A green non-acid-catalyzed process for direct N=N–C group formation: comprehensive study,modeling, and optimization

The aim of this work is to introduce, model, and optimize a new non-acid-catalyzed system for a direct N\(=\)N–C bond formation. By reacting naphthols or phenol with anilines in the presence of the sodium nitrite as nitrosonium (\(\hbox {NO}^{+})\) source and triethylammonium acetate (TEAA), a N\(=\)N–C group can be formed in non-acid media. Modeling and optimization of the reaction conditions were investigated by response surface method. Sodium nitrite, TEAA, and water were chosen as variables, and reaction yield was also monitored. Analysis of variance indicates that a second-order polynomial model with F value of 35.7, a P value of 0.0001, and regression coefficient of 0.93 is able to predict the response. Based on the model, the optimum process conditions were introduced as 2.2 mmol sodium nitrite, 2.2 mL of TEAA, and 0.5 mL \(\hbox {H}_{2}\hbox {O}\) at room temperature. A quadratic (second-order) polynomial model, by analysis of variance, was able to predict the response for a direct N=N–C group formation. Predicted response values were in good agreement with the experimental values. Electrochemistry studies were done to introduce new Michael acceptor moieties. Broad scope, high yields, short reaction time, and mild conditions are some advantages of the presented method.     

Interaction of longitudinal phonons with discrete breather in strained graphene

We numerically analyze the interaction of small-amplitude phonon waves with standing gap discrete breather (DB) in strained graphene. To make the system support gap DB, strain is applied to create a gap in the phonon spectrum. We only focus on the in-plane phonons and DB, so the issue is investigated under a quasi-one-dimensional setup. It is found that, for the longitudinal sound waves having frequencies below 6 THz, DB is transparent and thus no radiation of energy from DB takes place; whereas for those sound waves with higher frequencies within the acoustic (optical) phonon band, phonon is mainly transmitted (reflected) by DB, and concomitantly, DB radiates its energy when interacting with phonons. The latter case is supported by the fact that, the sum of the transmitted and reflected phonon energy densities is noticeably higher than that of the incident wave. Our results here may provide insight into energy transport in graphene when the spatially localized nonlinear vibration modes are presented.     

The effect of real viscosity on the heat transfer of water based Al2O3 nanofluids in a two-sided lid-driven differentially heated rectangular cavity

The heat transfer and fluid flow behavior of water based Al₂O₃ nanofluids are numerically investigated inside a two-sided lid-driven differentially heated rectangular cavity. Physical properties which have major effects on the heat transfer of nanofluids such as viscosity and thermal conductivity are experimentally investigated and correlated and subsequently used as input data in the numerical simulation. Transport equations are numerically solved with finite volume approach using SIMPLEC algorithm. It was found that not only the thermal conductivity but also the viscosity of nanofluids has a key role in the heat transfer of nanofluids. The results show that at low Reynolds number, increasing the volume fraction of nanoparticles increases the viscosity and has a deteriorating effect on the heat transfer of nanofluids. At high Reynolds number, the increase in the viscosity is compensated by force convection and the increase in the volume fraction of nanoparticles which results in an increase in heat transfer is in coincidence with experimental results.     

Numerical solution of the Klein–Gordon equation via He’s variational iteration method

In this paper, we present the solution of the Klein--Gordon equation. Klein--Gordon equation is the relativistic version of the Schrödinger equation, which is used to describe spinless particles. The He’s variational iteration method (VIM) is implemented to give approximate and analytical solutions for this equation. The variational iteration method is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. Application of variational iteration technique to this problem shows rapid convergence of the sequence constructed by this method to the exact solution. Moreover, this technique reduces the volume of calculations by avoiding discretization of the variables, linearization or small perturbations.     

Highly Efficient,Four Component,One-pot Synthesis of Tetrasubstituted Imidazoles Using a Catalytic Amount of FeCl<Subscript>3</Subscript> · 6H<Subscript>2</Subscript>O

Summary. An efficient and improved procedure for the synthesis of tetrasubstituted imidazoles by FeCl₃ · 6H₂O catalyzed four-component one-pot synthesis in refluxing ethanol is described.     

Stereoselective Hydrolysis of Substituted Cyclopropanedicarboxylates with Pig Liver Esterase

The hydrolysis of the meso-cyclopropane-1,2-dicarboxylates 1a - 3a , 4 , 5a , 6a , and 9 , containing various substituents at C(3), and of the rac-3-phenylcyclopropane-1,2-dicarboxylates 7a , 8a , and 10 with pig liver esterase (PLE) is described. The stereoselectivtty and absolute configurations of the products were determined. An interpretation of results was attempted on the basis of a recent active-site model for PLE.     

Supported Preyssler Nanoparticles in Synthesis of 1,3‐Diaryl‐5‐Spirohexahydropyrimidines

Silica‐supported Preyssler nanoparticles (H₁₄[NaP₅W₃₀O₁₁₀])/SiO₂ are used as a new and recyclable catalyst for the preparation of 1,3‐diaryl‐5‐spirohexahydropyrimidines via a one‐pot condensation of anilines, formaldehyde, and cyclohexanone.     

Students’ ways of understanding a proof

We present a model for describing the growth of students’ understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important transitions in this path. The other path focuses on the surface-level form of the proof, and the use of symbolic representations. At the end of this path, students understand how and why symbolic computations formally establish a claim, at a syntactic level. We make distinctions between states in the model and illustrate them with examples from early secondary students’ mathematical activity. We then apply the model to one student’s developing understanding in order to show how the model works in practice. We close with some suggestions for further research.     

Reductive amination of aldehydes and ketones to their corresponding amines with N-methylpyrrolidine zinc borohydride

A simple and convenient procedure for reductive amination of aldehydes and ketones using N-methylpyrrolidine zinc borohydride (ZBHNMP) as a reducing agent is described. The reactions are carried out with 1 equiv of amine and 1 equiv of aldehyde or ketone using 1 equiv of ZBHNMP in methanol under neutral conditions at room temperature.