iosr-Jm   Volume-10 ~ Issue-5 ~ Sep-Oct 2014

Abstract: In this paper we establish a common fixed point theorem for six self of occasionally weakly compatible maps in dislocated metric space which generalizes and improves similar fixed point results. Mathematics Subject Classification: 47H10, 54H25

Keywords: dislocated metric, weakly compatible maps, common fixed point, occasionally weakly compatible maps

[1]. A. Isufati, Fixed Point Theorem in Dislocated Quasi-Metric Space, Ap-plied Math. Sci., 4 (5),(2010), 217-223.
[2]. C. T. Aage and J. N.Salunke, The Results on Fixed Points theorems in Dislocated and Dislocated Quasi-Metric Space, Applied Math. Sci., 2 (59)(2008), 2941 - 2948.
[3]. C. T. Aage and J. N. Salunke, Some Results of Fixed Point Theo-rem in Dislocated Quasi-Metric Spaces, Bull. Marathwada Math. Soc., 9 (2),(2008),1-5.
[4]. F. M. Zeyada, G. H. Hassan and M. A. Ahmed, A Generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces, The Arabian J. Sci. Engg., 31 (1A)(2006), 111-114.
[5]. G. Jungck and B.E. Rhoades, Fixed Points For Set Valued Functions without Continuity, Indian J. Pure Appl. Math., 29 (3)(1998), 227-238

Abstract: The present research is aimed at analyzing rainfall pattern and classification to evaluate the district wise data in Tamilnadu and make possible the result in various seasons to understand the climate change. The dataset relates to monthly rainfall from various districts of Tamilnadu in the period of January to December from the Indian Meteorological Department database. The time frame of the data pertaining to the present study is 2004-2010. The salient feature of this study is the application of Factor Analysis, K-means clustering and GIS (Geographical Information System) Map as data mining tools to explore the hidden pattern present in the dataset for each of the study periods. Factor analysis is applied first and the factor scores of extracted factors are used to find initial groups by k-means clustering algorithm. Finally, data mining tools are applied and the groups are identified as rainfall belonging to ER (Excess Rainfall), NR (Normal Rainfall) and DR (Deficient Rainfall). The results of the present study indicate that Data Mining Tools can be used as a feasible tool for the analysis of large set of rainfall data.

Keywords: Rainfall, Data mining, Factor Analysis, GIS Map and K-means clustering

[1] Anderson T W (1984), An Introduction to Multivariate Statistical Analyis, 2/e, John Wiley and Sons, Inc., New York.

[2] M.C.Ramos.2001.Rainfall distribution pattern and their over time in a Mediterranean area. Theoretical and Applied Climatology.69.163170.

[3] Pramanik, S.K., and Jagannathan, P., (1954), Climate change in India – 1: rainfall. Indian Journal of Meteorology Geophysics , 4, 291–309.

[4] Parthasarathy, B., (1984), Inter annual and long term variability of Indian summer monsoon rainfall. In: Proceedings of the Indian Academy of Sciences (Earth Planetary Sciences), vol. 93, pp. 371–385.

[5] Parthasarathy, B., and Dhar, O.N., (1978), Climate Fluctuations Over Indian Region – Rainfall: a Review, vol. 31. Indian Institute of Tropical Meteorology, Pune. Research Report No. RR-025.

Abstract: Emergent evacuation in buildings becomes necessary in case of an accident such as fire, earthquake, toxic gas release etc. Bomb threat also makes it prudent for the occupants to escape out in a minimum possible time. Emergent evacuation is possible when minimum but adequate numbers of escape routes are available to the occupants for efficient movement and rapid evacuation. Inadequate size of routes creates bottlenecks and backtracking that may cause stampede, crushing and trampling. Therefore, it is imperative to examine the building design with respect to numbers & size of exits, stairwells and other substantial features of the building egress plan. Planning of the movement of people is of great importance to the safety measures. Therefore, the systematic scheduling for exit of occupant inside the building is the fundamental requirement for efficient evacuation to minimize the loss of life and avoiding the congestion, backtracking and circling. In this direction, many mathematical models have been developed to compute the evacuation time. In CBRI, attempts have been made to compute the possible time of evacuation with adequate number of escape routes of adequate size to avoid stampede, crushing and trampling. In this paper the attention has been drawn on the rapid evacuation of a building without bottlenecks in the escape routes. The model discussed here based on graph theoretical approach considering the parameters like Dynamic Capacity (DC) and Traversal Time Step (TTS) of each evacuation path. The waiting time for each path has also been minimized using queuing theory. For optimal utilization of paths, the service rate, throughput and response time of each path has also been considered.

