A classical method for partition generating function is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results partitions n n </mm...

Abstract Recently, several approaches for multiscale simulations problems with high contrast and no scale separation are introduced. Among them is nonlocal multicontinua (NLMC) method, which introduces multiple macroscopic variables in each computational grid. These explore the entire coarse block resolution one can obtain optimal convergence results independent of scales. However, these not am...

We characterize those classes C of separable Banach spaces admitting a separable universal space Y (that is, a space Y containing, up to isomorphism, all members of C) which is not universal for all separable Banach spaces. The characterization is a byproduct of the fact, proved in the paper, that the class NU of non-universal separable Banach spaces is strongly bounded. This settles in the aff...

The 2-D discrete wavelet transform (DWT) can be found in the heart of many image-processing algorithms. Until recently, several studies have compared the performance of such transform on various shared-memory parallel architectures, especially on graphics processing units (GPUs). All these studies, however, considered only separable calculation schemes. We show that corresponding separable part...

‎We prove that a remainder $Y$ of a non-locally compact‎ ‎rectifiable space $X$ is locally a $p$-space if and only if‎ ‎either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact‎, ‎which improves two results by Arhangel'skii‎. ‎We also show that if a non-locally compact‎ ‎rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal‎, ‎then...

We investigate the computational complexity of some basic problems regarding non-unique probe selection using separable matrices. In particular, we prove that the Minimal d̄-Separable Matrix problem is DP -complete, and the d̄-Separable Submatrix with Reserved Rows problem, which is a generalization of the decision version of the Minimum d̄-Separable Submatrix problem, is Σ2 -complete.

in this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the hypercyclicity criterion. we characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional banach space .

A simple computational procedure has been developed by using Monte Carlo for allocating redundancy among subsystems so as to achieve maximum reliability of a complex systems subjected to multiple constraints which may be linear, non linear separable or non separable. Two examples of linear, non linear separable and non separable constraints with having twenty problems are solved.