iosr-Jm   Volume-11 ~ Issue-4 ~ July-Aug 2015

Abstract: The purpose of this paper is to extend and improve fixed point theorem on cone2- metric spaces for contractive mapping. Our results generalize and unify some well know results in the literature of [15].

Key words: Cone 2- metric spaces, contractive mappings, fixed point, non- normal cone, contractive mapping

[1]. Banach'sSur les operations dans les ensembles abstraits et leur applications aux equations integrals, fundamental mathematicae,3(7), .(1922), 133-181.
[2]. S. Gahler, 2-metricsche Raume und ihre topologische structure, Math. Nachr. 26(1963),115-148.
[3]. S. Gahler, Uber die Uniformisierbarkeit 2-metricsche Raume, Math. Nachr. 28(1995),235-244.
[4]. S. Gahler, Zur geometric 2-2-metricsche Raume, Revne Roumaine der Mathem. Pures e tAppliques, 11(1966), 665-667.
[5]. K. Iseki, Fixed point theorems in 2-metric spaces, Math. Seminar Notes, Kobe Univ., 3 (1975), 133-136.

Abstract: This research work tends to describe volatility in the consumer prices of some selected commodities in Nigerian market. This is achieved by examining the presence or otherwise of the volatility in their prices using ARCH and GARCH models with the monthly Consumer Price Index (CPI) of five selected commodities over a period of time (1997 – 2007) collected from National Bureau of Statistics, Headquarters, Abuja. The data obtained were analyzed using MS-Excel and E- view software packages. Akaike information Criteria (AIC) and Bayesian Information Criteria were used to test the adequacy of the models. Langragean Multiplier test was also used to test for the presence of ARCH effects and the data for the prices showed varying degree of ARCH effects.

Keywords: Volatility, Inflation Rates, ARCH, GARCH, Volatility Clustering

[1]. Abbasali, K.M., Asokan, M.V. and Shojaeddin, C. (2000): ARCH and GARCH Models, Waterlo University, Canada
[2]. Adedayo, A.O. (1998): Understanding Statistics, JAS Publishers Ltd, Lagos
[3]. Andre, F. (2004): Business Mathematics and Statistics, 6th Edition, Ashford Colour Press Gosport Hampshire, U.K.
[4]. Anyawu, J.C. (1993): Monetary Economics; Theory, Policy and Institution, 1st Edition, Hybrid Publisher Ltd., Onitsha, Nigeria.
[5]. Ari, A. and Francisco, J.V. (2006): International Monetary Fund Working Paper, WP/06/212, Asian Pacific Department.
[6]. Bera, A.K. and Higgins, M.L. (1993): "‟ARCH models; Properties, Estimation and Testing‟‟, Journal of Econometrics surveys, vol. 7 No.4, pp. 307 – 366..

Abstract: Motivated by some results on orthogonal derivations of semiprime rings, in2, orthogonal reverse derivations on semiprime gamma rings, in 9 and introduction of semiderivations in 7, we, authors have defined the notion of orthogonal semiderivations on semiprime semirings. We also investigated some necessary and sufficient conditions for two semiderivations to be orthogonal.

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[3]. Posner E.C, Derivation in Prime rings, American math soc., 8, 1957, 1093-1100. http://dx.doi.org/10.1090/s0002-9939-1957-
0095863-0.
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[5]. Chuang, Chen-Lian, On the structure of semiderivations in prime rings, Proc.Amer.Math.Soc., 108(4),(1990, 867-869.
[6]. Alev Firat, Some Results For Semi derivations Of Prime Rings, International Journal of Pure and Applied Mathematics., 28(3),
2006, 363-368.

Abstract: This paper deals with the study of Ruban's cosmological model in presence of bulk stress source in the framework of General theory of relativity. Exact solution of Einstein's field equations are obtained by using a supplementary condition between metric potentials and curvature parameter k . The viscosity coefficient of bulk viscous fluid is assumed to be a simple power function of mass density whereas the coefficient of shear viscosity is consider as proportional to the scale of expansion in the model. The time dependent  -term is found to be positive and is a decreasing function of time. Also some physical and geometrical properties of the
model are discussed.
Keywards: Ruban's space time, viscous fluid models: variables  -term.

