Partitioning a graph using graph separators, and particularly clique separators, are well-known techniques to decompose a graph into smaller units which can be treated independently. It was previously known that the treewidth was bounded above by the sum of the size of the separator plus the treewidth of disjoint components, and this was obtained by the heuristic of filling in all edges of the ...

A novel membrane based on silicon dioxide (SiO₂) and hydroxypropyl guar gum (HPG) as binder is presented and tested as a separator for lithium-ion batteries. The separator is made with renewable and low cost materials and an environmentally friendly manufacturing processing using only water as solvent. The separator offers superior wettability and high electrolyte uptake due to the optimized po...

The performance of the electric submersible pump (ESP) significantly affected by Gas Void Fraction (GVF). Thus, using of a Rotary Gas Separator (RGS) is a suitable solution for this issue. The performance of the RGS is function of different parameters such as geometry of impeller, rotating speed, boundary conditions, media viscosity and GVF. In this study, the influences of GVF, viscosity, ...

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...