State-crossing from a Locally Excited to an Electron Transfer State(SLEET) Model Rationalizing the Aggregation-induced Emission Mechanism of (Bi)piperidylanthracenes

Luminogens with aggregation-induced emission(AIE)characteristics(or AIEgens)have been widely used in various applications due to their excellent luminescent properties in molecular aggregates and the solid state.A deep understanding of the AIE mechanism is critical for the rational development of AIEgens.In this work,the“state-crossing from a locally excited to an electron transfer state”(SLEET)model is employed to rationalize the AIE phenomenon of two(bi)piperidylanthracenes.According to the SLEET model,an electron transfer(ET)state is formed along with the rotation of the piperidyl group in the excited state of(bi)piperidylan-thracene monomers,leading to fluorescence quenching.In contrast,a bright state exists in the crystal and molecular aggregates of these compounds,as the intermolecular interactions restrict the formation of the dark ET state.This mechanistic understanding could inspire the deployment of the SLEET model in the rational designs of various functional AIEgens.     

工件的释放时间和加工时间具有一致性的单机在线排序问题研究

工件的释放时间和加工时间具有一致性, 是指释放时间大的工件其加工时间不小于释放时间小的工件的加工时间, 即若$r_{i}\geq r_{j}$, 则$p_{i}\geq p_{j}$。本文在该一致性约束下, 研究最小化最大加权完工时间单机在线排序问题, 和最小化总加权完工时间单机在线排序问题, 并分别设计出$\frac{\sqrt{5}+1}{2}$-竞争的最好可能在线算法。     

Perpetual cutoff method and CDE′(K,N) condition on graphs

By using the perpetual cutoff method, we prove two discrete versions of gradient estimates for bounded Laplacian on locally finite graphs with exception sets under the condition of CD{E}^{\prime }(K,N). This generalizes a main result of F. Münch who considers the case of CD(K, \infty) curvature. Hence, we answer a question raised by Münch. For that purpose, we characterize some basic properties of radical form of the perpetual cutoff semigroup and give a weak commutation relation between bounded Laplacian \text{Δ} and perpetual cutoff semigroup P_t^W in our setting.     

局部对称的黎曼流形中的极小子流形

主要研究了局部对称的黎曼流形中的定向紧致无边极小子流形的内蕴刚性问题,利用一个矩阵不等式,得到了这类子流形的一个刚性定理．所得结果部分改进了已有的一个结论．     

A survey on book-embedding of planar graphs

The book-embedding problem arises in several area, such as very large scale integration (VLSI) design and routing multilayer printed circuit boards (PCBs). It can be used into various practical application fields. A book embedding of a graph G is an embedding of its vertices along the spine of a book, and an embedding of its edges to the pages such that edges embedded on the same page do not intersect. The minimum number of pages in which a graph G can be embedded is called the pagenumber or book-thickness of the graph G. It is an important measure of the quality for book-embedding. It is NP-hard to research the pagenumber of book-embedding for a graph G. This paper summarizes the studies on the book-embedding of planar graphs in recent years.     

Convergent sequences of sparse graphs: A large deviations approach

Models based on sparse graphs are of interest to many communities: they appear as basic models in combinatorics, probability theory, optimization, statistical physics, information theory, and more applied fields of social sciences and economics. Different notions of similarity (and hence convergence) of sparse graphs are of interest in different communities. In probability theory and combinatorics, the notion of Benjamini‐Schramm convergence, also known as left‐convergence, is used quite frequently. Statistical physicists are interested in the the existence of the thermodynamic limit of free energies, which leads naturally to the notion of right‐convergence. Combinatorial optimization problems naturally lead to so‐called partition convergence, which relates to the convergence of optimal values of a variety of constraint satisfaction problems. The relationship between these different notions of similarity and convergence is, however, poorly understood. In this paper we introduce a new notion of convergence of sparse graphs, which we call Large Deviations or LD‐convergence, and which is based on the theory of large deviations. The notion is introduced by “decorating” the nodes of the graph with random uniform i.i.d. weights and constructing corresponding random measures on and . A graph sequence is defined to be converging if the corresponding sequence of random measures satisfies the Large Deviations Principle with respect to the topology of weak convergence on bounded measures on . The corresponding large deviations rate function can be interpreted as the limit object of the sparse graph sequence. In particular, we can express the limiting free energies in terms of this limit object. We then establish that LD‐convergence implies the other three notions of convergence discussed above, and at the same time establish several previously unknown relationships between the other notions of convergence. In particular, we show that partition‐convergence does not imply left‐ or right‐convergence, and that right‐convergence does not imply partition‐convergence. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 52–89, 2017     

Comment on “Kirchhoff index in line,subdivision and total graphs of a regular graph”

Let G$G$ be a connected regular graph. Denoted by t(G)$t\left(G\right)$ and Kf(G)$Kf\left(G\right)$ the total graph and Kirchhoff index of G$G$, respectively. This paper is to point out that Theorem 3.7 and Corollary 3.8 from “Kirchhoff index in line, subdivision and total graphs of a regular graph” [X. Gao, Y.F. Luo, W.W. Liu, Kirchhoff index in line, subdivision and total graphs of a regular graph, Discrete Appl. Math. 160(2012) 560–565] are incorrect, since the conclusion of a lemma is essentially wrong. Moreover, we first show the Laplacian characteristic polynomial of t(G)$t\left(G\right)$, where G$G$ is a regular graph. Consequently, by using Kf(G)$Kf\left(G\right)$, we give an expression on Kf(t(G))$Kf\left(t\left(G\right)\right)$ and a lower bound on Kf(t(G))$Kf\left(t\left(G\right)\right)$ of a regular graph G$G$, which correct Theorem 3.7 and Corollary 3.8 in Gao et al. (2012)  [2].     

Central limit theorem for quadratic forms for sparse tables

Sufficient conditions for asymptotic normality for quadratic forms in {n_t − np_t} are given, where {n_t} are the observed counts with expected cell means {np_t}. The main result is used to derive asymptotic distributions of many statistics including the Pearson's chi-square.     

Uniformly locally o-minimal structures and locally o-minimal structures admitting local definable cell decomposition

We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a locally o-minimal structure which admits local definable cell decomposition.