Current Trends in Analysis, its Applications and Computation: Proceedings of the 12th ISAAC Congress, Aveiro, Portugal, 2019

Preface
Contents
Part I Applications of Dynamical Systems Theory in Biology
	Bifurcation Analysis of the Topp Model
		1 Introduction
		2 Analysis of the 3-Dimensional Topp Model
		References
	Optimal Harvesting in Age- and Size-Structured Population Models
		1 Introduction
		2 Age- and Size-Dependent Population Models
		3 Harvesting Control
		4 Optimization in Age-, Size-Structured Models
			4.1  Optimization in Age-Structured Models
			4.2 Optimization in Size-Structured Models
		References
Part II Complex Analysis and Partial Differential Equations
	Dirichlet Problem for Inhomogeneous Biharmonic Equation in Clifford Analysis
		1 Introduction
		2 Integral Representations in Complex Clifford Algebra
			2.1 Dirac Equation
			2.2 Poisson Equation
			2.3 Second-Order Poisson Equation
		3 Dirichlet Problem
		References
	A Note on the Schwarz Problem in a Ring Domain
		1 Introduction
		2 Preliminaries
		3 Schwarz Problem for Inhomogeneous Cauchy–Riemann Equations
		4 Schwarz Problem for Generalized Beltrami Equations in a Ring Domain
			4.1 The Operators TR and R
			4.2 Solution of a Generalized Beltrami Equation
		References
	On Hierarchical Models of Elastic Shallow Shells with Voids
		1 Introduction
		2 Basic Three-Dimensional Relations
		3 Construction of Hierarchical Models for Elastic Shallow Shells with Voids
		4 The N=0 Approximation for the Plate
		References
	Well-Posedness and Numerical Results to 3D Periodic Burgers\' Equation in Lebesgue-Gevrey Class
		1 Introduction
		2 Well-Posedness Result
		3 Numerical Result
		References
	BVP for the First Order Elliptic Systems in the Plane
		References
	Applications of Zalcman\'s Lemma in CN
		1 Introduction
		2  Marty\'s Criterion
		3 Non-normal Families
		4 Montel\'s Theorem in CN
		5  Criterion of Normality
		References
	To the Theory of One Class of Three-Dimensional Integral Equation with Super-Singular Kernels by Tube Domain
		1 Integral Representations of a Variety of Solutions
		2 Inversion Formula
		References
Part III Complex Geometry
	Principal Higgs Bundles and Schottky Representations
		1 Introduction
		2 Schottky Representations
		3 Principal Higgs Bundles and Branes
		4 Schottky Representations and Branes
		References
	On Hodge Polynomials of Singular Character Varieties
		1 Introduction
		2 Preliminaries on Hodge-Deligne Polynomials, Affine GIT and Character Varieties
		3 The Free Abelian Case
		4 Generating Functions for E-Polynomials
		5 The Free Group Case
		References
	Diagonal Double Kodaira Structures on Finite Groups
		1 Introduction
		2 Diagonal Double Kodaira Structures
		3 The Case of Extra-Special p-Groups
		4 Geometric Interpretation: From Diagonal Double Kodaira Structures to Diagonal Double Kodaira Fibrations
		References
	Symmetric Differentials and the Dimension of Hitchin Components for Orbi-Curves
		1 Hitchin Components for Orbifold Fundamental Groups
			1.1 Compact Orbi-Surfaces of Negative Euler Characteristic
			1.2 Fundamental Group and Hyperbolic Structures
			1.3 Hitchin Components
		2 Analytic Parameterisation of Hitchin Components
			2.1 Analytic Orbi-Curves
			2.2 The Riemann-Roch Formula
			2.3 Spaces of Symmetric Differentials
		References
Part IV Complex Variables and Potential Theory
	Extremal Decomposition of a Multidimensional Complex Space with Poles on the Boundary of a Polydisk
		1 Preliminaries
		2 Main Results
		References
	Some Properties of the Solutions Space of Irregular Elliptic Systems
		1 Introduction and Motivation
		2 Main Theorem
		References
	Bases in Commutative Algebras of the Second Rank and Monogenic Functions Related to Some Casesof Plane Orthotropy
		1 Statement of the Problem
		2 Two-Dimensional Algebras Over the Field of Complex Numbers and Their Bases Related to Plane Orthotropy
		3 Monogenic Functions in the Plane Generated by a Basis Satisfying Condition (1.6)
		4 Monogenic Functions Related to Eq.(1.3) and System (1.4)
		References
	On the Behavior at Infinity of One Class of Homeomorphisms
		1 Introduction
		2 Main Results
