Application of He's variational iteration method for solving the Cauchy reaction–diffusion problem

In this paper, the solution of Cauchy reaction–diffusion problem is presented by means of variational iteration method. Reaction–diffusion equations have special importance in engineering and sciences and constitute a good model for many systems in various fields. Application of variational iteration technique to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. Moreover, this technique does not require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computations.     

A seminumeric approach for solution of the Eikonal partial differential equation and its applications

In this work, a partial differential equation, which has several important applications, is investigated, and some techniques based on semianalytic (or quasi‐numerical) approaches are developed to find its solution. In this article, the homotopy perturbation method (HPM), Adomian decomposition method, and the modified homotopy perturbation method are proposed to solve the Eikonal equation. HPM yields solution in convergent series form with easily computable terms, and in some case, yields exact solutions in one iteration. In other hand, in Adomian decomposition method, the approximate solution is considered as an infinite series usually converges to the accurate solution. Moreover, these methods do not require any discretization, linearization, or small perturbation, and therefore reduce the numerical computation a lot. Several test problems are given and results are compared with the variational iteration method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Comprehensive study of the interaction between hydrogen halides and methanol derivatives

The R? CH₂? HO…H? X (R = SCl, Cl, SH, NO₂, OMe, CHO, CN, C₂H₅, CH₃, H; X = F, Cl, Br) complexes are considered here as the interest sample for the consideration of different measures of H‐bond strength. The intermolecular interaction energies are predicted by using MP2/6‐31++G(d,p) and B3LYP/6‐31++G(d,p) methods with basis set superposition error and zero‐point energy corrections. The results showed that intermolecular hydrogen bonds for complexes with HF are stronger than such interactions in complexes with HCl and HBr. Quantum theory of “Atoms in Molecules” and natural bond orbitals method were applied to analyzed H‐bond interactions. The gas phase thermodynamic properties of complexes were predicted using quantum mechanical computations. The obtained results showed a strong influence of the R and X substituents on the thermodynamic properties of complexes. Numerous correlations between topological, geometrical, thermodynamic properties and energetic parameters were also found. © 2011 Wiley Periodicals, Inc.     

Synthesis of new indolyl crown ethers catalyzed with ferric hydrogensulfate

Efficient reaction of bis-indolyl podand with different aldehydes using Fe（HSO₄）₃ as catalyst to afford the corresponding new indolyl crown ethers is described.The structures of three distinct isomers have been optimized using HyperChem geometry optimizations.Also percentage of each isomer was obtained with ¹H NMR spectroscopy.     

Base-free green synthesis of copper(II) oxide nanoparticles using highly cross-linked poly(curcumin) nanospheres: synergistically improved antimicrobial activity

Research on Chemical Intermediates - Antimicrobial activity of metal containing formulas has drawn attention and been widely investigated. In this research, CuO/hc-pCUR nanocomposite composed of...     

Modeling the Stretch Behavior of the Single-Crystal Ni–Al Alloy and Its Molecular Dynamics Simulation

Physics of the Solid State - Molecular dynamics simulation was employed in this study to investigate the atomistic mechanisms involved in the Ni–Al alloy homogeneous deformation and the...     

Synthesis of new TCH/Ni‐based nanocomposite supported on SBA‐15 and its catalytic application for preparation of benzimidazole and perimidine derivatives

A stable nickel‐decorated SBA‐15 nanocomposite (Ni/TCH@SBA‐15) was synthesized through surface modification of silica nanoparticles with 3‐chloropropyltriethoxysilane (CPTES) and thiocarbohydrazide (TCH) followed by metal–ligand coordination with Ni (II). The structure of this organometallic nanocomposite was characterized by Fourier transform‐infrared, field emission‐scanning electron microscopy, EDAX, transmission electron microscopy, atomic absorption spectroscopy and N₂ adsorption–desorption (Brunauer–Emmett–Teller) techniques. The catalytic performance of Ni/TCH@SBA‐15 (NNTS‐15) was determined for the synthesis of 2‐aryl‐substituted benzimidazoles and 2,3‐dihydroperimidines. The excellent yields within shorter reaction times, simplicity of catalytic methods, non‐toxicity and clean reactions, mild reaction conditions and easy work‐up procedure are the important merits of these synthetic protocols. Moreover, the Ni (II) bonded to the SBA‐15 surface was stable under the catalytic reaction conditions resulting in its efficient recycling and reuse.     

Analysis of functionally graded thick truncated cone with finite length under hydrostatic internal pressure

Finite Element Method based on Rayleigh–Ritz energy formulation is applied to obtain the elastic behavior of functionally graded thick truncated cone. The cone has finite length, and it is subjected to axisymmetric hydrostatic internal pressure. The inner surface of the cone is pure ceramic and the outer surface is pure metal, and the material composition varying continuously along its thickness. Using this method, the effects of semi-vertex angle of the cone and the power law exponent on distribution of different types of displacements and stresses are considered.     

Integrating Data Transformation in Principal Components Analysis

Principal component analysis (PCA) is a popular dimension-reduction method to reduce the complexity and obtain the informative aspects of high-dimensional datasets. When the data distribution is skewed, data transformation is commonly used prior to applying PCA. Such transformation is usually obtained from previous studies, prior knowledge, or trial-and-error. In this work, we develop a model-based method that integrates data transformation in PCA and finds an appropriate data transformation using the maximum profile likelihood. Extensions of the method to handle functional data and missing values are also developed. Several numerical algorithms are provided for efficient computation. The proposed method is illustrated using simulated and real-world data examples. Supplementary materials for this article are available online.