A study on the convergence conditions of generalized differential transform method

This paper deals with constructing generalized ‘fractional’ power series representation for solutions of fractional order differential equations. We present a brief review of generalized Taylor's series and generalized differential transform methods. Then, we study the convergence of fractional power series. Our emphasis is to address the sufficient condition for convergence and to estimate the truncated error. Numerical simulations are performed to estimate maximum absolute truncated error when the generalized differential transform method is used to solve non‐linear differential equations of fractional order. The study highlights the power of the generalized differential transform method as a tool in obtaining fractional power series solutions for differential equations of fractional order. Copyright © 2016 John Wiley & Sons, Ltd.     

Statistical analysis and exposure status classification of transmembrane beta barrel residues

Several computational methods exist for the identification of transmembrane beta barrel proteins (TMBs) from sequence. Some of these methods also provide the transmembrane (TM) boundaries of the putative TMBs. The aim of this study is to (1) derive the propensities of the TM residues to be exposed to the lipid bilayer and (2) to predict the exposure status (i.e. exposed to the bilayer or hidden in protein structure) of TMB residues. Three novel propensity scales namely, BTMC, BTMI and HTMI were derived for the TMB residues at the hydrophobic core region of the outer membrane (OM), the lipid-water interface regions of the OM, and for the helical membrane proteins (HMPs) residues at the lipid-water interface regions of the inner membrane (IM), respectively. Separate propensity scales were derived for monomeric and functionally oligomeric TMBs. The derived propensities reflect differing physico-chemical properties of the respective membrane bilayer regions and were employed in a computational method for the prediction of the exposure status of TMB residues. Based on the these propensities, the conservation indices and the frequency profile of the residues, the transmembrane residues were classified into buried/exposed with an accuracy of 77.91% and 80.42% for the residues at the membrane core and the interface regions, respectively. The correlation of the derived scales with different physico-chemical properties obtained from the AAIndex database are also discussed. Knowledge about the residue propensities and burial status will be useful in annotating putative TMBs with unknown structure.     

A new indole alkaloid,antioxidant and antibacterial activities of crude extracts from Saccocalyx satureioides

Abstract

The new acylated indole alkaloid glucoside indole-3-carboxylic acid-(6'-O-caffeoyl)-β-D-glucoside 1 has been isolated from the ethyl acetate (EtOAC) extract of Saccocalyx satureioides Coss. & Dur. (Lamiaceae) together with eight known secondary metabolites 2-9. Two indoles 2 and 3, five methylated flavone aglycones 4-8 and one monoterpene glucoside 9 were reported for the first time in the genus Saccocalyx. The structural elucidation of these compounds was accomplished by spectroscopic methods including 1?D (¹H and ¹³C) and 2?D (COSY, HSQC and HMBC) NMR techniques, and mass spectrometry, and by comparison with literature data. Light petroleum, EtOAc, chloroform and n-butanol (n-BuOH) extracts of S. Satureioides were screened for their antioxidant activity using DPPH radical scavenging and β-carotene bleaching methods. The antibacterial activity of these extracts indicates that n-BuOH and EtOAc extracts possess the strongest activity.     

Series solution for heat transfer from a continuous surface in a parallel free stream of viscoelastic fluid

This work is concerned with the influence of uniform suction or injection on flow and heat transfer analysis of a second order fluid. The resulting nonlinear problem for velocity is solved by means of homotopy analysis method (HAM). The comparison between the numerical solution of Hady and Gorla (Acta Mec 128 (1998), 201–208 and HAM solution is discussed with the help of numerical tables and graphs. Nonsimilar solutions to the stream function and temperature are developed. The influence of important parameters is seen on the velocity, temperature, skin friction coefficient, and temperature gradient. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1511–1524, 2011     

Hall effect on the pipe flow of a Burgers’ fluid: An exact solution

An analysis is made to see the influences of Hall current on the flow of a Burgers’ fluid. The velocity field corresponding to the flow in a pipe is determined. The closed form analytical solutions for several Newtonian and non-Newtonian fluid models can be obtained from the present analysis as the limiting cases.     

Exact flow of a third-grade fluid on a porous wall

The flow of a third-grade fluid occupying the space over a wall is studied. At the surface of the wall suction or blowing velocity is applied. By introducing a velocity field, the governing equations are reduced to a non-linear partial differential equation. The resulting equation is analysed analytically using Lie group methods.     

Peristaltic flow of a Johnson-Segalman fluid through a deformable tube

To understand theoretically the flow properties of physiological fluids we have considered as a model the peristaltic motion of a Johnson–Segalman fluid in a tube with a sinusoidal wave traveling down its wall. The perturbation solution for the stream function is obtained for large wavelength and small Weissenberg number. The expressions for the axial velocity, pressure gradient, and pressure rise per wavelength are also constructed. The general solution of the governing nonlinear partial differential equation is given using a transformation method. The numerical solution is also obtained and is compared with the perturbation solution. Numerical results are demonstrated for various values of the physical parameters of interest.      

MHD UNSTEADY FLOWS DUE TO NON—COAXIAL ROTATIONS OF A DISK AND A FLUID AT INFINITY

Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only due to its own theoretical interest, but also due to applications to geophysics and engineering. The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established. The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field, the frequency and rotation parameters.     

Rotating flow of a second-order fluid on a porous plate

A study is made of the unsteady flow engendered in a second-order incompressible, rotating fluid by an infinite porous plate exhibiting non-torsional oscillation of a given frequency. The porous character of the plate and the non-Newtonian effect of the fluid increase the order of the partial differential equation (it increases up to third order). The solution of the initial value problem is obtained by the method of Laplace transform. The effect of material parameters on the flow is given explicitly and several limiting cases are deduced. It is found that a non-Newtonian effect is present in the velocity field for both the unsteady and steady-state cases. Once again for a second-order fluid, it is also found that except for the resonant case the asymptotic steady solution exists for blowing. Furthermore, the structure of the associated boundary layers is determined.     

Exact solutions for the unsteady flow of a Burger’s fluid in a duct induced by time-dependent prescribed volume flow rate

In this investigation, some unsteady flows in a circular duct have been studied. The fluid obeys viscoelastic non-Newtonian model with the Burgers’ constitutive equation and all fluid properties are constant. The flows in a duct are due to the prescribed arbitrary time dependent inlet volume flow rates. Four types of flow situations are considered. The governing equations are first developed and then solved using Laplace transform technique. Results indicate the strong effect of Burgers’ fluid parameter on the velocity fields and pressure gradients.