Related papers: Some remarks on mixed problems
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
In this paper, we explore the interaction between two monoidal structures: a multiplicative one, for the encoding of pairing, and an additive one, for the encoding of choice. We propose a colored PROP to model computation in this framework,…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
We study conformal deformation problems on manifolds with boundary which include prescribing $\sigma_k\equiv0$ in the interior. In particular, we prove a Dirichlet principle when the induced metric on the boundary is fixed and an Obata-type…
In this paper, we analyze the variation of the gravitational action on a bounded region of spacetime whose boundary contains segments with various characters, including null. We develop a systematic approach to decompose the derivative of…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is…
In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation…
Numerical experiments with smooth surface extension and image inpainting using harmonic and biharmonic functions are carried out. The boundary data used for constructing biharmonic functions are the values of the Laplacian and normal…
We demonstrate, using the symbolic method together with p-adic and resultant methods,the existence of systems with exactly one or two generalized symmetries. Since the existence of one or two symmetries is often taken as a sure sign (or as…
One of the main obstacles for developing flexible AI systems is the split between data-based learners and model-based solvers. Solvers such as classical planners are very flexible and can deal with a variety of problem instances and goals…
In the article, in a rectangular domain, by the Fourier method, the initial boundary value problem for a high-order equation with two lines of degeneracy with a fractional derivative in the sense of Caputo is investigated for uniqueness and…
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
I present the most fundamental features of an implemented system designed to manipulate representations of regular languages. The system is structured into two layers, allowing regular languages to be represented in an increasingly compact,…
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface…
We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential…
Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high…
In this paper we investigate the existence of solutions for a system consisting of two inequalities of variational type. Each inequality is formulated in terms of a nonlinear bifunction $\chi$ and $\psi$, respectively and a coupling…