iosr-Jm   Volume-12 ~ Issue-3 ~ May-June 2016

Abstract:In 2006, Turkoglu et al. [18] extended the notion of compatible mappings to IFM spaces. Alaca [2] weakened the notion of compatibility by using the notion of weakly compatible maps in IFM spaces and showed that every pair of compatible mappings is weakly Compatible but reverse is not true. Many authors have proved a number of fixed point theorems for different contractions in IFM-spaces (see. 4,6,11].

[1] Aamri, M. and Mountawakli, D.El.,Some new common fixed point theorem under strict contractive
conditions,J.Math.Anal.Appl.270(2000),181-188.
[2] Alaca, C., "A common fixed point theorem for weak compatible mappings in intuitionistic fuzzy metric spaces", Int. J. Pure Appl.
Math., 32(4):537-548(2006).
[3] Alaca, C., Turkoglu D., Yildiz,C., "Common fixed points of compatible maps in intuitionistic fuzzy metric spaces", Southeast Asian
Bull. Math., 32(1):21-33(2008).
[4] Alaca,C., "On fixed point theorems intuitionistic fuzzy metric spaces", Commun Korean Math. Soc., 24(4):565-579(2009).
[5] Atanassov, K., "Intuitionistic fuzzy sets", Fuzzy Sets Syst., 20(1):87-96(1986).

Abstract:In this paper we indentify the patterns of continued fractions of rational numbers p q with k  p  q . Here we try to find minimum number of distinct patterns that will give rise to the remaining patterns.
Keywords: Continued fraction algorithm, Continued fractions, Euclidean algorithm, Euler's formula, Simple continued fractions.

[1] A. Ya. Khinchin, "Continued Fractions" , Dovers books on mathematics,1997.
[2] Brezinski, Claude, "History of Continued Fractions and Pade Approximants", Springer- Verlag: New York, 1980.
[3] David M. Burton, "Elementary Number Theory" seventh edition, Mcgraw Hill Education, 2012.
[4] George E. Andrews, "Number Theory", W.B. Saunders Company.
[5] Ivan Niven , Herbert S. Zuckerman, Hugh L. Montgomery, "An introduction to theory of numbers", Fifth edition, Wiley Student Edition.

Abstract: If we get any point which is represented with respect to three co-ordinate then where it can be point out or drawn in matrix. If we get any point having one co-ordinate is related with respect to the relation between two co-ordinates. hence if the position of any point does not laying in two – dimension graph then where it should be drawn .this is the thinking to develop the 2D plane with respect to the third axis . A particular point replacing its co-ordinate with respect to 2D graph, but at the stage it is not able to point out in 2D graph. Then where it should be drawn
Keywords: Co-ordinate, Dimension, Matrix, Polerix, Transformation

[1]. R. vasistha , Krishna prakashan media (P) limited 2005 ,384 pages

Abstract: There is a natural relationship to the post-Newtonian expansion scheme that is used to describe sources of gravity which are not too far from Newtonian, i.e, not too relativistic. Here the expantion can lead to the solutions for the exterior fields of such sources. Till now the post-Newtonian expansion known to high order, in some cases 8th order. This paper has provided a high order expansion of the vacuum axisymmetric equations and also shows how some of our expanded terms relate to the known post-Newtonian ones for the particular case of homogeneous rotating bodies (generalized Maclaurin spheroids).
Keywords: Post-Newtonian approximation, Maclaurin spheroids.

[1]. Salam, M. A., IOSR Journal of Mathematics (IOSR-JM) Volume 12, Issue 2 Ver I (Mar.-Apr. 2016), PP 18-32 (Paper III)
[2]. Chandrasekhar, S. Ellipsoidal Figures of Equilibrium, Yale University Press, New Haven (1969).
[3]. Chandrasekhar, S. Astrophys. J., 167, 447 (1971).
[4]. Chandrasekhar, S., and Lebovitz, N.R. Astrophys. J., 136, 1032 (1962).
[5]. Chandrasekhar, S., and Lebovitz, N.R. Astrophys. J., 137, 1162 (1963).

