Related papers: On the regularity of the polar factorization for t…
In my previous paper I have contrived a Ginzburg-Landau heat flow with a time-dependent parameter and by using it, I constructed a harmonic heat flow into spheres with a monotonical inequality and a reverse Poincar\'{e} inequality. This…
We investigate the well-posedness of the radiative transfer equation with polarization and varying refractive index. The well-posedness analysis includes non-homogeneous boundary value problems on bounded spatial domains, which requires the…
In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial…
In this article, we study mappings acting between domains of two factor spaces by certain groups of M\"{o}bius automorphisms of the unit ball that act discontinuously and do not have fixed points. For such mappings, we have established…
We consider the Fokker-Planck equation on metric graphs. Vertex boundary conditions are imposed in the form of weight continuity and the probability current conservation. Exact solution of the is obtained for star, tree and loop graphs.…
We associate an integrable generalized complex structure to each 2-dimensional symplectic Monge-Amp\`ere equation of divergent type and, using the Gualtieri $\bar{\partial}$ operator, we characterize the conservation laws and the generating…
In the tropical limit of matrix KP-II solitons, their support at fixed time is a planar graph with "polarizations" attached to its linear parts. In this work we explore a subclass of soliton solutions whose tropical limit graph has the form…
In this paper, we extend the enumerative study of planar hypermaps with an alternating boundary introduced in an earlier work of Bouttier and the second author. In that article, an explicit rational parametrization was obtained for the…
We consider bivariate polynomials over the skew field of quaternions, where the indeterminates commute with all coefficients and with each other. We analyze existence of univariate factorizations, that is, factorizations with univariate…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
Multidimensional factorization method is formulated in arbitrary curvilinear coordinates. Particular cases of polar and spherical coordinates are considered and matrix potentials with separating variables are constructed. A new class of…
We develop a fast algorithm for computing the bound of an Ore polynomial over a skew field, under mild conditions. As an application, we state a criterion for deciding whether a bounded Ore polynomial is irreducible, and we discuss a…
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
A factorization formula for certain automorphisms of a Poisson algebra associated to a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing…
The investigation and classification of non-unique factorization phenomena have attracted some interest in recent literature. For finitely generated monoids, S.T. Chapman and P. Garcia-Sanchez, together with several co-authors, derived a…
We continue studying the problem of analytic approximation of matrix functions. We introduce the notion of a partial canonical factorization of a badly approximable matrix function $\Phi$ and the notion of a canonical factorization of a…
We examine factorisation in the connected prescription of Yang-Mills amplitudes. The multi-particle pole is interpreted as coming from representing delta functions as meromorphic functions. However, a naive evaluation does not give a…
We introduce the notion of semi-characteristic polynomial for a semi-linear map of a finite- dimensional vector space over a field of characteristic p. This polynomial has some properties in common with the classical characteristic…
This paper contributes to the solution of the Poincare problem, which is to bound the degree of a (generalized algebraic) leaf of a (singular algebraic) foliation of the complex projective plane. The first theorem gives a new sort of bound,…
Algebraic topology studies topological spaces with the help of tools from abstract algebra. The main focus of this paper is to show that many concepts from algebraic topology can be conveniently expressed in terms of (normal) factor graphs.…