion 44.5 Conclusions References45 Large Strains of a Spherical Shell with Distributed Dislocations and Disclinations Leonid M. Zubov and Mikhail I. Karyakin45.1 Introduction 45.2 The Model of a Nonlinear Elastic Micropolar Shell 45.3 Continuously Distributed Dislocations in an Elastic MicropolarShell 45.4 Transformation of Incompatibility Equations and EquilibriumEquations 45.5 Equilibrium of a Closed Spherical Shell with DistributedDislocations and Disclinations 45.6 Numerical Results 45.7 Conclusions References

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Book SynopsisThis book constitutes the refereed proceedings of the 14th International Conference on Metaheuristics, MIC 2022, held in Syracuse, Italy, in July 2022.The 48 full papers together with 17 short papers presented were carefully reviewed and selected from 72 submissions. The papers detail metaheuristic techniques.Chapter “Evaluating the Effects of Chaos in Variable Neighbourhood Search” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

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Book SynopsisThis book contains a selection of the best papers presented at the Computational Urban Planning and Urban Management (CUPUM) conference, held in June 2023 at McGill University in Montreal, Quebec. Major themes of this book are smart cities, urban big data, and shared mobility. This book also contains chapters with cutting-edge research on urban modeling, walkability and bikeability analysis, and planning support systems (PSS).Table of ContentsIntroduction.- Part 1: Digital cities.- Hybrid smartness: Seeking a balance between top-down and bottom-up smart city approaches.- Interpreting the smart city through topic modelling.- The venue code: digital surveillance, spatial (re)organization, and infrastructural power during the COVID pandemic in China.- The platformization of public participation: Considerations for urban planners navigating new engagement tools.- Part 2: Mobility futures.- Shared micro-mobility: A panacea or a patch for our urban transport problems?- Understanding bikeability: Insight into the cycling–city relationship using massive dockless bike-sharing records in Beijing.- Disclosing the impact of micro-level environmental characteristics on dockless bikeshare trip volume: A case study of Ithaca.- A planning support system for boosting bikeability in Seoul.- Integrating big data and a travel survey to understand the gender gap in ride-hailing usage: evidence from Chengdu, China.- Urban airspace route planning for advanced air mobility operations.- Part 3: Fine-scale urban analysis.- “Eyes on the Street”: Estimating natural surveillance along Amsterdam’s city streets using street-level imagery.- Automatic evaluation of street-level walkability based on computer vision techniques and urban big data: A case study of Kowloon West, Hong Kong.- Promoting sustainable travel through a web-based tourism support system.- Applying the Aurin walkability index at the metropolitan and local levels by sex and age in Australia.- Predicting urban heat island mitigation with random forest regression in Belgian cities.- A framework to probe the uncertainties in urban cellular automata modeling with multilevel density for the Wallonia region, Belgium.

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Book SynopsisThis book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Numerical Methods and Applications, NMA 2022, held in Borovets, Bulgaria, in August 2022.The 30 revised regular papers presented were carefully reviewed and selected from 38 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.Table of ContentsSUSHI for a Bingham Flow.- Two-Phase Algorithm For Solving Vehicle Routing Problem with Time Windows.- Topological dynamic consistency of numerical methods for dynamical models in biosciences?.- Parameter Estimation Inspired by Temperature Measurements for a Chemotactic Model of Honeybee Thermoregulation.- On the Consistency and Convergence of Repeated Richardson Extrapolation.- Convergence Analysis of a Finite Volume Scheme for a Distributed Order Diffusion Equation.- SUSHI for a Non-Linear Time Fractional Diffusion Equation with a Time Independent Delay.- On the Numerical Simulation of Exponential Decay and Outbreak Data Sets Involving Uncertainties.- Rational approximation preconditioners for multiphysics problems.- Rational approximation preconditioners for multiphysics problems.- Analysis of Effective Properties of Poroelastic Composites with Surface Effects Depending on Boundary Conditions in Homogenization Problems.- Ant Algorithm for GPS Surveying Problem with Fuzzy Pheromone Updating.- Covering a set of points with a minimum number of equal disks via simulated annealing.- Mathematical modelling of nonlinear heat conduction with relaxing boundary conditions.- Random Sequences in Vehicle Routing Problem.- A database of high precision trivial choreographies for the planar three-body problem.- Evaluation of the Effective Material Properties of Media with Voids Based on Numerical Homogenization and Microstructure Data.- Variable Neighborhood Search Approach to Community Detection Problem.- Simulation Investigations of Pyramidal Cells Layer Effect on Conscious Visual Perception.- On Decision Making Under Uncertainty.- An Inequality for Polynomials on the Standard Simplex.- A Theoretical Analysis on the Bound Violation Probability in Differential Evolution Algorithm.- On the Extreme Zeros of Jacobi Polynomials.- Sensitivity Analysis of an Air Pollution Model Using Innovative Monte Carlo Methods in Calculating Multidimensional Integrals.- Demanded scale for modern numerical optimisation.- RMSD Calculations For Comparing Protein Three-Dimensional Structures.- On the Application of a Hierarchically Semi-Separable Compression for Space-Fractional Parabolic Problems with Varying Time Steps.- Optimized Stochastic Approaches Based on Sobol Quasirandom Sequences for Fredholm Integral Equations of the Second Kind.- Intuitionistic Fuzzy Knapsack Problem trough the Index Matrices Prism.- Simulation of the Mechanical Wave Propagation in a Viscoelastic Media with and without Stiff Inclusions.

