Numerical analysis Books

Book SynopsisThis book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem. The next four chapters address applications of increasing complexity in the field of computational mechanics: linear elasticity, hyperelasticity, wave propagation, contact, friction, and plasticity. The last chapter provides an overview of the main implementation aspects including some examples of Matlab code. The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.Table of Contents1.Getting Started: Linear Diffusion.- 2.Mathematical Aspects.- 3.Some Variants.- 4.Linear Elasticity and Hyperelasticity.- 5.Elastodynamics.- 6.Contact and Friction.- 7.Plasticity.- 8.Implementaion Aspects.- References.

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Book SynopsisThe volume covers most of the topics addressed and discussed during the Workshop INdAM "Recent advances in kinetic equations and applications", which took place in Rome (Italy), from November 11th to November 15th, 2019. The volume contains results on kinetic equations for reactive and nonreactive mixtures and on collisional and noncollisional Vlasov equations for plasmas. Some contributions are devoted to the study of phase transition phenomena, kinetic problems with nontrivial boundary conditions and hierarchies of models. The book, addressed to researchers interested in the mathematical and numerical study of kinetic equations, provides an overview of recent advances in the field and future research directions.Table of Contents- Sharpening of Decay Rates in Fourier Based Hypocoercivity Methods. - Quantum Drift-Diffusion Equations for a Two-Dimensional Electron Gas with Spin-Orbit Interaction. - A Kinetic BGK Relaxation Model for a Reacting Mixture of Polyatomic Gases. - On Some Recent Progress in the Vlasov–Poisson–Boltzmann System with Diffuse Reflection Boundary. - The Vlasov Equation with Infinite Mass. - Mathematical and Numerical Study of a Dusty Knudsen Gas Mixture: Extension to Non-spherical Dust Particles. - Body-Attitude Alignment: First Order Phase Transition, Link with Rodlike Polymers Through Quaternions, and Stability. - The Half-Space Problem for the Boltzmann Equation with Phase Transition at the Boundary. - Recent Developments on Quasineutral Limits for Vlasov-Type Equations. - A Note on Acoustic Limit for the Boltzmann Equation. - Thermal Boundaries in Kinetic and Hydrodynamic Limits. - Control of Collective Dynamics with Time-Varying Weights. - Kinetic Modelling of Autoimmune Diseases. - A Generalized Slip-Flow Theory for a Slightly Rarefied Gas Flow Induced by Discontinuous Wall Temperature. - A Revisit to the Cercignani–Lampis Model: Langevin Picture and Its Numerical Simulation. - On the Accuracy of Gyrokinetic Equations in Fusion Applications.

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Book SynopsisThis open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.Table of Contents1 M. Berger, Asteroid-Generated Tsunamis: A Review.- 2 A. Bermúdez, Some Case Studies in Environmental and Industrial Mathematics.- 3 Z. Cai et al., Hyperbolic Model Reduction for Kinetic Equations.- 4 A. Cohen et al., State Estimation - The Role of Reduced Models.- 5 C. Conca, Modelling Our Sense Of Smell.- 6 L. Edelstein-Keshet, Pattern formation inside living cells.- 7 M. Garzon et al., Efficient Algorithms for Tracking Moving Interfaces.- 8 K. Lauter, Private AI: Machine Learning on Encrypted Data.- 9 C. Le Bris, Mathematical approaches for contemporary materials science: Addressing defects in the microstructure.- 10 H. Leng et al., An iterative thresholding method for topology optimization for the Navier-Stokes flow.- 11 K. Sako, Cryptography and Digital Transformation.- 12 H. Suito et al., Numerical Study for Blood Flows in Thoracic Aorta.- 13 J.A.C. Weideman, Dynamics of Complex Singularities of Nonlinear PDEs: Analysis and Computation.

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Book SynopsisThis book gathers papers presented at the 13th International Conference on Mesh Methods for Boundary-Value Problems and Applications, which was held in Kazan, Russia, in October 2020. The papers address the following topics: the theory of mesh methods for boundary-value problems in mathematical physics; non-linear mathematical models in mechanics and physics; algorithms for solving variational inequalities; computing science; and educational systems. Given its scope, the book is chiefly intended for students in the fields of mathematical modeling science and engineering. However, it will also benefit scientists and graduate students interested in these fields.Table of ContentsTheory of the mesh methods for the boundary-value problems in Mathematical Physics.- Non-linear mathematical models in mechanics and physics.- Algorithms for solving variational inequalities.- Computing Science and educational systems.

