An Efficient Numerical Scheme to Solve a Quintic Equation of State for Supercritical Fluids

In this study, an efficient iterative algorithm is devised to handle a nonlinear equation arising in estimation of thermodynamic properties at supercritical conditions. The approach is based on a synergistic combination of the classic Newton-Raphshon algorithm and the Adomian decomposition method. We demonstrate that the proposed method enjoys a higher degree of accuracy while requiring fewer iterations to reach a specific solution compared to that by the Newton-Raphson algorithm. To illustrate the efficiency of the aforementioned solution technique, several numerical examples are provided. The proposed method has been easily implemented in computer codes to provide parametric, not just numeric, solutions to the model equations. Consequently, one can derive other thermodynamic properties, which have not been treated parametrically to date, based on our new combined approach.     

Direct calculation of modal parameters from matrix orthogonal polynomials

The object of this paper is to introduce a new technique to derive the global modal parameter (i.e. system poles) directly from estimated matrix orthogonal polynomials. This contribution generalized the results given in Rolain et al. (1994) [5] and Rolain et al. (1995) [6] for scalar orthogonal polynomials to multivariable (matrix) orthogonal polynomials for multiple input multiple output (MIMO) system.Using orthogonal polynomials improves the numerical properties of the estimation process. However, the derivation of the modal parameters from the orthogonal polynomials is in general ill-conditioned if not handled properly. The transformation of the coefficients from orthogonal polynomials basis to power polynomials basis is known to be an ill-conditioned transformation. In this paper a new approach is proposed to compute the system poles directly from the multivariable orthogonal polynomials. High order models can be used without any numerical problems.The proposed method will be compared with existing methods (Van Der Auweraer and Leuridan (1987) [4] Chen and Xu (2003) [7]). For this comparative study, simulated as well as experimental data will be used.     

Some Power Mappings with Low Differential Uniformity

 Differentially uniform power mappings of the form f (x)=x ^d over GF(p ⁿ ) are considered. We construct an infinite family of 2-uniform mappings in the binary case. In the nonbinary case we give two large families of k-uniform mappings with low values of k. We also show how to construct families of sequences from differentially 1-uniform power mappings, which have parameters as good as the best presently known comparable families of sequences. Received: November 4, 1996; revised version: February 14, 1997     

用于三维像散厄米-高斯光束对称化的新型光学系统

基于矩阵合成和分解理论,提出了可将三维像散厄米高斯光束变换为对称拉盖尔高斯光束的两种新型光学系统,并以数值计算例加以说明。     

Hermite polynomial smoothing in beam-to-beam frictional contact

In this paper a smoothing procedure is suggested for the 3D beam-to-beam contact. A smooth segment is defined basing on current position vectors of three nodes limiting two adjacent finite elements. The approximated fragment of a beam axis as a 3D curve spans between the centre points of these elements. The curve is described parametrically using three Hermite polynomials. The four boundary conditions necessary to determine the coefficients for each of these polynomials involve co-ordinates and slopes at the curve ends. The slopes are defined in terms of the element nodal co-ordinates, too. There is no dependence on nodal rotations so this formulation can be embedded in a beam analysis using any type of beam finite element. This geometric representation of the curve is incorporated into the 3D beam-to-beam frictional contact model with the penalty method used to enforce contact constraints. The residual vector and the corresponding tangent stiffness matrix are determined for the normal part of contact and for the stick or slip state of friction. A few numerical examples are presented to show the performance of the suggested smoothing procedure in the cases featuring large frictional sliding.     

Efficient realization of the Galerkin method in view of new properties of Chebyshev polynomials

The Galerkin method is used taking account of new properties of Chebyshev polynominals of the first and second kinds to demonstrate the possibility of simplifying the asymptotic analysis and synthesis of various systems governed by operator equations.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 140–148, November–December 2004.This revised version was published online in April 2005 with a corrected cover date.     

Aliasing probability transients

Test data reduction for digital systems is often accomplished through the use of a feedback shift register. This method, known as signature analysis, can exhibit error masking or aliasing. Recent analysis has shown that the use of a primitive polynomial for the register feedback can reduce the probability of aliasing. In this work we demonstrate that not all primitive polynomials are created equal. Some primitive polynomials can have very large transients in their aliasing probability. For example, 1 +X ¹³ +X ³³ can exhibit an aliasing probability more than a million times larger than its asymptotic value of 2^–33. An evaluation procedure is presented which can identify polynomials with good transient characteristics. Some recommended feedback polynomials are given.     

基于Hermite插值的捷联惯导姿态解算算法

将Hermite插值定理用于某远程多用途导弹捷联惯性导航系统的姿态解算 ,解决了弹体高动态特性与相对较低的传感器采样频率之间的矛盾 .对仿真结果进行了分析 ,为远程多用途导弹采用捷联惯导方案获取弹体信息并进行制导提供了可能性 .     

On the stability of a general polynomial in the space of Markov parameters

Markov parameters and the associated stability criterion were first introduced for continuous-time real polynomials. Recently, robust stability of such polynomials was considered in Markov parameters space, where efficient robust stability tests were obtained based on the Markov theorem. This has motivated the authors to extend the above idea to more general types of polynomials, and develop Markov parameters and the associated stability criterion for complex continuous-time as well as real and complex discrete-time polynomials. Moreover, for each polynomial type, we present compact relations in order to recover the coefficients of a polynomial corresponding to a given set of Markov parameters. The stability results presented here may be useful for 1-D and 2-D filtering and control applications.     

一种正交多项式混沌全局建模方法

本文研究了一种正交多项式混沌全局建模方法 ,所用正交多项式集以吸引子不变测度为核 .通过对H啨ｎｏｎ映射数据和电离层参数实测数据的分析 ,表明在待建模系统不很复杂时 (其内在机理可用较低阶多项式表达 ) ,这种全局建模方法能得到系统动力学特性 .在低噪声情况下模型还能充分精确地重构系统方程式 .在噪声较大或系统内在机理很复杂时建模结果仍可用于一步预测 ,且具有较好效果