混凝土中氯离子扩散的二次有限元分析

大量研究表明,氯离子在混凝土中的扩散严重影响了混凝土的耐久性.基于Fick第二定律,考虑二维扩散问题,采用灵活度较好的三角形剖分单元和精确度更高的二次插值基函数,建立了氯离子在混凝土中扩散的二次有限元模型,并进行了收敛性分析.同时,对常数边界、线性边界、振荡边界的二次有限元模型进行数值模拟,有效地预测了氯离子在三种边界条件下的扩散趋势.     

双周期二次样条的插值逼近

§1.引言 考虑矩形区域Ω=[0,1]?[0,1],Δ_(mn)~((2))为Ω的均匀四方向网,它将Ω分成4mn个小三角形单元. 样条空间 S_2~1(Δ_(mn)~((2)))由满足以下条件的S(x,y)组成:     

一个新的时间序列的插值模型

在这篇文章里,通过使用二次B样条,给出了一个用于数据挖掘的新的插值法方法,给出了时间序列的局部插值模型,插值曲线是C1连续的,该方法具有不需要解线性方程组的优点,应用上海股票指数进行了数值实验,实验性结果表明方法是有效的.     

关于构建二次模型中单纯形方法的使用

本文我们研究了直接法中的二次插值模型逼近方法.在单纯形方法的基础上,通过组合算法迭代所体现的问题的局部信息来构建新的搜索方向,从而构建新的搜索子空间.然后,在所得的新的搜索子空间求解原目标函数的近似二次模型.我们的动机是利用算法前面的步骤所体现的信息来构造更有可能下降快速的方向.实验表明,对于大多数测试问题,我们的方法可以显著的减少函数值的计算次数.     

磨削加工具有复杂母线的旋转体的微分模型

综合运用微分几何、坐标变换、分段二次Hermite插值及微分方程等数学工具,将磨削加工具有复杂母线的旋转体的问题,通过建立微分模型,然后根据求出的解,设计出了具体的加工方案.对于具有抛物线母线的工件,给出了一个在上台电机进给速度恒定的条件下,加工时间尽可能短的加工方案.对于具有一般母线的工件,利用分段二次Hermite插值,转化为抛物线的情形,也得到了很好的解决.还编写了一系列Matlab程序,作为解决过程中的产品,它们的输出可以直接用于控制磨床,加工具有任意母线的工件.此外,在使得砂轮表面的磨损尽量均匀的问题上,做了富有创造性的探索,并且给出了一个使得圆柱形砂轮磨损比较均匀的加工方案.总体而言,模型具有适用范围广、加工精度高等优点.     

单输入多时滞离散系统的线性二次调节问题

研究了单输入多时滞的离散时间系统的线性二次调节问题(LQR问题),给出了求解最优控制输入序列的一种简单有效而又新颖的方法.将该动态的离散时滞系统的LQR最优控制问题最终转化成了一个静态的、不带时滞的数学规划模型——带等式线性约束的严格凸二次规划问题,并利用两种方法解这个二次规划问题,均成功地导出了系统的最优控制输入序列.仿真结果验证了我们的方法的正确有效性.     

INTERPOLATION WITH RESTRICTED ARC LENGTH

AbstractFor given data (t_i,y_i),i=0, 1,…,n,0=t_0相似文献   

几种基于散乱数据拟合的局部插值方法

本文首先针对散乱数据拟合的Shepard方法,结合截断多项式、B样条基函数和指数函数来构造其权函数,使新的权函数具有更高的光滑度和更好的衰减性,并且其光滑性和衰减性可以根据实际需要自由调节,从而提高了曲面的拟合质量．同时还给出一种类似的局部插值方法．另外,本文还基于多重二次插值,结合多元样条的思想,给出了两个局部插值算法．该算法较好地继承了多重二次插值曲面的性质,从而保证了拟合曲面具有好地光顺性和拟合精度．曲面整体也具有较高的光滑性．     

弧长约束下的二次样条插值

1 引言 具有约束的插值与逼近在曲线及曲面的设计中有重要的意义。目前已有很多有关保持单调性,凸性等性质的样条插值的结果。另一种很重要的约束就是保持曲面在某些区域上的面积,例如在汽车工业中,由于受实际因素的限制,性能的原因甚至是美学的原因,需要曲面满足在某些区域的有界性,特别在飞机的进气道的设计中,经常遇到如下问题:如何构造具有面积约束的插值曲面?这个问题在一元的情形即是保持弧长约束,它是由Wang &Damme首先提出来的,它可以用来解决旋转不变曲面的面积约束插值。Wang&Damme针对S_3~1(△)给出了插值的适定性及误差估计,但对S_2~1(△),因为其自由度最多是2,从而不能满足弧长约束。采用加细剖分的办法,使结点数增加,但让新增结点上的y值自由,这样就相应地增加了自由度,从而可用来解决这个问题。     

加权二次有理Bézier插值曲线

在本文中,给定一组有序空间数据点列及每个数据点的切矢向量,利用加权二次有理Bézier曲线对数据点作插值曲线,使该曲线具有C1连续性,并且权因子只是对相应顶点曲线附近产生影响,同调整两个相邻的权因子可以调整这两个相邻顶点之间的曲线和它的控制多边形.     