Abstract : This paper focused on the algorithmic building for a simple alternative nonparametric fuzzy linear regression method through SAS algorithm. This modified method can be used as an alternative method of data analysis. This modified method comprises of normality checking, transforming data into normality, data bootstrapping and fuzzy regression modelling as improvement of regression modelling. In this paper, we provide an alternative algorithm which can be used as a tool for the option of data analyzed.
Keywords: Bootstrap, Bayesian and Fuzzy Regression

[1]. Diem Ngo, T.H., La Puente, C.A. (2012). The Steps to Follow in a Multiple Regression Analysis. SAS Global Forum 2012: Statistics and Data Analysis. Paper 333-2012, Pp 1-12.
[2]. Cassel, D.L., 2010. Bootstrap Mania: Re sampling the SAS. SAS Global Forum 2010: Statistics and Data Analysis. Paper 268-279 In: Proceedings of the SAS Global Forum 2010 Conference. Cary (NC): SAS Institute Inc.
[3]. Jung, B.C., Jhun, M., Lee, J.W., 2005. Bootstrap Tests for Overdispersion in a Zero-Inflated Poisson Regression Model. Biometrics 61, pp.626-629.
[4]. Kacprzyk J. and Fedrizzi M. (1992) Fuzzy Regression Analysis, Omnitech Press, Warsaw.
[5]. Efron, Bradley and Robert J. Tibshirani. 1993. An Introduction to the Bootstrap. New York, NY: Chapman and Hall.

Abstract: The present paper deals with a Markovian queueing model for maintenance float system, which has following elements: workstations, repair stations and a set of standby components. In case of long queue of the failed machines, the reneging of failed machine takes place. Particularly we consider exponential repair and failure. We determine the four optimal parameters; population size (M), size of repair crew (S), the mean repair rate  and reneges exponentially with parameter ν such that the total cost is minimized.
Keywords: Repair, Failure, Optimal Cost, Reneging.

[1]. Shanthikumar, J. G and Yao, D. D. (1987): Optimal server allocation in a system of multi server stations, J. Mgmt. Sci., Vol. 9, pp.
117-1180.
[2]. Madu, C. N. (1988): A closed queueing maintenance network with two repair centres, J. Oper. Res. Soc., Vol. 9(10), pp. 959-967.
[3]. Albright, S. C. and Soni, A. (1988): Markovian multi echelon repairable inventory system, Naval Res. Logis., Vol. 5, pp. 49-61.
[4]. Georgantzas, N. C. and Madu, C. N. (1989): Maintenance float policy estimation with imperfect information, Comp. and Industrial
Engg., Vol. 1(2), pp.57-68.
[5]. Madu, C. N. (1990): An economic design for optimum maintenance float policy, J. Computers and Industrial Engg., Vol. 18(4), pp.
457-469

Abstract: In this paper we use the gram-Schmid method to define an orthogonal Polynomials such as Legendre – Hermit – Laguir with their corresponding weight functions. Also we get a new generating function for Legendre polynomials.
Keywords: Gram – Schamidt – Orthogonal functions - Weight functions-Generating functions

[1]. Boas.M"Mathemtical methods in the physical sinces (2006)
[2]. Debnath.l and Bhatta "Integral trnsforms and their application"(2003)
[3]. Sanson.G"Expansion in series of Legendre polynomials and spherical harnomics "pp 169-294 (1991)

Abstract: In this study; where the x, y, z numbers are unknowns, a and n positive integers, existence of x, y, z integer solutions' for each positive n integers of 2 2 x ay z n   Diophantine equation was shown by induction. Also change of x was analyzed according to the values which a will take and each situation was exemplified.

Keywords: Exponential Diophantine Equations, Higher Degree Equations

[1]. Terai N., 1994, "The Diophantine Equation ax  b y  cz I", Proc. Japan Acad. 70 A, 22 – 26,
[2]. Terai N., 1995, "The Diophantine Equation ax  b y  cz II", Proc. Japan Acad. 71 A, 109 – 110.
[3]. Cihangir A. ve Şenay H.; 1998," a p  bq  cr Diophantine Denkleminin Tamsayı Çözümleri Üzerine", Sel. Ün. Eğ. Fak. D.(Fen Bil.), 7A, 77 – 85.
[4]. Cihangir A. ve Şenay H.; 2000," a p  bq  cr Diophantine Denkleminin Tamsayı Çözümleri Üzerine II", S. Ü. Eğitim Fakültesi Fen Dergisi, 8(1) 137 – 143.
[5]. Cihangir A.,1998, "Pythagorean Üçlüleri Grubu ile z2  ay2  x2 Denkleminin Çözüm Üçlüleri Kümesinin Cebirsel

Abstract: The habit of smoking affects the health of both the active and passive smokers and their descendents. The health problems are potential enough leading to loss of lives, social and economical problems. Smoking is a bad habit and has become a big problem of the entire world. Despite of the health risks and economic losses, the spread of smoking habit has been increasing and socially accepted worldwide. These facts encourage mathematicians to model and simulate the dynamics of populations subject to the smoking habit.......
Keywords: Smoking habit, Mathematical modeling, Mortality, Stability analysis, Numerical simulation, Government.

