We give O( √ logn)-approximation algorithms for the Min UnCut, Min 2CNF Deletion, Directed Balanced Separator, and Directed Sparsest Cut problems. The previously best known algorithms give anO(logn)-approximation for Min UnCut [9], Directed Balanced Separator [17], Directed Sparsest Cut [17], and an O(logn log logn)approximation for Min 2CNF Deletion [14]. We also show that the integrality gap ...

The control of particle size distribution of fabricated alumina nanoparticles from general alumina that has a large geometric standard deviation (GSD) is studied. A thermophoretic separator was used to control the GSD of the fabricated alumina nanoparticles. Unevaporated particles and primary particles were separated to yield a small GSD for fabricated alumina nanoparticles. The fabricated alum...

In this paper we study the ring of graph invariants, focusing mainly on the invariants of simple graphs. We show that all other invariants, such as sorted eigenvalues, degree sequences and canonical permutations, belong to this ring. In fact, every graph invariant is a linear combination of the basic graph invariants which we study in this paper. To prove that two graphs are isomorphic, a numbe...

A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable (resp. a locally threshold testable) separator. In both cases, we design a decision procedure based on the occurrence of special patterns in automata accepting...

This document is meant to outline the steps that are necessary to produce a rare-ion beam using a projectile fragment separator with the specific example of the NSCL-A1900. Planning for other uses of a separator generally will require some additional interaction with NSCL personnel and are not described here. The procedure we describe represents important planning that does not require a physic...

Lithium-sulfur batteries are one of the most promising next-generation batteries due to their high theoretical specific capacity, but are impeded by the low utilization of insulating sulfur, unstable morphology of the lithium metal anode, and transport of soluble polysulfides. Here, by coating a layer of nano titanium dioxide and carbon black onto a commercial polypropylene separator, we demons...

A new approach is described for the combination of electron ionization and LC–MS based on sample ionization as vibrationally cold molecules in a supersonic molecular beam (Cold EI). Cold EI of sample compounds in liquid solutions (methanol, acetonitrile, water, etc.) is achieved through spray formation, followed by soft thermal vaporization of the sample particles prior to their supersonic expa...

This article presents the boundary conditions for the problem of turbulent supersonic gas flow in a plane channel with a perpendicular injection jets. The non-reflection boundary conditions for direct modeling of compressible viscous gases are studied. A formulation using the NSCBC (NavierStocks characteristic boundary conditions) through boundaries is derived for the subsonic inflow and subson...

The Kronecker product of two connected graphs G1,G2, denoted by G1 × G2, is the graph with vertex set V (G1 ×G2) = V (G1)×V (G2) and edge set E(G1 ×G2) = {(u1, v1)(u2, v2) : u1u2 ∈ E(G1), v1v2 ∈ E(G2)}. The kth power Gk of G is the graph with vertex set V (G) such that two distinct vertices are adjacent in Gk if and only if their distance apart in G is at most k. A connected graph G is called s...

Alon Hever, Corey Oses, 3 Stefano Curtarolo, 3 Ohad Levy, 3, 4 and Amir Natan 3, 5, ∗ Department of Physical Electronics, Tel-Aviv University, Tel-Aviv 69978, Israel Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, United States Center for Materials Genomics, Duke University, Durham, North Carolina 27708, United States Department of Phys...