(X+K)mod2n和X(+)K相容程度分析

"与K模2n加"-Y=(X+K)mod2n是密码算法中一个常用的基本编码环节,这里的K表示一个固定的常数.该环节具有较好的非线性性质,在许多分组密码、流密码算法以及杂凑函数中都有着广泛的应用.研究了(X+K)mod2n和X(+)K的相容程度,给出了噪声函数N(x)=(X+K)mod2nX(+)K在各点概率的计算公式以及在各点概率值平方和的一些性质.     

MIX函数的模加差分概率分析

S函数由Nicky Mouha提出,是只需输入字的第i个bit和第i个运算状态S[i]即可计算出输出字的第i个bit的一类函数,利用其可以有效研究模加、异或运算的性质。为研究Skein算法的核心部件MIX函数的模加差分性质,将MIX函数转化为S函数的形式,给出了一种精确计算MIX函数模加差分概率的方法,通过理论分析,说明相对于通过求各运算部件概率之积以获得整体函数的概率的一般方法,利用S函数的方法得到的结果更为精确。     

一种加群Z上离散对数问题的DNA计算算法

加群Zp+上离散对数问题在公钥密码系统分析中具有非常广泛的应用。研究一种加群Zp+上离散对数问题的DNA计算算法。算法主要由解空间生成器、并行乘法器、并行加法器、解转换器及解搜索器组成。其中解空间生成器借鉴传统计算机中3表算法的思想,将解空间的生成分为3个部分来完成,极大减少了非法解的搜索空间。本算法的生物操作时间复杂度为O(k2),需要O(1)个试管数、O(2k)条DNA链,最长DNA链长为O(k2)(其中k为加群上离散对数问题群阶p的二进制编码位数)。最后,通过DNA计算通用的试验方法对算法进行了仿真,验证了算法的可行性和有效性。     

模2n加的异或差分概率的快速计算方法

分析模2n加变换的异或差分概率计算算法的计算复杂性,利用以空间换时间的思想,将该算法中的矩阵乘积运算预先计算并予以存储,从而以查表运算替代多个矩阵乘积运算等方法对模2n加变换的异或差分概率计算算法进行改进,改进后算法的计算复杂性小于现有方法计算复杂性的7.7%。     

振动信号频谱分析中的加窗及加窗幅值修正

在振动信号频谱中,为了消除加窗导致的信号频谱幅度的不一致问题,通常需要对加窗后信号的频谱进行幅值修正。一般情况下,幅值修正过程遵循两个原则：幅值相等原则和能量相等原则。结合航空发动机振动信号处理中的类似问题,遵循幅值相等原则,结合工程实践,通过理论分析和数值仿真分析的方法,提出了一种基于正弦校准信号的加窗幅度修正的方法。该方法利用正弦校准信号频谱的特点,以及相关的信号处理理论和方法分析得出,加窗幅度修正系数为窗函数序列的直流分量。此外,依据该方法给出了5种常用窗函数的加窗幅值修正系数,并用数值仿真的方法对     

网孔处理机阵列上最小生成树算法

已知一加权无向图G(V,E),|V|=n.本文基于网孔处理机阵列,运用分而治之策略和数据归约技术给出了一种新的最小生成树算法.此算法需O(n~2/p)时间,使用了O(p)个处理机(1≤p≤n).当p=n时,此算法仅需O(n)时间和O(n)处理机.而目前基于同一计算模型上此问题的最好算法需O(n)时间和O(n~2)个处理机,因而这里给出的算法在使用处理机数目方面改进了O(n)因子.     

S形加减速算法前瞻处理研究

由于S形加减速算法的表达式是分段表达式且包括无理表达式,在应用S形加减速算法进行前瞻处理时出现了两个问题:1、方程表达式难以确定;2、需要求解无理方程.针对第一问题,提出一种仅需要少量计算和比较的方法.为了求解无理方程,本文提出使用拉格朗日逼近法构造二次方程来逼近无理方程,详细分析了逼近产生的误差并给出一种误差校正的方法.文中提出的方法在Matlab平台仿真实现,并已通过实际加工NURBS曲线验证可行.     

构造二叉树的两个改进算法

在数据结构中,已知一棵二叉树的先序序列和中序序列,可唯一确定此二叉树.本文在分析建立二叉树经典算法的时间复杂度的基础上,给出了两个改进算法:①利用哈希函数,使得改进后的算法在最差情况下,时间复杂度由O(n2)降为O(n);②利用栈和控制输入的结点序列构造二叉树,时间复杂度也由O(n2)降为O(n).     

一个由pH滴定数据计算加质子常数的通用程序—PCPS

以S=∑[(pH~(calc))_j-(pH~(exp))_j]~2为目标函数,采用无约束条件最优化计算中的直接方法,编制出一个从pH滴定数据计算弱酸根和弱碱加质子常数的通用程序,并给出各参数的标准误差和相关系数.     

基于PC104的机载数据加卸载设备的设计

针对目前航空兵部队机载电子对抗设备种类繁多、数据加卸载复杂的问题,提出了将机载设备作为PC104嵌入式计算机外部设备的设计方案,利于多路I/O接口技术,解决了外场数据加卸载以及内场数据传送的设备通用性问题,实现了数据加卸载设备的微型化、通用化.     

