Exact Solutions of Fractional-Order Biological Population Model

In this paper, the Adomian's decomposition method (ADM) is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.     

Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form

The problems of determining the B–spline form of a C ² Pythagorean–hodograph (PH) quintic spline curve interpolating given points, and of using this form to make local modifications, are addressed. To achieve the correct order of continuity, a quintic B–spline basis constructed on a knot sequence in which each (interior) knot is of multiplicity 3 is required. C ² quintic bases on uniform triple knots are constructed for both open and closed C ² curves, and are used to derive simple explicit formulae for the B–spline control points of C ² PH quintic spline curves. These B-spline control points are verified, and generalized to the case of non–uniform knots, by applying a knot removal scheme to the Bézier control points of the individual PH quintic spline segments, associated with a set of six–fold knots. Based on the B–spline form, a scheme for the local modification of planar PH quintic splines, in response to a control point displacement, is proposed. Only two contiguous spline segments are modified, but to preserve the PH nature of the modified segments, the continuity between modified and unmodified segments must be relaxed from C ² to C ¹. A number of computed examples are presented, to compare the shape quality of PH quintic and “ordinary” cubic splines subject to control point modifications.     

Improvement in energy conversion of electrostrictive composite materials by new approach via piezoelectric effect: Modeling and experiments

This study proposes a new model that couples the piezoelectric and electrostrictive behavior to minimize the polarization power of composite polymer. The development of this model is capable to predict the energy harvesting abilities of an electrostrictive composite. To improve the dielectric permittivity of electrostrictive polymer, the particles of PZT have been incorporated in order to increase the conversion efficiency of the composite. Dielectric characterization tests showed an increase in dielectric permittivity by a factor of 4.5 compared to pure polymer. Experimental measurements of harvested power validate the analytical model and demonstrate a good correlation between the two data. An equivalent of an electrical scheme has been developed, which allows modeling the two behaviors. The harvested power density under low frequency at 2% of strain can reach 0.30 μW/cm³ for 33% of PZT without the polarization field, including the conversion efficiency becomes higher. The energy harvester property of this material composite has excellent potential for several self‐powered applications such as wireless sensor networks and the internet of things.     

Application of the Taguchi method to investigate the effects of experimental parameters in hydrothermal synthesis of Na-P1 zeolite from coal fly ash

Research on Chemical Intermediates - The aim of this study is to optimize the hydrothermal parameters to maximize Na-P1 (Na6Al6Si10O32·12H2O) zeolite crystallization from fly ash using the L9...     

On the solution of the fractional nonlinear Schrödinger equation

We present the nonlinear Schrödinger (NLS) equation of fractional order. The fractional derivatives are described in the Caputo sense. The Adomian decomposition method (ADM) in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these schemes, the solution constructed in power series with easily computable components.     

A staggered control volume scheme for unstructured triangular grids

The purpose of this work is to introduce and validate a new staggered control volume method for the simulation of 2D/axisymmetric incompressible flows. The present study introduces a numerical procedure for solving the Navier–Stokes equations using the primitive variable formulation. The proposed method is an extension of the staggered grid methodology to unstructured triangular meshes for a control volume approach which features ease of handling of irregularly shaped domains. Two alternative elements are studied: transported scalars are stored either at the sides of an element or at its vertices, while the pressure is always stored at the centre of an element. Two interpolation functions were investigated for the integration of the momentum equations: a skewed mass-weighted upwind function and a flow-oriented exponential shape function. The momentum equations are solved over the covolume of a side or of a vertex and the pressure–velocity coupling makes use of a localized linear reconstruction of the discontinuous pressure field surrounding an element in order to obtain the pressure gradient terms. The pressure equation is obtained through a discretization of the continuity equation which uses the triangular element itself as the control volume. The method is applied to the simulation of the following test cases: backward-facing step flow, flow over a two-dimensional obstacle and flow in a pipe with sudden contraction of cross-sectional area. All numerical investigations are compared with experimental data from the literature. A grid convergence and error analysis study is also carried out for flow in a driven cavity. Results compared favourably with experimental data and so the new control volume scheme is deemed well suited for the prediction of incompressible flows in complex geometries. © 1997 John Wiley & Sons, Ltd.     

Synthesis of thiadiazoles and 1,2,4-triazoles derived from cyclopropane dicarboxylic acid

New heterocyclic derivatives of cyclopropane dicarboxylic acid comprising thiadiazole and 1,2,4-triazole moieties are reported. Reaction of 1,1-cyclopropane dicarboxylic acid (1) with thiosemicarbazide and phosphorous oxychloride resulted in 1,1-bis (2-amino-1,3,4-thiadiazol-5- yl)cyclopropane (2). Cyclopropane dicarboxylic acid thiosemicarbazide (6) was converted into 1,1-bis(3-thio-4H-1,2,4-triazol-5-yl) cyclo- propane (7) by ring closure in an alkaline medium. The thiadiazole 2 and the triazole 7 were converted into a variety of derivatives.     

Benzimidazole condensed ring systems. 4. New approaches to the synthesis of substituted pyrimido[1,6-a]-benzimidazole-1,3(2H,5H)-diones

The synthesis of some substituted 1,3-dioxopyrimido[1,6-a]benzimidazole-4-carbonitriles 6a,b and 4-ethyl carboxylates 6c,d through condensation of 1H-benzimidazole-2-acetonitriles 3a,b and ethyl 1H-benzimidazole-2-acetates 3c,d , respectively, with ethoxycarbonyl isocyanate 4 are reported. The esters 6c,d were also obtained by condensing 3c , or d with chlorosulfonyl isocyanate 7. The alkylation of 5 and 6 with trimethyl or triethyl phosphate 9a , or b to obtain the N,N-dialkyl derivatives 10a-e and 11 are also described. Representative compounds were tested against P-388 lymphocytic leukemia in mice and for herbicidal and plant fungicidal activities but were inactive.     

Exact Solutions of Fractional-Order Biological Population Model

In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.     

Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method

In this paper, we use Mittag-Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.