iosr-Jm   Volume-10 ~ Issue-4 ~ July-August 2014

Abstract: This proof was conceived in order to introduce a different way of calculating a level region. By the end of the paper I will calculate the area of a level region using continuous functions.
Keywords: calculate, area, enclosed, level, region

[1]. Aligniac, G. 1995 Mathematics, Athens, Aithrio
[2]. Apostol, T 1962 differential and integral calculus, Athens, Atlantis
[3]. Brand, L. 1984 Mathematical Analysis, Athens E.M.E.
[4]. Boyce , W. & Diprima, R. (1999) Elementary differential equations and boundary value problems, NTUA
[5]. Rudin, W. (2000) Principles of Mathematical Analysis, athens , Leader Books
[6]. Spiegel, M. (1982) higher Mathematics, ESPI
[7]. Thomas, G.B. & Finney, R.L. (2001) Advanced Calculus, Volume A, Crete

Abstract: In this paper, we define the notion of intuitionistic fuzzy sub HX ring of a HX ring and some of their related properties are investigated. We define the necessity and possibility operators of an intuitionistic fuzzy subset of an intuitionistic fuzzy HX ring and discuss some of its properties. We introduce the concept of an image, pre-image of an intuitionistic fuzzy subset and discuss in detail a series of homomorphic and anti homomorphic properties of an intuitionistic fuzzy set are discussed.

Keywords: intuitionistic fuzzy set, fuzzy HX ring, intuitionistic fuzzy sub HX ring, homomorphism and anti homomorphism of an intuitionistic fuzzy HX ring, image and pre-image of an intuitionistic fuzzy set.

[1]. Atanassov.K.T, intuitionistic fuzzy sets,Fuzzy Sets and System 20 (1986) ,pp 87-96.
[2]. Bing-xueYao and Yubin-Zhong, Upgrade of algebraic structure of ring, Fuzzy information and Engineering (2009)2:219-228.
[3]. Bing-xueYao and Yubin-Zhong, The construction of power ring, Fuzzy information and Engineering (ICFIE),ASC 40,pp.181-
187,2007.
[4]. Dheena.P and Mohanraaj.G, On intuitionistic fuzzy k ideals of semi rings, International Journal of computational cognition,
Volume 9, No.2, 45-50, June 2011
[5]. Li Hong Xing, HX group, BUSEFAL, 33(4), 31-37, October 1987
[6]. Li Hong Xing, HX ring, BUSEFAL, 34(1) 3-8, January 1988.

Abstract: Census is the procedure of systematically acquiring and recording information about the members of a given population. It is a regularly occurring and official count of a particular population. In this paper, we consider the existing discrete Malthusian growth model and the modified version for estimating human population in Nigeria. The later is applied at any point in time unlike the former where emphasis is made on equal time intervals (per decade) of conducting census. The numerical simulation carried out shows that the estimated population are higher than the actual census figure apart from the data recorded in 1963 and 1973 our findings indicates a non constant population growth rate as result of human and environmental factors .Using our model all Nigerians are hopefully of achieving an estimated population of 220.55865 million in 2016.

Keywords: Census, modified model, growth rate, fitting a straight line, estimated population

[1]. Anthony ,T. E. And Agoyi, M. (2011) . A Biometrics Approach to Population Census and National Identification in Nigeria: A Prerequisite for Planning and Development International Relations Department1, Computer Engineering Department2 Cyprus International University, Lefkosa, Mersin 10, Turkey1, 2 aeniayejuni@yahoo.com1, magoyi@ciu.edu.tr 2
[2]. Ajayi, B(2005) The Population and Nigeria data Contradictions. hptt.//.Nigerian world.com.
[3]. Bamgbose J .A., (2009) Falsification of population census data in aheterogeneous Nigerian state: The fourth republic example .Political Science Department Lagos State University, Lagos, Nigeria. E-mail: bamgboseja@yahoo.com.
[4]. Centre for bureau of statistics , state of Israel (2014)
[5]. Isiak, A. and Mannir, A.D.(1991). Breaking the myth; Shehu Musa and the 1991 census; Sepectrum books Limited

Abstract:In this paper, a comparative study of Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM) were considered on various types of integrodifferential equation; which are Fredholm, Volterra and Fredholm-Volterra equations. From the examples considered, it was observed that these methods were compared favorably with the exact solution. VIM has an advantage over ADM due to non-requirement of Adomian polynomial and hence converges faster to the exact solution for some nonlinear problems.
Keywords: Adomian decomposition method, Adomian polynomial, Integro-Differential equation, Lagragiam multiplier, variational iteration method.

