Related papers: Index theory for linear self-adjoint operator equa…
In this paper following the same methods in [M. Kadakal, O. Sh. Mukhtarov, Sturm-Liouville problems with discontinuities at two points, Comput. Math. Appl., 54 (2007) 1367-1379] we investigate discontinuous two-point boundary value problems…
We give an exposition of the Morse Index Theorem in the Riemannian case in terms of the Maslov index, following and expanding upon Arnold's seminal paper. We emphasize the symplectic arguments in the proof and aim to be as self-contained as…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
Second-order variational type equations for spatial point processes are established. In case of log linear parametric models for pair correlation functions, it is demonstrated that the variational equations can be applied to construct…
We consider families of theories with large N=4 superconformal symmetry. We define an index generalizing the elliptic genus of theories with N=2 symmetry. In contrast to the N=2 case, the new index constrains part of the non-BPS spectrum.…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
We present an asymptotic control theory for a system of an arbitrary number of linear oscillators under a common bounded control. We suggest a design method of a feedback control for this system. By using the DiPerna-Lions theory of…
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real…
The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…
This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of -- mainly linear -- system identification. We emphasize tools we deem particularly useful for a range of problems in this domain, such as…
We consider two special cases of the connection problem for the second Painlev\'e equation (PII) using the method of uniform asymptotics proposed by Bassom et al.. We give a classification of the real solutions of PII on the negative…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
The main focus of these notes is recent work on linear systems in which line arrangements play a role, including problems such as semi-effectivity, containment problems of symbolic powers of homogeneous ideals in their powers, bounded…
This article deals with the asymptotic behavior of fourth order differential equation where the coefficients are perturbations of linear constant coefficient equation. We introduce a change of variable and deduce that the new variable…
The paper has three parts. In the first part we apply the theory of commuting pairs of (pseudo) difference operators to the (formal) asymptotics of orthogonal polynomials: using purely geometrical arguments we show heuristically that the…
We study an abstract family of asymptotically degenerating variational problems. Those are natural generalisations of families of problems emerging upon application of a rescaled Floquet-Bloch-Gelfand transform to resolvent problems for…
The existence of a nontrivial solution is proved for a class of quasilinear elliptic equations involving, as principal part, either the p-Laplace operator or the operator related to the p-area functional, and a nonlinearity with p-linear…
In this work we present a new approach for the implementation of operational Tau method for the solutions of linear differential and integral equations. In our approach we use the three terms relation of an orthogonal polynomial basis to…
We consider a planar Hamiltonian system of the type $Jz' = \nabla_z H(t,z)$, where $H: \mathbb{R} \times \mathbb{R}^2 \to \mathbb{R}$ is a function periodic in the time variable, such that $\nabla_z H(t,0) \equiv 0$ and $\nabla_z H(t,z)$ is…