Keywords: Evacuation, Escape Route, Egress, Network, Optimization, Mathematical Modeling

[1] I. Furin, Pedestrian planning and design, Metropolitan association of urban designers and environmental planners, New York, 1971
[2] L.G. Chalmet, R.L Francis and P.B. Saunders, Network Models For Building Evacuation, Management Science, Vol. 28, No. 1, pp. 86-105, January, 1982.
[3] R,L Francis, and L.G. Chalmet, A Negative Exponential Solution To An Evacuation Problem, Research Report No. 84-86, National Bureau of Standards, Center for Fire Research, Washington DC, 20234, October, 1984.
[4] T.M. Kisko, and R.L. Francis, EVACNET+: A Computer Program to Determine Optimal Building Evacuation Plans, Fire Safety Journal, 9:211-222, 1985.
[5] M.Y. Roytman,, Principles of Fire Safety Standards for Building Construction, published for the National Bureau of Standards, Washington, DC By Amerind Publishing Co., Pvt. Ltd. New Delhi, India, 1975.
[6] V.M. Predtechenskii and A.I. Milinskii, Planning for foot traffic flow in buildings, New Delhi, Amerind publishing co. pvt. Ltd., 1978

Abstract: In this paper, we study the concepts of generalized higher reverse derivation and Jordan generalized higher reverse derivation and Jordan generalized triple higher reverse derivation on -ring M. The aim of this paper is prove that every Jordan generalized higher reverse derivation of -ring M is generalized higher reverse derivation of M. Mathematics Subject Classification: 16U80, 16W25

Key word: -ring, prime -ring, semiprime-ring, derivation, higher derivation, generalized higher derivation of -ring, reverse derivation of R

[1]. M. Asci and S. ceran, "The commutativity in prime gamma rings with left derivation", International Mathematical ,Vol. 2, No.3, pp. 103-108, 2007.
[2]. W. E. Barnes "On The -rings of Nobusawa ", Pacific J . Math ,Vol. 18 ,PP .411-422, 1966.
[3]. M. Bresar and J. Vukman , On Some additive mappings in rings with involution, Aequation Math., 38(1989), 178-185.
[4]. Y. Ceven and M. A.Ozlurk" On Jordan Generalized Derivation in Gamma rings ", Hacettepe, J. of Mathematics and Statistics, Vol.33 ,pp. 11-14 ,2004
[5]. S. Chakraborty and A .c. Paul, "On Jordan K-derivation of 2-torision free N-ring" Punjab University J-of Math., Vol. 40 , pp.97-101, 2008.
[6]. T. K. Dutta and S . K .Sadar, "Semmiprime Ideals and Irreducible Ideal Of -semirings" , Novi sad J. Math , Vol.30 ,No.1 ,pp.97-108 ,2000

Abstract: In this paper, the authors investigate the summation-complete relation to certain type of generalized
higher order   difference equation to find the value of m( )  series to circular functions in the field of
finite difference methods. We provide an example to illustrate the m( )  series to circular functions.
Key words: Generalized  -difference equation, summation solution, complete solution, circular functions

[1] Jerzy Popenda and Blazej Szmanda, On the Oscillation of Solutions of Certain Difference Equations, Demonstratio Mathematica,
XVII(1), (1984), 153 - 164.
[2] R. A. C. Ferreira and D. F. M. Torres, Fractional h-difference equations arising from the calculus of variations, Applicable Analysis
and Discrete Mathematics, 5(1) (2011), 110-121.
[3] M. M. Susai Manuel, G.B. A. Xavier, V. Chandrasekar and R. Pugalarasu, Theory and application of the Generalized Difference
Operator of the
th n kind(Part I), Demonstratio Mathematica,vol.45,no.1,pp.95-106,2012.
[4] M.Maria Susai Manuel, V.Chandrasekar and G.Britto Antony Xavier, Solutions and Applications of Certain Class of  -Difference
Equations, International Journal of Applied Mathematics, 24(6) (2011), 943-954.
[5] M.Maria Susai Manuel, V.Chandrasekar and G.Britto Antony Xavier, Theory of Generalized  -Difference Operator and its
Applications in Number Theory, Advances in Differential Equations and Control Processes, 9(2) (2012), 141-155

