Solution of Lane–Emden type equations using rational Bernoulli functions

In this paper, a numerical method for solving Lane‐Emden type equations, which are nonlinear ordinary differential equations on the semi‐infinite domain, is presented. The method is based upon the modified rational Bernoulli functions; these functions are first introduced. Operational matrices of derivative and product of modified rational Bernoulli functions are then given and are utilized to reduce the solution of the Lane‐Emden type equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical iterative method for Volterra equations of the convolution type

The objective of this paper is to present an algorithm from which a rapidly convergent solution is obtained for Volterra integral equations of Hammerstein type. Such equations are often encountered when describing the response of viscoelastic materials where the time dependency of the material properties is often expressed in the form of a convolution integral. Frequently, singularity is encountered and often ignored when dealing with the constitutive equations of viscoelastic materials. In this paper, the singularity is incorporated in the solution and the iterative scheme used to solve the equation converges within six iterations to a typical toleration error of 10^?5. The algorithm is applied to the strain response of a polymer under impulsive (constant) loading and the results show excellent correlation between the experimental and analytical solution. Copyright © 2010 John Wiley & Sons, Ltd.     

A prediction problem in

For a nonnegative integrable weight function on the unit circle , we provide an expression for , in terms of the series coefficients of the outer function of , for the weighted distance , where is the normalized Lebesgue measure and ranges over trigonometric polynomials with frequencies in , , . The problem is open for .

     

A spatio-temporal dynamic regression model for extreme wind speeds

This paper presents a hierarchical regression type model for analyzing the dependency of sample extremes on time, space and a covariate effect. The model is based on the assumption that the observations follow independently a generalized extreme value distribution given location, scale and shape parameters. Then a multivariate spatial process is considered to accommodate the association and spatial correlation in the distribution parameters. The mean of the process incorporates the underlying dynamics which is elaborated on the lower stage of hierarchy. Finally, three spatio-temporal dynamic linear models drive independently this mean function to take the variations in the parameters separately into account. In a Bayesian setting, the model structure leads to parallel implementation of the Markov chain Monte Carlo algorithm in a sense that it is less time consuming. Our methodology is applied to the monthly maxima of wind speed with temperature as a covariate for which the relationship is expressed in terms of a penalized spline regression model. The comparison of the proposed model with several simpler ones suggests considerable improvements in wind speed analysis.     

A Spectral Method for the Electrohydrodynamic Flow in a Circular Cylindrical Conduit

This paper presents a combination of the hybrid spectral collocation technique and the spectral homotopy analysis method(SHAM for short) for solving the nonlinear boundary value problem(BVP for short) for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. The accuracy of the present solution is found to be in excellent agreement with the previously published solution. The authors use an averaged residual error to find the optimal convergence-control parameters. Comparisons are made between SHAM generated results, results from literature and Matlab ode45 generated results, and good agreement is observed.     

An Approximate Approach for Systems of Singular Volterra Integral Equations Based on Taylor Expansion

In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.     

Dendrimer‐encapsulated Cu(Π) nanoparticles immobilized on superparamagnetic Fe3O4@SiO2 nanoparticles as a novel recyclable catalyst for N‐arylation of nitrogen heterocycles and green synthesis of 5‐substituted 1H‐tetrazoles

In this study, dendrimer‐encapsulated Cu(Π) nanoparticles immobilized on superparamagnetic Fe₃O₄@SiO₂ nanoparticles were prepared via a multistep‐synthesis. Then, the synthesized composite was fully characterized by various techniques such as fourier transform infrared (FT‐IR) spectroscopy, X‐ray diffraction (XRD), dynamic light scattering (DLS), UV‐vis spectroscopy, energy dispersive X‐ray analysis (EDX), thermogravimetric analysis (TGA) and vibration sample magnetometer (VSM). From the information gained by FE‐SEM and TEM studies it can be inferred that the particles are mostly spherical in shape and have an average size of 50 nm. Also, the amount of Cu is determined to be 0.51 mmol/g in the catalyst by inductively coupled plasma (ICP) analyzer. This magnetic nano‐compound has been successfully applied as a highly efficient, magnetically recoverable and stable catalyst for N‐arylation of nitrogen heterocycles with aryl halides (I, Br) and arylboronic acids without using external ligands or additives. The catalyst was also employed in a one‐pot, three‐component reaction for the efficient and green synthesis of 5‐substituted 1H‐tetrazoles using various aldehydes, hydroxylamine hydrochloride and sodium azide in water. The magnetic catalyst can be easily separated by an external magnet bar and is recycled seven times without significant loss of its activity.     

Application of chromium‐doped fullerene as a carrier for thymine and uracil nucleotides: Comprehensive density functional theory calculations

The interactions of the nucleobases thymine (C₅H₆N₂O₂) and uracil (C₄H₄N₂O₂) with Cr‐doped C₂₀ fullerene (C₁₉Cr) are investigated by performing density functional theory calculations. The adsorption of these nucleobases on C₁₉Cr leads to two distinct geometries (P1 and P2) differing in the orientation of the nucleobases. The interaction of the nucleobases with the C₁₉Cr nanocluster is highly exothermic, revealing that they are chemically adsorbed on C₁₉Cr. The results show that the binding energy of the thymine–C₁₉Cr complex is slightly higher than that of the uracil–C₁₉Cr complex. In addition, the P2 geometry is more stable compared to P1 due to the higher binding energy in the former configuration. However, based on the results of natural bond orbital and frontier molecular orbitals analyses, the C₁₉Cr nanocage has higher reactivity with the nucleobases in P1 geometry in comparison with P2 due to the larger charge transfer and orbital hybridization in the former geometry. Moreover, the band gap of the C₁₉Cr nanocage decreases after interaction with the nucleobases, and interestingly the impact is more pronounced for P1 geometry, confirming the higher sensitivity of C₁₉Cr to the nucleobases in P1 geometry. Our findings reveal the promising potential of C₁₉Cr as an organometallic carrier for nucleobases thymine and uracil.     

Unraveling the role of binder concentration on the electrochemical behavior of mesocarbon microbead anode in lithium–ion batteries: understanding the formation of the solid electrolyte interphase

Journal of Solid State Electrochemistry - Binders play a significant role in the electrochemical performance of anodes in lithium–ion batteries. In this study, mesocarbon microbead (MCMB)...