THE INTERVAL ESTIMATIONS FOR THE PARAMETERS AND OTHER RELIABILITY CHARACTERS OF A THREE PARAMETER WEIBULL DISTRIBUTION

ＴＨＥＩＮＴＥＲＶＡＬＥＳＴＩＭＡＴＩＯＮＳＦＯＲＴＨＥＰＡＲＡＭＥＴＥＲＳＡＮＤＯＴＨＥＲＲＥＬＩＡＢＩＬＩＴＹＣＨＡＲＡＣＴＥＲＳＯＦＡＴＨＲＥＥＰＡＲＡＭＥＴＥＲＷＥＩＢＵＬＬＤＩＳＴＲＩＢＵＴＩＯＮＣＨＥＮＤＩＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐ...     

DEGREE ONE MAPS OF THE CIRCLE WITH NON－TRIVIAL AND NON－PERSISTENT ROTATION SETS

ＤＥＧＲＥＥ　ＯＮＥ　ＭＡＰＳ　ＯＦ　ＴＨＥ　ＣＩＲＣＬＥ　ＷＩＴＨ　ＮＯＮ－ＴＲＩＶＩＡＬ　ＡＮＤ　ＮＯＮ－ＰＥＲＳＩＳＴＥＮＴ　ＲＯＴＡＴＩＯＮ　ＳＥＴＳＤＥＧＲＥＥＯＮＥＭＡＰＳＯＦＴＨＥＣＩＲＣＬＥＷＩＴＨＮＯＮ－ＴＲＩＶＩＡＬＡＮＤＮＯＮ－...     

GLOBAL BEHAVIOUR OF THE SOLUTIONS OF A CLASS OF THREE－DIMENSIONSAL COMPETITIVE SYSTEM

ＧＬＯＢＡＬＢＥＨＡＶＩＯＵＲＯＦＴＨＥＳＯＬＵＴＩＯＮＳＯＦＡＣＬＡＳＳＯＦＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＳＡＬＣＯＭＰＥＴＩＴＩＶＥＳＹＳＴＥＭＣｈｅｎｇＣｈｕｎＣｈｏｒＬｉｔｗｉｎ（ＨｏｎｇＫｏｎｇＩｎｓｔｉｔｕｔｅＯｆＥｄｕｃａｔｉｏｎ）Ａｂ...     

BEHAVIOR AS t→∞ OF THE SOLUTIONS OF THE LINEAR SYSTEM OF ELASTIC THEORY ON NON－STAR－SHAPED EXTERIOR DOMAINS

（刘德辅）ＢＥＨＡＶＩＯＲＡＳｔ→∞ＯＦＴＨＥＳＯＬＵＴＩＯＮＳＯＦＴＨＥＬＩＮＥＡＲＳＹＳＴＥＭＯＦＥＬＡＳＴＩＣＴＨＥＯＲＹＯＮＮＯＮ－ＳＴＡＲ－ＳＨＡＰＥＤＥＸＴＥＲＩＯＲＤＯＭＡＩＮＳ￥ＬｉｕＤｅｆｕ（Ｄｅｐｔ．ｏｆＡｐｐｌＭａｔｈ．，Ｂｅｉ...     

广义Chebyshev－Vandermonde方程组的快速算法与求逆公式

广义Ｃｈｅｂｙｓｈｅｖ－Ｖａｎｄｅｒｍｏｎｄｅ方程组的快速算法与求逆公式成礼智（国防科技大学）ＩＮＥＲＳＩＯＮＦＯＲＭＵＬＡＡＮＤＦＡＳＴＳＯＬＵＴＩＯＮＦＯＲＧＥＮＥＲＡＬＣＨＥＢＹＳＨＥＶ－ＶＡＮＤＥＲＭＯＮＤＥＥＱＵＡＴＩＯＮＳ￥ＣｈｅｎｇＬｉ...     

ELLIPTIC H~2－VOLTERRA PROJECTION AND THE H~1－GALERKIN METHODS FOR THE INTEGRO－DIFFERENTIAL EQUATIONS OF EVOLUTION

ＥＬＬＩＰＴＩＣＨ~２－ＶＯＬＴＥＲＲＡＰＲＯＪＥＣＴＩＯＮＡＮＤＴＨＥＨ~１－ＧＡＬＥＲＫＩＮＭＥＴＨＯＤＳＦＯＲＴＨＥＩＮＴＥＧＲＯ－ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＯＦＥＶＯＬＵＴＩＯＮ￥ＳＵＮＰＥＮＧＴＡＯＡｂｓｔｒａｃｔ：Ｔｈｉｓｐ...     

