Banach空间中超线性Hammerstein型积分方程的解及其应用

本文利用不动点指数理论研究Ｂａｎａｃｈ空间中超线性Ｈａｍｍｅｒｓｔｅｉｎ型积分方程正解及非零解的存在性，并应用于Ｂａｎａｃｈ空间中超线性常微分方程的Ｓｔｕｒｍ－Ｌｉｏｕｖｉｌｌｅ问题，最后，本文给出了一个非线性常微分方程无穷组存在正解的例子．     

Formation of Cs molecules via Feshbach resonances stabilized by spontaneous emission: theoretical treatment with the Fourier grid method

This paper proposes a general method to investigate Feshbach resonances in atomic collisions similar to Cs(6 s ) + Cs(6 p ) in the thermal or cold regime. In order to compute the predissociation widths of the C ¹ Π _u (6 s + 5 d ) bound vibrational levels of Cs₂, coupled both with the (2) ³ Σ ⁺ _u (6 s + 6 p ) continuum and with the (2) ³ Π _u (6 s + 5 d ) vibrational series, a Fourier grid method is implemented, with an optical potential. A convenient way of optimizing the latter is proposed. A large number of resonances are found and calculations of their cross-sections for stabilization into ground state molecules show that the rate may be important. This confirms the interpretation of Lintz and Bouchiat [Phys. Rev. Lett. 80, 2570 (1998)] who observed dimer formation in cell experiments. Possible generalization to the cold regime relies on the possibility to tune the position of a resonance to coincide with the maximum of the collisional energy distribution. Received 14 February 2002 Published online 28 June 2002     

蜕化抛物型方程广义解的界性

解的有界性为探讨解的正则性所必需。本文在很一般的结构条件下证明下面方程(1)的广义解的有界性,并对(1)的一种特殊情形作出广义解最大模的光验估计。这是椭圆型方程相应结果的推广。设G为n维欧氏空间E~n的有界区     

Solution of shallow water equations for complex flow domains via boundary-fitted co-ordinates

Many problems of applied oceanography and environmental science demand the solution of the momentum, mass and energy equations on physical domains having curving coastlines. Finite-difference calculations representing the boundary as a step function may give inaccurate results near the coastline where simulation results are of greatest interest for numerous applications. This suggests the use of methods which are capable of handling the problem of boundary curvature. This paper presents computational results for the shallow water equations on a circular ring of constant depth, employing the concept of boundary fitted grids (BFG) for an accurate representation of the boundary. All calculations are performed on a rectangle in the transformed plane using a mesh with square grid spacing. Comparisons of the simulations of transient normal mode oscillations and analytic solutions are shown, demonstrating that this technique yields accurate results in situations (provided that there is a reasonable choice of grid) involving a curved boundary. The software developed allows application to any two-dimensional area, regardless of the complexity of the geometry. Simulation runs were made with two co-ordinate systems. For the first system, the grid point distribution was obtained from polar co-ordinates. For the second one, grid point positions were calculated numerically, solving Poisson's equation. It was found that small variations in the metric coefficients do not deteriorate the accuracy of the simulation results. Moreover, comparisons of surface elevation and velocity components at grid points near the inner and outer radii obtained from an x?y Cartesian grid model with the BFG simulation were made. The former model produced inacccuracies at grid points near boundaries, and, owing to the large number of mesh points used to yield the necessary fine resolution, the computation time was found to be a factor of three higher.     

Low energy excitations of a quasi-2D Bose-Einstein condensate

Starting from the Gross-Pitaevskii energy functional of the 3D Bose-Einstein Condensate, we derive approximately the energy functional and the effective coupling constant of the quasi-2D condensate. The evolution of the quasi-2D condensate wave function is studied by a variational method. Low energy excitation spectra for both positive and negative scattering lengths are analyzed. The condition of collapse instability of a quasi-2D Bose gas with attractive particle interaction is also proposed. Received 31 October 2001 / Received in final form 1st March 2002 Published online 28 June 2002     