[1]. G. Adomian, A review of the decomposition in applied Mathematics. J. Math.Anal. Appl. 135(1988) 501-544.
[2]. G. Adomian, Solving frontier problems of Physics: The decomposition method, Kluwer Academic Publishers, Boston. 1994.
[3]. A.M. Wazwaz, Necessary condition for the appearance of noise terms in decomposition solution series, Appl. Math. Comput. (81),
1997, 265-274.
[4]. A.M. Wazwaz, A new technique for calculating Adomian polynomial for nonlinear polynomials, Appl. Math. Comput. 111(1),
2000, 33-51.

Abstract: In this paper, new types of Intuitionistic fuzzy graphs are introduced and also some properties of the defined graphs are discussed. Also we defined the semi global Intuitionistic fuzzy dominating set and its number of Intuitionistic fuzzy graphs. Some results and bounds on semi global Intuitionistic fuzzy dominating number are derived, which is used in defence problems and bank transactions.

Keywords: Intuitionistic fuzzy graph, effective degree, semi complementary IFG, Semi-complete IFG, semi global Intuitionistic fuzzy dominating set. 2010Mathematics Subject Classification: 03E72, 03F55, 05C69, 05C72

[1]. Atanassov KT. Intuitionistic fuzzy sets: theory and applications. Physica, New York, 1999.
[2]. Harary,F., Graph Theory, Addition Wesley, Third Printing, October 1972.
[3]. Nagoor Gani. A and Shajitha Begum.S, Degree, Order and Size in Intuitionistic Fuzzy Graphs, International Journal of Algorithms, Computing and Mathematics,(3)3 (2010).
[4]. Parvathi, R. and Karunambigai, M.G., Intuitionistic Fuzzy Graphs, Computational Intelligence, Theory and applications, International Conference in Germany, Sept 18 -20, 2006.
[5]. Parvathi,R., and Thamizhendhi, G. Domination in Intuitionistic fuzzy graphs, Fourteenth Int. conf. on IFGs, Sofia, NIFS Vol.16, 2, 39-49, 15-16 May 2010.

Abstract: In this paper we have extended a result of Nevanlinna theory to Euler's gamma function which is known to be a meromorphic function.
Key Words: Nevanlinna theory, Euler's gamma function.

[1] HAYMAN W. K. (1964) : Meromorphic functions, Oxford Univ. Press, London.
[2] ZHUAN YE (1999) : Note – The Nevanlinna functions of the Riemann Zeta function, Jl. of math. ana. and appl. 233, 425-435.

Abstract: This paper considers a two commodity continuous review inventory system. Continuous review inventory control of a single item at a single location had been considered by many researchers in past. We extend this inventory control strategy to two-echelon system, which is a building block for serial supply chain. The inventory control system consists of two warehouse (WHi), Two Distribution Centre's (DCi) each associated with a retailer and handling two non-identical products. A (s, S) type inventory system with Poisson demand and exponentially distributed lead times is assumed at retailer node. The items are supplied to the retailers in packs of Qi (= Si-si) items from the distribution center (DCi) which has instantaneous replenishment facility from an abundant source (manufacturer). The steady state probability distribution and the operating characteristics are obtained explicitly. The measures of system performance in the steady state are obtained. The results are illustrated with numerical examples.

Keywords: Supply Chain, Inventory control, Multi-echelon system, two commodity continuous review inventory, Optimization.

[1] Anbazhagan N & Arivarignan G, 2000, Two-commodity continuous review inventory system with coordinated reorder policy, International Journal of Information and Management Sciences, 11(3), pp. 19–30.
[2] Arivarignan G & Sivakumar B, 2003, Inventory system with renewal demands at service facilities, pp. 108–123 in Srinivasan SK & Vijayakumar A (Eds), Stochastic point processes, Narosa Publishing House, New Delhi.
[3] Axsäter, S. 1990. Simple solution procedures for a class of two-echelon inventory problems. Operations research, 38(1), 64-69.
[4] Benita M. Beamon. 1998. Supply Chain Design and Analysis: Models and Methods. International Journal of Production Economics.Vol.55, No.3, pp.281 294.
[5] Cinlar, E. Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, NJ, 1975.