LARGE－TIME BEHMIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGHPOROUS MEDIA

ＬＡＲＧＥ－ＴＩＭＥＢＥＨＭＩＯＲＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＣＯＭＰＲＥＳＳＩＢＬＥＡＤＩＡＢＡＴＩＣＦＬＯＷＴＨＲＯＵＧＨＰＯＲＯＵＳＭＥＤＩＡ￥ＸＩＡＯＬＩＮＧ（Ｌ．ＨＳＩＡＯ）Ｄ．ＳＥＲＲＥ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔ...     

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR A CLASS OF THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATION

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＴＨＥＯＲＥＭＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＴＨＥＳＹＳＴＥＭＳＯＦＭＩＸＥＤＭＯＮＯＴＯＮＥＯＰＥＲＡＴＯＲＥＱＵＡＴＩＯＮＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＨＥＮＰＥＩＬＯＮＧ...     

THE NON－EXISTENCE OF PERIODIC SOLUTIONS OF A CERTAIN CLASS OF N－TH ORDER DIFFERENTIAL EQUATIONS

ＴＨＥ　ＮＯＮ－ＥＸＩＳＴＥＮＣＥ　ＯＦ　ＰＥＲＩＯＤＩＣ　ＳＯＬＵＴＩＯＮＳ　ＯＦ　Ａ　ＣＥＲＴＡＩＮ　ＣＬＡＳＳ　ＯＦ　Ｎ－ＴＨ　ＯＲＤＥＲ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳＴＨＥＮＯＮ－ＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵ...     

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR BOUNDARY VALUE PROBLEMS OF VOLTERRA－HAMMERSTEIN TYPE INTEGRODIFFERENTIAL EQUATION

ＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＮＯＮＬＩＮＥＡＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＦＶＯＬＴＥＲＲＡ－ＨＡＭＭＥＲＳＴＥＩＮＴＹＰＥＩＮＴＥＧＲＯＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮ￥ＷａｎｇＧ...     

ON THE REGULARITY UP TO THE BOUNDARY OF SOLUTIONS OF ELLIPTIC BOUNDARY VALUE PROBLEMS

Abstract

We consider the regularity up to the boundary of solutions of those elliptic boundary value problems that can be treated by the non-variational theory developed by Schechter and others. The usual method of differential quotients is replaced by a method of Schappel [5] which is based on the properties of a Laplace-type operator 1-?2. In this paper the results of Schappel, which are given for boundary value problems in variational form, are extended to the non-variational case. We make important use of fractional order Sobolev spaces on the boundary and trace theorems.     

APPROXIMATION, STABILITY AND FAST EVALUATION OF EXACT ARTIFICIAL BOUNDARY CONDITION FOR THE ONE-DIMENSIONAL HEAT EQUATION

In this paper we consider the numerical solution of the one-dimensional heat equation on unbounded domains. First an exact semi-discrete artificial boundary condition is derived by discretizing the time variable with the Crank-Nicolson method. The semi-discretized heat equation equipped with this boundary condition is then proved to be unconditionally stable, and its solution is shown to have second-order accuracy. In order to reduce the computational cost, we develop a new fast evaluation method for the convolution operation involved in the exact semi-discrete artificial boundary condition. A great advantage of this method is that the unconditional stability held by the semi-discretized heat equation is preserved. An error estimate is also given to show the dependence of numerical errors on the time step and the approximation accuracy of the convolution kernel. Finally, a simple numerical example is presented to validate the theoretical results.     

W_2~m空间中样条插值算子与线性泛函的最佳逼近

In this paper,the convergency of spline interpolation operators is obtained,these spline operators are determined by linear differential operators and constraint functionals.The errors of the interpolating spline with EHB fanctionals are estimated.The best approximation of linear functionals on W2^n spaces are investigated,which let to a useful computational method for the approximation solution of higher order linear differential equations with multipoint boundary value conditions.     

