We develop a randomized approximation algorithm for the size of set union problem |A1∪A2∪...∪Am|, which is given list sets A1,...,Am with approximate mi Ai mi∈((1−βL)|Ai|, (1+βR)|Ai|), and biased random generators probability Prob(x=RandomElement(Ai))∈[1−αL|Ai|,1+αR|Ai|] each input element x∈Ai, where i=1,2,...,m αL,αR,βL,βR∈(0,1). The ratio |A1∪A2∪...∪Am| in range [(1−ϵ)(1−αL)(1−βL),(1+ϵ)(1+αR...

in this paper, using the best proximity theorems for an extensionof brosowski's theorem. we obtain other results on farthest points. finally, wede ne the concept of e- farthest points. we shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (x; ||.||). if z in w is a e-farthest point from an x in x, then z is also a-best ...

In this paper we get some results and applications for duals and approximate duals of g-frames in Hilbert spaces. In particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of Hilbert spaces. We also obtain some results for perturbations of approximate duals.

Larynx cancer patients receive radiotherapy as a non-invasive alternative to surgery and cure rates are high. Inevitably this impacts vocal fold functional-ity. Hence, voice recovery as a prerequisite for resuming normal life is of special interest. Voicing recovery following radiotherapy is studied in this paper. Complexity analysis, using approximate entropy to concisely quantify the collecti...

We use entropy to extend the rough set based notion of a reduct. We show that the order based genetic algorithms, applied to the search of classical decision reducts, can be used in exactly the same way in case of extracting optimal approximate entropy reducts from data.

In this paper we consider several new versions of approximate string matching with gaps. The main characteristic of these new versions is the existence of gaps in the matching of a given pattern in a text. Algorithms are sketched for each version and their time and space complexity is stated. The specific versions of approximate string matching have various applications in computerized music an...

The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta. First, approximate best point proximity points on fuzzy normed linear spaces are defined and four general lemmas are given regarding approximate fixed point and approximate best proximity pair of cyclic maps on fuzzy normed spaces. U...