in this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the fourier transform. as a consequence, we extend the fundamental theorems of abelian fourier transform to non-abelian case.

In this paper we study spaces in which each compact subset is a Gδ-set and compare them to H. W. Martin’s c-semi-stratifiable (CSS) spaces, i.e. spaces in which compact sets are Gδ-sets in a uniform way. We prove that a (countably) compact subset of a Hausdorff space X is metrizable and a Gδ-subset of X provided X has a δθ-base, or a point-countable, T1-point-separating open cover, or a quasi-G...

in this paper we formulate and prove some xed and common xed pointtheorems for self-mappings dened on complete lower transversal functionalprobabilistic spaces.

We show that any compact semi-algebraic subset of mixed action profiles on a fixed player set can be represented as the projection of the set of equilibria of a game in which additional binary players have been added. Even stronger, we show that any semi-algebraic continuous function, or even any semi-algebraic upper-semicontinuous correspondence with nonempty values, from a bounded semi-algebr...

In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is P-chaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itse...

Abstract It is proved that for an extremally disconnected S -paracompact- T 2 spaces the properties semi-Menger, Menger, strongly star star-Menger, almost star-Menger are equivalent. We show a weakly semi-continuous (strongly θ -semi-continuous) image of semi-Menger (almost semi-Menger) (semi-Menger), respectively. The characterizations and also provided.

In this paper, we concern with SLLN for sums of independent random upper-semicontinuous fuzzy sets. We first give a generalization of SLLN for sums of independent and level-wise identically distributed random fuzzy sets, and establish a SLLN for sums of random fuzzy sets which is independent and compactly uniformly integrable in the strong sense. As a result, a SLLN for sums of independent and ...

A set has local scaling if in a neighborhood of a point the structure of the set can be mapped onto a finer scale structure of the set. These scaling transformations are compact sets of locally affine contractions (that is, contractions with uniformly α-Hölder continuous derivatives). In this setting, without the open set condition or any other assumption on the spacing of these contractions, w...

We introduce semicontinuity concepts for functions f with values in the space C(Y ) of closed convex subsets of a finite dimensional normed vector space Y by appropriate notions of upper and lower limits. We characterize the upper semicontinuity of f : X → C(Y ) by the upper semicontinuity of the scalarizations σf( · )(y∗) : X → R by the support function. Furthermore, we compare our semicontinu...

In Machine Learning (ML) algorithms, one of the crucial issues is the representation of the data. As the data become heterogeneous and large-scale, single kernel methods become insufficient to classify nonlinear data. The finite combinations of kernels are limited up to a finite choice. In order to overcome this discrepancy, we propose a novel method of ”infinite” kernel combinations for learni...