Issue 4 − B Volume 3 (2015)

ISSUE 4 − A ISSUE 4 − B ISSUE 4 − C ISSUE 4 − D ISSUE 4 − E ISSUE 4 − F
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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 : 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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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 : A New Chain Ratio-Ratio-Type Exponential Estimator Using Auxiliary Information in Sample Surveys
Country : India
Authors : Housila P.Singh || Surya K.Pal

Abstract: This paper advocates the problem of estimating the finite population mean using auxiliary information in sample surveys. We have suggested a new chain ratio-ratio- type exponential estimator and its properties are studied up to first degree of approximation. It has been shown that the proposed estimator is more efficient than the usual unbiased estimator, classical ratio estimator, Bahl \cite{(1991b)} ratio-type exponential estimator and Kadilar \cite{(2003k)} chain ratio-type estimator under very realistic condition. Generalized version of the suggested chain ratio-ratio-type estimator is also given alongwith its properties. An empirical study is given in support of the present study.

Keywords: Study variate, Auxiliary variate, Chain ratio ratio-type exponential estimator, Bias, Mean squared error.

Surya K.Pal
School of studies in Statistics, Vikram University, Ujjain, M.P, India.
E-mail: suryakantpal6676@gmail.com


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Article Type : Research Article
Title : The Minimum Monopoly Energy of a Graph
Country : India
Authors : Ahmed Mohammed Naji || N.D.Soner

Abstract: In a graph $G(V,E)$, a subset $M \subseteq V(G)$ is called a monopoly set of $G$ if every vertex $v\in V - M$ has at least $\frac{d(v)}{2}$ neighbors in $M$. The monopoly size of $G$ is the minimum cardinality of a monopoly set among all monopoly sets in $G$, denoted by $mo(G)$. In this paper, we introduce minimum monopoly energy, denoted $E_M(G)$, of a graph $G$ and computed minimum monopoly energies of some standard graphs. Upper and lower bounds for $E_M(G)$ are established.

Keywords: Monopoly Set, Monopoly Size, Minimum Monopoly Matrix, Minimum Monopoly Eigenvalues, Minimum Monopoly Energy of a Graph.

Ahmed Mohammed Naji
Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru, India.
E-mail: ama.mohsen78@gmail.com


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Article Type : Research Article
Title : $(1,2)^\star$-$g^\star$-Closed Sets
Country : India
Authors : O. Ravi || M. Jeyaraman || M. Sajan Joseph || R. Muthuraj

Abstract: The aim of this paper is to introduce a new class of sets namely $(1,2)^\star$-$g^\star$-closed sets in bitopological spaces. This class lies between the class of $\tau_{1,2}$-closed sets and the class of $(1,2)^\star$-g-closed sets. The complement of an $(1,2)^\star$-$g^\star$-closed set is called an $(1,2)^\star$-$g^\star$-open set. Moreover we introduce two new spaces namely, $(1,2)^\star$-T$_{g}^\star$-spaces and $(1,2)^\star$-$_{g}$T$_{g}^\star$-spaces.

Keywords: $(1,2)^\star$-$g^\star$-closed set, $(1,2)^\star$-$g^\#$-closed set, $(1,2)^\star$-$\alpha g$-closed set, $(1,2)^\star$-T$_{1/2}$-space, $(1,2)^\star$-T$_{g}^\star$-space, $(1,2)^\star$-$_{g}$T$_{g}^\star$-space.

O. Ravi
Department of Mathematics, P. M. Thevar College, Usilampatti, Madurai Dt, Tamil Nadu, India.
E-mail: siingam@yahoo.com


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Article Type : Research Article
Title : Voronovskaja Type Asymptotic Approximation by General Gamma Type Operators
Country : India
Authors : Alok Kumar

Abstract: In the present paper, we studied the voronovskaja type theorem for general Gamma type operators. Also, we obtain an error estimate for general Gamma type operators.

Keywords: General Gamma type operators, Voronovskaja type theorem, Approximation order, Modulus of continuity.

Alok Kumar
Department of Computer Science, Dev Sanskriti Vishwavidyalaya Haridwar, Haridwar, India.
E-mail: alokkpma@gmail.com


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Article Type : Research Article
Title : Compactness on Rough Intuitionisitic Fuzzy Structure Subgroup Space
Country : India
Authors : H.Jude Immaculate || I.Arockiarani

Abstract: This paper aims to initiate the notion of rough intuitionistic fuzzy compact subgroup, rough intuitionistic fuzzy extremal compact spaces in the light of rough intuitionistic fuzzy sets. We characterize rough intuitionistic structure subspace space by applying various topological notions.Few of its properties are discussed.

Keywords: Rough intuitionistic fuzzy compact subgroup, Rough intuitionistic fuzzy extremal compact spaces, Intuitionistic fuzzy sets.

H.Jude Immaculate
Department of Mathematics, Nirmala College for Women, Coimbatore, Tamil Nadu, India.
E-mail: juderaj.h@gmail.com