Related papers: Analytic integrability around a nilpotent singular…
This paper is devoted to proving the differential invariance of the multiplicity of real and complex analytic sets. In particular, we prove the real version of Gau-Lipman's Theorem, i.e., it is proved that the multiplicity mod 2 of real…
We give a classification of the principal and distinguished nilpotent pairs in all classical Lie algebras. As a classification of the principal pairs in the exceptional simple Lie algebras was obtained earlier (see Appendix to Ginzburg's…
The problem of constructing an exact solution of singular integro-differential equations related to problems of adhesive interaction between elastic thin semi-infinite homogeneous patch and elastic plate is investigated. For the patch…
In this work we study the problem of existence of symplectic structures on free nilpotent Lie algebras. Necessary and sufficient conditions are given for even dimensional ones. The one dimensional central extension for odd dimensional free…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
This paper is a contribution to the development of the non associative algebras theory. More precisely, this work deals with the classification of the complex 4-dimensional Leibniz algebras. Note that the classification of 4-dimensional…
We consider the differential system $y'-x^{-1}Ay-q(x)y=\rho By $ with $n\times n$ matrices $A,B, q(x)$, where $A,B$ are constant, $B$ is diagonal, $A$ and $q(x)$ are off-diagonal, $q(\cdot)\in W^1_1[0,\infty)$. Some distinguished…
In this paper we extend the Lie theory of integration in two different ways. First we consider a finite dimensional Lie algebra of vector fields and discuss the most general conditions under which the integral curves of one of the fields…
We continue the program initiated in a previous work, of applying integro-differential methods to Neumann Homogenization problems. We target the case of linear periodic equations with a singular drift, which includes (with some regularity…
The geometric approach to mechanics based on the Jacobi metric allows to easily construct natural mechanical systems which are integrable (actually separable) at a fixed value of the energy. The aim of the present paper is to investigate…
We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…
Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with essentially the same toolbox, when one looks for analytic solutions in closed form. The basic tool…
We establish a version of a semistable reduction theorem over a log point with a non-trivial nilpotent structure. In order to do this we extend the classical desingularization theories to non-reduced schemes with generically principal…
This article is dedicated to the proof of the existence of classical solutions for a class of non-linear integral variational problems. Those problems are involved in nonlocal image and signal processing.
Reliable controllers with high flexibility and performance are necessary for the control of intricate, advanced, and expensive systems such as aircraft, marine vessels, automotive vehicles, and satellites. Meanwhile, control allocation has…
In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations contained in a class of equations…
We prove several general results on non existence of analytic first integrals for analytic diffeomorphisms possessing a hyperbolic fixed point.
We prove that a Lie conformal algebra L with bounded locality function is embeddable into an associative conformal algebra A with the same bound on the locality function. If L is nilpotent, then so is A, and the nilpotency index remains the…
In this paper, we classify the generic singularities of 2-parameter plane congruences in $\mathbb{R^4}$ and the generic singularities of affine normal plane congruences. We also study the generic singularities of the family of affine…