Syntheses,Structures, and Magnetic Properties of Two Cobalt(II) Metal‐Organic Frameworks Based on Y‐shaped 3,5,4′‐Azobenzenetricarboxylic Acid and Different N‐donor Ligands

Two metal‐organic frameworks, [Co₂(ABTC)(bimh)(OH)] · 2H₂O ( 1 ) and [Co₃(ABTC)₂(dimb)₄]_n ( 2 ) [H₃ABTC = 3,4′,5‐azobenzenetricarboxylic acid, bimh = 1,1′‐(1,4‐hexanediy)bis(imidazole), dimb = 1,4‐bis(1H‐imidazol‐1‐yl)benzene], were prepared under solvothermal conditions and structurally characterized. Complex 1 demonstrates a complicated 3D (3,8)‐connected tfz‐d net with (4³)₂(4⁶.6¹⁷.8⁵) topology. The framework of 2 can be classified as a rare 3D (3,6,6)‐connected net with the Schäfli symbol of (4.6²)₂(4².6¹⁰.8³)(4⁴.6¹⁰.8), and exhibits an intriguing self‐penetrating motif. Meanwhile, the thermal stabilities and magnetic properties for 1 and 2 were also probed.     

Comment on: “Topology identification and adaptive synchronization of uncertain complex networks with adaptive double scaling functions” [Commun Nonlinear Sci Numer Simul 2011;16:3337-43]

In this comment letter we point out that the main result of the recent paper [Xu Y, Zhou W, Fang J, Sun W. Topology identification and adaptive synchronization of uncertain complex networks with adaptive double scaling functions. Commun Nonlinear Sci Numer Simul 2011;16(18):3337-43] has certain errors. The mistakes are corrected and a correct version is presented in this letter. We further indicate that a sufficient condition has been neglected in a series of articles discussing the same topic of network topology identification; hence we hope this letter can help clarify some unclear concepts about this topic.     

On Felbin-type Fuzzy 2-normed Spaces and Its Fuzzy Ⅰ-topologies

In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two Ⅰ-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy Ⅰ-topologie...     

On some types of covering rough sets from topological points of view

The concept of coverings is one of the fundamental concepts in topological spaces and plays a big part in the study of topological problems. This motivates the research of covering rough sets from topological points of view. From topological points of view, we can get a good insight into the essence of covering rough sets and make our discussions concise and profound. In this paper, we first construct a type of topology called the topology induced by the covering on a covering approximation space. This notion is indeed in the core of this paper. Then we use it to define the concepts of neighborhoods, closures, connected spaces, and components. Drawing on these concepts, we define several pairs of approximation operators. We not only investigate the relationships among them, but also give clear explanations of the concepts discussed in this paper. For a given covering approximation space, we can use the topology induced by the covering to investigate the topological properties of the space such as separation, connectedness, etc. Finally, a diagram is presented to show that the collection of all the lower and upper approximations considered in this paper constructs a lattice in terms of the inclusion relation ⊆.     

An integrative in silico approach to the structure of Omp33-36 in Acinetobacter baumannii

Omp33-36 in A. baumannii, a bacterium causing serious nosocomial infections, is a virulence factor associated with the pathogen metabolic fitness as well as its adherence and invasion to human epithelial cells. This protein is also involved in interaction of the bacteria with host cells by binding to fibronectin. Moreover, Omp33-36 renders cytotoxicity to A. baumannii in addition to inducing apoptosis and modulation of autophagy. In the present study, an integrated strategy is launched to pierce into the 3D structure of Omp33-36 protein. The signal peptide within the sequence was determined, then, topology as well as secondary and tertiary structures of the protein were predicted. The mature protein assigned as a 14-stranded barrel in which residues 1–19 is removed as signal peptide. The obtained 3D models were evaluated in terms of quality; and then, served as queries to find similar protein structures. The hits were analyzed regarding topology among which 14-stranded were considered. The most qualified model was refined and then its sequence aligned to its counterpart similar structure protein (CymA from Klebsiella oxytoca). The determined structure of Omp33-36 could justify its porin function and carbapenem-resistance associated with the loss of this protein.     

Topology vs generalized rough sets

This paper investigates the relationship between topology and generalized rough sets induced by binary relations. Some known results regarding the relation based rough sets are reviewed, and some new results are given. Particularly, the relationship between different topologies corresponding to the same rough set model is examined. These generalized rough sets are induced by inverse serial relations, reflexive relations and pre-order relations, respectively. We point that inverse serial relations are weakest relations which can induce topological spaces, and that different relation based generalized rough set models will induce different topological spaces. We proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology.     

决策信息系统中的拓扑学方法

在决策信息系统中引入拓扑结构,借助拓扑学的基本概念(拓扑、内部和闭包等)研究决策问题,用它们刻画决策信息系统中的一些重要概念(决策协调集、决策约简集、下近似协调集、下近似约简集、上近似协调集、上近似约简集),并利用它们把这些重要概念推广到最一般的情况,建立起相应的约简理论.     

一类基于分层量化的Domain上的广义Alexander拓扑

文献[8]提出了一类基于分层量化的偏序集结构(以下简称R-偏序集).此结构是sfe[5]的非对称推广,也是拟度量空间(quasi-metric spaces,qms)[3]和广义超度量空间(generalized ultrametric spaces,gums)[4]的一种特殊情形.本文定义了其上的广义Alexande...     

Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method

The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm.     

Molecular engineering of CxNy: Topologies,electronic structures and multidisciplinary applications

As a class of metal-free two-dimensional (2D) semiconductor materials, polymeric carbon nitrides have attracted wide attention recently due to its facile regulation of the molecular and electronic structures, availability in abundance and high stability. According to the different ratios of C and N atoms in the framework, a series of C_xN_y materials have been successfully synthesized by virtue of various precursors, which further triggers extensive investigations of broad applications ranging from sustainable photocatalytic reactions and highly sensitive optoelectronic biosensing. In view of topological structures on their electronic structures and material properties, the as-reported C_xN_y could be generally classified into two main categories with three- or six-bond-extending frameworks. Owing to the effective n→π* transition in most C_xN_y materials, the relative energy level of the lone-pair electrons on N atoms is high, which thus endows the materials with the capability of visible light absorption. Meanwhile, the different repeating units, bridging groups and defect sites of these two kinds of C_xN_y allow them to effectively drive a diverse of promising applications that require specific electronic, interfacial and geometric properties. This review paper aims to summarize the recent progress in topological structure design and the relevant electronic band structures and striking properties of C_xN_y materials. In the final part, we also discuss the existing challenges of C_xN_y and outlook the prospect possibilities.