Laplacians and the Cheeger Inequality for Directed Graphs

We consider Laplacians for directed graphs and examine their eigenvalues. We introduce a notion of a circulation in a directed graph and its connection with the Rayleigh quotient. We then define a Cheeger constant and establish the Cheeger inequality for directed graphs. These relations can be used to deal with various problems that often arise in the study of non-reversible Markov chains including bounding the rate of convergence and deriving comparison theorems.Received September 8, 2004     

Quantum Dynamics of Systems Connected by a Canonical Transformation

Quantum Hamiltonian systems corresponding to classical systems related by a general canonical transformation are considered. The differential equation to find the unitary operator, which corresponds to the canonical transformation and connects quantum states of the original and transformed systems, is obtained. The propagator associated with their wave functions is found by the unitary operator. Quantum systems related by a linear canonical point transformation are analyzed. The results are tested by finding the wave functions of the under-, critical-, and over-damped harmonic oscillator from the wave functions of the harmonic oscillator, free-particle system, and negative harmonic potential system, using the unitary operator to connect them, respectively.     

用横波推导简谐波的能量

本文提出用横波推导简谐波能量的方法，并就此进行了具体时推导。     

Saddle point and generalized convex duality for multiobjective programming

In this paper we consider the dual problems for multiobjective programming with generalized convex functions. We obtain the weak duality and the strong duality. At last, we give an equivalent relationship between saddle point and efficient solution in multiobjective programming.     

Writing Fiber Grating of Different Wavelength Using the Same Phase Mask

Chirped fiber grating was used in dispersion compensator. We tried to use the same phase mask to write fiber grating of different wavelength with two methods to reduce the price of the fiber grating.     

某些类氖离子和类镍离子等离子体状态对应关系的研究

利用一维拉格朗日流体动力学程序Med103详细研究了产生类镍Ag,Cd,In,Sn, Sb离子和类氖Fe,Co,Ni,Cu,Zn离子的等离子体状态.通过对电子温度、离子丰度、离子数密度等状态参量的分析比较，得到了这两类等离子体状态之间的对应关系.即类镍银的等离子体状态与类氖铁 的相近，类镍镉的与类氖钴的相近，依次类推.利用这一对应关系可以方便地由类氖机理x射线激光的等离子体状态来对相应元素的类镍x射线激光的等离子体状态进行判断. 关键词： 类氖 类镍 等离子体状态 x射线激光     

Microwave-assisted Regioselective 1-O-Deacylation of Peracylated Glycopyranoses on Alumina

A facile, rapid and regioselective method for the 1-O-deacylation of peracylated glycopyranoses is described which occurs under mild conditions by absorption onto alumina using microwave irradiation.     

度量空间的CS-π映象

讨论了具有紧可数点星网的空间与度量空间的CS-π映象之间的关系．     

磁AB效应及其理论解释

本文介绍磁AB效应及其两种理论解释 ,进而说明经典电动力学具有局限性 ,量子力学是更高层次的物理理论     

酸糖蛋白手性柱分离6种手性化合物

通过考察缓冲液种类、浓度及其pH值对对映体在手性柱上的保留和分离行为的影响,以及流动相中加入不同种类、不同浓度的不带电荷的有机溶剂乙腈、甲醇、正丙醇、异丙醇、流动相流速和柱温对对映体分离能力的影响,优化了含碳手性中心的碱性药物苯丙哌林、酸性化合物MT-A5及MT-酸和含硫手性中心的质子泵抑制剂奥美拉唑、泮托拉唑、雷贝拉唑对映体分离条件,最佳手性分离条件为:苯丙哌林,0.05 mol/L磷酸二氢铵缓冲液(pH 3.0)-乙腈(95∶5,V/V)为流动相,流速为0.7 mL/m in,柱温为20℃;MT-A5及MT-酸,流动相为0.01 mol/L醋酸铵缓冲液(pH 5.0)-乙腈(74∶26,V/V),流速为0.9 mL/m in,柱温为20℃;泮托拉唑,流动相为10 mmol/L醋酸铵缓冲液(pH 5.5)-乙腈(93∶7,V/V),流速为0.9 mL/m in;柱温为20℃;奥美拉唑和雷贝拉唑,流动相为0.01 mol/L醋酸铵缓冲液(pH 3.0)-乙腈(95∶5,V/V),流速为0.7 mL/m in,柱温为20℃。实现了应用高效液相色谱法在α1-酸糖蛋白手性柱上对上述化合物的对映体分离,并成功用于手性药物合成中的对映体过量百分率的测定。