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Book SynopsisThis book contains works on mathematical and simulation modeling of processes in various domains: ecology and geographic information systems, IT, industry, and project management. The development of complex multicomponent systems requires an increase in accuracy, efficiency, and adequacy while reducing the cost of their creation. The studies presented in the book are useful to specialists who involved in the development of real events models-analog, management and decision-making models, production models, and software products. Scientists can get acquainted with the latest research in various decisions proposed by leading scholars and identify promising directions for solving complex scientific and practical problems. The chapters of this book contain the contributions presented on the 16th International Scientific-practical Conference, MODS, June 28–July 01, 2021, Chernihiv, Ukraine.Table of ContentsMathematical Modeling of Information System Designing Master Plan of the Building Territory Based on OLAP Technology.- Models and information technologies of coverage of the territory by sensors with energy consumption optimization.- Transport of Reactive Tracer in Compacting Multi-fraction Bottom Sediments.- Pillars for establishing a durable and future-proof IT architecture maturing along with the NSC: Approaches from Continuous Integration to Service Mesh.- Optimal Control of Buried Point Sources in a Two-Dimensional Richards-Klute Equation.

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Book SynopsisIn this monograph, the authors develop a methodology that allows one to construct and substantiate optimal and suboptimal algorithms to solve problems in computational and applied mathematics. Throughout the book, the authors explore well-known and proposed algorithms with a view toward analyzing their quality and the range of their efficiency. The concept of the approach taken is based on several theories (of computations, of optimal algorithms, of interpolation, interlination, and interflatation of functions, to name several). Theoretical principles and practical aspects of testing the quality of algorithms and applied software, are a major component of the exposition. The computer technology in construction of T-efficient algorithms for computing ε-solutions to problems of computational and applied mathematics, is also explored. The readership for this monograph is aimed at scientists, postgraduate students, advanced students, and specialists dealing with issues of developing algorithmic and software support for the solution of problems of computational and applied mathematics.Table of Contents-Preface.- Introduction.- List of symbols and abbreviations.- 1. Elements of the computing theory.- 2. Theories of computational complexity.- 3. Interlination of functions.- 4. Interflatation of functions.- 5. Cubature formulae using interlanation functions.- 6. Testing the quality of algorithm programs.- 7. Computer technologies of solving problems of computational and applied mathematics with fixed values of quality characteristics.- Bilbiography.- Index.- About the Authors.

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Book SynopsisThe developments in mesh generation are usually driven by the needs of new applications and/or novel algorithms. The last decade has seen a renewed interest in mesh generation and adaptation by the computational engineering community, due to the challenges introduced by complex industrial problems.Another common challenge is the need to handle complex geometries. Nowadays, it is becoming obvious that geometry should be persistent throughout the whole simulation process. Several methodologies that can carry the geometric information throughout the simulation stage are available, but due to the novelty of these methods, the generation of suitable meshes for these techniques is still the main obstacle for the industrial uptake of this technology.This book will cover different aspects of mesh generation and adaptation, with particular emphasis on cutting-edge mesh generation techniques for advanced discretisation methods and complex geometries.Table of Contents1 Carolyn Woeber, Advances in H-P Mesh Adaptation for Finite Element Methods.- 2 Chiara Nardoni, Remeshing techniques in shape and topology optimization.- 3 Dimitrios Papadimitrakis, Building direction fields on the medial object to generate 3D domain decompositions for hexahedral meshing.- 4 Franck Ledoux, Interecode hexahedral meshing from Eulerian to Lagrangian simulations.- 5 Jean-Francois Remacle, A robust approach for mesh generation of surfaces with irregular/singular parametrizations.6 Jens Lang, Sample Adaptive Multilevel Stochastic Collocation Schemes in Uncertainty Quantification of Gas Transport in Networks.- 7 Jessica Zhang, Hexahedral dominant mesh generation and spline modeling for isogeometric analysis.- 8 Juan José Ródenas, Mesh adaptivity in the framework of the Cartesian grid finite element method, cgFEM.- 9 Mario Ricchiuto, h- and r-adaptation on simplicial meshes: implementation and applications.- 10 Onkar Sahni, Geometry and Adaptive Mesh Update Procedures for Ballistics Simulations.- 11 Per-Olof Persson, HOIST: High-Order Implicit Shock Tracking using an optimization-based discontinuous Galerkin method.- 12 Rainald Lohner, Breakthrough ‘workarounds’ in unstructured mesh generation.- 13 Simone Appella, An adaptive moving mesh method with conservative interpolation based on local projection.- 14 Suzanne Shontz, Global optimization strategies for automated edge grid generation.

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Book SynopsisThis book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.Trade Review“Each chapter ends with an exercise section … . While primarily addressed to researchers, the book can be used for graduate courses in optimization, by undergraduate and graduate students for theses and projects as well as by researchers and practitioners from other fields where tools from convex analysis, variational analysis and optimization play a role. All in one, the reviewer warmly recommends this book to anyone interested.” (Sorin-Mihai Grad, zbMATH 1506.90001, 2023)“This outstanding book will certainly be useful to anyone interested to learn convex analysis, in particular to graduate students and researchers in the field. Most parts of it can also serve as the basis of advanced courses on a variety of topics. In view of the excellence of this first volume, one can expect the best of the announced second one, which will deal with applications of convex analysis.” (Juan Enrique Martínez-Legaz, Mathematical Reviews, February, 2023)“Every chapter of the book has one section of exercises and one section of commentaries. These sections provide the reader with a lot of information and give him/her great benefits in self-learning. … The book under review has many things to offer and, surely, it will play an important role in the development of convex analysis … . The book is very useful for theoretical research and practical use. Thanks to the art of writing of the authors … .” (Nguyen Dong Yen, Journal of Global Optimization, Vol. 85, 2023)Table of ContentsFundamentals.- Basic theory of convexity.- Convex generalized differentiation.- Enhanced calculus and fenchel duality.- Variational techniques and further subgradient study.- Miscellaneous topics on convexity.- Convexified Lipschitzian analysis.- List of Figures.- Glossary of Notation and Acronyms.- Subject Index.