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Abstract: In this paper, we prove Hyers-Ulam Stability of a class of Quadratic and Cubic functional equations in Paranormed spaces.
Keywords: Hyers-Ulam Stability, Quadratic Functional Equations, Cubic Functional Equations, Paranormed Spaces

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Abstract: In this Paper, we study of an implicit finite-difference technique is applied to study on effects of hall current on the magneto hydrodynamic flow through porous medium past an infinite vertical plate oscillating in its plane in the presence of a temperature gradient dependent heat source. The results are obtained for velocity and temperature profiles. The numerical results are presented graphically for different values of the parameters entering into the problem.

Key words : Finite difference scheme, porous medium, MHD, heat source, heat transfer, hall current

[1]. Stokes, G.G., 1851, On the effect of the internal friction of fluids on the motion of pendulums: Cambridge Philosophical Society, Transactions, v. 9, no. 8, p.287.
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Abstract: In this paper, we studied the theory of fuzzy rings, the concept of fuzzy ring with operators, fuzzy ideal and anti-fuzzy ideal with operators, fuzzy homomorphism with operators etc., and their some elementary properties.

Keywords: Fuzzy rings, fuzzy ring with operators, fuzzy ideal with operators, anti-fuzzy ideal, and homomorphism.

[1]. W.J.Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and systems 8 (1982), 133-139.
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Abstract: In this paper we investigate the existence, equivalence and some other features of [5,3]error correcting codes overGF(7) .
Key-Words: Linear code, generator matrix, equivalent code.

[1]. Pless, V. (2003) Introduction to the Theory of Error Correcting Codes, Wiley Student Edition, John Wiley & Sons (Asia) Pte. Ltd.,
Singapore.
[2]. Hill, R. (1986) A First Course in Coding Theory, The Oxford University Press, Oxford, UK.
[3]. Huffman,W.C. and Pless,V. (2003) Fundamentals of Error Correcting Codes, Cambridge University Press, New York.

Abstract: One of the most widely known topological descriptors is the Wiener index or (Wiener number) named after American chemist Harold Wiener in 1947. Wiener number of a connected graph G is defined as the sum of the distances between distinct pairs of vertices of G..It correlates between physico- chemical and structural properties. Recently an edge version of Wiener Index was introduced by Ali Iranmanesh.In this paper, we have determined Wiener numbers of link of graphs.

Keywords: distance sum , edge Wiener index ,link of graph, topological indices.

[1] Trinajsti N., Chemical Graph Theory, CRC Press, Boca Raton, FL, 1983; 2nd revised edition, 1992.
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Abstract: The aim of this paper is to introduce and study hyperconnectedness in supra topological spaces, which we called, supra hyperconnectedess and denoted by  * S hyperconnectedness. Several characterizations of supra hyperconnectedness are provided. We give conditions under which supra hyperconnectedness is preserved. Further, we introduce and study strong forms of supra hyperconnected spaces and obtain some characterizations of hyperconnected spaces.
Keywords: supra topology, supra open set, hyperconnectedness,  * S hyperconnectedness,  * S dense.

[1]. Mashhour, A. S., Allam A. A., Mahmoud F. S., Khedr F. H, On supra topological spaces, Indian J. Pure and Appl. Math. 14(4),
(1983), 502- 510.
[2]. Devi, R. S., Sampathkumar and Caldas M., On supra  - open sets and  -contiuous maps. General Mathematics, 16(2), (2008),
77- 84.
[3]. Arockiarani, I., On generalized b- regular closed sets in supra topological spaces. Asian J. of Current Engineering and Maths.,
(2012),1(1): 1-4.
[4]. Sayed O. R. and Noiri T., On supra b- open sets and supra b- continuity on topological spaces. European Journal of Pure and
Applied Mathematics, 3(2), (2010), 295- 302.
[5]. Ravi, O. G., Ramkumar and M. Kamaraj, On supra  - open sets and supra- continuity on topological spaces. Proceedings of UGC
Sponsored National Seminar on Recent Developments in Pure and Applied Mathematics, Sivakasi, India, (2011), 20- 21.