BASIC CONCEPTS AND FORMULATIONS - Concepts in Linear Algebra - Point Latices - Some Functional Spaces - Generalized Derivatives and Pdm@ve Functions - Densi@ of Fin4e Fundons - P@ncipal Embedding Theorems for We@hted Spaces - Fundons of a Discrete kgument - Generalized Functions - Fou@er Transformabon of Generalized Functions - Periodic Functions and Generalized Functions - Generalized Spherical Harmonics - POLYHARMONIC EQUATION - Green's Formula - Fundamental Solution of a Polyharmonic Equation - Differential Prope@ies of Solutons of a Polyharmonic Equation - Behavior of Polyharmonic Functions in the Neighborhood of Infinity - Almansi's Theorem and Kelvin Transformation - P@ncipal Solutions of a Polyharmonic Equation - Expansion of Polyharmonic Functions in Principal Solutions - Polyharmonic Functons from W,@ in the Neighborhood of Intini@ - Boundary Value Problems for a Polyharmonic Equation in a Bounded Domain - Kelvin of bodies adrature s revised of these s topics Problem in An Infinite Domain - Exterior Variational Problem for a Polyharmonic Equation - Extension of a Funct ion from the Region i2 on R' with the Least Norm - Values of Functions from Wpm) at the Lattice Points Explicit Method of Regularization of Divergent Integrals - TWO SIMPLE PROBLEMS OF THE THEORY OF COMPUTATIONS - Interpolation Construction oi Cubature Formulas - Functional Formulation of the Problems, Extremal Function of a Cubature Formula - Error Functional in W'2 n, (RI Square of the Norm of the Error Functional - Deviation of Error of a Cubature Formula from the Optimal - ORDER OF CONVERGENCE OF CUBATURE FORMULAS - Lower Estimate of the Norm of the Error Functional Approximate Upper Estimate of the Norm of the Error Functional CUBATURE FORMULAS CONSIDERING A REGULAR BOUNDARY LAYER Formulas for Periodic Functions - Norm of the Error Functional for Periodic Functions - Composition of Formulas with Small Suppoas - Error for Finite Functions - Construction of Formulas with a Regular Boundary Layer - Norm of the Error Functional of Cubature Formulas with a Regular Boundary Layer in the Space L(')(R) - Norm of the Error of Formulas with Regular Boundary 2 Layer in L(al(Q) - OPTIMAL FORMULAS - Formulation of the Problem on 2 Optimal Coefficients - Fourier Transformation of a Discrete Potential - Prope@ies of the Operator D(m@[pl' - Discrete Analog of a Polyharmonic h Operator - Optimal Coefficients of One-Dimensional Formulas - CONVERGENCE OF CUBATURE FORMULAS IN VARIOUS CLASSES AND DIFFERENT FUNCTIONS - Functional Class (D(PIA) - Functional Class T(plo) - Cubature Formulas for Infinitely Differentiable Functions - Convergence oi Cubature Formulas for an Arbitrary Function (P(x) c @ll - CUBATURE FORMULAS FOR RATIONAL POLYHEDRA - Convex Polyhedra Euler's Formula - Rational Polyhedra - Structure of Formulas for Rational Polyhedra - Cubature Formulas for a Polyhedron and Its Solid Angles - Formulas with a Formal Boundary Layer
Reported are results of one study of the critical conditions for stationary propagation of a combustion wave, i.e. the conditions for the transition from a high-temperature to a low-temperature combustion regime, on the basis of an analysis of conjugate heat transfer between layers of fuel and an inert material. The mathematical analysis indicates that the critical thickness of the fuel for a stationary regime of combustion wave propagation depends to a large extent on the thermophysical and dimensions of the inert material. 2 figures.
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