二类1错误矩阵方程增优置换变换求解及其在城市交通管理中的应用研究

消错学的错误矩阵可表达错误逻辑里所定义的分解、相似、增加、置换、毁灭、单位变换等转化词,针对其中的置换变换,构建了二类1错误矩阵方程增优置换变换错误矩阵方程,并讨论了该类错误矩阵方程的求解.用交通管理问题对错误矩阵进行了举例,并构建相应的错误矩阵方程,利用上述的求解方法,对二类1方程置换变换进行了求解.     

基于空间分解变换的模糊错误矩阵方程求解

模糊错误逻辑对现实世界的对象用(u,x)表示为((U,S(t),■T(t),L(t)),(x(t)=f((u(t),■),GU(t)),GU(t)),用模糊错误变换矩阵可以表示分解、相似、增加、置换、毁灭、单位变换等6种变换方法,本论文基于求解方程XA′=B,针对■的分解,研究了基于空间分解变换的错误矩阵方程求解。以期从矩阵方程求解的角度对错误转化规律进行探索研究。     

The approximation of Laplace–Stieltjes transformations with finite order on the left half plane

In this paper, we study the error in approximating the analytic function defined by a Laplace–Stieltjes transformation of finite order, which converges on the left half plane, and obtain the relation theorems between the error, the coefficients, and the proximate order of the Laplace–Stieltjes transformation.     

错误系统结构的分解变换研究

对于错误系统的结构分解,需要先弄清楚错误系统的结构,再把该错误系统以某种基本结构分解成若干子系统,然后对子系统又以某种基本结构分解成下一层次的若干子系统,如此下去,直到所有子系统都为基本结构子系统为止.在此基础上,研究以串联、并联、扩缩、蕴含、反馈和其它型等六种基本型为基础的分解变换的分解方式,分解类型.同时采用图说明相应变换,采用系统结构与错误函数定量描述变换的逻辑规律,利用结构与功能的关系定量描述系统结构与错误的关系,最后给出了变换体系.     

Eine Approximation der Binomialverteilung durch die Normalverteilung der Ordnung 1/n

Summary The class (1) of transformations of a binomial variablek is studied. The famous De Moivre-Laplace local and integral limit theorems are generalized for the asymptotically standardized transformations (2). The transformation (4) respectively (3) is singled out as the only one with an error of order 1/n. Besides it is shown, that the error term of ordern ^–1/2 of the identical transformation, the angular transformation, and the logarithmic transformation are in proportion to 1/6, –1/12, and –1/3. Results on the influence of a correction of unbiasedness are mentioned in the last section. Such corrections allow a slight improvement of our new transformation.     

Further Discussion on the Error Bound for Generalized Linear Complementarity Problem over a Polyhedral Cone

In this paper, we consider the global error bound for the generalized linear complementarity problem over a polyhedral cone (GLCP). Based on the new transformation of the problem, we establish its global error bound under milder conditions, which improves the result obtained by Sun and Wang (2009) for GLCP by weakening the assumption.     

模糊错误集上的置换变换及其在投资决策中的应用

研究模糊错误集上的置换变换在错误的传递、转化与消除过程中的性质和规律 ,建立了避免投资决策错误的模糊数学模型 ,介绍了置换变换在消除投资决策错误中的应用方法 .     

Efficient quadrature rules with a priori error estimates for integrands with end point singularities

In this paper we present details of an efficient numerical integration rule based upon error function transformation of the integration variable. We also derive an a priori error estimate for our method and present numerical results to highlight various features of the rule as applied to integrals with end point singularities in the low order derivatives of their integrands.     

On optimal triangular meshes for minimizing the gradient error

Summary Construction of optimal triangular meshes for controlling the errors in gradient estimation for piecewise linear interpolation of data functions in the plane is discussed. Using an appropriate linear coordinate transformation, rigorously optimal meshes for controlling the error in quadratic data functions are constructed. It is shown that the transformation can be generated as a curvilinear coordinate transformation for anyC data function with nonsingular Hessian matrix. Using this transformation, a construction of nearly optimal meshes for general data functions is described and the error equilibration properties of these meshes discussed. In particular, it is shown that equilibration of errors is not a sufficient condition for optimality. A comparison of meshes generated under several different criteria is made, and their equilibrating properties illustrated.This work was supported by the Natural Sciences and Engineering Research Council of Canada, by the Information Technology Research Centre, which is funded by the Province of Ontario, by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc., and through an appointment to the U.S. Department of Energy Postgraduate Research Program administered by Oak Ridge Associated Universities     

错误数据集的变换研究

首先介绍错误数据集C的定义;再者引出错误数据集合的变换,最后研究各类错误数据集的有关运算及这些运算所满足的运算律.得出错误数据集的变换包括逆、或、积;错误集的变换类型有7种包括单位变换、置换变换、分解变换、组合变换、毁灭变换、增加变换、相似变换.     

Multiplicative Error Analysis of Matrix Transformation Algorithms

The author's recently introduced relative error measure forvectors is applied to the error analysis of algorithms whichproceed by successive transformation of a matrix. Instead ofmodelling the roundoff errors at each stage by A: = T(A)+E onemodels them by A: =e^E T(A) where E is a small linear transformation.This can simplify analyses considerably. Applications to theparallel Jacobi method for eigenvalues, and to Gaussian elimination,are given.     

