Structures,vibrational spectra,and relative energies of HXSiS (X = H,F, and Cl) isomers

The potential energy surface for the decomposition of HXSiS (X = H, F, and Cl) on the singlet state has been explored by B3LYP and CCSD(T) calculations. Five different types of reaction are proposed: (A) 1,1‐HX elimination, (B) 1,2‐H shift, (C) 1,2‐X shift, (D) H · and XSiS · radical formation, and (E) X · and HSiS · radical formation. These results show interesting trends for the HXSiS isomers. Our theoretical investigations suggest that the doubly bonded species HXSiS should be the lowest energy structure among the isomers from both kinetic and thermodynamic viewpoints. We also report theoretical predictions of molecular parameters and vibrational infrared (IR) spectra of the monohalogen‐substituted silanethione, which should be useful for future experimental observations. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 14–25, 2001     

Synthesis of trans-1,2-diphenyl-3,4-bis[4-(2,6-diphenyl-4H- pyranylidenyl)]cyclobutane: correction and structure proof

The reaction of phenyl lithium acetylide ($\text{2}$) with 2,6-diphenylpyrylium perchlorate ($\text{1}$) is solvent dependent. With diethyl ether as solvent, the isolated product differed from that previously reported and is reassingned as 2,6-diphenyl-4-phenylacetylenyl-4$\text{H}$-pyran ($\text{5}$). On the other hand, in THF the title compound ($\text{6}$) was obtained; its structure confirmed by single-crystal x-ray crystallography.     

The accurate calculation of dipole moments and dipole polarizabilities using Gaussian-based density functional methods

Dipole moments and static dipole polarizabilities have been calculated for a number of small molecules using the linear combination of Gaussian-type orbitals–local spin density method. The effect of augmenting standard orbital basis sets with polarization functions has been investigated. A set of optimum ζ_d, for use in calculating polarizabilities, has been derived for the first-row atoms C, N, O, and F. The results of this optimized doubly polarized double-zeta basis set compare well with results obtained using a double-zeta basis set augmented by four even-tempered ζ_d polarization functions. The results of the optimized basis set, and a basis set augmented with only a single ζ_d polarization function derived from it, compare very favorably with those obtained from Møller–Plesset perturbation theory and with experimental data. They show a marked improvement on results obtained using standard Hartree–Fock self-consistent-field molecular orbital methods where no treatment of electron-correlation is included.     

DEA models for minimizing weight disparity in cross-efficiency evaluation

Cross-efficiency evaluation is a commonly used approach for ranking decision-making units (DMUs) in data envelopment analysis (DEA). The weights used in the cross-efficiency evaluation may sometimes differ significantly among the inputs and outputs. This paper proposes some alternative DEA models to minimize the virtual disparity in the cross-efficiency evaluation. The proposed DEA models determine the input and output weights of each DMU in a neutral way without being aggressive or benevolent to the other DMUs. Numerical examples are tested to show the validity and effectiveness of the proposed DEA models and illustrate their significant role in reducing the number of zero weights.     

各向异性本构关系在板料成形数值模拟中的应用

对几种能表达面内各向异性的屈服准则Hill、Barlat-Lian、Barlat进行了比较。以弹性变形服从各向同性广义虎克定律的情况下，给出了基于张量算法推导的弹塑性本构关系的一般表达式，并由此导出了相应屈服准则的弹塑性本构关系的显式表达。借助ABAQUS软件本构模块用户子程序接口，分别实现了这些屈服准则在ABAQUS的嵌入。以模拟方形盒的拉延过程为例，分析了不同的屈服准则在板料成形过程数值模拟中的应用。模拟结果表明，基于弹塑性本构关系一般表达所列出的相应屈服准则的显式表达式是正确的；在采用壳元来模拟板料成形时，采用Barlat准则的模拟结果和采用Barlat-Lian准则的结果差别不大。     

A Multiobjective Hybrid Metaheuristic Approach for GIS-based Spatial Zoning Model

This paper presents a multiobjective hybrid metaheuristic approach for an intelligent spatial zoning model in order to draw territory line for geographical or spatial zone for the purpose of space control. The model employs a Geographic Information System (GIS) and uses multiobjective combinatorial optimization techniques as its components. The proposed hybrid metaheuristic consists of the symbiosis between tabu search and scatter search method and it is used heuristically to generate non-dominated alternatives. The approach works with a set of current solution, which through manipulation of weights are optimized towards the non-dominated frontier while at the same time, seek to disperse over the frontier by a strategic oscillation concept. The general procedure and its algorithms are given as well as its implementation in the GIS environment. The computation has resulted in tremendous improvements in spatial zoning.     

A note on strongly π-regular rings

Let R be an associative ring with unit and let N(R) denote the set of nilpotent elements of R. R is said to be stronglyπ-regular if for each x∈R, there exist a positive integer n and an element y∈R such that x ⁿ=x ^{n +1} y and xy=yx. R is said to be periodic if for each x∈R there are integers m,n≥ 1 such that m≠n and x ^m=x ⁿ. Assume that the idempotents in R are central. It is shown in this paper that R is a strongly π-regular ring if and only if N(R) coincides with the Jacobson radical of R and R/N(R) is regular. Some similar conditions for periodic rings are also obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

On Finite Groups and the Small Square Property

Let G be a finite group written multiplicatively and k a positive integer. If X is a non-empty subset of G, write X ² = |xy | x, y X . We say that G has the small square property on k-sets if |X ²| < k ² for any k-element subset X of G. For each group G, there is a unique m = m _G such that G has the small square property on (m + 1)-sets but not on m-sets. In this paper we show that given any positive integer d, there is a finite group G with m _G = d.     

Efficient Algorithms for Finding the Maximum Number of Disjoint Paths in Grids

In a rectangular grid, given two sets of nodes, (sources) and (sinks), of size each, the disjoint paths (DP) problem is to connect as many nodes in to the nodes in using a set of “disjoint” paths. (Both edge-disjoint and vertex-disjoint cases are considered in this paper.) Note that in this DP problem, a node in can be connected to any node in . Although in general the sizes of and do not have to be the same, algorithms presented in this paper can also find the maximum number of disjoint paths pairing nodes in and . We use the network flow approach to solve this DP problem. By exploiting all the properties of the network, such as planarity and regularity of a grid, integral flow, and unit capacity source/sink/flow, we can optimally compress the size of the working grid (to be defined) from O(N²) to O(N^1.5) and solve the problem in O(N^2.5) time for both the edge-disjoint and vertex-disjoint cases, an improvement over the straightforward approach which takes O(N³) time.