Estimates of modeling errors for linear elliptic problems

We derive new estimates of modeling errors for linear elliptic boundary value problems with periodic coefficients solved by homogenization method. Our approach is based on the concept of functional a posteriori error estimation. The estimates are obtained for the energy norm and use solely the global flux of the non-oscillatory solution of the homogenized model and solution of a boundary value problem on the cell of periodicity. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The fast Fourier transform and the numerical solution of one-dimensional boundary integral equations

Summary Here we present a fully discretized projection method with Fourier series which is based on a modification of the fast Fourier transform. The method is applied to systems of integro-differential equations with the Cauchy kernel, boundary integral equations from the boundary element method and, more generally, to certain elliptic pseudodifferential equations on closed smooth curves. We use Gaussian quadratures on families of equidistant partitions combined with the fast Fourier transform. This yields an extremely accurate and fast numerical scheme. We present complete asymptotic error estimates including the quadrature errors. These are quasioptimal and of exponential order for analytic data. Numerical experiments for a scattering problem, the clamped plate and plane estatostatics confirm the theoretical convergence rates and show high accuracy.     

Some applications of a galerkin-collocation method for boundary integral equations of the first kind

Here we apply the boundary integral method to several plane interior and exterior boundary value problems from conformal mapping, elasticity and fluid dynamics. These are reduced to equivalent boundary integral equations on the boundary curve which are Fredholm integral equations of the first kind having kernels with logarithmic singularities and defining strongly elliptic pseudodifferential operators of order - 1 which provide certain coercivity properties. The boundary integral equations are approximated by Galerkin's method using B-splines on the boundary curve in connection with an appropriate numerical quadrature, which yields a modified collocation scheme. We present a complete asymptotic error analysis for the fully discretized numerical equations which is based on superapproximation results for Galerkin's method, on consistency estimates and stability properties in connection with the illposedness of the first kind equations in L₂. We also present computational results of several numerical experiments revealing accuracy, efficiency and an amazing asymptotical agreement of the numerical with the theoretical errors. The method is used for computations of conformal mappings, exterior Stokes flows and slow viscous flows past elliptic obstacles.     

采用可变边界层法削弱一类非线性变结构系统的抖振

针对一类非线性系统,提出一种削弱变结构控制系统抖振的新方法-可变边界层法,推导出变结构控制系统的稳态误差与饱和特性宽度之间定量的数学关系,通过系统的稳态误差指标可以设计出边界层宽度变化的饱和特性,从而既削弱了系统的抖振又满足系统稳态误差指标,仿真结果验证了该方法的有效性.     

On the effect of numerical integration in the Galerkin boundary element method

Summary. We discuss the effect of cubature errors when using the Galerkin method for approximating the solution of Fredholm integral equations in three dimensions. The accuracy of the cubature method has to be chosen such that the error resulting from this further discretization does not increase the asymptotic discretization error. We will show that the asymptotic accuracy is not influenced provided that polynomials of a certain degree are integrated exactly by the cubature method. This is done by applying the Bramble-Hilbert Lemma to the boundary element method. Received May 24, 1995     

A POSTERIORI ERROR ESTIMATE FOR BOUNDARY CONTROL PROBLEMS GOVERNED BY THE PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

In this paper, we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations. Three different a posteriori error estimators are provided for the parabolic boundary control problems with the observations of the distributed state, the boundary state and the final state. It is proven that these estimators are reliable bounds of the finite element approximation errors, which can be used as the indicators of the mesh refinement in adaptive finite element methods.     

二维可压缩油水两相渗流动边值问题的特征差分方法

可压缩可混溶油、水两相渗流动边值问题的研究,对重建盆地发育中油气资源运移、聚集的历史和评估油气资源的勘探与开发有重要的价值,其数学模型是一组非线性偶合偏微分方程组的动边值问题．本文对二维有界域的两类边值问题提出一类新的特征差分格式,应用区域变换、时间的变步长、粗细网格配套、变分形式、先验估计的理论和技巧,得到了最佳阶l2误差估计结果．将J．Douglas,Jr．提出的著名方法,成功地拓广到这一新领域,并得到实质性进展．它对这一领域的模型分析,数值方法和软件研制均有重要的价值．