iosr-Jm   Volume-11 ~ Issue-1 ~ Jan-Feb 2015

Abstract: The aim of this paper to introduce and study fuzzy 𝛿-open set and the relations of some other class of fuzzy open sets like (R-open set ,𝜃-open set , 𝛾-open set , Δ-open set) , introduce and study some types of fuzzy 𝛿-separation axioms in fuzzy topological space on fuzzy sets and study the relations between of themand study some properties and theorems on this subject

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[3]. A.M.Zahran "fuzzy δ-continuous , fuzzy almost Regularity (normality) on fuzzy topology No fuzzy set"fuzzy mathematics,Vol.3,No.1,1995,pp.89-96
[4]. Kandil1 A. , S. Saleh2 and M.M Yakout3 "Fuzzy Topology On Fuzzy Sets: Regularity and Separation Axioms" American Academic & Scholarly Research Journal Vol. 4, No. 2, March (2012).
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Abstract: We adopted the method of interpolation of the approximation and collocation of its differential equation and with Legendre polynomial of the first kind as basis function to yield a continuous Linear Multistep Method with constant step size. The methods are verified to be consistent and satisfies the stability condition. Our methods was tested on first order Ordinary Differential Equation (ODE) and found to give better result when compared with the analytical solution.

Keywords: Collocations, Legendre polynomial, Interpolation, Continuous scheme.

[1]. Adeniyi, R.B., Alabi, M.O. and Folaranmi, R.O. (2008): A Chebyshev collocation approach for a continuous formulation of hybrid methods for Initial Value Problems in ordinary differential equations. Journal of the Nigerian Association of Mathematical Physics, 12: 369-378
[2]. Awoyemi, D.O. (1992). On some continuous linear multistep methods for initial value problem Unpublished Phd thesis, University of Ilorin, Ilorin Nigeria.
[3]. Areo, E.A., Ademiluyi, R.A. and Babatola, P.O. (2008). Accurate collocation multistep method for integration of first order ordinary differential equation, Int.J.Comp.maths,2(1):15-27.
[4]. Ehigie, J.O., Okunuga, S.A. and Sofoluwa, A.B. (2011). A class of 2-step continuous hybrid implicit linear multistep method for IVP's, Journal of Nigerian Mathematical Society, 30 145-161.
[5]. Odejide, S.A and Adeniran, A.O. (2012). A Hybrid linear collocation multistep scheme for solving first order initial value problems. Journal of Nigerian mathematical society. 31:229-241.

Abstract: We search for pairs of distinct Pythagorean triangles suchthat the difference between their perimeters is represented by (i)
k 2 (ii) k ,n 2 n   (iii) 3 2 3 N P (iv) 12Pt2N

Keywords: Pair of Pythagorean triangles, Special Polygonal numbers 2010 Mathematics Subject Classification: 11D09, 11Y50.

1]. L.E. Dickson, History of Theory of numbers, vol.2, Diophantine analysis, New York, Dover, 2005.
[2]. L.J. Mordell, Diophantine Equations, Academic press, New York, 1969.

Abstract: The notions of intuitionistic fuzzy T-ideals in BCI-algebras are introduced.Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy T-idealare provided. Using a collection of T-ideals, intuitionistic fuzzy T-ideals areestablished.

Keywords: T-ideal; intuitionistic fuzzy sub-algebra; (closed) intuitionistic fuzzy ideal; intuitionistic fuzzy T-ideal.

[1]. K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and Systems, 20(1986), 87-96
[2]. K.T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy sets and Systems, 61(1994), 137-142
[3]. Kiyoshi iseki and T. Shotaro, An introduction to the theory of BCK-algebras, Math Japon, 23(1978), 1-26.
[4]. Kiyoshi iseki and T. Shotaro, Ideal theory of BCK-algebras, Math. Japonica, 21(1976), 351-366.
[5]. Jianming Zhan and Zhisong Tan, Characterizations of doubt fuzzy H-ideals in BCK-algebras, Soochow Journal of Mathematics, 29(2003), 290-293.
[6]. Y.B. Jun and K.H. Kim, Intuitionistic fuzzy ideals of BCK-algebras, Internat J. Math and Mtha. Sci., 24(2000), 839-849.
[7]. B. Satyanarayana and R. Durga Prasad, Product of intuitionistic fuzzy BCK-algebras, Advances in Fuzzy Mathematics, 4(2009), 1-8.

Abstract: Exact solutions are important not only in its own right as solution of particular flows, but also serve as accuracy check for numerical solution. Exact solution of the Navier-Strokes equation are, for example, those of steady and unsteady flows near a stagnation point, Stagnation point flows can either be viscous or inviscid, steady or unsteady, two dimensional or three dimensional, normal or oblique and forward or reverse. The classic problems of two dimensional and three dimensional stagnation point flow are associated with the names of Hiemenz and Homan A novel radial stagnation point flow impinging axi symmetrically on a circular cylinder was reported by Wang. The present paper deals with the laminar boundary layer flow and heat transfer in the stagnation region of a rotating and translating sphere with uniform magnetic fields. The governing equations of flow are derived for ξ = 0 (t*=0) and ξ=1 (t*→∞) and solutions in the closed form are obtained. The temperature and velocity fields for ξ = 0 are numerically computed. This shows that the thermal boundary layer thickness decreases as Prandtl number Princreases.The surface heat transfer (28) increases with the Prandtl number Pr. The surface heat transfer (28) at the starting of motion is found to be strangely dependent on the Prandtl number Pr. But it is dependent of magnetic field, buoyancy force Bp and Rotation Parameter Ro.

Keywords: Temperature field, velocity field,uniform magnetic field, buoyancy force, Rotation Parameter.

