Related papers: Homogenization problems in the Calculus of Variati…
We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is…
This paper concerns a space-time homogenization limit of nonnegative weak solutions to porous medium equations. In particular, the so-called homogenized matrix will be characterized in terms of solutions to cell problems, which drastically…
Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.
We present a subdivision method to solve systems of congruence equations. This method is inspired in a subdivision method, based on Bernstein forms, to solve systems of polynomial inequalities in several variables and arbitrary degrees. The…
Representation of the quantum measurement with the help of non-orthogonal decomposition of unit is presented in the paper for the first time. Methods for solution of the quantum detection and measurement problems based on the suggested…
This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results
In this paper, the discriminant of homogeneous polynomials is studied in two particular cases: a single homogeneous polynomial and a collection of n-1 homogeneous polynomials in n variables. In these two cases, the discriminant is defined…
Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…
The method of higher covariant derivative regularization of gauge theories is reviewed. The objections raised in the literature last years are discussed and the consistency of the method is proven. New approach to regularization of…
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
We present a new theoretical and numerical assessment methodology for a one-dimensional process chain with general applicability to management problems such as the optimization of decision chains or production chains. The process is thereby…
This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.
Cohomology of the variational bicomplex in the calculus of variations in classical field theory are computed in the class of exteriror forms of finite jet order. This provides a solution of the global inverse problem of the finite order…
Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…
The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…
We exhibit a numerical method to solve fractional variational problems, applying a decomposition formula based on Jacobi polynomials. Formulas for the fractional derivative and fractional integral of the Jacobi polynomials are proven. By…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
We apply general difference calculus in order to obtain solutions to the functional equations of the second order. We show that factorization method can be successfully applied to the functional case. This method is equivariant under the…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
In this paper, we derive multicontinuum poroelasticity models using the multicontinuum homogenization method. Poroelasticity models are widely used in many areas of science and engineering to describe coupled flow and mechanics processes in…