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Category: Issue 1

On bilateral generating functions involving modified Jacobi Polynomials from the group –theoretic view point

A. K. CHONGDAR1 and C.S. BERA2
1Department of Mathematics, Bengal Engineering and Science University, Shibpur. P.O. Botanic Garden, Howrah-(INDIA)
2Department of Mathematics, Bagnan college, P.O. Bagnan, Howrah-711303 (INDIA)

ABSTRACT:

In this note, we have obtained some novel results on bilateral generating functions involving P( n, ) (x) n k , a modified form of Jacobi Polynomials by group theoretic method. In fact, in section 1, we have introduced a linear partial differential operator R which do not seem to have appeared in the earlier investigations and then we have obtained the extended form of the group generated by R. Finally, in section 2, we have obtained a novel generating relation involving the polynomial under consideration with the help of which, we have proved a general theorem on bilateral generating relations of P( n, ) (x) n kSome particular cases of interest are also discussed.

KEYWORDS: Bilateral generating relation, Jacobi Polynomials, AMS-2000 classification code : 33C65


In this note, we have obtained some novel results on bilateral generating functions involving P( n, ) (x) n k , a modified form of Jacobi Polynomials by group theoretic method. In...

Motions in a Riemannian space and some integrability conditions

K.S. RAWAT and MUKESH KUMAR
Department of Mathematics H.N.B.Garhwal University CampusBadshahi Thaul, Tehri (Garhwal)-Uttarakhand (INDIA)
Email-mukesh.nautiyal2@gmail.com

ABSTRACT:

Knebelman1 studied and defined collineations and motions in generalised spaces. Levine3 studied motions in linearly connected two dimensional spaces. Takano2, studied on the existence of affine motion in a space with recurrent curvature tensor. Further, Negi and Rawat6 studied affine motion in an almost Tachibana recurrent space. Rawat and Dobhal9, studied on Projective motion in a Tachibana symmetric space
.
In the present paper, we have studied Affine motion, Projective motion, Conformal motion, Integrability conditions of Killing equations also several theorems have been established and proved therein.

KEYWORDS: Riemannian space


Knebelman1 studied and defined collineations and motions in generalised spaces. Levine3 studied motions in linearly connected two dimensional spaces. Takano2, studied on the existence of affine motion in a space with recurrent...

Common fixed point theorems for two mappings in fuzzy metric space

RAJESH KUMAR MISHRA*, SANJAY CHOUDHARY ** and RAJESH SHRIVASTAVA
*HOD-Deptt. of Mathematics. BERI., Bhopal, M.P. (INDIA)
**H.O.D-Deptt.of Mathematics, Govt. P.G. N. M. V. Hoshangabad, M.P. (INDIA)
H.O.D. Department of Mathematics Govt Science and Commerce College Benazir, Bhopal, M.P. (INDIA

ABSTRACT:

The concept of fuzzy sets was introduced initially by Zadeh in 1965. Georgeand Veeramani3 modified the concept of fuzzy metric space introduced5. Fisher2, Aliouche and Fisher1, Telci10 proved some related fixedpoint theorems in compact metric spaces. Recently, Rao et. al.7 proved8,9 some fixed point theorems in sequentially compact fuzzy metric spaces.Motivated by a work due to Popa6, we have observed that proving fixed point theorems using an implicit relation is a good idea since it covers several contractive conditions rather than one contractive condition.

KEYWORDS: fuzzy metric space, fixed point theorems


The concept of fuzzy sets was introduced initially by Zadeh in 1965. Georgeand Veeramani3 modified the concept of fuzzy metric space introduced5. Fisher2, Aliouche and Fisher1, Telci10 proved some related fixedpoint theorems in compact...

A Note on the form of Wave Equation used in Harish-Chandra’s Paper ‘Motion of an Electron in the Field of a Magnetic Pole

VINOD KUMAR YADAV
Senior Research Fellow (CSIR), Department of Mathematics, V.S.S.D. (P.G.) College, Kanpur-208002, U.P. (INDIA)
E-mail: vinodkumaryadav3@gmail.com

ABSTRACT:

In this paper we have tried to go through the research paper1 of Prof. Harish-Chandra with the intention of getting some idea of method of thinking and working of that great mathematician as well as of his Ph.D. thesis supervisor Prof. P.A.M. Dirac. The wave equation for the motion of an electron derived by Dirac2,3 has been transformed to the form suitable to the problem under consideration by Harish-Chandra. It is interesting and enjoying to clarify the steps directly written by him. For us it is a great job to fill the gaps to verify his steps. This paper is consequence of our effort in this direction.

KEYWORDS: Wave function, Hamiltonian, Wave equation, Pauli operators, Magnetic pole, Metric tensor 2010 Mathematics Subject Classification Number: 81-02, 81R15.


In this paper we have tried to go through the research paper1 of Prof. Harish-Chandra with the intention of getting some idea of method of thinking and working of that great...