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Book SynopsisThis book is a self-contained treatment for those who study or work on the computational aspects of classical modular forms. The author describes the theory of modular forms and its applications in number theoretic problems such as representations by quadratic forms and the determination of asymptotic formulas for Fourier coefficients of different types of special functions. A detailed account of recent applications of modular forms in number theory with a focus on using computer algorithms is provided. Computer algorithms are included for each presented application to help readers put the theory in context and make new conjectures. Table of ContentsDirichlet Characters.- Modular Forms: Definition and Some Properties.- Application: Quadratic Forms.- Application: Eta Quotients.- Various Applications.

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Book SynopsisThis book constitutes the refereed proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2023, held in Madison, WI, USA, during June 21–23, 2023. The 33 full papers presented were carefully reviewed and selected from 119 submissions. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.

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Book SynopsisThis volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.Table of ContentsCTRW approximations for fractional equations with variable order (Kolokoltsov).- Fractional Elliptic Problems on Lipschitz Domains: Regularity and Approximation (Borthagaray).- Regularity estimates and open problems in kinetic equations (Silvestre).- An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions (Littlewood).- Nonlocal diffusion models with consistent local and fractional limits (Du).- A one-dimensional symmetric force-based blending method for atomistic-to-continuum coupling (Li).- A note on estimates of level sets and their role in demonstrating regularity of solutions to nonlocal double phase equations (Mengesha).- An overview of Almost Minimizers of Bernoulli-Type Functionals (Garcia).

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Book SynopsisThis book constitutes the refereed proceedings of the 17th International Joint Conference on Theoretical Computer Science-Frontier of Algorithmic Wisdom (IJTCS-FAW 2023), consisting of the 17th International Conference on Frontier of Algorithmic Wisdom (FAW) and the 4th International Joint Conference on Theoretical Computer Science (IJTCS), held in Macau, China, during August 14–18, 2023.FAW started as the Frontiers of Algorithmic Workshop in 2007 at Lanzhou, China, and was held annually from 2007 to 2021 and published archival proceedings. IJTCS, the International joint theoretical Computer Science Conference, started in 2020, aimed to bring in presentations covering active topics in selected tracks in theoretical computer science. To accommodate the diversified new research directions in theoretical computer science, FAW and IJTCS joined their forces together to organize an event for information exchange of new findings and work of enduring value in the field. The 21 full papers included in this book were carefully reviewed and selected from 34 submissions. They were organized in topical sections as follows: algorithmic game theory; algorithms and data structures; combinatorial optimization; and computational economics.Table of ContentsUnderstanding the Relationship Between Core Constraints and Core-Selecting Payment Rules in Combinatorial Auctions.- An Improved Analysis of the Greedy+Singleton Algorithm for k-Submodular Knapsack Maximization.- Generalized Sorting with Predictions Revisited.- Eliciting Truthful Reports with Partial Signals in Repeated Games.- On the NP-hardness of two scheduling problems under linear constraints.- On the Matching Number of k-Uniform Connected Hypergraphs with Maximum Degree.- Max-Min Greedy Matching Problem: Hardness for the Adversary and Fractional Variant.- Approximate Core Allocations for Edge Cover Games.- Random Approximation Algorithms for Monotone k-Submodular Function Maximization with Size Constraints.- Additive Approximation Algorithms for Sliding Puzzle.- Differential Game Analysis for Cooperation Models in Automotive Supply Chain under Low-Carbon Emission Reduction Policies.- Adaptivity Gap for Influence Maximization with Linear Threshold Model on Trees.- Physically Verifying the First Nonzero Term in a Sequence: Physical ZKPs for ABC End View and Goishi Hiroi.- Mechanism Design in Fair Sequencing.- Red-Blue Rectangular Annulus Cover Problem.- Applying Johnson's Rule in Scheduling Multiple Parallel Two-Stage Flowshops.- The Fair k-Center with Outliers Problem: FPT and Polynomial Approximations.- Constrained Graph Searching on Trees.- EFX Allocations Exist for Binary Valuations.- Maximize Egalitarian Welfare for Cake Cutting.- Stackelberg Strategies on Epidemic Containment Games.

