iosr-Jm   Volume-9 ~ Issue-3

Abstract: A numerical method based on parametric spline with adaptive parameter is given for the secondorder singularly perturbed two-point boundary value problems of the form 0 1  y  p(x)y  q(x)y  r(x); y(a)  ; y(b)  The derived method is second-order and fourth-order convergence depending on the choice of the two parameters  and  . Error analysis of a method is briefly discussed. The method is tested on an example and the results found to be in agreement and support the predicted theory. Keywords: Singular perturbation; parametric spline functions; BVPs; ODEs.

[1] A.K. Aziz, Numerical Solution of Two Point Boundary-Value Problem, Blaisdal, NewYork, 1975.
[2] G. Micula, S. Micula, Hand Book of Splines, Kluwer Academic Publishers, Dordrecht,London, Boston, 1999.
[3] H.G. Roos, M. Stynes, L. Tobiska, Numerical Methods for Singularly-Perturbed Differential Equations, Springer, New York, 1996.
[4] P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, Wiley, NewYork, 1962.
[5] P.M. Prenter, Spline E.A. As and Variational Methods, Wiley, New York, 1975.
[6] U.M. Ascher, R.M.M. Mattheij, R.D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Prentice-Hall, Englewood Clis, NJ, 1988.

Abstract:In this paper we have tried to state that Kaprekar's constant is a fixed point of iterative function defined on set of all positive four digit numbers where none of its any three digits are equal. Hence consequently we have given the definition of Kaprekar's constant in terms of function.

Key words: Kaprekar's constant, Fixed point, Iterative function, Four digit numbers.

[1] Investigations into the Kaprekar Process by Robert W. Ellis and Jason R. Lewis
[2] An Interesting Property of the Number 6174, Scripta Math, 21(1955)304 by D R Kaprekar
[3] The Determination of Kaprekar Convergence and Loop Convergence of All Three-Digit numbers. American Monthly,95(1988,105-
112) by Klaus E. Eldridge and Seok Sangong
[4] The Kaprekar Routine and Other Digit Games for Undergraduate Exploration by K Peterson and H Pulapaka
[5] Mac Tutor History of Mathematics, Article by J J O‟Connor and E F Robertson

Abstract: Principal Component Analysis(PCA) is a data analysis tool that is used to reduce the dimensionality of a large number of interrelated variables while retaining as much of the information as possible. In this paper, PCA has been utilized on the crime data of Nigeria to discover the distinct influential variables; in addition which variables have silence in the identification of State being safe or dangerous. From the result, four Principal Components (PCs) have been retained using both scree plot and Kaiser's criterion which accounted for 75.024% of the total variation.

Key words: Principal Component Analysis (PCA), crime data.

[1] Cleen (2007). The Nigerian Police as at November 2007. http://www.cleen.org/sumarry%20crime% 20statistics% 20in%20nigeria%202007.p [2] Danbazau, A.B. (2007). Criminology Justice. 2nd edition. Ibadan: Spectrum Books Limited. [3] Ifeanyi (2004) Nigeria Crime Statistics [4] Tappan (1964:32) Definition of crime
[5] Wiki/cr (2009). Crime, http://en.wikipedia.org/wiki/criminal_94. [6] Lombroso, C. (1911). The Criminal Man, New York: Putman. [7] Sutherland, E.H. (1939). The white-colar criminal. American Sociological Review, 5: 1-12 [8] Oyebanji, J.O. (1982). Economic Development and the Geography of crime: an Empirical Analysis. [9] Akpan, A.U. (2002). Notion of causes of crime among Nigerians. International Journal of Social and Policy Issues: 1(1): 36-40 [10] Kutigi, I. (2008). Puberty, Ignorance and Evil Intentions as strong crime factors. Tribune, Monday 23/06/2008.

Abstract:In this paper, magneto hydrodynamics boundary layer heat transfer over a moving flat plate is discussed, using similarity transformation momentum and energy equations that are reduced in to nonlinear ordinary differential equations. The nonlinear differential equations are solved using implicit finite difference Keller box method. Graphical results of fluid velocity and temperature profile are presented and discussed for various parameters.