A COMPARATIVE STUDY OF CHAIN DYNAMICS OF DI-AND TRI-BLOCK COPOLYMERS IN SEMIDILUTE SOLUTION IN A NON-SELECTIVE SOLVENT

The chain dynamics of a pair of diblock poly(styrene-b-butadiene) (PS210-b-PB960) and triblock poly(styrene-b-butadiene-b-styrene) (PS200-b-PB1815-b-PS200) copolymers in both dilute and semidilute toluene solutions has been comparatively studied by dynamic laser light scattering. As expected, the mutual diffusion of individual chain changes into a fast cooperative diffusion of the chain segments (“blobs“) between two neighboring entanglement points for both the copolymers as the solution changes from dilute to semidilute. Further increases of the concentration lead to a second slow relaxation mode. For the triblock chains, there exists an additional middle relaxation between the fast and the slow modes.with 0.33 ＜α＜ 0.44, much smaller than 0.75 predicted or 0.72 observed for linear homopolymer chains in good solvent. It implies that the solvent quality of toluene for PB might not be as good as that for PS. Due to such a difference in solubility, it is reasonable to speculate that the PB and PS blocks are transiently segregated in semidilute solution. The relaxation of these transient PB and PS richer domains leads to the observed slow relaxation. Such a speculation is supported by the appearance of an additional slow relaxation mode in the study of polyisoprene-b-polystyrene-b-polyisoprene in semidilute solution in cyclohexane, a non-selective solvent, in which we alternated the solubility difference by a variation of the solution temperature.     

Spectrochemical Properties of Noncubical Transition Metal Complexes in Solutions. XV. Solution Properties of bis(Salicylideneaniline)Copper(II)

The complex obtained by condensation of salicylideneaniline with copper(II) acetate was studied in a variety of solvents. This deep-brown crystalline compound is soluble in common solvents, such as, chloroform, toluene, dioxane, methanol, ethanol, dimethyl formamide, dimethyl sulfoxide, and acetonitrile—a necessary condition for observing solvatochromism. The complex has been characterized by elemental analysis, molar conductivity, EPR, and ultraviolet (UV) and visible (VIS) spectroscopy. The available X-ray data shows planar coordination geometry for the copper center. Combined multi-technique experiments have been applied to confirm the structure of the complex in solution. The molar conductivities indicate nonelectrolytic properties. EPR measurements preclude the possibility of solvent coordination at the axial positions of the complex. Spectroscopic measurements were used to study the coordination properties of donor atoms and their bonding ability, as well as trichromaticity coordinate calculations. The results obtained show that the interactions of metal with donors depend on donor strength and polarity of solvent.     

Pressure dependence of the demixing of polymer solutions determined by viscometry

Summary From the break-down in the viscosity of a polymer solution, associated with the entrance into the two phase region, the pressure dependence of the demixing temperatures of solutions of polystyrene (M = 600.000) in cyclohexane, cyclopentane, diethylmalonate and 1-phenyldecane was measured up to 1000 bar. The application of pressure increases the solubility of polystyrene in cyclopentane and diethylmalonate, but decreases that in 1-phenyldecane; in the case of cyclohexane, a pressure of optimum miscibility is observed at ca. 120 bar.The discussion of these findings, together with further information from the literature, demonstrates that current theories cannot even predict the pressure influences qualitatively. For an easy forecast of the effects, the distance of the (upper) critical solution temperature,T _c from the melting point of the solvent,T _MP, can, however, serve as a guideline: From the present material it can be concluded thatT _c is increased by pressure if (T —T _MP)/T _MP (K/K) is less than 0,20 but decreased it if it exceeds 0,25.Dedicated to Prof. Dr. K. Ueberreiter in honor of his 70th birthday.     

Structural effects in low temperature radioluminescence of aqueous ionic systems

Structural effects in the radioluminescence spectra of glassy and polycrystalline aqueous solutions of chloride and alkaline ices observed by pulse radiolysis at temperatures 6–110 K are reported. The luminescence efficiency as well as position of λ_max of the emission spectra are dependent on the physical state and temperature of the matrix. For all the investigated aqueous polycrystalline matrices and for H₂O ice, the emission band peaking at about 330 nm, assigned to OH*A²Σ→X²Π transition appears at temperatures below 40 K. This UV band was not observed for glassy matrices. Luminescence bands observable in the visible range of spectrum (400–600 nm) can be associated with the emission of (OH⁻)*, the radiative capture of trapped electrons e⁻_t by metal cations Me⁺(Me²⁺) and trapped atoms H√_t. For polycrystalline chloride matrices a contribution of the emission of (Cl²⁻₂)* must be taken into account.     

Reporting Molar Refractions

It has become common practice to report the deviation of molar refraction from a volume fraction average of the molar refractions of the components for binary liquid mixtures in anticipation of assessing intermolecular electronic interactions. It is demonstrated here that this method does not yield information about such interactions but, in effect, reveals information almost exclusively related to the difference between volume fraction and mole fraction. The deviation of molar refraction from a mole fraction average of the refractions of the components, i.e., the excess molar refraction, provides the proper basis for assessing intermolecular electronic interactions.