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Book SynopsisThis book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications. Table of ContentsPart I: Linear Dynamical Systems: B. Joseph, The rational interpolation problem: Grassmannian and Loewner-matrix approaches.- B. Jean-Paul, The conditioning of a linear barycentric rational interpolant.- D. Zlatko, Learning low-dimensional dynamical-system models from noisy frequency-response data with Loewner rational interpolation.- E. Mark, Pseudospectra of Loewner Matrix Pencils.- R. Paolo, A Loewner matrix approach to the identification of linear time-varying systems.- V. D. Paul, Linear System Matrices of Rational Transfer Functions.- Part II: Nonlinear Dynamical Systems: C. Xingang, Interpolation-based Model Order Reduction for Quadratic-Bilinear Systems and H2 Optimal Approximation.- C. Sridhar, An Adaptive Sampling Approach for the reduced basis method.- K. Boris, Balanced Truncation Model Reduction for Lifted Nonlinear Systems.- L. Sanda, Modeling the buck converter from measurements of its Harmonic Transfer Function.- P. Mihaly, Model reduction and realization theory of linear switched systems.- Part III: Structured Dynamical Systems: F. F. Damasceno, Developments in the Computation of Reduced Order Models with the Use of Dominant Spectral Zeros.- M. Volker, Structure-preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems.- P. D. Igor, Data-Driven Identification of Rayleigh-Damped Second-Order Systems.- S. Tatjana, Balanced truncation model reduction for 3D linear magneto-quasistatic field problems.- Van der S. Arjan, Structure-preserving model reduction of physical network systems.- Part IV: Model Reduction for Control: B. Tobias, H2-gap model reduction for stabilizable and detactable systems.- H. Matthias, Reduced Order Model Hessian Approximations in Newton Methods for Optimal Control.- P.-V. Charles, Interpolation-based irrational model control design and stabilty analysis.- Part V: Applications: D. Clifford, Oscillations in Biology: G. Eduardo, Model-Order Reduction for Coupled Flow and Linear Thermal-Poroplasticity with Applications to Unconventional Reservoirs.- I. Roxana, Challenges in model reduction for real-time simulation of traction chain systems.- N. Masaaki, Sparse Representation for Sampled-data Hinf Filter.- S. Eduardo, Analysis of a reduced model of epithelial–mesenchymal fate determination in cancer metastasis as a singularly-perturbed monotone system.

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Book SynopsisThis volume is addressed to people who are interested in modern mathematical solutions for real life applications. In particular, mathematical modeling, simulation and optimization is nowadays successfully used in various fields of application, like the energy- or health-sector. Here, mathematics is often the driving force for new innovations and most relevant for the success of many interdisciplinary projects. The presented chapters demonstrate the power of this emerging research field and show how society can benefit from applied mathematics.Table of ContentsPart I Prognostic MR Thermometry for Thermal Ablation of Liver Tumours.- 1 Sebastian Blauth et al., Mathematical Modeling and Simulation of Laser-Induced Thermotherapy for the Treatment of Liver Tumors.- 2 Matthias Andres and René Pinnau, The Cattaneo Model for Laser-Induced Thermotherapy: Identification of the Blood-Perfusion Rate.- 3 Kevin Tolle and Nicole Marheineke, On Online Parameter Identification in Laser-Induced Thermotherapy.- Part II Energy-efficient High Temperature Processes via Shape Optimisation.- 4 Robert Feßler at al., Feasibility Study on Simulating a 3D Furnace Including the Effects of Reactions and Vaporization.- 5 Thomas Marx et al., Shape Optimization for the SP1–Model for Convective Radiative Heat Transfer- 6 Nicolas Dietrich et al., Diffusive Radiation Models for Optimal Shape Design in Phosphate Production.- 7 Ruben Sanchez at al., Adjoint-based sensitivity analysis in high-temperature fluid flows with participating media.

