浅谈方差稳定性的变量变换

首先分析了方差非齐性存在的普遍性，进而提出了实现方差稳定性的变换问题；其次介绍了随机变量方差稳定化的一般变换方法；最后给出了特殊分布变量以及模型残差变量的方差稳定化变换的方法。

用R语言计算冬小麦品种品质性状的安全指数

旨在提供"安全第一指数"(SFI)的便捷计算方法,完善冬小麦品质性状稳定性评价体系。使用R语言设计了一个计算SFI的程序(Safety),利用冬小麦面团稳定时间数据,介绍了使用方法,验证了可靠性。结果表明,Safety程序使用便捷、运行高效,计算结果与电子表格完全一致。仅需提供待分析的数据对象和可以接受的风险比率(α),Safety可以同时计算品种均值、置信区间、shukla方差、环境方差和SFI。因为Safety程序的方差分量估计方法为"方差分析法",所以方差分量的估计值可能出现负值。综上所述,SFI能够定量地描述品质性状稳定性和达标率,Safety程序将有助于SFI在冬小麦品质性状稳定性分析领域中的推广。

基于神经网络的OD分布矩阵反推方法

以道路网络的路段流量为基础进行OD分布矩阵估计.与以往文献不同的是本文应用了多层前馈神经网络的方法.由于路段流量与相关的OD矩阵分布之间存在连续性关系,这为神经网络模型的逼近特性提供了可行性.本文的方法适用于OD分布矩阵的实时校正.在已知OD分布矩阵的前提下,对两种情境———试验网络和实际Naples农村道路网进行仿真分析.主成分分析法的应用减少了变量个数并有利于改进输入数据.估计误差相对较低,与分析方法相反的是处理的时间几乎是实时的,因此这种方法可用于动态交通管理.本文的神经网络方法在误差和计算时间方面优于传统商业软件得到的OD估计结果.

Stability of Difference Systems with Finite Delay

In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theorems, ΔV is not required to be always negative, where ΔV(n,x n)≡V(n+1,x(n+1)) -V(n,x(n))=V(n+1,f(n,x n))-V(n,x(n)), especially, in Theorem 1, ΔV may be even positive, which greatly improve the known results and are more convenient to use.

The Stability Research for the Finite Difference Scheme of a Nonlinear Reaction-diffusion Equation

In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.

Improving the Stability Problem of the Finite Difference Scheme for Reaction-diffusion Equation

This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.

Second-order difference scheme for a nonlinear model of wood drying process

A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result.

Trajectory tracking control for underactuated unmanned surface vehicles with dynamic uncertainties

The trajectory tracking control problem for underactuated unmanned surface vehicles(USV) was addressed, and the control system took account of the uncertain influences induced by model perturbation, external disturbance, etc. By introducing the reference, trajectory was generated by a virtual USV, and the error equation of trajectory tracking for USV was obtained, which transformed the tracking problem of underactuated USV into the stabilization problem of the trajectory tracking error equation. A backstepping adaptive sliding mode controller was proposed based on backstepping technology and method of dynamic slide model control. By means of theoretical analysis, it is proved that the proposed controller ensures that the solutions of closed loop system have the ultimate boundedness property. Simulation results are presented to illustrate the effectiveness of the proposed controller.

The Two Patterns of High Exact Difference in Convection Equation

This paper gives two patterns of high exact d ifference in solving convection equation. The error of cut section is to O(Δ t 2+Δx 4).

Laws of motion of particles in a jigging process

The laws of motion of particle groups in a jigging process are studied. These describe the macroscopic phenomena that occur during jigging. During jigging the heavier and bigger particles concentrate at the bed bottom while lighter and smaller particles move to the upper part of the bed. Particles with equivalent properties tend to concentrate at a certain position centered around the inherent height of their distribution. The particle distribution variance gradually diminishes to some asymptotic value. The state equation group of the jigging bed is deduced and a calculation method, called the λ value judgment method, is proposed. The method is used to calculate the layer number and the inherent height of each particle group. A mathematical expression for the particle distribution variance is also given.

Attributional Styles in Adolescents with Transfusion-dependent Thalassemia

This study focused on the way that Adolescents with Transfusion- dependent thalassemia explained negative or positive events in their life （Attributional Styles）. It is defined by three dimensions describing the cognitive appraisal of the events： internal-external, stable-unstable, and global-specific. With cross-sectional research design, the observations consist of 102 adolescents （48 males, 54 females） who diagnosed with Transfusion-dependent thalassemia （more than 50 times for blood transfusions） completed the measure of Attributional Styles and Anxiety Questionnaires. The correlations in the predicted directions among variables examine with Pearson product-moment correlation coefficients, t-test, and One-way ANOVA to ascertain a significant between the group differences on attributional factors and levels of anxiety symptoms. The results show that Adolescent samples with higher levels of anxiety revealed statistically significant relationship among three negative attributional dimensions （overall composite F = 4.5, p 〈 0.05; negative composite F = 4.99, p 〈 0.01; negative-internality F = 4.99 p 〈 0.01; negative-stability F = 3.42, p 〈 0.05 and negative-globality F = 3.77, p 〈 0.05）. In addition, significant age- group differences were found for the total negative-globality （t = 2.05, p 〈 0.05） and negative- globality （t = -2.22, p 〈 0.05）. These data are consistent with the reformulated learned helplessness model of depression. In finding, the individuals who attribute negative life events to internal, stable, and global causes will be more vulnerable to anxiety than those who make external, unstable, and specific attributions. Most interestingly, those adolescents more than 17 years evidence more negative-globality attfibutional style than group less than 16 years, and female adolescents may influence this pattern. These results suggest that targeting Adolescents with Transfusion-dependent thalassemia may be important for improving aspect of coping on psychological adjustment to their chronic illness.

