五阶势MKdV方程的一个不变性

§1Introduction Asweknow,Backlundtransformation[1-3]isaverypowerfulwayforfindingnonline evolutionequations.Inrecentdecades,Painlevéanalysis[4]hasbecomeaverypopu methodtoobtainBacklundtransformation.Inreference[5],fordevelopingthetheory Painlevéanalysis,AndrewPickeringintroduceanewexpansionvariableZwhichsatisf thefollowingRicattiSystem:Zx=1-AZ-BZ2,Zt=-C+(AC+Cx)Z-(D-BC)Z2.(1.Astheapplicationofthenewexpansionvaraible,thepotentialfifth-orderMKd equation(PMKdV5)-vxt+(vxxxxx-10k2v2…     

扩展的Boussinesq系统Lax对的Bcklund变换和递推求解公式的导出

本文研究2+1维的扩展经典Boussinesq系统。首先,研究了系统的Lax对,找出了一个形式十分新颖的带有一个任意函数的Bcklund变换。然后,又导出了Lax对的特征函数的生成公式。最后,利用Bcklund变换和Lax对特征函数生成公式相结合得出了Lax对的递推求解公式。利用此递推公式,求出了一些Lax对的解。     

Multigrid algorithms for a vertex–centered covolume method for elliptic problems

Summary. We analyze V–cycle multigrid algorithms for a class of perturbed problems whose perturbation in the bilinear form preserves the convergence properties of the multigrid algorithm of the original problem. As an application, we study the convergence of multigrid algorithms for a covolume method or a vertex–centered finite volume element method for variable coefficient elliptic problems on polygonal domains. As in standard finite element methods, the V–cycle algorithm with one pre-smoothing converges with a rate independent of the number of levels. Various types of smoothers including point or line Jacobi, and Gauss-Seidel relaxation are considered. Received August 19, 1999 / Revised version received July 10, 2000 / Published online June 7, 2001     

Electro-optic mapping systems of electric-field using CW laser diodes

Two novel systems are proposed to perform the electro-optic (EO) mapping of the electric-field strength close to electrode structure using CW laser diodes. By these systems, mappings of both static (DC) and high-frequency electric-field can be obtained. For the static field, the field is chopped to increase the sensitivity performance. For the high-frequency field, an intensity modulation laser, instead of a pulse laser, is used to perform the mapping measurement in frequency domain, instead of in time domain. This approach greatly simplifies the system. An experiment set-up using a vertical cavity surface emitted laser diode (VCSEL) of a wavelength 850 nm and its mapping results for a coplanar waveguide (CPW) with the signal frequency around 1 GHz are reported.     

Analysis of Phenylpropanolamine by Micellar Electroknetic Chromatography with Laser‐induced Fluorescence Detection

A new analytical method for phenylpropanolamine based on micellar electrokinetic chromatographic separation and laser‐induced fluorescence detection has been developed. Naphthalene‐2,3‐dicarboxaldehyde was used for precolumn derivatization of the nonfluorescent drug. Optimal separation and detection were obtained with an electrophoretic buffer of 50 mM sodium borate (pH 9.5) containing 15 mM sodium dodecyl sulfate and a He‐Cd laser (Δ_ex: 442 nm, Δ_em: 500 nm). Linearity (r ≥ 0.99) of two orders of magnitude was generally obtained and the concentration limit of detection was in the ng/mL level. Coupled with a simple cleanup procedure, the method can be applied to the analysis of phenylpropanolamine in human plasma, with a limit of detection at 15 ng/mL. Recovery of phenylpropanolamine from plasma samples was about 90%.     

SYMMETRIES AND GROUP-INVARIANT SOLUTIONS OF DIFFERENTIAL EQUATIONS

ＳＹＭＭＥＴＲＩＥＳＡＮＤＧＲＯＵＰ－ＩＮＶＡＲＩＡＮＴＳＯＬＵＴＩＯＮＳＯＦＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＴＩＡＮＣＨＯＵＡｂｓｔｒａｃｔ：Ｆｏｒａｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ，ａｔｈｅｏｒｅｔｉｃａｌｐｒｏｏｆｏｆｔｈｅｒ...     

A study of high spin states in the transitional nucleus90Mo

The reaction⁵⁸Ni(³⁶Ar, 4p)⁹⁰Mo has been studied at a beam energy of 149 MeV. A detector array consisting of the OSIRIS spectrometer (12 Compton-suppressed Ge detectors), four charged-particleδE detectors and seven NE-213 neutron detectors at the VICKSI accelerator in Berlin has been used to measure the gamma radiation inγγ- and particle-γγ-coincidence mode. An additional Ge detector was placed at 162? to the beam direction to provide information on DCO ratios. The level scheme of⁹⁰Mo has been extended up to an excitation energy of about 12 MeV and probable spin 23?. Some 70 transitions and 40 levels have been newly identified. Spin assignments have been proposed on the basis of measured DCO ratios. Shell model calculations in a model space consisting of the proton 1f _5/2, 2p _3/2, 2p _1/2, and 1g _9/2 orbits and the neutron 2p _1/2, 1g _9/2, 1g _7/2, 2d _5/2, 2d _3/2, and 3s _1/2 orbits with some truncation were made for states above 9? and the predicted structure of these states is discussed.     

Infinite products of relations, set-valued series and uniform openness of multifunctions

Using the notations of convergent series of sets and convergent products of relations, general open mapping theorems are presented which encompass classical results of Banach, Ptak, Khanh, and others.     

Theoretical investigations of the molecular conformation and reorganization energies in the organic diamines as hole‐transporting materials

Recently, organic diamine compounds have been widely used as hole‐transporting materials. In this work, DFT B3LYP method with the 6‐31G^* basis set was performed to investigate the influence of molecular conformation on the reorganization energy of a series of tetra(aryl)benzidine‐based hole‐transport materials. The results indicate that there are two types (i.e., ISB and BD/TPD) of geometric differences of the organic diamines with the relaxation processes. The reorganization energy of the ISB type is lower than that of the BD/TPD type. For the ISB type, the terminal phenyl moiety of the molecular framework plays an important role in determining the Marcus‐type reorganization energy and the central biphenyl moiety does not. A methyl group attached to a terminal phenyl can be used to tune the reorganization energy. According to the statistical analysis, four geometric parameters could affect the reorganization energy of the BD/TPD type. The conformation of either the central biphenyl or the terminal phenyl moiety of the BD/TPD type determines the Marcus‐type reorganization energy associated with the charge transport process at the molecular level. Presumably, this calculation can be employed to predict the electroluminescence (EL) character of the other organic diamines and to improve the design of new hole‐transporting materials in organic light‐emitting devices (OLEDs). Copyright © 2007 John Wiley & Sons, Ltd.