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Book SynopsisThis graduate textbook provides an alternative to discrete event simulation. It describes how to formulate discrete event systems, how to convert them into Markov chains, and how to calculate their transient and equilibrium probabilities. The most appropriate methods for finding these probabilities are described in some detail, and templates for efficient algorithms are provided. These algorithms can be executed on any laptop, even in cases where the Markov chain has hundreds of thousands of states. This book features the probabilistic interpretation of Gaussian elimination, a concept that unifies many of the topics covered, such as embedded Markov chains and matrix analytic methods.The material provided should aid practitioners significantly to solve their problems. This book also provides an interesting approach to teaching courses of stochastic processes. Trade Review“This monograph is an exciting addition to the queueing/stochastic processes literature, written by two highly respected senior researchers. … The writing is precise and clear. Well-known models are used as examples to illustrate the methods presented. … It has a huge number of powerful techniques that are not given sufficient focus elsewhere. This may be one of the best books to introduce graduate students … . This monograph is essential for the bookshelf … of every serious queueing theorist.” (Myron Hlynka, Mathematical Reviews, December, 2023)Table of ContentsBasic Concepts and Definitions.- Systems with Events Generated by Poisson or by Binomial Processes.- Generating the Transition Matrix.- Systems with Events Created by Renewal Processes.- Systems with Events Created by Phase-type Processes.- Computational Complexity and Rounding and Truncation Errors.- Transient Solutions of Markov Chains.- Moving Toward the Statistical Equilibrium.- Equilibrium Solutions of Markov Chains and Related Topics.- Reducing the State Space Through Censoring and Embedding.- Systems with Independent or Almost Independent Components.- Infinite-State Markov Chains and Matrix Analytic Methods.

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Book SynopsisThis open access book provides insights into the novel Locally Refined B-spline (LR B-spline) surface format, which is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline surface has an overall smooth behavior and allows the modeling of local details with only a limited growth in data volume. In regions where many data points belong to the same smooth area, LR B-splines allow a very lean representation of the shape by locally adapting the resolution of the spline space to the size and local shape variations of the region. The iterative method can be modified to improve the accuracy in particular domains of a point cloud. The use of statistical information criterion can help determining the optimal threshold, the number of iterations to perform as well as some parameters of the underlying mathematical functions (degree of the splines, parameter representation). The resulting surfaces are well suited for analysis and computing secondary information such as contour curves and minimum and maximum points. Also deformation analysis are potential applications of fitting point clouds with LR B-splines.Table of ContentsIntroduction.- Locally Refined Splines.- Adaptive surface Fitting with Local Refinement: LR B-spline Surfaces.- A Statistical Criterion to Judge the Goodness of Fit of LR B-splines Surface Approximation.- LR B-splines for Representation of Terrain and Seabed: Data Fusion, Outliers, and Voids.- LR B-spline Surfaces and Volumes for Deformation Analysis of Terrain Data.- Conclusion.

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Book SynopsisThis book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2021. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance.The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.Table of ContentsPart I Physics.- Part II Molecules, Interfaces, and Solids.- Part III Reactive Flows.- Part IV Computational Fluid Dynamics.- Part V Transport and Climate.- Part VI Computer Science.- Part VII Miscellaneous Topics.

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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 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 SynopsisMonte Carlo simulation has been a powerful computational tool for physics models, and when combined with the programming language Excel, this book is a valuable resource for readers who wish to acquire knowledge that can be applied to more complex systems.

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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 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 Synopsis

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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 SynopsisChapter 1. Introduction to Elastic Postbuckling Behavior of Structures.- Chapter 2. A Co-Rotation-Based Secant Matrix Procedure for the Elastic Postbuckling Analysis of Truss Structures.- Chapter 3. Variable Order Secant Matrices for the Kinematically Exact Postbuckling Analysis of Beams and Frames.- Chapter 4. Variable Order Secant Matrices for Geometric Nonlinear Analysis of Thin-Walled Open Sections.- Chapter 5. Improved secant matrices for the postbuckling analysis of thin initially imperfect plates.- Chapter 6. Postbuckling Analysis of Shallow Shells Using Secant Matrices Based on Marguerre's Shell Theory.- Chapter 7. Closing Remarks.

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Book SynopsisThis new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes. The book is divided into two main parts: Deterministic methods and stochastic methods in computational physics. Based on concrete problems, the first part discusses numerical differentiation and integration, as well as the treatment of ordinary differential equations. This is extended by a brief introduction to the numerics of partial differential equations. The second part deals with the generation of random numbers, summarizes the basics of stochastics, and subsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. The final two chapters discuss data analysis and stochastic optimization. All this is again motivated and augmented by applications from physics. In addition, the book offers a number of appendices to provide the reader with information on topics not discussed in the main text. Numerous problems with worked-out solutions, chapter introductions and summaries, together with a clear and application-oriented style support the reader. Ready to use C++ codes are provided online.Table of ContentsSome Basic Remarks.- Part I Deterministic Methods.- Numerical Differentiation.- Numerical Integration.- The KEPLER Problem.- Ordinary Differential Equations – Initial Value Problems.- The Double Pendulum.- Molecular Dynamics.- Numerics of Ordinary Differential Equations - Boundary Value Problems.- The One-Dimensional Stationary Heat Equation.- The One-Dimensional Stationary SCHRÖDINGER Equation.- Partial Differential Equations.- Part II Stochastic Methods.- Pseudo Random Number Generators.- Random Sampling Methods.- A Brief Introduction to Monte-Carlo Methods.- The ISING Model.- Some Basics of Stochastic Processes.- The Random Walk and Diffusion Theory.- MARKOV-Chain Monte Carlo and the POTTS Model.- Data Analysis.- Stochastic Optimization.- Appendix: The Two-Body Problem.- Solving Non-Linear Equations. The NEWTON Method.- Numerical Solution of Systems of Equations.- Fast Fourier Transform.- Basics of Probability Theory.- Phase Transitions.- Fractional Integrals and Derivatives in 1D.- Least Squares Fit.- Deterministic Optimization.

