基于电磁力近似算法的驱动电机NVH快速仿真方法

电动汽车驱动电机产生的电磁噪声是汽车NVH关注的重点问题,对其进行全转速段多工况NVH仿真通常需要耗费大量时间和计算资源。该文通过有限单元分析揭示了电机气隙电磁力随转速变化的规律,并根据这一规律提出了基于外特性曲线的电磁力时间缩放及插值的近似算法。文章采用电磁力到结构网格的映射算法对结构振动有限元模型进行激励力加载,使用声场有限元方法计算电机的辐射噪声,最终实现了车用驱动电机的电磁振动及噪声的快速仿真。使用该方法对车用电机进行全转速段振动噪声仿真,可大大压缩多工况电磁场有限元分析所需的计算时间,提升仿真效率。     

Hermite Subdivision Schemes and Taylor Polynomials

We propose a general study of the convergence of a Hermite subdivision scheme ℋ of degree d>0 in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called Taylor subdivision (vector) scheme . The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of is contractive, then is C ⁰ and ℋ is C ^d . We apply this result to two families of Hermite subdivision schemes. The first one is interpolatory; the second one is a kind of corner cutting. Both of them use the Tchakalov-Obreshkov interpolation polynomial.      

A symmetric integrated radial basis function method for solving differential equations

In this article, integrated radial basis functions (IRBFs) are used for Hermite interpolation in the solution of differential equations, resulting in a new meshless symmetric RBF method. Both global and local approximation‐based schemes are derived. For the latter, the focus is on the construction of compact approximation stencils, where a sparse system matrix and a high‐order accuracy can be achieved together. Cartesian‐grid‐based stencils are possible for problems defined on nonrectangular domains. Furthermore, the effects of the RBF width on the solution accuracy for a given grid size are fully explored with a reasonable computational cost. The proposed schemes are numerically verified in some elliptic boundary‐value problems governed by the Poisson and convection‐diffusion equations. High levels of the solution accuracy are obtained using relatively coarse discretisations.     

第二类端点奇异Fredholm积分方程的分数阶退化核方法

本文针对第二类端点奇异Fredholm积分方程构造基于分数阶Taylor展开的退化核方法，设计了两种计算格式，一是在全区间上使用分数阶Taylor展开式近似核函数，二是在包含奇点的小区间上采用分数阶插值，在剩余区间上采用分段二次多项式插值逼近核函数.讨论了两种退化核方法收敛的条件，并给出了混合插值法的收敛阶估计.数值算例表明对于非光滑核函数分数阶退化核方法有着良好的计算效果，且混合二次插值法比全区间上的分数阶退化核方法有着更广泛的适用范围.     

一种修正的拟Grünwald插值在Orlicz空间内的逼近度

修正了以第二类Chebyshev多项式的零点为插值结点组的拟Grünwald插值多项式,使之转化为积分形式,并利用不等式技巧和Hardy-Littlewood极大函数的方法,研究了此积分型拟Grünwald插值算子在带权Orlicz空间内的逼近问题,得出了意义相对广泛的逼近度估计的结果.     

Stationary binary subdivision schemes using radial basis function interpolation

A new family of interpolatory stationary subdivision schemes is introduced by using radial basis function interpolation. This work extends earlier studies on interpolatory stationary subdivision schemes in two aspects. First, it provides a wider class of interpolatory schemes; each 2L-point interpolatory scheme has the freedom of choosing a degree (say, m) of polynomial reproducing. Depending on the combination (2L,m), the proposed scheme suggests different subdivision rules. Second, the scheme turns out to be a 2L-point interpolatory scheme with a tension parameter. The conditions for convergence and smoothness are also studied. Dedicated to Prof. Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 41A05, 41A25, 41A30, 65D10, 65D17. Byung-Gook Lee: This work was done as a part of Information & Communication fundamental Technology Research Program supported by Ministry of the Information & Communication in Republic of Korea. Jungho Yoon: Corresponding author. Supported by the Korea Science and Engineering Foundation grant (KOSEF R06-2002-012-01001).     

The Projective Beth Property and Interpolation in Positive and Related Logics

We look at the interplay between the projective Beth property in non-classical logics and interpolation. Previously, we proved that in positive logics as well as in superintuitionistic and modal ones, the projective Beth property PB2 follows from Craig's interpolation property and implies the restricted interpolation property IPR. Here, we show that IPR and PB2 are equivalent in positive logics, and also in extensions of the superintuitionistic logic KC and of the modal logic Grz.2. Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-2069.2003.1. __________ Translated from Algebra i Logika, Vol. 45, No. 1, pp. 85–113, January–February, 2006.     

联系Butterworth滤波器的双正交小波

联系Butterworth滤波器的双正交小波称为Butterworth小波,它们具有很好的性质:包括对称性,插值性及消失矩．本文定义了离散空间L~2(Z)中的双正交小波并给出一个易于验证的充分条件．利用这一条件,重新得到Butterworth小波;进一步,构造了一类双正交小波．它们不仅具有Butterworth小波的前述所有性质,而且具有最短可能的支集．     

闭区间[0,1]上的分形插值函数的分数阶积分

介绍了分形插值函数和迭代函数系统以及v阶黎曼-刘准尔分数阶积分的概念及相关定理.利用这些概念及定理讨论了分形插值函数的分数阶积分在[0,1]上连续性及判定[0,1]上的分形插值函数的分数阶积分也是[0,1]上的分形插值函数,并给予了证明.