Construction of graphs with given circular flow numbers

Suppose r ≥ 2 is a real number. A proper r‐flow of a directed multi‐graph is a mapping such that (i) for every edge , ; (ii) for every vertex , . The circular flow number of a graph G is the least r for which an orientation of G admits a proper r‐flow. The well‐known 5‐flow conjecture is equivalent to the statement that every bridgeless graph has circular flow number at most 5. In this paper, we prove that for any rational number r between 2 and 5, there exists a graph G with circular flow number r. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 304–318, 2003     

AREA FUNCTIONS ON HARDY SPACES ASSOCIATED TO SCHRDINGER OPERATORS

In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.     

Multiobjective optimization problem with variational inequality constraints

 We study a general multiobjective optimization problem with variational inequality, equality, inequality and abstract constraints. Fritz John type necessary optimality conditions involving Mordukhovich coderivatives are derived. They lead to Kuhn-Tucker type necessary optimality conditions under additional constraint qualifications including the calmness condition, the error bound constraint qualification, the no nonzero abnormal multiplier constraint qualification, the generalized Mangasarian-Fromovitz constraint qualification, the strong regularity constraint qualification and the linear constraint qualification. We then apply these results to the multiobjective optimization problem with complementarity constraints and the multiobjective bilevel programming problem. Received: November 2000 / Accepted: October 2001 Published online: December 19, 2002 Key Words. Multiobjective optimization – Variational inequality – Complementarity constraint – Constraint qualification – Bilevel programming problem – Preference – Utility function – Subdifferential calculus – Variational principle Research of this paper was supported by NSERC and a University of Victoria Internal Research Grant Research was supported by the National Science Foundation under grants DMS-9704203 and DMS-0102496 Mathematics Subject Classification (2000): Sub49K24, 90C29     

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.     

层次分析法与人工智能相互关系的比较研究

以解决和分析宏观、复杂决策问题为主要特点的AHP方法同以解决具体、微观问题的专家系统之间有本质的联系。本文从分析和比较二者的特点出发,将不同层次的决策知识形式化地统一表示成IF-THEN型的规则,通过引入MYCIN系统中的不精确推理,来推导出所要排序的结论。这种推理与AHP中的合成算法有类似之处,但由于AHP合成时忽略了同层元素间不可避免的相关性,因而,二者在证据对结论支持的量值上略有不同。可是,在通常情况上不会导致排出次序的变化。此外,本文中所建议的方法对于准则层元素之间如果存在“与”或“或”的关系时,用推理的方法仍可求出不同的排序结果,这无疑在实际应用中具有相当的实用价值。本文所提出的方法除了保留原AHP的特点外,还对“定性推理”所需的知识获取过程有重要意义,而且,它为利用深层知识来解释浅层知识开辟了一条途径。     

A study of the density of gap states in amorphous semiconductors from thermostimulated conductivity spectra

A theoretical analysis of thermostimulated conductivity spectra _TSC(T) has been applied to determine the density of gap states g(E) in a-Si: H and a-Si: H/a-SiN _x : H multilayer structures. The results for g(E) are consistent with the results deduced from Fritzsche's analytical approach as well as other methods. A comparison has been made between the two different analytical approaches for _TSC(T). We discuss the relationship between the energy of maximum thermostimulated current emission E _m and quasi-Fermi level E _q. We demonstrate that E _q could be a better parameter than E _m in the general theoretical treatment of thermostimulated conductivity.     

Theory on the optical-phonon Raman scattering in GaAs/AlAs heterostructures

A microscopic theory of Raman scattering by optical phonons in GaAs/GaAlAs heterostructures is worked out systematically, on the basis of recent advances in our knowledge of the electronic structure and the optical-phonon modes in superlattices and quantum wells. Theories have shown that specific features of the intermediate states are of special importance for a quantitative theory. Thus, the heavy and light hole mixing effect, and the angular momentum state of the four-component excitons, can play a decisive role in determining the predominant scattering channels. Special attention has been paid to the Frolich-interaction induced scattering, which is dipole forbidden in bulk materials but allowed in multiple quantum wells owing to the barrier penetration and the hole mixing. Based on the microscopic theory, explanations are provided for such experimental facts as the asymmetry between the incoming and the outgoing resonance, the line shape of Raman spectra and the features of two-phonon Raman scattering in quantum well systems.     

GaAs／AlGaAs发光二极管列阵场分布特性的电光测量

应用一种新颖的无损伤测量技术－连续波电光检测法（ＣＷＥＯＰ）对ＧａＡｓ／ＧａＡｌＡｓ单异质结发光管列阵电场分布进行了扫描测量。实验结果反映了器件内电流注入的方向和载流子扩展情况；通过比较各单元电场分布，反映器件发光均匀性。文中详细介绍了测量原理、实验装置和实验结果及讨论，最后用计算机对电场分布作了模拟计算并与实验结果进行了对照。     

人造聚晶翡翠宝石

 综述了翡翠宝石的人工合成的进程及各种实验结果，给出了6×8MN六面顶高压装置的压力和温度工作曲线，对比了两面顶高压装置及六面顶高压装置上合成翡翠宝石的优缺点及解决办法，并做了合成高品级翡翠宝石的尝试。