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.     

剩余格与FI代数的可嵌入性

给出剩余格可嵌入于全序剩余格的乘积的充要条件。还给出定义在格上的FI代数可嵌入于全序FI代数的乘积的充要条件。     

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.     

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.     

分布耦合系数对线性啁啾光栅色散的影响

本文从光栅反向耦合波方程出发,经相位共轭变换用Runge-Kuta-Gil方法对其数值求解。针对线性啁啾光栅耦合系数变化服从不同的分布,分析了各种分布对光栅反射谱特性和色散特性的影响。     

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.     

PREPARATION AND CHARACTERIZATION OF SHISH-KEBAB TYPE LIQUID CRYSTALLINE POLY（p-PHENYLENEVINYLENE）

Novel shish-kebab type liquid crystalline poly（p-phenylenevinylene） derivatives were synthesized by Stille coupling reaction from 2,5-bis[（4-n-alkoxyl）benzoyloxy]1,4-dibromobenzene （monomer l） and 1,2-bis（tributylstannyl） ethylene （monomer 2）. The polymers with alkoxy groups are soluble in common organic solvents and exhibit blue fluorescence. Both the cast film and the annealed film have large red-shifts in fluorescence spectra and show yellow fluorescence. The polymers with CN and NO2 groups show poor solubility and green fluorescence. All the polymers possess liquid crystalline smectic phases. The melting point （Tm） of the polymers decreases when the length of the alkoxy tails of the mesogenic units increases. The polymers are easily aligned under a magnetic field of 10 Tesla. It is found that the conjugated backbone and LC side chain are aligned perpendicular and parallel to the magnetic field, respectively. The polymers show optical dichroism in fluorescence spectra, suggesting that they are available for advance materials with linear optical polarization.     

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.