A note on a characterization of P-matrices

In this note we show that the characterization results for P-matrices due to K.G. Murty and A. Tamir which state that a given square matrixM of ordern is a P-matrix if and only if the linear complementarity problem (q, M) has a unique solution for allq in a specified finite subset of ⁿ depending onM are incorrect whenn > 3.Research supported by Dr. K.S. Krishnan (DAE) fellowship for research in Mathematics and Computer Science, Bombay, India.     

A path following algorithm for a class of convex programming problems

We present a primal-dual path following interior algorithm for a class of linearly constrained convex programming problems with non-negative decision variables. We introduce the definition of a Scaled Lipschitz Condition and show that if the objective function satisfies the Scaled Lipschitz Condition then, at each iteration, our algorithm reduces the duality gap by at least a factor of (1–/n), where is positive and depends on the curvature of the objective function, by means of solving a system of linear equations which requires no more than O(n³) arithmetic operations. The class of functions having the Scaled Lipschitz Condition includes linear, convex quadratic and entropy functions.     

On the validity of the counterpoise correction for the basis set superposition error including the fragment relaxation terms

It is demonstrated that relatively large geometrical changes make Emsley et al.'s assumption (J Am Chem Soc (1978) 100:3303) on the counterpoise correction for the basis set superposition error including the fragment relaxation terms unacceptable. Received: 23 September 1997 / Accepted: 31 October 1997     

X-H (X = C, N, O, Si, P, S) 键离解能计算的密度泛函方法研究

使用了不同密度泛函方法计算X-H (X = C, N, O, Si, P, S) 键离解能，并分析不同密度泛函方法的计算精度。研究发现大多数密度泛函方法包括B3LYP, B3P86, B3PW91, G96LYP, PBE1PBE，和BH&HLYP都明显低估键离解能13-25 kJ/mol。该现象与是否使用无限基组无关，因为即使使用无限基组键离解能仍然被低估。因此密度泛函方法不适合用于键离解能的估算。其中B3P86方法的偏差最小。进一步分析表明，使用限制性开壳层计算并无任何优势，在大多数情况下非限制性开壳层计算实际上比限制性开壳层计算要好。最后，我们发现了密度泛函方法对键离解能的低估是系统的，因此建议利用校准后的UDFT/6-311++G(d, p)方法计算化学键离解能。     

GRECP/5e‐MRD‐CI calculation of the electronic structure of PbH

The correlation calculation of the electronic structure of PbH is carried out with the generalized relativistic effective core potential (GRECP) and multireference single‐ and double‐excitation configuration interaction (MRD‐CI) methods. The 22‐electron GRECP for Pb is used and the outer core 5s, 5p, and 5d pseudospinors are frozen using the level‐shift technique, so only five external electrons of PbH are correlated. A new configuration selection scheme with respect to the relativistic multireference states is employed in the framework of the MRD‐CI method. The [6, 4, 3, 2] correlation spin–orbit basis set is optimized in the coupled cluster calculations on the Pb atom using a recently proposed procedure, in which functions in the spin–orbital basis set are generated from calculations of different ionic states of the Pb atom and those functions are considered optimal that provide the stationary point for some energy functional. Spectroscopic constants for the two lowest‐lying electronic states of PbH (²Π_1/2, ²Π_3/2) are found to be in good agreement with the experimental data. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

A class of simplicial restart fixed point algorithms without an extra dimension

In an earlier paper we introduced an algorithm for approximating a fixed point of a mapping on the product space of unit simplices. Ideas of that paper are used to construct a class of triangulations ofR ⁿ. More precisely, for somek, 1 k n, and positive integersm ₁ , m_k with sumn, a triangulation ofR ⁿ is obtained by triangulating the cells which are formed by taking the product of given triangulations ofR ^mj, j = 1, ,k. The triangulation of each cell will be defined in relation to an arbitrarily chosen pointv inR ⁿ, being the starting point of the algorithm. Fork = n we obtain theK triangulation originally due to Todd. Each element of the class can be used to find a simplex which approximates a fixed point of a mapping onR ⁿ by generating a unique path of adjacent simplices of variable dimension starting with the pointv. We also give convergence conditions. It is indicated how in casek = n a connected set of fixed points can be generated. Moreover, we give some computational experience.     

TH型区间值模糊正规子群

本文在区间值模糊集空间上，引入了幂等区间范数ＴＨ，在此基础上，定义了ＴＨ型区间值模糊正规子群，并研究了它的一些性质和结构特征，从而拓广了区间值模糊集的理论。     

The Degree Preserving Spanning Tree Problem: Valid Inequalities and Branch-and-cut method

Given a connected undirected graph G, the Degree Preserving Spanning Tree Problem (DPSTP) consists in finding a spanning tree T of G that maximizes the number of vertices that have the same degree in T and in G. In this paper, we introduce Integer Programming formulations, valid inequalities and a Branch-and-cut algorithm for the DPSTP. Reinforced with new valid inequalities, the upper bounds provided by the formulation behind our Branch-and-cut method dominate previous DPSTP bounds in the literature.     

粒度空间约简及其粗糙集模型研究

针对交可约粒度空间中覆盖、基和粒结构的关系,结合偏序关系的哈斯图,给出一种约简粒度空间的方法.另外,通过限定上、下近似算子的取值范围,重新定义了交可约粒度空间上的粗糙集模型,并讨论了其相关性质.     

A Unified Fixed Point Theory for Countably P -Concentrative Multimaps

New fixed point results and Leray-Schauder alternatives are presented for countably P -concentrative multimaps. The notion of an essential map is also introduced for a wide class of maps.