幂函数的一些密码学性质

二元域上n数组空间上的非线性置换在分组码，杂凑函数与流密码等密码学领域中有重要应用.域GF（2n）上的幂函数提供了二元域上n数组空间上的一类非线性置换．本文着重研究幂函数的强完全性、完全性与非线性度等密码学性质．作为结果，本文证明了幂函数具有完全性；证明了具有强完全性的函数必有较高的拓扑非线性度；木文找到一类具有强完全性的幂函数；周时也定出了幂函数的代数非线性度．     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION

The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures.     

金融时间序列分析与建模

介绍了金融时间序列分析与建模的主要理论、方法,着重论述了近20多年发展起来的非平稳时间序列的建模方法及工具,指出进一步的研究方向.最后,对上证综合指数这一金融时间序列进行了实证分析.     

NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD, the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1-and L2-norm space estimates and the 0((△t)2) estimate for time variable are obtained.     

双－全氟烷基氮氧自由基从取代苯甲醛的攫氢反应──用EPR方法建立取代基自旋离域参数σ的新尝试

Ｒ_ＦＮ（Ｏ　）Ｒ_Ｆ和Ｒ_ＦＮＯ的Ｆ１１３溶液在室温下与一系列的对位取代苯甲醛反应，得到稳定的对位取代苯甲酰基全氟烷基氮氧自由基。由△ａ_Ｎ和△ａ_Ｆ~β的σ单参数相关以及△ａ_Ｎ与σ和σ　双参数相关表明：极性效应是影响氟烷基酰基氮氧自由基中氮原子自旋密度变化的主要因素，而自旋离域效应的影响是很小的。     

一类广义非线性混合拟变分包含组

本文引入了一类新的带松弛单调映射和松弛Lipschitz映射的广义非线性混合拟变分包含组 ,构造了求解该类变分包含组的迭代算法 ,证明了该类变分包含组解的存在性以及由本文构造的迭代算法产生的迭代序列的强收敛性 .所得结果推广和改进了大量文献中的最新结果[1 5 ] .     

Oscillations of the Solutions of Nonlinear Delay Hyperbolic Partial Differential Equations

In this paper, oscillatory properties of solutions of certain hyperbolic partial differential equations with multi-delays are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delays.