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Book SynopsisTable of Contents1. Einleitung.- 2. Algebraische Grundlagen.- 3. Geringte Räume.- 4. Supermannigfaltigkeiten.- 5. Analysis auf Supergebieten.- 6. Anwendungen.- 7. Lie—Algebren und Grundbegriffe der Darstellungstheorie.- 8. Höchstgewichtsdarstellungen der Virasoro-Algebra.- 9. Vertexoperatoren.- 10. Beweis der Kac’schen Determinantenformel.- 11. Konstruktion singulärer Vektoren im Fockraum.- 12.Unitäre Höchstgewichtsdarstellungen der Virasoro-Algebra.

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Book SynopsisDas Buch ist ein Hilfsmittel zur Bearbeitung von Übungsaufgaben bzw. zur Vorbereitung auf die Prüfung zur Vorlesung in Numerischer Mathematik bzw. wissenschaftliches Rechnen. Es ist unabhängig von einem bestimmten Lehrbuch konzipiert und umfaßt den Standardstoff einer einführenden Vorlesung in Numerik oder in das wissenschaftliche Rechnen. Es ist in Paragraphen gegliedert, welche jeweils einem bestimmten Sachgebiet der Numerik entsprechen. Jedem Paragraphen ist in ein bis zwei Seiten eine kurze Zusammenstellung der wichtigsten Tatsachen und Formeln vorangestellt, die als Arbeitsgrundlage und Verweismöglichkeit bei den Aufgaben dient. Jeder Paragraph enthält eine Sammlung für das Gebiet typischer Übungsaufgaben mit mustergültig ausgearbeiteten Lösungen.Table of ContentsRechnerarithmetik - Polynome und Interpolation - Numerische Differentiation und RICHARDSON-Extrapolation - BANACHscher Fixpunktsatz und Konvergenzordnung - Nichtlineare Gleichungen - Matrixanalyse und Normen - Lineare Gleichungssysteme

