On the compatibility between vapor pressure data and the critical constants: Use of the van der Waals family of cubic equations of state to study the cases of 2-methoxyethanol and 2-ethoxyethanol

The performance of five cubic equations of state (EOSs) for the correlation of vapor-pressure data of 2-methoxyethanol and 2-ethoxyethanol are compared. The cubic EOSs considered are the van der Waals EOS, modified with Soave's approach (MvdW), the Soave-Redlich-Kwong (SRK), the Peng-Robinson (PR), and the two versions of the Peng-Robinson-Stryjek-Vera EOSs: PRSV and PRSV2. Three sets of critical constants for 2-methoxyethanol are considered and new acentric factor is proposed for this compound. New critical constants and acentric factor for 2-ethoxyethanol are proposed. Pure compound parameters for the PRSV and the PRSV2 EOSs for 2-methoxyethanol and 2-ethoxyethanol are evaluated using a genetic algorithm (GA) optimization technique. The results show the importance of using compatible information in vapor liquid equilibrium studies.     

Some model theory of fibrations and algebraic reductions

Let \(p= \mathrm{tp }(a/A)\) be a stationary finite rank type in an arbitrary stable theory and \({\mathbb {P}}\) an \(A\) -invariant family of partial types. The following property is introduced and characterised: whenever \(c\) is definable over \((A,a)\) and \(a\) is not algebraic over \((A,c)\) , then \(\mathrm{tp }(c/A)\) is almost internal to \({\mathbb {P}}\) . The characterisation involves among other things an apparently new notion of “descent” for stationary types. Motivation comes partly from results in Sect. 2 of (Campana et al. in J Differ Geom 85(3):397–424, 2010) where structural properties of generalised hyperkähler manifolds are given. The model-theoretic results obtained here are applied back to the complex-analytic setting to prove that the algebraic reduction of a nonalgebraic (generalised) hyperkähler manifold does not descend. The results are also applied to the theory of differentially closed fields, where examples coming from differential-algebraic groups are given.     

Best proximity points: global minimization of multivalued non-self mappings

In this article, we give a best proximity point theorem for generalized contractions in metric spaces with appropriate geometric property. We also, give an example which ensures that our result cannot be obtained from a similar result due to Amini-Harandi (Best proximity points for proximal generalized contractions in metric spaces. Optim Lett, 2012). Moreover, we prove a best proximity point theorem for multivalued non-self mappings which generalizes the Mizoguchi and Takahashi’s fixed point theorem for multivalued mappings.     

A novel nanomagnetic solid acid catalyst for the synthesis of new functionalized bis-coumarin derivatives under microwave irradiations in green conditions

In this study, a novel, green, environmentally friendly and magnetically heterogeneous catalyst based on the immobilization of sulfosalicylic acid onto Fe₃O₄ nanoparticles (Fe₃O₄@sulfosalicylic acid MNPs) is reported. The bis-coumarin analogs were synthesized in high yield using the reaction of 1 equivalent of aryl aldehydes with 2 equivalents of 4-hydroxycoumarin in water under microwave irradiation conditions. Scanning electron microscopy, transmission electron microscopy, energy-dispersive X-ray spectroscopy, X-ray diffraction, thermogravimetric analysis, dynamic light scattering, vibrating sample magnetometry, Fourier transform infrared spectroscopy, UV–visible absorption, and Brunauer-Emmett-Teller (BET) techniques confirmed the successful synthesis of the catalyst. The main attractive characteristics of the presented green protocol are very short reaction times (10–15 min), excellent yields, and the avoidance of hazardous or toxic reagent and solvents. Thermal durability, easy separation, and high reusability are important advantages of the new catalyst in comparison to other catalysts.     

Kinetic study of in situ normal and AGET atom transfer radical copolymerization of n–butyl acrylate and styrene: Effect of nanoclay loading and catalyst concentration

The effect of clay nanolayers and catalyst concentration on the kinetics of atom transfer radical copolymerization of styrene and butyl acrylate initiated by activators generated by electron transfer (AGET initiation system) or an alkyl halide (normal initiation system) was studied. Monomer conversion was studied by attenuated total reflection–Fourier transform infrared spectroscopy, and also proton nuclear magnetic resonance (¹H NMR) spectroscopy was utilized to evaluate the heterogeneity in the composition of poly(styrene‐co‐butyl acrylate) chains. A decrease in the copolymerization rate of styrene and butyl acrylate in the presence of clay platelets was observed since clay layers confine the accessibility of monomer and growing radical chains. Considering the linear first‐order kinetics of the polymerization, successful AGET and normal atom transfer radical polymerization (ATRP) in the presence of clay nanolayers were carried out. Consequently, poly(styrene‐co‐butyl acrylate) chains with narrow molecular weight distribution and low polydispersity indices (1.13–1.15) were obtained. The linearity of ln([M]₀/[M]) versus time and molecular weight distribution against conversion plots indicates that the proportion of propagating radicals is almost constant during the polymerization, which is the result of insignificant contribution of termination and transfer reactions. Controlled synthesis of poly(styrene‐co‐butyl acrylate)/clay is implemented with the diminishing catalyst concentration of copper(I) bromide/N,N,N′,N′′,N′′‐pentamethyl diethylene triamine without affecting the copolymerization rate of normal ATRP. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 44: 789–799, 2012     

Investigation of third-grade non-Newtonian blood flow in arteries under periodic body acceleration using multi-step differential transformation method

In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the thirdgrade non-Newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient. The hybrid multi-step differential transformation method (Hybrid-MsDTM) and the Crank-Nicholson method (CNM) are used to solve the partial differential equation (PDE), and a good agreement between them is observed in the results. The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered. The results show that increasing the amplitude, A_g, and reducing the lead angle of body acceleration, φ, make higher velocity profiles on the center line of both arteries. Also, the maximum wall shear stress increases when A_g increases.     

The converse of the Loewner–Heinz inequality via perspective

The Loewner–Heinz inequality is not only the most essential one in operator theory, but also a fundamental tool for treating operator inequalities. The aim of this paper is to investigate the converse of the Loewner–Heinz inequality in the view point of perspective and generalized perspective of operator monotone and multiplicative functions. Indeed, we give perspective inequalities equivalent to the Loewner–Heinz inequality.     

Pillar[5]arene‐Stabilized Silver Nanoclusters: Extraordinary Stability and Luminescence Enhancement Induced by Host–Guest Interactions

Herein, we report the synthesis of a new class of functional silver nanoclusters (AgNCs) capped with pillar[5]arene (P5)‐based host ligands. These NCs are readily prepared through direct synthesis or ligand exchange synthesis and are stable at room temperature for over 4 months. The pillar[5]arene‐stabilized NCs (Ag₂₉(LA‐P5)₁₂(TPP)₂) endorse reversible host–guest interactions with neutral alkylamines and cationic quaternary ammonium guests. This results in the formation of spherical assemblies with unparalleled changes in their optical properties including an astonishing circa 2000‐fold luminescence enhancement. This is the highest luminescence enhancement ratio reported so far for such atomically precise NCs. Our synthetic protocol paves the way for the preparation of a new generation of metal nanoclusters protected by macrocyclic ligands with molecular recognition and selectivity toward specific guests.     

A heuristic method to simulate the pulse propagation in nonlinear fiber bragg gratings

In this paper we simulated the pulse propagation and the switching effects in nonlinear fiber Bragg gratings using a combination of Fourier series analysis technique and Jacobi iterative method. The effects of nonlinearity and dispersion on the pulse propagation have been studied extensively. An all optical self switch was designed by this simulation. This switch is operated based on the input power.     

An Algebraic Approach to the Generalized Symmetrical Double-Well Potential

We have obtained the energy eigenvalues and the corresponding eigenfunctions for the generalized double-well potential in the non-relativistic Schr?dinger equation. We have calculated the creation and annihilation operators directly from the eigenfunction and we have shown these operators satisfy the commutation relation of the SU(2) group. We have expressed the Hamiltonian in terms of the su(2) algebra. Some interesting result including the standard symmetrical double-well potential, reflectionless-type potential and V ₀tanh ²(r/d) potential are also discussed.