快速傅里叶变换中计算倒序的新思路

为了提高快速傅里叶变换的运算效率,减少运算时间,该文研究了FFT中倒序序列的计算。研究发现不同长度的倒序序列不相互独立,它们之间有深刻的联系,长度为N的倒序序列可以由长度为N/2的倒序序列生成。根据不同长度的倒序序列之间的相互关联性,给出了新的倒序序列的计算方法及相应的算法流程。通过计算仿真,验证了算法的正确性。该算法实现简单,而且运算效率高。与传统算法相比,新算法可将计算效率提高3个数量级。     

变换光学中的几个数学问题分析及其在隐身毯设计中的应用

变换光学(TO)是目前电磁领域的一个研究热点,为了对基于TO的隐身斗篷设计提供更深入的理论支持,该文对TO的3个基本数学问题进行了讨论。首先分析了基于Maxwell方程组3维坐标变换下变换形式的唯一性问题,提出了不同于参考文献的新变换方式,指出了可以灵活调整变换空间特性阻抗的变换方法。以此为基础,提出了以自由空间的场分布为原始空间,通过变换获取到可以隐藏在介质包围区域中并和介质阻抗匹配的隐身斗篷设计方法。然后以基于波动方程的2维TO为研究对象,分析了以电场分量波动方程为基础进行2维变换时,磁场所满足的变换关系和对应的边界条件特性,同样指出了可以隐藏在介质包围区域中并和介质阻抗匹配的隐身斗篷设计方法。最后从数学上证明了2维变换下共形变换对于设计出非各向异性介质隐身斗篷的充分必要性。以上述讨论为基础,该文给出了一个嵌入式斗篷的仿真验证示例。该文的研究内容和结论对基于TO的各种电磁应用提供了理论支持。     

基于固有模态能量熵的微弱目标检测算法

该文分析了海杂波能量在各固有模态函数(IMF)间的分布特点,研究了目标对海杂波能量在各IMF间分布的影响。研究发现,无目标时,海杂波的能量主要集中于先分解出的3个IMF中,而当目标出现时,海杂波的能量将向后分解出的6个IMF扩散,且固有模态能量熵恰能描述目标出现引起的海杂波能量分布的这种变化,因此该文提出了采用固有模态能量熵检测微弱目标的算法。仿真结果表明,与基于盒维数的微弱目标检测算法、频域CFAR检测方法和多脉冲CA-CFAR(100个脉冲)检测算法相比,该算法的检测性能较好,有效增强了雷达对海杂波中微弱目标的检测能力。     

A novel and facile synthesis of 7,8-diacylcoumarins

Oxidation of N-carbonylhydrazones of 7-hydroxy-8-acetylcoumarin with lead tetraacetate results in the synthesis of 7,8-diacylcoumarins in good yields. The reaction proceeds via the transformation of a hydroxy into an acyl group reported for the first time in heterocyclic chemistry.     

曲线选配的模糊性

对样本进行回归分析时不可避免地遇到曲线类型选配的困难。本文指出，相关关系不确定因素中存在模糊性，即选配曲线是一个模糊问题。     

Residues in toric varieties

We study residues on a complete toric variety X, which are defined in terms of the homogeneous coordinate ring of X.We first prove a global transformation law for toric residues. When the fan of the toric variety has a simplicial cone of maximal dimension, we can produce an element with toric residue equal to 1. We also show that in certain situations, the toric residue is an isomorphism on an appropriate graded piece of the quotient ring. When X is simplicial, we prove that the toric residue is a sum of local residues. In the case of equal degrees, we also show how to represent X as a quotient (Y\{0})/C* such that the toric residue becomes the local residue at 0 in Y.     

An easy applicable method for the design of asymmetrical finline and slotline tapers

In this paper, some utilities for the developement of asymmetrical circular arc tapes are described. Basing on a polygon-approximation of characteristic impedance a method for to determine the geometrical parameters of the taper is explained. The applicability of the method presented here is proved by extensive measurements.     

基于空间分解变换的模糊错误矩阵方程求解

模糊错误逻辑对现实世界的对象用(u,x)表示为((U,S(t),■T(t),L(t)),(x(t)=f((u(t),■),GU(t)),GU(t)),用模糊错误变换矩阵可以表示分解、相似、增加、置换、毁灭、单位变换等6种变换方法,本论文基于求解方程XA′=B,针对■的分解,研究了基于空间分解变换的错误矩阵方程求解。以期从矩阵方程求解的角度对错误转化规律进行探索研究。     

Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem

In this paper, we first give an interesting operator identity. Furthermore, using the q-exponential operator technique to the multiple q-binomial theorem and q-Gauss summation theorem, we obtain some transformation formulae and summation theorems of multiple basic hypergeometric series.     

On Global Asymptotic Stability of Second Order Nonlinear Differential Systems

This paper investigates the global asymptotic stability of the autonomous planar systems $ \dot {x} = p_2(y)q_2(x)y $ , $ \dot {y} = p_3(y)q_3(x)x + p_3(y)q_4(x)y $ and $ \dot {x} = f_1(x) + h_2(x)y $ , $ \dot {y} = f_3(x) + h_4(x)y $ , under the assumption that all functions involved in the equations are continuous and that the origin is a unique equilibrium. We present necessary and sufficient conditions for the origin to be globally asymptotically stable.