This paper studies the use of a generalized hierarchical basis transformation at each level of a multilevel block factorization. The factorization may be used as a preconditioner to the conjugate gradient method, or the structure it sets up may be used to define a multigrid method. The basis transformation is performed with an averaged piecewise constant interpolant and is applicable to unstruc...

In this paper, a new network structure called generalized Hierarchical Completely-Connected networks (HCCs) is proposed, and its properties and features are evaluated. Simple routing strategies for HCCs are also developed for shortest-paths routing algorithms. A set of HCCs constructed by the proposed method includes some conventional hierarchical networks, then it is called generalized one. Th...

In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...

We prove that the dimension of bivariate tensor–product spline spaces of bi– degree (d, d) with maximum order of smoothness on a multi–cell domain (more precisely, on a set of cells from a tensor–product grid) is equal to the number of tensor–product B–spline basis functions, defined by only single knots in both directions, acting on the considered domain. A certain reasonable assumption on the...

‎Recently‎, ‎a new distribution‎, ‎named as extended generalized exponential distribution‎, ‎has been introduced by Kundu and Gupta (2011). ‎In this paper‎, ‎we consider the extended generalized exponential distribution with known shape parameters α and β. ‎At first‎, ‎the exact expressions for marginal and product moments of o...

Let G be a finite group acting on the finite set X such that the corresponding (complex) permutation representation is multiplicity free. There is a natural rank and order preserving action of the wreath product G ∼ Sn on the generalized Boolean algebra BX(n). We explicitly block diagonalize the commutant of this action.

In this paper, we introduce the concept of family of local atoms in a 2-inner product space and then this concept is generalized to an atomic system. Besides, a characterization of an atomic system lead to obtain a new frame. Actually this frame is a generalization of previous works.

In this paper, by using the generalized Hadamard product and the orthogonal decomposition of projection matrix, we propose a new general approach to construct mixed-level orthogonal arrays. As an application of the method, some new mixed-level orthogonal array’s of run sizes 36 and 72 are constructed. c © 2001 Elsevier Science B.V. All rights reserved.

This paper elaborates on the coordination and management of evolving software product-lines, where development teams work around a shared and reusable domain infrastructure. The trend away from monolithic applications and towards component-based, product-line architectures has enabled the development of complex software to be undertaken by autonomous and often, geographically separated teams. T...

In this paper, we introduce a new product operation of association schemes in order to generalize the notion of semidirect products and wreath product. We then show that our construction covers some association schemes which are neither wreath products nor semidirect products of two given association schemes.