Analysis of the problems faced by poor rural students studying in chennai city Colleges using FCM models

FR K. AMAL S. J.1 and LILLIES THIVAGAR2
1Loyola College Chennai-34 (INDIA)
2Arul Ananthar College Karumathur, Madurai (INDIA)

ABSTRACT:

In this paper for the first time we study the problems faced by poor rural students studying in Chennai city colleges using Fuzzy Cognitive Maps (FCMs) model. This paper has four sections. In section, one the problems faced by these students as taken from data collected from them is described and justification for using FCMs is also given. Section two briefly describes the FCM model. Section three gives the two FCM models given by students and the teachers. The hidden pattern and the conclusions based on this study is given in the final section

KEYWORDS: FCM, hidden pattern, thresholding, updating, adjacency matrix, state vectors, limit cycle, fixed point


In this paper for the first time we study the problems faced by poor rural students studying in Chennai city colleges using Fuzzy Cognitive Maps (FCMs) model. This paper has four...

Bianchi type I inflationary cosmological model with cosmological constant 

RAJ BALI* and SWATI
Department of Mathematics University of Rajasthan, Jaipur – 302004 (INDIA)
*E-mail : balir5@yahoo.co.in

ABSTRACT:

Inflationary cosmological model with cosmological constant in the structure of Bianchi Type I space-time is investigated. To get the deterministic model of the universe, it has been assumed that ABC=e3Ht and V() = constant, where A,B,C are metric potentials, H the Hubble constant, V the flat potential,  the Higg’s field. It is found that inflationary scenario exists in Bianchi Type I space-time, the Higg’s field decreases with time, the cosmological constant decreases with time and  tends to constant quantity when t  . Since shear   0 for large values of t, hence anisotropy is maintained for large values of t. However, when a=0, d = 0 then the model isotropizes. The physical aspects of the model in context to inflationary scenario are also discussed

KEYWORDS: Bianchi I, Inflationary, Cosmological, CosmologicalConstant () PACS Nos.: 04.20.-q, 04.020 jb, 04.20.Dv, 04.20. Ex


Inflationary cosmological model with cosmological constant in the structure of Bianchi Type I space-time is investigated. To get the deterministic model of the universe, it has been assumed that...

On some generating functions of modified jacobi polynomials

C.S. BERA and A.K.CHONGDAR*
1Department of Mathematics, Bengal Engineering and Science University, Shibpur. P.O. Botanic Garden, Howrah- (INDIA)
E mail- chongdarmath@yahoo.co.in

ABSTRACT:

n this note, we have obtained a novel extension of a theorem on bilateral generating function of modified Jacobi polynomials from the existence of quasi – bilateral generating function by group theoretic method.

KEYWORDS: generating functions, Jacobi polynomials. AMS Subject Classification Code : 33A65 , 33A75.


n this note, we have obtained a novel extension of a theorem on bilateral generating function of modified Jacobi polynomials from the existence of quasi – bilateral generating function by group...

On the existence of supremum and infimum of fuzzy random variables

J. EARNEST LAZARUS PIRIYAKUMAR1 and M. VASUKY2
1Department of Mathematics, Tranquebar Bishop Manickam Lutheran College, Porayar – 609 307, S. India
2Department of Mathematics, Seethalakshmi Achi College for Women, Pallathur – 630 107, S. India
Email1: jelpriyakumar@yahoo.com

ABSTRACT:

This paper investigates upon the characteristics on the existence of supremum and infimum of fuzzy random variables. This paper provides an improved version of the supremum and infimum of fuzzy random variables which plays a crucial role in the theoretical framework of the same. Finally the existence of supremum and infimum of the level continuous fuzzy valued measurable functions on a closed interval is examined and a necessary and sufficient condition with which
its supremum and infimum can be attained, is provided

KEYWORDS: Fuzzy random variables, Fuzzy numbers, Fuzzy valued functions.


This paper investigates upon the characteristics on the existence of supremum and infimum of fuzzy random variables. This paper provides an improved version of the supremum and infimum of...

Order-dimensional topological spaces

*KIRAN SHRIVASTAVA, **VIJETA IYER and ***ABHA GOLHANI
*Department of mathematics, S.N.G.G.P.G. College, Bhopal (INDIA)
**Department of mathematics, S.N.G.G.P.G. College, Bhopal (INDIA)
***Department of mathematics, S.N.G.G.P.G. College, Bhopal (INDIA)
*Email: kiranshri_1@rediffmail.com
**Email: vijeta_iyer@yahoo.com

ABSTRACT:

In is paper order – dimensional topological spaces are introduced. Several basic properties relating to order – dimension defined in terms of order of elements are established. The definitions of order of an element and of a set in a topological space are taken from4 and 5 respectively.

KEYWORDS: order of an element, order of a set, order of a topology, finite order dimensional, order topological dimension Subject Classification : AMS (2000) : 54 A 99.


In is paper order – dimensional topological spaces are introduced. Several basic properties relating to order – dimension defined in terms of order of elements are established. The definitions of order...

A Solution of Longitudinal dispersion of miscible fluid flow through porous media by Bender-Schmidt method

TWINKLE SINGH
AMHD, SVNIT, Surat-395007 (INDIA)
Applied Mathematics and Humanites Department Sardar Vallabhbhai National
Institute of Technology Surat-395.007, Gujarat (INDIA

Email:-twinklerpatel@gmail.com

ABSTRACT:

The present paper discusses the solution of longitudinal dispersion of miscible fluid flow in porous media by numerical
method.

KEYWORDS: Longitudinal dispersion ,Bender-Schmidt method


The present paper discusses the solution of longitudinal dispersion of miscible fluid flow in porous media by numerical method.