网络安全产品研究

本文在研究了网络安全的国内外有关情况后对网络安全技术进行了探讨 ,介绍了一种简单而实用的网络安全产品 ,添补了这方面的空白 ,而且本文介绍的产品已经应用到了许多部门 ,为网络安全做出了贡献     

标准体系的使用期的模型与分析

本文提出了关于标准体系使用期的两个模型。首先定义了标准使用期,然后讨论了模型的合理性。通过模型讨论了标准使用期的性质,给出了数值示例。提出了需进一步研究的问题。     

态R_0代数

本文研究了R_0代数上有关态算子的问题.利用MV-代数上内态的引入方法引入了态算子,定义了态R_0代数,它是R_0代数的一般化.给出了一些非平凡态R_0代数的例子并讨论了态R_0代数的一些基本性质.在此基础上给出了态滤子和态局部R_0代数的概念,并利用态滤子刻画了态局部R_0代数.推广了局部R_0代数的相关理论.     

高阶数值微分的积分方法

本文研究了高阶数值微分问题,利用Groetsch的思想,获得了可以稳定逼近近似已知函数的任意阶导数的积分方法,并在一定条件下,给出了收敛率.给出了二阶、三阶和四阶数值微分问题的数值实验,实验结果表明了方法的有效性.     

模糊幂格

本文研究了格向其模糊幂集上提升的问题.利用模糊集理论,引入了模糊幂格的概念,获得了模糊幂格及其模糊理想的若干基本性质,推广了格的结果.     

基于质量控制的供应链计划问题研究

为了研究基于质量控制的供应链计划问题,采用了优化建模的方法,分析了易腐物品生命周期函数的选用及拟合原则,建立起了质量衰减成本与时间之间的关系,考虑了涉及交通及天气情况的运输风险,最终建立了优化模型,以实现供应链运行总成本最小。最后,提出了动态规划的求解方法,并通过仿真实验证明了算法的有效性。     

秩为1矩阵的性质及应用

给出了秩1矩阵的结构,讨论了这类矩阵在矩阵运算、对角化、标准型等方面的性质,推广和改进了文[1]的一些相关结果,并指出了它的若干应用,重点讨论了一类矩阵,得到了有关结论和方法.     

探究两个一次函数图像的对称规律

在学习了反比例函数后,老师带大家总结了两个点及函数图像的对称性.对于两个一次函数对称的情况,我自己进行了探索,发现了     

基于最大满意度的研究生录取问题

采用了模糊数学的知识和优化方法讨论解决了研究生的录取问题.首先对相关数据进行了合理的量化,然后定义了导师与学生之间的相互满意度,建立了择优录取和双向选择的优化模型,通过求解得到了理想的结果.     

以研促教 教研相长——一次集体教研活动纪实

在一次集体教研活动中,通过对一道试题的探究、引申、延展,不仅深化了教师的思维,提升了“四基”“四能”,强化了学科素养的渗透,提高了教学站位,更难能可贵的是激发了教师们的教研热情,唤醒了他们的专业自觉,充分彰显了集体智慧和集体力量的伟大.     

On farthest points of sets

For a convex closed bounded set in a Banach space, we study the existence and uniqueness problem for a point of this set that is the farthest point from a given point in space. In terms of the existence and uniqueness of the farthest point, as well as the Lipschitzian dependence of this point on a point in space, we obtain necessary and su.cient conditions for the strong convexity of a set in several infinite-dimensional spaces, in particular, in a Hilbert space. A set representable as the intersection of closed balls of a fixed radius is called a strongly convex set. We show that the condition “for each point in space that is sufficiently far from a set, there exists a unique farthest point of the set” is a criterion for the strong convexity of a set in a finite-dimensional normed space, where the norm ball is a strongly convex set and a generating set.     

The KdV soliton crosses a dissipative and dispersive border

We demonstrate the behavior of the soliton which, while moving in non-dissipative and dispersion-constant medium encounters a finite-width barrier with varying dissipation and/or dispersion; beyond the layer dispersion is constant (but not necessarily of the same value) and dissipation is null. The transmitted wave either retains the form of a soliton (though of different parameters) or scatters a into a number of them. And a reflection wave may be negligible or absent. This models a situation similar to a light passing from a humid air to a dry one through the vapor saturation/condensation area. Some rough estimations for a prediction of an output are given using the relative decay (or accumulation) of the KdV conserved quantities in a dissipative area; in particular for a restriction for a number of solitons in the transmitted signal.     

