一类具无穷时滞泛函微分方程的周期解

讨论具有无穷时滞中立型泛函微分方程$ \frac{\rm d}{{\rm d}t}\left(x(t)-\int_{-\infty}^{0}g(s,x(t+s)){\rm d}s\right) =A(t,x(t))x(t)+f(t,x_t)$的周期解问题,利用重合度理论中的延拓定理得到了周期解的存在性和唯一性条件;特别地,当$g(s,x)\equiv 0, A(t,x)=A(t)$时, 给出了存在唯一稳定周期解的条件.     

Lefschetz Formulae for p-Adic Groups

In this paper,Lefschetz formulae for torus actions on p-adic groups are proven. These are similar to comparable formulae for real Lie groups.Applications lie in the realm of dynamical zeta functions.     

p-Laplace方程正解的存在性和多重性

这篇文章讨论边值问题-(| u′|p-2u′)′=λf(t ,u) ,t∈(0,1) ,p >1,u(0) =u(1) =0,其中f(t ,u)≥-M( M是正常数) ,对(t ,u)∈0,1×0,∞) .我们利用度理论和锥上的不动点定理得到方程存在两个正解.     

Topological order in the phase diagram for high-temperature superconductors with point defects

Applying a Lindemann like criterion obtained previously by Kierfeld et al. [J. Kierfeld, T. Nattermann, T. Hwa, Phys. Rev. B 55 (1997) 626], we estimate the magnetic field and temperature for a high-T_c superconductor, at which a topologically ordered vortex glass phase becomes unstable with respect to a disorder-induced formation of dislocations. The employed criterion is shown to be equivalent to a conventional phenomenological Lindemann criterion including the values for the numerical factors, i.e., for the Lindemann number. The positional correlation length of the topologically ordered vortex glass is calculated.     

Zur Theorie der Chiralitätsfunktionen

The Algebraic Theory of Chirality Functions is derived by means of exclusively qualitative considerations. Hence, the significance of quantitative results is questionable. Moreover the construction of “Näherungsansätze” (”Approximation-Ansatz”), which may be interpreted as semiempirical methods, is achieved on the basis of plausibility and mathematical simplicity. Since physical arguments are not included, the consistency or inconsistency of “Näherungsansätze” with experimental results do not justify direct physical conclusions.     

Optimum gas chromatographic conditions in wall-coated capillary columns. Extended and simplified forms of the Golay-equation

Band broadening in capillary columns is satisfactorily described by the Golay-equation extended to situations of appreciable pressure drop by Giddings. In practice, however, several simplifications are often made. The effect of these simplifications on the calculated values of the minimum plate height and optimum carrier gas velocity are treated systematically.     

氯化1-乙基-3-甲基烷基咪唑分子结构及其氢键作用能的密度泛函研究

采用量子化学密度范函方法计算研究了氯化1-乙基-3-甲基咪唑盐（[EMIM]C1）正负离子间相互作用的平衡构型和Cl^-离子从不同方位与咪唑阳离子的结合能．计算发现Cl^-可在咪唑环平面上结合形成离子键，其结合能为．368．97kJ／mol，还可与环上的三个H原子形成氢键，其氢键键长和结合能分别为0．2000nm／-378．03kJ／mol、0．2339nm／-344，69kJ／mol和0．2301nm／-346，01kJ／mol．结合能包括氢键作用能和正负离子的静电作用能，后者为主要贡献．从理论上展示了该离子液体的氢键结构．     

Computation of equilibrium oxidation and reduction potentials for reversible and dissociative electron-transfer reactions in solution

Equilibrium free-energy cycles relating oxidation and reduction potentials in solution to ionization potentials and electron affinities in the gas phase are constructed and the utilities of various levels of theory for computing particular free-energy changes within these cycles are discussed within the context of several examples. Emphasis is placed on the use of quantum-mechanical continuum solvation models to compute free energies of solvation. Key systems discussed include quinones, substituted anilines, substituted phenols, and reductive dechlorination reactions.Dedicated to Prof. Jean-Louis Rivail, whose pioneering efforts in developing and exploiting continuum solvent models were critical in making quantum chemistry more applicable to solution phenomenaProceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Changes in peak width and concentration at the inlet and outlet of a chromatographic column

The original plate model of chromatography is extended to the sorption process occurring at the column inlet and the desorption process at the column exit. At the column inlet it is shown that sufficiently wide feed bands undergo no change in concentration but a fall in band width, i.e., the volume of mobile phase occupied by the solute band is reduced. The reduction factor is (1 + k) where k is the mass distribution ratio (capacity factor). Narrower bands suffer partial reduction in both band width and concentration. On desorption at the outlet, however, the change is always in band width and not concentration. A perfect detector registers the true concentration-time profile of the band in the column if the solute mass fraction in the stationary phase is below 10^?3 at the column outlet. The risks of stripping the stationary phase at high solute concentrations in analytical and preparative or production gas chromatography are compared.