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Book SynopsisThis book presents the state of the art in High-Performance Computing on modern supercomputer architectures.

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Book SynopsisThis monograph provides a comprehensive study of the Riemann problem for systems of conservation laws arising in continuum physics. It presents the state-of-the-art on the dynamics of compressible fluids and mixtures that undergo phase changes, while remaining accessible to applied mathematicians and engineers interested in shock waves, phase boundary propagation, and nozzle flows. A large selection of nonlinear hyperbolic systems is treated here, including the Saint-Venant, van der Waals, and Baer-Nunziato models. A central theme is the role of the kinetic relation for the selection of under-compressible interfaces in complex fluid flows. This book is recommended to graduate students and researchers who seek new mathematical perspectives on shock waves and phase dynamics. Table of Contents1 Overview of this monograph.- 2 Models arising in fluid and solid dynamics.- 3 Nonlinear hyperbolic systems of balance laws.- 4 Riemann problem for ideal fluids.- 5 Compressible fluids governed by a general equation of state.- 6 Nonclassical Riemann solver with prescribed kinetics. The hyperbolic regime.- 7 Nonclassical Riemann solver with prescribed kinetics. The hyperbolic-elliptic regime.- 8 Compressible fluids in a nozzle with discontinuous cross-section. Isentropic flows.- 9 Compressible fluids in a nozzle with discontinuous cross-section. General flows.- 10 Shallow water flows with discontinuous topography.- 11 Shallow water flows with temperature gradient.- 12 Baer-Nunziato model of two-phase flows.- References.- Index.

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Book SynopsisThis book constitutes the refereed post-conference proceedings of the 15th International Conference, Évolution Artificielle, EA 2022, held in Exeter, UK, during October 31–November 2, 2022.The 15 full papers were carefully reviewed and selected from 18 submissions. The papers cover a wide range of topics in the field of artificial evolution, including, but not limited to: evolutionary computation, evolutionary optimization, coevolution, artificial life, population dynamics, theory, algorithmic and modeling, implementations.Table of ContentsOn the Active Use of an ND-Tree-Based Archive for Multi-Objective Optimisation.- HyTEA: Hybrid Tree Evolutionary Algorithm.- A Game Theoretic Decision Tree for Binary Classification.- Evaluating a New Genetic Algorithm for Automated Machine Learning in Positive-Unlabelled Learning.- Neural Network-based Virtual Analog Modeling.- Defining a Quality Measure Within Crossover: An Electric Bus Scheduling Case Study.- Maximizing the Number of Satisfied Charging Demands in Electric Vehicle Charging Scheduling Problem.- Fine-Grained Cooperative Coevolution in a Single Population: Between Evolution and Swarm Intelligence.- One-Class Ant-Miner: Selection of Majority Class Rules for Binary Rule-based Classification.- Towards a Many-Objective Optimiser for University Course Timetabling.- Empirical Investigation of MOEAs for Multi-objective Design of Experiments.- Evolutionary Continuous Optimization of Hybrid Gene Regulatory Networks.- Designing Attention based Convolutional Neural Network (CNN) Architectures for Medical Image Classification using Genetic Algorithm based on Variable Length-encoding Scheme.- A Multi-objective 3D Offline UAV Path Planning Problem with Variable Flying Altitude.- An Elitist Non-dominated Heuristic Resolution for the Dynamic Asset Protection Problem.