		References
	Domain Perturbation for the Solution of a Periodic Dirichlet Problem
		1 Introduction
		2 Preliminary Results
		3 Analyticity of the Solution
		References
	Real Analyticity of Periodic Layer Potentials Upon Perturbation of the Periodicity Parameters and of the Support
		1 Introduction
		2 Preliminary Technical Results
		3 Analyticity of the Integral Operators Associated with Layer Potentials
		References
	Directional Derivatives and Stolz Condition for Bicomplex Holomorphic Functions
		1 Introduction
		2 Some Basic Results on Bicomplex Holomorphic Theory
		3 The Stolz Condition
		References
Part V Constructive Methods in the Theory of Composite and Porous Media
	Fast Method for 2D Dirichlet Problem for Circular Multiply Connected Domains
		1 Introduction
		2 Description of the Fast Poincaré Series Method
		3 Conclusions
		References
	Local Stationary Heat Fields in Fibrous Composites
		1 Introduction
		2 Methodology
		3 Numerical Examples
		4 Conclusion
		References
	The Robin Problem for Quasi-Linear Elliptic Equation p(x)-Laplacian in a Domain with Conical Boundary Point
		1 Introduction
		2 L∞: Estimate of Bounded Weak Solutions
		3 The Behavior of Weak Solutions Near the Angular or Conical Point of the Boundary
		4 Existence of Bounded Weak Solutions
		5 Transmission Robin Problem
		References
	Analysis of Distributions of Stadiums on the Plane Using e-Sums
		1 Introduction
		2 Structural Sums
		3 Applications of Structural Sums in Description of the Geometry of Distributions of Stadiums
		4 Conclusions
		References
	Boundary Value Problems and Their Applications to 2D Composites Theory
		1 Introduction
		2 General Formulae for Effective Conductivity
		3 General Formulae for Effective Shear Moduli
			3.1 Statement the Problem
			3.2 Effective Constants Up to O(f3)
		References
	Selected Aspects of Visualization in Education of Functions
		1 Introduction
		2 Threshold Concepts and Using ICT in the Education of Functions
		3 Visualization as a Helping Tool for Explanation of Misconceptions
		4 The Notion of the Inverse Function
		5 Conclusions
		References
	Key Cell Method Based on the ARVE. How Not to Fall Into the Representative Cell ``Trap\'\'
		1 Introduction
		2 Methodology of the Study Composite Structures
			2.1 Eisenstein–Rayleigh-Mityushev Sums (ERM-Sums)
			2.2 Determination of the Key RVEc  and RVEa  Cells
			2.3 Results of RVEc and RVEa Cells Analysis
			2.4 Summary and Conclusion
		References
	Neutral Inclusion and Spectral R-Linear Problem
		1 Introduction
		2 Eigenvalue Problem
		3 R-Linear Eigenvalue Problem
		4 Functional Equation
		5 Conclusion
		References
	Regularization Method for Stable Structural Features
		1 Introduction
		2 Structural Sums and Structural Features
			2.1 Definition of Structural Sum
			2.2 Structural Features
		3 Numerical Experiments
			3.1 Structural Features of Poisson Point Process
			3.2 Stable Features with the Nearest Neighbour Radii
		4 Conclusions
		References
	Multidimensional Potential and Its Application to Social Networks
		1 Introduction
		2 Structural Approximation in Rd
		3 Discrete Network in Rd
		4 Discussion
		References
	Heat and Energy Consumption Management of a Public Object
		1 Introduction
		2 Materials and Methods
		3 Results and Discussion
		4 Conclusion
		References
Part VI Function Spaces and Applications
	A Generalized Hardy Operator on Rearrangement Invariant Spaces
		1 Introduction
		2 Some Results on Weights
		3 The Main Theorem
		References
	Restricted Boundedness of Translation Operators on Variable Lebesgue Spaces
		1 Introduction
		2 Auxiliary Results
		3 The Proof of the Main Result
		References
	Fourier Convolution Operators with Symbols Equivalent to Zero at Infinity on Banach Function Spaces
		1 Introduction
		2 Mollification in Separable Banach Function Spaces
		3 Density of the Set S0(R)
		4 Proof of Theorem 1.2
		References
Part VII Generalized Functions and Applications
	On Almost Periodicity and Almost Automorphy
		1 Introduction
		2 Smooth E-Functions
		3 E-Distributions
		4 Application
		5 E-Generalized Functions
		References
