Related papers: Local $t$-dimension
In this article, we study an analogue of $tt$-reducibility for points in computable metric spaces. We characterize the notion of the metric $tt$-degree in the context of first-level Borel isomorphism. Then, we study this concept from the…
This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments of recent experiments and observations of…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
We introduce the notion of negative topological dimension and the notion of weight for the asymptotic topological dimension. Quantizing of spaces of negative dimension is applied to linguistic statistics.
A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…
This paper proposes a novel localized Fourier extension method for approximating non-periodic functions via domain segmentation. By partitioning the computational domain into subregions with uniform discretization scales, the method…
In this paper a novel numerical approximation of parametric eigenvalue problems is presented. We motivate our study with the analysis of a POD reduced order model for a simple one dimensional example. In particular, we introduce a new…
This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent's series of complex functions in complex fractal…
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 derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius $R$ and taking the limit as $R \to \infty$. These relations take the form of mass…
The Pareto dominance relation of a preference profile is (the asymmetric part of) a partial order. For any integer n, the problem of the existence of an n-agent preference profile that generates the given Pareto dominance relation is to…
In previous work the authors introduced a notion of generic states and obtained criteria for local equivalence of them. Here they introduce the concept of CHG states maintaining the criteria of local equivalence. This fact allows the…
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…
The main new notions are the notions of tangent-like spaces and local monoids. The main result is the pasage from a local monoid to its tangent-like space which is a local Leibniz algebra.
We have observed a common problem of solving for the marginal covariance of parameters introduced in new observations. This problem arises in several situations, including augmenting parameters to a Kalman filter, and computing weight for…
We construct projections from the space of differential k-forms which belong to L2 and whose exterior derivative also belongs to L2, to finite dimensional subspaces of piecewise polynomial differential forms defined on a simplicial mesh.…
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
This expository note explores Laplacian eigenfunction localization for compact domains. We work in the context of a particular numerically determined, localized, low frequency eigenfunction.
A new proposal for a Lorentz-invariant spontaneous localization theory is presented. It is based on the choice of a suitable set of macroscopic quantities to be stochastically induced to have definite values. Such macroscopic quantities…