Preparation and characterization of a silica‐based magnetic nanocomposite and its application as a recoverable catalyst for the one‐pot multicomponent synthesis of quinazolinone derivatives

An environmentally benign magnetic silica‐based nanocomposite (Fe₃O₄/SBA‐15) as a heterogeneous nanocatalyst was prepared and characterized using Fourier transform infrared and ultraviolet–visible diffuse reflectance spectroscopies, scanning electron microscopy, X‐ray diffraction, vibrating sample magnetometry and Brunauer–Emmett–Teller multilayer nitrogen adsorption. Its catalytic activity was investigated for the one‐pot multicomponent synthesis of 2,3‐dihydroquinazolin‐4(1H)‐ones starting from isatoic anhydride, ammonium acetate and various aldehydes under mild reaction conditions and easy work‐up procedure in refluxing ethanol with good yields. The nanocatalyst can be recovered easily and reused several times without significant loss of catalytic activity. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical analysis nonlinear multi‐term time fractional differential equation with collocation method via fractional B‐spline

In this work, we present numerical analysis for nonlinear multi‐term time fractional differential equation which involve Caputo‐type fractional derivatives for . The proposed method is based on utilization of fractional B‐spline basics in collocation method. The scheme can be readily obtained efficient and quite accurate with less computational work numerical result. The proposal approach transform nonlinear multi‐term time fractional differential equation into a suitable linear system of algebraic equations which can be solved by a suitable numerical method. The numerical experiments will be verify to demonstrate the effectiveness of our method for solving one‐ and two‐dimensional multi‐term time fractional differential equation.     

Shock tube investigation of methyl tert butyl ether and methyl tetrahydrofuran high-temperature kinetics

The autoignition and pyrolysis of two C5 ethers, methyl tert butyl ether (MTBE) and 2-methyltetrahydrofuran (2-MTHF), are investigated using the shock tube reactor. The experiments are carried out at pressures of 3.5 and 12 atm at temperatures above 1000 K with argon as a diluent gas. By means of direct laser absorption, carbon monoxide time histories and associated chemical kinetic timescales are also determined. It is observed that the competition between ignition and pyrolysis times depends on the temperature and equivalence ratio of the ignition mixture, such that there is a temperature above which pyrolysis predominates oxidative kinetics. This crossover temperature shifts toward higher temperatures for reactive systems with a fixed fuel concentration but higher oxygen content. The resulting experimental observations are also compared with predictions of existing chemical kinetic models from the literature. The results point to differences in chemical reactivity, such that in pyrolysis conditions, the reactivity of the cyclic ether, 2-MTHF, is generally higher than that of the aliphatic ether, MTBE. While agreement between experimental observations and model predictions is observed under certain conditions, significant variance between observations and predictions is observed under other conditions. With respect to prediction of the pyrolysis time used to capture the global kinetics of pyrolysis, it is observed that the relation of this time to the time needed to attain 90% of the equilibrium CO concentration varies greatly with the result that the models used in this work generally predict a faster initial formation of CO but a much slower approach to the equilibrium concentration. This is thought to arise from the slow transformation of intermediate CH₂O and CH₂CO to CO. The chemical kinetic models considered in this work are therefore not capable of predicting the CO time histories during pyrolysis.     

Improvements of physical and mechanical properties of electron beam irradiation—crosslinked EVA foams

In this work, ethylene–vinyl acetate (EVA) copolymer foams were prepared and crosslinked by using high‐energy electron beam (e‐beam) radiation (10 MeV). The effect of parameters such as irradiation dose, the contents of foaming agent, radiation activator, and radiation sensitizer on improvement of physical and mechanical properties of the EVA foamed samples were investigated. The foams were obtained through a four‐step process of melt mixing, forming, crosslinking, and foaming. During the melt mixing process EVA was compounded with different amounts of azodicarbonamide (ADCA) as a blowing agent, zinc oxide (ZnO) as a radiation activator, and trimethylol propane‐trimethacrylate (TMPTMA) as a radiation sensitizer. The samples were compression molded into flat sheets at low temperature (110°C) and were then radiation‐crosslinked by 20–80 kGy e‐beam. Finally, the crosslinked samples were converted to foams by a high temperature (210°C) compression molding process. The foamed samples were analyzed in terms of gel content, density, compression molding set, tensile properties, and micro‐structural features. It was found that an increase in absorbed radiation dosage increases crosslink density, elasticity, percentage recovery, tensile strength, and compression properties of the EVA foams. Due to the increased recovery the percentage of compression set was reduced. Similarly increasing the TMPTMA content in the formulation increased the crosslink density and the resulting mechanical properties. Contrary to these findings, addition of ADCA led to the formation of extra gases which in turn reduced the crosslink density, and resulted in the deterioration of the mechanical properties and hence an increase in the compression set. However, addition of ZnO and TMPTMA led to the formation of smaller and more uniform cell size with improved mechanical properties. Copyright © 2008 John Wiley & Sons, Ltd.     

