The incompressible viscous flow problem between two concentric rotating spheres is a simple model for the geophysical flow around the earth. Firstly, we obtain rational expresstion of eigenvalue and eigenfunction of Stokes problem by using rational polynomial form of spherical bessel function in this case. Secondly, we obtain spectral approximate solutions of Navier-Stokes equation, and if we take three model as bases functions in spectral approximate, a quasi-lorenz system is obtained. In this paper, the bifurcation phenomena and attractors are discussed.

本文讨论了正定矩阵平方根的计算与摄动问题。在第一部分,提供了一种计算方法,其特点在于可以不用特征值与特征向量的计算,计算具有很好的收敛性。在第二部分,讨论了正定矩阵平方根的摄动问题,给出了摄动界限的估计。

In this paper, we give the fast algorithm for inverting a tridiagonal matrix of n order. Its calculating quantity of arithmetic operation is only n²+7n-8. At the same time, we give the expression on the elements of the inverse tridiagonal matrix, on which we get exact estimate. It greatly expands and improves the results of [2], [3].

The present paper proves the existence and uniqueness (in some given sense) of the LDL^T decomposition of real symmetric non-negative definite matrices, where L is a unit lower triangular matrix with real elements and D is a diagonal matrix with real elements. The proof is made in a constructive way. By taking advantage of this decomposition, a criterion for the consistency of the linear equation with such a coefficient matrix and its whole solution set (or the least-squares solution if it is inconsistent) are obtained. Since it involves no row or column permutation, the process may be combined with any sparse technique on the computer, and hence is of practical importance in treating the large scale sparse matrices derived from such problems as the structure design by finite elements methods. Finally, the stability of such a decomposition is discussed and a backward error analysis is given.

This paper discusses the properties of a system of controlling equations of pipeline networks, gives a new convex programming method to solve the system of equations with a unique solution, and proves the global convergence. an d the superlinear rate of convergence of the new method. Meanwhile, the paper also establishes a nonlinear programming model for solving the optimization problem of the design and control of the pipeline networks, presents a constrained variable metric algorithm, and proves the.convergence of the algorithm under quite weak conditions.

相关函数估计和功率谱密度函数估计是数字时间序列分析的重要内容之一.[1]中提出了用快速富氏变换(FFT)计算相关函数估计的间接方法,此法大大快于直接算法.但这个方法对于长度为N的数据计算了滞后数从0直到N-1的全部相关函数估计值.在许多情形,特别是在估计功率谱密度的情形,估计相关函数所需要的滞后数与数据长度相比只是一个小的分数.在这种情况下使用[1]的方法就会显得有点浪费而还可提高效率.[2]中注意到了这点,提出了一个更有效的计算自相关函数估计的改进算法.

本文通过将未知函数展开成复数形式的Fourier级数, 求出了一类二阶偏微分方程的 三角级数形式的解析解, 并严格证明了其收敛性. 三维稳态与二维稳态和二维非稳态 晶体生长控制方程都是这类二阶偏微分方程特例. 利用这一特点, 本文求出了三维稳 态与二维稳态和二维非稳态晶体生长控制方程的解析解. 理论结果有助于揭示稳态晶 体生长的本质特性. 本文还给出了三维非稳态晶体生长控制方程的解析解.

在曲线、曲面的拟合和光顺理论中有两种三次参数样条曲线插值是经常遇到的:一种是以连接各有序型值点的累加弦长为其参数值的三次多项式表示,一种是所谓基样条的函数插值,这两种插值法在各分段曲线两端曲率的符号相同的情况下都有可能产生这段曲线上不应该出现的、即所谓多余的拐点,以致引起整条曲线的不光顺,本文是经过船体数学放样的一些实践写成的,其中作出了一些准则,用来检查多余的拐点是否出现,提出了如何消除这种现象的具体措施,并纠正了以前文献中的某些错误。

在造船,航空等工业中都需要很好地解决样条曲线拟合的问题。即对于给定的一组离散的有序点列要求连出适当的曲线使得保持光顺,而且要便于数控绘图的数据处理,本文目的是提供一种曲线拟合和数控绘图方法,即采用转轴三次样条(样条为二阶连续可微)拟合,再用双圆弧逼近,从而把样条曲线看作为一连串直线或圆弧的组合,称为圆弧样条。

This paper discusses the problem of the left(right) relative prime of two polynomial matrices.Using the theory of control system,we give the necessary and sufficient condition in general form for discriminating whether two polynmial matrices are left(right) prime only by employing their coefficient matries.That is the immediate and simple extesion of the resultant theorem for deciding the relative prime of two polynomials.

