has density one in Z with respect to some sequence of intervals Ik = [ak, bk] with bk−ak → ∞. (This means that d{Ik}(S) = lim k→∞ |S∩Ik| bk−ak+1 = 1.) A vector f ∈ H is called weakly wandering if there is an infinite set S ⊆ Z such that for any n,m ∈ S, n 6= m, one has 〈Uf, Uf〉 = 0. The following theorem due to U. Krengel gives a characterization of weak mixing in terms of weakly wandering vect...

It is shown that the tensor product JH⊗̃ǫJH fails Pe lczńyski’s property (u). The proof uses a result of Kwapień and Pe lczńyski on the main triangle projection in matrix spaces. The Banach space JH constructed by Hagler [1] has a number of interesting properties. For instance, it is known that JH contains no isomorph of l, and has property (S): every normalized weakly null sequence has a subseq...

Let f n (; !) be a sequence of stochastic processes which converge weakly to a limit process f 0 (; !). We show under some assumptions the weak inclusion of the solution sets n (!) = f : f n (; !) = 0g in the limiting solution set 0 (!) = f : f 0 (; !) = 0g. If the limiting solutions are a.s. singletons, then weak convergence holds. Results of his type are called Z-theorems (Zero-theorems). Mor...

In the present study, commonly used weakly compressible lattice Boltzmann method and Guo incompressible lattice Boltzmann method have been used to simulate fluid flow in a stirred tank. For this purpose a 3D Parallel code has been developed in the framework of the lattice Boltzmann method. This program has been used for simulation of flow at different geometries such as 2D channel fluid flow an...

in the present paper‎, ‎we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function $phi$‎. ‎we also define the concept of weakly related mappings on an ordered space‎. ‎moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space‎.

The objective of the present paper is to study 4-dimensional weakly Ricci symmetric spacetimes $(WRS)_4$ with non-zero constant scalar. We prove that such a satisfying $F(R)$-gravity field equations represents perfect fluid vanishing vorticity. Some energy conditions are studied under current setting constrain functional form $F(R)$. examine couple popular toy models in $F(R)$-gravity, $F(R)=e^...

‎In this paper‎, ‎we propose an algorithm to obtain an approximation set of the (weakly) nondominated points of nonsmooth multiobjective optimization problems with equality and inequality constraints‎. ‎We use an extension of the Wolfe duality to construct the separating hyperplane in Benson's outer algorithm for multiobjective programming problems with subdifferentiable functions‎. ‎We also fo...