Abstract: In this paper, we use the finite Hankel and Laplace transforms to determine the velocity field corresponding to the flow of Oldroyd-B fluid in the annular region between two infinitely long coaxial cylinders. Initially, the fluid is at rest and the motion is produced by the inner cylinder pulled with a constant shear and outer cylinder moving with time dependent velocity. The obtained solution is presented under a series form in terms of the generalized G functions. Finally, the influence of different values of parameters, constants and fractional coefficient on the velocity field are also analyzed using graphical illustration.
Keywords: Fractional Calculus, Hankel transform, Laplace transform, Oldroyd-B fluid, Velocity field.

[1] T.W. Ting, Certain non-steady flows of second-order fluids, Arch. Rational Mech. Anal., 14, 1963, 1–23.
[2] P.N. Srivastava, Non-steady Helical flow of a viscoelastic liquid, Arch. Mech. Stos., 18, 1966, 145–150.
[3] N.D. Waters and M.J. King, The unsteady flow of an Elastico-viscous liquid in a straight pipe of circular cross section, J. Phys. D
Appl. Phys., 4, 1971, 204–211.
[4] R. Bandelli and K.R. Rajagopal, Start-up flows of second grade fluids in domains with one finite dimension, Int. J. Non-Linear
Mech., 30, 1995, 817-839.
[5] D. Tong, R. Wang and H. Yang, Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe,
Science in China Ser. G Physics, Mechanics & Astronomy, 48, 2005, 485-495.

Abstract: In this paper, we prove a common fixed point theorem in complex valued metric space for weakly compatible mappings. Also, we prove common fixed point theorems for weakly compatible mappings with E.A. property and CLR property. We will generalized and extended the result of S.M. Kang [7]. AMS Subject Classification: 47H10, 54H25

Key Words: CLR property, complex valued metric space, E.A. property, weakly compatible mapping

[1] A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim. 32 (2011), 243-253, doi: 10.1080/01630 563 .2011.533046.

[2] C. Vetro, On Branciaris theorem for weakly compatible mappings, Appl. Math. Lett., 23 (2010), 700-705, doi: 10.1016/j.aml.2010.02.011.

[3] G. Jungck, Common fixed points for non-continuous non-self mappings on non-metric spaces, Far East J. Math. Sci., 4 (1996), 199-212.

[4] M. Aamri, D.El. Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181- 188, doi: 10.1016/S0022-247X(02)00059-8.

[5] R.K. Verma, H.K. Pathak, Common fixed point theorems using property (E.A) in complex valued metric spaces, Thai J. Math., 11 (2013), 347–355.

Abstract: In this paper, we prove common fixed point theorems for φ-weakly expansive mappings, which generalize and extend the results of S. M. Kang[10] using the concept of weak reciprocal continuity in metric spaces. we introduce the concept of φ-weakly expansive mappings. AMS Subject Classification: 47H10, 54H25

Key Words: compatible mapping, R-weakly commuting mapping, R-weakly commuting mapping of type (𝐴𝑓), of type 𝐴𝑔 and of type (P),φ- weakly expansive mapping, weak reciprocal continuity.

[1] G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly, 83, No. 4 (1976), 261-263, doi: 10.2307/2318216.

[2] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9, No. 4 (1986), 771-779, doi: 10.1155/S0161171286000935.

[3] H.K. Pathak, Y.J. Cho, S.M. Kang, Remarks of R-weakly commuting mappings and common fixed point theorems, Bull. Korean Math. Soc., 34, No. 2 (1997), 247-257.

[4] R.P. Pant, Common fixed points of non-commuting mappings, J. Math. Anal. Appl., 188, No. 2 (1994), 436-440, doi: 10.1006/jmaa.1994.1437.

[5] R.P. Pant, Common fixed points of four mappings, Bull. Calcutta Math. Soc., 90, No. 4 (1998), 281-286

[6] R.P. Pant, A common fixed point theorem under a new condition, Indian J. Pure Appl. Math., 30, No. 2 (1999), 147-152.

[7] R.P. Pant, R.K. Bisht, D. Arora, Weak reciprocal continuity and fixed point theorems, Ann. Univ. Ferrara, 57, No. 1 (2011), 181-190, doi: 10.1007/s11565-011-0119-3.