In this paper the relationship between homotopy algorithms and penalty function methods for nonlinear programming problems is brought to light and the convergency of the former is discussed. Some computational results are presented to show that the piecewise-linear homotopy algorithms exploiting structure are efficient for nonlinear programming problems with special structure.

In this paper, we give a unconstrained method for linear inequalities, compute 17 problems in NETLIB and obtain satisfactory results.

Consider the regression model Y_i=X_i¹β+g(t_i)+e_i,…,n. Here g is an unknown function on R¹,β is a p×1 parameter vectors to be estimated and e_i is an unobserved random error. In this paper, the additivity of the model is used to analyse the data, and the useful estimations and are established. It's shown that and have some nice properties.

This paper gives a new method for solving the system of difference equation with constant coefficients. We introduce the conception of the series of cyclical characteristic vectors and construct the general solution of system (1) by the series of cyclical characteristic vectors.

In this paper, we emphasize on the nonconvex relaxation of the semidefinite matrix rank minimization problem and the involved properties. Firstly, we apply a nonconvex relaxation, the Schatten p-norm (0<p<1) semidefinite program, for solving the desired rank minimization problem. Next, by defining the semidefinite restricted isometry/orthogonal constant, we propose a sufficient condition for the uniqueness of the solution to (P). Finally, with the semidefinite restricted isometry property (semi-RIP), we give a sufficient condition under which the Schatten p-norm relaxation and the underlying matrix rank minimization share the unique common solution. In particular, for any 0<p<1, we obtain a uniform exact recovery condition.

In this paper, for one dimensional Schödinger operator, we prove that the potential is continuous dependent on the A-function based on Simon's uniqueness theorem (the potential is determined by A-function uniquely); conversely, if the potential q∈L¹(0,∞), it is concluded that the A-function is also continuous dependent on the potential.

在试验设计中当因素较多时,常用正交试验法^[3].为了叙述的方便,目前仅限于讨论各因素水平相等的试验,设水平数为q.用正交表安排多因素试验,试验的数目为rq²,r为自然数,当q比较大时所需的试验数目就很可观,例如安排一个9水平试验,则至少要9²次试验,在许多情况下做这么多试验是不允许的.在试验费用很贵的时候,也希望尽量减少试验次数.

In this paper, we consider the uniqueness, recurrence and decay properties of the Interacting Branching Collision Processes with Immigration and Resurrection (BCP- IR). Some important properties of the generating functions for BC-IR q-matrix are firstly investigated in detail. It is proved that there exists a unique BCP-IR, and a good sufficient conditions for it to be recurrent is given. Moreover, the exact value of the decay parameter λ_Z is obtained in the critical explosion case. It is shown that this λ_Z can be directly given from the generating functions of the corresponding q-matrix. Finally, the λ_Z-invariant vectors/measures are presented.

By connecting each vertex of a graph G to each vertex of a graph H, join graph, denoted by G ∨ H, is obtained. In this paper, we have proved that the crossing number of S₅ ∨ C_n is Z(6,n)+4?n/2?+3, where Z(m,n)=?m/2??m-1/2??n/2??n-1/2? and both m and n are nonnegative integers.

A environment mathematical model with delays: is discussed. By using Hale-Watlman's Theorem on uniform persistence, it is proved that the system is uniformly persistent if it has a positive equilibrium. It is also shown that the positive equilibrium of the model is globally asymptotically stable.

