Improved zero-sum distinguisher for full round <Emphasis Type="Italic">Keccak-f</Emphasis> permutation

Keccak is one of the five hash functions selected for the final round of the SHA-3 competition,and its inner primitive is a permutation called Keccak-f.In this paper,we observe that for the inverse of the only nonlinear transformation in Keccak-f,the algebraic degree of any output coordinate and the one of the product of any two output coordinates are both 3,which is 2 less than its size of 5.Combining this observation with a proposition on the upper bound of the degree of iterated permutations,we improve the zero-sum distinguisher for the Keccak-f permutation with full 24 rounds by lowering the size of the zero-sum partition from 21590 to 21575.     

正则图的代数连通度

设G=(V,E)是一个具有n个顶点的简单图,A(G)是G的邻接矩阵,D(G)表示G的度对角矩阵,图G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).若矩阵L(G)的特征值为μ1≥μ2≥…≥μn-1≥μn=0,则称μn-1为G的代数连通度.研究了正则图的代数连通度,得到了下列结论:μn-1≤(nrln(n-l))/(6n-8-4r-nln(n-1))这里,r表示正则图的度.     

关于不定方程x^2＋16=y^13的解

利用代数数论的方法,证明了不定方程x^2＋16=y^13无整数解．     

退化时滞微分系统全时滞稳定的代数判据

本文利用复平面变换及多项式理论给出了退化时滞微分系统全时滞稳定的充要条件。     

低扭矩环锭纱的结构分析

从纤维在空间上的三维形态以及在纱线横截面上的分布分析了低扭矩环锭纱中纤维的三维结构特征.研究结果表明,低扭矩环锭纱中大量的纤维轨迹呈非同轴异形螺旋线,其螺旋轴线与纱线轴线不一致,且螺旋半径不断显著变化,同时,很多纤维片段的螺旋线方向与纱线正常捻度方向相反.此外,低扭矩纱线中纤维在纱线横截面上的分布较为集中,有利于拉伸变形时纤维同时受力.低扭矩环锭纱的这些结构特征揭示了其独特的物理性能,即低残余扭矩、低捻度、高强力.     

2-D algebraic test for robust stability of time-delay systems with interval parameters

1. INTRODUCTION The robust stability test of time-delay systems with interval parameters is to determine whether the eigenvalues of the characteristic polynomials of the systems are located at open left half complex plane. Different from classical 1-D systems, the eigenvalues of the characteristic polynomials are infinite, classical robust stability results (Kharitonov extreme test and Edge test) for 1-D systems are not suitable for the stability test of the characteristic polynomials of…     

对平面激波的数值研究

从数学分析的角度，定量地研究造成平面激波脱体的物理条件。将来流Mach数M1、壁面转折角δ以及激波角β所满足的函数关系式转换为代数方程，建立完整的平面激波激波角的数值计算方法，给出激波前后气流物理量的变化关系。     

随机系数代数方程平均实根个数的估计

考虑随机系数代数方程Ｆｎ（ｗ,ｔ）＝０（ｗ）＋１（ｗ）ｔ＋…＋ｎ－１（ｗ）ｔｎ－１＝０,其中ｉ（ｗ）（ｉ＝０,１,…,ｎ－１）为独立且服从标准正态分布的随机变量。令ＥＮＦ（ｗ）表示Ｆｎ（ｗ,ｔ）的平均实根个数。本文证明了ＥＮＦ（ｗ）＜２πｌｎｎ－２ｎπ＋１．２３７２７７１。     

Torsional Models of Two - ply Yarn

In this paper,the vector equation of a generaliseddoubly wound helix was derived.Treloar's pliedyarn geometry could be obtained as a special case ofthe generalised doubly wound helix.The shortest fi-bre length around the surface of a helical tube(formed by fibre helices)was determined by apply-ing variational principles.The fibre length as calcu-lated by using Treloar's geometry was compared in-directly with the shortest possible fibre length at dif-ferent levels of yarn deformation when some of Tre-loar's rigid geometrical constraints were relaxed.Anew idea based on non-concentric circles was intro-duced to approximate the fibre helix movement in atwo-ply yarn.A torsional model of two-ply yarnwas developed and the theoretical predictions werecompared with some preliminary experimental re-sults.     

关于“3x+1”问题的探讨

讨论了“３ｘ＋１”问题中存在的结构,且指出对ｘ∈Ｎ,在Ｆ的任意作用下是有界的。