STABLE DOUBLE LR ALGORITHM AND ITS ERROR ANALYSIS

In this paper, the normative matrices and their double LR transformation with origin shifts are defined, and the essential relationship between the double LR transformation of a normative matrix and the QR transformation of the related symmetric tridiagonal matrix is proved. We obtain a stable double LR algorithm for double LR transformation of normative matrices and give the error analysis of our algorithm. The operation number of the stable double LR algorithm for normative matrices is only four sevenths of the rational QR algorithm for reed symmetric tridiagonal matrices.     

Modeling for optical ray tracing and error analysis

One of the most popular mathematical tools in fields of robotics, mechanisms, and computer graphics is the 4×4 homogeneous transformation matrix. We extend the use of that matrix to the optical domain of:

(1) skew ray tracing to determine the paths of skew rays; and

(2) error analysis to investigate the various deviations of imagines due to imperfect placement of optical elements.

In order to trace a skew ray, the reflection and refraction laws of optics are formulated in the language of homogeneous transformation matrices. Then an error matrix to describe the position errors and orientation errors of optical elements is introduced in order to analyze their effects on rays' path. This ray tracing procedure can result in very powerful and fast optical design programs. The error analysis can provide the sensitivity of each error component of elements to a system's accuracy and is crucial to upgrade the precision of optical systems in design stage.     

一类自适应的奇异小波有限元法

本文对一类具有孤立奇点的奇异椭圆型微分方程,通过小波变换自动检测出奇点和奇异度,基于此,导出了一类自适应的奇异小波有限元法,在网格均匀剖分下可以达到饱和阶,     

关于伪欧氏空间

本文提出了一些新概念，ｐ—伪转置阵，ｐ—伪正交阵，ｐ—伪对称阵，从而能以这些矩阵为工具研究伪欧氏空间的性质以及空间中两个特殊线性变换，伪正交变换和伪对称变换．本文得到的主要结果是定理２，定理３，定理４及定理６．本文还指出了北大编《高等代数》第二版中的伪正交变换习题的一个错误．     

基于函数arccos(px+q)变换的灰色预测模型研究

借助于函数变换理论和灰色系统建模理论,并结合反余弦函数和线性函数的特点,提出了反余弦函数和线性函数相结合的变换方法并建立了一个改进的GM(1,1)模型.证明了这种变换一方面能提高序列的光滑比并压缩序列的级比;另一方面可以使还原误差减小.具体算例结果表明,经过反余弦函数和线性函数相结合建立的改进GM(1,1)模型的拟合精度优于传统GM(1,1)模型和基于反余弦函数变换的GM(1,1)模型的拟合精度.     

基于生存数据的半参数变换的删失回归估计

生存数据经过未知的单调变换后等于协变量的线性函数加上随机误差, 随机误差的分布函数已知或是带未知参数的已知函数\bd 本文先给出未知单调变换的一个相合估计, 再对删失数据做变换, 在此基础上给出了协变量系数的最小二乘估计, 并讨论它的大样本性质.     

On the Comparisons of Unit Dual Quaternion and Homogeneous Transformation Matrix

This paper reveals the differences and similarities between two popular unified representations, i.e. the UDQ (unit dual quaternion) and the HTM (homogeneous transformation matrix), for transformation in the solution to the kinematic problem, in order to provide a clear, concise and self-contained introduction into dual quaternions and to further present a cohesive view for the UDQ and HTM representations as used in robotics. Specifically, after investigating some fundamental algebraic properties of the UDQ, it is revealed that the kinematical equations represented by the UDQ and the HTM are accordant, and afterwards the direct relationship of UDQ-based error kinematical models in spatialframe and in body-frame are further discussed, with conclusion that either error kinematic model can be chosen for designing kinematical control laws. Finally, the comparative study on the proportional control algorithms based on the logarithmical mapping of the HTM and the UDQ shows that the UDQ-based control law is indeed higher in computational efficiency.     

模糊错误集上的置换变换

本文研究了模糊错误集上的置换变换在错误的传递、转化与消除过程中的性质和规律     

New maximum entropy-based algorithm for structural design optimization

A new algorithm based on nonlinear transformation is proposed to improve the classical maximum entropy method and solve practical problems of reliability analysis. There are three steps in the new algorithm. Firstly, the performance function of reliability analysis is normalized, dividing by its value when each input is the mean value of the corresponding random variable. Then the nonlinear transformation of such normalized performance function is completed by using a monotonic nonlinear function with an adjustable parameter. Finally, the predictions of probability density function and/or the failure probability in reliability analysis are achieved by looking the result of transformation as a new form of performance function in the classical procedure of maximum entropy method in which the statistic moments are given through the univariate dimension reduction method. In the proposed method, the uncontrollable error of integration on the infinite interval is removed by transforming it into a bounded one. Three typical nonlinear transformation functions are studied and compared in the numerical examples. Comparing with results from Monte Carlo simulation, it is found that a proper choice of the adjustable parameter can lead to a better result of the prediction of failure probability. It is confirmed in the examples that result from the proposed method with the arctangent transformation function is better than the other transformation functions. The error of prediction of failure probability is controllable if the adjustable parameter is chosen in a given interval, but the suggested value of the adjustable parameter can only be given empirically.