ON A PAIR OF NON-ISOMETRIC ISOSPECTRAL DOMAINS WITH FRACTAL BOUNDARIES AND THE WEYL-BERRY CONJECTURE

ＯＮＡＰＡＩＲＯＦＮＯＮＩＳＯＭＥＴＲＩＣＩＳＯＳＰＥＣＴＲＡＬＤＯＭＡＩＮＳＷＩＴＨＦＲＡＣＴＡＬＢＯＵＮＤＡＲＩＥＳＡＮＤＴＨＥＷＥＹＬＢＥＲＲＹＣＯＮＪＥＣＴＵＲＥＳＬＥＥＭＡＮ，Ｂ．Ｄ．ＣＨＥＮＨＵＡＭａｎｕｓｃｒｉｐｔｒｅｃ...     

Parametric and Non Homogeneous Semi-Markov Process for HIV Control

In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed. A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct times and follow-up has an impact on the evolution of patients.      

A Generalized Unpaired Electron Spin Density Equation and Organic Hyperconjugation Mechanism

A large class of stereochemcial and related interactions in organic chemistry are repulsive and others are attractive, but the relative orientation of two methyl groups and the amount of energy required to twist one relative to the other (the hindered rotation energy barriers), or the alignment of such a group with respect to a conjugated ring to which it is attached (widely attributed to a mechanism called “hyperconjugation”) are estimated to be small in compared with the total energy of the molecule. We used theories of both isotropic and anisotropic proton hyperfine interactions in the π‐electron systems developed in the early sixties. They are approximated by the magnetic dipole nteractions between each proton and an electron spin magnetization that is distributed in 2s and 2p Slater atomic orbitals center on carbon atoms. We have extended these theories to the non‐planar olefinic cation radicals, which are very important in biochemistry as well as in petroleum catalysis. A three dimensional electron spin density equation has been developed in this paper to handle some Jahn‐Teller vibronic molecules. The new electron spin density equation related the observed proton hyperfine splittings to the non‐planar structures of the open‐chain alkene cation radicals generated by radiolysis and various chemical oxidation methods. The spin densities and the conformational calculations based on valence bond theory and symmetry principles are compared with some more elaborated molecular orbital calculations in the literature. The localized valence bond approaches are better in accord with our experimental results. The anomalous line‐width effect of the four methyl groups observed in the 2,3‐dimethyl‐2‐butene cation radicals also confirmed the positive sign of the electron‐proton hyperfine constant of hyper‐conjugation mechanism. A methyl substituent attached to a conjugated molecule often behaves as if it formed part of the region of conjugation; the charge appears to flow from the methyl group into the π electron system and it may also give rise to an appreciable dipole moment. Methylation also gives rise to an appreciable dipole moment, and the resultant red shift of electronic absorption bands is of some importance in the design of dye molecules.     

The Huber theorem for non-compact conformally flat manifolds

It was proved in 1957 by Huber that any complete surface with integrable Gauss curvature is conformally equivalent to a compact surface with a finite number of points removed. Counterexamples show that the curvature assumption must necessarily be strengthened in order to get an analogous conclusion in higher dimensions. We show in this paper that any non compact Riemannian manifold with finite -norm of the Ricci curvature satisfies Huber-type conclusions if either it is a conformal domain with volume growth controlled from above in a compact Riemannian manifold or if it is conformally flat of dimension 4 and a natural Sobolev inequality together with a mild scalar curvature decay assumption hold. We also get partial results in other dimensions. Received: April 14, 2000; revised version: March 20, 2001     

A discontinuous Galerkin method/HLLC solver for the Euler equations

This paper proposes a fully three‐dimensional non‐linear Euler methodology for solving aerodynamic and acoustic problems in the presence of strong shocks and rarefactions. It uses a discontinuous Galerkin method (DGM) within the element, and a Riemann solver (HLLC) at the boundaries to propagate rarefactions while preserving the entropy condition and capturing shocks with no spurious oscillations. This approach is thought to marry the best aspects of finite element and finite volume methods, achieving conservation while not requiring the solution of a large matrix. Examples in which shock and rarefaction waves are well captured are presented and the propagation of acoustic pulses is well demonstrated. Copyright © 2003 John Wiley & Sons, Ltd.     

氨基酸与钠离子非共价键相互作用的电喷雾质谱研究

实验研究中常常观察到钠离子与一些多肽或蛋白质有较强的非共价键结合能力,这种非共价键相互作用可能与生物的一些功能和活性有关。为了进一步了解这一结合作用,我们应用电喷雾质谱研究了常见的20种氨基酸与钠离子在溶液中的非共价键相互作用。实验研究中发现脯氨酸和苯丙胺酸与钠离子有较强的非共价键结合能力。     

尼龙66/蒙脱土复合材料结晶行为的研究

在密炼机中采用熔融共混法制备蒙脱土重量分数为 2 5 %、4 5 %的尼龙 6 6 /蒙脱土复合材料 .通过DSC法对非等温结晶行为及在 2 2 8～ 2 4 0℃范围内的等温结晶行为进行研究 ,并与纯尼龙 6 6进行比较 .从其等温和非等温结晶行为的研究表明 ,蒙脱土起成核剂的作用 ,它的填入使尼龙 6 6结晶速率提高 ,但填料与基体间的相互作用使其链段运动困难 ,结晶活化能提高 ;在研究的填料含量变化范围内 ,结晶行为变化不大 ,并且找到该复合材料在 2 2 8～ 2 34℃范围结晶对温度的不敏感区 ;对非等温结晶过程分析 ,刘结平 莫志深方程是适用的 ,而Ozawa方程则是不适用的 .     

Organophosphorus π-conjugated materials: the rise of a new field

The synthesis and electronic properties of new linear organic π-conjugated systems incorporating phosphole rings are described. Well defined α,α′-(phosphole-thiophene) oligomers possess low HOMO-LUMO gaps and their optical and electrochemical properties can be tuned via chemical modifications of the P-atoms. The physical properties of these compounds make them valuable materials for OLED’s. The coordination ability of phosphole-based dipoles has been exploited for the synthesis of efficient multipolar NLO-phores. Lastly, phospholes have been used for the synthesis of assemblies exhibiting through-bond interaction between two π-systems via P-P σ-skeletons.     

刚性微粒填充高聚物的宏观本构关系

用微观力学和统计方法研究了含损伤过程的刚性粒子填充高聚物的非线性本构关系．在材料的变形过程中，粒子与基体间界面的开裂引发微孔洞的成核与长大，这虽然弱化了材料的宏观力学性能，但是带来了宏观本构的非线性效应，这为材料的增韧奠定了基础．该文分析了刚性粒子对材料的强化作用和微孔洞演化对材料的弱化作用，以及这两种竞争机制的耦合效应对宏观本构关系的影响，并从理论上给出了界面强度，粒径分散度，平均粒径等参量对材料宏观力学行为影响的定量分析结果．     

二水草酸锌脱水的热分解动力学研究

提出一种多升温速率-等温法确定机理函数g(α)的新方法;并用迭代的等转化率法求出较为可靠的活化能Ea;在Ea和g(α)的基础上计算出指前因子A.用该法对二水草酸锌（ZnC2O4•2H2O）脱水反应的热分解动力学三因子进行了求算,得出Ea为87.22 kJ•mol－1, A为4.2120×108～7.2328×108 s－1;以及随机成核和随后生长型机理函数Am（Avrami-Erofeer）,其积分形式g(α)=[－ln(1－α)] 1/m和微分形式f(α)=m(1－α)•[－ln(1－α)](1－1/m),调节因子m=1.85～2.00.