	Note on Vector Valued Hardy Spaces Related to Analytic Functions Having Distributional Boundary Values
		1 Introduction
		2 Notation
		3 Distributional Boundary Values in Lp(Rn,X)
		4 Poisson Integral Representation
		References
	On the Projective Description of Spaces of Ultradifferentiable Functions of Roumieu Type
		1 Introduction
		2 Spaces of Ultradifferentiable Functions of Roumieu Type
		3 Projective Description of E{M}(Ω)
		References
	Singular Solutions to Equations of Fluid Mechanics and Dynamics Near a Hurricane\'s Eye
		1 Introduction
		2 Jump Condition at the Singular Support
			2.1 Statement of the Problem
			2.2 The Framework of Colombeau Algebras
			2.3 Proof of the Jump Condition Theorem
		3 Asymptotics of the Wind Field Near the Eye of a Hurricane
		4 Summary and Conclusion
		References
	Dirac Delta-Function in Optimal Control of Age-StructuredPopulations
		1 Introduction
		2 Impulse Controls in Optimal Harvesting of Age-Structured Populations
		3 Optimal Investment in Old Capital Under Technological Change and Learning-by-Doing
		References
	Generalized Solutions to Equations for Probabilistic Characteristics of Levy Processes
		1 Introduction
		2 Direct and Backward Equations for Probabilistic Characteristics Based on the Ito Formula
		3 The Approach via Limit Relations
		References
Part VIII Geometric and Regularity Properties of Solutions to Elliptic and Parabolic PDEs
	Asymptotic Regularity for a Random Walk over Ellipsoids
		1 Uniformly Elliptic PDEs in Non-divergence Form
		2 An Asymptotic Mean Value Property
		3 The Ellipsoid Process
		4 Asymptotic Regularity: the Coupling Method
		5 Limits as →0
		References
	Short-Time Asymptotics for Game-Theoretic p-Laplacian and Pucci Operators
		1 Introduction
		2 Varadhan-Type Formulas
		3 Asymptotics for q-Means
		References
	Geometric Properties for a Finsler Bernoulli Exterior Problem
		1 Introduction
		2 Notation
		3 Preliminary Results
		4 Proof of Theorem 1.1
		5 Monotonicity and Uniqueness Results
		References
	Symmetry Breaking Solutions for a Two-Phase Overdetermined Problem of Serrin-Type
		1 Introduction and Main Result
		2 Proof of Theorem 1.3 for N = 2
		3 Proof of Theorem 1.3 for N≥3
		References
	Regularity Results for Nonlocal Minimal Surfaces
		1 Introduction
		2 Classification of s-Minimal Cones in Low Dimensions
		3 Quantitative Flatness Results and Perimeter Estimates for Stable Sets
		References
	A Short Survey on Overdetermined elliptic Problems in Unbounded Domains
		1 Introduction
		2 New Nontrivial Solutions
			2.1 Bifurcation from a Known Solution
			2.2 Perturbation of a Constant-Mean-Curvature Surface
		3 Harmonic Overdetermined Problems
			3.1 Catenoidal Domains
			3.2 Classification of Harmonic Overdetemined Problems in the Plane
		4 Rigidity Results
			4.1 Exterior Domains
			4.2 Half-Space Type Domains
		References
Part IX Geometries Defined by Differential Forms
	Adjoint Representations of Symmetric Groups
		1 Introduction
		2 Notation and Background
			2.1 Symmetric Functions and Plethysm
			2.2 Partial Transformations and Loop Augmented Forests
		3 Proof of Theorem 1.1
		4 Proofs of Theorem 1.2 and Corollary 1.1
		References
	Examples of Equivariant Lagrangian Mean Curvature Flow
		1 Introduction
		2 Preliminaries
		3 Tori: Embedded Closed Curves
		4 Spheres: Immersed Closed Curves
		5 Cylinders: Embedded Open Curves
		6 Outlook
		References
	Some Useful Facts on Invariant Connections
		1 Introduction
			1.1 Context
			1.2 Summary and Organization
		2 Principal Bundles with Connections on Homogeneous Spaces
		3 Invariant Sections and Connections
		4 Moduli Space of Invariant Connections Modulo Gauge
		5 Extending Invariant Tensors Over Singular Orbits
		References
	Almost Symplectic Structures on Spin(7)-Manifolds
		1 Introduction
		2 Spin(7)-Structures
		3 Almost Symplectic Structures and Spin(7)-Structures
		4 A Motivating Example
		5 Interesting Questions
		References
	On Sub-Riemannian and Riemannian Spaces Associated to a Lorentzian Manifold
		1 Some Notations and Conventions
		2 Causal Set Theory
		3 Sub-Riemannian Space
			3.1 Sub-Riemannian Metrics
				3.1.1 The Sub-Riemannian Distance and Geodesics
