Heinz type inequalities for mappings satisfying Poisson’s equation

In this paper, we study the Heinz type inequalities for mappings satisfying Poisson’s equation. Some results generalize the ones obtained by Partyka and Sakan.     

Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

A Near-Infrared-Controllable Artificial Metalloprotease Used for Degrading Amyloid-β Monomers and Aggregates

Proteolysis of amyloid-β (Aβ) is a promising approach against Alzheimer's disease. However, it is not feasible to employ natural hydrolases directly because of their cumbersome preparation and purification, poor stability, and hazardous immunogenicity. Therefore, artificial enzymes have been developed as potential alternatives to natural hydrolases. Since specific cleavage sites of Aβ are usually embedded inside the β-sheet structures that restrict access by artificial enzymes, this strongly hinders their efficiency for practical applications. Herein, we construct a NIR (near-IR) controllable artificial metalloprotease (MoS₂-Co) using a molybdenum disulfide nanosheet (MoS₂) and a cobalt complex of 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid (Codota). Evidenced by detailed experimental and theoretical studies, the NIR-enhanced MoS₂-Co can circumvent the restriction by simultaneously inhibition of β-sheet formation and destroying β-sheet structures of the preformed Aβ aggregates in living cell. Furthermore, our designed MoS₂-Co is an easy to graft Aβ-target agent that prevents misdirected or undesirable hydrolysis reactions, and has been demonstrated to cross the blood brain barrier. This method can be adapted for hydrolysis of other kinds of amyloids.     

非齐度量测度空间上Morrey-Herz空间上的广义分数次积分算子及其交换子

设(χ,d,μ)是一个同时满足上双倍条件和几何双倍条件的非齐度量测度空间,对于引进的一类非齐度量测度空间上的Morrey-Herz空间,利用非齐度量测度空间的特征,证明了广义分数次积分算子及其交换子在非齐度量测度空间上MorreyHerz空间的有界性.     

富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.