An investigation of preservice teachers’ use of guess and check in solving a semi open-ended mathematics problem

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a specific heuristic strategy. The results showed that the primary strategy PTs employed in attempting to solve the triangle problem task was guess and check; however, from the PTs’ reflections, we found there existed misapplications of guess and check as a systematic problem-solving strategy. In order to prepare prospective teachers to effectively teach, teacher educators should pay more attention to the mathematical proficiency of PTs, particularly their abilities to systematically and efficiently use guess and check while solving problems and explain their solutions and reasoning to middle-school students.     

“Painlevé 34” equation: Equivalence test

We give the complete solution of the Equivalence Problem for “Painlevé 34” equation.     

Universal conditions for algebraic travelling salesman problems to be efficiently solvable

We consider Travelling Salesman Problems (TSPs) where the cost of a tour is an algebraic composition of the cost coefficients that are elements of a totally ordered, commutative semigroup. Conditions for the cost matrix are stated which allow to solve these problems in polynomial time. In particular, we investigate conditions which guarantee that an optimal tour is pyramidal and can therefore be determined in O(n ²) time. Furthermore, we discuss TSP_s with Brownian as well as those with left-upper-triangular cost matrices.     

Extreme fluxes in solar energetic particle events: Methodological and physical limitations

In this study, all available data on the largest solar proton events (SPEs), or extreme solar energetic particle (SEP) events, for the period from 1561 up to now are analyzed. Under consideration are the observational, methodological and physical problems of energy-spectrum presentation for SEP fluxes (fluences) near the Earth's orbit. Special attention is paid to the study of the distribution function for extreme fluences of SEPs by their sizes. The authors present advances in at least three aspects: 1) a form of the distribution function that was previously obtained from the data for three cycles of solar activity has been completely confirmed by the data for 41 solar cycles; 2) early estimates of extremely large fluences in the past have been critically revised, and their values were found to be overestimated; and 3) extremely large SEP fluxes are shown to obey a probabilistic distribution, so the concept of an “upper limit flux” does not carry any strict physical sense although it serves as an important empirical restriction. SEP fluxes may only be characterized by the relative probabilities of their appearance, and there is a sharp break in the spectrum in the range of large fluences (or low probabilities). It is emphasized that modern observational data and methods of investigation do not allow, for the present, the precise resolution of the problem of the spectrum break or the estimation of the maximum potentialities of solar accelerator(s). This limitation considerably restricts the extrapolation of the obtained results to the past and future for application to the epochs with different levels of solar activity.     

卤化钙钛矿太阳能电池材料理论研究进展

卤化钙钛矿由于具有低成本、高效率等特点,最近作为非常有前景的太阳能电池吸收层材料被广泛研究。卤化钙钛矿型太阳能电池效率在短短的几年间由3.8%(2009年)迅速增加到22.1%(2016年)。卤化钙钛矿型太阳能电池的出现彻底改变了太阳能电池领域,不仅因为它们快速增长的效率,而且因为它们在材料生长和结构方面的可控性。卤化钙钛矿型太阳能电池的优越性能说明卤化钙钛矿材料具有独特的物理性质。在本综述中,我们总结了卤化钙钛矿材料最近几年在结构、电学、光学方面的理论研究成果,这些都与它们在太阳能电池方面的应用密切相关。我们也将探讨一些卤化钙钛矿型太阳能电池目前遇到的挑战以及可能的理论解决途径。     

化学浴沉积方法制备硫化铟敏化太阳电池及其性能研究

硫化铟是一种稳定、低毒性的半导体材料. 本文采用低成本的化学浴沉积方法制备了硫化铟敏化太阳电池, X射线衍射(XRD)、光电子能谱(XPS)和扫描电镜(SEM)结果表明形成了硫化铟敏化的二氧化钛薄膜. 化学浴沉积温度对所得硫化铟敏化薄膜的形貌有显著的影响, 进而影响电池性能. 温度太低时, 化学浴沉积反应速率太低, 只发生少量沉积; 温度太高时, 化学浴沉积反应速率较快, 硫化铟来不及沉积到二氧化钛多孔薄膜内部. 当温度在40℃时, 硫化铟沉积均匀性最好, 薄膜的光吸收性能最佳, 电池的短路电流最大, 另外, 填充因子达到最佳, 为65%, 电池总体光电转换效率为0.32%.     

Trash GGBFS-based geopolymer as a novel sunlight-responsive photocatalyst for dye discolouration

In this study, we report a waste material-ground granulated blast furnace slag (GGBFS) as a low cost geopolymer, hybridised with ZnO to form a novel and efficient photocatalyst capable of discolouring textile wastewater. GGBFS is a waste material in an iron industry. Methylene blue was used as the probe dye and natural sunlight was used for activation of the photocatalyst. It was observed that under the experimental conditions, ZnGP-40 exhibited twice the discoloration efficiency than conventionally used ZnO or TiO₂. This enhanced performance is majorly attributed to increased surface area of ZnO when strewn in the GGBFS matrix. The photocatalysts were characterized by SEM, TEM, PSA, TGA, BET and UV–Vis/NIR. The effect of photocatalyst loading, speed of agitation and solar insolation has also been studied. Since this study has been performed in direct sunlight, it exhibits a realizable application of solar energy in the treatment of wastewater.     

Superatomic chemistry

Superatoms are atomic clusters with tailored size and composition that mimic the chemistry of atoms in the periodic table. However, unlike the atoms whose chemistry is governed by their valence electron orbitals, the chemistry of superatoms is governed by their highest occupied molecular orbitals. In addition, due to their large size and non-spherical geometry, superatoms can promote unusual reactions and serve as the building blocks of cluster assembled materials with properties very different from conventional materials. This perspective highlights the unique role of superatoms in chemical and material sciences by focusing on superhalogens, which not only possess electron affinities larger than those of halogens but also can be stable when multiply charged. We discuss how these unique features of superhalogens enable noble gas atoms like argon to form chemical bonds at room temperature and zinc to exhibit an oxidation state of +3. The advantages of using superhalogens in the synthesis of water-resistant materials for solar cells, halogen-free electrolytes for solid-state batteries, and multiferroic materials are also discussed.     

Experimental design approach for petrochemical waste water treatment using solar assisted photo Fenton process

In this study, the effect of photo-Fenton process on the treatment of petrochemical waste water treatment was investigated. The influence of process conditions were determined by factorial design. Optimization of the process conditions were performed by central composite design. Under, optimized conditions lab scale and solar assisted pilot scale of petrochemical waste water treatment was performed. Three factors namely initial pH, H₂O₂ concentration (mM) and Fe²⁺ concentration (mM) executed the essential role in petrochemical waste water treatment. Central composite design resulted in the prediction of optimized value as 6.5 initial pH, 15.65 mM of H₂O₂ concentration and 2.09 mM of Fe²⁺ concentration. Under these conditions, the reduction in chemical oxygen demand (COD) percentage reached about 68.67 ± 2.8% after 280 min in pilot scale of solar assisted photo Fenton process of petrochemical waste water treatment. Thus, experimental design combined with advanced Fenton process can become a feasible unconventional method for petrochemical waste water treatment.