The local grid refinement technique can resolve localized characteristics efficiently. The solution of the semiconductor problem device processes highly localized characteristics in the vicinity of p-n node. The momentary state of a semiconductor device of heat conduction is described by a system of four nonlinear partial differential equations. One elliptic equation is for the electrostatic, two parabolic equations are for the electron concentration and the hole concentration, and one heat exchange equation is for the temperature. According to the necessary of practical numerical simulations, a finite difference scheme for three-dimensional transient behavior of a semiconductor device of heat conduction on grids with local refinement in time is constructed and studied. Error analysis is presented and is illustrated by a numerical example. These researches are of great importance for the research on algorithmic theory, practical application and software development of numerical simulations of semiconductor devices.

The moving least squares (MLS) approximation is widely used in meshless method, however, the approximation sometimes is unstable owing to a singular or ill-conditioned matrixA. In order to assure the non-singularity of the matrixA, some necessary geometric conditions for supported points set were proved. Based on that, some inferences for judging the condition ofAwere obtained. For avoiding an ill-conditionedAin some special cases, MLS core approximation method using a core basis was presented. The results have offered a simple criteria for ensuring the stability of the approximation, suggested an effective strategy for improving the stability of the approximation, provided an initial theoretical basis for rationalizing the numerical implementation of meshless method.

本文研究了奇异二阶常微分方程边值问题 {$$ \cases u''(t)+h(t)f(u(t))=0, \ \ &0<1,\\alpha u(0)-\beta u'(0)=0, \ \ &\gamma u(1)+\delta u'(1)=0, \endcases $$ 其中$\alpha,\beta,\gamma,\delta \geq0, \ \rho=\alpha\gamma+\gamma\beta+\delta\alpha>0$, 并且允许$h(t)$在$t=0$和$t=1$处奇异, $f(s)$在$s=0$处奇异. 在关于相应线性算子第一特征值的条件下, 得到正解的存在性结论.

We study the existence and multiple positive solutions for a class of one-dimen-sional Sturm-Liouville-like p-Laplacian boundary value problems, by applying a fixed point theorem in cone.

A kind of new generalized convex sets in real linear spaces is introduced. Some properties, the Minkowski functions and separation theorems with respect to the generalized convex sets are discussed. Our results extended or improved the corresponding results in the classical convex analysis.

This paper present several case-deletion as well as local influence measures for assessing the influence of an observation for Semi-parametric Beta Regression Model with Longitudinal Data. The essential idea is to treat the latent random effects in the model as missing data and get the estimate algorithm by adding penalized spline to estimate the non-parameters. We generate generalized Cook distance and generalized DFIT for the parametric and nonparametric part respectively based case-deletion model by Q-function. Four different perturbation schemes are discussed. Two numeric examples are presented to illustrate the results.

In this paper, based on the Facchinei-Fischer-Kanzow active set identification technique, a new QP-Free algorithm is proposed for solving inequality constrained optimization problem. At each iteration, an auxiliary direction or a system of linear equations is computed to obtain a search direction. When the iteration is sufficiently large, only a system of linear equations is solved. In particular, the auxiliary direction is obtained by using a reduced matrix, the scale of which is much smaller than that of the Generalized Projection Gradient matrix. Without strict complementarity, the new algorithm is proved to be globally convergent with a superlinear convergence rate under assumptions milder than the strong second order sufficient condition.

In this paper, by using the fixed point principle and the Krasnosel’skii fixed point theorem, the authors discuss the existence of positive and multiple positive solutions for the singular differential equations of infinite boundary value problems in a special cone. The results significantly extend and improve many known results even for non-singular cases.  

An Hermite-type rectangular element approximation is discussed for a class of nonlinear Sine-Gordon equations under semi-discrete scheme. The optimal error estimate with order O(h²) and the superclose property with order O(h³) in H¹ norm are derived by use of high accuracy analysis of the element and the derivative transfering technique with respect to the time t. Moreover, the superconvergence result is obtained by the interpolation post-processing method. At the same time, the extrapolation solution with order O(h⁴) is deduced through constructing a new extrapolation scheme, which is as same as that of the linear case.

