The asymmetric contact process at its second critical value

The asymmetric contact process onZ has two distinct critical values ₁ > ₂ (at least with sufficient asymmetry). One can consider the process on {0,...,N} and analyze the time (which we call _N ) till complete vacany starting from complete occupation. Its behavior has already been resolved for all regions of except for =₂. For this value, Schinazi proved that lim _N log _N /logN=2 in probability and conjectured that _N /N ² converges in distribution. It is that result that we prove in this paper. We rely heavily on the Brownian motion behavior of the edge particle, which comes from Galves and Presutti and Kuczek.     

Compressing Coefficients While Preserving Ideals in K-Theory for C*-Algebras

An invariant based on orderedK-theory with coefficients in _n>1 /n and an infinite number of natural transformations has proved to be necessary and sufficient to classify a large class of nonsimple C* -algebras. In this paper, we expose and explain the relations between the order structure and the ideals of the C* -algebras in question.As an application, we give a new complete invariant for a large class of approximately subhomogeneous C*-algebras. The invariant is based on ordered K-theory with coefficients in /. This invariant is more compact (hence, easier to compute) than the invariant mentioned above, and its use requires computation of only four natural transformations.     

Polarizations and hook partitions

In this paper, we relate combinatorial conditions for polarizations of powers of the graded maximal ideal with rank conditions on submodules generated by collections of Young tableaux. We apply discrete Morse theory to the hypersimplex resolution introduced by Batzies–Welker to show that the L-complex of Buchsbaum and Eisenbud for powers of the graded maximal ideal is supported on a CW-complex. We then translate the “spanning tree condition” of Almousa–Fløystad–Lohne characterizing polarizations of powers of the graded maximal ideal into a condition about which sets of hook tableaux span a certain Schur module. As an application, we give a complete combinatorial characterization of polarizations of so-called “restricted powers” of the graded maximal ideal.     

最大度为4的图的无圈列表边染色

对于图G=(V(G),E(G)),如果一个映射φ:E(G)→{1,2,…,k},使得G中任意相邻的两边e₁,e₂满足φ(e₁)≠φ(e₂),并且G中不含有双色圈,则称φ为G的一个无圈边染色.对于给定的列表分配L={L(e)|e∈E(G)},如果存在图G的一个无圈边染色φ,使得对于任意边e∈E(G),均有φ(e)∈L(e),则称染色φ为G的一个无圈L-边染色.如果对于任意的列表分配L,当对所有的边e∈E(G)满足|L(e)|≥k时,图G均存在无圈L-边染色,那么称G是无圈k-边可选的.使图G无圈k-边可选的最小的正整数k,称为G的无圈列表边色数,用a’_l(G)表示.本文证明了对于最大度△≤4的连通图G,如果|E(G)|≤2|V(G)|-1,则a’_l(G)≤6,扩展了Basavaraju和Chandran文[J.Graph Theory,2009,61(3):192-209]的结果.     

An algebraic multigrid method for elasticity based on an auxiliary topology with edge matrices

This article introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second-order partial differential equations. Based on a discrete energy made up of edge and vertex contributions, we are able to develop coarsening criteria that guarantee two-level convergence even for systems of equations such as linear elasticity . This energy also allows us to construct prolongations with prescribed sparsity pattern that still preserve kernel vectors exactly. These allow for a straightforward optimization that simplifies parallelization and reduces communication on coarse levels. Numerical experiments demonstrate efficiency and robustness of the method and scalability of the implementation.     

Extreme values of the resurgence for homogeneous ideals in polynomial rings

We show that two ostensibly different versions of the asymptotic resurgence introduced by E. Guardo, B. Harbourne and A. Van Tuyl in 2013 are the same. We also show that the resurgence and asymptotic resurgence attain their maximal values simultaneously, if at all, which we apply to a conjecture of E. Grifo. For radical ideals of points, we show that the resurgence and asymptotic resurgence attain their minimal values simultaneously. In addition, we introduce an integral closure version of the resurgence and relate it to the other versions of the resurgence. In closing we provide various examples and raise some related questions, and we finish with some remarks about computing the resurgence.     

Topological photonic states in gyromagnetic photonic crystals: Physics,properties, and applications

Topological photonic states (TPSs) as a new type of waveguide state with one-way transport property can resist backscattering and are impervious to defects, disorders and metallic obstacles. Gyromagnetic photonic crystal (GPC) is the first artificial microstructure to implement TPSs, and it is also one of the most important platforms for generating truly one-way TPSs and exploring their novel physical properties, transport phenomena, and advanced applications. Herein, we present a brief review of the fundamental physics, novel properties, and practical applications of TPSs based on GPCs. We first examine chiral one-way edge states existing in uniformly magnetized GPCs of ordered and disordered lattices, antichiral one-way edge states in cross magnetized GPCs, and robust one-way bulk states in heterogeneously magnetized GPCs. Then, we discuss the strongly coupling effect between two co-propagating (or counter-propagating) TPSs and the resulting physical phenomena and device applications. Finally, we analyze the key issues and prospect the future development trends for TPSs in GPCs. The purpose of this brief review is to provide an overview of the main features of TPSs in GPC systems and offer a useful guidance and motivation for interested scientists and engineers working in related scientific and technological areas.     

Finite basis for radical well-mixed difference ideals generated by binomials

In this paper, we prove a finite basis theorem for radical well-mixed difference ideals generated by binomials. As a consequence, every strictly ascending chain of radical well-mixed difference ideals generated by binomials in a difference polynomial ring is finite, which solves an open problem in difference algebra raised by Hrushovski in the binomial case.     

Band structure and optical transitions in the Hg3Se2Cl2 crystals

First-principles calculations of the band structure for Hg₃Se₂Cl₂ crystal were performed by means of density functional theory (DFT). The exchange and correlation potential was described within a framework of the local density approximation based on exchange-correlation energy optimization to calculate the total energy. DOS/PDOS and valence charge distribution were studied in details. Absorption near the fundamental edge was found to be due to indirect and direct allowed transitions. For device applications based on Hg₃Se₂Cl₂ crystal, understanding these fundamental issues is highly important and essential. It should be noted that optoelectronic applications of Hg₃Se₂Cl₂ are caused by coexistence of the large polarized Hg cations and a huge contribution of an harmonic phonon subsystem caused by anions.