Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

We investigate the critical behavior of a stochastic lattice model describing a General Epidemic Process. By means of a Monte Carlo procedure, we simulate the model on a regular square lattice and follow the spreading of an epidemic process with immunization. A finite size scaling analysis is employed to determine the critical point as well as some critical exponents. We show that the usual scaling analysis of the order parameter moment ratio does not provide an accurate estimate of the critical point. Precise estimates of the critical quantities are obtained from data of the order parameter variation rate and its fluctuations. Our numerical results corroborate that this model belongs to the dynamic isotropic percolation universality class. We also check the validity of the hyperscaling relation and present data collapse curves which reinforce the accuracy of the estimated critical parameters.     

A new modified Laplace decomposition method for higher order boundary value problems

In this article, we suggest modified Laplace decomposition method for analytical solution of eighth-order boundary value problems (BVPs). The numerical application indicates the effectiveness and stability of the proposed algorithm. The efficiency of proposed method is examined with the help of linear and nonlinear problems.     

Heteropolyacid anchored on SBA-15 functionalized with 2-aminoethyl dihydrogen phosphate: a novel and highly efficient catalyst for one-pot,three-component synthesis of trisubstituted 1,3-thiazoles

Heteropolyacid anchored on SBA-15 functionalized with 2-aminoethyl dihydrogen phosphate (SBA-15@AEPH₂-HPA) was synthesized as a novel and highly efficient heterogeneous mesoporous catalyst. Characterization of the as-synthesized catalyst was successfully performed using various techniques such as FT-IR, BET, small-angle XRD, SEM, EDX, TEM, TGA, ICP-OES and elemental analysis. The new catalyst revealed a superb catalytic activity towards the one-pot synthesis of a wide verity of trisubstituted 1,3-thiazole derivatives. This protocol involved the three-component reactions of arylglyoxals, cyclic 1,3-dicarbonyls and thioamides under mild reaction conditions. Surprisingly, the current methodology is far superior to the only literature precedent used in this regard. The most promising features which highlight the presented approach are: furnishing a very important class of pharmaceutically and biologically active 1,3-thiazoles in excellent yields within short reaction times, mildness of the reaction conditions, using water as the reaction media and facile catalyst reusability for at least nine successive runs without any appreciable loss of its activity. Importantly, the small-angle XRD analysis and TEM images of the 9th recovered catalyst clearly proved the privileged durability and stability of the introduced catalytic system, under the applied reaction condition.     

Reliable controller for nonlinear multiagent system with additive time varying delay and nonlinear actuator faults

In this paper, the problem of nonlinear multiagent system with reliable control is taken into account. The prescribed system consists of additive time-varying delay, actuator faults with both linear and nonlinear functions. The main focus of this paper is to design a reliable control which guarantees the stability and consensus condition of the proposed system. Actuator faults with linear and nonlinear functions are considered in the control input. From the implementation of integral inequality, the linear matrix inequality format is derived by constructing the suitable Lyapunov Krasovskii functional for the specified system. Terminally numerical examples are furnished for the efficiency of the specified method.     

A quadratically convergent local algorithm on minimizing sums of the largest eigenvalues of a symmetric matrix

In this paper, we consider the problem on minimizing sums of the largest eigenvalues of a symmetric matrix which depends on the decision variable affinely. An important application of this problem is the graph partitioning problem, which arises in layout of circuit boards, computer logic partitioning, and paging of computer programs. Given 0, we first derive an optimality condition which ensures that the objective function is within error bound of the solution. This condition may be used as a practical stopping criterion for any algorithm solving the underlying problem. We also show that, in a neighborhood of the minimizer, the optimization problem can be equivalently formulated as a smooth constrained problem. An existing algorithm on minimizing the largest eigenvalue of a symmetric matrix is shown to be applicable here. This algoritm enjoys the property that if started close enough to the minimizer, then it will converge quadratically. To implement a practical algorithm, one needs to incorporate some technique to generate a good starting point. Since the problem is convex, this can be done by using an algorithm for general convex optimization problems (e.g., Kelley's cutting plane method or ellipsoid methods), or an algorithm specific for the optimization problem under consideration (e.g., the algorithm developed by Cullum, Donath, and Wolfe). Such union ensures that the overall algorithm has global convergence with quadratic rate. Finally, the results presented in this paper are readily extended on minimizing sums of the largest eigenvalues of a Hermitian matrix.Some of results in this paper were given in [19] without proofs.     

