Recurrence relations for semilocal convergence of a Newton-like method in Banach spaces

The aim of this paper is to establish the semilocal convergence of a multipoint third order Newton-like method for solving F(x)=0 in Banach spaces by using recurrence relations. The convergence of this method is studied under the assumption that the second Fréchet derivative of F satisfies Hölder continuity condition. This continuity condition is milder than the usual Lipschitz continuity condition. A new family of recurrence relations are defined based on the two new constants which depend on the operator F. These recurrence relations give a priori error bounds for the method. Two numerical examples are worked out to demonstrate the applicability of the method in cases where the Lipschitz continuity condition over second derivative of F fails but Hölder continuity condition holds.     

Modelling the Recurrence of Bladder Cancer

The risk of a new tumor recurrence after transurethral resection (surgical operation) in patients with primary superficial bladder carcinoma is evaluated. As the exact time of the event is not known, it is suggested to consider interval-censored survival data methodology. We use the model of Farrington to perform a prognostic model for predicting a new recurrence and to determine the clinicopathologic factors associated within interval-censored data framework. The implementation of this method is easy using standard statistical packages. Anyway, we use diagnostic methods for the validation of the model developed by the same author for interval-censored data. The obtained model is easily interpretable and let us to individualize the course of follow-up and treatment of each patient in order to improve the patient’s quality of life.      

A REMARK ON EXTINCTION OF A CLASS OF SUPERPROCESSES

1.IntroductionSuperprocesses,i.e.,measure-vauedMarkovprocesses,havebeenanattractivetopicintherecenty6ars,whichcanbedefinedasfollows.Let((,Px)..MbeaMarkovprocesswithstrongcontinuousMarkovsemigroupSt(denotebyAitsinfinitesimaloperator,andbyPt(x,y)theassociatedtransitiollfunction).DenotebyMPthesetofallRadonmeasurespsatisfyingandbypC(t)(resp.pCc(t))thesetofpositivelycontinuousfUnctions(resp.withcompactsupport)int-Thesthcalledsuperprocess(X,P#).6MPwithparameters(andopandtakingvalueinMrisdete…     

消荧光现象与表面谐波产生

消荧光现象是激光与物质表面非线性相互作用的结果，这是一种普遍现象。在表面谐波产生的研究中，它常常被忽略。大量研究表明：表面谐波产生与消荧光现象，有着密切的内在联系。本文以消荧光观点详细讨论了表面谐波产生的机制，提出了表面谐波产生的消荧光模型。新机制可归纳为：（ａ）多光子受激吸收产生消荧光光斑，（ｂ）激光热效应等促进自发辐射转向准受激辐射，（ｃ）伴随荧光消失，部分产生荧光的激光能量转换为产生表面谐波     

Recurrence time statistics in chaotic dynamics. I. Discrete time maps

The dynamics of transitions between the cells of a finite-phase-space partition in a variety of systems giving rise to chaotic behavior is analyzed, with special emphasis on the statistics of recurrence times. In the case of one-dimensional piecewise Markow maps the recurrence problem is cast into a-renewal process. In the presence of intermittency, transitions between cells define a non-Markovian, non-renewal process reflected in the presence of power-law probability distributions and of divergent variances and mean values.     

Stochastic systems with cross-correlated Gaussian white noises

This paper theoretically investigates three stochastic systems with cross-correlation Gaussian white noises.Both steady state properties of the stochastic nonlinear systems and the nonequilibrium transitions induced by the cross-correlated noises are studied.The stationary solutions of the Fokker-Planck equation for three specific examples are analysed.It is shown explicitly that the cross-correlation of white noises can induce nonequilibrium transitions.     

Phase diagram and tricritical behavior of an metamagnet in uniform and random fields

A two-sublattice Ising metamagnet in both uniform and random fields is studied within the mean-field approach based on Bogoliubov’s inequality for the Gibbs free energy. We show that the qualitative features of the phase diagrams are dependent on the parameters of the model and the uniform field values. The tricritical point and reentrant phenomenon can be observed on the phase diagram. The reentrance is due to the competition between uniform and random interactions.     

Easy axis reorientation and magneto-crystalline anisotropic resistance of tensile strained (Ga,Mn)As films

We present a study of magnetic anisotropy by using magneto-transport and direct magnetization measurements on tensile strained (Ga,Mn)As films. The magnetic easy axis of the films is in-plane at low temperatures, while the easy axis flips to out-of-plane when temperature is raised or hole concentration is increased. This easy axis reorientation is explained qualitatively in a simple physical picture by Zener’s p-d model. In addition, the magneto-crystalline anisotropic resistance was also investigated experimentally and theoretically based on the single magnetic domain model. The dependence of sheet resistance on the angle between the magnetic field and [1 0 0] direction was measured. It is found that the magnetization vector M in the single-domain state deviates from the external magnetic field H direction at low magnetic field, while for high magnetic field, M continuously moves following the field direction, which leads to different resistivity function behaviors.