SOLUTIONS FOR THE QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENTS

In this article, we study the quasilinear elliptic problem involving critical Hardy Sobolev exponents and Hardy terms. By variational methods and analytic techniques, we obtain the existence of sign-changing solutions to the problem.     

二阶椭圆问题新的混合元格式

本文基于二阶椭圆问题一种新的混合变分形式,给出同时满足强椭圆性和B-B条件的任意次的求解格式.理论分析表明这些单元论证简单而且用了较少的自由度达到最优误差估计.同时我们还给出了它们在各向异性网格下的误差估计.     

梯度计算的集合变分方案及其在大气Ekman层湍流系数反演中的应用

大气Ekman层湍流系数的准确计算对数值天气预报和污染物扩散计算有着重要的意义. 将集合计算和变分法结合起来, 提出了目标泛函梯度计算的集合变分方案, 并根据正演模式的线性化情况提出了两种计算流程. 利用这种集合变分梯度算法及两种流程对Ekman层湍流系数进行了反演试验, 结果表明这种算法实施简单、方便, 根据观测资料能够比较准确地反演湍流系数值. 关键词： 梯度计算 集合变分 湍流系数 反演     

非下采样小波变换红外光谱数据去噪

为了降低噪声对实测红外光谱信号的影响,引入了一种非下采样小波变换的红外光谱数据去噪方法。采用非下采样小波变换对原始光谱信号进行多尺度分解,提取信号的多尺度细节特征;根据光谱信号和噪声在不同尺度上的差异,通过应用变分偏微分方程方法调整分解后的各子带系数;重构各子带就可以将原始光谱信号中真实信号和噪声分离,从而达到剔除噪声的目的。通过两组实验对比传统小波和该方法针对红外光谱数据的消噪效果,实验结果表明:非下采样小波变换在红外光谱数据去噪方面具有明显的优势,不仅能够有效地去除噪声,很好地保持信号的形状,并且均方误差较小;在实际的红外光谱数据处理中能够获得较好的去噪效果。     

One Dimensional Organic Superconductivity in (TMTSF)2PF6 and (TMTSF)2C104 Detected Via Tunnel Spectroscopy

Electron tunnelling data in (TMTSF)₂ X-GaSb Schottky barriers support the idea that strong superconducting fluctuations exist in quasi-one-dimensional (TMTSF)₂X up to temperatures which are about one order or magnitude higher than the 3-D ordering critical temperature. Other tunnelling data tend to indicate that stabilization of superconductivity is possible at high temperature via chain cross-linking.     

A Study of a Ferroelectric Liquid Crystal Using Second Optical Harmonic Generation

The phase-matched generation of the optical second harmonic was investigated in the chiral smectic C* phase of a classical ferroelectric liquid crystal (DOBAMBC). The phase-matching was achieved either by incidence angle or by temperature tuning. The temperature behaviour of the second order nonlinear susceptibility was studied.     

Clusters of bound particles in the derivative δ-function Bose gas

In this paper we discuss a novel procedure for constructing clusters of bound particles in the case of a quantum integrable derivative δ-function Bose gas in one dimension. It is shown that clusters of bound particles can be constructed for this Bose gas for some special values of the coupling constant, by taking the quasi-momenta associated with the corresponding Bethe state to be equidistant points on a single circle in the complex momentum plane. We also establish a connection between these special values of the coupling constant and some fractions belonging to the Farey sequences in number theory. This connection leads to a classification of the clusters of bound particles associated with the derivative δ-function Bose gas and allows us to study various properties of these clusters like their size and their stability under the variation of the coupling constant.     

混沌直接序列扩频信号盲解调的硬件电路实现

提出了基于现场可编程门阵列 (FPGA) 技术的混沌直接序列扩频信号盲解调的硬件电路实现方法. 设计了混沌直接序列扩频信号发射机与接收机. 发射机可产生10种不同的混沌直接序列扩频信号. 为方便接收机的硬件电路实现, 对无先导卡尔曼滤波混沌拟合盲解调算法进行了简化, 在简化模型的基础上设计了接收机硬件结构. 提出了一种动态调整偏移因子的新方法, 使接收机能实时适应混沌映射的变化. 通过高斯白噪声信道及多径信道条件下的盲解调实验, 验证了盲解调算法硬件实现的抗噪声与抗多径性能, 以及对10种不同的混沌直接序列扩频信号的自适应破译效果. 关键词： FPGA 混沌直接序列扩频通信 盲解调     

A hybrid steepest-descent method for variational inequalities in Hilbert spaces

A Mann-type hybrid steepest-descent method for solving the variational inequality ?F(u*), v ? u*? ≥ 0, v ∈ C is proposed, where F is a Lipschitzian and strong monotone operator in a real Hilbert space H and C is the intersection of the fixed point sets of finitely many non-expansive mappings in H. This method combines the well-known Mann's fixed point method with the hybrid steepest-descent method. Strong convergence theorems for this method are established, which extend and improve certain corresponding results in recent literature, for instance, Yamada (The hybrid steepest-descent method for variational inequality problems over the intersection of the fixed-point sets of nonexpansive mappings, in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, D. Butnariu, Y. Censor, and S. Reich, eds., North-Holland, Amsterdam, Holland, 2001, pp. 473–504), Xu and Kim (Convergence of hybrid steepest-descent methods for variational inequalities, J. Optim. Theor. Appl. 119 (2003), pp. 185–201), and Zeng, Wong and Yao (Convergence analysis of modified hybrid steepest-descent methods with variable parameters for variational inequalities, J. Optim. Theor. Appl. 132 (2007), pp. 51–69).