Abstract: In this paper, we proposed a new three steps iterative method of order six for solving nonlinear equations. The method uses predictor–corrector technique, is constructed based on a Newton iterative method and the weight combination of mid-point with Simpson quadrature formulas. Several numerical examples are given to illustrate the efficiency and performance of the iterative methods; the methods are also compared with well known existing iterative method.

Keywords: Newton method, Order of convergence, Predictor-Corrector method, Quadrature method

[1] J.M. Ortega, W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.

[2] S. Abbasbandy, Improving Newton Raphson method for nonlinear equations by modified Ado-mian decomposition method, Appl. Math. Comput, 145 (2003), 887{893.

3] C. Chun, Iterative method improving Newton's method by the decomposition method, Comput. Math. Appl, 50 (2005), 1559{1568. [4] M.T. Darvishi and A. Barati, A third-oredr Newton-type method to solve system of nonlinear equations, Appl. Math. Comput, 187 (2007), 630{635. Math. Comput, 169 (2004), 161{169.

[5] S. Weerakoon and T.G.I. Fernando, A variant of Newton's method with accelerated third-order convergence, Appl. Math. Lett 13(8)(2000) 87:93.

[6] Cordero, A. and Torregrosa, J. R., (2007). Variants of Newton's Method using fifth-order quadrature formulas. Appl. Math. Comput., 190:686-698.

Abstract: Operator theory owes its origin in the book titled "Theorie des Operators Lineaires" by Stefan
Banach before the middle of 20th century. The convergence of a class of operators is important since a number
of iterations have been developed. The aim of this paper is to established that the Mann iteration converges
faster than the Noor Iteration for the class of Zamfirescu operators of an arbitrary closed convex subset of a
Banach Space.

[1]. V. Berinde, Comparing Krasnoselskij and Mann iterations for Lipschitzian generalized pseudocontractive operators, Proc. Int. Conf.
Fixed Point Theory and Applications (Valencia, 2003), Yokohama Publishers, Yokohama, in press.
[2]. V. Berinde, On the convergence of Mann iteration for a class of quasi contractive operators, in preparation, 2004.
[3]. H. K. Xu, A note on the Ishikawa iteration scheme, J. Math. Anal. Appl. 167 (1992), no. 2, 582 – 587.
[4]. T. Zamfirescu, Fix point theorems in metric spaces, Arch. Math. (Basel) 23 (1972), 292 – 298.
[5]. V. Berinde, On the convergence of the Ishikawa iteration in the class of quasi contractive operators, Acta Mathematica
Universitatics comeniance. New Series 73 (2004), no. 1, 119 – 126

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.The hyper wiener index denoted by WW of a graph G was introduced by Randic and his definition is applicable to trees only. Klein, Lukovits and Gutman introduced the formula for both trees and cycle containing structures. The Hyper Wiener index is defined as WW (G) = (Σd2(u ,v)+Σd(u,v))/2, where d(u,v) denotes the distance between the vertices u and v in the graph G and the summations run over all distinct pairs of vertices of G. Recently an edge version of Hyper Wiener Index was introduced by Ali Iranmanesh.In this paper, we have determined Hyper Wiener numbers of some Cluster graphs and also for some bipartite cluster graphs

Keywords: distance sum ,nanostar, Vertex and edge Wiener index, Vertex and edge Hyper Wiener index

[1] Trinajsti N., Chemical Graph Theory, CRC Press, Boca Raton, FL, 1983; 2nd revised edition, 1992.
[2] Wiener. H., Structural determination of parafinboiling , J. Am. Chem . Soc. 69 , (1947) 17-20.
[3] Randic,M., Novel molecular descriptor for structure property studies .Chem. Phys. Lett. 1993 ,211,478-483
[4] Klein, D.J.; Lukovits, I.; Gutman, I., On the definition of the hyper –Wiener index for cycle – containing structures. J.Chem. Inf. Comput. Sci. 1995,35,50-52.
[5] Ali Iranmanesh ,Gutman . I , OmidKhormali , Mahmian .A , The edge version of Wiener Index , MATCH Commun.Math.Comput.Chem ., 61 (2009) , 663 – 672.
[6] Ali Iranmanexh , SoltaniKafrani.A ., OmidKhormali , A New Version of Hyper – Wiener Index , MATCH Commun.Math.Comput.Chem ., 65 (2011) , 113 – 122

