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.     

Sparse shape functions for tetrahedral <Emphasis Type="Italic">p</Emphasis>-FEM using integrated Jacobi polynomials

Summary In this paper, we investigate the discretization of an elliptic boundary value problem in 3D by means of the hp-version of the finite element method using a mesh of tetrahedrons. We present several bases based on integrated Jacobi polynomials in which the element stiffness matrix has nonzero entries, where p denotes the polynomial degree. The proof of the sparsity requires the assistance of computer algebra software. Several numerical experiments show the efficiency of the proposed bases for higher polynomial degrees p.      

带不等式约束的线性相位FIR数字滤波器的Chebyshev设计

本文主要讨论带不等式约束的线性相位FIR数字滤波器的Chebyshev设计问题.我们知道,交错点组定理是Remez算法的理论基础,而此算法很好的解决了无约束线性相位FIR数字滤波器Chebyshev设计问题.本文中给出并证明了一个与交错点组定理类似的定理,并以此定理为依据设计算法求解具有不等式约束的线性相位FIR滤波器Chebyshev设计问题,此算法可通过对Matlab中remez()函数的修改来实现.     

Method for FIR filters design with compressed cosine using Chebyshev's norm

This paper considers a new method for FIR filters design. The method uses an L_∞ optimality norm. To achieve a better approximating effect, a new modulating function which compresses the oscillations of the cosine is proposed. A parameter sets the gradient of the modulating function, with respect to the oscillations’ compression. The approximating polynomial is carried out using Remez’ exchange algorithm. An optimal polynomial with lowest possible (four) degree, that approximates an ideal filter's response with high precision is proposed. With the proposed method a FIR filter with arbitrary specifications can be designed. Design examples of FIR filters with a minimization of calculation are performed. The obtained filter's responses are close to the ideal response. The design examples demonstrate that the proposed approach may be a good alternative in several applications.     

用Lagrange插值法平滑拟合凸轮实测廓线

以ＳＧＴ２０２多臂３号凸轮为例,用Ｌａｇｒａｎｇｅ插值多项式平滑拟合实测凸轮廓线,以便于数控机床编程和提高凸轮廓线的加工质量,介绍的方法具有普遍性。     

ON GENERALIZED FRACTIONAL PROCESSES

Abstract. A class of stationary long-memory processes is proposed which is an extension of the fractional autoregressive moving-average (FARMA) model. The FARMA model is limited by the fact that it does not allow data with persistent cyclic (or seasonal) behavior to be considered. Our extension, which includes the FARMA model as a special case, makes use of the properties of the generating function of the Gegenbauer polynomials, and we refer to these models as Gegenbauer autoregressive moving-average (GARMA) models. While the FARMA model has a peak in the spectrum at f = 0, the GARMA process can model long-term periodic behavior for any frequency 0 f 0.5. Properties of the GARMA process are examined and techniques for generation of realizations, model identification and parameter estimation are proposed. The use of the GARMA model is illustrated through simulated examples as well as with classical sunspot data.