Related papers: Local $t$-dimension
We compute support of formal cohomology modules in a serial of non-trivial cases. Applications are given. For example, we compute injective dimension of certain local cohomology modules in terms of dimension of their's support.
The dimension of a partially-ordered set (poset), introduced by Dushnik and Miller (1941), has been studied extensively in the literature. Recently, Ueckerdt (2016) proposed a variation called local dimension which makes use of partial…
Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationship between these two concepts. In this article we will…
We consider a relation between local and global characteristics of a differential algebraic variety. We prove that dimension of tangent space for every regular point of an irreducible differential algebraic variety coincides with dimension…
In this paper, we give some properties and remarks of the new fractional Sobolev spaces with variable exponents. We also study the eigenvalue problem involving the new fractional $p(\cdot)$-Laplacian.
Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…
In this article, we present a new characterization of the completeness of a partial metric space--which we call \textit{orbital characterization}-- using fixed point results.
We investigate a quasisymmetrically invariant counterpart of the topological Hausdorff dimension of a metric space. This invariant, called the topological conformal dimension, gives a lower bound on the topological Hausdorff dimension of…
In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new…
We propose an order parameter for the one dimensional Mott-Hubbard transition and provide numerical evidence and general theoretical arguments for the correctness of our proposal. In addition, we discuss some of the implications of this…
Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.
We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these…
In this paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact (or monotonically countably metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps.…
The purpose of this article is to review the developments related to the notion of local fractional derivative introduced in 1996. We consider its definition, properties, implications and possible applications. This involves the local…
In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…
This article develops a periodic version of a time varying parameter fractional process in the stationary region. It is a partial extension of Hosking (1981)'s article which dealt with the case where the coefficients are invariant in time.…
We introduce several new constructions of finite posets with the number of linear extensions given by generalized continued fractions. We apply our results to the problem of the minimum number of elements needed for a poset with a given…
We study some new invariant measures arising from local inverse iterates. Examples are also given.
This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.
The local a priori estimate for the finite element approximation is essential for underlying the local and parallel technique. It is well known that the constant coefficients in the inequality is independent of the mesh size. But it is not…