Rare-earth-doped bifunctional alkaline-earth metal fluoride nanocrystals via a facile microwave-assisted process

Rare-earth-doped magnetic-optic bifunctional alkaline-earth metal fluoride nanocrystals have been successfully synthesized via a facile microwave-assisted process. The as-prepared nanocrystals were monodisperse and could form stable colloidal solutions in polar solvents, such as water and ethanol. They show bright-green fluorescence emisson. Furthermore, Gd(3+)-doped ones exhibit paramagnetic behavior at room temperature and superparamagnetic behavior at 2 K.     

用传统光学薄膜技术改进菲涅耳波带板

利用二元光学理论改进菲涅耳波带板, 能大幅度提高衍射效率.本文介绍利用传统的照相复制和真空镀膜技术制作位相型菲涅耳波带板的方法, 指出了膜料选择和膜厚控制的依据, 实测了位相台阶数为2时的衍射效率, 为通常菲涅耳波带板的近4 倍.     

1H NMR spectral studies on the polymerization mechanism of indole and its derivatives

The existence of NH bond according to the hydrogen nuclear magnetic resonance ((1)H NMR) spectra of polyindole and its derivatives, such as poly(5-bromoindole), poly(5-cyanoindole), poly(5-nitroindole), poly(5-methylindole), proved polymerization of high-quality polyindoles, which were electrosynthesized from middle strong Lewis acid boron trifluoride diethyl etherate (BFEE) and its mixed electrolytes with additional diethyl ether, occurred at 2,3-position. The elongation of the conjugation length made the chemical shift of all the protons of polyindoles to lower field in comparison with those of monomers.     

How is cultural influence manifested in the formation of mathematics textbooks? A comparative case study of resource book series between Shanghai and England

Focusing on issues about the development of mathematics textbooks from a cultural perspective, this study examined a widely-used curriculum resource series, One Lesson One Exercise, published in China, and its adapted English series, published in the UK, to explore how cultural influence is manifested in the two series of resource books. For the study we established a conceptual framework classifying culture into six types in relation to people’s beliefs, values and ways of interacting about them, for data collection and analysis. The results indicate that there exist considerable differences between the Chinese and the English series that are related to cultural factors. It appears that, to a large extent, culture plays an essential role in the development of mathematics textbooks. Concerning the different types of culture, the results show that most adaptations between the Chinese series and the English series are related to ‘ways of behaving and customs’ and ‘artifacts, flora and fauna’, followed by ‘identities’ and ‘geography’, and the least are related to ‘organisations’ and ‘history’. Based on the study, we argue that the relevance and importance of culture to the development of mathematics textbooks must not be underestimated, and more research in this direction is needed.     

Band-limited refinable functions for wavelets and framelets

Extending band-limited constructions of orthonormal refinable functions, a special class of periodic functions is used to generate a family of band-limited refinable functions. Characterizations of Riesz bases and frames formed by integer shifts of these refinable functions are obtained. Such families of refinable functions are employed to construct band-limited biorthogonal wavelet bases and biframes with desirable time-frequency localization.     

金属无润滑磨损过程的原位观察与研究

作者借助于新研制的可以直接观察磨损动态过程的试验装置和扫描电镜原位观察了无润滑条件下金属滑动表面的磨损特征与变化,发现摩擦表面可以划分为真实接触区和过渡磨损区,两者的磨损机理不同,真实接触区发生的是粘着磨损,而且磨粒沿摩擦力方向有明显增大的趋势;随着真实接触区的磨损,过渡磨损区可以逐渐转变为真实接触区,而且由于磨粒增多,非磨损区也可以逐渐转变为过渡磨损区。对磨损过程中摩擦力变化的测试结果表明,当磨损表面发生粘着时的粘着力与Bowden和Tabor粘着理论计算值十分接近。     

Canonical Basis for Quantum {\mathfrak{osp}(1|2)}

We introduce a modified quantum enveloping algebra as well as a (modified) covering quantum algebra for the ortho-symplectic Lie superalgebra ${\mathfrak{osp}(1|2)}$ . Then we formulate and compute the corresponding canonical bases, and relate them to the counterpart for ${\mathfrak{sl}(2)}$ . This provides a first example of canonical basis for quantum superalgebras.     

Sustainable synthesis of quinolines (pyridines) catalyzed by a cheap metal Mn(I)-NN complex catalyst

This study represents the first example of a bidentate phosphine-free manganese(I)-NN complex catalyst for the synthesis of quinolines (pyridines) through acceptorless dehydrogenative condensation of various secondary alcohols with amino alcohols. The coupling reactions occurred at 3 mol% catalyst loading and 110°C, and tolerated diverse functional groups. Moderate to excellent yields ranging from 45% to 89% were achieved after 12 hr of reaction. The present protocol provides a concise and environmentally friendly method for the construction of heterocyclic compounds.     

The effect of behavior of wearing masks on epidemic dynamics

Nonlinear Dynamics - Recently, COVID-19 has attracted a lot of attention of researchers from different fields. Wearing masks is a frequently adopted precautionary measure. In this paper, we...     

An efficient synthesis of 9-anthrone lactone derivatives via the Knoevenagel condensation and intramolecular cyclization

One-step synthesis of 9-anthrone lactone derivatives from 1-acetyloxyanthraquinone with a variety of dicarbonyl substrates in the presence of K₂CO₃ by Knovenagel condensation and intramolecular cyclization is developed. Possible reaction mechanisms have been investigated using the density functional theory (DFT), which has been widely used in the study of reaction mechanism. The strategy could be useful for the synthesis of the core structure of marine natural product aspergiolide.