Infinitely many solutions of dirichlet problem for <Emphasis Type="Italic">p</Emphasis>-mean curvature operator

The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator: is considered, where Θ is a bounded domain in R ⁿ (n>p>1) with smooth boundary ∂Θ. Under some natural conditions together with some conditions weaker than (AR) condition, we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if . Supported by the National Natural Science Foundation of China (10171032) and the Guangdong Provincial Natural Science Foundation (011606).     

Spectral and Pseudospectral Approximations Using Hermite Functions: Application to the Dirac Equation

We consider in this paper spectral and pseudospectral approximations using Hermite functions for PDEs on the whole line. We first develop some basic approximation results associated with the projections and interpolations in the spaces spanned by Hermite functions. These results play important roles in the analysis of the related spectral and pseudospectral methods. We then consider, as an example of applications, spectral and pseudospectral approximations of the Dirac equation using Hermite functions. In particular, these schemes preserve the essential conservation property of the Dirac equation. We also present some numerical results which illustrate the effectiveness of these methods.     

A NECESSARY AND SUFFICIENT CONDITION FOR THE COEXISTENCE OF A CLASS OF CUBIC CURVE SEPARATRIX CYCLES AND LIMIT CYCLES TO THE CUBIC SYSTEM

In this paper, we give the necessary and sufficient condition for the coexistence of a class of cubic curve separatrix cycles and limit cycles to the cubic system, and study their topological structures.     

改进的部分子演化模型及其对EMC效应和核Drell－Yan过程的解释

用解析方法证明了部分子演化模型可为双重Ｘ重新标度模型提供物理基础，进而利用修正的Ａｌｔｅｒａｌｌｉ－Ｐａｒｉｓｉ方程描述小ｘ区域的核遮蔽和反遮蔽效应，以改进部分子演化模型，使我们不必引入核遮蔽因子便可统一地描述ＥＭＣ效应、核遮蔽和反遮蔽效应．最后，利用改进的部分子演化模型相当好地解释了核Ｄｒｅｌｌ－Ｙａｎ过程的实验数据．     

双折射光纤中克尔效应及光纤－光学逻辑门

本文详细地研究了单模双折射光纤中的克尔效应．讨论了其应用于光纤－光学逻辑门的优点,给出了有关的理论分析和计算结果以实验装置,确定了强度型逻辑门的“１／０”状态,测出了输出光脉冲宽度．理论分析和实验结果符合良好．     

LD泵浦Nd：BGO晶体的自调Q激光器

首次实现了ＬＫ泵浦Ｎｄ∶ＢＧＯ固体激光器的１．０６４μｍ的激光输出，泵浦阈值功率为２５ｍＷ，在连续运转状态下得到最大为４０ｍＷ的ＴＥＭ００模输出，光－光效率为１３．３％，根据法拉第磁光效庆理论，了ＬＤ泵浦Ｎｄ∶ＢＧＯ自调Ｑ激光器的各种参数，并研制成该激光器，在该器件中，作为损耗调制元件的磁光调制器就是绕有线圈的Ｎｄ∶ＢＧＯ晶体本身，实验在重复率为１ＫＨｚ的条件下得到了ＦＷＨＭ为１００ｎｓ的稳定脉冲     

求一类多元多峰函数全局极小的区间斜率方法

Based on the interval analysis, an interval slope method is proposed for finding all global minimizers of a several peaks function f on domain X^0包含于R^n, which is given by interval slope discard tests and interval extension of objective function.Numerical results of representative test functions show that this method is practical and effective.     

p阶平均曲率算子Dirichlet问题的无穷多个解

§ 1　 IntroductionSince the Mountain Pass Theorem came out,the existence of nontrivial solutions,pos-sibly multiple,ofnonlinear elliptic equations has been extensively studied.In this paper,weconsider the following Dirichlet problem for p-(generalized) mean curvature operator:-div((1 +| u|2 ) p- 22 u) =f(x,u) ,　 x∈Ω,u∈ W1 ,p0 (Ω ) , (1 .1 )whereΩ is a bounded domain in Rn(n>p>1 ) with smooth boundary Ω.First let us recall the following Dirichletproblem for p-Laplacian:-Δpu≡ -div…     

The wavelet dimension function is the trace function of a shift-invariant system

In this note, we observe that the dimension function associated with a wavelet system is the trace of the Gramian fibers of the shift-invariant system generated by the negative dilations of the mother wavelets. When this shift-invariant system is a tight frame, each of the Gramian fibers is an orthogonal projector, and its trace, then, coincides with its rank. This connection leads to simple proofs of several results concerning the dimension function, and the arguments extend to the bi-frame case.

     

Evolution of the electronic structure of 1T-Cu(x)TiSe(2)

The electronic structure of a new charge-density-wave system or superconductor, 1T-Cu(x)TiSe(2), has been studied by photoemission spectroscopy. A correlated semiconductor band structure is revealed for the undoped case, which resolves a long-standing controversy in the system. With Cu doping, the charge-density wave is suppressed by the raising of the chemical potential, while the superconductivity is enhanced by the enhancement of the density of states, and possibly suppressed at higher doping by the strong scattering.