[1]. B. O. Osu and C. Olunkwa, accepted 1 July, 2010, "An empirical mathematical model for smoke attributed mortality", Department of Mathematics, Abia state University, Nigeria.
[2]. Obaid J. Algahtani, Anwar Zeb Gul Zaman Shahar Momani, I. H. Jung, December 2015, "Mathematical study of smoking Model by Incorporating campaign class," Department of Mathematics King Saud University ,Saud Arabia.
[3]. Gul Zaman, October 29/2009. "Qualitative behavior of giving up smoking model," center for advanced Mathematics and physics, National University of Sciences and Technology, Peshawar Road, Rawalpindi 46000, Pakistan.
[4]. Zainab Alkhudhari, Sarah Al-sheikh, Salma Al-Tuwairqi, Stability analysis of a giving up smoking model, International Journal of Applied Mathematics Research, Vol. 3, No. 02, 2014.
[5]. Z. Alkhudari, S. Al-Tuwairqi, June 1, 2014, The effect of occasional smokers on the dynamics of a smoking Model.

Abstract: Pneumonia is one of the leading causes of serious illness and deaths among children around the world. In this paper we develop a deterministic Susceptible-Exposed-Infectious-Recovered or SEIR model to study the spread of pneumonia using data from the Boloso Sore of Ethiopia. The study also evaluates the impact of control measures, mainly vaccination, the spread Streptococcus pneumonia disease. Conditions for the clearance or persistence of the pneumonia infection through the stability of the equilibria are derived..........
Keywords: Pneumonia, Mathematical modeling, SEIR Modeling, vaccination, stability, basic reproduction number.

[1] Baker C. J. and Healy C. M. (2006). Prospects for prevention of childhood infections by maternal immunization. Current opinion in infectious diseases, 19, 271 – 76.
[2] Brauer F. Castillo – Chvez (2001). Mathematical models in population biology and epidemiology. Springer Verlag, New York.
[3] Bridy – Pappas A. E., Margolis M. B., Center K. J. and Isaacman D. J. (2005). Streptococcus pneumonia: description of the pathogen, disease epidemiology, treatment, and prevention. Pharmacotherapy, 25, 1193 – 1212.
[4] Eric Shu Num for Mathematical Modeling, Simulation, and Time Series Analysis of Seasonal Epidemics.
[5] G. Ashby, Bonnie Turkington Carol. The encyclopedia of infectious diseases, 3rd edition. New York, Facts on File. p. 242. ISBN0-8160- 6397-4. Retrieved on 2011-04-2.

Abstract: Salem and Zygmund have studied the equi-summability problem of factored Fourier series and conjugate series the factor being 𝑛𝛾,0<𝛾<1. In the present work we study the rate of equi- summability of same series forfunctions belonging to 𝐻𝑝(𝜔) space ,p≥1. AMS Mathematicesl subject classification(2000) number : 42A24, 41A25..........
Keywords: Equi-summability , Abel mean, Generalised H𝑜 lder metric , 𝐻𝑝(𝜔)space , Poisson's kernel.

[1]. M.Bhuyan, G.Das and B.K.Ray, Rate of Convergence of Fourier Series in the generalised H¨ older metric by Rogosinski Mean, Journal of the Orissa Mathematical Society, Vol.27, No 1 & 2 (2008), p. 21-36.
[2]. G.Das,T.Ghosh and B.K.Ray,Degree of approximation of functions by their Fourier series in the generalised H¨ older metric, Proc.IndianAcad.Sci (Math.Sci.)106, 1996, pp.139-153.
[3]. G.Das, AnasuyaNath and B.K.Ray,An estimate of the rate of convergence of Fourier se- ries in the generalized H¨ older metric,Analysis and Applications,H.P.Dikshit and PawanK.Jain(Eds),2002,Narosa Publishing House,New Delhi
[4]. 43-60.
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Abstract: In this work we can apply the fixed point theorem of Volterra to the Cauchy problem associated with 1st-order equations..........
Keywords: fixed point of Volterra, Cauchy problem, Cauchy sequence, linear applicationrnel.

