The number of limit cycles of cubic Hamiltonian system with perturbation

In this paper, by using qualitative analysis, we investigate the number of limit cycles of perturbed cubic Hamiltonian system with perturbation in the form of (2n+2m) or (2n+2m+1)th degree polynomials . We show that the perturbed systems has at most (n+m) limit cycles, and has at most n limit cycles if m=1. If m=1, n=1 and m=1, n=2, the general conditions for the number of existing limit cycles and the stability of the limit cycles will be established, respectively. Such conditions depend on the coefficients of the perturbed terms. In order to illustrate our results, two numerical examples on the location and stability of the limit cycles are given.     

非线性Schrdinger方程的高精度守恒差分格式

本文首先分析线性Schrodinger方程一种高阶差分格式的构造方法,得到方程的耗散项.在此基础上对三次非线性Schrodinger方程,提出了一种精度为O(r2 h2)的差分格式,证明了该格式保持了连续方程的两个守恒量,且是收敛的与稳定的.并通过数值例子与已有隐格式进行了比较,结果表明,本文格式在计算量类似的情况下,提高了数值精度.     

Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow

A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded. Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function theorem. Supported by the Swiss National Science Foundation. Fellowship PBEL2–114311.     

Perturbed recurrence relations II the general case

In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations are given.     

非线性物理简介:8.光学孤子及其在光纤通讯中的应用

本文介绍了光学孤子的形成、特性及其在光纤通讯中的应用．     

TDPAC studies of Hf doped YBCO

Time differential perturbed angular correlation measurements of the 133–482 keVγ-γ cascade of¹⁸¹Ta in Hf-doped YBa₂Cu₃O_7−x are presented. The¹⁸¹Hf precurser nuclei are incorporated into the sample by thermal neutron irradiation. Two quadrupole interaction frequencies are observed in the as-irradiated sample:v _Q1=161±10 MHz with intensityf ₁=75%, asymmetry parameterη ₁=0.32 and damping parameter Λ₁=0.42, andv _Q2=1108±40 MHz withf ₂=25%,η ₂=0.62, and Λ₂=0.60. On annealing the sample in air at various temperaturesT _a and quenching to room temperature,f ₁ remained nearly constant forT _a<600°C andv _Q1 for all annealing temperatures indicating that these are insensitive to oxygen stoichiometry. This frequency is interpreted to be due to¹⁸¹Hf substitutingY sites. BeyondT _a=600°C,f ₁ increased and reached a constant value of 90% forT _a=800°C. The value ofv _Q2 showed a slight variation between 1086 and 1160 MHz, whilef ₂ remained nearly constant at 25% forT _a<600°C. This component is identified to be due to¹⁸¹Hf substituting Cu 1 sites in the Cu-O chains of YBCO. Above 600°Cv _Q2 decreased and reached a value of 808 MHz beyond 750°C.     

The variational Lyapunov function and strict stability theory for differential systems

In this paper, we investigate strict stability of differential systems by variational Lyapunov function. We obtain some sufficient conditions and comparison theorems.     

Multiple local solutions to nonlinear control processes

We use the topological tool of Nielsen fixed-point theory to study the controllability of perturbed linear control processes whose control space can be reduced to a finite-dimensional one. These methods produce a lower bound on the number of controls that achieve a given target. We concentrate particularly on the case where the perturbation has sublinear growth, and we exhibit examples of multiple controls of various types that are detected by the Nielsen theory method.This research was partly supported by the Research Grant Teoria del Controllo dei Sistemi Dinamici, Ministero della Pubblica Istruzione, Roma, Italy.     

Decay rates of energy of the 1D damped original nonlinear wave equation

We consider the decay rate of energy of the 1D damped original nonlinear wave equation. We first construct a new energy function. Then, employing the perturbed energy method and the generalized Young’s inequality, we prove that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This allows us to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively. Unlike the linear wave equation, the exponential decay rate constant depends on the initial data, due to the nonlinearity.     

Lithium insertion into In2S3 studied by perturbed γ-γ angular correlation

Li_xIn₂S₃ was electrochemically prepared with different small amounts x of lithium (0?x?0.13) in order to maintain the initial crystallographic structure of the thiospinel In₂S₃. About 10¹² radioactive ¹¹¹In ions have been implanted into these samples at 400 keV to perform PAC experiments in the temperature range from 10 to 773 K. The results are compared to previous experiments with undoped In₂S₃ samples. According to the structure of In₂S₃ in the β-phase, which belongs to the I4₁/amd space group having a unit cell with 32 In and 48 S atoms and the cell parameters α=7.61 Å and c=32.28 Å, three different electric field gradients were observed. Within two different temperature ranges dynamical EFGs occur, which are clearly influenced by the insertion of Lithium. The strong dependence of one EFG on the Li concentration x can be correlated to the effective charge of the In ions. This correlation is discussed with respect to XRD analyses of the Li_xIn₂S₃ samples and to XANES measurements on a similar sample.