Related papers: One class of linear Fredholm integral equations wi…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
We present a linear functional calculus with both the safety guarantees expressible with linear types and the rich language of combinators and composition provided by functional programming. Unlike previous combinations of linear typing and…
We introduce a new model of linear regression for random functional inputs taking into account the first order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our…
We consider elliptic problems with nonclassical boundary conditions that contain additional unknown functions on the border of the domain of the elliptic equation and also contain boundary operators of higher orders with respect to the…
The paper concerns inference in the ill-conditioned functional response model, which is a part of functional data analysis. In this regression model, the functional response is modeled using several independent scalar variables. To verify…
In this paper, using the similarity method, we construct particular solutions with singularities for degenerate high-order equations. The considered equations have singularities of the first and second kind. Particular solutions are…
We consider the problem of obtaining higher order in regularization parameter $\epsilon$ analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct…
We present a machine learning approach to the inversion of Fredholm integrals of the first kind. The approach provides a natural regularization in cases where the inverse of the Fredholm kernel is ill-conditioned. It also provides an…
We consider fractional differential equations of order $\alpha \in (0,1)$ for functions of one independent variable $t\in (0,\infty)$ with the Riemann-Liouville and Caputo-Dzhrbashyan fractional derivatives. A precise estimate for the order…
In this work we present some classes of models whose the corresponding two coupled first-order nonlinear equations can be put into a linear form, and consequently be solved completely. In these cases the so-called trial orbit method is…
A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which…
Nonlocal problems for higher-order elliptic operators in dihedral and plane angles are considered. The Green formula is obtained, which leads to adjoint problems that take the form of nonlocal transmission problems in dihedral and plane…
This paper concerns linear first-order hyperbolic systems in one space dimension of the type $$ \partial_tu_j + a_j(x,t)\partial_xu_j + \sum\limits_{k=1}^nb_{jk}(x,t)u_k = f_j(x,t),\; x \in (0,1),\; j=1,\ldots,n, $$ with periodicity…
This is the revised version of the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory,…
In this paper we present a method to derive Pi(x) and other Arithemtical functions that can be generated by a Dirichlet series by variational principles,we use a variational method to determine the solution for a Fredholm integral equation…
The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
We study the effects of adding a local perturbation in a pattern forming system, taking as an example the Ginzburg-Landau equation with a small localized inhomogeneity in two dimensions. Measuring the response through the linearization at a…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
In the first part of the article we establish the existence in the sense of sequences of solutions in $H^{2}(R)$ for some nonhomogeneous linear differential equation in which one of the terms has the argument translated by a constant. It is…