Derivation of Korteweg–de Vries flow equations from the short‐wave model equation

We perform a multiple‐time scales analysis and compatibility condition to the short‐wave model equation. We derive Korteweg–de Vries flow equation in the bi‐Hamiltonian form as an amplitude equation. Copyright © 2013 John Wiley & Sons, Ltd.     

Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity

In this paper, to consider all surface effects including surface elasticity, surface stress, and surface density, on the nonlinear free vibration analysis of simply-supported functionally graded Euler–Bernoulli nanobeams using nonlocal elasticity theory, the balance conditions between FG nanobeam bulk and its surfaces are considered to be satisfied assuming a cubic variation for the component of the normal stress through the FG nanobeam thickness. The nonlinear governing equation includes the von Kármán geometric nonlinearity and the material properties change continuously through the thickness of the FG nanobeam according to a power-law distribution of the volume fraction of the constituents. The multiple scale method is employed as an analytical solution for the nonlinear governing equation to obtain the nonlinear natural frequencies of FG nanobeams. The effect of the gradient index, the nanobeam length, thickness to length ratio, mode number, amplitude of deflection to radius of gyration ratio and nonlocal parameter on the frequency ratios of FG nanobeams is investigated.     

Computing economies of vertical integration,economies of scope and economies of scale using partial frontier nonparametric methods

So far, in the nonparametric literature only full frontier nonparametric methods have been applied to search for economies of scope and scale, particularly the data envelopment analysis method (DEA). However, these methods present some drawbacks that might lead to biased results. This paper proposes a methodology based on more robust partial frontier nonparametric methods to look for scope and scale economies. Through this methodology it is possible to assess the robustness of these economies, and in particular to assess the influence that extreme data or outliers might have on them. The influence of the imposition of convexity on the production set of firms was also investigated. This methodology was applied to the water utilities that operated in Portugal between 2002 and 2008. There is evidence of economies of vertical integration and economies of scale in drinking water supply utilities and in water and wastewater utilities operating mainly in the retail segment. Economies of scale were found in water and wastewater utilities operating exclusively in the wholesale, and in some of these utilities diseconomies of scope were also found. The proposed methodology also allowed us to conclude that the existence of some smaller utilities makes the minimum optimal scales go down.     

Generalized elementary functions

We use the theory of generalized linear differential equations to introduce new definitions of the exponential, hyperbolic and trigonometric functions. We derive some basic properties of these generalized functions, and show that the time scale elementary functions with Lebesgue integrable arguments represent a special case of our definitions.     

Averaging on slow and fast cycles of a three time scale system

Pontryagin–Rodygin?s Theorem for slow and fast systems describes the slow drift during the rolling up of the trajectories around the cycles of the fast dynamics. This drift is approximated by the averaging on the cycles. The calculation of this average is generally a difficult task since it requires the knowledge of the closed orbits and their periods. We present two paradigms of three time scale systems where we can overcome this limitation. It is the case of systems the fast dynamics of which have cycles with relaxation presenting or not a canard phenomenon. We can not apply Pontryagin–Rodygin?s Theorem to these systems because their fast equation is itself singularly perturbed. We also investigate the extension of the results to unbounded time intervals. The results are stated classically and proved within the framework of nonstandard analysis.     

Optimum life testing plans in presence of hybrid censoring: A cost function approach

Hybrid censoring scheme is a combination of Type‐I and Type‐II censoring schemes. Determination of optimum hybrid censoring scheme is an important practical issue in designing life testing experiments to enhance the information on reliability of the product. In this work, we consider determination of optimum life testing plans under hybrid censoring scheme by minimizing the total cost associated with the experiment. It is shown that the proposed cost function is scale invariant for some selected distributions. Optimum solution cannot be obtained analytically. We propose a method for obtaining the optimum solution and consider Weibull distribution for illustration. We also studied the sensitivity of the optimal solution to the misspecification of parameter values and cost components through a well‐designed sensitivity analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

中国对外直接投资的贸易效应研究:基于对北美自贸区、欧盟、东盟投资的比较分析

中国对外贸易发展成熟、国际地位显著,但从长期看,其边际收益呈现递减趋势.而对外直接投资虽规模较小,且尚在起步阶段,但其发展速度快、市场潜力巨大.在拓展Anderson和Wincoop模型基础上,理论分析了对外直接投资与贸易之间的关系.然后通过建立计量模型,利用1995-2011年面板数据进行固定模型分析.由于中国对外直接投资的贸易效应存在明显的区域性,以北美自贸区、欧盟和东盟作为研究对象,实证检验了中国对外直接投资与贸易的关系,旨在考察中国对三种不同类型区域一体化组织投资的贸易效应差异.研究结果表明,从长期看,中国对北美自由贸易区、欧盟和东盟投资均具有明显的贸易创造效应.这种贸易创造效应的大小依次是东盟欧盟北美自贸区.     

我国国债规模对宏观经济影响实证分析

随着以希腊债务危机为导火索的欧洲债务危机的愈演愈烈,国债对宏观经济的影响再一次成为了经济学讨论的热点.首先从直观图形着手,运用H-P滤度法去除趋势后,计算各变量的偏离趋势百分比,对比国债规模代替变量与宏观经济效应代替变量之间的偏离趋势图,从图形得到的定量关系为后面的实证分析做好准备.然后进一步进行协整分析,并在向量自回归(VAR)框架下通过脉冲响应函数考察变量之间的相互影响路径,最后通过建立误差修正模型(ECM)分析各个变量之间的长期均衡关系和短期波动特征,以量化各变量之间影响程度的大小.全面系统地研究了国债对宏观经济增长的影响程度并做出实证分析,对于深刻认识国债的本质,规避国债的风险,科学合理地制定国债政策有着重要的理论价值和实际意义.     

气候政策的经济环境效应分析与比较—基于碳税、许可交易和总量控制的动态微分博弈

基于产品差别化假设,建立双寡头动态微分博弈模型,比较碳税和许可交易以及总量控制3种气候政策的经济环境效应.研究发现,不同气候政策对两国的经济效应不同.进一步研究还发现,在企业产品差别化竞争时,从碳排放流量来看,碳税政策和许可交易政策与总量控制政策之间没有严格的优劣之分;碳排放存量对碳税政策最敏感.从碳存量对政策的边际影响来看,许可交易政策与总量控制政策是相同的,而碳税政策与之相反.当两国生产的产品完全同质时,从均衡碳排放流量和碳排放存量来看,许可交易政策最优,总量控制政策次之,碳税政策最差.若政府单纯以控制碳排放量为目的,许可交易政策是最佳选择.