Consider the Cauchy principal value integral I(kf;X)=i k{x)F^Ldx, -1<A<1. 7-1 x — A If we approximate f(x) by Yli=oajP¡(x'i w) where {p } is a sequence of orthonormal polynomials with respect to an admissible weight function w and û, = (/. P.), then an approximation to I(kf; X) is given by X!/=o ajl(kp¡ ; ^)If, in turn, we approximate a¡ by ajm = £TM , wimf(x¡m)Pj(xim), then we get a double seq...

Let X be a Banach space and (fn)n be a bounded sequence in L (X). We prove a complemented version of the celebrated Talagrand’s dichotomy i.e we show that if (en)n denotes the unit vector basis of c0, there exists a sequence gn ∈ conv(fn, fn+1, . . . ) such that for almost every ω, either the sequence (gn(ω)⊗en) is weakly Cauchy in X⊗̂πc0 or it is equivalent to the unit vector basis of l. We the...

Introduction/purpose: This paper considers, generalizes and improves recent results on fixed points in rectangular metric spaces. The aim of this is to provide much simpler shorter proofs some new Methods: Some standard methods from the point theory generalized spaces are used. Results: obtained improve well-known literature. approach has proved that Picard sequence Cauchy used prove existence ...

Noise can help signal detection at the nano–level. Experiments on a single–walled carbon nanotube transistor confirm that a threshold exhibits stochastic resonance: a judicious amount of noise can help a threshold–like nanotube transistor detect subthreshold signals while large amounts of noise overwhelm the signals. The nanotube produced this stochastic–resonance effect using three types of sy...

The computability of reals was introduced by Alan Turing [20] by means of decimal representations. But the equivalent notion can also be introduced accordingly if the binary expansion, Dedekind cut or Cauchy sequence representations are considered instead. In other words, the computability of reals is independent of their representations. However, as it is shown by Specker [19] and Ko [9], the ...

In this paper we present two different results in the theory of Cauchy-Stieltjes Kernel (CSK) families. We firstly provide construction free Sheffer systems with CSK associate a additive convolution semigroup probability measures to any and prove that is only one leads an orthogonal systems. also show orthogonality occurs if associated generates families quadratic variance function. Secondly, a...

The range process Rn of a random walk is the collection sites visited by up to time n. In this paper we deal with question whether or cocycle over an ergodic transformation almost surely Følner sequence and show following results: (a) size inner boundary |∂Rn| recurrent aperiodic walks on Z2 finite variance in Z standard domain attraction Cauchy distribution, divided n∕log2(n), converges consta...

A difficult step in the derivation of the strong forms of the Cauchy theorem, Green's lemma, and related theorems from the corresponding weak forms is the construction, for a given rectifiable Jordan curve J, of a sequence of Jordan polygons lying interior to / , converging to J", and having uniformly bounded lengths. This note presents what the author believes to be a simpler elementary constr...

The notion of lacunary ideal convergence in intuitionistic fuzzy normed linear space (IFNLS) was introduced by the present corresponding author [P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl., 63 (2012), 708-715] and an open problem in that paper was whether every lacunary I-convergent sequence is lacunary I-Cauchy. Further, a new concep...