非齐次线性微分方程解的增长性

研究了非齐次线性微分方程f^{(k)}+A_{k-1}(z)f^{(k-1)}+...+A_{s}(z)f^{(s)}+...+A_{0}(z)f=F(z) 解的增长性,其中A_{j}(j=0,1,\cdots,k-1)及F是整函数. 在A_{s}比其他系数有较快增 长的情况下,得到了上述非齐次微分方程在一定条件下的超越整函数解的超级的精确估计.     

Approximate Homotopy Symmetry Reduction Method： Infinite Series Reductions to Kawahara Equation

The Kawahara equation is studied through the approximate homotopy symmetry method. Under this method we get the similarity reduction solutions of the Kawahara equation, leading to the corresponding homotopy series solutions. Furthermore, the similarity solutions of the corresponding reduced linear ordinary differential equations are also considered.     

Legendre polynomial solutions of high-order linear Fredholm integro-differential equations

In this study, a Legendre collocation matrix method is presented to solve high-order Linear Fredholm integro-differential equations under the mixed conditions in terms of Legendre polynomials. The proposed method converts the equation and conditions to matrix equations, by means of collocation points on the interval [−1, 1], which corresponding to systems of linear algebraic equations with Legendre coefficients. Thus, by solving the matrix equation, Legendre coefficients and polynomial approach are obtained. Also examples that illustrate the pertinent features of the method are presented and by using the error analysis, the results are discussed.     

邻苯二甲酸二甲酯系材料中α-弛豫的降温介电谱测量与分析

对邻苯二甲酸二甲酯(dimethyl phthalate)、邻苯二甲酸二乙酯(diethyl phthalate)、邻苯二甲酸二丁酯(dibutyl phthalate)和邻苯二甲酸二异辛酯 (dioctyl phthalate)系列材料中, α-弛豫的降温介电谱进行了测量, 得出了相应材料α-弛豫的平均弛豫时间τ_α^a 随温度T的变化关系. 通过τ_α^a 的实验结果与经验的Vogel-Fulcher-Tammann)定律τ_α^a = τ_α⁰ exp (A/(T-T₀))的拟合, 获得了上述系列材料的τ_α⁰, A和T₀. 分析发现, 随邻苯二甲酸二甲酯系列分子侧链中碳原子数目n的变化, 材料的τ_α⁰, A, T₀ 和T_g 表现出一定的规律性, 具体为随n的增加, 即分子内部自由度的增多, A和T_g 都表现出近乎相同的先减后再增的趋势, 而1/τ_α⁰ 和T₀ 则表现出基本相同的先快速减小, 然后保持基本上不变的趋势. 关键词： 玻璃化转变 介电谱 α-弛豫')" href="#">α-弛豫 邻苯二甲酸二甲酯系列材料     

Solution of the skin effect problem with an arbitrary coefficient of specular reflection

An analytical solution of the skin effect problem in a metal with specular-diffuse boundary conditions is obtained. A new analytical method is developed that makes it possible to obtain a solution up to an arbitrary degree of accuracy. The method is based on the idea of representing not only the boundary condition on the field in the form of a source (which is conventional) but also the boundary condition on the distribution function. The solution is obtained in the form of a von Neumann series.     

A note on parameter estimations of panel vector autoregressive models with intercorrelation

This note considers parameter estimation for panel vector autoregressive models with intercorrelation. Conditional least squares estimators are derived and the asymptotic normality is established. A simulation is carried out for illustration.     

Higher-order accurate polyspectral estimation with flat-top lag-windows

Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical estimators with second-order kernels. A simple, data-dependent algorithm for selecting the bandwidth is introduced and is shown to be consistent with estimating the optimal bandwidth. The combination of the specialized family of kernels with the new bandwidth selection algorithm yields a considerably improved polyspectral estimator surpassing the performances of existing estimators using second-order kernels. Bispectral simulations with several standard models are used to demonstrate the enhanced performance with the proposed methodology.     

New methods for calculating the dew/bubble curves of classical model fluids

We describe two new methods for locating the dew/bubble curves of fluids. One is a numerical method and the other an analytical method based on the use of series expansions. The utility of these two methods is illustrated by application to a simple one-component fluid model and to several model polydisperse fluids. The numerical method is based on a new geometric representation of the equilibrium conditions-similar in spirit to the geometric representations often used for solving the equilibrium conditions of pure fluids. Our calculations show that the series-expansion technique can be quite effective at producing accurate representations of the phase boundaries.     

Flat Power Series over a Finite Field

We define and describe a class of algebraic continued fractions for power series over a finite field. These continued fraction expansions, for which all the partial quotients are polynomials of degree one, have a regular pattern induced by the Frobenius homomorphism.This is an extension, in the case of positive characteristic, of purely periodic expansions corresponding to quadratic power series.     

On expansions of functions of two variables in mixed Fourier-Jacobi series and their application for estimation of errors of cubature formulas

Some problems of expansion of functions of two variables in mixed Fourier-Jacobi series are discussed. In particular, estimates of the convergence rate of these series on classes of functions of two variables characterized by generalized moduli of continuity are given. Applications of these results and estimation of residues of some Chebyshev-type mixed cubature formulas are discussed.