Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional

We study the generalization of the Willmore functional for surfaces in the three-dimensional Heisenberg group. Its construction is based on the spectral theory of the Dirac operator entering into theWeierstrass representation of surfaces in this group. Using the surfaces of revolution we demonstrate that the generalization resembles the Willmore functional for the surfaces in the Euclidean space in many geometrical aspects. We also observe the relation of these functionals to the isoperimetric problem.     

Ab-initio simulation of elastic constants for some ceramic materials

Athermal elasticity for some ceramic materials (α-Al₂O₃, SiC (α and β phases), TiO₂ (rutile and anatase), hexagonal AlN and TiB₂, cubic BN and CaF₂, and monoclinic ZrO₂) have been investigated via density functional theory. Energy-volume equation-of-state computations to obtain the zero pressure equilibrium volume and bulk modulus as well as computations of the full elastic constant tensor of these ceramics at the experimental zero pressure volume have been performed. The present results for the single crystal elasticity are in good agreement with experiments both for the aggregate properties (bulk and shear modulus) and the elastic anisotropy. In contrast, a considerable discrepancy for the zero pressure bulk modulus of some ceramics evaluated from the energy-volume fit to the computational zero pressure volume has been observed.     

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.     

2+1维SU(2)格点规范场胶球质量的七阶RPA近似

采用无规相近似(RPA)方法,用空心图作为试探波函数,利用Feymann?Hellman定理计算七阶2?+?1维SU(2?)格点规范场的胶球质量,在弱耦合区1/g2?=1.0?–?1.8胶球质量表现出良好的标度行为,基本趋于常数(m/e2?≈1.2?0±0?.0?1)?.     

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     

Solitary wave solutions of nonlinear financial markets :data-modeling-concept-practicing

This paper seeks to solve the difficult nonlinear problem in financial markets on the complex system theory and the nonlinear dynamics principle, with the data-model-concept-practice issue-oriented reconstruction of the phase space by the high frequency trade data. In theory, we have achieved the differentiable manifold geometry configuration, discovered the Yang-Mills functional in financial markets, obtained a meaningful conserved quantity through corresponding space-time non-Abel localization gauge symmetry transformation, and derived the financial solitons, which shows that there is a strict symmetry between manifold fiber bundle and guage field in financial markets. In practical applications of financial markets, we have repeatedly carried out experimental tests in a fluctuant evolvement, directly simulating and validating the existence of solitons by researching the price fluctuations (society phenomena) using the same methods and criterion as in natural science and in actual trade to test the stock Guangzhou Proprietary and the futures Fuel Oil in China. The results demonstrate that the financial solitons discovered indicates that there is a kind of new substance and form of energy existing in financial trade markets, which likely indicates a new science paradigm in the economy and society domains beyond physics.