Construction of continuous solutions and stability for the polynomial-like iterative equation

Most of known results such as existence, uniqueness and stability for polynomial-like iterative equations were given under the assumption that the coefficient of the first order iteration term does not vanish. The existence with a non-zero leading coefficient was therefore raised as an open problem. It was positively answered for local C¹ solutions later. In this paper this problem is answered further by constructing C⁰ solutions. Moreover, we discuss the stability of those C⁰ solutions, which consequently implies a result of the stability for iterative roots.     

Asymptotic Inference for Unit Roots in Spatial Triangular Autoregression

A spatial autoregressive process with two parameters is investigated both in the stable and in the unstable case. It is shown that the limiting distribution of the least squares estimator of these parameters is normal and the rate of convergence is n ^3/2 if one of the key parameters equals zero and n otherwise.     

Biomorphic SiC from lotus root

Biomorphic silicon carbide (bioSiC) with macro-channels and alveolate micropores was prepared by spon-taneous infiltration of melted silicon into a carbon template derived from lotus root at 1600 ℃. The carbon template and purified bioSiC samples were characterized by X-ray diffraction, scanning electron microscopy, camera and mercury intrusion. The results suggest that the bioSiC mainly consists of β-SiC and perfectly replicates the shape and microstructure of the carbon template. The bioSiC has a mean pore diameter of 91.1 μm and a porosity of 50.1%, both similar to those of the carbon template, 92.3 μm and 50.7%, respectively.     

On duality for square root convex programs

Conjugate function theory is used to develop dual programs for nonseparable convex programs involving the square root function. This function arises naturally in finance when one measures the risk of a portfolio by its variance–covariance matrix, in stochastic programming under chance constraints and in location theory.     

Determining the multiplicity of a root of a nonlinear algebraic equation

Newton’s method is most frequently used to find the roots of a nonlinear algebraic equation. The convergence domain of Newton’s method can be expanded by applying a generalization known as the continuous analogue of Newton’s method. For the classical and generalized Newton methods, an effective root-finding technique is proposed that simultaneously determines root multiplicity. Roots of high multiplicity (up to 10) can be calculated with a small error. The technique is illustrated using numerical examples.     

关于耦合振子运动的研究

本文从动力学方程入手，对耦合双振子系统的运动进行了细致求解，并对结果的物理意义和系统能量问题作了深入讨论     

Singular Perturbation Elliptic Boundary-Value Problems in the Case of a Nonisolated Root of the Degenerate Equation

For a singularly perturbed elliptic equation (the Neumann boundary-value problem), we prove a theorem on the passage to the limit for the case in which the degenerate equation has a nonisolated root.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 26–36.Original Russian Text Copyright © 2005 by V. F. Butuzov, M. A. Terent’ev.     

The order of a zero of a Wronskian and the theory of linear dependence

Every root of the top Wronskian of a Wronskian matrix whose rank at the root is equal to the number of columns, is of integer order even if the highest derivatives exist only at the root. If the rank of a Wronskian matrix is constant and smaller than the number of rows, then the number of independent linear relations between the functions in the first row is equal to the number of functions minus the rank. These results were proved under additional assumptions by Bôcher, Curtiss, and Moszner. Their proofs are simplified.     

关于正算子的n次方根

本文首先给出复的Hilbert空间上正算子n次方根存在唯—性的构造性证明．然后讨论了关于—个正算子T的n次方根序列{m√T}的极限的三种结果．     

基于周期异方差季节单位根的加权估计与检验

为检验周期异方差的季节单位根模型,基于加权最小二乘估计,提出检验统计量,并在原假设下得到检验统计量的极限分布,与各个季节的周期异方差无关,是标准Wiener过程的泛函.模拟结果和实例分析都表明了用该方法检验季节单位根模型的有效性.