Abstract: 2-metric space is an interesting nonlinear generalization of the classical one of metric space. In this paper we established fixed point theorems in 2-Metric Spaces by using some new extensions of Kannan fixed point theorem obtained by Kannan [1,2]. The result can be considered as an extension and generalization of fixed point theorems on 2-metric spaces and kannan fixed point theorems, given by many well known authors announced in the available literature.

Keywords: Fixed point, Metric Spaces, 2 Metric Spaces, Kannan type mapping , Kannan fixed point theorem

[1]. R. Kannan, Some results on Fixed Point , Bull. Cal. Math. Soc.,60, 1968, 71-76.
[2]. R. Kannan, Some results on Fixed Point II, Amer.Math.Monthly,76, 1969, 405-408.
[3]. S. Gӓhler, 2-Metrische Rӓume and ihre topologische strucktur, Math. Nachr., 26, 1963, 115 - 148.
[4]. S. Gӓhler, Uber die unifromisieberkeit 2-metrischer Rӓume, Math. Nachr., 28, 1965, 235 - 244.
[5]. M . Imdad, M. S. Kumar and M.D. Khan, A Common fixed point theorem in 2-Metric spaces, Math., Japonica, 36(5), 1991, 07-914.
[6]. P. P. Murthy, S. S. Chang, Y. J. Cho, B. K. Sharma., Compatible mappings of type (A) and common fixed point theorem, Kyungpook Math. J., 32, 1992, 203–16.

Abstract: In the present paper , we improve upon a result on common fixed point theorems for compatible mappings of type (𝑃) in metrically convex metric spaces by relaxing continuity restriction of two out of four mappings. MSC: 47H10,54H25

Key Words: Metrically convex metric spaces , Compatible mappings ,Compatible mappings of type (𝑃)

[1]. Hadzic O.: On coincidence theorems for a family of mappings in convex metric spaces,Internat.J. Math. and Math. Sci. ,10,453-460 (1987)
[2]. Jungck ,G. : Compatible mappings and common fixed points ,Internat.J. Math. and Math. Sci. 9,771-779 (1986)
[3]. Jungck ,G. : Compatible mappings and common fixed points(2) ,Internat.J. Math. and Math. Sci. 11, 285-288 (1988)
[4]. Pathak H.K.,Cho Y.J.,Kang S.M.,Lee B.S. : Fixed point theorems for compatible mappings of type(P)and applications to dynamic programming ,Le Matematiche Vol.L, 15-33 (1995) .
[5]. Pathak H.K.,Cho Y.J.,Chang S.S.,Kang S.M.: Compatible mappings of type(P) and fixed point theorems in metric spaces and probabilistic metric spaces.

Abstract: This study was conducted to investigate heat and mass transfer of unsteady MHD oscillatory slip flow of optically thin fluid through a channel filled with saturated porous medium and non-uniform walls temperature. The governing equations of oscillatory fluid flow were non-dimensionalised, simplified and solved. The closed-form solutions were obtained for the velocity, temperature and concentration. The numerical computations were presented graphically to show the salient features of the fluid flow , heat and mass transfer characteristics. The skin friction ,Nusselt number and Sherwood number were also analyzed.
Key words: Chemical reaction, Porous medium, MHD oscillatory flow, Navier slip

[1]. A.S. Eegunjobi and O.D. Makinde, Combined effect buoyancy force and Naiver slip on entropy generation in a Vertical porous
channel, Entropy 14, 2012, 1028-1044.
[2]. O.D.Makinde and E. Osalusi, MHD steady flow in a channel with slip at the permeable boundaries, Rom. J.Physis 51 , 2006, 319-
328.
[3]. A. Mehmood and A. Ali, The effect of slip condition on unsteady MHD oscillatory flow of a viscous fluid in a planner channel,
Rom.J.Physis, 52, 2007,85-91.
[4]. S.O. Adesanya and O.D. Makinde, MHD oscillatory slip flow and Heat transfer in a channel filled with porous media,
Rom.J.Physics,76, 2014, 197-204.
[5]. D. Vijaya and G.R. Viswanadh, Effects of chemical reaction on MHD free convective oscillatory flow past a porous plate with
dissipation and heat sink, Advance in Applied science Research, 3(5), 2012, 206-215.