一道数学竞赛题的讨论

对浙江省大学生数学竞赛题的一道试题从试题结论的推广及新的结论等方面进行了讨论.     

Some Remarks on One-dimensional Functions and Their Riemann–Liouville Fractional Calculus

A one-dimensional continuous function of unbounded variation on [0,1] has been constructed.The length of its graph is infnite,while part of this function displays fractal features.The Box dimension of its Riemann–Liouville fractional integral has been calculated.     

Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain

A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn（f; t） of generalized Fourier series on a parallel hexagon domain Ω associating with threedirection partition. We prove that an operator Wn（f; t） with the new kernel function converges uniformly to any continuous function f（t） ∈ Cn（Ω） （the space of all continuous functions with period Ω） on Ω. Moreover, the convergence order of the operator is presented for the smooth approached function.     

抽象度量空间上的一致连续函数空间

本文主要讨论抽象度量空间上的一致连续函数空间的Banach空间结构,代数结构和格结构．     

函数零点问题中参数取值的求解

函数的零点主要涉及三个方面的问题：连续函数零点的存在性;连续函数零点个数的判定;求连续函数零点的近似解（二分法）．在以上三个问题的考查中,常常涉及到参数取值范围的求解,主要从问题的逆向方面进行考察．这类问题是目前新课标下高考的重点、难点、热点,如何引导学生解决这类问题？笔者认为应从两方面入手．     

多星联合鲁棒性调度模型研究

在多星联合调度过程中,存在着很多不确定性因素,其中云层覆盖变化是主要的不确定性来源.本文针对考虑云层覆盖变化的多星联合调度问题,借鉴了连续函数的鲁棒性优化思想,提出了一种基于邻域的鲁棒性指标.在此基础上,建立了多星联合鲁棒性调度模型,给出了观测任务优先级的计算方法.实例研究表明,本文建立的模型能够在保证调度方案性能的基础上,获得鲁棒性强的调度方案.     

联合最佳逼近

本文研究了二元函数用紧Hausdorff空间上的连续函数集的联合逼近问题,建立了包括特征定理、唯一性定理、强唯一性定理和dela Vallée Poussin定理在内的Chebyshev逼近理论。给出了求解最佳逼近元的Remes型第一算法和两种一般的简化方法。     

Oscillation Theorems of the Second Order Linear Matrix Differential System with Damping

By using the Riccati technique and the technique, new oscillation criteria are obtained for the second order matrix differential system(P(t)Y′(t))′ r(t)P(t)Y′(t) Q(t)Y(t) = 0, t≥t0.These results in the present paper generalize and improve many known conclusions. Furthermore, some results are different from the most known ones in the sense that they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. In particular, our results complement a number of existing results and handle the ease that is not covered by the known criteria.     

测度链上的柯西不等式

研究了测度链上的柯西不等式,给出测度链上柯西不等式的具体形式.此外,还对测度链上的柯西不等式作了推广.