Renormalized oscillation theory for Dirac operators

Oscillation theory for one-dimensional Dirac operators with separated boundary conditions is investigated. Our main theorem reads: If and if solve the Dirac equation , (in the weak sense) and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection equals the number of zeros of the Wronskian of and . As an application we establish finiteness of the number of eigenvalues in essential spectral gaps of perturbed periodic Dirac operators.

     

On k‐ary spanning trees of tournaments

It is well known that every tournament contains a Hamiltonian path, which can be restated as that every tournament contains a unary spanning tree. The purpose of this article is to study the general problem of whether a tournament contains a k‐ary spanning tree. In particular, we prove that, for any fixed positive integer k, there exists a minimum number h(k) such that every tournament of order at least h(k) contains a k‐ary spanning tree. The existence of a Hamiltonian path for any tournament is the same as h(1) = 1. We then show that h(2) = 4 and h(3) = 8. The values of h(k) remain unknown for k ≥ 4. © 1999 John & Sons, Inc. J Graph Theory 30: 167–176, 1999     

On k-ordered Hamiltonian graphs

A Hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v₁, v₂, …, v_k of k distinct vertices of G, there exists a Hamiltonian cycle that encounters v₁, v₂, …, v_k in this order. Define f(k, n) as the smallest integer m for which any graph on n vertices with minimum degree at least m is a k-ordered Hamiltonian graph. In this article, answering a question of Ng and Schultz, we determine f(k, n) if n is sufficiently large in terms of k. Let g(k, n) = − 1. More precisely, we show that f(k, n) = g(k, n) if n ≥ 11k − 3. Furthermore, we show that f(k, n) ≥ g(k, n) for any n ≥ 2k. Finally we show that f(k, n) > g(k, n) if 2k ≤ n ≤ 3k − 6. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 17–25, 1999     

Exact size consistency of multireference Møller–Plesset perturbation theory

Single‐reference closed‐shell Møller–Plesset perturbation theory is well known for its size consistency, a quality that is essential for consistent comparisons of calculations on molecules of different size. However, it is far from obvious whether this quality can be retained in the multireference case. In this work it is shown that an exactly size consistently generalization to multireference perturbation theory can be constructed. The central result is that the zeroth‐order Hamiltonian should be constructed using separate projection operators for each excitation level, i.e., it should contain no couplings between different excitation levels. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 549–558, 1999     

Monogenic functions and representations of nilpotent Lie groups in quantum mechanics

We describe several different representations of nilpotent step two Lie groups in spaces of monogenic Clifford‐valued functions. We are inspired by the classic representation of the Heisenberg group in the Segal–Bargmann space of holomorphic functions. Connections with quantum mechanics are described. Copyright © 1999 John Wiley & Sons, Ltd.     

Off-diagonal long-range order, η-pairing,and Friedel oscillations in high Tc cuprate superconductors and the ground state of the extended Hubbard model

It is argued that Yang's η-paired wave function is the electronic ground state of high T_c cuprate superconductors. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 675–684, 1997     

复合材料力学的Hamilton体系和辛几何方法(Ⅲ)——弯曲问题和板的振动*

把本文第一部分建立的方法用于求解各向异性板的弯曲问题和振动问题.     

Composition of composite material

On the basis of a certain theory if we can predict the composition of a specified material in engineering and we can successfully produce the very material instantly according to the theoretical results, this is what the engineering hopes in the practical application. For fulfilling this purpose, the auther had to investigate an appropriate theory and chose few materials to make composites, so that enabling the produced composite materials to be in good agreement with the object material given beforehand. In this paper the theory is presented in the three proceeding parts and the results are given in the fourth part. Theoretical calculations were worked out for the composites of the two object materials given in engineering. Composites were produced according to the computational resultes. Experiments were made and their results were satisfactory.The N. W. Institute of Nuclear Technology     

THE RELAXATIONAL OSCILLATION SOLUYION FOR FITZHUGH'S NERVE CONDUCTION EQUATION

By using the matching asymptotic method, we calculated the analytic expression of relaxational osillation sochition for Fitznugr’s nerve conduction equation, oscillation period and the parametric region in which the relaxational oscillation occurs.     

Solitary wave and similarity solutions of the combined KdV equation

In this paper, we discuss a property of solitary wave solutions of the combined KdV equation. Meantime, we point out that the combined KdV equation can be reduced to the Painlevé equation. Furthermore, utilizing special transformations of similarity variables, we derive a kind of new partial differential equations.