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.     

Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.     

Thermoresponsive polymersome from a double hydrophilic block copolymer

The article describes synthesis and thermally triggered self‐assembly of a Poly (ethylene oxide)‐block‐poly (N‐insopropylacrylamide) (PEO‐b‐PNIPAm) in aqueous medium. At rt, the polymer remains as unimer, however, at lower critical solution temperature (LCST) of PNIPAm (32 °C), it forms a rather large undefined aggregate which at slightly elevated temperature (～40 °C) converges to well defined polymersome structure (Critical aggregation concentration = 0.45 mg/mL) with hydrodynamic diameter of 40–50 nm. By lowering the temperature, initial swelling of the compact vesicle followed by reversible disassembly to unimer was noticed. The polymersome exhibits encapsulation ability to a hydrophilic dye Calcein which can be spontaneously released by lowering the temperature below cloud point. Likewise a hydrophobic dye namely 8‐Anilino‐1‐naphthalenesulfonic acid (ANS) can also be encapsulated and released by thermal trigger. Detail photoluminescence studies reveal ANS dye can be used as a generalized probe molecule for detecting LCST of a thermoresponsive polymer by “fluorescence on” above LCST even by cursory observation. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2444–2451     

关于循环环的理想、素理想和极大理想

研究了循环环R=的理想、素理想和极大理想的个数和结构,得到了如下结论:1)理想:(1)若|R|=∞,则R共有无穷多个理想:;(2)若|R|=n,设n的正因数个数为T(n),则R共有T(n)个理想:.2)素理想:(1)若|R|=∞,设a^2=ka(k≥0),①当k=0时,R的素理想只有R;②当k>0时,R的素理想共有无穷多个,它们是:{0}、R及;(2)若|R|=n>1,设a^2=ka,0≤k.3)极大理想:(1)若|R|=∞,则R有无限多个极大理想,它们是;(2)若|R|=n>1,设n的互不相同的素因数个数为ψ(n),则R共有ψ(n)个极大理想:(pa|p是n的素因数).     

金色梦想，一触即发——化学专业校外实践教学基地建设与思考

高等教育要适应世界潮流和时代变化,本科教育须进一步提高实践教学的比重,加强理论教学与实践教学相结合,完善协同育人机制。结合学科发展和企业发展需求,中山大学化学学院与金发科技股份有限公司(简称金发科技)共同建设大学生实践教学基地。本文以中山大学-金发科技本科实践教学基地为例,探讨大学生校外实践基地建设过程中遇到的问题以及实践基地的建设内容与成果体会。     

不同版本高中化学教科书中学生必做实验的分析与启示——基于“科学探究与创新意识”素养

以人教版、苏教版、鲁科版(2019年版)和沪科版(2020年版)高中化学教科书中的学生必做实验文本为研究对象,基于“科学探究与创新意识”素养构建高中化学教科书中学生必做实验文本的分析框架,分析和比较4个版本教科书中学生必做实验文本“科学探究与创新意识”素养的体现及其异同,为学生必做实验教学提供启示和建议。     

Bioinspired Design of a Giant [Mn86] Nanocage-Based Metal-Organic Framework with Specific CO2 Binding Pockets for Highly Selective CO2 Separation

Adsorption-based removal of carbon dioxide (CO₂) from gas mixtures has demonstrated great potential for solving energy security and environmental sustainability challenges. However, due to similar physicochemical properties between CO₂ and other gases as well as the co-adsorption behavior, the selectivity of CO₂ is severely limited in currently reported CO₂-selective sorbents. To address the challenge, we create a bioinspired design strategy and report a robust, microporous metal–organic framework (MOF) with unprecedented [Mn₈₆] nanocages. Attributed to the existence of unique enzyme-like confined pockets, strong coordination interactions and dipole-dipole interactions are generated for CO₂ molecules, resulting in only CO₂ molecules fitting in the pocket while other gas molecules are prohibited. Thus, this MOF can selectively remove CO₂ from various gas mixtures and show record-high selectivities of CO₂/CH₄ and CO₂/N₂ mixtures. Highly efficient CO₂/C₂H₂, CO₂/CH₄, and CO₂/N₂ separations are achieved, as verified by experimental breakthrough tests. This work paves a new avenue for the fabrication of adsorbents with high CO₂ selectivity and provides important guidance for designing highly effective adsorbents for gas separation.