We perform compressive tests of polypropylene battery separator in

This thesis deals with the multi-terminal vertex separator problem. Given a graph G = (V ∪T,E) with V ∪T the set of vertices, where T is a set of terminals, and a weight function w : V → Z, associated with nonterminal nodes, the multi-terminal vertex separator problem consists in partitioning V ∪T into k+1 subsets {S, V1, . . . , Vk} such that there is no edge between two different subsets Vi a...

We develop a new method for deriving a geometric separator for a set of grid points. Our separator has a linear structure, which can effectively partition a grid graph. For example, we prove that for a grid graph G with a set of n points P in a two-dimensional grid, there is a separator with at most 1.129 √ n points in P that partitions G into two disconnected grid graphs each with at most 2n 3...

The occurrences of huge reserves of garnet deposits have been reported from different parts of Iran specially those of Kohe-E-Gabri area which is very high grade in nature. These deposits can not be directly used as abrasives, filter aid and many others because of some impurities present. To know the mineralogical composition, the type of garnet, the shape of the particles, the chemical charact...

G. A. Dirac characterized chordal graphs as those in which minimal vertex separators always induce complete subgraphs. I generalize a traditional (2-)vertex separator to a k-vertex separator — meaning a set S of vertices whose removal puts k independent vertices into k separate components. Generalizing Dirac’s theorem, the {P5, 2P3}-free chordal graphs are the graphs in which minimal k-separato...

For undirected graphs G (V, E) and G0 (V0 , E0), say that G is a region intersection graph over G0 if there is a family of connected subsets {Ru ⊆ V0 : u ∈ V} of G0 such that {u , v} ∈ E ⇐⇒ Ru ∩ Rv , ∅. We show if G0 excludes the complete graph Kh as a minor for some h > 1, then every region intersection graph G over G0 with m edges has a balanced separator with at most ch √ m nodes, where ch i...

The characteristics of fluid flow and phase separation in an oil-water separator were numerically analysed as part of the work presented herein. Simulations were performed for different velocities and droplet diameters, and the way this parameters can influence the separator geometry was studied. The simulations were carried out using the software package Fluent 6.2, which is designed for numer...

statement of the problem in order to replace lost tooth of patients, we use dental implants which are common. therefore, accurate measuring of bone height and width before placing implants is necessary. the aim of this study is evaluating the accuracy of linear and spiral tomography in careful determination of implant site sizes in comparison with gold standard (cbct). material and methods this...

A permutation σ ∈ Sn is a k-separator if all of its patterns of length k are distinct. Let F (k) denote the maximal length of a k-separator. Hegarty (2013) showed that k + ⌊√ 2k − 1 ⌋ − 1 6 F (k) 6 k + ⌊√ 2k − 3 ⌋ , and conjectured that F (k) = k + ⌊√ 2k − 1 ⌋ − 1. This paper will strengthen the upper bound to prove the conjecture for all sufficiently large k (in particular, for all k > 320801).

Separators in graphs are instrumental in the design of algorithms, having proven to be the key technical tool in approximation algorithms for many optimization problems. In the geometric setting, this naturally translates into the study of separators in the intersection graphs of geometric objects. Recently a number of new separator theorems have been proven for the case of geometric objects in...