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Book SynopsisI. In this second volume, we continue at first the study of non­ homogeneous boundary value problems for particular classes of evolu­ tion equations. 1 In Chapter 4 , we study parabolic operators by the method of Agranovitch-Vishik [lJ; this is step (i) (Introduction to Volume I, Section 4), i.e. the study of regularity. The next steps: (ii) transposition, (iii) interpolation, are similar in principle to those of Chapter 2, but involve rather considerable additional technical difficulties. In Chapter 5, we study hyperbolic operators or operators well­ defined in thesense of Petrowski or Schroedinger. Our regularity results (step (i)) seem to be new. Steps (ii) and (iii) are all3.logous to those of the parabolic case, except for certain technical differences. In Chapter 6, the results of Chapter'> 4 and 5 are applied to the study of optimal control problems for systems governed by evolution equations, when the control appears in the boundary conditions (so that non-homogeneous boundary value problems are the basic tool of this theory). Another type of application, to the characterization of "all" well-posed problems for the operators in question, is given in the Ap­ pendix. Still other applications, for example to numerical analysis, will be given in Volume 3.Table of Contents4 Parabolic Evolution Operators. Hilbert Theory.- 1. Notation and Hypotheses. First Regularity Theorem.- 1.1 Notation.- 1.2 Statement of the Problems.- 1.3 (Formal) Green’s Formulas.- 1.4 First Existence and Uniqueness Theorem (Statement).- 1.5 Orientation.- 2. The Spaces Hr, s(Q). Trace Theorems. Compatibility Relations.- 2.1 Hr, s-Spaces.- 2.2 First Trace Theorem.- 2.3 Local Compatibility Relations.- 2.4 Global Compatibility Relations for a Particular Case.- 2.5 General Compatibility Relations.- 3. Evolution Equations and the Laplace Transform.- 3.1 Vector Distribution Solutions.- 3.2 L2-Solutions.- 4. The Case of Operators Independent of t.- 4.1 Hypotheses.- 4.2 Basic Inequalities.- 4.3 Solution of the Problem.- 5. Regularity.- 5.1 Preliminaries.- 5.2 Basic Inequalities.- 5.3 An Abstract Result.- 5.4 Solution of the Boundary Value Problem.- 6. Case of Time-Dependent Operators. Existence of Solutions in the Spaces H2r m, m(Q), Real r ? 1.- 6.1 Hypotheses. Statement of the Result.- 6.2 Local Result in t.- 6.3 Proof of Theorem 6.1.- 6.4 Regular Non-Homogeneous Problems.- Adjoint Isomorphism of Order r.- 7.1 The Adjoint Problem.- 7.2 Adjoint Isomorphism of Order r.- 8. Transposition of the Adjoint Isomorphism of Order r. (I): Generalities.- 8.1 Transposition.- 8.2 Orientation.- 8.3 The Spaces H??, ??(Q), H??, ??(?), ?, ? ? 0.- 8.4 (Formal) Choice of L.- 9. Choice of f. The Spaces ?2rm,r(Q).- 9.1 The Space ?2rm,r(Q).- 9.2 The Space ??2rm,?r(Q).- 9.3 Choice of f. The Space D?(r?1)(P)(Q).- 10. Trace Theorems for the Spaces D?(r?1)(P)(Q), r ? 1.- 10.1 Density Theorem.- 10.2 Trace Theorem on ?.- 10.3 Continuity of the Trace on Surfaces Neighbouring ?.- 10.4 Trace Theorem on ?0.- 10.5 Continuity of the Trace on Sections Neighbouring ?.- 11. Choice of gj and uo. The Spaces H2?m ??(?).- 11.1 The Spaces H2?m ??(?).- 11.2 Choice of gj.- 11.3 Choice of uo.- 12. Transposition of the Adjoint Isomorphism of Order ?. (II): Results; Existence of Solutions in H2mr,r(Q)-Spaces, Real r ? 0.- 12.1 Final Choice of L.- 12.2 Results.- 12.3 Complements.- 13. State of the Problem. Complements on the Transposition of the Adjoint Isomorphism of Order 1.- 13.1 State of the Problem.- 13.2 Complements on the Transposition of the Adjoint Isomorphism of Order 1.- 13.3 Orientation.- 14. Some Interpolation Theorems.- 14.1 Notation. Statement of the Main Result.- 14.2 Outline of the Proof.- 14.3 First Auxiliary Interpolation Theorem.- 14.4 Second Auxiliary Interpolation Theorem.- 14.5 Third Auxiliary Interpolation Theorem.- 14.6 Proof of Theorem 14.1.- 15. Final Results; Existence of Solutions in the Spaces H2mr,r(Q), 0 < r < 1. Applications.- 15.1 Application of the Results of Section 14.- 15.2 Examples; Generalities.- 15.3 Examples (I).- 15.4 Examples (II).- 15.5 Some Complements on the Dirichlet Problem.- 16. Comments.- 17. Problems.- 5 Hyperbolic Evolution Operators, of Petrowski and of Schroedinger. Hilbert Theory.- 1. Application of the Results of Chapter 3 and General Remarks.- 1.1 Notation. Hypotheses.- 1.2 Application of the Results of Chapter 3.- 1.3 A Counter-Example.- 2. A Regularity Theorem (I).- 3. Regular Non-Homogeneous Problems.- 3.1 Statement of the Problem.- 3.2 The Compatibility Relations.- 3.3 The Case of the Dirichlet Problem.- 4. Transposition.- 4.1 Adjoint Isomorphism.- 4.2 Transposition.- 4.3 Choice of L.- 4.4 Conclusion.- 5. Interpolation.- 5.1 Statement of the Problem.- 5.2 Some Interpolation Results.- 5.3 Consequences.- 5.4 The Case of the Dirichlet Problem.- 6. Applications and Examples.- 6.1 General Results.- 6.2 Examples.- 7. Regularity Theorem (II).- 7.1 Statement.- 7.2 Proof of Theorem 7.1.- 8. Non-Integer Order Regularity Theorem.- 8.1 Orientation.- 8.2 Interpolation in r.- 8.3 Interpretation of the Space V(2r?1)m,2r(Q), r ? 1.- 9. Adjoint Isomorphism of Order r and Transposition.- 9.1 Adjoint Isomorphism of Order r.- 9.2 Transposition.- 9.3 Formal Choice of L.- 10. Choice of f, $$ \vec g $$, u0, u1.- 10.1 Choice of f.- 10.2 The Space $$ D_{A + D_t^2}^{ - \left( {2r - 1} \right)}\left( Q \right) $$.- 10.3 Choice of gj.- 10.4 Choice of u0, u1.- 10.5 Conclusion.- 11. Trace Theorems in the Space $$ D_{A + D_t^2}^{ - \left( {2r - 1} \right)}\left( Q \right) $$.- 11.1 Density Theorem.- 11.2 Traces on ?.- 11.3 Continuity of the Trace on Neighbouring Surfaces.- 11.4 Traces on ?0.- 11.5 Continuity of the Trace on Sections Neighbouring ?0.- 11.6 Remark.- 12. Schroedinger Type Equations.- 12.1 Notation.- 12.2 First Regularity Theorem. Parabolic Regularization.- 12.3 Second Regularity Theorem.- 12.4 r-Isomorphism Theorem.- 12.5 Choice of L.- 12.6 Trace Theorem.- 13. Comments.- 14. Problems.- 6 Applications to Optimal Control Problems.- 1. Statement of the Problems for the Linear Parabolic Case.- 1.1 Notation.- 1.2 Optimization Problems.- 2. Choice of the Norms in the Cost Function.- 2.1 Reminder. Condition on K1(Q).- 2.2 Space Described by $$ \vec S\,y $$. Conditions on K2(?).- 2.3 Space Described by y(x, T; u). Condition on K3(?).- 3. Optimality Condition for Quadratic Cost Functions.- 3.1 Notation.- 3.2 Optimality Condition.- 4. Optimality Condition and Green’s Formula.- 4.1 Optimality Condition. Application of Section 3.2.- 4.2 The Isomorphisms ?i.- 4.3 The “Adjoint” Problem.- 4.4 New Form of the Optimality Condition.- 5. The Particular Case $$ \mu \,\, = \,\,m\,\, + \,\,\frac{1}{2} $$, E3 ? 0.- 5.1 Properties of y.- 5.2 Choice of K1(Q).- 5.3 Choice of K2(?) and K3(?).- 5.4 Adjoint Problem and Optimality Condition.- 6. Consequences of the Optimality Condition (I).- 6.1 Generalities.- 6.2 Consequences of Theorem 6.1.- 7. Consequences of the Optimality Condition (II).- 7.1 Additional Hypotheses.- 7.2 Optimality Condition.- 8. Complements on the Choice of the Spaces Ki.- 8.1 Orientation.- 8.2 Choice of K1(Q).- 8.3 Choice of K2(?).- 8.4 Choice of K3(?).- 9. Examples.- 10. Non-Parabolic Cases. Statement of the Problems. Generalities.- 10.1 Notation.- 10.2 Cost Function.- 10.3 Optimality Condition (I).- 10.4 Adjoint Problem.- 10.5 Green’s Formula.- 10.6 Optimality Condition (II).- 10.7 Consequences.- 11. Applications. Examples.- 11.1 Control in the Boundary Conditions.- 11.2 Choice of K1.- 11.3 Choice of K2.- 11.4 Examples.- 12. Comments.- 13. Problems.- Boundary Value Problems and Operator Extensions.- 1. Statement of the Problem. Well-Posed Spaces.- 1.1 Notation.- 2. Abstract Boundary Conditions.- 2.1 Boundary Spaces and Operators.- 2.2 Characterization of Well-Posed Spaces.- 3. Example 1. Elliptic Operators.- 3.1 Notation.- 3.2 The Boundary Operators and Spaces.- 3.3 Consequences.- 3.4 Various Remarks.- 4. Example 2. Parabolic Operators.- 4.1 Notation.- 4.2 The Boundary Operators and Spaces.- 4.3 Consequences.- 5.1 Notation.- 5.2 Formal Results.- 6. Comments and Problems.

