基于增广矩阵束方法的平面天线阵列综合

针对平面阵列的稀布优化问题,提出了一种基于增广矩阵束方法的减少阵元数目、求解阵元位置和设计幅度激励的优化方法。首先对期望平面阵的方向图进行采样并由采样点数据构造增广矩阵,对此矩阵进行奇异值(SVD)分解,确定在误差允许范围内所需的最小阵元数目;然后基于广义特征值分解分别计算两组特征值,并根据类ESPRIT算法对特征值进行配对;最后在最小二乘准则条件下根据正确的特征值对求解平面阵列的阵元位置和激励。仿真结果表明该算法具有较高的计算效率和数值精度。     

Application of the modified Taylor approximation

In this paper we introduce and describe a new scheme for the numerical integration of smooth functions. The scheme is based on the modified Taylor expansion and is suitable for functions that exhibit near-sinusoidal or repetitive behaviour. We discuss the method and its rate of convergence, then implement it for the approximation of certain integrals. Examples include integrands involving Airy wave, Bessel, Gamma, and elliptic functions. The results, from the data in the tables, demonstrate that the method converges rapidly and approximates the integral as well as some well-known numerical integration methods used with sufficiently small step sizes.     

Some quadrature formulas for functions partially holomorphic with respect to each variable in a Jordan polydomain in C 2 and a complex double integral formula

In this paper, quadrature formulas with remaining term in integral form for functions partially holomorphic with respect to each variable in a Jordan polydomain in C ² and a complex double integral formula are given. For this, we used the Cauchy Integral formula for Jordan polydomain in C ².     

多群中子散射角分布L阶截断出负的改进

蒙特卡罗方法或离散纵标法模拟多群中子输运方程，散射角分布通常按Legendre级数展开，取L阶截断近似。当L较小时，近似角分布在[-1，1]定义域的多处出负，面积不归一，进而导致非物理解。文章针对这一问题，利用矩和Legendre系数等价关系，给出离散广义Gauss求积组，并用该求积组作节点构造等概率阶梯函数，逼近实际角分布，从而消除非物理解。计算取得了与实验和连续截面蒙特卡罗MCNP程序一致的结果。     

再生核空间 H_0~1[a,b]中样条插值算子

讨论了再生核空间Ｈ１０［ａ，ｂ］中，样条插值算子、分段再生核插值算子及最佳插值逼近算子的一致性．这一结果，不仅深化了对再生核空间中插值逼近问题的研究，而且应用这３种算子可相互取长补短，灵活运用，为数值计算提供了方便．     

An algorithm for polygonal approximation of a digital object

A fast and simple heuristic algorithm for polygonal approximation is presented. The algorithm is based on a mark and sweep technique. Results of computer implementation with various images are reported.     

横向各向同性介质Thomsen近似公式的适用范围

Thomsen为横向各向同性（TI）介质提出的各向异性参数和线性近似公式被广泛采用,但目前对Thomsen近似公式的适用范围的认识仍很模糊。针对这一问题,研究了TI介质P波和SV波Thomsen近似公式最大相对误差随各向异性参数变化的特征以及近似公式的适用范围。研究结果表明,波速比α0/β0=1．5时,在-0．12≤ε≤0.16且-0.16≤δ≤0.24,或｜ε-δ｜〈0.17（ε和δ为正）时,P波相速度近似公式的最大相对误差不超过l％,随着了0／0的增大,适用范围略有扩大。SV波近似公式的精度比P波要低一些,在｜ε｜≤0.1且｜δ｜≤0.14,或｜ε-δ｜〈O．02（ε和占为正）时,SV波相速度平方线性近似公式的最大相对误差不超过1％,随着α0/β0的增大,适用伪范围明显缩小。总体来说,P波近似公式适用范围较大,对一些中等强度的各向异性也适用;SV波近似公式尤其是群速度近似公式适用范围很小,必要时需要使用高阶近似或者精确解。     

Variable-order fractional derivatives and their numerical approximations

This paper addresses the different possible definitions of variable-order derivatives and their numerical approximations; both approximations based upon the definitions and approximations consisting of non-linear transfer functions (in particular combining existing approximations of constant-order fractional derivatives, such as the Crone approximation, with fuzzy logic) are considered. There are different possible configurations, implementing variable-order fractional derivatives both with and without memory of past values of the time-dependent differentiation order.     

Axiomatization and conditions for neighborhoods in a covering to form a partition

In this paper, we study the axiomatic issue of a type of covering upper approximation operations. This issue was proposed as an open problem. We also further some known results by using only a single covering approximation operator to characterize the conditions for neighborhood {N(x): x ∈ U} to form a partition of universe U.     

Parametric macromodeling based on amplitude and frequency scaled systems with guaranteed passivity

We propose a novel parametric macromodeling method for systems described by scattering parameters, which depend on multiple design variables such as geometrical layout or substrate features. It is able to build accurate multivariate macromodels that are stable and passive over the entire design space. Poles and residues are parameterized indirectly. The proposed method is based on an efficient and reliable combination of rational identification, a procedure to find amplitude and frequency scaling system coefficients and positive interpolation schemes. Pertinent numerical examples validate the proposed parametric macromodeling technique. Copyright © 2011 John Wiley & Sons, Ltd.