The BMO L space and Riesz transforms associated with Schrödinger operators

Let L =△ ＋ V be a SchrSdinger operator in Rd, d ≥ 3, where the nonnegative potential V belongs to the reverse HSlder class Sd. We establish the BMOL-boundedness of Riesz transforms З/ЗxiL-1/2, and give the Fefferman-Stein type decomposition of BMOL functions.     

Almost complex structure and the quotient four-manifold by an anti-symplectic involution

Suppose that X is a closed, symplectic four-manifold with an anti-symplectic involution σ and its two-dimensional fixed point set. We show that the quotient X/σ admits no almost complex structure if .As a partial converse if X is simply-connected and , then the X/σ admits an almost complex structure.Also we show that the quotient X/σ admits an almost complex structure if X is Kähler and .     

Filling polygonal holes with minimal energy surfaces on Powell-Sabin type triangulations

In this paper we present two different methods for filling in a hole in an explicit 3D surface, defined by a smooth function f in a part of a polygonal domain D⊂R². We obtain the final reconstructed surface over the whole domain D. We do the filling in two different ways: discontinuous and continuous. In the discontinuous case, we fill the hole with a function in a Powell-Sabin spline space that minimizes a linear combination of the usual seminorms in an adequate Sobolev space, and approximates (in the least squares sense) the values of f and those of its normal derivatives at an adequate set of points. In the continuous case, we will first replace f outside the hole by a smoothing bivariate spline s_f, and then we fill the hole also with a Powell-Sabin spline minimizing a linear combination of given seminorms. In both cases, we obtain existence and uniqueness of solutions and we present some graphical examples, and, in the continuous case, we also give a local convergence result.     

以T型三羧酸配体构筑的具有2D→3D穿插结构的金属有机框架的合成、结构及性质

采用溶剂热合成法,利用T型三羧酸配体3,4',5-联苯三羧酸(H₃BPT=biphenyl-3,4',5-tricarboxylicacid)制备并表征了2个2D→3D穿插结构的金属有机框架结构,{[Ni₃(BPT)₂(bpe)₂(H₂O)₆]·2DMF·7H₂O}_n(1)和{[Ni₃(BPT)₂(bpea)₂(H₂O)₆]·2DMF·5H₂O}_n(2)(bpe=1,2-bis(4-pyridyl)ethylene,bpea=1,2-bis(4-pyridyl)ethane,DMF=N,N-dimethylformamide)。在这2个化合物中,BPT配体和含氮配体bpe或bpea共同连接相邻的Ni(Ⅱ)中心,形成(3,4)-连接的(63)(65.8)二维双层结构。相邻双层结构间相互穿插,形成具有聚轮烷结构的2D→3D互锁结构。气体吸附性质表明,化合物1对CO₂和N₂具有一定的吸附能力。     

Splittings of Mapping Tori of Free Group Automorphisms

We present necessary and sufficient conditions for the existence of a splitting over of the mapping torus of a free group automorphism .     

Coding‐theoretic constructions for (t,m,s)‐nets and ordered orthogonal arrays

(t,m,s)‐nets are point sets in Euclidean s‐space satisfying certain uniformity conditions, for use in numerical integration. They can be equivalently described in terms of ordered orthogonal arrays, a class of finite geometrical structures generalizing orthogonal arrays. This establishes a link between quasi‐Monte Carlo methods and coding theory. The ambient space is a metric space generalizing the Hamming space of coding theory. We denote it by NRT space (named after Niederreiter, Rosenbloom and Tsfasman). Our main results are generalizations of coding‐theoretic constructions from Hamming space to NRT space. These comprise a version of the Gilbert‐Varshamov bound, the (u,u+υ)‐construction and concatenation. We present a table of the best known parameters of q‐ary (t,m,s)‐nets for qε{2,3,4,5} and dimension m≤50. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 403–418, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10015     

Global attraction to solitary waves for Klein–Gordon equation with mean field interaction

We consider a U(1)$\mathbf{U}(1)$-invariant nonlinear Klein–Gordon equation in dimension n?1$n?1$, self-interacting via the mean field mechanism. We analyze the long-time asymptotics of finite energy solutions and prove that, under certain generic assumptions, each solution converges as t→±∞$t\to \pm \infty$ to the two-dimensional set of all “nonlinear eigenfunctions” of the form ?(x)e−iωt$?(x)e^{-i\omega t}$. This global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersive radiation.     

整体式 Cu-ZSM-5 催化剂上 NH3 选择性催化还原 NO 活性

 采用浸渍法制备了一系列不同 Cu 含量的 Cu-ZSM-5 催化剂, 并用于 NH₃ 选择性催化还原 (SCR)NO 反应. 结果表明, 当 Cu 含量为 8%时, Cu-ZSM-5 催化剂的活性最高; 当空速为 30 000 h^–1. , 在 198~440 ^oC 反应时 NO 转化率均高于 80%, 最高可达 97%, 且空速的影响较小. 经快速水热老化后, 该催化剂活性明显优于商用 V 基催化剂. H₂O 和 SO₂ 对 Cu-ZSM-5 催化剂的 SCR 活性有所影响, 但可明显恢复. X 射线衍射和 NH3 程序升温脱附结果表明, 当 Cu-ZSM-5 中 Cu 含量为 8% 时, 进入 ZSM-5 中阳离子位的 Cu 较多, 催化剂的活性较高, 且其表面具有较多的酸中心和酸量, 从而有利于 SCR 反应.     

Perfect Graphs with No Balanced Skew‐Partition are 2‐Clique‐Colorable

A graph G is perfect if for all induced subgraphs H of G, . A graph G is Berge if neither G nor its complement contains an induced odd cycle of length at least five. The Strong Perfect Graph Theorem [9] states that a graph is perfect if and only if it is Berge. The Strong Perfect Graph Theorem was obtained as a consequence of a decomposition theorem for Berge graphs [M. Chudnovsky, Berge trigraphs and their applications, PhD thesis, Princeton University, 2003; M. Chudnovsky, N. Robertson, P. Seymour, and R. Thomas, The strong perfect graph theorem, Ann Math 164 (2006), 51–229.], and one of the decompositions in this decomposition theorem was the “balanced skew‐partition.” A clique‐coloring of a graph G is an assignment of colors to the vertices of G in such a way that no inclusion‐wise maximal clique of G of size at least two is monochromatic, and the clique‐chromatic number of G, denoted by , is the smallest number of colors needed to clique‐color G. There exist graphs of arbitrarily large clique‐chromatic number, but it is not known whether the clique‐chromatic number of perfect graphs is bounded. In this article, we prove that every perfect graph that does not admit a balanced skew‐partition is 2‐clique colorable. The main tool used in the proof is a decomposition theorem for “tame Berge trigraphs” due to Chudnovsky et al. ( http://arxiv.org/abs/1308.6444 ).     

Non-simultaneous blow-up and blow-up rates for reaction-diffusion equations

This paper considers blow-up solutions for reaction-diffusion equations, complemented by homogeneous Dirichlet boundary conditions. It is proved that there exist initial data such that one block or two (separated or contiguous) blocks of n components blow up simultaneously while the others remain bounded. As a corollary, a necessary and sufficient condition is obtained such that any blow-up must be the case for at least two components blowing up simultaneously. We also show some other exponent regions, where any blow-up of k(∈{1,2,…,n}) components must be simultaneous. Moreover, the corresponding blow-up rates and sets are discussed. The results extend those in Liu and Li [B.C. Liu, F.J. Li, Non-simultaneous blow-up of n components for nonlinear parabolic systems, J. Math. Anal. Appl. 356 (2009) 215-231].