ABSTRACT: The object of this paper is to establish a general Eulerian integral involving the multivariable Aleph-function and multivariable I-function which provides unification and extension of numerous results. Several particular cases will be studied.

Mathematical Expressions of MHD Couette Flow in a Rotating System and Homotopy Analysis Method K. M. Dharmalingam, M. Subha

ABSTRACT: In this article, we have considered the first and second law of thermodynamics to investigate the flow and thermal decomposition in a variable viscosity couette flow of conducting fluid in a rotating system under the combined effect of magnetic field and Hall current. The non-linear differential equations are solved analytically. The analytical expressions of dimensionless fluid velocity and temperature profiles are derived by using the Homotopy analysis method. We also derived the analytical expressions of the entropy generation rate, Bejan number, Skin friction coefficients and Nusselt number. The graphical representations of temperature, velocity, entropy generation rate, Bejan number, Nusselt number and Skin friction coefficients are also presented by various values of thermophysical parameters. The entropy production is more at the lower fixed plate region while the effect of heat transfer irreversibility at the upper moving plate region increased by fluid rotation.

On Third Hankel Determinant for a Subclass of Analytic Functions Subordinate to a Bilinear Transformation Gagandeep Singh and Gurcharanjit Singh

ABSTRACT: In this paper we investigate the third Hankel H_{3}(1) determinant for normalized univalent functions belonging to the class R(α; A,B) in the unit disc E={z:|z|<1}. The class includes very important subclass of the family of univalent functions- the class of functions whose derivative has a positive real part denoted by R. Our results therefore includes the special cases of the third Hankel determinants for the two classes of functions.

Mean Square Calculus for Cauchy Problems Stochastic Heat and Stochastic Advection Models M.E. Fares, M.A. Sohaly, M.T. Yassen, I.M. Elbaz

ABSTRACT: In this paper, the solutions of Cauchy problems for the stochastic advection and stochastic diffusion equations are obtained using the finite difference method. In the case when the flow velocity is a function of stochastic flow velocity and also, the diffusion coefficient in the stochastic heat equation is a function of stochastic diffusion coefficient, the consistency and stability of the finite difference scheme we are used need to be performed under mean square calculus.

A Class of Improved Ratio Estimators for Population Mean Using Conventional Location Parameters Mir Subzar, Muhammad Abid, S. Maqbool, T. A. Raja, Mir Shabeer, B A Lone

ABSTRACT: In sample surveys, it is usual to make use of auxiliary information to increase the precision in estimating the population parameters to be estimated. In the present paper we propose a new class of improved ratio type estimators in simple random sampling without replacement for estimating finite population mean using the linear combinations of population deciles, median and correlation coefficient, coefficient of variation of the auxiliary variable, obtain their mean square error (MSE), bias and compare with the existing estimators. By this comparison we conclude that our proposed estimators are more efficient than the existing estimators. Numerical study is provided to support the theoretical results.

Some Oscillation Criteria for a Class of Third Order Nonlinear Damped Differential Equations O. MOAAZ, E. M. ELABBASY, AND E. SHAABAN

ABSTRACT: The present study concerned with trinomial delay differential equation of third-order with the hypothesis that the differential equation of second-order is nonoscillatory. By means of a generalized Riccati transformation technique, we established new oscillation results for this equation. An example is provided to illustrate the fundamental results.

ABSTRACT: We have considered the β−change of Finsler metric L →L given by L = f(L, β), where f is any positively homogeneous function of degree one in L and one-form β. The purpose of the present paper is to find the condition under which a β−change of Douglas space becomes a Douglas space. We have also found the necessary and sufficient condition under which a β−change becomes a projective change.

How to Find Determinants by Using Exponential Generating Functions Masreshaw Walle Abate

ABSTRACT: As we know, let alone to find the determinant of infinite matrix, it is difficult to find the determinant of some n x n matrixes by the usual methods like, the cofactor method and Crammer’s rule. But now we will show how to find the determinant of some n x n matrices and how to find the determinant of some infinite matrix by using Exponential Generating Functions. In this paper we will consider matrices having 1, 2, 3, 4, 5,…on the supper diagonal, 0"s on the upper and identical entries on each diagonal below the supper diagonal. Here we will try how to obtain the determinant of n x n upper left corner sub matrix of a given infinite matrix by introducing Exponential Generating functions of some sequences and how to get a sequence by calculating the determinant of n x n upper left corner sub matrix of infinite matrix. We will also check the correctness of the determinant by using Numerical method.