A Quantum Homogeneous Space of Nilpotent Matrices

A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum quasi- homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known quantum homogeneous spaces are revisited.     

Spin–orbit coupling in bulk GaAs

We study the spin–orbit coupling in the whole Brillouin zone for GaAs using both the sp³s^*d⁵ and sp³s^* nearest-neighbor tight-binding models. In the Γ-valley, the spin splitting obtained is in good agreement with experimental data. We then further explicitly present the coefficients of the spin splitting in GaAs L- and X-valleys. These results are important to the realization of spintronic device and the investigation of spin dynamics far away from equilibrium.     

MULTIPLICITY OF PERIODIC SOLUTIONS OF DUFFING’S EQUATIONS WITH LIPSCHITZIAN CONDITION

This paper deals with the existence and multiplicity of periodic solutions of Duffing equations . The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided thatg(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.     

Time periodic solutions of a class of degenerate parabolic equations

1.IntroductionManypapershavebeendevotedtotheexistenceoftimeperiodicsolutionsforsemilinearparabolicequations,see[1--8].Atthesametime,thestudyofquasilinearperiodic-parabolicequationsalsoattractedmanyauthors,seealso[9--141.Inparticular,recentlyHess,PozioandTesei[13]usedthemonotonicitymethodstodealwiththeequationsonot=aam a(x,t)u,wherem>1andaisafunctionperiodicint,andMizoguchi[lllappliedtheLeray-Schauderdegreetheorytoinvestigatetheequationswithsuperlinearforcingtermwherem>1,hisapositiveperiodicf…     

相对映射的周期点

相对Nielsen周期点理论是讨论形如f:(X,A)→(X,A)映射的周期点个数估计问题,本文对已知的估计量给予统一的处理.利用这种方法,定义了两个新的Nielsen型数, NPn(f;X-A)和NΦn(f;X-A),它们分别是映射f在cl(X-A)中的n周期点和最小周期为n的周期点个数的下界.     

Periodic crystallisation of magnesium hydroxide in agar-agar gel. Influence of temperature

The influence of temperature on periodic crystallisation of magnesium hydroxide in agar-agar gel has been studied. The increase in velocity constant with temperature is attributed to the increase in the diffusion constant with temperature. The activation energy for diffusion of aqueous ammonia is calculated from the temperature — velocity constant correlation. The solubility of Mg(OH)₂ decreases with temperature. The decrease in the spacing coefficient and fiocculation value of Mg(OH)₂ with temperature is also explained because of the increase in temperature. Matalon and Packter’s equation correlating the spacing coefficient and concentration of the inner electrolyte is suitably modified to satisfy the temperature dependence of the spacing coefficient.     

A nonparametric procedure to detect periods in time series

Suppose that for a given time series the experimenter knows that it has a certain periodic property and that he wishes to find out the length of the period. For this problem a nonparametric procedure is proposed. It consists of a new smoothing technique based on Kendall's Tau and a specific counting method. The procedure is studied under a simple model of periodic time series which are composed of periodic (deterministic) functions, a linear trend and exchangeable (stochastic) sequences. The performance of the procedure is illustrated by a simple example.     

Suboptimal feedback control of linear periodic systems

A method is developed for the approximate design of an optimal state regulator for a linear periodically varying system with quadratic performance index. The periodic term is taken to be a perturbation to the system. By making use of a power-series expansion in a small parameter, associated with periodic terms, a set of matrix equations is derived for determining successively a feedback gain. Given periodic terms of a Fourier-series form, explicit solutions are obtained for those matrix equations. A sufficient condition for existence and periodicity of the solution is also shown. Further, the performance degradation resulting from a truncation of the power-series solution is investigated. The method may effectively be used in a computer-programmed computation.     

Invariant distributions supported on the nilpotent cone of a semisimple Lie algebra

Let be a semisimple complex Lie algebra with adjoint group and be the algebra of differential operators with polynomial coefficients on . If is a real form of , we give the decomposition of the semisimple -module of invariant distributions on supported on the nilpotent cone.