Morse指标和闭测地线的稳定性

令ind(c)为n+1维Riemann流形M上闭测地线c的Morse指标.我们证明:对于闭测地线c,如果它是定向的且n+ind(c)是奇数,或它是非定向的且n+ind(c)为偶数,则c不稳定.Poincaré的一个著名定理说Riemann面上的极小闭测地线是不稳定的,我们的结果是该结论的一个推广.     

Eighth-order methods with high efficiency index for solving nonlinear equations

In this paper, we derive a new family of eighth-order methods for solving simple roots of nonlinear equations by using weight function methods. Per iteration these methods require three evaluations of the function and one evaluation of its first derivative, which implies that the efficiency indexes are 1.682. Numerical comparisons are made to show the performance of the derived methods, as shown in the illustration examples.     

The nonidealness index of rank-ideal matrices

A polyhedron is integral if all its extreme points have 0, 1 components and in this case the matrix M is called ideal. When Q has fractional extreme points, there are different ways of classifying how far M is away from being ideal, through the polyhedral structure of Q. In this sense, Argiroffo, Bianchi and Nasini (2006) [1] defined a nonidealness index analogous to an imperfection index due to Gerke and McDiarmid (2001) [10].In this work we determine the nonidealness index of rank-ideal matrices (introduced by the authors (2008)). It is known that evaluating this index is NP-hard for any matrix. We provide a tractable way of evaluating it for most circulant matrices, whose blockers are a particular class of rank-ideal matrices, thereby following similar lines as done for the imperfection ratio of webs due to Coulonges, Pêcher and Wagler (2009) [7].Finally, exploiting the properties of this nonidealness index, we identify the facets of the set covering polyhedron of circulant matrices, having maximum strength with respect to the linear relaxation, according to a measure defined by Goemans (1995) [9].     

Decompositions for edge-coloring join graphs and cobipartite graphs

An edge-coloring is an association of colors to the edges of a graph, in such a way that no pair of adjacent edges receive the same color. A graph G is Class 1 if it is edge-colorable with a number of colors equal to its maximum degree Δ(G). To determine whether a graph G is Class 1 is NP-complete [I. Holyer, The NP-completeness of edge-coloring, SIAM J. Comput. 10 (1981) 718-720]. First, we propose edge-decompositions of a graph G with the goal of edge-coloring G with Δ(G) colors. Second, we apply these decompositions for identifying new subsets of Class 1 join graphs and cobipartite graphs. Third, the proposed technique is applied for proving that the chromatic index of a graph is equal to the chromatic index of its semi-core, the subgraph induced by the maximum degree vertices and their neighbors. Finally, we apply these decomposition tools to a classical result [A.J.W. Hilton, Z. Cheng, The chromatic index of a graph whose core has maximum degree 2, Discrete Math. 101 (1992) 135-147] that relates the chromatic index of a graph to its core, the subgraph induced by the maximum degree vertices.     

Valuation of guaranteed annuity options using a stochastic volatility model for equity prices

Guaranteed annuity options are options providing the right to convert a policyholder’s accumulated funds to a life annuity at a fixed rate when the policy matures. These options were a common feature in UK retirement savings contracts issued in the 1970’s and 1980’s when interest rates were high, but caused problems for insurers as the interest rates began to fall in the 1990’s. Currently, these options are frequently sold in the US and Japan as part of variable annuity products. The last decade the literature on pricing and risk management of these options evolved. Until now, for pricing these options generally a geometric Brownian motion for equity prices is assumed. However, given the long maturities of the insurance contracts a stochastic volatility model for equity prices would be more suitable. In this paper explicit expressions are derived for prices of guaranteed annuity options assuming stochastic volatility for equity prices and either a 1-factor or 2-factor Gaussian interest rate model. The results indicate that the impact of ignoring stochastic volatility can be significant.     

GL(n,K)中一类准可解子群的结构及其在Fuchsian系统中的应用(英文)

本文研究了单值群的可解性与Fuchsian方程可积性之间的关系.利用可解群及GL(n,K)的性质,获得GL(n,K)中一类准可解子群的结构定理,并将之心用于Fuchsian系统的可积性研究之中.     

Optimal ordering and pricing policy for an inventory system with trial periods

It is a business practice that home shopping companies offer a free trial period for their products with a goal of increasing sales. Under this policy, if for any reason customers are not satisfied with the purchase, they can return the product for a refund within the trial period. To develop inventory strategies in such environment, home shopping companies should take the return phenomenon into account so as to increase their profit. This paper considers this phenomenon and develops a seasonal inventory model to deal with the problem. Two scenarios are analyzed. In the first scenario, demand is assumed to be linearly price-dependent while in the second one, it is assumed to be exponentially price-dependent. The purpose of this research is to maximize the total profit over a given planning period by determining the optimal ordering quantity and price. The analytical results demonstrate that the optimal ordering quantity and prices are obtained using closed-form formulas.     

Joint decision on production and pricing for online dual channel supply chain system

Online dual channel supply chain system and its joint decision on production and pricing under information asymmetry are investigated. First, optimal production and pricing strategies are depicted according to the centralized system. Next, two kinds of contracts are designed for the decentralized system to coordinate the channel system, and their production and pricing decisions are depicted using a principle-agent method for the asymmetric information on the traditional channel. Finally, some interesting insights are found: the centralized system is not always being better than the decentralized system with a feasible contract if the traditional and professional retailer has lower selling cost. When uncertainty in the traditional channel information is higher, the manufacturer prefers a menu of contracts according to different channel settings. When uncertainty is lower, the manufacturer prefers a single contract. Furthermore, the higher the uncertainty in the traditional channel, the more the information welfare of the traditional retailer will gain. Performance with a menu of contracts cannot outperform that with a single contract integrating optimistic and pessimistic market setting well; their difference in performance is bigger when uncertainty in the traditional channel information is less.     

微纳光纤布拉格光栅折射率传感特性研究

利用光纤布拉格光栅方程和光纤基模有效折射率随纤芯半径和环境折射率的函数关系, 建立了微纳光纤布拉格光栅(MNFBG)反射波长随环境折射率变化的数学模型, 给出了波长灵敏度函数, 并指出MNFBG反射波长的变化规律决定于有效折射率随纤芯半径和环境折射率变化的关系. 详细探究了有效折射率及其灵敏度的变化规律, 结果表明: 有效折射率随纤芯半径和环境折射率的减小而非线性减小, 其对环境折射率变化的灵敏度随环境折射率的增大而非线性增加, 而且随纤芯半径减小, 有效折射率的灵敏度、线性度以及线性响应范围均呈递增规律. 通过对纤芯半径为0.5 μm的MNFBG在1.20–1.30和1.33–1.43 环境折射率范围内的波长响应关系拟合, 分别获得了477.33 nm/RIU和856.30 nm/RIU的波长灵敏度以及99.58 %和99.7%的高线性度, 论证了分析结论以及折射率区间划分测量方案的正确性, 为MNFBG折射率传感器的设计、优化以及应用提供了参考依据. 关键词： 微纳光纤 光纤布拉格光栅 折射率传感 数值模拟     

聚合物波导型表面等离子体共振传感器的特性研究

基于表面等离子体共振理论,将SU-8作为波导芯层材料,以聚甲基丙烯酸甲酯(PMMA)为下包层材料,设计了一款聚合物波导型SPR传感器。理论计算了波导芯层折射率、被测物折射率、不同金属薄膜及其厚度等因素对表面等离子体共振曲线的影响。分析结果表明,在可测试范围内,被测物折射率越大,灵敏度越高;波导芯层折射率减小,共振峰向长波方向移动,被测物检测范围整体向折射率小的方向偏移,波导芯层折射率增大则相反。