光触发自修复聚合物研究进展

近几年,由于光触发自修复聚合物具有可控快速等优势,其在自修复聚合物领域中占据了重要的地位。光触发自修复聚合物实现自修复的方法主要分为3类,分别是基于光交联反应的自修复、基于光触发交换反应的自修复和基于光热效应的自修复。本文主要从光触发自修复聚合物的修复机制以及修复过程中涉及的化学本质两个方面,重点阐述了上述3类光触发自修复方法的最新研究进展,强调3种光触发自修复之间的联系和共同点。同时,对光触发自修复聚合物未来的发展前景进行了展望。     

Surface modification of aluminum hypophosphite and its application for polyurethane foam composites

Aluminum hypophosphite (AHP) is surface modified by melamine derivative to fabricate reactive solid flame retardant (MCAHP) for polyurethane foam. MCAHP is successfully prepared and characterized by FTIR and SEM. The flame-retarded efficiency of MCAHP in PU is higher than that of AHP. It demonstrated that MCAHP has better compatibility in PU matrix compared with AHP based on the SEM observation. After surface modification, due to the reaction between MCAHP and PU matrix, crosslinking might be formed between MCAHP and PU matrix, which contributes to the excellent compatibility of MCAHP in PU matrix, and as a result, the glass transition temperature of PU/MCAHP is 4 °C higher than that of PU/AHP. The thermal behavior of PU composites is characterized by TG and TG-FTIR, and results suggest the sublimation of melamine at about 320 °C because of the decomposition of the melamine derivative. The sublimation of melamine can consume abundant heat and dilute the oxygen concentration, which is benefit for the improvement of flame retardancy.     

自由Rota-Baxter代数的因子分解

近年来,Rota-Baxter代数在数学和物理学中有着广泛的应用,受到越来越多的关注,自由Rota-Baxter代数分别用括号字,根树以及Motzkin路径得到了构造.因子分解在代数学中是一个很重要的问题.本文主要考虑用括号字构造的自由RotaBaxter代数,得到了自由Rota-Baxter代数中基元素的因子分解.     

大族长度为pq的伪随机k元序列

Mauduit与Sárkzy在一系列论文中研究了κ元序列的伪随机性.本文通过对模pq剩余类环Z_(pq)进行分割,进而结合离散对数的方法,构造了一大族长度为pq的伪随机κ元序列,并证明其具有很好的伪随机性.     

Reflecting Diffusion Processes on Manifolds Carrying Geometric Flow

Let \(L_t:=\Delta _t+Z_t\) for a \(C^{\infty }\)-vector field Z on a differentiable manifold M with boundary \(\partial M\), where \(\Delta _t\) is the Laplacian operator, induced by a time dependent metric \(g_t\) differentiable in \(t\in [0,T_\mathrm {c})\). We first establish the derivative formula for the associated reflecting diffusion semigroup generated by \(L_t\). Then, by using parallel displacement and reflection, we construct the couplings for the reflecting \(L_t\)-diffusion processes, which are applied to gradient estimates and Harnack inequalities of the associated heat semigroup. Finally, as applications of the derivative formula, we present a number of equivalent inequalities for a new curvature lower bound and the convexity of the boundary. These inequalities include the gradient estimates, Harnack inequalities, transportation-cost inequalities and other functional inequalities for diffusion semigroups.     

On entire solutions of two types of systems of complex differential-difference equations

In this paper, we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations, and obtain some interesting results. It extends some results concerning complex differential (difference) equations to the systems of differential-difference equations.     

一个二元叠加码M_q(t,k,d)生成的二元等重码

研究了二元叠加码Mq(t,k,d)也是一个二元等重码,给出了它成为最佳等重码的条件,研究了它的检错性.     

灰色GM(1,1)模型研究综述

GM(1,1)是灰色预测理论的核心模型和基础模型.从累加生成方法、初值优化、背景值优化、参数估计方法、模型性质和模型拓展的视角,梳理了GM(1,1)模型的研究进展.明确了有待进一步研究的问题,对GM(1,1)模型的未来研究方向提出了建议.     

正交约束优化问题的一阶算法

带有正交约束的矩阵优化问题在材料计算、统计及数据分析等领域中有着广泛的应用.由于正交约束的可行域是Stiefel流形,一直以来流形上的优化方法是求解这一问题的主要方法.近年来,随着实际应用问题所要求的变量规模的扩大,传统的流形优化方法在计算上的劣势显现出来,而一些迭代简单、收敛快的新算法逐渐被提出.通过收缩方法、非收缩可行方法、不可行方法三个类别分别来介绍求解带有正交约束的矩阵优化问题的最新算法.通过分析这些方法的主要特性,以及应用问题的要求,对这类问题算法设计的研究进行了展望.     

微积分与线性代数教学的渗透与融合

通过典型问题,探讨如何将《微积分》与《线性代数》两门不同的数学基础课程相互渗透与融合,从而揭示这两门课之间的密切联系,开阔学生思路,提高学生将所学知识融会贯通的能力.