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Book SynopsisDieses Lehrbuch vermittelt die Wirkungsweise vieler unterschiedlicher Grundbausteine numerischer Algorithmen. Übergeordnete Zielsetzung ist die Stärkung der Fähigkeit, numerische Ergebnisse einschätzen und bewerten zu können, sowie die numerischen Werkzeuge auch in komplexeren Anwendungsszenarien flexibel und sachgemäß kombinieren und anpassen zu können. Besonderer Wert wird dabei von Anfang an auf ein solides Verständnis der Konzepte Kondition (eines Problems) und Stabilität (eines Lösungsverfahrens) gelegt. Aufgrund der Vielzahl der in der Praxis benötigten numerischen Bausteine wird eine methodenorientierte Einführung zu den relevanten Themenschwerpunkten angeboten: Direkte und iterative Verfahren zur Lösung von Gleichungssystemen, Ausgleichsrechnung, Singulärwertzerlegung, Eigenwertberechnung, Interpolation, schnelle Fouriertransformation, numerische Integration sowie numerische Verfahren für gewöhnliche Differentialgleichungen. Zahlreiche illustrierende Beispiele vermitteln den konkreten Ablauf von Verfahren und verdeutlichen neue Konzepte, abschließende Übungsaufgaben runden die Kapitel ab. Die Inhalte selbst sind – soweit möglich – so gestaffelt, dass den „Pflichtinhalten“ optionale Vertiefungen folgen, in denen konzeptionelle Gesichtspunkte, übergreifende Zusammenhänge sowie rigorose Begründungen stärker betont werden. Das Buch eignet sich daher sowohl als Grundlage einer einsemestrigen einführenden als auch einer weiterführenden Numerik-Vorlesung im Ingenieurstudium, bietet aber auch die konzeptionellen Grundlagen für die Numerikausbildung im Mathematikstudium.Die Autoren stellen auf Ihrer Webseite zusätzlich Vorlesungsfolien für Dozenten, Multiple-Choice-Aufgaben sowie Matlabdemos bereit.Für die 3. Auflage wurde das Buch vollständig überarbeitet und noch besser strukturiert.Table of ContentsEinleitung.- Fehleranalyse: Kondition, Rundungsfehler, Stabilität.- Lineare Gleichungssysteme.- Lineare Ausgleichsrechnung.- Nichtlineare Gleichungssysteme.- Nichtlineare Ausgleichsrechnung.- Eigenwertprobleme.- Interpolation.- Splinefunktionen.- Numerische Integration.- Gewöhnliche Differentialgleichungen.