9-Acylation of 1-acyldipyrromethanes containing a dialkylboron mask for the alpha-acylpyrrole motif

1,9-Diacyldipyrromethanes are important precursors to porphyrins, yet synthetic access remains limited owing to (1) poor conversion in the 9-acylation of 1-acyldipyrromethanes and (2) handling difficulties because acyldipyrromethanes typically streak upon chromatography and give amorphous powders upon attempted crystallization. A reliable means for converting a dipyrromethane to a 1-acyldipyrromethane-dialkylboron complex was recently developed, where the dialkylboron (BR(2)) unit renders the complex hydrophobic and thereby facilitates isolation. Herein a refined preparation of 1,9-diacyldipyrromethanes is presented that employs the 1-acyldipyrromethane-BR(2) complex as a substrate for 9-acylation. The dialkylboron unit provides protection for the alpha-acylpyrrole unit. 9-Acylation requires formation of the pyrrolyl-MgBr reagent and the presence of 1 equiv of a nonnucleophilic base to quench the proton liberated upon alpha-acylation. Reaction of the 1-acyldipyrromethane-BR(2) complex (1 equiv) with mesitylmagnesium bromide (2 equiv) followed by the addition of an acylating agent (S-2-pyridyl thioate or acid chloride, 1.1 equiv) gives the corresponding 1,9-diacyldipyrromethane-BR(2) complex. The acylation method afforded 1,9-diacyldipyrromethane-BR(2) complexes with limited or no chromatography in yields of 64-92%. The 1,9-diacyldipyrromethane-BR(2) complexes are stable to routine handling, are readily soluble in common organic solvents, crystallize readily, and can now be prepared in multigram quantities through use of stoichiometric quantities of reagents.     

Effect of Dielectric Constant of Solvents on the Particle Size and Bandgap of La/SnO2‐TiO2 Nanoparticles and Their Catalytic Properties

Lanthanum (La) supported on tin oxide‐titanium oxide (SnO₂‐TiO₂ ) nanoparticles were prepared by a sol–gel method followed by a hydrothermal method. Effect of different solvents (ethyl acetate, benzyl alcohol, ethylene glycol) on the particle size and catalytic activity was investigated. The nanomaterial was characterized by transmission electron microscopy, powder X‐ray diffraction, scanning electron microscopy, fourier transform infrared spectroscopy, and energy dispersive X‐ray. The catalytic and optical properties were studied using solid‐phase spectrophotometry and ultraviolet–visible spectroscopy, respectively. Gas chromatography‐mass spectrometry (GC‐MS) was used to detect the intermediates during the catalytic degradation of methylene blue. It was observed that with decrease in the dielectric constant (ε) of the solvent, the bandgap and particle size decrease and catalytic efficiency increases. Hence, the highest catalytic activity was observed with the solvent having the least dielectric constant.     

A Green,Solvent‐Free,Microwave‐Assisted,High‐Yielding YbCl3 Catalyzed Deprotection of THP/MOM/Ac/Ts Ethers of Chalcone Epoxide and 2′‐Aminochalcone and Their Sequel Cyclization

Under microwave and solvent‐free conditions, YbCl₃ efficiently catalyzed the deprotection of tetrahydropyran‐2‐yl, methoxymethyl (MOM), acetyl, and tosyl groups and sequel cyclization of chalcone epoxide to 2‐hydroxyindanone and 2′‐aminochalcone to aza‐flavanone. The reaction afforded the products in excellent yield (78–99%) at 850 W microwave heating within 1–5 min under eco‐friendly conditions. The merits of the presented protocol include high yield, use of microwave irradiation, solvent‐free condition, catalyst reusability, and no need for purification with column chromatography. The present method is very much milder but more advanced than those reported earlier.