High‐order difference scheme for the solution of linear time fractional klein–gordon equations

In this article, we apply a high‐order difference scheme for the solution of some time fractional partial differential equations (PDEs). The time fractional Cattaneo equation and the linear time fractional Klein–Gordon and dissipative Klein–Gordon equations will be investigated. The time fractional derivative which has been described in the Caputo's sense is approximated by a scheme of order , and the space derivative is discretized with a fourth‐order compact procedure. We will prove the solvability of the proposed method by coefficient matrix property and the unconditional stability and ‐convergence with the energy method. Numerical examples demonstrate the theoretical results and the high accuracy of the proposed scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1234–1253, 2014     

A Proline-Based Aminophosphinic Acid Ligand and It’s Vanadyl Complex: Synthesis,Characterization and In Vitro Inhibitory Effects on α-Amylase And α-Glucosidase

Abstract

A proline-based aminophosphinic acid ligand and it's vanadium complex have been synthesized and characterized by spectroscopic techniques. The inhibitory activity on pancreatic α-amylase and Baker's yeast α-glucosidase has been examined in vitro. The novel complex showed more inhibitory potency against pancreatic α-amylase and Baker's yeast α-glucosidase compared to acarbose as an antidiabetic drug.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Thermal inactivation and conformational lock studies on glucose oxidase

In this study, the dissociative thermal inactivation and conformational lock theories are applied for the homodimeric enzyme glucose oxidase (GOD) in order to analyze its structure. For this purpose, the rate of activity reduction of glucose oxidase is studied at various temperatures using β-d-glucose as the substrate by incubation of enzyme at various temperatures in the wide range between 40 and 70 °C using UV–Vis spectrophotometry. It was observed that in the two ranges of temperatures, the enzyme has two different forms. In relatively low temperatures, the enzyme is in its dimeric state and has normal activity. In high temperatures, the activity almost disappears and it aggregates. The above achievements are confirmed by dynamic light scattering. The experimental parameter “n” as the obvious number of conformational locks at the dimer interface of glucose oxidase is obtained by kinetic data, and the value is near to two. To confirm the above results, the X-ray crystallography structure of the enzyme, GOD (pdb, 1gal), was also studied. The secondary and tertiary structures of the enzyme to track the thermal inactivation were studied by circular dichroism and fluorescence spectroscopy, respectively. We proposed a mechanism model for thermal inactivation of GOD based on the absence of the monomeric form of the enzyme by circular dichroism and fluorescence spectroscopy.     

LOCAL GAUSSIAN-COLLOCATION SCHEME TO APPROXIMATE THE SOLUTION OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS USING VOLTERRA INTEGRAL EQUATIONS

This work describes an accurate and effective method for numerically solving a class of nonlinear fractional differential equations.To start the method,we equivalently convert these types of differential equations to nonlinear fractional Volterra integral equations of the second kind by integrating from both sides of them.Afterward,the solution of the mentioned Volterra integral equations can be estimated using the collocation method based on locally supported Gaussian functions.The local Gaussian-collocation scheme estimates the unknown function utilizing a small set of data instead of all points in the solution domain,so the proposed method uses much less computer memory and volume computing in comparison with global cases.We apply the composite non-uniform Gauss-Legendre quadrature formula to estimate singular-fractional integrals in the method.Because of the fact that the proposed scheme requires no cell structures on the domain,it is a meshless method.Furthermore,we obtain the error analysis of the proposed method and demon-strate that the convergence rate of the approach is arbitrarily high.Illustrative examples clearly show the reliability and efficiency of the new technique and confirm the theoretical error estimates.     

Analytical Nusselt number for forced convection inside a porous-filled tube with temperature-dependent thermal conductivity arising from high-temperature applications

Journal of Thermal Analysis and Calorimetry - The convection heat transfer inside a tube filled with a porous material under the constant heat flux thermal boundary condition which is widely used...     

On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation

Numerical solution of hyperbolic partial differential equation with an integral condition continues to be a major research area with widespread applications in modern physics and technology. Many physical phenomena are modeled by nonclassical hyperbolic boundary value problems with nonlocal boundary conditions. In place of the classical specification of boundary data, we impose a nonlocal boundary condition. Partial differential equations with nonlocal boundary specifications have received much attention in last 20 years. However, most of the articles were directed to the second‐order parabolic equation, particularly to heat conduction equation. We will deal here with new type of nonlocal boundary value problem that is the solution of hyperbolic partial differential equations with nonlocal boundary specifications. These nonlocal conditions arise mainly when the data on the boundary can not be measured directly. Several finite difference methods have been proposed for the numerical solution of this one‐dimensional nonclassic boundary value problem. These computational techniques are compared using the largest error terms in the resulting modified equivalent partial differential equation. Numerical results supporting theoretical expectations are given. Restrictions on using higher order computational techniques for the studied problem are discussed. Suitable references on various physical applications and the theoretical aspects of solutions are introduced at the end of this article. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

THE UNIT BALL OF C^＊-ALGEBRA AND DIFFERENTIABILITY OF SUPPORT FUNCTION

In this paper we show that the unit ball of an infinite dimensional commutative C^*-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points in the Frechet differentiability of support convex functions.     

A fast and efficient two-grid method for solving d-dimensional poisson equations

The aim of this paper is to introduce a fast and efficient new two-grid method to solve the d-dimensional (d=1,2,3) Poisson elliptic equations. The finite difference equations at all interior grid points form a large sparse linear system, which needs to be solved efficiently. The solution cost of this sparse linear system usually dominates the total cost of solving the discretized partial differential equation. The finite difference equations are based on applying a finite difference scheme of two- and four-orders (compact finite difference method) for discretizing the spatial derivative. The obtained linear systems of Poisson elliptic equations have been solved by a new two-grid (NTG) method and we also note that the NTG method which is used for solving the large sparse linear systems is faster and more effective than that of the standard two-grid method. We utilize the local Fourier analysis to show that the spectral radius of the new two-grid method for 1D and 2D models is less than that of the standard two-grid method. As well as, we expand the corresponding algorithm to the new multi-grid method. The numerical examples show the efficiency of the new algorithms for solving the d-dimensional Poisson equations.     

The dual reciprocity boundary integral equation technique to solve a class of the linear and nonlinear fractional partial differential equations

In this paper, we apply the boundary integral equation technique and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of linear and nonlinear time‐fractional partial differential equations (TFPDEs). The main aim of the present paper is to examine the applicability and efficiency of DRBEM for solving TFPDEs. We employ the time‐stepping scheme to approximate the time derivative, and the method of linear radial basis functions is also used in the DRBEM technique. This method is improved by using a predictor–corrector scheme to overcome the nonlinearity that appears in the nonlinear problems under consideration. To confirm the accuracy of the new approach, several examples are presented. The convergence of the DRBEM is studied numerically by comparing the exact solutions of the problems under investigation. Copyright © 2015 John Wiley & Sons, Ltd.