Abstract: Let R be a commutative ring with unity. Let Z(R) be the set of all zero-divisors of R. For x  Z(R),
let ann (x) {yR | yx  0} R . We define the annihilator graph of R, denoted by ANNG(R), as the
undirected graph whose set of vertices is Z(R)* = Z(R)  {0}, and two distinct vertices x and y are adjacent
if and only if ann (xy) ann (x) ann (y) R R R   . In this paper, we study the ring-theoretic properties of R
and the graph-theoretic properties of ANNG(R). For a commutative ring R, we show that ANNG(R) is
connected, the diameter of ANNG(R) is at most two and the girth of ANNG(R) is at most four provided that
ANNG(R) has a cycle. For a reduced commutative ring R, we study some characteristics of the annihilator
graph ANNG(R) related to minimal prime ideals of R. Moreover, for a reduced commutative ring R, we
establish some equivalent conditions which describe when ANNG(R) is a complete graph or a complete
bipartite graph or a star graph.
Keywords: Annihilator graph, diameter, girth, zero-divisor graph.
2010 Mathematics Subject Classification: Primary 13A15; Secondary 05C25, 05C38, 05C40.

[1]. D. F. Anderson, On the diameter and girth of a zero-divisor graph II, Houston J. Math. 34, 2008, 361 – 371.
[2]. D. F. Anderson, P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217, 1999, 434 – 447.
[3]. D. F. Anderson , S.B. Mulay, On the diameter and girth of a zero-divisor graph, J. Pure Appl. Algebra 210 , 2007, 543 – 550.
[4]. M. Axtel, J. Coykendall, J. Stickles, Zero-divisor graphs of polynomials and power series over commutative rings, Comm. Algebra
33(6), 2005, 2043 – 2050.
[5]. A. Badawi, On the annihilator graph of a commutative ring, Comm. Algebra 42 , 2014, 1 – 14.
[6]. I. Beck, Coloring of commutative rings, J. Algebra 116, 1988, 208 – 226.

Abstract:The analytic solution for the unsteady flow of generalized Oldroyd- B fluid on oscillating rectangular
duct is studied. In the absence of the frequency of oscillations, we obtain the problem for the flow of generalized
Oldroyd- B fluid in a duct of rectangular cross- section moving parallel to its length. The problem is solved by
applying the double finite Fourier sine and discrete Laplace transforms. The solutions for the generalized
Maxwell fluids and the ordinary Maxwell fluid appear as limiting cases of the solutions obtained here.
Finally, the effect of material parameters on the velocity profile spotlighted by means of the graphical
illustrations.
Keywords: Generalized Oldroyd-B fluid, oscillating rectangular duct, velocity field.

[1]. A. K. Johri and M. Singh; "Oscillating Flow of a Viscous Liquid in a Porous Rectangular Duct", Def. Sci. J. 38(1), (1988) 21-27.
[2]. D. Vieru, Corina Fetecau and C. Fetecau; "Flow of a Viscoelastic Fluid with the Fractional Maxwell", Applied Mathematics and Computations 200 (2008) 459-464.
[3]. H. Qi and M. Xu; "Stokes' First Problem for a Viscoelastic Fluid with the Generalized Oldroyd-B Model", Acta. Mathematica Sinica 23 (2007) 463-469.
[4]. I. Podlubny;"Fractional Differentional Equations" Academic Press, San Diego, 1999.
[5]. L. Debnath and D. Bhatta; " Integral Transforms and their Applications" Boca Raton, London, New York: Chapman & Hall, CRC; 2007.
[6]. L. Zheng, Z. Guo and X. Zhang; "3D Flow of a Generalized Oldroyd-B Fluid Induced by a Constant Pressure Gradient between Two Side Walls Perpendicular to a Plate", Nonlinear Anal RWA 12 (2011) 3499-3508