Zeros of eigenfunctions of a class of generalized second order differential operators on the Cantor set

Generalized second order differential operators of the form when μ is a selfsimilar measure whose support is the classical Cantor set are considered. The asymptotic distribution of the zeros of the eigenfunctions is determined. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类具非线性边界条件的高阶方程的双参数奇摄动问题

研究了一类含双参数的非线性高阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性.     

变系数二阶线性微分方程的一个新的可解类型

通过双变换——未知函数的线性变换和自变量变换 ,将一类变系数线性微分方程化为二阶常系数线性微分方程 ,从而得到变系数二阶线性微分方程的一个新的可解类型 ,推广了著名的二阶 Euler方程 .     

一类具非线性边界条件的高阶方程的奇摄动问题

通过引入伸展变量和非常规的渐近序列{∈}）,运用合成展开法,对一类具非线性边界条件的非线性高阶微分方程的奇摄动问题构造了形式渐近解,再运用微分不等式理论证明了原问题解的存在性及所得渐近近似式的一致有效性．     

非均匀切向荷载下弹性半空间二阶效应的实例计算*

继文[1],本文详细讨论了一个实例,对二阶弹性材料在Z方向的位移和应力作了数值计算,我们发现,二阶效应使Z方向位移减小而使应力t_rz的值在荷载作用圆内减小而在圆外却增加。     

Uniform stability for solutions of a structural acoustics PDE model with no added dissipative feedback

A rate of rational decay is obtained for smooth solutions of a PDE model, which has been used in the literature to describe structural acoustic flows. This structural acoustics model is composed of two distinct PDE systems: (i) a wave equation, to model the interior acoustic flow within the given cavity Ω and (ii) a structurally damped elastic equation, to describe time‐evolving displacements along the flexible portion Γ₀ of the cavity walls. Moreover, the extent of damping in this elastic component is quantified by parameter η∈[0,1]. The coupling between these two distinct dynamics occurs across the boundary interface Γ₀. Our main result is the derivation of uniform decay rates for classical solutions of this particular structural acoustic PDE, decay rates that are obtained without incorporating any additional boundary dissipative feedback mechanisms. In particular, in the case that full Kelvin–Voight damping is present in fourth‐order elastic dynamics, that is, the structural acoustics system as it appears in the literature, solutions that correspond to smooth initial data decay at a rate of . By way of deriving these stability results, necessary a priori inequalities for a certain static structural acoustics PDE model are generated here; these inequalities ultimately allow for an application of a recently derived resolvent criterion for rational decay. Copyright © 2016 John Wiley & Sons, Ltd.     

A high resolution finite difference method for a model of structured susceptible‐infected populations coupled with the environment

We develop a general model describing a structured susceptible‐infected (SI) population coupled with the environment. This model applies to problems arising in ecology, epidemiology, and cell biology. The model consists of a system of quasilinear hyperbolic partial differential equations coupled with a system of nonlinear ordinary differential equations that represents the environment. We develop a second‐order high resolution finite difference scheme to numerically solve the model. Convergence of this scheme to a weak solution with bounded total variation is proved. Numerical simulations are provided to demonstrate the high‐resolution property of the scheme and an application to a multi‐host wildlife disease model is explored.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1420–1458, 2017     

二阶常微初值问题的单步格式

讨论二阶常微分方程初值问题utt+au=f,u(0)=u0，ut(0)=v0 的一种单步格式，采用u及v=ut为未知量，计算简单. 证明了此格式的稳定性及对u，v皆有二阶精度. 此格式可用于双曲问题.     

二阶常系数线性微分方程的积分形式通解及首次积分

利用一阶线性微分方程的通解 ,导出了二阶常系数线性微分方程的积分形式通解 .研究了通解的结构 ,并给出了首次积分 .     

A fractional tumor-growth model and the determination of the power law for different cancers based on data fitting

We study a fractional model for tumor growth and derive its general solution, the blow-up time and the radius of convergence. The model is simplified then to fit human data. The results show that there is a noticeable variation in the value of the scaling exponent depending on whether the model is fractional or integer. This supports the idea that the inclusion of memory effects may become relevant in the study of tumor growth via the scaling exponent.     

A fractional‐order model for chronic lymphocytic leukemia and immune system interactions

In this study, a mathematical, fractional‐order model was developed for B cell chronic lymphocytic leukemia, with immune system, and then analyzed. Interactions between B leukemia cells, natural killer cells, cytotoxic T cells, and T‐helper cells are considered to be incorporated into a system consisting of four fractional differential equations. For estimation of the parameters, clinical data of six patients were used. By numerical solution of the system, the interactions between the leukemia cell population and the immune system cell populations for values of α ∈ (0,1) at different times were explained. By determining points of equilibrium and stability of the system were met. Bifurcation analysis showed that use of the fractional‐order model, figure out unpredictable behaviors of the system such as saddle‐node, bistability and hysteresis phenomenon occurred in the system by changing the values of some of the parameters, it was predictable.     

