A difference-analytical method for the computation of eigenvalues of the fourth-order equations with separated boundary conditions

We propose a method for the computation of eigenvalues with odd multiplicities for spectral boundary-value problems of the 4th order with separated boundary conditions. In this method approximate eigenvalues appear as zeros of a certain function f(λ) which admits an explicit representation.     

Iterative method for finding the eigenfunctions of a system of two Schrödinger equations with combined nonlinearity

An iterative method is proposed to determine the eigenfunctions of a system of two nonlinear Schrödinger equations governing the interaction of two femtosecond pulses in a medium with quadratic and cubic nonlinearity. The method produces soliton solutions of a new form for a wide range of nonlinearity coefficients corresponding to the first and second eigenvalues. A specially chosen initial approximation is required to determine the third and higher eigenfunctions.     

一类两边界条件含参数的Sturm-Liouville问题

考虑第一个边界条件为参数的线性函数，第二个边界条件为有理函数的Sturm-Liouville问题．给出问题的特征值、特征函数的渐近式以及特征函数的振荡理论，并给出相应的应用实例．     

Modeling and prediction of children’s growth data via functional principal component analysis

We use the functional principal component analysis (FPCA) to model and predict the weight growth in children. In particular, we examine how the approach can help discern growth patterns of underweight children relative to their normal counterparts, and whether a commonly used transformation to normality plays any constructive roles in a predictive model based on the FPCA. Our work supplements the conditional growth charts developed by Wei and He (2006) by constructing a predictive growth model based on a small number of principal components scores on individual’s past. This work was supported by National Natural Science Foundation of China (Grant No. 10828102), a Changjiang Visiting Professorship, the Training Fund of Northeast Normal University’s Scientific Innovation Project (Grant No. NENU-STC07002) and the National Institutes of Health Grant of USA (Grant No. R01GM080503-01A1).     

Noise-induced transitions in a double-well potential at low friction

A new integral representation of the transition rate holds for any friction and is shown to allow a feasible evaluation in a wide friction range. Analytic approximations include the (high-friction) Kramers result with the leading correction, as well as a low-friction case. The method is complementary to a recent one of Melnikov and Meshkov.     

Spectra and essential spectral radii of composition operators on weighted Banach spaces of analytic functions

We determine the spectra of composition operators acting on weighted Banach spaces of analytic functions on the unit disc defined for a radial weight v, when the symbol of the operator has a fixed point in the open unit disc. We also investigate in this case the growth rate of the Koenigs eigenfunction and its relation with the essential spectral radius of the composition operator.     

New proof of the Hörmander multiplier theorem on compact manifolds without boundary

On compact manifolds without boundary, the gradient estimates for unit band spectral projection operators are proved for a second order elliptic differential operator . A new proof of the Hörmander Multiplier Theorem (first proved by A. Seeger and C.D. Sogge in 1989) is given in this setting by using the gradient estimates and the Calderón-Zygmund argument.

     

同调谐振子谱空间上的对称性和参量双粒子模型

研究了同调谐振子谱空间上的对称性，通过适当的参量代换给出形象的图示. 得到归一化的本征函数解析表达式， 并证明了线性谐振子是同调谐振子的退化. 揭示出同调谐振子是参量双粒子模型，并给出该模型的相干态，该相干态自动包含用Glauber相干态构 造的奇、偶相干态. 关键词： 同调谐振子 赝角动量方法 本征值谱 本征函数 参量双 光子模型     

关于广义Sublaplacian算子特征函数的展开

本文研究了广义Ｓｕｂｌａｐｌａｃｉａｎ算子特征函数的展开．通过定义广义　－扭曲卷积，我们得到相应的Ｐｌａｎｃｈｅｒｅｌ定理及Ｈａｕｓｄｏｒｆｆ－Ｙｏｕｎｇ不等式，最后，我们还给出了当广义Ｓｕｂｌａｐｌａｃｉａｎ算子的特征值为离散时的一些结果．     

受与速度平方成正比的力的变频率谐振子

受与速度平方成正比的力的变频率谐振子(THOFQV)可以用一个适当的Lagrangian量来描述，可以求出THOFQV的普遍解.再利用不变量算子求解该系统的Schrdinger方程，得到本征函数和本征值. 关键词： 谐振子 不变量 本征函数 本征值