Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates

This article proposes a global, chaos-based procedure for the discretization of functionals of Brownian motion into functionals of a Poisson process with intensity $\lambda >0$. Under this discretization we study the weak convergence, as the intensity of the underlying Poisson process goes to infinity, of Poisson functionals and their corresponding Malliavin-type derivatives to their Wiener counterparts. In addition, we derive a convergence rate of $O\left({\lambda }^{?1∕4}\right)$ for the Poisson discretization of Wiener functionals by combining the multivariate Chen–Stein method with the Malliavin calculus. Our proposed sufficient condition for establishing the mentioned convergence rate involves the kernel functions in the Wiener chaos, yet we provide examples, especially the discretization of some common path dependent Wiener functionals, to which our results apply without committing the explicit computations of such kernels. To the best our knowledge, these are the first results in the literature on the universal convergence rate of a global discretization of general Wiener functionals.     

New classes of second order difference equations solvable by factorization method

Under some assumptions we find a general solution of the factorization problem for a family of second order difference equations.     

A New Approach for Synthesis of Low‐moisture Glycidyl Azide Polymer

In this work, low‐moisture glycidyl azide polymer (GAP) was successfully prepared using a modified two‐step method. The modified method resembles the structure of the classical two‐step method, which is widely used to prepare the GAP. Firstly, epichlorohydrin (ECH) is polymerized into polyepicholorohydrin (PECH), which is subjected afterward to azidation step using sodium azide (NaN₃). Interestingly, minimizing the water content in the final GAP product, which is a challenging when dealing with GAP as a rocket propellant binder, was effectively achieved by utilizing low boiling point solvents instead of the relatively high boiling point Dimethyl formamide (DMF), monitoring the volatility of ECH and controlling the exothermicity of the reaction. Prepared GAP samples were investigated using Fourier transformer infra‐red (FT‐IR), gel‐permeation chromatography (GPC) and elemental analysis apparatus (CHNS) were used to characterize the product. The moisture % in the final product was examined using the Karl‐Fisher Technique. Results showed the successful preparation of GAP with low water content (<0.01 %), high average molecular weight (> 2000 g · mol^–1), 42.82 % nitrogen, a viscosity of 3484 cP at 20 °C, yield ranges between 95–98 % and a polydispersity index of 1.2. The prepared GAP is promising for replacement of the classical GAPs in the energetic materials applications.     

NUMERICAL SIMULATION OF FIBROBLAST DUROTAXIS MIGRATION INDUCED BY STIFFNESS GRADIENT OF SUBSTRATE1)

建立了一种细胞趋硬性迁移的理论模型和有限元分析框架,为连续变刚度人工基质的试验设计提供理论依据。考虑了细胞体的黏弹性属性,以及细胞与基质间的配受体动态反应过程,并以配受体合成时间为时间步长,将细胞运动方程化为静力学形式进行求解。对有限元过程提出一种动约束,便于消除其结构矩阵的奇异性。结果表明,模型能够模拟黏着斑内部力的快速波动现象,细胞的运动速度与观测数据一致,可有效模拟20,h以上的长时程问题。     

THE NEW ASSESSMENT METHOD FOR THE COURSE OF STRENGTH OF MATERIALS 1)

现有考核评价方式侧重期末考试而忽略过程考核，结合材料力学课程，探索一套注重过程考核的评价体系，综合评价学生对本课程的掌握程度，即将期末考试成绩在总评中的占比由70%降低至50%，平时作业、随堂测验、模块测验、实验考核和案例分析成绩各占比10%。新评价方式更加注重对学生学习过程的考核，使学生在整个课程学习过程中保持高度紧张感，提高学习的时效性和目的性，进而提高学生学习材料力学的热情和材料力学课堂教学效果。     

Pull-in Instability Analysis of Nanoelectromechanical Rectangular Plates Including the Intermolecular,Hydrostatic, and Thermal Actuations Using an Analytical Solution Methodology

The current paper presents a thorough study on the pull-in instability of nanoelectromechanical rectangular plates under intermolecular, hydrostatic, and thermal actuations. Based on the Kirchhoff theory along with Eringen's nonlocal elasticity theory, a nonclassical model is developed. Using the Galerkin method(GM), the governing equation which is a nonlinear partial differential equation(NLPDE) of the fourth order is converted to a nonlinear ordinary differential equation(NLODE) in the time domain. Then, the reduced NLODE is solved analytically by means of the homotopy analysis method. At the end, the effects of model parameters as well as the nonlocal parameter on the deflection, nonlinear frequency, and dynamic pull-in voltage are explored.     

一致分数阶非线性微分方程的精确解

同时考虑了Kudryashov方法和Khalil一致分数阶变换,构造了求解一致分数阶非线性微分方程精确解的新方法,并将其用于求解时间-空间一致分数阶Whitham-Boroer-Kaup方程,得到了Whitham-Boroer-Kaup方程新的精确解,验证了该方法的有效性和可行性.     

On the complexity of extending the convergence ball of Wang’s method for finding a zero of a derivative

Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study.