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Random Riemannian Geometry in 4 Dimensions
We construct and analyze conformally invariant random fields on 4-dimensional Riemannian manifolds (M, g). These centered Gaussian fields h, called...
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Approximation in Weighted Analytic Besov Spaces and in Generalized Fock Spaces
We study weighted analytic Besov spaces in the unit disk, and prove that the analytic polynomials are dense in weighted analytic Besov spaces if the...
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Biharmonic Monogenic Functions and Biharmonic Boundary Value Problems
We consider a commutative algebra B over the field of complex numbers with a basis {e 1, e 2} satisfying the conditions...
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A roadmap for Generalized Plane Waves and their interpolation properties
This work focuses on the study of partial differential equation (PDE) based basis function for Discontinuous Galerkin methods to solve numerically...
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On Toeplitz Operators with Biharmonic Symbols
In this article, we study the commuting problem of Toeplitz operators acting on the Bergman space of the unit disk when one of the symbols is...
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Limit Behaviour of a Singular Perturbation Problem for the Biharmonic Operator
We study here a singular perturbation problem of biLaplacian type, which can be seen as the biharmonic counterpart of classical combustion models. We...
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A High-Order Kernel-Free Boundary Integral Method for the Biharmonic Equation on Irregular Domains
This work proposes second-order and fourth-order versions of a Cartesian grid based kernel-free boundary integral (KFBI) method for the biharmonic...
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An adaptive kernel-split quadrature method for parameter-dependent layer potentials
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular...
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Reduction of the Two-Dimensional Thermoelasticity Problems for Solids with Corner Points to Key Integrodifferential Equations
We propose a generalization of the method of direct integration of the original equations of two-dimensional problems of thermoelasticity for solids...
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Analysis of Heatline and Entropy Generation during Magnetohydrodynamic Natural Convection in a Trapezoidal Enclosure
This paper presents an analysis of steady natural convection flow in a trapezoidal enclosure with various aspect ratios in presence of magnetic field...
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A priori and a posteriori error analysis for discontinuous Galerkin finite element approximations of biharmonic eigenvalue problems
In this paper, we express and analyze mixed discontinuous Galerkin(DG) methods of biharmonic eigenvalue problems as well as present the error...
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Schwartz-Type Boundary Value Problems for Monogenic Functions in a Biharmonic Algebra
We consider Schwartz-type boundary value problems for monogenic functions in a commutative algebra...
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Boundary Integral Equations
In Chapter 1 we presented basic ideas for the reduction of boundary value problems of the Laplacian to various forms of boundary integral equations...
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Triharmonic Curves in 3-Dimensional Homogeneous Spaces
We first prove that, unlike the biharmonic case, there exist triharmonic curves with nonconstant curvature in a suitable Riemannian manifold of...
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Algorithm for Construction of Quadrature Formulas with Exponential Convergence for Linear Operators Acting on Periodic Functions
We propose an algorithm for construction of quadrature formulas for linear operators acting on periodic functions. For analytic functions, the order...
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On Regularization of Singular Solutions of Orthotropic Elasticity Theory
AbstractThe problem of the mechanics of cracks in an orthotropic plate is considered. A general solution form is proposed as a generalized...
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Thermal Stressed State of a Half Space with Free or Rigidly, Smoothly, or Flexibly Fastened Boundary Under the Conditions of Heat Insulation in a Domain Located in the Plane Parallel to the Boundary
We construct the Green functions of the stationary problems of heat conduction and thermoelasticity for half spaces with free or rigidly, smoothly,...