Mathematical programming models for revenue management under customer choice

We study a network airline revenue management problem with discrete customer choice behavior. We discuss a choice model based on the concept of preference orders, in which customers can be grouped according to a list of options in decreasing order of preference. If a customer’s preferred option is not available, the customer moves to the next choice on the list with some probability. If that option is not available, the customer moves to the third choice on the list with some probability, and so forth until either the customer has no other choice but to leave or his/her request is accepted. Using this choice model as an input, we propose some mathematical programs to determine seat allocations. We also propose a post-optimization heuristic to refine the allocation suggested by the optimization model. Simulation results are presented to illustrate the effectiveness of our method, including comparisons with other models.     

对称超二次二阶哈密尔顿系统的周期解

我们利用Ambrosetti-Rabinowitz对称形式的山路引理证明了给定周期T的对称超二次二阶哈密尔顿系统具有无穷多个反T/2-周期且奇的周期解.     

鲁棒半监督ν-支持向量分类机

支持向量机在近十年成为机器学习的主要学习技术,而且已经成功应用到有监督学习问题中。Fung和Mangasarian利用支持向量机对于既有已标类别样本又有未知类别样本的训练集进行训练,方法主要是利用少量已标明类别的样本进行训练得到一个分类器的同时对于未标明类别的样本进行分类,使得间隔最大化。此优化问题中假定样本是精确的,而在现实生活中,样本通常带有统计误差。因此,考虑样本带有扰动信息的半监督两类分类问题,给出鲁棒半监督v-支持向量分类算法。该算法的参数v易于选择,而数值试验也表明该算法具有良好的稳定性和较好的分类结果。     

基于多重工作休假的成批到达离散时间排队的性能分析

研究了一个成批到达的离散时间 Geom$^{[X]}$/Geom/1 多重工作休假排队. 首先,建立了模型的二维马尔可夫链,利用矩阵分析的方法, 导出了稳态队长复杂的概率母函数. 其次, 为了展示此模型与经典无休假Geom$^{[X]}$/Geom/1排队的联系, 给出稳态队长的随机分解结果. 尤其重要的是,发现了条件负二项分布的双参数加法定理, 利用这些结论,得到了矩母函数序下的稳态等待时间的上下界. 进一步,求出了平均队长和平均等待时间的上下界. 最后,提出一些数值例子以验证结论.     

有限级拟亚纯映射在Borel方向上的充满圆

对于开平面上有限正级的K-拟亚纯映射在Borel方向上的性质进行了研究,用比较简单的方法证明了有限正级K-拟亚纯映射在其Borel方向上一定存在充满圆序列.把A.Rauch关于亚纯函数的结果推广到K-拟亚纯映射上.     

折现的未决赔款准备金估计的随机逼近

凸序意义下的随机界是估计具有相依性随机变量和分布的良好工具.在考虑货币时间价值的基础上,通过随机上下界的两种不同形式的凸组合对未决赔款准备金的估计进行逼近,并通过矩匹配法,给出了最优权数的计算公式.通过一个实例对所述方法进行验证.     

THE EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF SECOND ORDER DIFFERENTIAL EQUATIONS

In this paper, a fixed point theorem in C1[0,1] space is established using the properties of the fixed point index. This theorem is applied to prove the existence of positive solution to the boundary value problems of second order differential equations.     

二重非齐次马氏链的遍历性及其应用

给出二重非齐次马氏链的强遍历性,绝对平均强遍历性,Cesaro平均收敛的概念．利用二维马氏链的遍历性和C-K方程,建立了二维马氏链与二重非齐次马氏链遍历性的关系．并讨论了齐次二重马氏链绝对平均强遍历与强遍历的等价性．最后给出Cesaro平均收敛在马氏决策过程和信息论中应用．     

Formulae for order one invariants of immersions of surfaces

The universal order 1 invariant fU of immersions of a closed orientable surface into R³, whose existence has been established in [T. Nowik, Order one invariants of immersions of surfaces into 3-space, Math. Ann. 328 (2004) 261-283], is the direct sum