Bounded Positive Solutions of Schrödinger Equations in Two-Dimensional Exterior Domains

We prove under quite general assumptions the existence of a bounded positive solution to the semilinear Schrödinger equation in a two-dimensional exterior domain.     

一种改进的自适应模糊阈值图象分割方法

自适应模糊阈值图象分割方法的关键和困难在于隶属函数窗宽的自动调整和阈值搜索范围的确定.依靠图象灰度的统计特性初步确定阈值搜索范围，提出了一种改进方法，进而得到隶属函数的窗宽.实验表明这种方法避免了确定图象灰度直方图峰位置的困难，对较低亮度图象分割效果良好.     

神经网络法计算镉（Ⅱ）,羟基及碳酸根三元体系的形态分布

采用前馈线笥网络ＢＰ算法，计算了Ｃｄ６２＋－ＯＨ＾－ＣＯ＾２－３三元体系的累积稳定常数。用Ｈｏｐｆｉｅｌｄ反馈网络研究了体系中络合物的形态分布。溶液中溶解的ＣＯ２对ｌｇβ１的计算结果有重要影响，对ｌｇβ２，ｌｇβ３，ｌｇβ４的结果影响不大。     

第I类非自共轭锥上的Gamma函数

本文将Ｇａｍｍａ函数及Ｓｉｅｇｅｌ积分推广到一般的第Ｉ类非自共轭锥上．作为其应用，显式给出了以这些锥为底的管状域（或第一类Ｓｉｅｇｅｌ域）的Ｃａｕｃｈｙ Ｓｚｅｇ¨ｏ核和形式Ｐｏｉｓｏｎ核．     

Gr-凝聚环的分次FP-内射维数

引进了分次FP-内射维数，对Gr-凝聚环的分次FP-内射维数作了刻划，将Stentrom等人的若干工作推广到分次环上．     

A Construction of Optimal Constant Composition Codes

In this paper, a construction of optimal constant composition codes is developed, and used to derive some series of new optimal constant composition codes meeting the upper bound given by [13].     

Effect of oxygen exposure on the magnetic properties of ultrathin Co/Ge(1 1 1) films

Influences of oxygen exposure on the magnetic properties of Co/Ge(1 1 1) ultrathin films have been investigated by surface magneto-optic Kerr effect technique. As the oxygen exposure increases on Co/Ge(1 1 1) films, their magnetic properties could be modified. As an example for 15 ML Co/Ge(1 1 1) films, the coercivity increases from 730 to 920 Oe and the remanence Kerr intensity is reduced for 500 Langmuir (L) of oxygen exposure. Corresponding compositions analyzed by Auger electron spectroscopy measurement shows that the amount of oxygen on the surface layers increases with increasing the oxygen exposure time. Oxygen distributes on the topmost layers of the film. The adsorbed oxygen influences the electronic density of states of Co and results in the changes of the magnetic properties. Besides, the appearance of O/Co/Ge interface could modify the stress anisotropy, and as a result the coercivity of ultrathin Co/Ge(1 1 1) film is enhanced.     

On potentially <Emphasis Type="Italic">H</Emphasis>-graphic sequences

For given a graph H, a graphic sequence π = (d ₁, d ₂,..., d _n) is said to be potentially H-graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially (K ₅ − e)-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to be potentially K ₅-graphic, where K _r is a complete graph on r vertices and K _r-e is a graph obtained from K _r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for a positive graphic sequence π to be potentially K ₆-graphic. Project supported by National Natural Science Foundation of China (No. 10401010).     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007