We give a counterexample to a conjecture of S.E. Morris by showing that there is a compact plane set X such that R(X) has no non-zero, bounded point derivations but such that R(X) is not weakly amenable. We also give an example of a separable uniform algebra A such that every maximal ideal of A has a bounded approximate identity but such that A is not weakly amenable.

We construct an Identity-Based Key Encapsulation Mechanism (IBKEM) in a generic “leveled” multilinear map setting and prove its security under multilinear decisional Diffie-Hellmanin assumption in the selective-ID model. Then, we make our IB-KEM translated to the GGH framework, which defined an “approximate” version of a multilinear group family from ideal lattices, and modify our proof of secu...

If a function f is of bounded variation on TN (N ≥ 1) and {φn} is a positive approximate identity, we prove that the area of the graph of f ∗φn converges from below to the relaxed area of the graph of f . Moreover we give asymptotic estimates for the area of the graph of the square partial sums of multiple Fourier series of functions with suitable discontinuities.

In a recent paper, S.-E. Takahasi defined the notion of a BSE Banach module over a commutative Banach algebra A with bounded approximate identity. We show that the multiplier space &f(X) of X can be represented as a space of sections in a bundle of Banach spaces, and we use bundle techniques to obtain shorter proofs of various of Takahasi’s results on P-algebra modules and to answer several que...

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...