上次对角双线性时间序列模型的近似三阶矩结构和双谱密度

本文讨论一类特殊的双线性时间序列模型，该模型中，每一个双线性项均为两个相关的随机变量的乘积，该模型的二阶结构(自协方差和谱)目前已经很清楚了，同线性ARMA模型类似，亦具有有理谱密度，理论上，为了识别该模型，通常是考虑三阶结构(三阶矩和双谱)，但由于该模型的复杂性，精确的三阶结构是无法求出的，本文给出一种计算近似三阶矩的公式，由此得到了近似的双谱密度，仿真计算验证了这种方法是有效的。     

一类具有转向点的三阶微分方程的边值问题的解的高阶渐近展开

利用上下解方法,研究如下一类具有转向点的三阶微分方程的边值问题{ε~2y″′=f(t,y,ε)y″ g(t,y,ε)y′ h(t,y,ε),a相似文献   

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.     

Stochastic bounds for attained levels

Asymptotic inequalities are obtained for the level attained by any test statistic in a given hypothesis testing problem. The bounds so obtained are themselves random. The inequalities subsume previous results by Bahadur and others about the asymptotic behavior of attained levels. Various remifications of the inequalities are discussed, including a notion of stochastic deficiency.     

不连续三阶两点边值问题的可解性

证明了非线性三阶两点边值问题u′″（t）-q（u″（t））f（t，u（t）），u（O）=a，u（1）=b，u″（0）=c解的一个存在定理．在这个问题中，f（t，u）是一个Carathéodory函数而边界条件是非齐次的．我们的结论表明该问题能够有一个解，只要在R。的某个有界集合上q（υ）的“本性高度”与f（t，u）的“最大高度”积分的乘积是适当的．     

三新戊氧基溴硼亚酞菁薄膜材料的三阶非线性光学特性

通过单光束Z扫描技术 ,在波长为 1.0 6 4μm和 5 32nm、脉宽为 38ps条件下研究了一种新的酞菁相关化合物三新戊氧基溴硼亚酞菁薄膜材料的三阶非线性光学特性。观察到在 1.0 6 4μm(离强吸收带很远 )下的双光子吸收和在 5 32nm下的反饱和吸收现象 ,并计算出了相应的非线性吸收系数。在 1.0 6 4μm下的非共振三阶非线性极化率和在 5 32nm下的共振三阶非线性极化率 χ(3 ) 分别为 6 .1× 10 - 1 2 esu和 6 .7× 10 - 1 0 esu ,显著大于相关酞菁的值。这些结果表明三新戊氧基溴硼亚酞菁薄膜材料在非线性光学方面具有潜在的应用前景。     

New Criteria on Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Dynamic Equations with Nonlinear Neutral Terms

In the paper, we provide sufficient conditions for the oscillatory and asymptotic behavior of a new type of third-order nonlinear dynamic equations with mixed nonlinear neutral terms. Our theorems not only improve and extend existing theorems in the literature but also provide a new approach as far as the nonlinear neutral terms are concerned. The main results are illustrated by some particular examples.     

Ultrashort pulse breaking in optical fiber with third-order dispersion and quintic nonlinearity

The optical wave breaking （OWB） characteristics in terms of the pulse shape, spectrum, and frequency chirp, in the normal dispersion regime of an optical fiber with both the third-order dispersion （TOD） and quintic nonlinearity （QN） are numerically calculated. The results show that the TOD causes the asymmetry of the temporal- and spectral-domain, and the chirp characteristics. The OWB generally appears near the pulse center and at the trailing edge of the pulse, instead of at the two edges of the pulse symmetrically in the case of no TOD. With the increase of distance, the relation of OWB to the TOD near the pulse center increases quickly, leading to the generation of ultra-short pulse trains, while the OWB resulting from the case of no TOD at the trailing edge of the pulse disappears gradually. In addition, the positive （negative） QN enhances （weakens） the chirp amount and the fine structures, thereby inducing the OWB phenomena to appear earlier （later）. Thus, the TOD and the positive （negative） QN are beneficial （detrimental） to the OWB and the generation of ultra-short pulse trains.     

Ag:Bi2O3复合膜的线性和非线性光学性质

从实验和理论两个方面，探讨了金属Ag不同掺杂浓度对Ag:Bi₂O₃复合膜线性和非线性光学性质的影响. 用吸收光谱研究了Ag浓度与Ag:Bi₂O₃复合膜表面等离子体共振带之间的关系；用皮秒Z-扫描技术研究了共振和非共振情况下(激发光波长分别为532nm和1064nm)，金属Ag浓度与复合膜三阶非线性极化率的关系. 基于表面等离子体共振理论和局域场增强理论对复合膜进行了分析，得到了不同Ag浓度时Ag:Bi₂O₃复合膜的三阶非线性效应，研究了激发波长和金属浓度对复合膜线性和非线性光学性质的影响. 结果表明，等离子体共振增强和合适的金属掺杂浓度使得三阶极化率增强二个量级，在Ag浓度为35％左右和接近等离子体共振频率(相应吸收带位于560nm—622nm)的532nm激发时，χ⁽³⁾具有最大值2.4×10^-9esu. 关键词： 金属纳米颗粒 复合膜 三阶非线性 表面等离子体共振