In one of the most important methods in Density Functional Theory – the FullPotential Linearized Augmented Plane Wave (FLAPW) method – dense generalized eigenproblems are organized in long sequences. Moreover each eigenproblem is strongly correlated to the next one in the sequence. We propose a novel approach which exploits such correlation through the use of an eigensolver based on subspace it...

We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The trees, which generate complete ultrametrics, totally bounded discrete ones, are characterized up to isomorphism. As corollary, we obtain a characterization of generating compact ultrametrics ultrametrics. It is also shown that every space tree contains dense subspace.

in this article‎, ‎we have characterized ideals in $c(x)$ in which‎ ‎every ideal is also an ideal (a $z$-ideal) of $c(x)$‎. ‎motivated by‎ ‎this characterization‎, ‎we observe that $c_infty(x)$ is a regular‎ ‎ring if and only if every open locally compact $sigma$-compact‎ ‎subset of $x$ is finite‎. ‎concerning prime ideals‎, ‎it is shown that‎ ‎the sum of every two prime (semiprime) ideals of e...

Let X be a non-locally convex F-space (complete metric linear space) whose dual X' separates the points of X. Then it is known that X possesses a closed subspace N which fails to be weakly closed (see [3]), or, equivalently, such that the quotient space XIN does not have a point separating dual. However the question has also been raised by Duren, Romberg and Shields [2] of whether X possesses a...

This note is devoted to the answers to the following questions asked by V. I. Bogachev, B. Kirchheim and W. Schachermayer: 1. Let T : l1 → X be a linear map into the infinite dimensional Banach spaceX. Can one find a closed infinite dimensional subspace Z ⊂ l1 such that T ∣∣ Z is continuous? 2. Let X = c0 or X = lp (1 < p <∞) and let T : X → X be a linear map. Can one find a dense subspace Z of...

Instead of finding clusters in full data space, subspace clustering has been an emergent task which aims at discovering clusters embedded in subspaces. Most of the previous works in the literature are grid and density based approaches, where the performance of clustering algorithms heavily depends on the partition of grids which may incur the serious loss of the real data distribution. In order...

In this paper , the completion of t^ω-approach spaces, isometric in space and equivalent sequences are defined. Every normed can be embedded Banach is proved, χ ̃ an isometry ψ from onto subspace F which dense introduced, as well as, shown uniquely up to isometry. addition, what mentioned above, some essential definitions, examples, important theorems included illustrate our work.