This defines an equivalence relation on M. The equivalence classes are called the orbits of D. Let S be an orbit of D. For each me S and each finite sequence £ = (X , . . . , X) of elements of D, let F^m denote the map {tu...,ta^Xll(XfjL---Xl{m)---)). It is clear that F^m is a C 00 mapping from an open subset U of R into M. Moreover the range of F^m is a subset of 5. We topologize S by the stro...

In 1965, Njastad [2] introduced the notion of α-sets in topological space. In 1983, Mashhour et al. [1] introduced, with the help of α-sets, a weak form of continuity which they termed as α-continuity. Noiri [3] introduced the same concept, but under the name strong semicontinuity. Noiri [4] defined with the aid of α-sets a new weakened form of continuous mapping called weakly α-continuous mapp...

OBJECTIVES The aim of this study is to assess the influence of the shape of the acoustic-to-electric mapping function on speech recognition in noise by cochlear implant listeners. DESIGN A new acoustic-to-electric mapping function is proposed for cochlear implant users in noisy environments. The proposed s-shaped mapping function was expansive for low input levels up to a knee point level and...

We establish continuity of the integral representation y(t) = x(t) + ∫ t 0 h(y(s)) ds, t ≥ 0, mapping a function x into a function y when the underlying function space D is endowed with the Skorohod M1 topology. We apply this integral representation with the continuous mapping theorem to establish heavy-traffic stochastic-process limits for many-server queueing models when the limit process has...

Dyadic interactions encapsulate rich emotional exchange between interlocutors suggesting a multimodal, cross-speaker and cross-dimensional continuous emotion dependency. This study explores the dynamic inter-attribute emotional dependency at the cross-subject level with implications to continuous emotion recognition based on speech and body motion cues. We propose a novel two-stage Gaussian Mix...

In the note we correct some errors that appeared in the article (Jiang and Li in Fixed Correction Upon critical examination of the main results and their proofs in [], we note some critical errors under the conditions of the main theorem and its proof in our article []. In this note, we would like to supplement some essential conditions, which will ensure that the mapping B is well defined, t...

In this section we want to understand what does the notation ∫ t 0 XsdWs mean. 1.1 Stochastic Process Xt Given a probability space {Ω,F,P} and time index set T , a stochastic process (Xs)s∈T is a measurable mapping from Ω×T to some space. In our most interested setting, the value space is R or Rd, while the time index set is T = [0,∞) with Borel σ-algebra. Another common option for T is the int...

According to mathematical properties of continuous function, the universal approximation properties of fuzzy mapping in only one interval are analyzed, and some related theorems are proposed and proved. Then, the sufficient conditions of the general T-S fuzzy systems with universal approximation are derived from these theorems, which helps establish the new relationship between approximation er...