6×n阶矩形网络等效电阻猜想的证明

任意k×n阶电阻网络等效电阻的公式研究属于科学难题,到目前为止已经获得了当k=1,2,…,5时的5种情形下的等效电阻公式,但对k≥6时的等效电阻的普适公式仅仅作为猜想给出.本文根据建立的任意k×n阶电阻网络等效电阻研究的方法,证明了k=6时的等效电阻公式的正确性,并且给出了其无穷网络的等效电阻公式,在对比验证时得到了一些新的三角恒等式.     

三维Zakharov-Kuznetsov方程解的衰减性

考虑三维Zakharov-Kuznetsov方程的初值问题,证明了该初值问题解的指数衰减性.这个性质与加权Sobolev空间中解的持久性及该问题解的唯一连续性相关.     

Resolving quantum dots and peptide assembly and disassembly using bending capillary electrophoresis

Despite the numerous techniques developed for the studying nanoparticle and peptide interaction nowadays, sensitive and convenient assay in the process of flow, especially to simulate the self‐assembly of quantum dots (QDs) and peptide inflow in blood vessels, still remains big challenges. Here, we report a novel assay for studying the self‐assembly of QDs and peptide, based on CE using a bending capillary. We demonstrate that the semicircles numbers of the bending capillary affect the self‐assembly kinetics of CdSe/ZnS QDs and ATTO‐D₃LVPRGSGP₉G₂H₆ peptide. Moreover, benefitting from this novel assay, the effect of the position on the self‐assembly has also been realized. More importantly, we also demonstrate that this novel assay can be used for studying the stability of the QDs–peptide complex inflow. We believe that our novel assay proposed in this work could be further used as a general strategy for the studying nanoparticle–biomolecule interaction or biomolecule–biomolecule interaction.     

Synthesis of nanocomposites from cationic polyacrylamide and modified carbon black: Application as flocculants for oily sludge suspension

Carbon black was modified using various liquid‐phase oxidation methods (modified carbon black = m‐CB, m = (1, 2, 3): 1, sulfuric acid/potassium permanganate method; 2, nitric acid method; 3, hydrogen peroxide method). With acetone–ethylene glycol as initiator, dimethyldiallylammonium chloride (DMDAAC) and acrylamide (AM) as monomer, cationic polyacrylamide (CPAM) was prepared by UV excitation of the monomer. The m‐CB/CPAM nanocomposites were synthesized using a hydrothermal method. The factors that affected the molecular weight of CPAM were investigated, including the total monomer concentration, the dosage of the complex initiator, the mass ratio of m_AM:m_DMDAAC and the UV irradiation time. The chemical structures and morphologies of the samples were characterized using Fourier transform infrared spectroscopy, thermogravimetric analysis, elemental composition, X‐ray diffraction and scanning electron microscopy. 1‐CB/CPAM was utilized to flocculate oil sludge suspension, and the effects of 1‐CB quality, 1‐CB/CPAM dosage, temperature and pH value on the flocculation performance of 1‐CB/CPAM were investigated. The flocculation mechanism of 1‐CB/CPAM was also analyzed. The results show that 1‐CB/CPAM has an outstanding flocculation effect, and it flocculates oil sludge particles by adsorption bridging and charge neutralization in acidic and alkaline conditions.