Key words: MHD boundary layer, moving surface, heat transfer, Keller box method.

[1] Rossow VJ, On the flow of electrically conducting fluid over a flat plate in the presence of transverse magnetic field.-MACA, Rept.(1958),1358
[2] Carrier GF and Greenspan HP, J. Fluid Mech. 67, 1959, 77.
[3] Afzal N, Int. J. Heat Mass Trans. 15, 1972, 863.
[4] Sakiadis B C, Boundary layer behaviour on continuous moving solid surfaces: I. Boundary layer equations for two dimensional and axi-symmetric flow, II. Boundary layer on continuous flat surface, III. Boundary layer on a continuous cylindrical surface. AICHE Journal, 7, 1961, 26-28, 221-225, 467-472.
[5] Erickson L E, Fan L T and Fox V G, Heat and mass transfer on a moving continuous flat plate with suction or injection, Ind. Engg. Chem. Fundam.5, 1966, 19-25.
[6] Tsou F K, Sparrow E M and Goldstein R J, Flow and heat transfer in the boundary layer on a continuous moving surface, Int J Heat Mass Transfer, 10, 1967, 219- 235.
[7] R. N. Jat, Abhishek Neemawat,Dinesh Rajotia, MHD Boundary Layer Flow and Heat Transfer over a Continuously Moving Flat Plate, International Journal of Statistika and Mathematika,3(3),2012,102-108.
[8] Cebeci T., Bradshaw P. Physical and computational Aspects of Convective Heat Transfer, (New York: Springer, 1988), 391-411.
[9] Na T.Y., Computational Methods in Engineering Boundary Value Problem, (New York: Academic Press 1979), 111-118.

Paper Type	:	Research Paper
Title	:	Non Conviction Based Criminal Forfeiture and Right to Own Property in Nigeria* Enhancing the Benefit and Engaging the Problems
Country	:	Nigeria
Authors	:	Dr. Babatunde ONI
	:	10.9790/5728-0932228

Abstract: The right to acquire and own movable and immovable properties must be legitimately done within the confines of law. Thus, acquisition of property by illegal means can be sanctioned through forfeiture or confiscation particularly where the culprit is not convicted of the crime. The paper examines some existing laws on criminal forfeiture, the various types of forfeiture in criminal trials in Nigeria and the constitutional rights to acquire property only within the provision of the law.

[1] Country report for Nigeria for the Eleventh United Nations Congress on Crime Prevention and Criminal Justice, Bangkok Thailand 18th -25th April 2005 P. 31
[2] See The Sunday Punch, September 10, 2006 p.13
[3] The Nation, August 22, 2007 p.6.

[4] Maxeiner, James "Bane of American Forfeiture Law-Banished at last? 62 Cornell L. 768, 779, 792 (1977).
[5] Ibid
[6] Sections 43 and 44 of the Constitution of Nigeria, 1999.
[7] Section 44 (2) (b) ibid
[8] Wagar "Modern Views of the Ideas of Progress" (1967) 28 J. History of Ideas p.50
[9] Obilade, A.O. "The Ideas of the Common Good in Legal Theory" in J.A. Omotola (ed.) Issues in Nigerian Law (Lagos: Faculty of Law, University of Lagos (1991) Chapter 1.
[10] Bentham J. An Introduction to the Principles of Morals and Legislation (ed. J.H Burns and H.L. Hart 1970, London: Athlone Press, University of London) Chapter

Paper Type	:	Research Paper
Title	:	On Contra D-Continuous Functions and Strongly D-Colsed Spaces
Country	:	India
Authors	:	K. Dass, J. Antony Rex Rodrigo
	:	10.9790/5728-0932938

Abstract: In[8], Dontchev introduced and investigated a new notion of continuity called contra-continuity. Recently, Jafari and Noiri ([12], [13], [14]) introduced new generalization of contra-continuity called contra-super-continuity, contra--continuity and contra-pre-continuity.It is the objective of this paper to introduce and study a new class of contra-continuous functions via

