We propose a class of graphs that would occur naturally in finite-element and finitedifference problems and we prove a bound on separators for this class of graphs. Graphs in this class are embedded in d-dimensional space in a certain manner. For d-dimensional graphs our separator bound is O(n(d−1)/d), which is the best possible bound. We also propose a simple randomized algorithm to find this ...

We introduce the notion of the width bounded geometric separator and develop the techniques for the existence of the width bounded separator in any d-dimensional Euclidean space. The separator is applied in obtaining 2 √ n) time exact algorithms for a class of NPcomplete geometric problems, whose previous algorithms take n √ n) time [2,5,1]. One of those problems is the well known disk covering...

BACKGROUND Polypropylene mesh used as a mid-urethral sling is associated with severe clinical complications in a significant minority of patients. Current in vitro mechanical testing shows that polypropylene responds inadequately to mechanical distension and is also poor at supporting cell proliferation. AIMS AND OBJECTIVES Our objective therefore is to produce materials with more appropriate...

Yannakakis’ Clique versus Independent Set problem (CL− IS) in communication complexity asks for the minimum number of cuts separating cliques from stable sets in a graph, called CS-separator. Yannakakis provides a quasi-polynomial CS-separator, i.e. of size O(n), and addresses the problem of finding a polynomial CS-separator. This question is still open even for perfect graphs. We show that a p...

A superfine Li0.33La0.557TiO₃ (LLTO, 69.4 nm) was successfully synthesized by a facile solvent-thermal method to enhance the electrochemical properties of the lithium-ion battery separator. Co-axial nanofiber of cellulose and Poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP) was prepared by a co-axial electrospinning technique, in which the shell material was PVDF-HFP and the core was...