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Book SynopsisThis book constitutes the refereed proceedings of the 17th International Conference on Learning and Intelligent Optimization, LION-17, held in Nice, France, during June 4–8, 2023.The 40 full papers presented have been carefully reviewed and selected from 83 submissions. They focus on all aspects of unleashing the potential of integrating machine learning and optimization approaches, including automatic heuristic selection, intelligent restart strategies, predict-then-optimize, Bayesian optimization, and learning to optimize.Table of ContentsAnomaly Classification to Enable Self-Healing in Cyber Physical Systems using Process Mining.- Hyper-box Classification Model using Mathematical Programming.- A leak localization algorithm in water distribution networks using probabilistic leak representation and optimal transport distance.- Fast and Robust Constrained Optimization via Evolutionary and Quadratic Programming.- Bayesian Optimization for Function Compositions with Applications to Dynamic Pricing.- A Bayesian optimization algorithm for constrained simulation optimization problems with heteroscedastic noise.- Hierarchical Machine Unlearning.- Explaining the Behavior of Reinforcement Learning Agents using Explaining the Behavior of Reinforcement Learning Agents using.- Deep Randomized Networks for Fast Learning.- Generative models via Optimal Transport and Gaussian Processes.- Real-world streaming process discovery from low-level event data.- Robust Neural Network Approach to System Identification in the High-Noise Regime.- GPU for Monte Carlo Search.- Learning the Bias Weights for Generalized Nested Rollout Policy Adaptation.- Heuristics selection with ML in CP Optimizer.- Model-based feature selection for neural networks: A mixed-integer programming approach.- An Error-Based Measure for Concept Drift Detection and Characterization.- Predict, Tune and Optimize for Data-Driven Shift Scheduling with Uncertain Demands.- On Learning When to Decompose Graphical Models.- Inverse Lighting with Differentiable Physically-Based Model.- Repositioning Fleet Vehicles: a Learning Pipeline.- Bayesian Decision Trees Inspired from Evolutionary Algorithms.- Towards Tackling MaxSAT by Combining Nested Monte Carlo with Local Search.- Relational Graph Attention-based Deep Reinforcement Learning: An Application to Flexible Job Shop Scheduling with Sequence-dependent Setup Times.- Experimental Digital Twin for Job Shops with Transportation Agents.- Learning to Prune Electric Vehicle Routing Problems.- A matheuristic approach for electric bus fleet scheduling.- Class GP: Gaussian Process Modeling for Heterogeneous Functions.- Surrogate Membership for Inferred Metrics in Fairness Evaluation.- The BeMi Stardust: a Structured Ensemble of Binarized Neural Network.- Discovering explicit scale-up criteria in crisis response with decision mining.- Job Shop Scheduling via Deep Reinforcement Learning: a Sequence to Sequence approach.- Generating a Graph Colouring Heuristic with Deep Q-Learning and Graph Neural Networks.- Multi-Task Predict-then-Optimize.- Integrating Hyperparameter Search into Model-Free AutoML with Context-Free Grammars.- Improving subtour elimination constraint generation in Branch-and-Cut algorithms for the TSP with Machine Learning.- Learn, Compare, Search: One Sawmill’s Search for the Best Cutting Patterns Across And/or Trees.- Dynamic Police Patrol Scheduling with Multi-Agent Reinforcement Learning.- Analysis of Heuristics for Vector Scheduling and Vector Bin Packing.- Unleashing the potential of restart by detecting the search stagnation.

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Book SynopsisThis book constitutes the refereed proceedings of the 5th Iberoamerican Conference and 4th Indo-American Conference on Knowledge Graphs and Semantic Web, KGSWC 2023, held jointly in Zaragoza, Spain, during November 13–15, 2023.The 18 full and 2 short papers presented were carefully reviewed and selected from 50 submissions. They focus on the following topics: knowledge representation; natural language processing/text mining; and machine/deep learning research.Table of ContentsAn ontology for Tuberculosis Surveillance System.- Should I Stay or Should I Go: A New Reasoner for Description Logic.- An Intelligent Article Knowledge Graph Formation Framework using BM25 Probabilistic Retrieval Model.- Defeasible Reasoning with Knowledge Graphs.- Recommendation of Learning Paths based on Open Educational Resources.- An enterprise architecture for interpersonal activity knowledge management.- Unlocking the Power of Semantic Interoperability in Industry 4.0: A Comprehensive Overview.- On the Representation of Dynamic BPMN Process Executions in Knowledge Graphs.- Towards a Framework for Seismic Data.- Using Pregel to create Knowledge Graphs subsets described by non-recursive Shape Expressions.- ITAQ : Image Tag Recommendation Framework for Aquatic Species integrating Semantic Intelligence via Knowledge Graph.- Automatic Semantic Typing of Pet E-Commerce Products Using Crowdsourced Reviews: An Experimental Study.- A Modular Ontology for MODS – Metadata Object Description Schema.- A Topic Model for the Data Web.- Automating the Generation of Competency Questions for Ontologies with AgOCQs.- KnowWhereGraph-Lite: A Perspective of the KnowWhereGraph.- Ontology-Based Models of Chatbots for Populating Knowledge Graphs.- An Ontology for Reasoning about Fairness in Regression and Machine Learning.- SCIVO: Skills to Career with Interests and Values Ontology.- Topic Modeling for Skill Extraction from Job Postings.

