Facile synthesis of graft copolymers containing rigid poly(dialkyl fumarate) branches by macromonomer method

Graft copolymers show microphase separated structure as seen in block copolymers and have lower intrinsic viscosity than block copolymers because of a branching structure. Therefore, considering molding processability, especially for polymers containing rigid segments, graft copolymers are useful architectures. In this work, graft copolymers containing rigid poly(diisopropyl fumarate) (PDiPF) branches were synthesized by full free‐radical polymerization process. First, synthesis of PDiPF macromonomers by addition‐fragmentation chain transfer (AFCT) was investigated. 2,2‐Dimethyl‐4‐methylene‐pentanedioic acid dimethyl ester was found to be an efficient AFCT agent for diisopropyl fumarate (DiPF) polymerization because of the suppression of undesired primary radical termination, which significantly took place when common AFCT agent, methyl 2‐(bromomethyl)acrylate, was used. Copolymerization of PDiPF macromonomer with ethyl acrylate accomplished the generation of the graft copolymer having flexible poly(ethyl acrylate) backbone and rigid PDiPF branches. The graft copolymer showed a microphase separated structure, high transparency, and characteristic thermal properties to PDiPF and poly(ethyl acrylate). © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2474–2480     

Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a $L^p$-Lebesgue space, of a function f in $W^k{L}^{\frac{pn}{n+kp},p}(\mathrm{\Omega })$, where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, $k,n\in \mathbb{N}$, $k<n$ and $\frac{n}{n?k}<p<+\infty$. This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings.     

A new endocytic model based on the co-rotational grid method

Endocytosis plays important roles in many cellular physiological processes, such as metabolism and immune. Many theoretical models have been proposed to study the endocytic process, but little has considered the tensile deformation of the membrane and the actin forces. In this paper, a new endocytic model is proposed based on the co-rotational grid method. Our model gives a direct estimation of the in-plane strain of the plasma membrane and provides a basis for the calculation of further scission process of the vesicle. The results fit well with experimental data in the literature. Moreover, it is suggested that the active forces of actin at the endocytic site is the main mechanism driving the invagination of the plasma membrane.     

QEPAS系统中石英音叉模态仿真计算与研究

对石英音叉增强型光声光谱(QEPAS)系统中常用的石英音叉进行了有限元模态计算，获得石英音叉前6阶振型与模态频率，认知了第4阶对称摆动振型为有效振动，利用单因素法分析了石英音叉的音臂长度l₁、音臂宽度w₁、音臂厚度t、音臂切角θ、音臂圆孔直径d及音臂圆孔高度h对低阶有效共振频率(Fre)的影响，敏感度依次为： l₁> w₁>d>θ>t>h，考虑实际设计情形，筛选出了l₁，w₁，d与h四个石英音叉设计变量，采用Box-Behnken实验设计方案与RSM(response surface methodology)方法，以Fre为函数目标，建立l₁，w₁，d与h的二次回归响应面模型，得到了参数之间的交互作用，利用Design-Expert软件对响应面模型进行设计参数反求，结果表明，在15 000 Hz≤Fre≤25 000 Hz计算区域内误差较小，基本满足QEPAS系统的计算需求，所提出的研究与设计方法具有一定通用性，可为QEPAS系统中石英音叉结构参数设计提供参考。     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

Multistrain edge‐based compartmental model on networks

Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models.     

Multiple positive solutions for Schrödinger‐Poisson system involving singularity and critical exponent

In this paper, the existence and multiplicity of positive solutions is established for Schrödinger‐Poisson system of the form where 0 ∈ Ω is a smooth bounded domain in , , and λ > 0 is a real parameter. Combining with the variational method and Nehari manifold method, two positive solutions of the system are obtained.     

求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析

本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法，分析当矩阵A，B，C，D均是Hermite正（负）定矩阵时，迭代矩阵的特征值表达式，给出了最优参数的确定方法，并提出了相应的加速算法.