and Applied Analysis 3 Definition 1.4 see 18, 20–23 . 1 The intersection of all fuzzy α-closed resp., semiclosed, preclosed, γ-closed, semi-preclosed, β-closed sets containing a fuzzy set A is called a fuzzy α-closure resp., semiclosure, preclosure, γ-closure, semi-preclosure, β-closure of A. 2 The union of all fuzzy α-open resp., semiopen, preopen, γ-open, semi-preopen, β-open sets contained i...

In this communication, Moore's result for the normalization constant of a closed queuing network of exponential servers is extended to the case of nondistinct traffic intensities. We then show that this result can be applied to various more general closed and semiclosed queuing networks with a product-form solution. Introduction Substantial progress has been made recently in extending the scope...

Abstract Verification has emerged as a means to provide formal guarantees on learning-based systems incorporating neural network before using them in safety-critical applications. This paper proposes new verification approach for deep networks (DNNs) with piecewise linear activation functions reachability analysis. The core of our is collection algorithms star sets (or shortly, stars), an effec...

The current study, setting a two-fold goal, attempted to see whether the preemptive focus on form (FonF) under either planned or unplanned conditions could contribute to increasing lexical diversity in written narratives and, second, to find whether there was a trade-off between the lexical diversity and accuracy. To this end, 32 beginner learners were selected following a Quick Oxford Placemen...