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Book SynopsisThe book is made up by several worked out problems concerning the application of reduced order modeling to different parametric partial differential equations problems with an increasing degree of complexity.This work is based on some experience acquired during lectures and exercises in classes taught at SISSA Mathematics Area in the Doctoral Programme Mathematical Analysis, Modelling and Applications, especially in computational mechanics classes, as well as regular courses previously taught at EPF Lausanne and during several summer and winter schools. The book is a companion for master and doctoral degree classes by allowing to go more deeply inside some partial differential equations worked out problems, examples and even exercises, but it is also addressed for researchers who are newcomers in computational mechanics with reduced order modeling. In order to discuss computational results for the worked out problems presented in this booklet, we will rely on the RBniCS Project. The

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Book SynopsisPart I Invited Articles: C. A. Beschle, A. Barth, Quasi Continuous Level Monte Carlo for Random Elliptic PDEs.- M. B. Giles, MLMC Techniques for Discontinuous Functions.- T. Helin, A. M. Stuart, A. L. Teckentrup, K. C. Zygalakis, Introduction to Gaussian Process Regression in Bayesian Inverse Problems, with new Results on Experimental Design for Weighted Error Measures.- V. Kaarnioja, Frances Y. Kuo, Ian H. Sloan, Lattice-Based Kernel Approximation and Serendipitous Weights for Parametric PDEs in Very High Dimensions.- E. Novak, Optimal Algorithms for Numerical Integration: Recent Results and Open Problems.- Chris. J. Oates, Minimum Kernel Discrepancy Estimators.- Gabriel Stoltz, Error Estimates and Variance Reduction for Nonequilibrium Stochastic Dynamics.- Part II Contributed Articles: F. Bernal, A. Berridi, Heuristics for the Probabilistic Solution of BVPs with Mixed Boundary Conditions.- Sou-Cheng T. Choi, Y. Ding, Fred J. Hickernell, J. Rathinavel, Aleksei G. Sorokin, Challenge

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Book SynopsisThe methodology has important and varied applications in machine learning, medicine, robotics, biology, computer vision, human biometrics, nanomanufacturing, signal processing, and image analysis, etc.The first chapter gives motivation examples, a wide range of applications, raised challenges, raised challenges, and some concerns.

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Book SynopsisRonald A. DeVore and Angela Kunoth, Prologue to Multiscale, Nonlinear and Adaptive Approximation II.- Ronald A. DeVore and Angela Kunoth, Introduction: Wolfgang Dahmen's mathematical work (as of 2009).- Markus Bachmayr and Albert Cohen, Multilevel Representations of Random Fields and Sparse Approximations of Solutions to Random PDEs.- Hassan Ballout and Yvon Maday and Christophe Prud'homme, Nonlinear compressive reduced basis approximation for multi-parameter elliptic problem.- Ido Ben Shaul and Shai Dekel, Sparse Besov Space Analysis of Representations in Machine Learning.- Benjamin Berkels and Peter Binev, Joint Denoising and Line Distortion Correction for Raster-Scanned Image Series.- Dietrich Braess and Wolfgang Hackbusch, The Approximation of Cauchy-Stieltjes and Laplace-Stieltjes Functions.- Andrea Bonito and Diane Guignard, Approximating Partial Differential Equations without Boundary Conditions.- Albert Cohen and Ronald DeVore and Eitan Tadmor, Constructions of Bounded Solutions of div u= f in Critical Spaces.- Jan-Christopher Cohrs and Benjamin Berkels, On the importance of the e-regularization of the distribution-dependent MumfordShah model for hyperspectral image segmentation.- Ronald DeVore, Guergana Petrova and Przemyslaw Wojtaszczyk, A Note on Best n-term Approximation for Generalized Wiener Classes.- Lars Grasedyck, Sebastian Krämer and Dieter Moser, Stable Truncation and Root-Independent Normalization of Tree Tensor Networks.- Diane Guignard and Olga Mula, Tree-Based Nonlinear Reduced Modeling.- Helmut Harbrecht and Michael Multerer, Samplets: Wavelet Concepts for Scattered Data.- Michael Herty, Adrian Kolb, and Siegfried Müller, A novel multilevel approach for the efficient computation of random hyperbolic conservation laws.- Kamen G. Ivanov, Gerard Kerkyacharian, George Kyriazis, and Pencho Petrushev, On the Construction of Bases and Frames with Applications.- Angela Kunoth and Mathias Oster and Reinhold Schneider, Towards a Continuous Mathematical Model for the Analysis of Classes of Deep Neural Networks.- Dominique Picard, Unstoppable Mathematicians.- Reinhold Schneider and Mathias Oster, Some Thoughts on Compositional Tensor Networks.- Rob Stevenson, Efficient least squares discretizations for Unique Continuation and Cauchy problems.