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Book SynopsisThe book serves as an introductory course for undergraduate and graduate students in engineering, science, and mathematics, encompassing all disciplines. It addresses key topics, such as numerical computation, linear systems of equations, algebraic and transcendental equation solutions, numerical differentiation, finite differences and interpolation, curve fitting, regression and correlation, numerical integration, and ordinary and partial differential equation solutions. The books language is simple and easy to understand, presented in a systematic and student-friendly manner, with a focus on numerical problem-solving. The balance between theory and practical examples is well-maintained. Each concept is supported by examples, which are unavailable in other books, helping students to better understand and remember the material. Exercise questions are provided at the end of each chapter for further practice.

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Book Synopsis1 Lezione 1 - Lo spazio e le curve.- 2 Lezione 2 - Funzioni di più variabili.- 3 Lezione 3 - Calcolo differenziale e approssimazioni.- 4 Lezione 4 - Massimi e minimi.- 5 Lezione 5 - Integrali curvilinei.- 6 Lezione 6 - Integrali doppi.- 7 Lezione 7 - Integrali tripli.- 8 Lezione 8 - Superficie parametriche.- 9 Lezione 9 - Teoremi della divergenza e di Green Stokes.- 10 Lezione 10 - Equazioni differenziali.

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Book SynopsisUnderstanding earth systems and its dynamic behavior requires objective insights into the complex observational data sets and their interrelationships. Drawing meaningful inferences from such data is not always an easy task as the deterministic relationships between various geological variables often remain obscured. These interrelationships need to be determined empirically through the analysis of a large set of data and validated through numerical simulations. The ever widening horizon of techniques of numerical analysis and simulation now provides a good number of tools to aid the interpretation. However, due to the inherent complexity of earth science data, expert supervision is required at all stages of analysis from collection to dissemination. This ensures that the most appropriate methodology is adopted and the results remain consistent with the geological principles. Discussions on these practical issues often lie beyond the scope of textbooks and this is precisely where this book is placed. In this book eminent geoscientists present their experiences in analyzing and managing earth science data as well as in designing numerical models to simulate earth processes. Apart from giving a discourse of their own approach towards a particular research problem they also discuss at length the relative merits of alternative methodologies. These seven authoritative articles, richly illustrated, will be a valuable resource for research students and professionals interested in research and teaching in various branches of earth science like, tectonics, GPS geodesy, sedimentology, geographical information science, and evolutionary biology.Table of Contents1. Active deformation in the Darjiling-Sikkim Himalaya based on 2000-2004 geodetic global positioning system measurements. 2. Preliminary results of a study of crustal deformation in the Himalayan Frontal zone in North Bengal using GPS Geodesy. 3. Spatial and temporal variations of the strain fields in orogenic belts: an analysis based on kinematic models. 4. Grain size distribution patterns of some rivers in the light of three model distributions. 5. Estimation of shape changes of skull roof bones in Benthosuchus Sushkini, a Temnospondyl amphibian from the Triassic of Russia. 6. Spatial mathematical models for mineral potential mapping. 7. Enterprise GIS in Geological Survey of India.

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Book SynopsisThis two-volume book provides an insight into the 10th International Conference on Soft Computing for Problem Solving (SocProS 2020). This international conference is a joint technical collaboration of Soft Computing Research Society and Indian Institute of Technology Indore. The book presents the latest achievements and innovations in the interdisciplinary areas of soft computing. It brings together the researchers, engineers and practitioners to discuss thought-provoking developments and challenges, in order to select potential future directions. It covers original research papers in the areas including but not limited to algorithms (artificial immune system, artificial neural network, genetic algorithm, genetic programming and particle swarm optimization) and applications (control systems, data mining and clustering, finance, weather forecasting, game theory, business and forecasting applications). The book will be beneficial for young as well as experienced researchers dealing across complex and intricate real-world problems for which finding a solution by traditional methods is a difficult task.Table of ContentsSwarm Programming using Multi-Verse Optimizer.- Muzzle Pattern based Cattle Identification Using Generative Adversarial Networks.- Diverse Sports Video Classification Using Large Space MPEG Features.- An Intelligent Method for Plastic Money Fraud Detection using Isolation Forest Classifier.- Mixed Differential Evolution and Genetic Algorithm Hybridization for Solving Global Optimization Problems.- Energy Neutral Classroom.

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