Constitutive equations for micropolar hyper-elastic materials

In this paper, the concept of hyper-elasticity in the micropolar continuum theory is investigated. The restrictions on the fourth-order elasticity tensors are investigated. Using the representation theorems, a general form of constitutive equations for micropolar hyper-elastic isotropic materials is presented. As some special cases, generalizations of the neo-Hookean and Mooney-Rivlin type materials to the micropolar continuum theory are presented. The generalized constitutive equations reduce to those of the microplar linear elasticity theory when the deformations are infinitesimal. Also, Updated Lagrangian finite element formulations for the micropolar hyper-elastic materials are presented. Considering two planar examples, it is shown that an increase in the micropolar parameter results in the reduction of the deformation of the bodies. Also, it is shown that for a specimen with very small dimensions, e.g. in the micron level, the micropolar effects are more sensible. Furthermore, it is shown that the influence of the micropolar parameters is dependent not only on the size of the body, but also to its geometry and loading conditions. For the problems in which the deformation is very close to a homogeneous state, the micropolar effects are negligible.     

Generalizations of Polya's urn Problem

We consider generalizations of the classical Polya urn problem: Given finitely many bins each containing one ball, suppose that additional balls arrive one at a time. For each new ball, with probability p, create a new bin and place the ball in that bin; with probability 1–p, place the ball in an existing bin, such that the probability that the ball is placed in a bin is proportional to $ m^\gamma $, where m is the number of balls in that bin. For p=0, the number of bins is fixed and finite, and the behavior of the process depends on whether is greater than, equal to, or less than 1. We survey the known results and give new proofs for all three cases. We then consider the case p>0. When =1, this is equivalent to the so-called preferential attachment scheme which leads to power law distribution for bin sizes. When >1, we prove that a single bin dominates, i.e., as the number of balls goes to infinity, the probability that any new ball either goes into that bin or creates a new bin converges to 1. When p > 0 and < 1, we show that under the assumption that certain limits exist, the fraction of bins having m balls shrinks exponentially as a function of m. We then discuss further generalizations and pose several open problems.AMS Subject Classification: 05D40, 60C05, 60G20, 68R10, 91C99.     

A comparison of the coordination preferences of Zn, Co, and Cd(II) with the heteroscorpionate ligand (2-hydroxy-3-t-butyl-methylphenyl)bis (3,5-dimethylpyrazolyl)methane

Reaction of the Zn, Cd, or Co nitrate salts with the deprotonated ligand (2-hydroxy-3-t-butyl-methylphenyl)bis(3,5-dimethylpyrazolyl)methane (L1O^–) in methanol produced the following complexes: [(L1OH)Zn(NO₃)₂] in two isomorphs, a = 40.983(8) Å, b = 9.571(2) Å, c = 15.667(8) Å, = 90, = 106.38(1), = 90, C2/c, and a = 13.027(3) Å, b = 14.781(4) Å, c = 16.107(3) Å, = 90, = 105.30(1), = 90, P2₁/n; [(L1OH)Cd(pz)(NO₃)₂] a = 14.7476(2) Å, b = 13.5411(2) Å, c = 16.7223(2) Å, = 90, = 110.3840(10), = 90, P2₁/c; and [(L1O)Co(pz)(NO₃)] a = 11.4240(2) Å, b = 13.4498(2) Å, c = 13.8056(2) Å, = 105.2080(10), = 105.8130(10), = 112.7470(10), P . The Zn adopts a pseudotetrahedral four-coordinate geometry where the potentially tridentate ligand is actually bidentate with a protonated and uncoordinated phenoxy arm. The Co complex is pseudooctahedral six-coordinate where the phenoxy arm is deprotonated and coordinated. Finally the Cd complex is seven-coordinate but the metal is not coordinated through the phenoxy group that is again protonated.