Finite-gap Solutions of the Fuchsian Equations

We find a new class of Fuchsian equations, with algebro-geometric solutions associated to a hyperelliptic curve. A method for calculating its arithmetic genus and branching points is suggested. Numerous examples are given.     

Coulomb blockade in molecular quantum dots

The rate-equation approach is used to describe sequential tunneling through a molecular junction in the Coulomb blockade regime. Such device is composed of molecular quantum dot (with discrete energy levels) coupled with two metallic electrodes via potential barriers. Based on this model, we calculate nonlinear transport characteristics (conductance-voltage and current-voltage dependences) and compare them with the results obtained within a self-consistent field approach. It is shown that the shape of transport characteristics is determined by the combined effect of the electronic structure of molecular quantum dots and by the Coulomb blockade. In particular, the following phenomena are discussed in detail: the suppression of the current at higher voltages, the charging-induced rectification effect, the charging-generated changes of conductance gap and the temperature-induced as well as broadening-generated smoothing of current steps.     

Stabilization of linear systems by rotation

We introduce the concept of “stabilization by rotation” for deterministic linear systems with negative trace. This concept encompasses the well-known concept of “vibrational stabilization” introduced by Meerkov in the 1970s and is a deterministic version of ‘stabilization by noise’ for stochastic systems as introduced by Arnold and coworkers in the 1980s. It is shown that a linear system with negative trace can be stabilized by adding a skew-symmetric matrix, multiplied by a suitable scalar so-called “gain function” (possibly a constant) which is sufficiently large. To overcome the problem of what is “sufficiently large”, we also present a servo mechanism which tunes the gain function by learning from the trajectory until finally the trajectory tends to zero. This approach allows to show that one of Meerkov's assumptions for vibrational stabilization is superfluous. Moreover, while Meerkov as well as Arnold and coworkers assume that a stabilizing periodic function or the noise has sufficiently large frequency and amplitude, we also provide a servo mechanism to determine this function dynamically in a deterministic setup.     

Chain length effect on dynamical structure of poly (vinyl pyrrolidone)-polar solvent mixtures in dilute solution of dioxane studied by microwave dielectric relaxation measurement

Dielectric relaxation study of the binary mixtures of poly(vinyl pyrrolidone) (PVP) (Mw=24000, 40000 and 360000 g mol⁻¹) with ethyl alcohol (EA) and poly(ethylene glycol)s (PEGs) (Mw=200 and 400 g mol⁻¹) in dilute solutions of dioxane were carried out at 10.1 GHz and 35°C. The relaxation time of PVP-EA mixtures was interpreted by the consideration of a wait-and-switch model in the local structure of self-associated ethyl alcohol molecules and also the PVP chain length as a geometric constraint for the reorientational motion of ethyl alcohol molecules. The formation of complexes and effect of PVP chain length on the molecular dynamics, chain flexibility and stretching of PEG molecules in PVP-PEG mixtures were explored from the comparative values of dielectric relaxation time. Further, relaxation time values in dioxane and benzene solvent confirm the viscosity independent molecular dynamics in PVP-EA mixtures but the values vary significantly with the non-polar solvent environment.     

Combinatorial computational chemistry approach of tight-binding quantum chemical molecular dynamics method to the design of the automotive catalysts

Recently, we have developed a new tight-binding quantum chemical molecular dynamics program “Colors” for combinatorial computational chemistry approach. This methodology is based on our original tight-binding approximation and realized over 5000 times acceleration compared to the conventional first-principles molecular dynamics method. In the present study, we applied our new program to the simulations on various realistic large-scale models of the automotive three-way catalysts, ultrafine Pt particle/CeO₂(111) support. Significant electron transfer from the Pt particle to the CeO₂(111) surface was observed and it was found to strongly depend on the size of the Pt particle. Furthermore, our simulation results suggest that the reduction of the Ce atom due to the electron transfer from the Pt particle to the CeO₂ surface is a main reason for the strong interaction of the Pt particle and CeO₂(111) support.     

Supramolecular chemistry

The article discusses molecular recognition and overviews the key concepts -storage and retrieval of chemical information by molecular structures, supramolecular reagents and catalysts, molecular transport, semiochemistry and self assembly. The prospects of controlling supramolecular architecture through engineered molecular recognition and design of ‘programmed systems’ controlled by molecular information are also discussed.     

吡啶团簇的多光子电离和离解研究

利用飞秒激光和飞行时间质谱结合从头计算对吡啶团簇的多光子电离和离解进行了研究. 给出了吡啶团簇的稳定结构和簇内的质子转移过程.     

Anharmonic effects in large-amplitude vibrations of metal clusters

Two types of extreme collective motion, large-amplitude many-phonon vibration of the ionic core and rotation of the cluster with high angular momenta, are considered. The interplay between vibration and collective motion towards fission is discussed. A new mechanism of formation and rupture of the neck is proposed which is based on the Franck-Condon principle, and accounts for the interplay between vibration and fission. Under rotation, the change of the shape of the cluster and a phase transition from axially symmetric to triaxial ellipsoid are predicted. For studying the effects, vibrational motion can be induced by laser radiation. Rotational motion may arise in collisions of clusters. Received 26 April 2001 and Received in final form 15 October 2001     

Multivalued differential equations on closed convex sets in Banach spaces

New derivation results for integrands and multifunctions via the Lipschitzean approximations are obtained. Applications to multivalued differential equations on closed convex sets are presented.     

外来的捕食物种对濒危物种的影响

In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke comparison theorem and some results in Cui and Chen‘s paper (1998), some sufficient conditions that guarantee the permanence of the species and global stability of a unique positive periodic solution are obtained. Biological implication of these results are discussed.