Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. VI*

The present Part VI of this series of articles provides a mathematical and methodical link between (i) fundamental methodology in the repeat space theory (RST), which is referred to as the approach via the aspect of form and general topology and which has universal unifying power to handle additivity problems of molecules that have many identical moieties, and (ii) frontier electron theory of reactivity indices. Using theoretical tools required to link (i) and (ii), we establish a theorem from which the Generalized Alpha Existence Theorem (a theorem essential in the RST and proved in the previous Part V) directly follows. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 389–400, 2001     

Notes on Amenability of Commutative Fusion Algebras

A commutative fusion algebra is proved to be amenable if and only if the associated regular representation is bounded.     

量子代数A_n（q_1,…,q_n,K）的强既约Groebner基

对于量子代数An（q1,…,qn,K）的左理想引入了强既约Groebner基,证明了这种基的存在性与惟一性,并给出了构造一个强既约Groebner基的算法。     

KMgF_3∶Ni~(2+)晶体局域结构研究

采用赵敏光等的μkα模型，在强场图象中建立了3d^8电子组态的多重态计算公式，利用高阶微挠公式推导出顺磁g因数的计算解析表达式，并在能量矩阵、g因数与掺杂真实晶体结构常数之间建立起关联公式．将此模型应用于KMgF3：Ni^2＋晶体，计算其d—d跃迁光谱和EPR谱并与实验数据对比，发现KMgF3晶体在掺入Ni^2＋后其结构应发生同向延伸变化，畸变量△R=0．004nm，计算结果与实验值符合较好．     

可数生成代数上的Hilbert零点定理

证明了Hilbert 零点定理可以推广到一个不可数域可数生成的代数上,还给出了它推广后的几何形式.     

Large-scale calculations for hadron spectroscopy

Some recent Monte Carlo calculations for quantum chromodynamics, performed on Euclidean lattices of rather large extent, are reviewed. The purpose of the calculations is to provide accurate determinations of quantities, such as interquark potentials or mass eigenvalues, which are relevant for hadronic spectroscopy. Results obtained in quenched QCD on 16³×32 lattices are illustrated, and a discussion of computational resources and techniques required for the calculations is presented.     

Dirichlet空间上的循环复合算子

该文主要证明了在Dirichlet空间上由复合算子{C\-φ:φ∈Aut(D)}生成的代数为循环算子代数;同时对任意的解析映射φ:D→D,C\-φ都不可能为超循环算子给出了证明.     

An analytical approach to global optimization

Global optimization problems with a few variables and constraints arise in numerous applications but are seldom solved exactly. Most often only a local optimum is found, or if a global optimum is detected no proof is provided that it is one. We study here the extent to which such global optimization problems can be solved exactly using analytical methods. To this effect, we propose a series of tests, similar to those of combinatorial optimization, organized in a branch-and-bound framework. The first complete solution of two difficult test problems illustrates the efficiency of the resulting algorithm. Computational experience with the programbagop, which uses the computer algebra systemmacsyma, is reported on. Many test problems from the compendiums of Hock and Schittkowski and others sources have been solved.The research of the first and the third authors has been supported by AFOSR grants #0271 and #0066 to Rutgers University. Research of the second author has been supported by NSERC grant #GP0036426 and FCAR grants #89EQ4144 and #90NC0305.     

KRS and Powers of determinantal ideas

The goal of this paper is to determine Göbner bases of powers of determinantal ideals and to show that the Rees algebras of (products of) determinantal ideals are normal and Cohen–Macaulay if the characteristic of the base field is non-exceptional. Our main combinatorial result is a generalization of Schensted's Theorem on the Knuth–Robinson–Schensted correspondence.     

Extended Toda Lattice

We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows.