线性模型中广义最小二乘参数估计误差分布的稳健性研究

研究了线性模型中广义最小二乘参数估计的误差分布稳健性问题.首先讨论了在线性统计模型里,设计矩阵为列降秩矩阵时,模型中给出了误差最大分布类,当误差向量的分布在此范围内变动时,LS估计和GLS估计在均方误差矩阵准则下是最优估计.然后进一步探讨广义最小二乘估计GLSE关于误差分布的稳健性,求出误差项所对应的最大分布族,进而证明了在该区间波动情况下,误差向量对应的始终为一致最优解.     

Difference operators for partitions under the Littlewood decomposition

Let n be a positive integer. Let \(\delta _3(n)\) denote the difference between the number of (positive) divisors of n congruent to 1 modulo 3 and the number of those congruent to 2 modulo 3. In 2004, Farkas proved that the arithmetic convolution sum

$$\begin{aligned} D_3(n):=\sum _{j=1}^{n-1}\delta _3(j)\delta _3(n-j) \end{aligned}$$

satisfies the relation

$$\begin{aligned} 3D_3(n)+\delta _3(n)={\sum _{\mathop {_{d \mid n}}\limits _{3 \not \mid d}}}d. \end{aligned}$$

In this paper, we use a result about binary quadratic forms to prove a general arithmetic convolution identity which contains Farkas’ formula and two other similar known formulas as special cases. From our identity, we deduce a number of analogous new convolution formulas.

     

Sustainable Route for Synthesizing Aluminosilicate EU-1 Zeolite

Developing sustainable routes for the synthesis of zeolites is still a vital and challenging task in zeolite scientific community. One of the typical examples is sustainable synthesis of aluminosilicate EU-1 zeolite, which is not very efficient and environmental-unfriendly under hydrothermal condition due to the use of a large amount of water as solvent. Herein, we report a sustainable synthesis route for aluminosilicate EU-1 zeolite without the use of solvent for the first time. The physicochemical properties of the obtained EU-1 zeolite are characterized by powder X-ray diffraction (XRD), scanning electron microscopy (SEM), thermogravimetry-differential thermal analysis (TG-DTA), N₂ sorption, inductively coupled plasma (ICP) analysis, and solid nuclear magnetic resonance (NMR), which show the product has high crystallinity, uniform morphology, large BET surface area, and four-coordinated aluminum species. Moreover, the impact of synthesis conditions is investigated in detail. The sustainable synthesis of aluminosilicate EU-1 zeolite under solvent-free     

Ultrafast synthesis of near-infrared-emitting aqueous CdTe/CdS quantum dots with high fluorescence

The traditional aqueous route to synthesis CdTe/CdS Core/shell (c/s) quantum dots (QDs) via decomposition of Cd-thiol complexes is usually time consuming. Herein, an ultrafast and facile aqueous synthetic approach under atmospheric pressure for CdTe/CdS c/s QDs with emission from the green to the near-infrared window (535–820 nm) is reported. With purified CdTe core QDs diluted in solution of Cd-3-mercaptopropionic acid (MPA) complexes, CdTe/CdS c/s QDs with emission wavelengths at 700 and 800 nm can be obtained within 20- and 45-min refluxing under the optimized experimental conditions, respectively. This is the most rapid way to prepare CdTe/CdS c/s QDs in aqueous phase, and the obtained QDs were highly luminescent without postsynthesis treatment. The influences of various experimental factors, including Cd²⁺ concentration, MPA-to-Cd ratio, pH value, and dilution ratio on the growth rate and luminescent properties of the obtained CdTe/CdS c/s QDs, have been taken into consideration. The three processes “purification-dilution-addition” ensure the synthesis environment with high pH value and low core concentration and have a marked impact on the rapid synthesis rate and the resulting high fluorescence of CdTe/CdS c/s QDs.     

Selection of hydrogel electrolytes for flexible zinc–air batteries

Flexible zinc–air batteries attract more attention due to their high energy density, safety, environmental protection, and low cost. However, the traditional aqueous electrolyte has the disadvantages of leakage and water evaporation, which cannot meet application demand of flexible zinc–air batteries. Hydrogels possessing good conductivity and mechanical properties become a candidate as the electrolytes of flexible zinc–air batteries. In this work, advances in aspects of conductivity, mechanical toughness, environmental adaptability, and interfacial compatibility of hydrogel electrolytes for flexible zinc–air batteries are investigated. First, the additives to improve conductivity of hydrogel electrolytes are summarized. Second, the measures to enhance the mechanical properties of hydrogels are taken by way of structure optimization and composition modification. Third, the environmental adaptability of hydrogel electrolytes is listed in terms of temperature, humidity, and air composition. Fourth, the compatibility of electrolyte–electrode interface is discussed from physical properties of hydrogels. Finally, the prospect for development and application of hydrogels is put forward.     

Foam/Film Alternating Multilayer Structure with High Toughness and Low Thermal Conductivity Prepared via Microlayer Coextrusion

Multilayer membranes prepared via microlayer coextrusion have attracted wide attention due to their unique properties and broad applications. In present study, the foam/film alternating multilayer sheets based on ethylene-vinyl acetate copolymer(EVA) and high-density polyethylene are successfully prepared via microlayer coextrusion. The cells in the sheets are single-cell-array along the foamed EVA layers with uniform cell size. In addition, the effects of layer number and foam relative thickness on morphology, mechanical properties, damping and heat insulation properties are investigated. The cell size decreases significantly with increasing layer number due to the enhanced confine effects. The tensile strength, elongation at break, and heat insulation also increase significantly. However, the mechanical damping properties change little in the observed frequency. Meanwhile, with higher relative thickness of EVA foam, the sheets have lower tensile strength and lower thermal conductivity, while the damping properties are enhanced in a specific frequency scope. The elongation at break of the optimized sample comes to 800% and the thermal conductivity decreases to 61 mW·m~(-1)·K~(-1), which shows high toughness and low thermal conductivity, indicating a possible method for preparing materials with high toughness and heat-insulating properties.     

酰胺连接的共价有机骨架的制备及其在水中高效光催化性能

光催化是将太阳能转换为化学能的绿色可持续发展途径,有望解决日益严重的能源危机和环境污染问题.在光催化过程中,半导体材料作为光催化剂,负责可见光的捕获、光生载流子的生成和传输以及氧化还原反应,在整个光催化系统中起着决定性的作用.共价有机骨架材料(COFs)是一类新兴的半导体光催化剂,已被证明在可见光诱导的水分解、二氧化碳还原、有机转化反应和水中污染物降解方面具有应用前景.然而,大部分COFs是通过可逆反应构筑的,在水中及苛刻条件下的稳定性差.因此,提升基于COFs的光催化剂在水相中的光催化活性和循环稳定性仍然面临巨大挑战.本文提出了一种新策略,即通过实现多重协同效应,设计和开发2D-COFs作为在水中的高效非均相光催化剂.通过后合成策略将亚胺键连接的2D-COFs氧化,制备了两种具有丰富三嗪结构单元的以酰胺键连接的2D-COFs(命名为COF-JLU18和COF-JLU19).结果表明,COF-JLU18和COF-JLU19具有高比表面积和孔体积,其比表面积分别为1156和541 m2/g;COF-JLU19具有比相似拓扑结构的亚胺COF-JLU17更好的水蒸气吸附性能.此外,COF-JLU19表现出了极高的化学稳定性,在水中、盐酸和氢氧化钠溶液中浸泡两天,其结构和结晶性均没有发生明显变化.由此可见,酰胺键不仅可以增加材料骨架的亲水性,还能够提高COFs对水的稳定性.本文制备的酰胺键连接的COF-JLU19材料,在光降解罗丹明B水溶液(RhB)反应中可以获得高达0.69 min?1的光降解速率常数,活性明显优于其他光催化剂,如C3N4等.COF-JLU19具有较好的催化活性主要归因于以下两方面:一方面,良好的亲水性和固有孔隙率之间的协同效应可以增强COFs在水中对染料的吸附能力,使其光催化活性得到有效提升;另一方面,高的结晶度和优秀的稳定性使酰胺键连接的COFs在多相光催化中实现稳定循环利用.为了扩展COFs的应用前景,本文还制备了一种基于酰胺键连接COFs的静电纺丝膜,在以太阳光为光源的光降解罗丹明B水溶液实验中表现出较高的光催化活性和重复使用性.综上,本文提出的多重协同效应为基于COFs的高效光催化剂的设计提供了一种有效策略.     

空心NiCo2S4纳米球助催化剂担载ZnIn2S4纳米片用于可见光催化制氢

纳米片与空心球上之间的合理界面调控是开发高效太阳能制氢光催化剂的潜在策略。在各类光催化材料中,金属硫化物由于具有相对较窄的带隙和优越的可见光响应能力而被广泛研究。ZnIn₂S₄是一种层状的三元过渡金属半导体光催化剂,其带隙可控(约2.4 eV)。在众多金属硫化物光催化剂中,ZnIn₂S₄引起了广泛兴趣。然而,单纯的ZnIn₂S₄光催化活性仍然相对较差,主要是因为光生载流子的复合率较高、迁移速率较慢。在半导体光催化剂上负载助催化剂是提升光催化剂性能的一种有效方法,因为它不仅可以加速光生电子和空穴的分离,而且还可以降低质子还原反应的活化能。作为一种三元过渡金属硫化物,NiCo₂S₄表现出较高的导电性、较低的电负性、丰富的氧化还原特性以及优越的电催化活性。这些特性表明,NiCo₂S₄可以作为光催化制氢的助催化剂,以加速电荷分离和转移。此外,NiCo₂S₄和ZnIn₂S₄都属于三元尖晶石的晶体结构,这可能有助于构建具有紧密界面接触的NiCo₂S₄/ZnIn₂S₄复合物,从而提高光催化性能。本文中,将超薄ZnIn₂S₄纳米片原位生长到非贵金属助催化剂NiCo₂S₄空心球上,形成具有强耦合界面和可见光吸收的NiCo₂S₄@ZnIn₂S₄分级空心异质结构光催化剂。最优NiCo₂S₄@ZnIn₂S₄复合样品(NiCo₂S₄含量：ca. 3.1%)的析氢速率高达78 μmol·h^-1,约是纳米片组装ZnIn₂S₄光催化剂析氢速率的9倍、约是1% (w, 质量分数)Pt/ZnIn₂S₄样品析氢速率的3倍。此外,该复合光催化剂在反应中表现出良好的稳定性。荧光和电化学测试结果表明,NiCo₂S₄空心球是一种有效的助催化剂,可促进光生载流子的分离和传输,并降低析氢反应的活化能。最后,提出了NiCo₂S₄@ZnIn₂S₄光催化析氢的可能反应机理。在NiCo₂S₄@ZnIn₂S₄复合光催化剂中,具有高导电性的NiCo₂S₄助催化剂可快速接受ZnIn₂S₄上的光生电子,用以还原质子生成氢气,而电子牺牲剂TEOA捕获光生空穴,进而完成光催化氧化还原循环。该研究有望为基于纳米片为次级结构的分级空心异质结光催化剂的设计合成及其光催化制氢研究提供一定的指导。     

电容去离子除氯电极的构建及其脱盐性能研究进展

电容去离子技术(Capacitive deionization,CDI)是一种新兴的脱盐技术,通过在电极两端施加较低的外加电场除去水中的带电离子和分子,由于其较低的能耗和可持续性而备受关注。基于储能电池领域近年来的迅猛发展,CDI电极材料实现了从以双电层作用机理为代表的碳材料到法拉第电极材料的跨越,使得脱盐性能有了大幅度提升。Na⁺的去除与Cl^-的去除同等重要,然而,CDI中针对氯离子高效去除的电极材料研究关注较少。本文从CDI装置的构型演变发展出发,系统地归纳与梳理了CDI中关于脱氯电极材料的分类,对比了不同类型脱氯电极材料的特点,并总结了Cl^-去除的机理,分别为基于双电层的电吸附、转化反应、离子插层和氧化还原反应。本文是首篇关于CDI阳极材料的进展综述和展望,为CDI除氯电极的后续研究提供理论基础和研究思路。     

关于刚体角速度定义的一个注解

给出了一种角速度定义方法. 这种方法基于固连坐标系基矢量和单位矢量的导数给出，但避免使用角速度矩阵概念. 另外从刚体上速度分布的角度，用速度场旋度的方法解释角速度. 可以帮助学生从另外一个角度来理解角速度概念.