Applications of Mathematics and Informatics in Natural Sciences and Engineering : AMINSE 2019, Tbilisi, Georgia, September 23-26

This book presents peer-reviewed papers from the 4th International Conference on Applications of Mathematics and Informatics in Natural Sciences and Engineering (AMINSE2019), held in Tbilisi, Georgia, in September 2019. Written by leading researchers from Austria, France, Germany, Georgia, Hungary, Romania, South Korea and the UK, the book discusses important aspects of mathematics, and informatics, and their applications in natural sciences and engineering. It particularly focuses on Lie algebras and applications, strategic graph rewriting, interactive modeling frameworks, rule-based frameworks, elastic composites, piezoelectrics, electromagnetic force models, limiting distribution, degenerate Ito-SDEs, induced operators, subgaussian random elements, transmission problems, pseudo-differential equations, and degenerate partial differential equations. Featuring theoretical, practical and numerical contributions, the book will appeal to scientists from various disciplines interested in applications of mathematics and informatics in natural sciences and engineering. Editorial Preface Contents On Variational Methods of Investigation of Mathematical Problems for Thermoelastic Piezoelectric Solids 1 Introduction 2 Dynamic Three-Dimensional Problem 3 Static Three-Dimensional Problem 4 Conclusions References On Nonparametric Kernel-Type Estimate of the Bernoulli Regression Function 1 Introduction 2 Assumptions and Notation 3 Asymptotic Normality of Statistics Un and Tn 4 Application of the Statistic Tn for Hypothesis Testing References Scaling Property for Fragmentation Processes Related to Avalanches 1 Introduction 2 Scaling Property for Jump Processes 3 Scaling Property for the SDE of Fragmentation 4 Numerical Results References Conflict Resolution Models and Resource Minimization Problems 1 Introduction 2 Description of Mathematical Models 3 First Mathematical Model in the Case of Constant Coefficients 4 Computer Modeling in the Case of Variable Model Coefficients. Optimization of Management Parameters 5 Conclusion References Modeling of Extreme Events and Regional Climate Variability on the Territory of the Caucasus (Georgia) 1 Introduction 2 Problem Formulation 2.1 Data and Methodology 3 Results and Discussion 4 Conclusions References Extending the ρLog Calculus with Proximity Relations 1 Introduction 2 Preliminaries 2.1 Terms, Hedges, Contexts, Substitutions 2.2 Proximity Relations 3 ρLog-prox: ρLog with Proximity Relations 3.1 Syntactic Matching and Proximity Matching Problems 3.2 ρLog-prox Programs and Proximity Relations 4 Solving Proximity Problems 5 Conclusion References Specification and Analysis of ABAC Policies in a Rule-Based Framework 1 Introduction 2 Preliminaries 2.1 The ρLog System 2.2 The Operational Model of ABACα 3 A Rule-Based Framework for ABACα 3.1 Rules for the Policies of the Configuration Points 3.2 Rules for the Operational Model 3.3 Safety Analysis 4 Conclusion References A Strategic Graph Rewriting Model of Rational Negligence in Financial Markets 1 Introduction 2 Background 2.1 Asset-Backed Securities 2.2 Port Graph Rewriting 3 The ABS-GTS Model 4 Model Properties 5 Conclusions References On Lie Algebras with an Invariant Inner Product 1 Introduction 2 Cohomology and Cyclic Cohomology 3 Deformations 4 Dimension 3 5 4-Dimensional Lie Algebras with Invariant Inner Product 5.1 The Direct Sum mathfraksl(2,mathbbC)oplusmathbbC and Its Real Forms 5.2 The Complex Diamond Algebra and Its Two Real Forms 5.3 The Real Diamond Algebra 5.4 The Real Oscillator Algebra 6 5-Dimensional Metric Lie Algebras 6.1 The Direct Sum mathfraksl(2,mathbbC)oplusmathbbC2 and Its Real Forms 6.2 The Complex Diamond Algebra Plus mathbbC 6.3 The Real Diamond Algebra Plus mathbbR 6.4 The Oscillator Algebra Plus mathbbR 6.5 The Nilpotent Lie Algebra W3 References Study of Three-Layer Semi-Discrete Schemes for Second Order Evolution Equations by Chebyshev Polynomials 1 Introduction 2 Abstract Hyperbolic Equation with a Constant Self-Adjoint Operator 2.1 Weighted Second-Order Scheme. A Priori Estimates of Solution to Difference Problems 2.2 Estimation for Two-Variable Chebyshev Polynomials 2.3 Proof of Theorem 1 2.4 Estimates for Chebyshev's Operator Polynomials 2.5 A Priori Estimates for Difference Analogues of First and Second Order Derivatives 2.6 Theorems on the Convergence of a Semi-Discrete Scheme 2.7 Approximation with Splines 3 Second Order Complete Equation 4 Remark Concerning Equations with a Variable Operator References Notes on Sub-Gaussian Random Elements 1 Sub-Gaussian and Related Random Variables 2 Sub-Gaussian Random Elements References Localized Boundary-Domain Integro-Differential Equations Approach for Stationary Heat Transfer Equation 1 Introduction 2 Localised Green's Formula and Boundary-Domain Integro-Differential Relations 3 Reduction to Systems of Boundary Domain Integro-Differential Equations 3.1 The Dirichlet Problem 3.2 The Robin Problem 4 Reduction to Segregated Systems of Boundary Domain Integral Equations for the Dirichlet Problem References Boundary Value Problems of the Plane Theory of Elasticity for Materials with Voids 1 Introduction 2 Basic Equations for Materials with Voids of the 3D Model 3 Basic (Governing) Equations of the Plane Strain 4 Kolosov–Muskhelishvili Formulas for (11) System 5 A Problem for a Circle 6 A Problem for the Plane with a Circular Hole 7 Conclusion References Objective and Subjective Consistent Criteria for Hypotheses Testing 1 Auxiliary Notions and Results 2 Subjective Consistent Criterion for Hypotheses Testing 3 Objective Consistent Criterion for Hypotheses Testing References Review of Rational Electrodynamics: Deformation and Force Models for Polarizable and Magnetizable Matter 1 Introduction 2 Balance Laws and Integral Theorems 3 Rational Electrodynamics 3.1 Electromagnetic Fields 3.2 Derivation of Maxwell's Equations in Matter 3.3 Charges in Materials 3.4 Universal Connections: The Maxwell-Lorentz-æther Relations 4 Coupling of Electromagnetism and Mechanics 5 Dielectrics 5.1 Electric Fields 5.2 Electrostriction 5.3 Total Force Analysis 5.4 Displacement Solutions 6 Total Forces and Moments Between Spherical Magnets 7 Summary 8 Derivation of Integral Theorems with Singular Surfaces 8.1 Generalized Gauss Theorem 8.2 Generalized Stokes Theorem 8.3 Generalized Volumetric Transport Theorem 8.4 Generalized Surface Transport Theorem 8.5 Generalized Surface Flux Theorem 9 Localization Theorem References