一类非线性方程转向点问题的激波解

本文是讨论一类非线性方程的转向点问题 .研究了转向点的所处位置 ,以及问题激波解的渐近性态     

具有转向点的一类奇摄动二阶微分方程的角层问题

考虑了一类具有转向点的奇摄动二阶线性边值问题.先分析在转向点处可能出现角层现象的条件,然后,利用中间变量匹配原则构造出在整个区间上一致有效的复合展开式,从而得到该问题具有角层性质的零次近似解.     

一类具有高阶转向点的二次奇摄动问题的尖层解(英文)

本文研究一类具有高阶转向点的二次奇摄动问题.在一定条件下,指出该问题的解在转向点t=0处呈尖层性态.用合成展开法构造出解的O(ε)阶近似,并应用微分不等式理论证明解的存在性及其渐近性质.     

非线性问题转向点的数值予测

本文讨论了一类非线性问题及其有限元逼近问题的转向点之数值予测,以及应用于定常的Navier-Stokes问题.     

求解奇异摄动转向点问题的一个二阶一致收敛格式

本文对奇异摄动转向点问题构造了一个关于ε一致收敛的二阶正型格式,并给出了数值例子.     

利用衔接法构造奇摄动激波层问题的渐近解

研究了一类具有转向点的奇摄动拟线性边值问题,指出在一定条件下解在转向点t=0呈激波层现象.先用合成展开法构造出问题的形式近似,然后利用衔接法将t=0左、右两边分别具有边界层性质的近似式光滑地衔接起来,从而形成在t=0处具有激波层性质的解,并应用微分不等式理论证明了解的存在性及其渐近性质.     

具有转向点的二阶非线性问题的奇摄动

具有转向点的二阶非线性问题的奇摄动吴钦宽（芜湖联合大学）１引言关于具有转向点的奇摄动边值问题，人们对线性边界条件的问题都已有不少研究，然而对非线性边界条件的问题的研究成果还不多见。本文考虑如下形式的非线性边值问题。其中。＞０是小参数．ｘ—０是转向点．...     

具有转向点的二阶非线性方程Robin问题的奇摄动(英)

本文应用微分不等式的方法，研究了具有转向点的二阶非线性方程Robin问题的奇摄动，根据fy在转向点附近的性态，边值问题的解将呈现冲击层现象和边界层现象，在适当的假设条件下，我们证明了该问题的存在性和不同的渐近性质。     

具有转向点的二阶非线性方程Robin问题的奇摄动

本文应用微２发不等式的方法，研究了盯有转向点的二阶非线性方程Ｒｏｂｉｎ问题的奇摄动，根据ｆｙ在转向点附近的性态，边值问题的解将呈现冲击层现象和边界层现象。在适当的假设条件下，我们证明了该问题解的存在性和不同的渐近性质。     

关于A-O共振问题——带转向点的边界层问题

本文研究带有转向点的边界层问题的一种所谓A-O共振现象,指出它与微分方程在转向点邻域存在非平凡解析解(关于自变量和摄动参数ε)的关系,得到了一些解析条件,由此可构造一系列呈现共振的边值问题。     

On necessary and sufficient conditions for numerical verification of double turning points

Summary. This paper describes numerical verification of a double turning point of a nonlinear system using an extended system. To verify the existence of a double turning point, we need to prove that one of the solutions of the extended system corresponds to the double turning point. For that, we propose an extended system with an additional condition. As an example, for a finite dimensional problem, we verify the existence and local uniqueness of a double turning point numerically using the extended system and a verification method based on the Banach fixed point theorem.Mathematics Subject Classification (2000): 65J15, 65G20, 65P30     

多约束二阶非线性常微分方程拐点的数值求法

提出了一种求解多约束二阶非线性常微分方程拐点的数值解法,并以具有平行反应的化学放热系统为例,给出了一个具体算例.     

Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation

A numerical verification method to confirm the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation is presented. Using certain systems of equations corresponding to a double turning point, we derive a sufficient condition for its existence whose satisfaction can be verified computationally. We describe verification procedures and give a numerical example as a demonstration.     

