Related papers: Center conditions: pull back of differential equat…
It is proved that the space of differential forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable differential forms. Mixed boundary conditions on weak Lipschitz domains are considered.…
A symmetric characteristic singular integral equation with two fixed singularities at the endpoints in the class of functions bounded at the ends is analyzed. It reduces to a vector Hilbert problem for a half-disc and then to a vector…
We consider a stochastic partial differential equation close to bifurcation of pitchfork type, where a one-dimensional space changes its stability. For finite-time Lyapunov exponents we characterize regions depending on the distance from…
Consider analytical three-dimensional differential systems having a singular point at the origin such that its linear part is $y\partial_x-\lambda z\partial_z$ for some $\lambda\neq 0$. The restriction of such systems to a Center Manifold…
In this paper we introduce a general type of differential equations with piecewise constant argument (EPCAG), and consider the problem of backward continuation of solutions. We establish the existence of global integral manifolds of…
It is established a continuous boundary extension of some class of mappings. Under some additional conditions, we have established that this extension is light in the closure of the definition domain. Under some stronger conditions, we also…
The theory of complete generalized Jordan sets is employed to reduce the PDE with the irreversible linear operator $B$ of finite index to the regular problems. It is demonstrated how the question of the choice of boundary conditions is…
In this paper we study polynomial maps of vector spaces and their eigenvectors and eigenvalues. The new quantity called complanart is defined. Complanarts determine complanarity of solution vectors of systems of polynomial equations.…
Starting from the notion of discriminantly separable polynomials of degree two in each of three variables, we construct a class of integrable dynamical systems. These systems can be integrated explicitly in genus two theta-functions in a…
Conditions for positive and polynomial recurrence have been proposed for a class of reliability models of two elements with transitions from working state to failure and back. As a consequence, uniqueness of stationary distribution of the…
In this article, we propose a general framework for the study of differential inclusions in the Wasserstein space of probability measures. Based on earlier geometric insights on the structure of continuity equations, we define solutions of…
The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.
This paper is concerned with reconstruction issue of inverse obstacle problems governed by partial differential equations and consists of two parts. (i) The first part considers the foundation of the probe and enclosure methods for an…
We prove the irreducibility of integer polynomials $f(X)$ whose roots lie inside an Apollonius circle associated to two points on the real axis with integer abscisae $a$ and $b$, with ratio of the distances to these points depending on the…
This note gives a unifying characterization and exposition of strongly irreducible elements and their duals in lattices. The interest in the study of strong irreducibility stems from commutative ring theory, while the dual concept of strong…
In this work, we are concerned with inverse problems involving poly-fractional operators, where the poly-fractional operator is of the form \[P( (-\Delta_g)^s)u := \sum_{i=1}^M \alpha_i(-\Delta_{g_i})^{s_i}u\] for $s=(s_1,\dots,s_M)$,…
We introduce a series of discrete mappings, which is considered to be an extension of the Hietarinta-Viallet mapping with one parameter. We obtain the algebraic entropy for this mapping by obtaining the recurrence relation for the degrees…
We show that for continuous time dynamical systems described by polynomial differential equations of modest degree (typically equal to three), the following decision problems which arise in numerous areas of systems and control theory…
We study a nonlinear decomposition of a positive definite matrix into two components: the inverse of another positive definite matrix and a symmetric matrix constrained to lie in a prescribed linear subspace. Equivalently, the inverse…
We study a graded vector space of polynomials associated to a square matrix, defined by a finite difference condition along the rows. We show this space coincides with one defined by directional derivatives, and prove it is…