For a given graph G, the Separator Problem asks whether a vertex or edge set of small cardinality (or weight) exists whose removal partitions G into two disjoint graphs of approximately equal sizes. Called the Vertex Separator Problem when the removed set is a vertex set, and the Edge Separator Problem when it is an edge set, both problems are NP-complete for general unweighted graphs [6]. Desp...

Example 1: The tree in Figure 1(a) has 26 vertices in which v1 is a centroid. The vertex v1 is a minimal 1/2-separator. As shown in (b), each branch contains no more than 13 vertices. But v1, or even the edge (v1, v2), is not a 1/3-separator because there exists a subtree whose number of vertices is nine, which is greater than 26/3. The path between v2 and v3 is a minimal 1/3-separator (Frame (...

A bilayered cellulose-based separator design is presented that can enhance the electrochemical performance of lithium-ion batteries (LIBs) via the inclusion of a porous redox-active layer. The proposed flexible redox-active separator consists of a mesoporous, insulating nanocellulose fiber layer that provides the necessary insulation between the electrodes and a porous, conductive, and redox-ac...

Four NP-hard optimization problems on graphs are studied: The vertex separator problem, the edge separator problem, the maximum clique problem, and the maximum independent set problem. We show that the vertex separator problem is equivalent to a continuous bilinear quadratic program. This continuous formulation is compared to known continuous quadratic programming formulations for the edge sepa...

The project of a new and more powerful in-flight fragment separator ACCULINNA2 at U-400M cyclotron in FLNR, JINR planned to build in addition to the existing separator ACCULINNA is presented. The new separator will provide high intensity RIBs in the lowest energy range (5÷50 MeV/nucleon) which is attainable for in-flight separators. The possibilities for the astrophysics studies at the proposed...

The potential of three types of separator materials found in conventional blood-collection tubes for interference in therapeutic drug measurements was assessed. None of the separators (based on acrylic, silicone, or polyester polymers) had any significant effect on the concentrations of seven drugs (theophylline, digoxin, phenytoin, phenobarbital, gentamicin, ethanol, and cyclosporine) in blood...

Given G = (V, E) an undirected graph and two speci ed nonadjacent nodes a and b of V , a cut separator is a subset F = δ(C) ⊆ E such that a, b ∈ V \C and a and b belong to di erent connected components of the graph induced by V \C. Given a nonnegative cost vector c ∈ R|E| + , the optimal cut separator problem is to nd a cut separator of minimum cost. This new problem is closely related to the v...

The performance of airlift bioreactors are closely related with their geometry, especially the gas-liquid separator design. In this study, the influence of the gas-liquid separator geometry on oxygen transfer and gas hold-up was evaluated in 10-L concentric-tube airlift bioreactor operating with distilled water and xanthan gum solution. The specific airflow rate (ɸAIR) exhibited the higher effe...

The separator is a critical, multi-functional component of a Li-ion cell that plays a key role in performance and safety during energy conversion and storage processes. Heat flow through the separator is important for minimizing cell temperature and avoiding thermal runaway. Despite the critical nature of thermal conduction through the separator, very little research has been reported on unders...

We provide a simple proof of the existence of a planar separator by showing that it is an easy consequence of the circle packing theorem. We also reprove other results on separators, including: (A) There is a simple cycle separator if the planar graph is triangulated. Furthermore, if each face has at most d edges on its boundary, then there is a cycle separator of size O ` ? dn ̆ . (B) For a set...