Some notes on Zadeh’s extensions

This paper shows that the Zadeh’s extensions of sendograph-metric-continuous fuzzy-valued functions are sendograph-metric-continuous fuzzy functions.     

Improved Scalar Multiplication on Elliptic Curves Defined over F2mn

We propose two improved scalar multiplication methods on elliptic curves over F_qn where q = 2^m using Frobenius expansion. The scalar multiplication of elliptic curves defined over subfield F_q can be sped up by Frobenius expansion. Previous methods are restricted to the case of a small m. However, when m is small, it is hard to find curves having good cryptographic properties. Our methods are suitable for curves defined over medium‐sized fields, that is, 10 ≤ m ≤ 20. These methods are variants of the conventional multiple‐base binary (MBB) method combined with the window method. One of our methods is for a polynomial basis representation with software implementation, and the other is for a normal basis representation with hardware implementation. Our software experiment shows that it is about 10% faster than the MBB method, which also uses Frobenius expansion, and about 20% faster than the Montgomery method, which is the fastest general method in polynomial basis implementation.     

NS2扩展突发性业务流：设计与实现

结合Markov调制泊松过程（MMPP）和混合泊松流,为突发性分组业务设计了Gamma调制泊松过程（GMPP）业务流模型。面向开源仿真器NS2的功能扩展,给出了纯泊松流、MMPP流和GMPP流的NS2扩展设计和实现方案,并经仿真实验进行了验证。分析表明GMPP更适用于实际业务流。     

块H-矩阵的简捷判据

Feingold与Varga引入了块对角占优的概念,基于它的优美性质,引起了许多学者的浓厚兴趣本文研究块H-矩阵(广义块对角占优矩阵)的实用判定,给出了块H-矩阵的两个新的简捷判据,并应用十矩阵正稳定性和亚正定性的判定。     

一种适用于信源数时变的自适应盲源分离算法

针对信源数动态变化情况下的盲源分离问题,首先采用一种基于交叉验证技术的估计方法用于估计时变的源数,然后推导了一种基于自然梯度和Frobenius范数相结合的自适应盲源分离算法,该算法不需要对源信号作任何约束性的假设,因此该算法适合于分离服从超高斯或亚高斯分布的信号。提出的算法通过了源数不变和源数动态变化2种方式实验的验证。     

无限柱形多孔催化剂颗粒中不可逆一级等温扩散反应的理论分析

无限柱形多孔催化剂粒内一级扩散反应是以贝塞乐方程方式描述的,它的求解不象无限片形和球形多孔催化剂对应方程的求解那样容易,本文采用Frobenius无限级数法对这一问题进行了求解,并在理论上对所求结果进行了分析。     

Photoshop脚本工具在金相图片制作上的应用

以景深扩展和视域扩展为例,介绍了Photoshop CS软件的脚本工具在高质量的金相图片制作上的应用实例,这些应用突破了光学金相显微镜和图像采集设备的物理限制,具有智能和高效的特点,可广泛应用在各种类型的金相图片制作中,丰富了金相图片的制作手段,提高了金相分析工作的质量和效率。同时也探讨了图像编辑软件在金相图片制作中的利与弊。     

Exact solutions for vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses

Exact solutions are presented for the free vibration and buckling of rectangular plates having two opposite edges (x=0 and a) simply supported and the other two (y=0 and b) clamped, with the simply supported edges subjected to a linearly varying normal stress σ_x=−N₀[1−α(y/b)]/h, where h is the plate thickness. By assuming the transverse displacement (w) to vary as sin(mπx/a), the governing partial differential equation of motion is reduced to an ordinary differential equation in y with variable coefficients, for which an exact solution is obtained as a power series (the method of Frobenius). Applying the clamped boundary conditions at y=0 and b yields the frequency determinant. Buckling loads arise as the frequencies approach zero. A careful study of the convergence of the power series is made. Buckling loads are determined for loading parameters α=0,0.5,1,1.5,2, for which α=2 is a pure in-plane bending moment. Comparisons are made with published buckling loads for α=0,1,2 obtained by the method of integration of the differential equation (α=0) or the method of energy (α=1,2). Novel results are presented for the free vibration frequencies of rectangular plates with aspect ratios a/b=0.5,1,2 subjected to three types of loadings (α=0,1,2), with load intensities N₀/N_cr=0,0.5,0.8,0.95,1, where N_cr is the critical buckling load of the plate. Contour plots of buckling and free vibration mode shapes are also shown.     

The Slice Algorithm for irreducible decomposition of monomial ideals

Irreducible decomposition of monomial ideals has an increasing number of applications from biology to pure math. This paper presents the Slice Algorithm for computing irreducible decompositions, Alexander duals and socles of monomial ideals. The paper includes experiments showing good performance in practice.