Degradation of azithromycin using Ti/RuO<Subscript>2</Subscript> anode as catalyst followed by DPV,HPLC–UV and MS analysis

The electrodegradation of azithromycin was studied by its indirect oxidation using dimensionally stable Ti/RuO₂ anode as catalyst in the electrolyte containing methanol, 0.05 M NaHCO₃, sodium chloride and deionized water. The optimal conditions for galvanostatic electrodegradation for the azithromycin concentration of 0.472 mg cm^?3 were found to be NaCl concentration of 7 mg cm^?3 and the applied current of 300 mA. The differential pulse voltammetry using glassy carbon electrode was performed for the first time in the above-mentioned content of electrolyte for the nine concentration of azithromycin (0.075–0.675 mg cm^?3) giving the limits of azithromycin detection and of quantification as: LOD 0.044 mg cm^?3 and LOQ 0.145 mg cm^?3. The calibration curve was constructed enabling the electrolyte analysis during its electrodegradation process. The electrolyte was analyzed by high-performance liquid chromatography and electrospray ionization time-of-flight mass spectrometry. The electrooxidation products were identified and after 180 min there was no azithromycin in the electrolyte while TOC analysis showed that 79% of azithromycin was mineralized. The proposed degradation scheme is presented.     

Thickness difference induced pore structure variations in cellulosic separators for lithium-ion batteries

The pore structure of the separator is crucial to the performance of a lithium-battery as it affects the cell resistance. Herein, a straightforward approach to vary the pore structure of Cladophora cellulose (CC) separators is presented. It is demonstrated that the pore size and porosity of the CC separator can be increased merely by decreasing the thickness of the CC separator by using less CC in the manufacturing of the separator. As the pore size and porosity of the CC separator are increased, the mass transport through the separator is increased which decreases the electrolyte resistance in the pores of the separator. This enhances the battery performance, particularly at higher cycling rates, as is demonstrated for LiFePO₄/Li half-cells. A specific capacity of around 100 mAh g^?1 was hence obtained at a cycling rate of 2 C with a 10 µm thick CC separator while specific capacities of 40 and close to 0 mAh g^?1 were obtained for separators with thicknesses of 20 and 40 µm, respectively. As the results also showed that a higher ionic conductivity was obtained for the 10 µm thick CC separator than for the 20 and 40 µm thick CC separators, it is clear that the different pore structure of the separators was an important factor affecting the battery performance in addition to the separator thickness. The present straightforward, yet efficient, strategy for altering the pore structure hence holds significant promise for the manufacturing of separators with improved performance, as well as for fundamental studies of the influence of the properties of the separator on the performance of lithium-ion cells.     

A High‐Quality Professional Development for Teachers of Grades 3–6 for Implementing Engineering into Classrooms

With the increasing emphasis on integrating engineering into K‐12 classrooms to help meet the needs of our complex and multidisciplinary society, there is an urgent need to investigate teachers' engineering‐focused professional development experiences as they relate to teacher learning, implementation, and student achievement. This study addresses this need by examining the effects of a professional development program focused on engineering integration, and how teachers chose to implement engineering in their classrooms as a result of the professional development. 198 teachers in grades 3–6 from 43 schools in 17 districts participated in a yearlong professional development program designed to help integrate the new state science standards, with a focus on engineering, into their teaching. Posters including lesson plans and student artifacts were used to assess teachers' engineering practices and the implementation in their classrooms. Results indicated that the majority of the teachers who participated in the professional development were able to effectively implement engineering design lessons in their classrooms suggesting that the teachers' success in implementing engineering lessons in their classroom was closely related to the structure of the professional development program.     

Clique-cutsets beyond chordal graphs

Truemper configurations (thetas, pyramids, prisms, and wheels) have played an important role in the study of complex hereditary graph classes (eg, the class of perfect graphs and the class of even-hole-free graphs), appearing both as excluded configurations, and as configurations around which graphs can be decomposed. In this paper, we study the structure of graphs that contain (as induced subgraphs) no Truemper configurations other than (possibly) universal wheels and twin wheels. We also study several subclasses of this class. We use our structural results to analyze the complexity of the recognition, maximum weight clique, maximum weight stable set, and optimal vertex coloring problems for these classes. Furthermore, we obtain polynomial -bounding functions for these classes.     

Limits of Functions as They Developed Through Time and as Students Learn Them Today

This article compares first-year university students' development of the concept of limits to mathematicians' historical development of the concept. The aim was to find out if students perceive the notion as mathematicians of the past did, as understandings of the concept evolved. The results imply that there are some similarities—for example, the struggle with rigor and attainability. Knowledge of such critical areas can be used to improve students' opportunities of learning limits of functions. Some teaching aspects related to the study are also discussed.     

Cross-diffusion induced instability and stability in reaction-diffusion systems

In a reaction-diffusion system, diffusion can induce the instability of a uniform equilibrium&nbsp; which is stable with respect to a constant perturbation, as shown by Turing in 1950s. We show that cross-diffusion can destabilize&nbsp; a uniform equilibrium&nbsp; which is stable for the kinetic and self-diffusion reaction systems; on the other hand, cross-diffusion can also stabilize&nbsp; a uniform equilibrium which is stable for the kinetic system but unstable for the self-diffusion reaction system. Application is given to predator-prey system with preytaxis and vegetation pattern formation in a water-limited ecosystem.     

Mathematics achievement and interest in mathematics from a differential perspective

In this article, we present results of an empirical study with 500 German students of grades 7 and 8. The study focussed on students' mathematics achievement and their interest in mathematics as well as on the relation between these two constructs. In particular, the results show that the development of an individual student's achievement between grade 7 and grade 8 depends on the achievement level of the specific classroom and therefore on the specific mathematics instruction Interest in mathematics could be regarded a predictor for mathematics achievement Moreover, our findings suggest that the students show hardly any fear of mathematics independent of their achievement level.     

Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation

We apply the method of homotopy analysis to the Zakharov system with dissipation in order to obtain analytical solutions, treating the auxiliary linear operator as a time evolution operator. Evolving the approximate solutions in time, we construct approximate solutions which depend on the convergence control parameters. In the situation where solutions are strongly coupled, there will be multiple convergence control parameters. In such cases, we will pick the convergence control parameters to minimize a sum of squared residual errors. We explain the error minimization process in detail, and then demonstrate the method explicitly on several examples of the Zakharov system held subject to specific initial data. With this, we are able to efficiently obtain approximate analytical solutions to the Zakharov system of minimal residual error using approximations with relatively few terms.     

Pricing of Claims in Discrete Time with Partial Information

We consider the pricing problem of a seller with delayed price information. By using Lagrange duality, a dual problem is derived, and it is proved that there is no duality gap. This gives a characterization of the seller’s price of a contingent claim. Finally, we analyze the dual problem, and compare the prices offered by two sellers with delayed and full information respectively.