Applications of density functional theory methods in millimeter‐wave spectroscopy

Density functional theory (DFT), using the most common functionals, and ab initio quantum chemistry methods are used to calculate the rotational constants and dipole moments of the astrophysically important molecules HCN, CH₃CN, CH₃CNH⁺, HCCCN, and HCCNC. As far as millimeter‐wave spectroscopy is of interest the DFT methods performed well with most functionals, giving results within ±1% of experiments for rotational constants and ±3% for dipole moments. Analyzing the results obtained with all theoretical models, it may be concluded that the Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP) and Becke's three‐parameter functional with Perdew–Wang correlational functional [B3PW91/6‐31G(d, p)] give the best performances. A detailed analysis of the electron correlation effects shows that HCCCN is more stable than is HCCNC, by 1.16 eV, with important contribution arising from triple excitations. This result is also compared with those obtained with DFT methods. Despite occasional difficulties, DFT with the currently available functionals are of great utility in quickly assessing spectroscopic parameters of astrophysical interest. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Controllability of Functional Integro-Differential Inclusions with an Unbounded Delay

In this paper, a sufficient condition is established for the controllability of neutral functional integro-differential inclusions with an unbounded delay in Banach spaces. The approach used is a fixed-point theorem for condensing maps due to Martelli and the theory of analytic semigroup of linear operators. Communicated by F. Zirilli Research supported by NNSF of China, by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China, and by the Qing Lan Talent Engineering Fund QL-05-164 of Lanzhou Jiaotong University. The authors are grateful to Professor F. Zirilli and two anonymous referees for valuable suggestions improving this paper.     

On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation

A multidimensional version of the first Darboux problem is considered for a model second-order degenerating hyperbolic equation. Using the technique of functional spaces with a negative norm, the correct formulation of this problem in the Sobolev weighted space is proved.     

Asymptotic properties of an HIV/AIDS model with a time delay

A mathematical model for HIV/AIDS with explicit incubation period is presented as a system of discrete time delay differential equations and its important mathematical features are analysed. The disease-free and endemic equilibria are found and their local stability investigated. We use the Lyapunov functional approach to show the global stability of the endemic equilibrium. Qualitative analysis of the model including positivity and boundedness of solutions, and persistence are also presented. The HIV/AIDS model is numerically analysed to asses the effects of incubation period on the dynamics of HIV/AIDS and the demographic impact of the epidemic using the demographic and epidemiological parameters for Zimbabwe.     

草酰胺分子构型、稳定性、IR光谱及分子轨道的密度泛函与从头算研究

运用多种密度泛函理论 (DFT)和从头算 (abinitio)方法研究了草酰胺顺、反异构体的分子几何构型 ,结果表明Beck88交换函数与LYP非局域相关函数形成杂化的DFT方法B3LYP与MP2方法计算结果比较吻合。在此基础上选择B3LYP方法对草酰胺分子电子结构、红外光谱和前线分子轨道组成进行了系统研究 ;与实验事实对比分析了气态草酰胺分子中配位原子的反应活性     

Quantitative theory of living free‐radical polymerization. III. Calculation of copolymerization products' spinodal

The problem of finding conditions of the loss of thermodynamic stability by the reaction system was solved on the basis of the developed theory of living free‐radical copolymerization. The spinodal's calculations were carried out for a significant number of systems differing in the values of kinetic, stoichiometric, and thermodynamic parameters. Analysis of the results of such calculations revealed some regularities in the spinodal curves' behavior and permitted us to classify their possible topological types. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 892–902, 2003     

复制缺陷型人泡沫病毒载体辅助质粒pΔGP的构建及转染小肠癌细胞的研究

在人泡沫病毒原病毒全长克隆pHRSV13的基础上,缺失突变gag和pol基因,并且用SV40polyA加尾信号替代人泡沫病毒的3′LTR,构建辅助质粒pΔGP.将复制缺陷型人泡沫病毒载体质粒pGPSNI EGFP和辅助质粒pΔGP分别转染和共转染小肠癌HIC细胞系,荧光显微镜检测发现共转染pGPSNI EGFP和pΔGP的HIC细胞能够强烈表达绿色荧光蛋白,转染有复制缺陷型人泡沫病毒载体质粒pGPSNI EGFP的HIC细胞能够表达少量的绿色荧光蛋白,而转染有辅助载体pΔGP的HIC细胞不表达绿色荧光.结果证明复制缺陷型人泡沫病毒载体的构建成功,表明人泡沫病毒env基因3′端的内部启动子IP具有弱启动子的活性,并且bel基因产生的调控蛋白能够反式激活人泡沫病毒内部启动子IP和5′LTR的启动子.     

Stability of solutions to the Cauchy problem for a plane hyperbolic system with time-periodic coefficients

Considering a plane hyperbolic system with time-periodic coefficients, we construct a version of the direct Lyapunov method with the condition on the derivative of the Lyapunov functional along the trajectories of the system which is weakened by use of periodicity of the coefficients. We exhibit an illustrative example.     

Circadian synchrony in networks of protein rhythm driven neurons

The interaction between gene activation and cellular activity has recently emerged as a critical aspect of brain behavior, but the dynamics of networks incorporating these interactions are poorly understood. An interesting phenomena arises when the genetic activation oscillates endogenously and a network of such cells synchronize to a coherent rhythm, such as is the case with the suprachiasmatic nucleus. To explain this synchronization, we propose a model in which a mRNA/protein expression cycle drives neurons electrical activity, and synaptic activation shifts the phase of the protein rhythm. Using lattice networks, we demonstrate that these interactions are sufficient to generate coherent oscillation. © 2006 Wiley Periodicals, Inc. Complexity 12: 67–72, 2006