有限维逼近无限维总极值的水平值估计方法

变分计算、最优控制、微分对策等常常要求考虑无限维空间中的总极值问题,但实际计算中只能得出有限维空间中的解.本文用有限维逼近无限维的方法来讨论函数空间中的总体最优化问题.用水平值估计和变侧度方法来求得有限维逼近总体最优化问题.对于有约束问题,用不连续精确罚函数法将其转化为无约束问题求解.     

Biological computation of the solution to the quadratic assignment problem

Biological computing provides a promising approach to attacking computationally intractable problems. The quadratic assignment problem (QAP) is a well-known NP-hard combinatorial optimization problem. This paper addresses the problem of how to solve QAP under the Adleman–Lipton-sticker model. A theoretically efficient DNA algorithm for solving QAP is proposed, which is executed by performing O(Kn⁴) operations on test tubes of DNA molecular strands with n² + K + 1 bit regions, where n is the number of facilities, and K is the length of the binary representation of an upper bound on the objective function. With the rapid progress of molecular biology techniques, the proposed algorithm might be of practical use in treating medium-sized instances of QAP.     

An alternative method for a global analysis of quadratic programs in a finite number of steps

This paper considers the global analysis of general quadratic programs in a finite number of steps. A procedure is presented for recursively finding either the global minimum or a halfline of the constraint set along which the minimand is unbounded below.Research was partially supported by the U.S. Energy Research and Development Administration Contract EY-76-S-03-0326 PA #18; the Office of Naval Research Contracts N00014-75-C-0267 and N00014-75-C-0865; and the National Science Foundation Grants MCS76-20019 and MCS76-81259.     

Quadratic convex reformulations for quadratic 0–1 programming

This is a summary of the author’s PhD thesis supervised by A. Billionnet and S. Elloumi and defended on November 2006 at the CNAM, Paris (Conservatoire National des Arts et Métiers). The thesis is written in French and is available from http://www.cedric.cnam.fr/PUBLIS/RC1115. This work deals with exact solution methods based on reformulations for quadratic 0–1 programs under linear constraints. These problems are generally not convex; more precisely, the associated continuous relaxation is not a convex problem. We developed approaches with the aim of making the initial problem convex and of obtaining a good lower bound by continuous relaxation. The main contribution is a general method (called QCR) that we implemented and applied to classical combinatorial optimization problems.      

Smooth lattices over quadratic integers

We construct lattices with quadratic structure over the integers in quadratic number fields having the property that the rank of the quadratic structure is constant and equal to the rank of the lattice in all reductions modulo maximal ideals. We characterize the case in which such lattices are free. The construction gives a representative of the genus of such lattices as an orthogonal sum of “standard” pieces of ranks 1–4 and covers the case of the discriminant of the real quadratic number field congruent to 1 modulo 8 for which a general construction was not known.      

Quadratic residues and the combinatorics of sign multiplication

If S is a nonempty finite set of positive integers, we find a criterion both necessary and sufficient for S to satisfy the following condition: if q is a fixed nonnegative integer, then there exists infinitely many primes p such that S contains exactly q quadratic residues of p. This result simultaneously generalizes two previous results of the author, and the criterion used is expressed by means of a purely combinatorial condition on the prime factors of the elements of S of odd multiplicity.     

Quadratic forms and congruences for ℓ-regular partitions modulo 3, 5 and 7

Let $b_{\ell }(n)$ be the number of ℓ-regular partitions of n. We show that the generating functions of $b_{\ell }(n)$ with $\ell =3,5,6,7$ and 10 are congruent to the products of two items of Ramanujan's theta functions $\psi (q)$, $f(-q)$ and ${(q;q)}_{\infty }^3$ modulo 3, 5 and 7. So we can express these generating functions as double summations in q. Based on the properties of binary quadratic forms, we obtain vanishing properties of the coefficients of these series. This leads to several infinite families of congruences for $b_{\ell }(n)$ modulo 3, 5 and 7.     

An L \infty/ L 1-Constrained Quadratic Optimization Problem with Applications to Neural Networks

Pattern formation in associative neural networks is related to a quadratic optimization problem. Biological considerations imply that the functional is constrained in the L_\infty norm and in the L₁ norm. We consider such optimization problems. We derive the Euler–Lagrange equations, and construct basic properties of the maximizers. We study in some detail the case where the kernel of the quadratic functional is finite-dimensional. In this case the optimization problem can be fully characterized by the geometry of a certain convex and compact finite-dimensional set.