对BJH方法计算孔径分布过程的解读

This paper introduces the geometric assumptions and neglects of the pore size distribution calculated by BJH method, the arithmetic approximation for simplified calculation, the derivation process of each parameter, the calculation steps and key points of the pore size distribution. This paper also introduces the application scope of BJH method at the current instrument level, and how to further integrate the data. In order to get the required analysis and test report, references are provided for the subsequent adjustment of test parameters and improvement of test methods. Some problems often encountered in reading experimental reports are also discussed.     

Theoretical modeling of the chemical synthesis and detonation performance of polynitrocubane derivatives

Theoretical work was performed based on experimental methods described in the literature to simulate and explore feasible routes for the synthesis of energetic octanitrocubane (ONC) and polynitrocubane derivatives. In respective gaseous and liquidous environments, using cubane as the raw material, ONC was successfully synthesized through carboxylation, amination, oxidation and nitration stages, and the related reaction energy barriers were simultaneously acquired. In particular, the polyparametric calibrated gaseous molecular formation enthalpy and the group additivity approach-estimated molecular density were incorporated using the Kamlet-Jacobs equation to evaluate the detonation performance of polynitrocubane derivatives. Some high-energy-density derivatives were found to have superior characteristics as compared with traditional hexagon (RDX) and octagon (HMX) explosives.     

Isobaric thermal expansivities of polyethylenes with various crystallinities over the pressure range from 0.1 to 300 MPa and over the temperature range from 303 to 393 K

A pressure-controlled scanning calorimeter (PCSC) has been applied for measuring the isobaric volume thermal expansivities (α_p) of crystalline polymers as a function of pressure up to 300 MPa at various temperatures. The measurements have been performed for several well-defined polyethylenes with various degrees of crystallinity at 302.6, 333.0, 362.6, and 393.0 K. The results are reported as values of coefficients in a correlation equation, which facilitates the use of reported data over large ranges of temperature and pressure. The general pressure-temperature behavior of α_p for all polyethylenes under study is such that α_p increases with temperature and decreases with pressure. The increase with temperature is smaller at high pressures and the isotherms of α_p have a tendency to converge at high pressures; α_p decreases linearly with the crystallinity of the polyethylene over the whole range of pressure and temperature under investigation. From the linear approximation of experimental data for polyethylenes with various crystallinities the estimated α_p for both crystal and amorphous phases of polyethylenes have been determined as a function of pressure up to 300 MPa at 302.6, 333.0, and 362.5 K. The obtained results have been compared with available literature crystallographic data and with the values derived from the Pastine theoretical equation of state for both crystalline and amorphous phases. © 1996 John Wiley & Sons, Inc.     

MODELLING OF WAVE PROPAGATION IN THE NEARSHORE REGION USING THE MILD SLOPE EQUATION WITH GMRES-BASED ITERATIVE SOLVERS

The mild slope equation in its linear and non-linear forms is used for the modelling of nearshore wave propagation. The finite difference method is used to descretize the governing elliptic equations and the resulting system of equations is solved using GMRES-based iterative method. The original GMRES solution technique of Saad and Schultz is not directly applicable to the present case owing to the complex coefficient matrix. The simpler GMRES algorithm of Walker and Zhou is used as the core solver, making the upper Hessenberg factorization unneccessary when solving the least squares problem. Several preconditioning-based acceleration strategies are tested and the results show that the GMRES-based iteration scheme performs very well and leads to monotonic convergence for all the test-cases considered.     

关于一类二阶微分方程的振动性的注记

考虑一类具连续分布滞量的二阶非线性泛函微分方程,获得了该方程的所有解振动的充分条件.     

正整数的一类三分拆的应用

利用正整数n的一类特殊的3分拆n=n1+n2+n3,n1>n2>n3≥1,且n2+n3>n1的Ferrers图将不定方程4x1+3x2+2x3=n(n≥9)的正整数解与这种分拆联系起来,从而得到了该不定方程的正整数解数公式;同时也给出了正整数n的一类4分拆的计数公式.此外,还给出了周长为n的整边三角形的计数公式的一个简单证明.     

n阶变系数线性差分微分方程的解

利用Mikusi'nski算符域中变系数算符概念和相应的算符系数移动算符幂级数的概念和结果,获得初值条件下n阶变系数线性差分微分方程的解.     

数学建模融入微积分教学单元

本文是教育部项目的子课题中期报告中样板单元,针对打假的机理问题设计了数学建模融入微积分的一个教学单元,文中详细地给出了单元的全文、讲授和实践(或计划讲授和实践)的学时的安排、师生的反映、体会和建议.     

变时滞Hopfield神经网络的全局吸引性和全局指数稳定性

对一类具时滞的Hopfeild型神经网络模型,在非线性神经元激励函数只要求满足Lipschitz连续的条件下,利用推广的Halanay时延微分析不等式、Dini导数以及泛函微分析技术,给出了这类模型的平衡点全局指数稳定性和全局吸引性的充分条件,这些条件易于检验,且改进和推广了前人的结论.此外,此文给出了研究神经网络模型的全局吸引性的微分不等式比较方法.     

Boussinesq方程行波解的存在性

利用平面动力系统方法的分支理论,研究了Boussinesq方程,通过对Boussinesq方程进行行波变换,得到了相应行波系统的首次积分和平衡点,给出了不同参数条件下的相图,证实了Boussinesq方程存在孤立波解和周期波解。