Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicators

In this work, a new global reanalysis technique for the efficient computation of stresses and error indicators in two‐dimensional elastostatic problems is presented. In the context of the boundary element method, the global reanalysis technique can be viewed as a post‐processing activity that is carried out once an analysis using Lagrangian elements has been performed. To do the reanalysis, the functional representation for the displacements is changed from Lagrangian to Hermite, introducing the nodal values of the tangential derivatives of those quantities as additional degrees of freedom. Next, assuming that the nodal values of the displacements and the tractions remain practically unchanged from the ones obtained in the analysis using Lagrangian elements, the tangent derivative boundary integral equations are collocated at each functional node in order to determine the additional degrees of freedom that were introduced. Under this scheme, a second system of equations is generated and, once it is solved, the nodal values of the tangential derivatives of the displacements are obtained. This approach gives more accurate results for the stresses at the nodes since it avoids the need to differentiate the shape functions in order to obtain the normal strain in the tangential direction. When compared with the use of Hermite elements, the global reanalysis technique has the attraction that the user does not have to give as input data the additional information required by this type of elements. Another important feature of the proposed approach is that an efficient error indicator for the values of the stresses can also be obtained comparing the values for the stresses obtained through the use of Lagrangian elements and the global reanalysis technique. Copyright © 2001 John Wiley & Sons, Ltd.     

On Hermite interpolation with B-splines

Polar forms are used to find the B-spline control points for Hermite interpolation.     

Padé-Legendre Interpolants for Gibbs Reconstruction

We discuss the use of Padé-Legendre interpolants as an approach for the postprocessing of data contaminated by Gibbs oscillations. A fast interpolation based reconstruction is proposed and its excellent performance illustrated on several problems. Almost non-oscillatory behavior is shown without knowledge of the position of discontinuities. Then we consider the performance for computational data obtained from nontrivial tests, revealing some sensitivity to noisy data. A domain decomposition approach is proposed as a partial resolution to this and illustrated with examples.Dedicated to our friend and mentor, Prof David Gottlieb, on the occasion of his 60th birthday     

基于第二类切比雪夫多项式的语音线性谱对参数的计算

对线性谱对(LSP)参数的计算方法提出改进算法，该算法利用第二类切比雪夫多项式的迭代性质对初始函数降阶。理论分析表明，改进算法可以获得更简洁的数学表达式。实验结果显示，改进算法中基本消除了乘法运算，同时随着线性预测分析阶数的增加可以进一步降低算法复杂度。     

Bivariate hermite subdivision

A subdivision scheme for constructing smooth surfaces interpolating scattered data in R³ is proposed. It is also possible to impose derivative constraints in these points. In the case of functional data, i.e., data are given in a properly triangulated set of points {(x_i, y_i)}_i=1^N from which none of the pairs (x_i,y_i) and (x_j,y_j) with i≠j coincide, it is proved that the resulting surface (function) is C¹. The method is based on the construction of a sequence of continuous splines of degree 3. Another subdivision method, based on constructing a sequence of splines of degree 5 which are once differentiable, yields a function which is C² if the data are not ‘too irregular’. Finally the approximation properties of the methods are investigated.     

波前像差引导准分子激光角膜消融的研究及实现

波前像差引导的准分子激光角膜消融是屈光手术的新方法 ,本文研究目的用像差来引导屈光手术 ,使人眼的视力能够达到 2 0 / 10以上 ,并避免当前PRK、LASIK屈光手术前后像差增大而引起的对视觉质量的影响。分析人眼像差的概念和产生的原因 ,并用Zernike多项式表示 ,理论上定量地分析了Zernike多项式表示的波前像差与角膜切削深度的关系 ,研究了准分子激光切削角膜的机理 ,给出了准分子激光人眼像差矫正系统的原理框图 ,达到了矫正人眼像差的目的。     

Some counterexamples in robust stability theory

This note deals with the problem of determining if a linear system whose characteristics polynomial depends multilinearly on n independent uncertain real parameters Δ_i, I = 1,…,n, is robustly stable. It is shown by example that a polynomial in n variables may have a unique real root, and that this observation disposes of several natural conjectures in robust stability theory. In particular, we show that, in a certain sense, there are no ‘edge’ or ‘m-dimensional face’ Kharitonov-like theorems for the general multilinear case. The result holds even when restricted to that subset of multilinear functions which can be written in the form f(Δ₁,…, Δ_n) = det(I + diag(Δ₁,…,Δ_n)M) for some complex matrix M.     

一种低复杂度的基站信道处理器实现方法

本文提出了一种降低基站信道处理器计算复杂度的方法.通过利用插值二阶多项式滤波器对IDFT滤波器组进行整形处理,IDFT滤波器组可以直接用作基站信道处理器.实现此信道处理器的复杂度更低,因此适合在以软件无线电技术实现的基站中采用.理论分析和仿真结果表明,在保持系统性能基本不变的条件下,该方法在实现信道滤波器方面比K.C.Zangi等^[1]提出的开放滤波器组(OFB)信道处理器提高效率17%.     

Some results on permutation polynomials over finite fields

This paper deals with two questions concerning permutation polynomials in several variables. Lidl and Niederreiter have considered the problem of when a sum of permutation polynomials in disjoint sets of variables is itself a permutation polynomial, and in the case of prime fields have shown that it is necessary and sufficient that at least one summand be a permutation polynomial. They also showed that in the case of non-prime fields this condition is not necessary. In this paper, a necessary and sufficient condition is obtained for the general case which specialises to the previous result for prime fields. The second part extends a criterion of Niederreiter for permutation polynomials over prime fields to any finite field.     

The Cayley method in computer aided geometric design

A thorough treatment of the Cayley method of elimination is given, with particular emphasis on its implementation to solve problems in computational geometry. An easily programmable formula for the Cayley matrix is derived, it is shown how to extract the birational correspondence from the Cayley matrix, numerous examples are worked, and the connection between the Cayley method and the Euclidean Algorithm is explained.