A Construction of 1-Resilient Boolean Functions with Good Cryptographic Properties

This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified functions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the “continuity” of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known 1-resilient functions modified by Tu-Deng and Tang-Carlet-Tang functions.     

一种求支持向量机光滑函数的新方法

光滑函数在支持向量机中起着重要作用.用插值函数的方法曾导出了一个求光滑函数的递推公式,然而,用该递推公式求光滑函数还很繁琐.针对该问题,用积分的方法得到了求多项式光滑函数的一个新递推公式.算例表明,用新递推公式求光滑函数比原递推公式简单得多,为研究支持向量机的光滑函数提供了一种新方法.     

A FRAMEWORK FOR REAL-VALUED CIPHER SYSTEMS

Most cipher systems designed thus far are binary-valued or integer-valued cipher systems. Their security relies on the assumption that one-way functions exist. Though the existence of one-way functions has not been proved yet, most cryptographic researchers believe that one-way functions exist. In addition, many candidates for one-way functions have been proposed. Therefore, the key step for developing real-valued cipher systems is to define real one-way functions and to propose candidates for them. In this paper, based on computational complexity theory over the real field, we give two definitions of real one-way functions; one is for digital one-way functions and the other is for general one-way functions. Candidates for these two classes of one-way functions are also proposed. Moreover, we present two examples to demonstrate that the candidates for both digital one-way functions and general one-way functions can be applied to construct secure real-valued cipher systems.     

基于属性价值函数估计的不确定多属性决策方法

针对属性权重为实数,且权重信息完全未知的不确定多属性决策问题,提出了一种基于属性价值函数估计的决策分析方法。首先,对多属性效用函数和价值函数进行了分析;然后,采用曲线拟合的方法确定属性价值函数的近似表达式,计算决策方案各属性的价值函数值,根据价值函数的可加性确定各方案的价值函数值,以此对方案进行排序与择优。最后给出一个算例,验证了所提方法的有效性。     

旅游资源需求函数模型及应用

自然旅游资源生态系统在人类活动中弱化了自支持能力, 基于社会福利经济学原理的旅游者对旅游资源的价值补偿研究逐渐成为热点.基于旅游者显示性(行为)和陈述性(意愿)偏好实证数据, 通过需求函数, 研究非市场社会(准)公共品自然旅游资源经济价值, 以反应旅游者享受旅游资源的价值补偿.采用需求函数的连续型函数、Box-Cox模型和计数模型形式系统分析显示性偏好数据, 指出半对数、Box-Cox Ⅰ 型和负二项分布计数模型的需求函数具有较大优势; 并用它们分析陈述性偏好数据.提出整合旅游者的显示性和陈述性数据需求函数模型分析旅游资源破坏与改善导致的价值补偿和可持续发展问题, 并给出大连滨海旅游资源分析案例.     

Results on permutation symmetric Boolean functions

This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions. The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties. The proposed method is algebraic in nature. As a by-product, the authors correct and generalize the corresponding results of St?nic? and Maitra (2008). Further, the authors give a complete classification of block-symmetric bent functions based on the results of Zhao and Li (2006), and the result is the only one classification of a certain class of permutation symmetric bent functions after the classification of symmetric bent functions proposed by Savicky (1994).     

同样对称性质的2重尺度函数及其多小波构造

提出了 2重尺度函数及其相应多小波的构造步骤。该尺度函数满足如下性质 :(1)各分量具有不同的紧支撑区间 ;(2 )各分量对称性相同 ;(3)正交。得出了不存在各分量满足反对称性的具有实用价值的 2重尺度函数的结果。讨论了构造过程中参数与尺度函数及其小波性质的关系 ,最后根据该类尺度函数及多小波的性质 ,构造了两种尺度函数和多小波。     

多变量逻辑函数化简的简便方法

研究了多变量逻辑函数化简的新颖而易行的方法,即根据本文提供的一个数学模型,可以产生两种化简方法,一是逻辑相邻表法,类似三角函数利用三角函数表可查出化简结果;二是根据数学模型通过计算机可直接打出结果．我们已经做到了十个以上逻辑变量的逻辑函数化简,均得到正确的化简结果．     

用于过程工程系统设计的MINLP整体最优化方法

本文应用Lagrange对耦函数作为外部近似函数, 对外部近似法进行了推广, 从而建立了一个求解过程工程系统设计中混合整数非线性规划(MINLP)问题的整体最优化方法。除理论分析, 本文还给出方法的几何解释及在工程问题上的应用。     

Strict Lyapunov functions for impulsive hybrid time-varying systems with discontinuous right-hand side

In this paper, explicit closed form expressions of nonsmooth strict Lyapunov functions for impulsive hybrid time-varying systems with discontinuous right-hand side is provided. Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters.     