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Book SynopsisMathematical models cannot be solved using the traditional analytical methods for dynamic equations on time scales. These models must be dealt with using computational methods. This textbook introduces numerical methods for initial value problems for dynamic equations on time scales. Hands-on examples utilizing MATLAB and practical problems illustrate a wide variety of solution techniques.

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Book SynopsisThe first part of this book is mainly intended as a textbook for students at the Sophomore-Junior level, majoring in mathematics, engineering, or the sciences in general. The book includes the basic topics in Ordinary Differential Equations, normally taught at the undergraduate level, such as linear and nonlinear equations and systems, Bessel functions, Laplace transform, stability, etc. It is written with ample flexibility to make it appropriate either as a course stressing application, or a course stressing rigor and analytical thinking. It also offers sufficient material for a one-semester graduate course, covering topics such as phase plane analysis, oscillation, Sturm-Liouville equations, Euler-Lagrange equations in Calculus of Variations, first and second order linear PDE in 2D. There are substantial lists of exercises at the ends of the chapters. In this edition complete solutions to all even number problems are given in the back of the book.The 2nd edition also includes some new problems and examples. An effort has been made to make the material more suitable and self-contained for undergraduate students with minimal knowledge of Calculus. For example, a detailed review of matrices and determinants has been added to the chapter on systems of equations. The second edition also contains corrections of some misprints and errors in the first edition.

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Book SynopsisThe organization of the material is presented as follows: This introductory chapter I represents a theoretical analysis of the computational algorithms for a numerical solution of the basic equations in continuum mechanics. In this chapter, the general requirements for computational grids, discretization, and iterative methods for black-box software are examined. Finally, a concept of a two-grid algorithm for (de-)coupled solving multidimensional non-linear (initial-)boundary value problems in continuum mechanics (multiphysics simulation) in complex domains is presented. Chapter II contains descriptions of the sequential Robust Multigrid Technique which is developed as a general-purpose solver in black-box codes. This chapter presents the main components of the Robust Multigrid Technique (RMT) used in the two-grid algorithm (Chapter I) to compute the auxiliary (structured) grid correction. This includes the generation of multigrid structures, computation of index mapping, and integral evaluation. Finite volume discretization on the multigrid structures will be explained by studying a 1D linear model problem. In addition, the algorithmic complexity of RMT and black-box optimization of the problem-dependent components of RMT are analysed. Chapter III provides a description of parallel RMT. This chapter introduces parallel RMT-based algorithms for solving the boundary value problems and initial-boundary value problems in unified manner. Section 1 presents a comparative analysis of the parallel RMT and the sequential V-cycle. Sections 2 and 3 present a geometric and an algebraic parallelism of RMT, i.e. parallelization of the smoothing iterations on the coarse and the levels. A parallel multigrid cycle will be considered in Section 4. A parallel RMT for the time-dependent problems is given in Section 5. Finally, the basic properties of parallel RMT will be summarized in Section 6. Theoretical aspects of the used algorithms for solving multidimensional problems are discussed in Chapters IV. This chapter contains the theoretical aspects of the algorithms used for the numerical solving of the resulting system of linear algebraic equations obtained from discrete multidimensional (initial-)boundary value problems.

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