《实变函数与泛函分析》课程改革——一维化方法和测度论,可测函数和积分论学习路径

本文探讨了《实变函数与泛函分析》课程内容改革,一是采用一维化方法从一维实数空间的测度论开始学习,二是采用测度的可数可加性圯叶戈洛夫定理圯有界收敛定理的学习路径学习测度论,可测函数和积分论的性质。此教学方案突出课程核心内容,减轻了课程难度,适合数学类和相关专业学生学习。

One-Dimensional ZnO Nanostructures： Solution Growth and Functional Properties

One-dimensional （1D） ZnO nanostructures have been studied intensively and extensively over the last decade not only for their remarkable chemical and physical properties, but also for their diverse current and future technological applications. This article gives a comprehensive overview of the progress that has been made within the context of 1D ZnO nanostructures synthesized via wet chemical methods. We will cover the synthetic methodologies and the corresponding growth mechanisms, various nanostructures grown, their doping and alloying, and position-controlled growth on substrates. Finally, we will review their functional properties in catalysis, hydrophobic surface modification, sensing, and electronic, optical, optoelectronic, and energy harvesting devices.

One-dimensional iron oxides nanostructures

Iron oxides, including α-Fe2O3, γ-Fe2O3, Fe3O4, etc. are one of the most widely investigated materials for their fundamental properties and potential applications. One-dimensional （1-D） iron oxides nanostructures are the focus of recent research activi- ties because of their wide applications in magnetic refrigeration, information storage, electronics, catalysts, Li-ion battery, pigment, gas sensors, etc. This review covers the recent progress in the synthesis, properties and applications of 1-D iron oxides nanostructures. The paper begins with the introduction to 1-D iron oxides nanostructures, followed by the typical synthetic methods developed for the synthesis of 1-D iron oxides nanostructures. Then, the typical 1-D iron oxides nanostructures, in- cluding nanowires/nanorods, nanotubes, nanobelts, nanochalns, and special 3-D structures built on 1-D building blocks, are introduced in detail. The properties of 1-D iron oxides nanostructures are then discussed, focusing on the magnetic, gas sensing, and electrochemical and photocatalytic properties. Finally, we draw conclusions and look at the prospects of 1-D iron oxides nanostructures.

Multi-band design for one-dimensional phononic crystals

Periodic composites with band gaps that prevent the propagation of elastic waves in certain frequency ranges can be used to control waves for a variety of engineering applications. Although studies on the characteristics of these materials, which are called phononic crystals (PCs), have yielded a large number of positive results in recent years, there is still a lack of effective design methods. In this work, a multi-objective optimization approach based on the band gap mechanism and an intelligent algorithm is used to design a one-dimensional (1D) slab construction of PCs. The design aims to fit pre-determined bands by arranging the available materials properly. Obtained by analyzing the wave transmission in periodic layers, the objective functions are linked to the optimization program to obtain a proper solution set. The results of the numerical simulations demonstrate that without constructing complicated structures, the design method is able to produce PCs that overcome the limitations of two-component PCs and hence can feasibly and effectively achieve the design targets. The design approach presented in this paper can be extended to two-or three-dimensional systems and has great potential for the development of sound/ultrasound isolation structures, multiple band frequency filters, and other applications.