An iterative method for suboptimal control of linear time-delayed systems

This article presents a new approach for solving the Optimal Control Problem (OCP) of linear time-delay systems with a quadratic cost functional. The proposed method can also be used for designing optimal control time-delay systems with disturbance. In this study, the Variational Iteration Method (VIM) is employed to convert the original Time-Delay Optimal Control Problem (TDOCP) into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Finally, Illustrative examples are included to demonstrate the validity and applicability of the technique.     

Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials

We extend the definition of the classical Jacobi polynomials withindexes α, β>−1 to allow α and/or β to be negative integers. We show that the generalized Jacobi polynomials, with indexes corresponding to the number of boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the use of generalized Jacobi polynomials leads to much simplified analysis, more precise error estimates and well conditioned algorithms.Mathematics subject classification 1991. 65N35, 65N22, 65F05, 35J05     

用金字塔图法匹配边界图象的三眼立体视觉方法

本文在分析了双眼立体视觉面临的本质困难之后，提出了用金字塔图法匹配特征基元的三眼立体视觉方法，这种方法由于建筑在透视投影几何原理的稳固基础上，无须任何先验限制，也不以图象相似性为基础，故可较好地解决精度与匹配难度的矛盾，且运用金字塔图法进行匹配传播使在保证精度的基础上，匹配速度大大提高，对计算机人工图象的匹配结果表明，误匹配率几乎为零，且有较高的匹配速度和精度。     

An Algorithm For Selecting a Generator of Z_p

How to select a generator of Zp* is an important problem in cryptographic applications, where p is an odd prime. In this paper, we mainly consider the especial case that p is a safe prime, and give an algorithm for selecting a generator of Zp*,and find all generators of Zp* , where p is a safe prime. Our algorithm is more faster than the algorithm in [1]. Based on the proposed algorithm, one could find all generators of Zp* as well, where p is a perfect prime.     

推广的Kantorovi多项式的L_p保持Lipschitz条件性

本文研究推广的Kantorovi多项式P_n~*(f, x)在L_p[0,1]空间中的保持Lipschitz条件性质。     

Brittle detachment of a stiffener bonded to an elastic plate

The diffusion of contact stresses between an elastic bar, bonded to an elastic half-plane and loaded longitudinally, requires the integration of a singular integral equation. The solution of this equation is not available in closed form, but only by a series expansion of the contact tangential force mutually transmitted between the stiffener and the plate. Since forty years it has been realized that the expansion of the solution in terms of Chebyshev polynomials is its most convenient method of representation. The procedure can also be extended to treat the brittle detachments of the tips of the stiffener when, according to Griffith's criterion of fracture, a balance can be virtually established between the increase of strain energy due to a propagation of cracks and the surface energy created.     

Towards an optimum language data model

Maximizing the satisfaction of a value in an engineering design is usually limited by tradeoffs in which other values become unacceptably sacrificed. In a few cases, however, the maximization is limited by a boundary between what is mathematically possible and what is not. Round wheels, vertical pillars, and binary memory elements are examples of optimum engineering structures which result from such mathematical limits. It is proposed that optimum characteristics of a language data model result similarly by minimizing the variety of primitive data objects, the complexity of those objects, and the number of objects needed to represent data states. Reducing these measures is needed to combine both rich data structure and powerful operations in one language. The minimizations lead to a narrow range of designs for language semantics in which the potential advantages of specialization is small compared with the advantages of commonality. Universal language for support of technical literacy appears to be an appropriate scope of generality in language design.     

零点位于左扇区的多项式菱形族

本文考虑多项式菱形族的左扇区稳定性,证明了多项式族左扇区稳定的充分必要条件是的至多4q(q—1)条特殊棱边左扇区稳定;进一步,在一定条件下,只要检验的4q个顶点多项式就可确定的左扇区稳定性。     

Finding nondegenerate Hopf bifurcation points for four-dimensional two-parametric systems

We establish a numerically feasible algorithm to find a simplicial approximation A to a certain part of the boundary of the set of stable (or Hurwitz) polynomials of degree 4. Moreover, we have that . Using this, we build an algorithm to find a piecewise-linear approximation to the intersection curve of a given surface contained in ⁴ with . We have also devised an efficient computer program to perform all these operations. The main motivation is to find the curve of nondegenerate bifurcation points in parameter space for a given 2-parametric Hopf bifurcation problem of dimension 4.