[1]. J. Antony Rex Rodrigo and K.Dass, A new type of generalized closed sets, Internat.J.Math. Archive -3(4),2012,1517 – 1523
[2]. J. Antony Rex Rodrigo and K.Dass, Weak and strong form of D-irresolute functions ( Accepted).
[3]. J. Antony Rex Rodrigo and K.Dass, D-continuous functions (communicated).
[4]. S.P.Arya and R.Gupta,On strongly continuous mappings,Kyungpook Math.J.,131-143.1974
[5]. K. Balachandran, P. Sundaram, H. Maki, On generalized continuous maps in topological spaces, Mem. Fac. Sci. Kochi Univ. Ser. A.Math 12 (1991),5-13.
[6]. M. Caldas, S. Jafari, T. Noiri, M. Simeos, A new generalization of contra-continuity Via Levines g-closed sets, Chaos Solitons Fractals 42 (2007),1595-1603.
[7]. M. Caldas, S. Jafari, Some properties of contra--continuous functions.Mem. Fac. Sci. Kochi Univ. Ser. A Math, 22 (2001), 19-28.
[8]. J. Dontchev, Contra-continuous functions and strongly S-closed spaces, Internat. J.Math. Math. Sci. 19 (1996), 303-310.
[9]. J. Dontchev, S. Popvassilev, D. Stovrova, On the -expansion topology for the co- semi. Regularization and midlyHausdorff spaces, Acta Math.Hungar. 80(1998),9-19.
[10]. J. Dontchev, T.Noiri, Contra-semicontinuous functions, Math. Pannon.10(1999),159-168

Paper Type	:	Research Paper
Title	:	On the vertex covering sets and vertex cover polynomials of square of paths
Country	:	India
Authors	:	Ayyakutty Vijayan, Thankappan Suseala Ida Helan
	:	10.9790/5728-0933944

Abstract: Let G be a graph of order n with no isolated vertex. Let (G,i) be the family of vertex covering sets in G with cardinality i and let c(G, i) = | |. The polynomial C(G, x) = c(G, i) is called the vertex cover polynomial of G. In this paper, we obtain some properties of the polynomial C( ) and its coefficients. Also ,we derive the reduction formula to calculate the vertex covering polynomial of square of path.
Key word: Square of path, vertex covering set, vertex covering number, vertex covering polynomial.

[1] Alikhani .S andHamzeh Torabi.2010,on Domination polynomials of complete partite Graphs,worled Applied sciences Journal,9(1) : 23-24
[2] Alikhani .Sand peng .y .H ,2008, domination sets and Domination polynomial of cycles, Global journal of pure and Applied Mathematics ,Vol.4 no 2.
[3] Alikhani .Sand Peng .Y .H ,2009, Introduction to Domination polynomial of a graph ,ar xiv:0905.225|v| [math.co] 14 may.
[4] Chartrand . G and Zhang.P, 2005, Introduction to graph Theory,Mc Graw Hill.Higher education.
[5] F.M Dong,M.D..Hendy,K.L.Teo and C.H.C.Little ,The vertex - Cover Polynomial of a graph, Discrete Math .250(2002),71,78.
[6] Maryam Atapour and NasrinSoltankhah, 2009,on total Domination sets in Graphs, Int.J.Contemp.Math .Sciences, Volume .4,no .6, 253-257.
[7] T.W.Haynes,S.T.Hedetniemi,andP.J.slater,Fundamental of Domination in graphs ,vol.208 of Monographs and Textbooks in pure and Applied Mathematics ,Marcel Dekker,new York,NY,USA,1998.
[8] Vijayan .A,SanalKumar.S.on Total Domination Polynomial of graphs, International Journal of Mathematics research. ISSN 0976-5840 Volume 4,Number 4 (2012), PP. 339-348.