Solitary Wave Transformation Due to a Change in Polarity

Solitary wave transformation in a zone with sign-variable coefficient for the quadratic nonlinear term is studied for the variable-coefficient Korteweg–de Vries equation. Such a change of sign implies a change in polarity for the solitary wave solutions of this equation. This situation can be realized for internal waves in a stratified ocean, when the pycnocline lies halfway between the seabed and the sea surface. The width of the transition zone of the variable nonlinear coefficient is allowed to vary over a wide range. In the case of a short transition zone it is shown using asymptotic theory that there is no solitary wave generation after passage through the turning point, where the coefficient of the quadratic nonlinear term goes to zero. In the case of a very wide transition zone it is shown that one or more solitary waves of the opposite polarity are generated after passage through the turning point. Here, asymptotic methods are effective only for the first (adiabatic) stage when the solitary wave is approaching the turning point. The results from the asymptotic theories are confirmed by direct numerical simulation. The hypothesis that the pedestal behind the solitary wave approaching the turning point has a significant role on the generation of the terminal solitary wave after the transition zone is examined. It is shown that the pedestal is not the sole contributor to the amplitude of the terminal solitary wave. A negative disturbance at the turning point due to the transformation in the zone of the variable nonlinear coefficient contributes as much to the process of the generation of the terminal solitary waves.     

Wavelet improvement in turning point detection using a hidden Markov model: from the aspects of cyclical identification and outlier correction

The hidden Markov model (HMM) has been widely used in regime classification and turning point detection for econometric series after the decisive paper by Hamilton (Econometrica 57(2):357–384, 1989). The present paper will show that when using HMM to detect the turning point in cyclical series, the accuracy of the detection will be influenced when the data are exposed to high volatilities or combine multiple types of cycles that have different frequency bands. Moreover, outliers will be frequently misidentified as turning points. The present paper shows that these issues can be resolved by wavelet multi-resolution analysis based methods. By providing both frequency and time resolutions, the wavelet power spectrum can identify the process dynamics at various resolution levels. We apply a Monte Carlo experiment to show that the detection accuracy of HMMs is highly improved when combined with the wavelet approach. Further simulations demonstrate the excellent accuracy of this improved HMM method relative to another two change point detection algorithms. Two empirical examples illustrate how the wavelet method can be applied to improve turning point detection in practice.     

Theorem on directed graphs,applicable to logic

A semicycle is said to turn at a point a if the arcs incident to a are both to it or both from it. We prove that if a nonempty set of points of a finite directed graph contains a turning point of each semicycle, then one of its members is a turning point of every semicycle to which it belongs; and we indicate the application of this result to mathematical logic through the modeling of arguments by graphs.     

An efficient algorithm for the determination of certain bifurcation points

Many practical problems require information about a branch of solutions of a system of nonlinear equations dependent upon a scalar parameter. We discuss some techniques for following such a branch through a turning point and describe an efficient method, with second order convergence, for finding the turning point. We also show that, if extra information is available about the solution branch, the method can be successfully applied to finding simple bifurcation points.     

Singular perturbations and vanishing passage through a turning point

The paper deals with planar slow-fast cycles containing a unique generic turning point. We address the question on how to study canard cycles when the slow dynamics can be singular at the turning point. We more precisely accept a generic saddle-node bifurcation to pass through the turning point. It reveals that in this case the slow divergence integral is no longer the good tool to use, but its derivative with respect to the layer variable still is. We provide general results as well as a number of applications. We show how to treat the open problems presented in Artés et al. (2009) [1] and Dumortier and Rousseau (2009) [13], dealing respectively with the graphics DI2a and DF1a from Dumortier et al. (1994) [14].     

Uniform Asymptotic Expansions for Ellipsoidal Wave Functions I. High Frequency Solutions of the Ellipsoidal Wave Equation

High frequency solutions of the ellipsoidal wave equation havebeen known for some time. However these solutions were non-uniform.A method for second order turning points of differential equationsis used to obtain uniform solutions of the equation. On accountof the nature of the turning point these solutions are necessarilyrelated to parabolic cylinder functions.