‎Let $G$ be a locally compact abelian group‎. ‎The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$‎. ‎Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level‎. ‎Also‎, ‎the construction of affine frames for $L^2(G)$ bas...

‎let $g$ be a locally compact abelian group‎. ‎the concept of a generalized multiresolution structure (gms) in $l^2(g)$ is discussed which is a generalization of gms in $l^2(mathbb{r})$‎. ‎basically a gms in $l^2(g)$ consists of an increasing sequence of closed subspaces of $l^2(g)$ and a pseudoframe of translation type at each level‎. ‎also‎, ‎the construction of affine frames for $l^2(g)$ bas...

‎A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert...

New realizations of Chua L-C and L-R mutators using current conveyors (CCII) and inverting current conveyors (CCII) are introduced. Two realizations are available in the literature using CCII for each of the types of L-C and L-R mutators. For the type 1a L-R mutator three new realizations using CCII and ICCII are introduced to complete a family of four realizations. For the type 1b L-R mutator ...

Abstract. In this paper, from a John-Nirenberg (JN) type inequality in BMO(R), we prove Gagliardo-Nirenberg (GN) type inequalities in Qα(R ) which mean the continuous embeddings L(R)∩Qα(R ) ⊆ L(R) for −∞ < α < β, 1/2 < β ≤ 1 and 2 ≤ r ≤ p < ∞. This result generalizes some known embeddings and implies the bilinear estimates in BMO(R) which are useful for studying Navier-Stokes equations. Meanwhi...

Let L = −∆+ V be a Schrödinger operator on R, d ≥ 3, where V is a nonnegative function, V 6= 0, and belongs to the reverse Hölder class RHd/2. The purpose of this paper is three-fold. First, we prove a version of the classical theorem of Jones and Journé on weak∗-convergence in H L(R ). Secondly, we give a bilinear decomposition for the product space H L(R )×BMOL(R). Finally, we study the commu...