An average fock operator technique of approximate open-shell LCAO-MO-SCF calculation

The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofF ^av can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofE ^ac with the UHF-energy shows thatE _UHF<E ^ac in each case revealing some kind of an upper bound nature ofE ^ac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed.     

Isometries of certain operator spaces

Let and be Banach spaces, and be the spaces of bounded linear operators from into In this paper we give full characterization of isometric onto operators of for a certain class of Banach spaces, that includes We also characterize the isometric onto operators of and the compact operators on Furthermore, the multiplicative isometric onto operators of , when multiplication on is taken to be the Schur product, are characterized.

     

A CLASS OF HARMONIC STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRIC POINTS ASSOCIATED WITH WRIGHT GENERALIZED HYPERGEOMETRIC FUNCTION

Making use of Wright operator we introduce a new class of complex-valued harmonic functions with respect to symmetric points which are orientation preserving, univalent and starlike. We obtain coefficient conditions, extreme points, distortion bounds, and convex combination.     

Analytic Calculation of Arbitrary Matrix Elements for Boson Exponential Quadratic Operators

By means of the transformation relation between the ordinary form of boson exponential quadratic operators (BEQO) and its anti-normal product form, we present an effective method to conveniently calculate arbitrary matrix elements of BEQO. By this method, many important matrix elements can be calculated analytically. As a direct application, we obtain the exact solutions of the density matrix and partition function for general boson quadratic Hamiltonian without any information about the energy level.     

基于广义WOWA算子的Pythagorean模糊决策方法

针对Pythagorean模糊信息的决策问题,构建广义Pythagorean模糊信息加权有序加权平均(PF-GWOWA)算子。首先,提出PF-GWOWA算子,并证明Pythagorean模糊广义加权平均(PF-GWA)算子、Pythagorean模糊加权有序加权平均(PF-WOWA)算子与Pythagorean模糊加权平均(PF-WA)算子均为PF-GWOWA算子的特例;其次,根据GWOWA算子属性综合权重计算模型,利用PF-GWOWA算子对信息进行集结;最后,通过算例分析和传统方法对比,说明本文提出方法的合理性与有效性。     

一种算子自定义小波薄板单元及应用

提出了基于提升方案的自适应算子自定义小波有限元法,构造了一种新的算子自定义小波薄板单元。建立二维Hermite型有限元多分辨空间和两尺度关系,并由广义变分原理推导薄板结构关于尺度函数和小波函数的内积关系式,即算子。为满足算子正交性,提出基于提升方案的算子自定义小波单元的构造方法,其优点在于可根据问题的需要来设计具有期望特性的小波基。提出基于两尺度误差的自适应算子自定义小波有限元方法,通过向大于误差阈值的局域添加算子自定义小波,实现薄板结构问题的高效求解。算子自定义小波有限元法节省了重新划分网格或提高插值函数的阶次所带来的大量有限元前处理时间,并且实现薄板问题的高效解耦运算。