Related papers: Partial Differential Chow Forms and a Type of Part…
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…
An equivariant characteristic quasi-polynomial is a quasi-polynomial in $q$ consisting of the permutation character on the mod $q$ complement of the corresponding Coxeter arrangement. This concept is a refinement of the conventional…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
We determine the second fundamental form of a variation of Hodge Structure of a smooth projective hypersurface using the classical identification of the Hodge structure and the action of the infinitesimal variation of Hodge structure with…
Given a smooth variety $X$ with an action of a finite group $G$, and a semiorthogonal decomposition of the derived category, $\mathcal{D}([X/G])$, of $G$-equivariant coherent sheaves on $X$ into subcategories equivalent to derived…
We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it…
In this paper, we analyze multi-dimensional Besicovitch almost periodic type functions. We clarify the main structural properties for the introduced classes of Besicovitch almost periodic type functions, explore the notion of…
We present a class of toric varieties $V$ which, over any algebraically closed field of characteristic zero, are defined by codim $V$+1 binomial equations.
The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the…
In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the…
Some connections between classical and nonclassical symmetries of a partial differential equation (PDE) are given in terms of determining equations of the two symmetries. These connections provide additional information for determining…
We consider Calabi-Yau $n$-folds $X$ arising from certain hyperplane arrangements. Using Fu-Vial's theory of distinguished cycles for varieties with motive of abelian type, we show that the subring of the Chow ring of $X$ generated by…
This paper is concerned with a class of partial differential equations, which are the linear combinations, with constant coefficients, of the classical flows of the KdV hierarchy. A boundary value problem with inhomogeneous boundary…
We first introduce the notion of Hamiltonian structure for a partial difference equation. Then we construct some infinite quivers, and realize the discrete KdV equation, the Hirota-Miwa equation and its various reductions as the mutation…
We know that semi-regular sub-varieties satisfy the variational Hodge conjecture i.e., given a family of smooth projective varieties $\pi:\mathcal{X} \to B$, a special fiber $\mathcal{X}_o$ and a semi-regular subvariety $Z \subset…
This article contains a new discussion for the generalized fractional Cauchy-type problem involving Hilfer-Katugampola-type fractional derivative. We study an existence and continuation of its solution. Firstly, we establish a new theorems…
We introduce three kinds of invariants of a virtual knot called the first, second, and third intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. The calculations of…
This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…
Mixed-dimensional partial differential equations arise in several physical applications, wherein parts of the domain have extreme aspect ratios. In this case, it is often appealing to model these features as lower-dimensional manifolds…
We propose a weak form of domination, called partially dominated splitting and the main result is that there is a partially dominated splitting over a nonsingular compact invariant set for a flow if, and only if, the associated linear…