Let {Xnk: k,n 1,2 be an array of row-wise independent random elements in a separable Banach space. Let {ank: k,n 1,2 be an array of Voo voo R+ real numbers such that /-k=l lank -< 1 and Ln=l exp(-a/A < for each c e where n V 2 Voo An kk=l ank. The complete convergence of l’k=l ank Xnk is obtained under varying moment and distribution conditions on the random elements. In particular, laws of lar...

Absrrucr: Applying Gauss-Seidel approach to the improvements of two simultaneous methods for finding polynomial zeros, presented in [9], two iterative methods with faster convergence are obtained. The lower bounds of the R-order of convergence for the accelerated methods are given. The improved methods and their accelerated modifications arc discussed in view of the convergence order and the nu...

Let KMM 󸀠󸀠(R) be the generalized tempered distributions of eeMMMMMM-growth with restricted order rr r N0, where the function MM(MM) grows faster than any linear functions as |MM| x x. We show the convergence of multiresolution expansions ofKMM(R) in the test function spaceKMM(R) ofKMM(R). In addition, we show that the kernel of an integral operatorKK K KMM(R) x KMM(R) provides approximation ord...

New fractional r -order seminorms, TGV r , r ∈ R , r ≥ 1 , are proposed in the one-dimensional (1D) setting, as a generalization of the integer order TGV k seminorms, k ∈ N . The fractional r -order TGV r -seminorms are shown to be intermediate between the integer order TGV k -seminorms. A bilevel training scheme is proposed, where under a box constraint a simultaneous optimization with respect...

in this study, we modify an iterative non-optimal without memory method, in such a way that is becomes optimal. therefore, we obtain convergence order eight with the some functional evaluations. to justify our proposed method, some numerical examples are given.

This defines an operator MK̄ , which we will call a Minkowski operator. Denote by A(C) the Frechet space of entire functions in n variables with the usual topology of the uniform convergence on compact sets in C, and C(R) the Frechet space of r times differentiable functions on R with the topology of the uniform convergence on compact sets in R of all partial derivatives up to the order r (1 ≤ r...

Abstract. Table of contents : §1. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1. §2. Conjugation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. §3. Reflection mapping R′ h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...