部分线性变系数模型的Profile Lagrange乘子检验

对于部分线性变系数模型附有约束条件时的估计与检验问题,基于Profile最小二乘方法给出了参数部分以及非参数部分的约束估计并研究了它们的渐近性质,并针对约束条件构造了Profile Lagrange乘子检验统计量,证明了该统计量在原假设下的渐近分布为χ2分布,从而将Lagrange乘子检验方法推广到了半参数模型上.     

稀缺资源的节省利用研究

本在建立模型的基础上，对稀缺资源的节省利用问题进行了研究，给出了稀缺资源能否节省的判别条件和具体作法。     

Numerical methods for nonlinear partial differential equations of fractional order

In this article, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when applied to partial differential equations of fractional order.     

Shape reconstruction of an inverse Stokes problem

This paper deals with the shape reconstruction of a viscous incompressible fluid driven by the Stokes flow. For the approximate solution of the ill-posed and nonlinear problem we propose a regularized Newton method. A theoretical foundation for the Newton method is given by establishing the differentiability of the initial boundary value problem with respect to the interior boundary curve in the sense of a domain derivative. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible.     

Formal and analytic linearizability of families of conformal map germs (ℂ, 0) → (ℂ, 0)

We consider a nondegenerate one-parameter family of germs of conformal maps of (?, 0) into (?, 0). We prove that such a family is analytically linearizable whenever it is formally linearizable. In this case, the linearizing coordinate change analytically depends on the parameter.     

线性互补问题的一类新的带参数价值函数的阻尼牛顿法

本文给出了线性互补问题LCP(q ,M)的一类新的带参数光滑价值函数 ,基此价值函数提出了一种阻尼牛顿类算法 ,并证明了当M为P 矩阵时 ,该算法全局收敛且有限步终止 .通过数值实验说明了该算法高效可靠 .与互补问题的磨光方程组中所采用的带参数价值函数不同 ,这里的参数最终并不趋向于零 ,而是趋向于被称作解的乘子向量 (与凸非线性极小极大问题的Lagrange乘子完全一致 ) ,这一思想是本文作者首次提出来的 ,同时本文中所采用的阻尼牛顿类方法也有其独到之处 ,在互补问题的研究中有进一步发展的潜力     

Thermal-mechanical behavior of styrene-based shape memory polymer tubes

Styrene-based shape memory polymer (SMP) tubes were fabricated and their basic mechanical properties in different deformation states were investigated. The tensile, compression, bending and twisting shape memory properties of the tubes were analyzed and discussed, and the results indicated that SMP tubes exhibit good shape fixity ratio and shape recovery ratio. In addition, the shape recovery behavior was investigated at different heating rates. These experimental results will provide guidance for future applications of SMP tube structures.     

Shape memory effect and recovery stress property of carbon nanotube/waterborne epoxy nanocomposites investigated via TMA

Shape memory polymers (SMPs) have received great attention and scientific interest in widespread technological development during last few decades. Besides the development of novel SMPs, various techniques have been practiced for characterization of shape memory effect (SME) of SMPs. In this study, the shape memory effect and recovery stress property of the carbon nanotube (CNT)/waterborne epoxy (WEP) nanocomposites below and above the glass transition temperature (T_g) of the nanocomposites and under isostrain and isostress were systematically investigated via thermal mechanical analysis (TMA), respectively. The experimental results showed that the nanocomposites exhibit excellent shape memory effect. The shape memory fixity and recovery ratios were approximately 100% even below glass transition temperature (T_g). A remarkable point is that the strain of the nanocomposites suddenly increased with the temperature decreasing in a certain period of the heating-cooling cycles under isostress condition and the strain increment increased with temperature in general. Especially at low temperature, the recovery stress was very sensitive to temperature under isostrain condition of ±0.25 °C temperature with differential of 25.5 °C developed pressure difference of 0.20 MPa. Moreover, TMA is a practical method for quantifying the SME and recovery stress properties of SMPs and their composites.     

Evaluating shape memory behavior of polymer under deep-drawing conditions

Thermoplastic polyurethanes (TPU) are a popular family of shape memory polymers (SMP) due to their excellent abrasion & weather resistant, and mechanical strength. However, conventional processing operations or their combination with other polymers by adhesion or blending can affect their unique shape memory behavior. Currently, there are no effective methods to study and quantify the shape memory behavior of SMP based polymer laminates as they would respond to deep drawing operations. In this paper, a new method was introduced to effectively quantify the recovery behavior of TPU based polymer laminates undergoing simultaneous stretching and bending operations at different processing temperatures. The results presented show the value of developing a shape recovery characterization method that resembles the stresses of thermoforming to properly assess formability of shape memory polymers used in laminate constructions.