Paper Type	:	Research Paper
Title	:	Some Summability Spaces of Double Sequences of Fuzzy Numbers
Country	:	India
Authors	:	Manmohan Das, Bipul Sarma
	:	10.9790/5728-0934549

Abstract:In this article we introduce and study the notions of double  -lacunary strongly summable, double  - Cesàro strongly summable, double  - statistically convergent and double  -lacunary statistically convergent sequence of fuzzy numbers. Consequently we construct the spaces respectively and investigate the relationship among these spaces. Further we show that are complete metric spaces.
Keywords: Sequence of fuzzy numbers; Difference sequence; lacunary strongly summable; Cesàro strongly summable; statistically convergent; lacunary statistically convergent; Completeness.

[1] P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, Fuzzy Sets and Systems 35 (1990) 241-249.
[2] B.C Tripathy ; A Dutta, Stastically convergent and Cesaro summable double sequences of fuzzy real numbers; Soochow journal of
mathematics 33(2007),835-848.
[3] H. Fast, Sur la convergence statistique, Colloq. Math. (1951) 241-244.
[4] J.A. Fridy and C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125(12) (1997) 3625-3631.
[5] A.R. Freedman, J.J. Sember and M. Raphael, Some Cesàro-type summability spaces, Proc. Lond. Math. Soc. 37(3) (1978) 508-520.
[6] H. Kizmaz, On certain sequence spaces, Canad. Math. Bull. 24(2) (1981) 168-176.
[7] M. Matloka, Sequences of fuzzy numbers, BUSEFAL 28 (1986) 28-37.
[8] I.J. Maddox, A Tauberian condition for statistical convergence, Math. Proc. Camb. Phil. Soc. 106 (1989) 277-280.
[9] S. Nanda, On sequence of fuzzy numbers, Fuzzy Sets and Systems 33 (1989) 28-37.
[10] F. Nuray and E. Savaş, Statistical convergence of sequences of fuzzy numbers, Math. Slovaca 45(3) (1995) 269-273.

Paper Type	:	Research Paper
Title	:	Comparison of Service Delivery by Atm in Two Banks: Application of Queuing Theory
Country	:	Nigeria
Authors	:	Ogunsakin, R. E., Babalola, B. T., Adedara, M. T.
	:	10.9790/5728-0935054

Abstract: Queuing Theory probabilistic methods as well as Birth- Death processing were discussed in this paper. The above method was applied to Access Bank and United Bank of Africa, Ado Ekiti branch. The distribution of arrival rate was Poisson distribution while queuing discipline in the branch was first come first served. This paper also emphasized on Markovian in Queues. From analysis, we were able to obtain the average arrival rate, average service rate, average time spent in the queue for Access bank as 2.01, 1.65, 0.5 respectively and UBA as 3.28, 1.75, 1.67minutes, respectively. The average number of waiting in the system and idle time were obtained for Access as 3minutes, 0.61(61%) and UBA as 7minutes, 0.86(86%) respectively. The utilisation factor for Access bank is 0.58 and that of UBA is 0.38.
Keywords: Queue, Balking, Reneging, Traffic Intensity, Customers, Arrival Rate, M/M/1, Server.

[1]. Bhat, W.W (1969). sixty years of Queueing Theory Management Science pp. 280-294
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[3]. Kathwaca (1958) Application of Quantitative techniques in large and small Organization in USA JURS 39, p981
[4]. Ellis H.F (1958). Written in a Queue Operation Research pp. 125- 187
[5]. Marse, P. M and Kimball G. F (1951). Methods of Operation Research New York John Miller and sons.
[6]. Miller, D.W and Starr M.K (1960). Executive Decision and operation Research, England Cliffs N. J. prentice pp. 104.
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[8]. Robert J. T and Robert C. K (1974). Decision making Through Operations research. Wikey International Education pp. 47- 80
[9]. Taha, H.A. (1987). Operation Research. an Introduction Fourth Edition. Macmillan Publishing company New York pp. 595-671
[10]. Taylor F.W. (1910) Principles of Scientific Management. New York and Bros pp. 140.