GENERALIZED INVERSE GROUP OF SIGNAL AND ITS IMPLEMENTATION WITH NEURAL NETWORKS

A new concept, the generalized inverse group (GIG) of signal, is firstly proposed and its properties, leaking coefficients and implementation with neural networks are presented. Theoretical analysis and computational simulation have shown that (1) there is a group of finite length of generalized inverse signals for any given finite signal, which forms the GIG; (2) each inverse group has different leaking coefficients, thus different abnormal states; (3) each GIG can be implemented by a grouped and improved single-layer perceptron which appears with fast convergence. When used in deconvolution, the proposed GIG can form a new parallel finite length of filtering deconvolution method. On off-line processing, the computational time is reduced to O(N) from O(N2). And the less the leaking coefficient is, the more reliable the deconvolution will be.     

The vulnerability of geometric sequences based on fields of odd characteristic

A new method of cryptologic attack on binary sequences is given, using their linear complexities relative to odd prime numbers. We show that, relative to a particular prime number p, the linear complexity of a binary geometric sequence is low. It is also shown that the prime p can be determined with high probability by a randomized algorithm if a number of bits much smaller than the linear complexity is known. This determination is made by exploiting the imbalance in the number of zeros and ones in the sequences in question, and uses a new statistical measure, the partial imbalance.This project was sponsored by the National Security Agency under Grant No. MDA904-91-H-0012. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation hereon.     

Sums of Two Exact Powers

An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb.     

完全可分的三元系TS(v,4)的支撑集

§ 1　 IntroductionA triple system of order v and indexλ,denoted by TS(v,λ) ,is a collection of3- ele-mentsubsets Aof a v- set X,so thatevery 2 - subsetof X appears in preciselyλ subsets of A.L etλ≥ 2 and (X,A) be a TS(v,λ) .If Acan be partitioned into t(≥ 2 ) parts A1,A2 ,...,Atsuch that each (X,Ai) is a TS(v,λi) for 1≤ i≤ t,then (X,A) is called de-composable.Otherwise it is indecomposable.If t=λ,λi=1for 1≤ i≤ t,the TS(v,λ) (X,A) is called completely decomposable.It …     

几类数列通项的矩阵求法

本利用矩阵给出了几类数列的通项公式的求法，把数列通项公式的求法转化为矩阵幂的计算，思路简单、计算简便，并能判别其敛散性。     

拟线性抛物型方程广义解的局部有界性

本文给出了一类较广泛的拟线性抛物型方程广义解的局部有界性,进而也得到了解的Holder连续性.     

On generalized gradients

In this paper we present a concept of the construction of generalized gradients by considering a development of directional derivatives into spherical harmonics. This leads to a derivation system as a system of generalized partial derivatives. Necessary conditions for local extrema for a broad class of not necessarily differentiable function can be given and a characterization of points of differentiability can be proved by using generalized gradients.     

基于广义最小均方的自适应递归滤波算法

本文提出了一种广义最小均方(GLMS)算法,分析了GLMS算法的性能,并根据GLMS算法,导出一种自适应递归滤波(ARF)算法。在推导中,ARF算法避开了超稳定定理,从而考虑自适应系统的严格正实条件和Popov不等式是不必要的。计算机模拟表明ARF算法具有很高的收敛速度。     

Asymptotic expansions of integrals of two Bessel functions via the generalized hypergeometric and Meijer functions

Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann—Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods — a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems.