金属覆层保偏光纤偏振器的五层波导模型及理论分析

对金属履层保偏光纤偏振器建立了五层波导变参量物理模型,设计了自适应套孔爬山法的数值计算方法求解含多层波导本征值的复超越方程,计算结果揭示了金属覆层偏光纤偏振器的物理机制,并对器件进行了优化设计,给出了实验结果。     

曹娥江径流特性及其对河口冲淤的影响

曹娥江径流具有浙闽山溪性强潮河口的若干特征,径流年际、年内变幅较大,洪水暴涨暴落,洪枯比极大,年内存在两个汛期,即梅汛期和台风汛期. 根据曹娥江径流特性,本文讨论了曹娥江河口河床洪冲枯淤变化特性,径流对潮汐大小的间接影响以及径流对曹娥江口门外主槽出口方向的影响.     

浅埋圆形孔洞附近的半圆形凸起对SH波的散射

采用"契合"的思想，给出了地下孔洞与地面上的半圆形凸起地形对SH波散射问题的 解答. 将整个求解区域分割成两部分来处理. 其一为包括半圆形凸起地形在内的一个圆形区 域I，其余为区域II. 在区域I和II中分别构造位移解，并在两个区域的"公共边界"上 实施"契合". 在区域I中构造一个上半部边界应力为零，而其余部分位移、应力任意的驻 波解，在区域II中构造出半圆形凹陷和浅埋圆孔的散射波，且要求它满足水平界面上应力 为零的约束条件. 然后再通过移动坐标，满足"公共边界"的"契合"条件和地下孔洞的边 界条件，建立起求解该问题的无穷代数方程组. 最后，给出了分析例题和数值结果，并 对其进行了讨论.     

Second-order schemes for solving decoupled forward backward stochastic differential equations

In this paper,by using trapezoidal rule and the integration-by-parts formula of Malliavin calculus,we propose three new numerical schemes for solving decoupled forward-backward stochastic differential equations.We theoretically prove that the schemes have second-order convergence rate.To demonstrate the effectiveness and the second-order convergence rate,numerical tests are given.     

基于模糊收益率的养老保险基金投资研究

结合中国养老保险基金投资现状,考虑预期收益率是模糊数的情形,利用可能性均值和可能性方差作为投资组合的预期收益率和风险,建立均值-方差组合投资模型.最后,利用lingo软件进行数值分析,表明此模型具有一定的实际应用价值.     

一道赛题的解法及问题之延伸--陕西省大学生高等数学竞赛题系列分析之四

对一道数学竞赛题,介绍欧拉公式解法,并用于求解其它问题;进而联想定积分定义设计出一种新解法,并将赛题引申,推广到复化中矩形求积公式和复化梯形求积公式情形,据此可以设计一些赛题。     

梯形模糊有序加权几何算子及其在决策中的应用

针对梯形模糊数据信息的集成问题,给出了梯形模糊数两两比较的可能度公式和梯形模糊有序加权几何(TFOWG)算子.基于可能度公式和TFOWG算子,提出了一种准则权重信息完全未知且准则值以梯形模糊数形式给出的不确定多准则决策方法.最后,实例分析表明了该方法的可行性和有效性.     

基于Hausdauff度量的模糊TOPSIS方法研究

针对模糊多属性决策中的模糊 TOPSIS方法 ,提出了一种基于 Hausdauff度量的模糊 TOPSIS方法 .首先由模糊极大集与模糊极小集确定模糊多属性决策问题的理想解与负理想解 ,进而由 Hausdauff度量获得不同备选方案到理想解与负理想解的距离及其贴近度 ,根据贴近度指标对方案进行排序 ,为决策者提供决策支持 .最后以 L-R梯形模糊数为例进行了实例研究 .     

Total ordering for intuitionistic fuzzy numbers

Intuitionistic fuzzy set plays a vital role in decision making, data analysis, and artificial intelligence. Many decision‐making problems consist of different types of datum, where fuzzy set theoretical approaches may fail to obtain the optimal decision. Numerous approaches for intuitionistic fuzzy decision‐making problem have been introduced in the literature to overcome these short comings. But there is no single approach that can be used to solve all kinds of problems because of the partial ordering defined on the collection of intuitionistic fuzzy numbers (IFNs). Even though ranking of fuzzy numbers have been studied from early seventies in the last century, a total order on the entire class of fuzzy numbers has been introduced by Wang and Wang (Fuzzy Sets Syst 2014, 243, 131–141) only on 2014. A total order on the collection of all IFN is an open problem till today. In this article, a total order on the entire class of IFN using upper lower dense sequence in the interval [0, 1] is proposed and compared with existing techniques using illustrative examples, further an algorithm (which is problem independent) for solving any intuitionistic fuzzy multicriteria decision‐making problem (Intuitionistic fuzzy MCDM) is introduced. This new total ordering on IFNs generalizes the total ordering defined in Wang and Wang ( 22 ) for fuzzy numbers. © 2016 Wiley Periodicals, Inc. Complexity 21: 54–66, 2016     

Scattering of SH-waves on triangular hill joined by semi-cylindrical canyon

Scattering of SH-waves on the triangular hill joined by semi-cylindrical canyon in half-space is studied using the method of complex function and moving coordinates. The model being studied is divided into two domains. The wave functions satisfying the required condition at each wedge are constructed in each equation. The equations are solved with Fourier expansion. Numerical results are provided to discuss the influence of scattering of SH-waves.