Cyclically antimonotone vector equilibrium problems

ABSTRACT

In this paper, we extend the notion of cyclic antimonotonicity (known for scalar bifunctions) to the vector case, in order to obtain a vectorial equilibrium version of Ekeland's variational principle. We characterize the cyclic antimonotonicity in terms of a suitable approximation from below of the vector bifunction, which allows us to avoid the demanding triangle inequality property, usually required in the literature, when dealing with Ekeland's principle for bifunctions. Furthermore, a result for weak vector equilibria in the absence of convexity assumptions is given, without passing through the existence of approximate solutions.     

Self‐dual and self‐petrie‐dual regular maps

Regular maps are cellular decompositions of surfaces with the “highest level of symmetry”, not necessarily orientation‐preserving. Such maps can be identified with three‐generator presentations of groups G of the form G = 〈a, b, c|a² = b² = c² = (ab)^k = (bc)^m = (ca)² = … = 1〉; the positive integers k and m are the face length and the vertex degree of the map. A regular map (G;a, b, c) is self‐dual if the assignment b?b, c?a and a?c extends to an automorphism of G, and self‐Petrie‐dual if G admits an automorphism fixing b and c and interchanging a with ca. In this note we show that for infinitely many numbers k there exist finite, self‐dual and self‐Petrie‐dual regular maps of vertex degree and face length equal to k. We also prove that no such map with odd vertex degree is a normal Cayley map. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory 69:152‐159, 2012     

三角形纳米银颗粒的制备及其热稳定性的研究

具有独特的光学和化学性质的纳米三角形银纳米颗粒在光电、催化和生物传感器等领域中有广泛的应用.提供一种简单的方法制备三角银纳米颗粒,对其进行表征研究,且详细讨论了其热力学稳定性.     

Spanning even subgraphs of 3‐edge‐connected graphs

By Petersen's theorem, a bridgeless cubic graph has a 2‐factor. H. Fleischner extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has a spanning even subgraph. Our main result is that, under the stronger hypothesis of 3‐edge‐connectivity, we can find a spanning even subgraph in which every component has at least five vertices. We show that this is in some sense best possible by constructing an infinite family of 3‐edge‐connected graphs in which every spanning even subgraph has a 5‐cycle as a component. © 2009 Wiley Periodicals, Inc. J Graph Theory 62: 37–47, 2009     

Geometry of plane sections of the infinite regular skew polyhedron {4, 6 | 4}

The asymptotic behavior of open plane sections of triply periodic surfaces is dictated, for an open dense set of plane directions, by an integer second homology class of the three-torus. The dependence of this homology class on the direction can have a rather rich structure, leading in special cases to a fractal. In this paper we present in detail the results for the skew polyhedron {4, 6 | 4} and in particular we show that in this case a fractal arises and that such a fractal can be generated through an elementary algorithm, which in turn allows us to verify for this case a conjecture of Novikov that such fractals have zero measure.      

吸波材料与微波暗室吸波性能研究

主要解决入射波在尖劈吸波材料几何空缺间反射过程的问题以及微波暗室性能是否满足导引仿真要求的问题.对于问题一,首先建立了二维情况下入射波线在尖劈几何空缺间反射过程的数学模型,提出了临界状态的概念,根据光学原理,三角几何原理推出了辐射波在各个反射点处的入射角及反射点距尖劈底面高度表达式,求出了最终反射波的方向、辐射强度.最后根据坐标分解法将其拓展到三维空间.对于问题二,综合考虑辐射波在六个面间的相互影响,运用微元法的思想和微积分的相关知识,推导出静区直接接收到微波信号的公式以及微波信号经整个微波暗室内壁一次反射后被静区接收到的微波功率公式,用数值积分的方法求得了静区得到的反射信号的功率与静区直接得到的微波功率之比,并对部分反射光难以计算的问题提出了数学模型修正的建议和方法.     

基于数量折扣合同和缺货损失的EOQ模型的改进

经济订购批量模型假定需求率、单位持有成本、订货成本为常数下得到总成本最低的订购批量,这些参数常数化的假设在现实中通常难以满足.假定需求和订货费为不确定的、库存成本包括年固定成本(与订货量无关)和年可变成本(与订货量有关),用三角模糊数表示年需求和订货费,通过引入数量折扣合同来量化单位产品进价,分别在不允许缺货和考虑缺货损失两种情况下得到最佳订货量.最后的算例表明了模型的合理性.     

双三角阵声靶测试系统研究

声靶容易构成较大的测试靶面,常用在大口径弹药的立靶密集度测试中。为了消除声波在空气中传播速度变化对声靶测试精度的影响,采用双三角阵声阵列模型使测量公式中不再引入声波速度。为了使测试系统紧凑、可靠,整个测试系统由双三角阵列、多通道数据采集仪、计算机系统构成。对测试系统进行了实弹射击实验,在2 m×2 m靶面内,弹着点测量误差为±10 mm。