Volume 3 (2015) Article in Press

ISSUE 4 − A ISSUE 4 − B
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Article Type : Research Article
Title : An Exact solution of Diffusion Equation with boundary conditions by Pade-Laplace Differential Transform Method
Country : India
Authors : Kiranta Kumari || Praveen Kumar Gupta || Gauree Shanker

Abstract: In this paper, we solve Diffusion equation with boundary conditions analytically by using a combined form of Laplace transform method and differential transform method (DTM) and Pade approximation. The aim of using the Laplace transform is to overcome the deficiency that is caused by unsatisfied boundary conditions in using differential transform method. The combined method is capable to handle diffusion equation with boundary conditions. The solutions obtained by proposed method are compared with the known exact solutions and found that our solutions are in good agreement with the known exact solutions. The obtained results show the simplicity of proposed method and massive reduction in calculations.

Keywords: Diffusion equation, Boundary condition, Laplace transforms, DTM, LDTM, Pade approximation.

Kiranta Kumari
Department of Mathematics \& Statistics, Banasthali University, Banasthali, Rajasthan, India.
E-mail: kiranta.bu@gmail.com


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Article Type : Research Article
Title : Analysis of Dual-Matrix Approach for Solving the Transportation Problems
Country : India
Authors : Vijay Sharma || Dr. Chandra Bhusan Sharma

Abstract: A transportation decision problem is considered. The existence of solution and characterization of solution space are established. The dual behavior of transportation problem is studied. The step by step procedure is described and an algorithm is proposed to solve the transportation problem. The whole procedure is illustrated step by step through a numerical example.

Keywords: Linear programming models, Transportation problem, Dual- Matrix, Dual simplex.

Vijay Sharma
Department of Mathematics, BBM College Okari, Jehanabad, (M.U.), India.
E-mail: vijaysharma0262@gmail.com


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Article Type : Research Article
Title : Lagrange Formalism for Electromagnetic Field in Terms of Complex Isotropic Vectors
Country : Rwanda
Authors : Dr.Bulikunzira Sylvestre

Abstract: In previous works, Weyl´s equation for neutrino has been written in tensor form, in the form of non-linear Maxwell´s like equations, through complex isotropic vector( F) ⃗=E ⃗+iH ⃗. It has been proved, that the complex vector F ⃗=E ⃗+iH ⃗ satisfies non-linear condition( F) ⃗^2=0, equivalent to two conditions for real quantities E ⃗^2-H ⃗^2=0 and( E) ⃗.H ⃗=0, obtained by separating real and imaginary parts in the equality( F) ⃗^2=0. Further, it has been proved, that Maxwell's equations can also be written through complex vector( F) ⃗=E ⃗+iH ⃗. However, in the general case, the solution of Maxwell's equations does not satisfy non-linear condition( F) ⃗^2=0. In this work, in the development of this new tensor formalism, we elaborated the Lagrange formalism for electromagnetic field in terms of complex isotropic vectors.

Keywords: Electromagnetic field, Lagrange formalism, complex isotropic vector.

Dr.Bulikunzira Sylvestre
University of Rwanda, University Avenue, B.P 117, Butare, Rwanda.
E-mail: S.BULIKUNZIRA@ur.ac.rw


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Article Type : Research Article
Title : Identifying the Elementary Concepts of Algebra and Their Rank Orders Used in I.C.S.E. Examination
Country : India
Authors : Dr. Sk. Samsul Alam

Abstract: In this paper, an attempt has been made to identify top forty four elementary concepts of algebra and their rank orders which were used to solve the mathematical problems of two question papers of mathematics of Indian Certificate of Secondary Education (I.C.S.E.) Examination (2005 & 2006) of The Council for the Indian School Certificate Examination (C.I.S.C.E.) through task analysis technique. This study has emphasized to remove the conceptual gaps in mathematics text books. The teachers as well as learners will be benefited in several ways like to diagnose the weakness of the learners, to find the difficult order of these concepts, to emphasize on the learning of these concepts at appropriate grade levels etc. after knowing these elementary concepts.

Keywords: Identifying, major concept, elementary concept, algebra, text book scanning process, task analysis technique, mathematics question papers.

Dr. Sk. Samsul Alam
Assistant Teacher, Silut Basantapur High School, Sahapur Basantapur, Burdwan, West Bengal, India.
E-mail: samsulalam_s@yahoo.in


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Article Type : Research Article
Title : Double Generating Functions for Jacobi and Laguerre Polynomials of Several Variables
Country : Yemen
Authors : Ahmed Ali Atash

Abstract: The aim of the present paper is to obtain some double generating functions for Jacobi and Laguerre polynomials of several variables. Some deductions from these results lead us to obtain a number of double generating functions for Sister Celine’s polynomials of two variables. A number of interesting special cases of our main resultsare also considered.

Keywords: Generating functions, Jacobi polynomials, Laguerre polynomials, Sister Celine’s polynomials, Multivariable extension of the Kampé de Fériet function.

Ahmed Ali Atash
Department of Mathematics, Aden University, Yemen.
E-mail: ah-a-atash@hotmail.com



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