本文讨论在数据是强相依的情况下函数系数部分线性模型的估计. 首先, 采用局部线性方法, 给出该模型函数项函数的估计；然后, 使用两阶段方法给出系数函数的估计. 并且讨论了函数项函数估计的渐近正态性, 以及系数函数估计的弱相合性和渐近正态性. 模拟研究显示, 这些估计是较为理想的.

Frailty model and additive hazard model provide two important methods for studying the association between various risk factors and the cause of disease. When it is less obviously to see which of the frailty model and the additive model gives a better fit to the data, the proportional excess hazard model, combing additive and frailty models, provide an alternative model. The frailty is considered basically unobservable and hence one need to consider the corresponding mixture model. Ageing properties and dependence properties of of mixed proportional excess hazards model are studied. Some stochastic comparisons relating to those random variables of this model are also presented.

It is showed that the stochastic Camassa-Holm equation with white noise can be solved path-wise and the unique solution generates a random dynamical system. Then a compact random attractor is obtained for this system in H₀² space by a priori estimate technique.

In this paper,we use the idea of the central projection transformation to prove that the geometric properties of a class of cubic vector field with star node depends on its geometric properties at infinity. We investigate its global topological structures,obtain 27 types of different topological classification without considering the number of limit cycles, obtain the necessary and sufficient conditions that the equator (points at infinity) is a closed orbit and conditions of the existence at least one limit cycles.

In industry, the degradation test is regular used in the analysis of product reliability. This paper considers accelerated degradation test under stresses with errors, and extends the minimum distance estimation methods to the focused model. Consistency and asymptotic normality of the proposed estimator are obtained. By simulation, the performance of the estimator is shown better than the least-square estimator, which ignores the random errors of test stresses.

本文利用重合度理论研究了一类三阶泛函微分方程方程 $$ x'''+ \sum\limits_{i=1}^{2} \big[a_{i}x^{(i)}(t)+b_{i}x^{(i)}(t-\tau_{i})\big] +\sum\limits_{i=0}^{m}c_{i}x (t-\sigma_{i})+\sum\limits_{i=0}^{n}g_{i} \big( x(t-\delta_{i})\big)=p(t). $$ 的$2\pi-$周期解的问题, 获得了该方程存在$2\pi$-周期解的若干新结论, 改进推广了有关文献中的已有结果.

In this paper, the authors establish a generalized renewal risk model based on the reality that unexpected heavy-tailed claims is one of important factors which result in ruin of the insurance companies, and obtain local asymptotic relationship of survival probabilities and tail equivalence relationship for the ruin probabilities under the assumption that the claims size is heavy-tailed F ∈ S^*. The results are uniform as that in the Cramer-Lundberg model and have their uniqueness either, and significantly extend and improve many known results.

It is mainly discussed finite time stability of autonomous systems with nonsmooth right-hand sides (in the sense of Filippov solutions) with time-delay. The definition of finite time stability of retarded nonsmooth systems and comparison principle are presented. Based on Filippov differential inclusions and nonsmooth Lyapunov-Krasovkii functional, Lyapunov theorem for finite time stability of retarded nonsmooth systems is shown.

本文研究ARMA 线性子系统串联分段线性函数的Wiener
系统的递推辨识问题. 利用相关分析法和Yule-Walker方程给出线性部分参数的递推辨识算法, 而对非线性部分参数用递推的最小二乘(LS)
算法给出估计, 并证明了这些算法都以概率1收敛到真值.

The Markov-modulated risk model U=(Q,G,F;J,S,X) is precisely depicted by using paths of stochastic processes,the model is vague generalization of available Markov-modulated risk models now. Based on the model U the Markov-modulated risk processes with premium-rate vector C and tax-vector γ, R^u={R^u(t), t≥0} and R^u(γ)={R^u(γ,t), t≥0}, are given respectively. Let a characteristic group A=(Q,G,F) be given, the model U is constructed by using probabilistic method. It establishes a rigorous foundation of stochastic processes researching Markov-modulated risk models and Markov-modulated risk processes by using the theory and methods of stochastic processes.