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。     

An algorithm for computing compatibly Frobenius split subvarieties

This paper describes an algorithm which produces all ideals compatible with a given surjective Frobenius near-splitting.     

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.     

在乘法扰动下延拓矩阵奇异空间的扰动界

在矩阵A和A有相同分块的奇异值分解和乘法扰动下,对于母矩阵为A的行延拓矩阵Rk(A)与其扰动矩阵RK(A),使用奇异值的双分离度获得左右奇异空间的分离,研究了延拓矩阵Rk(A)与其扰动矩阵RK(A)的奇异空间在Frobenius范数下的扰动界.     

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。     

Poincaré Normal Form for a Class of Driftless Systems in a One-Dimensional Submanifold Neighborhood

In this paper, motivated by the restrictive conditions required to obtain an exact chained form, we propose a quadratic normal form around a one-dimensional equilibrium submanifold for systems which are in a chained form in their first approximation. In the case considered here, in contrast to the case of approximated feedback linearization, not all the state and input components have the same approximation meaning. Because of this, we use a very simplified version of dilation, which is a useful way to design a homogeneous control law for driftless systems. Date received: December 2, 1999. Date revised: October 24, 2001.     

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.     

The scattering of electro-elastic waves by a spherical piezoelectric particle in a polymer matrix

This paper is devoted to the study of scattering of plane harmonic waves by a piezoelectric sphere with spherical isotropy embedded in an unbounded isotropic polymer matrix. The scattered displacement field and the electric potential in the matrix are expressed in terms of spherical vector wave functions and spherical harmonic functions, respectively. For the field points inside the inhomogeneity, new displacement functions are introduced. Expansion of the new displacement functions and the electric potential in terms of spherical harmonic functions, the equations of motion and electrostatic lead to four second order ordinary differential equations (odes), where three of them are coupled. The coupled system of odes is solved by the generalized Frobenius series. This approach is readily used to handle low and high frequencies. Three different types of piezoelectric inhomogeneities, PZT-4, PZT-5H, and BaTiO₃ are considered and the associated piezoelectric effects on the electro-mechanical fields, differential and total scattering cross-sections are addressed.     

Fast Multiplication on Elliptic Curves over Small Fields of Characteristic Two

We discuss new algorithms for multiplying points on elliptic curves defined over small finite fields of characteristic two. This algorithm is an extension of previous results by Koblitz, Meier, and Staffelbach. Experimental results show that the new methods can give a running time improvement of up to 50 % compared with the ordinary binary algorithm for multiplication. Finally, we present a table of elliptic curves, which are well suited for elliptic curve public key cryptosystems, and for which the new algorithm can be used. Received 14 January 1997 and revised 4 September 1997