EXISTENCE OF 0-1 UNIVERSAL MINIMAL TOTAL DOMINATING FUNCTIONS

In this paper, we study the existence of 0-1 universal minimal total dominating functions in a graph. We establish a formulation of linear inequalities to characterize universal minimal total dominating functions and show that for a kind of graphs whose adjacent matrices are balanced, the existence of universal minimal total dominating functions coincides with that of 0-1 ones. It is also proved that for general graphs, the problem of testing the existence of 0-1 universal minimal total dominating functions is NP-hard.     

基于分数阶傅立叶变换的自适应时频表示

提出采用高斯函数的分数阶傅立叶变换作为基函数的自适应信号扩展方法,并给出了相应的时频分布,该分布具有较高的时频分辨率,没有窗效应,无交叉项干扰。分数阶傅立叶变换使基函数的时频分布旋转了α角度,结合尺度,时移和频移,为基函数匹配信号提供了更大的灵活性。仿真结果表明,该方法可以更加准确地描述信号的时频特征。     

TOPSIS价值函数模型

综合研究了TOPSIS函数的结构和性质，在构建单向规范化向量空间的基础上，定义并归纳了6种TOPSIS函数，证明了这6种函数都是价值函数，最后经过分析比较，推荐其中两种函数作为正统的TOPSIS价值函数模型。     

A Combinatorial Condition and Boolean Functions with Optimal Algebraic Immunity

This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above Boolean functions. This class of balanced Boolean functions have optimal algebraic degree and high nonlinearity. Both classes have optimal algebraic immunity based on a general combinatorial conjecture.     

基于决策者风险态度的多准则决策的Vague集方法

决策时应该考虑到决策者的风险态度,决策者的风险态度对决策结果有重要的影响.现有的基于Vague集的记分函数法没有考虑到决策者的风险态度,存在不足.分析了现有的基于Vague集记分函数法在决策时存在的局限性和不足,考虑到决策者的风险态度,提出了Vague集的决策者态度函数,同时进一步提出了三种新的记分函数.通过运用这三种记分函数有效地解决了决策时存在的局限性和不足,能够提供更为合理、精确的决策排序.     

系统辨识中支持向量机核函数及其参数的研究

具有不同核函数和参数的支持向量机（SVM）的性能存在很大差异，核函数及其参数的选择是SVM应用和理论研究中的一个重要问题。在简要介绍非线性系统辨识的支持向量机方法后，重点对常用的核函数及其参数的选择进行了研究，并采用具有不同核函数的SVM进行非线性系境辩识。大量实验结果表明，采用SVM方法进行系统辨识时，径向基核函数（RBKF）比其它核函数的辨识效果好，且RBKF的参数选择较容易，当参数在有效范围内改变时，空间复杂度变化小，易于实现。因此，RBKF是系统辨识SVM的较好选择。     

基于广义模糊CMAC的强化学习算法

针对传统的小脑模型,提出了一种广义模糊小脑模型神经网络(GFCMAC)。它采用模糊隶属度函数作为接收域函数,可以获得较常规CMAC连续性强且有解析微分的复杂函数近似,具有计算量少,学习效率高等优点。研究了GFCMAC接收域函数的映射方法、隶属度函数及其参数的选取规律和学习算法。结合强化学习,提出了一种基于GFCAMC的强化学习算法,讨论了其实现过程。应用于船舶航向控制的仿真结果表明,在有各种风浪干扰下,船舶航向跟踪快且操舵动作合理,适合船舶转向控制要求。     

一种广义模糊小脑模型神经网络及其仿真研究

针对传统的小脑模型，在保留CMAC原有增强和局部特性的基础上，结合模糊逻辑的思想，采用模糊隶属度函数作为接收域函数，提出了一种广义模糊小脑模型神经网络（GFAC）。研究了GFAC接受域函数的映射规律、隶属度函数及其参数的选取规律和学习算法。仿真结果表明GFAC具有良好的泛化能力和逼近精度，利用GFAC可以获得较常规CMAC连续性强且有解析微分的复杂函数近似。     

A Kind of Equivalence of Three Nonlinear Scalarization Functions in Vector Optimization

In this paper, by the notions of base functionals and augmented dual cones, the authors indicate firstly that the norms, Gerstewitz functionals and oriented distance functions have common characteristics with base functionals. After that, the equivalence of these three sublinear functions on the ordering cone is established by using the structures of augmented dual cones under the assumption that it has a bounded base. However, the authors show that two superlinear functions do not have similar relations with the norms ahead. More generally, the equivalence of three sublinear functions outside the negative cone has also been obtained in the end.     

ON THE CRITERIA AND ENUMERATION OFBOOLEAN FUNCTIONS USEDIN STREAM CIPHERS

1.IntroductionInstreamciphers,booleanfunctionf:Z7~ZZhasbeenusedtoproducekeysequences.Butwhichkindofbooleanfunctionisbettertogeneratekeysequencesisnotcertain,andweshouldconsideritaccordingtodifferentcriteria.In[1],C.Mitchellgavesomecriteriaandenumeratedthe…