Stampacchia generalized vector quasi-equilibrium problem with set-valued mapping

In this paper, the solvability of Stampacchia generalized vector quasi-equilibrium problem (in short, GVQEP) with set-valued mapping is studied. By using continuous selection theorem and fixed point theorems, some existence theorems for (GVQEP) are obtained without any monotonicity assumption. These theorems unify and improve some results in the recent references.     

Approximating the maximum 2- and 3-edge-colorable subgraph problems

For a fixed value of a parameter k≥2, the Maximum k-Edge-Colorable Subgraph Problem consists in finding k edge-disjoint matchings in a simple graph, with the goal of maximising the total number of edges used. The problem is known to be -hard for all k, but there exist polynomial time approximation algorithms with approximation ratios tending to 1 as k tends to infinity. Herein we propose improved approximation algorithms for the cases of k=2 and k=3, having approximation ratios of 5/6 and 4/5, respectively.     

Direct numerical method for an inverse problem of a parabolic partial differential equation

A coefficient inverse problem of the one-dimensional parabolic equation is solved by a high-order compact finite difference method in this paper. The problem of recovering a time-dependent coefficient in a parabolic partial differential equation has attracted considerable attention recently. While many theoretical results regarding the existence and uniqueness of the solution are obtained, the development of efficient and accurate numerical methods is still far from satisfactory. In this paper a fourth-order efficient numerical method is proposed to calculate the function u(x,t) and the unknown coefficient a(t) in a parabolic partial differential equation. Several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method.     

The impact of customer returns on pricing and order decisions

In this paper, we address the simultaneous determination of price and inventory replenishment when customers return product to the firm. We examine cases when the quantity of returned product is a function of both the quantity sold and the price, in single and multi-period problems, with and without uncertainty in demand.     

Disjoint Paths in Decomposable Digraphs

The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].     

单架飞机受干扰后飞机路径恢复多项式算法研究

飞机路径恢复是航班调整中保证航班能够运行的必要条件之一,而传统目标下的飞机路径优化问题是NP-hard的。本文针对单架飞机受到干扰后,基于最小最大目标的同机型飞机路径最优化问题,给出了一个新的多项式时间算法。首先基于航空公司调整航班的常用原则,提出把最大航班延误时间最小化作为问题的目标。然后根据问题的一些特点和目标形式,设计出解构造算法,得到飞机路径恢复问题的最优解,并分析出算法的复杂度为O(n²)。相对于一般的最小最大二分图匹配算法(复杂度为O(n³log(n))),该算法具有较小的时间复杂度。最后用实例验证了解构造算法的有效性。该研究结果将为航空公司减少航班延误提供理论和方法支持。     

具重特征的偏微分方程柯西问题的离散现象

1.引言 众所周知,人们对主型方程,即无重实特征的线性偏微分方程,已有了很好的了解,而对远较主型方程复杂得多的具重特征方程却认识得较少,目前大体上还只停留在个别例子的水平上。грушпн,в.в.首先举例指出重特征方程在解的光滑性问题中有所谓离散现象,即方程中的参量取一些离散的例外值时,解突然失去了光滑性。接着Treves,F.在类似的例子中发现了这种离散现象也出现在Cauchy问题解的唯一性问题中,王光寅等对Treves例子的离散现象作了进一步的深刻揭示。Menikoff,A.曾讨论了以下Treves例子为特例的更广泛一类的重特征方程     

两个极限的注记

利用数值积分方法给出了波利亚的名著中两个极问题的证明,并给出了两个结论更强的结果.     

基于化学学科核心素养发展的元素化合物教学案例研究*

通过“燃煤污染与防治”“金属矿物的开发利用”等2个典型的元素化合物教学案例,探讨如何将元素化合物的学习置于一定挑战性的问题情境中,形成问题解决基本思路,从化学视角分析解决实际问题,促进学生化学学科核心素养的发展。     

以问题为导向的点-面式教学法在药剂学教学中的应用——以“手性”知识的教学为例

在药剂学课程教学中,为讲解传授“手性”相关的知识和概念,设计了一种新的教学法,并进行了实践应用。通过对该教学方法的总结和提炼,将以上教学法命名为“以问题为导向的点-面式教学法”。该教学法是以“反应停”具体事例为问题引导,提出和确定问题后,引出知识点,从药学相关领域知识面展开教学活动后,进行知识点总结,最后达成最终的教学目标。该教学法对教学实践工作有一定的参考价值。