具非线性边界条件的奇异扩散方程

本文讨论具非线性第二边界条件的一端无界的奇异扩散方程的初边值间题,利用先验估计方法得到的主要结果是:存在唯一的整体光滑解,且解连续依赖于初值．     

基于正态分布宽带信号的无源互调特征行为分析

在现代无线通信中,无源互调是影响通信信号传输质量的重要因素。双音互调测试能够有效衡量无源器件的非线性特性,却无法准确预测出器件在宽带信号激励下的非线性失真。因此本文提出了一种基于正态分布的宽带信号激励下的射频连接器无源互调特性分析方法。通过双音互调测试,建立射频连接器无源非线性传输数学模型,并将基于正态分布的等效宽带信号作为非线性传输模型的激励源进行模拟仿真。结果表明,宽带无源互调功率分布与宽带信号功率分布相同,n阶宽带无源互调带宽为原宽带信号带宽的n倍,宽带信号的无源互调产物相较于双音测试信号有所增强,且信号的信噪比下降,说明宽带信号在传输过程中受到的干扰更加严重。电路仿真和数值计算呈现出良好的一致性,证明了本分析方法的有效性。     

非线性不等式组的光滑近似方法及其收敛性

将非线性不等式组的求解转化成非线性最小二乘问题,利用引入的光滑辅助函数,构造新的极小化问题来逐次逼近最小二乘问题.在一定的条件下,文中所提出的光滑高斯-牛顿算法的全局收敛性得到保证.适当条件下,算法的局部二阶收敛性得到了证明.文后的数值试验表明本文算法有效.     

Asymptotics of estimates in constrained nonlinear regression with long-range dependent innovations

The purpose of this paper is to investigate the asymptotic properties of the least squares estimates (L ₂-estimates) and the least absolute deviation estimates (L ₁-estimates) of the parameters of a nonlinear regression model subject to a set of equality and inequality restrictions, which has a long-range dependent stationary process as its stochastic errors. Then we will compare the asymptotic relative efficiencies of the above estimators.     

Discrete exact solutions to some nonlinear differential-difference equations via the (G′/G)-expansion method

We extended the (G′/G)-expansion method to two well-known nonlinear differential-difference equations, the discrete nonlinear Schrödinger equation and the Toda lattice equation, for constructing traveling wave solutions. Discrete soliton and periodic wave solutions with more arbitrary parameters, as well as discrete rational wave solutions, are revealed. It seems that the utilized method can provide highly accurate discrete exact solutions to NDDEs arising in applied mathematical and physical sciences.     

Spatial chaos in boundary layer transition

Experiments have been performed on a laminar flat plate boundary layer undergoing transition to turbulence. Reproducible disturbances were introduced via a loudspeaker embedded at some upstream location and their evolution over the plate measured using hot-wire anemometry. A new technique has been used to estimate the number of nonlinearly independent modes in the reconstructed phase portraits. Nonlinear maps were then fitted that explicitly model the spatial evolution of disturbances. These maps are consistent with classical linear stability theory for small disturbances, and give rise to Smale horse-shoe like behaviour for larger amplitude distrubances. Thus a mechanism for generating chaos has been uncovered.     

一般非线性渗流方程正性的扩展

本文研究一般非线性渗流方程解的一种性态.利用De Giorgi方法与BCP估计相结合,得到了一般非线性渗流方程正性的扩展性质,推广了非线性渗流方程的结果.     

自发产生相干对探测场的色散和吸收影响

在Y形四能级原子系统中,分析了自发产生相干对探测场的色散和吸收影响. 结果发现,随着自发产生相干的增强,系统呈现的电磁感应透明窗口逐渐变窄,并在共振处出现反常色散,吸收从负值变为正值. 同时,当抽运场和耦合场的相对强度不同时,共振处附近吸收为零或出现增益,而两场强相等或接近时,系统对探测场表现为吸收. 关键词： 非线性光学 电磁感应透明 自发产生相干     

(1+2)维强非局域空间光孤子的相互作用

强非局域空间光孤子是指满足强非局域条件的空间孤子.在Snyder和Mitchell工作的基础上，获得了不共面对称斜入射(1+2)维强非局域空间光孤子对相互作用问题的精确解析解.结果表明，光束初始中心距离在大范围尺度内变化时，双孤子的演化都能形成类似DNA结构的稳定缠绕，这种稳定缠绕的结构与双孤子的初始相位差无关；光束中心在横截面上的投影轨迹一般是一个斜椭圆，通过改变两光束的初始中心距离和倾斜度可以控制该椭圆轨迹的变化.指出了利用(1+2)维强非局域空间光孤子的相互作用特性实现平面全光开关和全光互联的潜在可能性. 关键词： (1+2)维非局域非线性介质 空间光孤子的相互作用 全光开关 全光互联     

COPOLYMERS OF 2-ACRYLAMIDO-2-METHYL-1-PROPANESULFONIC ACID/MALEIC ACID： SYNTHESIS, CHARACTERIZATION AND ANTIMICROBIAL ACTIVITY

2-Acrylamido-2-methy1-1-propanesulfonic acid(AMPS),and maleic acid(MA)copolymerized with different feed ratios using N,N-dimethylformamide as a solvent and benzoyl peroxide(Bz_2O_2)as an initiator at 70℃.Structure and composition of copolymers for a wide range of monomer feed were determined by elemental analysis(content of N for AMPS-units).Monomer reactivity ratios for AMPS(M_1)-MA(M_2)pair were determined by the application of conventional linearization methods such as Fineman-Ross(F-R),Kelen-Tüd(?)s(KT)and Extended Kelen-Tüds(EKT)and a nonlinear error invariable model method using a computer program RREVM.The characterizations were done by Fourier transform infrared spectroscopy(FTIR),differential scanning calorimetry(DSC)thermal gravimetry analysis(TGA),and and X-ray diffraction.The antimicrobial effects of polymers were also tested on various bacteria,and yeast.