Frequency-weighted optimal Hankel-norm approximation of stable transfer functions

This paper shows how to introduce arbitrary frequency weighting into the optimal Hankel-norm approximation problem for scalar, finite-dimensional, linear, time-invariant systems. The procedure has applications to the closed-form design of reduced-order controllers.     

Kernel shapes of fuzzy sets in fuzzy systems for function approximation

The shapes of if-part fuzzy sets affect the approximating capability of fuzzy systems. In this paper, the fuzzy systems with the kernel-shaped if-part fuzzy sets are built directly from the training data. It is proved that these fuzzy systems are universal approximators and their uniform approximation rates can be estimated in the single-input-single-output (SISO) case. On the basis of these rates, the relationships between the approximating capability and the shapes of if-part fuzzy sets are developed for the fuzzy systems. Furthermore, the sinc functions that serve as input membership functions are proved to have the almost best approximation property in a particular class of membership functions. The theoretical results are confirmed from the simulation data. In addition, the estimations of the uniform approximation rates are extended to the multi-input-single-output (MISO) case.     

渐进迭代逼近方法在等距曲线逼近中的应用

渐进迭代逼近(PIA)方法在CAD领域有很好的自适应性和收敛稳定性,在曲线或曲面的逼近和拟合问题上具有很好的应用前景.文中将该方法应用于二维自由曲线的等距曲线(也称offset曲线)的逼近,提出基于PIA的等距曲线逼近算法.首先在等距曲线上采样数据点,采用Floater的方法对数据点进行参数化,并以这些采样点作为初始控制顶点,由这些初始控制顶点产生初始逼近曲线;然后考察相同参数值处采样点和逼近点的误差,并运用PIA方法逐步逼近等距曲线.该算法分别考虑了等距曲线的多项式逼近和有理逼近.数值实例结果表明,综合控制顶点数和算法误差这2项因素,文中算法具备较好的优势.     

隐式曲面的光滑逼近

给出了隐式曲面的光滑逼近和保凸逼近曲面的构造,所构造的曲面是分段三次的,其光滑度高于Ｃ＾１。     

动态粒度下的粗糙集双向近似

经典的粗糙集理论刻画目标概念运用静态的粒度分析,不便于刻画人们问题求解的动态认知过程。已有文献分别用正向近似和逆向近似对目标概念和目标决策进行刻画,并成功地应用于分层聚类算法和规则提取方面。基于动态粒度原理,提出双向近似的概念,获得双向近似的一些重要性质,并将其应用于决策表中决策规则的获取。     

New topological approach of rough set generalizations

In this paper, we introduce a generalization of rough set theory using topological structures generated by any binary general relation. The class of all after-composed sets and the class of all fore-composed sets defined here are used to generate two topological spaces. These topologies are used to approximate sets topologically. Lower and upper approximations are defined topologically and some of their properties are studied using these topologies. Also, membership, equality, inclusion relations and power set notions in the generalized approximation space are studied. Many differences are shown between notions of ordinary set theory and notions of rough set theory. These notions introduced in this work are good future work to knowledge discovery and data mining.     

A parallel approach to calculate lower and upper approximations in dominance based rough set theory

Feature selection plays an important role in data mining and machine learning tasks. Rough set theory has been a prominent tool for this purpose. It characterizes a dataset by using two important measures called lower and upper approximation. Dominance based rough set approach (DSRA) is an extension to conventional rough set theory. It is based on persistence of preference order while extracting knowledge from datasets. Dominance principal states that objects belonging to a certain decision class should follow the preference order. Preference order states that an object having higher values of conditional attributes should belong to higher decision classes. However, some of the basic concepts like checking preference order consistency of a dataset, dominance based lower approximation and upper approximation are computationally too expensive to be used for large datasets. In this paper, we have proposed a parallel incremental approach called Parallel Incremental Approximation Calculation or PIAC for short, for calculating these measures of lower and upper approximations. The proposed approach incrementally calculates lower and upper approximations using parallel threads. We compare our method with the conventional approach using ten widely used datasets. Whilst achieving the same accuracy levels as the conventional approach, our approach significantly reduces the average computation time, i.e., 71% for the lower approximation and 70% for the upper approximation. Over all datasets, the decrease in memory usage achieved was 99%.     

Some experiments in waveform approximation

Two methods of waveform approximation were compared, one based on maximal homogeneous neighborhoods, the other on recursive subdivision of nonuniform subintervals. The compactness/error tradeoff was found to favor the former method.     

闭环连续系统仿真若干问题的分析研究

分析研究了对闭环系统的纯滞后环节如何处理的问题,找到开环系统和闭环系统的理论输出值计算方法,并比较3种Pade近似和全极点近似的精度。将此算法应用到闭环系统中,进一步比较4种近似,以求得闭环系统中误差最小的近似方法。同时提出在计算过程中对纯滞后处理的改进方法,使得误差大大减小,精度提高了一个数量级。研究结果表明,在开环系统和闭环系统,全极点近似由于没有引入零点,使得误差最小;改进方法使误差精度提高了一个数量级。     

Weierstrass-type approximation theorems with Pythagorean hodograph curves

We prove the Weierstrass-type approximation theorem that states every C¹ curve in the 2-dimensional or 3-dimensional Euclidean space or in the 3-dimensional Minkowski space can be uniformly approximated by Pythagorean hodograph curves in the corresponding space. This abundance of PH curves is another theoretical confirmation of the usefulness and the versatility of the PH curves. We also address some algorithmic aspects of proposed PH approximation schemes and their convergence rates.