A Barrier Function Method for the Nonconvex Quadratic Programming Problem with Box Constraints

In this paper a barrier function method is proposed for approximating a solution of the nonconvex quadratic programming problem with box constraints. The method attempts to produce a solution of good quality by following a path as the barrier parameter decreases from a sufficiently large positive number. For a given value of the barrier parameter, the method searches for a minimum point of the barrier function in a descent direction, which has a desired property that the box constraints are always satisfied automatically if the step length is a number between zero and one. When all the diagonal entries of the objective function are negative, the method converges to at least a local minimum point of the problem if it yields a local minimum point of the barrier function for a sequence of decreasing values of the barrier parameter with zero limit. Numerical results show that the method always generates a global or near global minimum point as the barrier parameter decreases at a sufficiently slow pace.     

Staircase Parameterization in Dynamical Selection

This paper deals with a variant of a dynamical selection scheme introduced by Attouch and Cominetti for ill-posed convex minimization which combines approximation with the steepest descent method by mean of a suitable parameterization of the approximation parameter as a function of the time. This variant applies to a general inclusion with a maximal monotone operator by mean of a staircase parameterization. A discrete analogue is also considered. Applications to selecting a particular zero of a maximal monotone operator or a particular fixed point of a nonexpansive mapping via regularization techniques are presented. Finally, the alternative use of well-posedness by perturbations is discussed.     

管状曲面在曲线论中的应用

研究了围绕曲线的管状曲面上的曲率线,渐近线与测地线,给出它们的方程,揭示了这些曲线与Bertrand曲线或Mannheim曲线之间的关系,采用新的方法给出一条曲线是Bertrand曲线或Mannheim曲线的充要条件的另一种证明以及Mannheim侣线的曲率与挠率之间的关系．     

Enumerating bases of self-dual matroids

We define involutively self-dual matroids and prove that an enumerator for their bases is the square of a related enumerator for their self-dual bases. This leads to a new proof of Tutte's theorem that the number of spanning trees of a central reflex is a perfect square, and it solves a problem posed by Kalai about higher dimensional spanning trees in simplicial complexes. We also give a weighted version of the latter result.We give an algebraic analogue relating to the critical group of a graph, a finite abelian group whose order is the number of spanning trees of the graph. We prove that the critical group of a central reflex is a direct sum of two copies of an abelian group, and conclude with an analogous result in Kalai's setting.     

Genus fields of Kummer extensions of rational function fields

In this paper we obtain the genus field of a general Kummer extension of a global rational function field. We study first the case of a general Kummer extension of degree a power of a prime. Then we prove that the genus field of a composite of two abelian extensions of a global rational function field with relatively prime degrees is equal to the composite of their respective genus fields. Our main result, the genus of a general Kummer extension of a global rational function field, is a direct consequence of this fact.     

Small periodic solutions of nonlinear systems of differential equations with constant deviation

We consider a nonlinear system of differential equations in a general case with a singular matrix at the derivatives, with a vector deviation which depends on a parameter. We seek for a periodic solution to the system in the set of trigonometric series such that the sequences of their coefficients belong to the space l ₁.We use the method, representing a space as a direct sum of subspaces, and the method of a fixed point of a nonlinear operator as the main investigation techniques.We reduce the question on the existence of a periodic solution to that of the solvability of an operator equation, whose principal part is defined in a finite-dimensional space.     

Convergence of Rothe scheme for a class of dynamic variational inequalities involving Clarke subdifferential

In the first part of the paper we deal with a second-order evolution variational inequality involving a multivalued term generated by a Clarke subdifferential of a locally Lipschitz potential. For this problem we construct a time-semidiscrete approximation, known as the Rothe scheme. We study a sequence of solutions of the semidiscrete approximate problems and provide its weak convergence to a limit element that is a solution of the original problem. Next, we show that the solution is unique and the convergence is strong. In the second part of the paper, we consider a dynamic visco-elastic problem of contact mechanics. We assume that the contact process is governed by a normal damped response condition with a unilateral constraint and the body is non-clamped. The mechanical problem in its weak formulation reduces to a variational–hemivariational inequality that can be solved by finding a solution of a corresponding abstract problem related to one studied in the first part of the paper. Hence, we apply obtained existence result to provide the weak solvability of contact problem.     

Scalarization of Henig Proper Efficient Points in a Normed Space

In a general normed space equipped with the order induced by a closed convex cone with a base, using a family of continuous monotone Minkowski functionals and a family of continuous norms, we obtain scalar characterizations of Henig proper efficient points of a general set and a bounded set, respectively. Moreover, we give a scalar characterization of a superefficient point of a set in a normed space equipped with the order induced by a closed convex cone with a bounded base.