Bent序列的构造及其相关值分布

本文研究了已知的Bent序列集的构造方法.利用有限域的理论确定了任一Bent序列集相关值的分布情况.同时,构造出了一类新的Bent序列集,给出了这类Bent序列的线性复杂度的精确值.     

GMW序列的迹表示

研究了长度为2n-1的二元GMW序列的迹表示,用从F2n到F2的迹函数的和式给出了GMW序列的一种简洁的迹表示,并且通过这种迹表示得到了一种新的快速生成GMW序列的方法和一种求GMW序列的极小多项式的方法.最后,还证明了两个GMW序列具有相同极小多项式的一个充要条件.     

一类新的广义割圆序列的线性复杂度及其自相关值

最近,丁存生基于新的割圆类(V_0,V_1)构造了循环码并研究了其性质.本文利用割圆类(V_0, V_1)构造了周期为pq的2阶二元序列,并计算了其自相关值、线性复杂度和极小多项式.     

一类随机规划逼近最优值和最优解集的收敛性

本文提出强上图收敛的概念,讨论了逼近随机规划的目标函数序列的强上图收敛性,研究了逼近随机规划最优值和最优解集的收敛性条件,得到了一类随机规划逼近最优值和最优解集的收敛性.     

Bent序列的相关值分布的研究

对已知的Bent序列集的构造方法作了研究,明确地给出了任一Bent序列集相关值的分配情况.同时,利用有限域上一类新的Bent函数,构造出了一类新的Bent序列集,给出了这类Bent序列的线性复杂度.     

一类基于m序列码的阵列码

通过对阵列 H码和 m序列码的分析 ,本文证明了阵列 H码中的一类正规 H码与 m序列码间的关系     

一类P元序列集的相关性和线性复杂度的分析

对于素数P和偶数n=2k,构造了一类周期为P^n-1的P”条序列组成的P元序列集s（r）,这里P^k≠2（rood3）,r与P^k=1互素．利用d-齐次函数的性质,确定了这类序列集的相关函数取-1±P^k-1,-1＋2·p^k四值及相应分布;使用推广的Key方法证明了这类序列集具有较大的线性复杂度下界．这类序列集可适用于CDMA通信系统和密码系统中．     

一类ρ元序列集的相关性和线性复杂度的分析

对于素数p和偶数n=2k,构造了一类周期为pn-1的pn条序列组成的p元序列集S(r),这里pk≠2(mod3),r与pk-1互素.利用d-齐次函数的性质,确定了这类序列集的相关函数取-1±pk,-1,-1+2.pk四值及相应分布;使用推广的Key方法证明了这类序列集具有较大的线性复杂度下界.这类序列集可适用于CDMA通信系统和密码系统中.     

一类新的广义集值变分包含问题解的辅助序列迭代算法

本文提出并研究了Banach空间中的一类新的广义集值变分包含问题：0∈N（ω，y）＋A（z，v），由集值m-增生映射的预解算子建立了广义集值变分包含与不动点问题的等价性，并利用Nadler定理和辅助序列建立了一些迭代算法，证明了解的存在性和算法的全局收敛性．     

拟完美序列的性质和一种构造方法

利用代数组合论中的差集 ,研究了在流密码和 CDMA移动通信中有重要应用的拟完美序列的性质 ,给出了构造拟完美序列的一种方法     

A New Family of Ternary Sequences with Ideal Two-level Autocorrelation Function

Let be a primitive element of . Letd=3^2k -3 ^k +1 wheren=3k. We show that the ternary sequence s(t) given by has a two-level idealautocorrelation function.     

A New Implicit Iteration Process with Errors for the Family of Strongly Pseudocontractive Mappings

A method is presented for generating a sequence of lower and upper bounds for the eigenvalues of the problem (i) Tu-λSu = 0, where T and S belong to a class of unbounded and nonsymmetric operators in a separable Hilbert space. Sufficient conditions are derived for the convergence of the sequence of bounds to the eigenvalues of (i), and the applicability of the method is illustrated by approximating the smallest eigenvalue of a non-selfadjoint differential eigenvalue problem.     

Optimal insurance design in the presence of exclusion clauses

The present work studies the design of an optimal insurance policy from the perspective of an insured, where the insurable loss is mutually exclusive from another loss that is denied in the insurance coverage. To reduce ex post moral hazard, we assume that both the insured and the insurer would pay more for a larger realization of the insurable loss. When the insurance premium principle preserves the convex order, we show that any admissible insurance contract is suboptimal to a two-layer insurance policy under the criterion of minimizing the insured’s total risk exposure quantified by value at risk, tail value at risk or an expectile. The form of optimal insurance can be further simplified to be one-layer by imposing an additional weak condition on the premium principle. Finally, we use Wang’s premium principle and the expected value premium principle to illustrate the applicability of our results, and find that optimal insurance solutions are affected not only by the size of the excluded loss but also by the risk measure chosen to quantify the insured’s risk exposure.     

区间关联函数的新定义及其应用研究

为了解决具有不确定性区间数的多属性决策问题,引入了区间关联函数的一种新定义,并获得了它的一个有用性质.为了区间关联函数的应用还给出了区间数排序的一种简捷方法.     

一个新的指数削减椭圆形分布族

A new family of univariate exponential slash distribution is introduced, which is based on elliptical distributions and defined by means of a stochastic representation as the scale mixture of an elliptically distributed random variable with respect to the power of an exponential random variable. The same idea is extended to the multivariate case. General properties of the resulting families, including their moments and kurtosis coefficient, are studied. And inferences based on methods of moment and maximum likelihood are discussed. A real data is presented to show this family is flexible and fits much better than other related families.     

有限族严格伪压缩映象具误差的隐迭代序列的强收敛性

在适当的条件下,证明了有限族严格伪压缩映象具误差的隐迭代序列强收敛于其公共不动点. 所得结果改进了Osilike 与 Xu, Ori 的相应结果.     

多项式带余除法定理的一种新证明

利用线性空间的理论,在高观点下给出了多项式带余除法定理的一个新证明.它避免了使用构造法这种技巧性较高的数学方法,使学生比较容易轻松掌握.     

A New Family of Cyclic Difference Sets with Singer Parameters in Characteristic Three

We construct a new family of cyclic difference sets with parameters ((3 ^d – 1)/2, (3 ^{d – 1} – 1)/2, (3 ^{d – 2} – 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets.     

某类带参数4n－阶微分算子的一个同胚与线性同胚定理

本文对某类由考察一些物体的运动性状而引出的４ｎ－阶线性非对称或非线性微分算子给出了一个正则性定理。这个定理包含在实（非线性）情形下２个同胚与扩张同胚类，或者在复（线性）情形下３个线性同胚与扩张线性同胚类。这对于揭示某些物体（例如，某些飞行器）在它们运动过程中的双向平稳性是有用的。     

一阶常系数线性微分方程组的另一种向量解法

讨论一阶常系数线性微分方程组通解问题,给出一种新的向量解法.