In this paper, we define a new and broad family of vector-valued random fields called tempered operator fractional operator-stable (TRF, for short). TRF is typically non-Gaussian generalizes stable stochastic processes. comprises moving average harmonizable-type subclasses that are constructed by tempering (matrix-) homogeneous, matrix-valued kernels in time- Fourier-domain integrals with respe...

This paper presents a method of constructing the switching function using edge-valued decision diagrams. The proposed method is as following. The edge-valued decision diagram is a new data structure type of decision diagram which is recently used in constructing the digital logic systems based on the graph theory. Next, we apply edge-valued decision diagram to function minimization of digital l...

We build a theoretical framework that enables to extend the concept of transitive closure to the class of complete crisp relations, the class of reciprocal 3-valued relations and the class of reciprocal [0, 1]valued relations. We present algorithms to compute the transitive closure of reciprocal [0, 1]-valued relations, where the type of transitivity is either weak stochastic transitivity or st...

We present a method for the efficient approximation of integrals with highly oscillatory vector-valued kernels, such as integrals involving Airy functions or Bessel functions. We construct a vector-valued version of the asymptotic expansion, which allows us to determine the asymptotic order of a Levin-type method. Levin-type methods are constructed using collocation, and choosing a basis based ...

We prove that an n-valued function that is lower semi-continuous is also upper semi-continuous and therefore continuous, that is, an n-valued map. Several conditions are shown to be equivalent to continuity for n-valued functions, in particular the continuity of a corresponding singlevalued function to a configuration space. Consequently, splitting is related to braid groups to prove a Splittin...

Let (Ω,F , {Ft}, P ) be a complete probability space with filtration {Ft}, (X ,H, μ) an abstract Wiener space of M-type 2, and {Bt : t ≥ 0} an X -valued Brownian motion such that the distribution of the random function t−1/2Bt : Ω → X is μ for any t > 0. We consider the strong solutions to a set-valued stochastic differential equation with a set-valued drift and a single valued diffusion driven...

Abstract The author discusses necessary and sufficient conditions of the complete convergence for sums of B-valued independent but not necessarily identically distributed r.v.′s in Banach space of type p, and obtain characterization of Banach space of type p in terms of the complete convergence. A series of classical results on iid real valued r.v.′s are extended. As application author gives th...

Using the existence of solutions for equilibrium equations with a Neumann type boundary condition as developed by Shi and Liao (J. Inequal. Appl. 2015:363, 2015), we obtain the Riesz integral representation for continuous linear maps associated with additive set-valued maps with values in the set of all closed bounded convex non-empty subsets of any Banach space, which are generalizations of in...

We introduce Vivid, a domain-independent framework for heterogeneous natural deduction that combines diagrammatic and sentential reasoning. The framework is presented in the form of a family of denotational proof languages (DPLs). Diagrams are represented as possibly partial descriptions of finite system states. This allows us to deal with incomplete information, which we formalize by admitting...