[1]. A.Avez, Calcul Différentiel.Masson.Paris.1983.
[2]. Alfed Wohlhauser, Aide-mémoire d'analyse. Presses polytechniques et universitaires Romands.2000.
[3]. C. Brezinski, Analyse Numérique Discrète. Publications du Laboratoire de Calcul de l'Université des Sciences et Techniques de Lille.
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Abstract: In this paper, we have analysed a two-warehouse inventory model for deteriorating items with quadratic demand with time varying holding cost. In the model considered here, shortages are allowed and partially backlogged. The backlogging rate is assumed to be dependent on the length of waiting for the next replenishment. The longer the waiting time is, the smaller the backlogging rate would be. Numerical example is provided to illustrate the model and sensitivity analysis is also carried out for the parameters.s kernel.

[1] Hartley, R.V., Operation Research — A Managerial Emphasis, Good Year Pub. Comp, 1976, 315–317.
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[3] Mishra V.K and Singh L.S., Deteriorating inventory model with time dependent demand and partial backlogging, App. Math.l Sci., 4(72), 2010, 3611-3619.
[4] Vinod Kumar Mishra, Inventory model for time dependent holding cost and deterioration with salvage value and shortages, The J. of Math. and Comp. Sci., 4(1), 2012, 37-47.
[5] Venkateswarlu R. and Mohan R., An Inventory Model with Weibull Deterioration, Time Dependent Quadratic Demand and Salvage Value, AIMS -10, Proceedings, 2013, Bangalore.

Abstract:We have considered the steady laminar flow over a linearly stretching sheet subjected to an order of chemical reaction. A similarity transformation is utilized to convert the governing nonlinear partial differential equations into ordinary differential equations. The exact solution to this study may obtained by exploiting the fact that some features of free-parameter method and the "separation of variables" method are alike. Similarity transformations are used to convert unsteady boundary layer equations to a non-linear ordinary differential equation. Finally we have solved the equation analytically.
Keywords: Laminar flow, Electric field, Chemical reaction, Similarity transformation, Heat and mass transfer, Stretching sheet.s kernel.

[1]. Mahapatra T. R. and Gupta A. S., Heat transfer in stagna-tion-point flow towards a stretching sheet, Heat and Mass Transfer, 38(6), 517-521, 2002.
[2]. Afify A. A., MHD free convective flow and mass transfer over a stretching sheet with chemical reaction, Heat and Mass Transfer,
40(6-7), 495-500, 2004.
[3]. Alam M. S., Ahammad. M.U.,Effects of variable chemical reaction and variable electric conductivity on free convec-tive heat and
mass transfer flow along an inclined stretching sheet with variable heat and mass fluxes under the influence of Dufour and Soret
effects, Nonlinear Anal-ysis: Modeling and Control, 16(1), 1-16, 2011.
[4]. Ferdows M., Qasem M. Al-Mdallal, Effects of Order of Chemical Reaction on a Boundary Layer Flow with Heat and Mass Transfer over a Linearly Stretching Sheet, Amer-ican Journal of Fluid Dynamics, 2(6), 89-94, 2012.

Abstract: In this paper, we prove some fixed point theorems for two and three maps of Jungck generalized contractive mappings on spherically complete Ultra metric space using generalized contractive mappings . Our results extend various known results in ultra metric space such as Pant and Mishra[13],Gajic[7] and others. kernel.

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Abstract:The objective of this paper is to study the dynamical behavior of three species syn-ecological models. Type of three species mathematical model involving different types of ecological interactions is proposed and analyzed. In the model Holling type –II functional response is a doubted to describe the behavior of predation, for the model, the existence, uniqueness and boundedness of the solution are discussed. The existences and the stability analysis of all possible equilibrium points are studied. Suitable Lyapunov functions are used to study the global dynamics of the proposed model. Numerical simulations are also carried out to investigate the influence of parameters on the dynamical behavior of the model and to support the obtained analytical results of the model.
Keywords: Equilibrium Point; Lyapunov Functionn's kernel.

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