Prediction of representative deformation modulus of longwall panel roof rock strata using Mamdani fuzzy system

Deformation modulus is the important parameter in stability analysis of tunnels, dams and mining struc- tures. In this paper, two predictive models including Mamdani fuzzy system （MFS） and multivariable regression analysis （MVRA） were developed to predict deformation modulus based on data obtained from dilatometer tests carried out in Bakhtiary dam site and additional data collected from longwall coal mines. Models inputs were considered to be rock quality designation, overburden height, weathering, unconfined compressive strength, bedding inclination to core axis, joint roughness coefficient and fill thickness. To control the models performance, calculating indices such as root mean square error （RMSE）, variance account for （VAF） and determination coefficient （R^2） were used. The MFS results show the significant prediction accuracy along with high performance compared to MVRA results. Finally, the sensitivity analysis of MFS results shows that the most and the least effective parameters on deformation modulus are weatherin~ and overburden height, respectively.

ULTIMATE STABILITY OF A TYPE OF CHARACTERISTIC EQUATION WITH DELAY DEPENDENT PARAMETERS

Delay differential systems are widely used in many different fields, It is important to determine the local stability of their equilibria, For systems with＇ delay dependent parameters, the stability analysis of equilibria is complicated and difficult In this paper, we shall investigate the ultimate stability of a type of characteristic equation with delay dependent parameters. Our results show that the characteristic equation with delay dependent parameters may be one of ultimately stable, ultimately unstable, and alternate between stable and unstable. Applying our results, the ultimate stability can be often decided directly and need not appeal to mathematic software. Two examples are given in this paper,

DISCRETE-TIME EPIDEMIC DYNAMICS WITH AWARENESS IN RANDOM NETWORKS

Human behavioral responses fundamentally influence the spread of infectious disease. In this paper, we study a discrete-time SIS epidemic process in random networks. Three forms of individual awareness, namely, local awareness, global awareness and contact awareness, are considered. The effect of awareness is to reduce the risk of infection. [3ased on the stability theory of matrix difference equation, we derive analytically the epidemic threshold. It is found that both local and contact awareness can raise the epidemic threshold, while the global awareness only decreases the epidemic prevalence. Our results are in line with a recent result using differential equation-based methods.

An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.

THE PERIODIC VOLTERRA MODEL WITH MUTUAL INTERFERENCE AND IMPULSIVE EFFECT

In this paper, a periodic Volterra model with mutual interference and impulsive effect is proposed and analyzed. By applying the Floquet theory of impulsive differential equa- tion, some conditions are obtained for the linear stability of semi-trivial periodic solution. Some sufficient conditions are also given for the permanence of the system. Further, stan- dard bifurcation theory is used to show the existence of coexistence state which arises near the semi-trivial periodic solution. Finally, theoretical results are confirmed by some special cases of the system.

A large deviation for occupation time of critical branching α-stable process

In this paper we establish a large deviation principle for the occupation times of critical branching α-stable processes for large dimensions d > 2α, by investigating two related nonlinear differential equations. Our result is an extension of Cox and Griffeath’s (in 1985) for branching Brownian motion for d > 4.

Dirac Quasinormal Modes of Static f(R) de Sitter Black Holes

Quasinormal modes （QNMs） for Dirac perturbations off（R） black holes （BHs） are described in this paper, involving two types of f（R） solution： f（R） （Sehwarzschild） BHs and f（R） （Maxwell） BHs. With the finite difference method, the stability of the f（R） black holes （BHs） is analysed and the threshold range off（R） （Schwarzschild） BHs and f（R） （Maxwell） BHs is defined respectively. The results show that due to the presence of the correction factor Ro, the damping rate of Dirac field decreases. Meanwhile, the influence of angular quantum number values [k] on the f（R） BHs is investigated. The results indicate that the QNMs oscillation becomes tenser and damping speed slowly decreases with ]k[ increasing. Furthermore, under the Dirac perturbation, the stability off（R） solutions can be reflected in the manner of Dirac QNMs. The relationships between the QNMs and the parameters （]k], charge Q and mass m） are discussed in massless, and massive cases, by contrast to the classical BHs.

Comparison of Synchronization Ability of Four Types of Regular Coupled Networks

We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of null solution of error equations, further, into the negative definiteness of some symmetric matrices, thus we get the sufficient synchronization stability conditions. To test the valid of the results, we take the Chua's circuit as an example. Although the theoretical synchronization thresholds appear to be very conservative, they provide new insights about the influence of topology and scale of networks on synchronization, and that the theoretical results and our numerical simulations are consistent.