		4 The Riemannian Space
		5 Some Remarks on the Minkowski Space Case
		References
	The Orbit Space and Basic Forms of a Proper Lie Groupoid
		1 Introduction
		2 Background
		3 Basic Differential Forms and Bibundles
		4 Linearisations and Proof of Theorem 1.1
		References
	Two-Frame Fields on Simply Connected Spin 7-Manifolds
		1 Introduction
		2 The Lifting Problem
		3 Secondary Compositions and Secondary Operations
		4 Conclusion
		References
Part X Partial Differential Equations on Curved Spacetimes
	Local Existence of Solutions to the Euler–Poisson System, Including Densities Without Compact Support
		1 Introduction
		2 Main Results
			2.1 Properties of the Solutions
			2.2 The Advantages of the Hs,δ Spaces
		3 Structure of the Proof
		Appendix A Useful Propositions
		References
	Isometric Flows of G2-structures
		1 Introduction
		2 Isometric G2-structures
		3 Energy Functional
		4 Gradient Flow
		References
	Remarks on the Navier-Stokes Equations in Homogeneous and Isotropic Spacetimes
		1 Introduction
		2 Derivation of the Equations
		References
Part XI Partial Differential Equations with Nonstandard Growth
	Ultra-Parabolic Kolmogorov-Type Equation with Multiple Impulsive Sources
		1 Introduction
		2 Problem 0: The Basic Formulation
		3 Parabolic Regularization of Problem 0
		4 Entropy Solutions of Problem 0
		5 Problem 0 as a Singular Limit Model Arising due to the Collapse of a Distributed Source
		References
Part XII Quaternionic and Clifford Analysis
	On a Sylvester Equation over a Division Ring
		1 Introduction
		2 Background
		3 The Regular Case
		4 The Singular Case
		References
	Hypercomplex Iterated Function Systems
		1 Preliminaries and Notation
			1.1 A Brief Introduction to Clifford Algebras
			1.2 Iterated Function Systems and Their Attractors
		2 Hypercomplex IFSs
		3 Systems of Hypercomplex Function Systems
		References
Part XIII Recent Progress in Evolution Equations
	Compactness of Localization Operators on Modulation Spaces of ω-Tempered Distributions
		References
	Lifespan Estimates for a Special Quasilinear Time-Dependent Damped Wave Equation
		1 Introduction
		2 Rewriting the Main Theorem
		3 Proof of Theorem 2.1
		References
	On a Criterion for Log-Convex Decay in Non-selfadjoint Dynamics
		1 Introduction
		2 A New Necessary Condition for Log-Convex Decay
		3 Main Results
		References
	A Uniform Resolvent Estimate for a Helmholtz Equation with Some Large Perturbations in An Exterior Domain
		1 Introduction and Result
		2 Some Inequalities
		3 Proof of Theorem 1.1 Under the Smallness Condition
		4 Another Inequality
		5 Proof of Theorem 1.1 Without the Smallness Condition
		References
Part XIV Wavelet Theory and Its Related Topics
	A Survey on the Time-Frequency Analysis on the Half Real Line
		1 Introduction
		2 Walsh Series-Based Wavelet Analysis in L2(R+) with R+=[0,∞)
		3 MD-Frame Theory in L2(R+) with R+=(0,∞)
		References
	Some Notes on the Inequalities for Parseval Generalized Continuous Frames
		1 Introduction
		2 Two Auxiliary Lemmas
		3 Main Results and their Proofs
		References
	Centering Projection Methods for Wavelet Feasibility Problems
		1 Wavelet Construction as a Feasibility Problem
		2 Centering Methods for Feasibility Problems
		3 Numerical Results
		4 Conclusion
		References
	Some Topics on the Gabor Wavelet Transformation
		1 Introduction
		2 Gabor Wavelet Transformation
			2.1 Fourier Transformation on the Sphere
			2.2 The Gaussian Function on the Sphere
			2.3 Windowed Fourier Transformation on the Sphere
			2.4 Gabor Wavelet Transformation on the Sphere
		3 Spherical Harmonics Expansion
		4 Expansion Formula
		5 Inverse Gabor Wavelet Transformation
		References
	Frames and Multirate Perfect Reconstruction Filter Banks in Multiple Dimensions
		1 Introduction
		2 Frames
		3 Multirate Filter Banks and Frames
		4 Lifting Scheme
		References
	Deficiencies of Holomorphic Curves for Linear Systems in Projective Manifolds
		1 Introduction
		2 Preliminaries
		3 Inequality of the Second Main Theorem Type
		4 Structure Theorems for the Set of Deficient Divisors
		5 Methods for Constructing Holomorphic Curves with Deficiencies
		References