Example of a suspension bridge ODE model exhibiting chaotic dynamics: A topological approach

Using an elementary phase-plane analysis combined with some recent results on topological horseshoes and fixed points for planar maps, we prove the existence of infinitely many periodic solutions as well as the presence of chaotic dynamics for a simple second order nonlinear ordinary differential equation arising in the study of Lazer-McKenna suspension bridges model.     

A numerical approach to solve the model of an electromechanical system

In this paper, the model of an electromechanical system, which is a system of linear differential equations, is studied. Haar wavelet collocation method (HWCM) is applied for finding the approximate solution of the model. HWCM reduces the system of the model into a matrix‐vector form that contains the unknown Haar coefficients, and these coefficients are easily calculated. To demonstrate the validity and applicability of HWCM, numerical solutions of the system for different parameter values in the system are presented. The obtained results demonstrate the efficiency and accuracy of the method. All of the computations are performed via a program written in Mathematica.     

Estimation of intrinsic growth factors in a class of stochastic population model

This article discusses the problem of parameter estimation with nonlinear mean-reversion type stochastic differential equations (SDEs) driven by Brownian motion for population growth model. The estimator in the population model is the climate effects, population policy and environmental circumstances which affect the intrinsic rate of growth r. The consistency and asymptotic distribution of the estimator θ is studied in our general setting. In the calculation method, unlike previous study, since the nonlinear feature of the model, it is difficult to obtain an explicit formula for the estimator. To solve this, some criteria are used to derive an asymptotically consistent estimator. Furthermore Girsanov transformation is used to simplify the equations, which then gives rise to the corresponding convergence of the estimator being with respect to a family of probability measures indexed by the dispersion parameter, while in the literature the existing results have dealt with convergence with respect to a given probability measure.     

Solvability of a functional integral equation of fractional order in the class of functions having limits at infinity

A functional integral equation of fractional order is investigated in the space of real functions which are defined, continuous and bounded on the real half-axis. Using the technique of measures of noncompactness and the fixed point theorem of Darbo type we prove that the equation in question has solutions in the mentioned function space. Moreover, a suitable choice of a measure of noncompactness enables us to prove that those solutions tend to limits at infinity. An example illustrating our result is also given.     

Initial classification of joint data in EM estimation of latent class joint model

The latent class mixture-of-experts joint model is one of the important methods for jointly modelling longitudinal and recurrent events data when the underlying population is heterogeneous and there are nonnormally distributed outcomes. The maximum likelihood estimates of parameters in latent class joint model are generally obtained by the EM algorithm. The joint distances between subjects and initial classification of subjects under study are essential to finding good starting values of the EM algorithm through formulas. In this article, separate distances and joint distances of longitudinal markers and recurrent events are proposed for classification purposes, and performance of the initial classifications based on the proposed distances and random classification are compared in a simulation study and demonstrated in an example.     

On the structure of fractional degree vortices in a spinor Ginzburg-Landau model

We consider a Ginzburg-Landau functional for a complex vector order parameter Ψ=(ψ₊,ψ₋), whose minimizers exhibit vortices with half-integer degree. By studying the associated system of equations in R² which describes the local structure of these vortices, we show some new and unconventional properties of these vortices. In particular, one component of the solution vanishes, but the other does not. We also prove the existence and uniqueness of equivariant entire solutions, and provide a second proof of uniqueness, valid for a large class of systems with variational structure.     

失业型贫困群体的创业意向-行为转化研究——应用半参数Cox风险模型的触发效应分析

研究应用事件史分析方法跟踪失业型贫困群体创业意向到创业行为转化的过程,解释是什么因素影响着这一独特群体创业行为的触发.在研究中,构建了包含情景因素的"意向一行为"解释框架,估计"意向一行为"的转化时间,将转化的时间间隔作为创业状态转换事件的"生存时间",应用事件史分析中的半参数Cox风险模型,考察外驱力和内驱力因素对这种时间间隔的触发效用差异.研究结果表明,"意向一行为"的转化时间在地区和性别之间的差异显著,并受到体制工作经验背景、创业培训、创业行为态度的多重影响.基于以上研究结论,针对缩短创业意向转化时间、维持创业者创业热情、鼓励女性创业等提出政策建议.     

Homogenization of an Elliptic System as the Cells of Periodicity are Refined in One Direction

We homogenize a second-order elliptic system with anisotropic fractal structure characteristic of many real objects: the cells of periodicity are refined in one direction. This problem is considered in the rectangle with Dirichlet conditions given on two sides and periodicity conditions on two other sides. An explicit formula for the homogenized operator is established, and an asymptotic estimate of the remainder is obtained. The accuracy of approximation depends on the exponent $\kappa$ ∈ (0, 1/2] of smoothness of the right-hand side with respect to slow variables (the Sobolev-Slobodetskii space) and is estimated by $O(h^\kappa )$ for $\kappa$ ∈ (0, 1/2) and by O(h ^1/2(1 + |log h|)) for $\kappa$ = 1/2.