[1]. Homann, F., Der Einfluss Grosser Zahigkeitbei der stromung um demzylinder und um deikugel. ZAMM 16, (1936), 153-164
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(1911),326
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[6]. Mishra, B.N. & Choudhary R.C: Plane Coutte flow with pressure gradient and suction Ranchi univ. Math. Jour. Vol 2 (1971)

Abstract: We will discuss an inventory model is investigates with variable demand rate and time dependent deteriorating items.In this study, we have taken shortages in inventory are allowed and fully backlogged. This model is studied under the condition for decaying items of permissible delay in payments which is most important and an outcome of interaction between product and financial markets which arises. This model based on time-dependent, holding cost, shortages cost and the combination of model is unique and practical.

[1]. Chang H.J, Hung C.H., Dye C.Y. (2001) 'An Inventory Model For Deterioration Items With Linear Trend Demand Under The Condition Of Permissible Delay In Payment', Production Planning & Control,12-3,274-282.
[2]. Goyal S.K. And Giri B.C. (2003) 'The Production-Inventory Problem Of A Product With Time Varying Demand, Production And Deterioration Rates', European Journal Of Operational Research 147, 549-557.
[3]. Hou K.L. (2006) 'An Inventory Model For Deteriorating Items With Stock-Dependent Consumption Rate And Shortages Under Inflation And Time Discounting', European Journal Of Operational Research 168, 463-474.
[4]. Mandal M. And Maiti M. (1999) 'Inventory Of Damageable Items With Variable Replenishment Rate, Stock-Dependent Demand And Some Units In Hand', Applied Mathematical Modelling 23,799-809.
[5]. Mandal B.N. And Phaujdar S. (1989) 'An Inventory Model For Deteriorating With Stock- Dependent Consumption Rate', Opsearch26, 43-46.
[6]. Mishra R.B. (1979) 'A Note Of Optimal Inventory Management Under Inflation', Navel Research Logistics Quarterly 26, 161-165.

Abstract: In this paper, we obtained two fractional integrals involving the product of two I-functions [10], general class of polynomials and Gauss hypergeometric function. By making use of these integrals, we have obtained two theorems based on modified Saigo operators of fractional integration.

Keywords: fractional integral, Saigo operators, Riemann-Liouville operator, Weyl operator, Erd𝑒 lyi- Kober operator, I-function, gauss hypergeometric function and general class of multivariable polynomial.

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J. Phys. A. Math. Gen. 20 (1987), 4119-4128.

Abstract: Deterioration is defined as decay, change, damage, spoilage or obsolescence that results in decreasing usefulness from its original purpose. Some kinds of inventory products (e.g., vegetables, fruit, milk, and others) are subject to deterioration. Ghare and Schrader (1963) first established an economic order quantity model having a constant deterioration. Chang gives a Partial Backlogging Inventory Model rate of deterioration and constant rate of demand over a finite planning horizon. Covert and Philip (1973) extended Ghare and Schrader‟s constant deterioration rate to a two parameter Weibull distribution. Dave and Patel (1981) discussed an inventory model for deteriorating items with time-proportional demand when shortages were not allowed. The related analysis on inventory systems with deterioration have been performed by Balkhi and Benkherouf (1996), Wee (1997), Mukhopadhyay et al. (2004),etc.

[1]. Balkhi,Z. T., and Benkherouf, L. (2004), "On an inventory model for deteriorating items with stock dependent and time-varying demand rates [J]," Computers & Operations Research, Vol. 31, pp. 223–240.
[2]. Balkhi, Z.T., Benkherouf, L., (1996) ,A production lot-size inventory model for deteriorating items and arbitrary production and demand rate. European Journal of Operational Research, Vol. 92, pp. 302-309.
[3]. Buzacott, J.A., (1975),
[4]. Economic order quantities with inflation. Operational Research Quarterly,26: 553-558.
[5]. Chang, H. and Dye, C. (1999), An EOQ model for deteriorating items with time varying demand and partial backlogging.Journal of the Operational Research Society, 50,1176–1182..

Abstract: Keeping in view the concern about environmental protection, the study incorporate the concept of repairing in a production inventory model consisting of production system and repairing system over infinite planning horizon. This study presents a forward production and reverse repairing system inventory model with a time dependent random deterioration function and increasing exponentially demand with the finite production rate is proportional to the demand rate at any instant. The shortages allow and excess demand is backlogged. Expressions for optimal parameter are obtained .We also obtained Production and repairing scheduling period, maximum inventory level and total average cost. Using calculus, optimum production policy is derived, which minimizes the total cost incurred

[1]. Alamri, A.A. (2010). Theory and methodology on the global optimal solution to a Reverse logistics inventory model for deteriorating items and time varying rates. Computer & Industrial Engineering,(60), 236-247.
[2]. Balkhi, Z. T. and Benkherouf, L. (1996 b)On the optimal replenishment schedule for an inventoy system with deteriorating items and time varying demand and production rates.Computers & Industrial Engineering, 30 ; 823-829..
[3]. Bhunia, A. K. and Maiti, M. (1998) A two warehouse inventory model for deteriorating items with a linear trend in demand and shortages.Jour of Opl. Res. Soc., 49 : 287-292.
[4]. Chang, H. J. and Dye, C. Y. (1999) An EOQ model for deteriorating items with time varying demand and partial backlogging.Jour, of Opl. Res. Soc., 50 : 1176-1182.
[5]. Chung, C. J., & Wee, H. M. (2011). Short life-cycle deteriorating product remanufacturing in a green supply chain inventory control system. International Journal of Production Economics, 129(1), 195-203.
[6]. Covert, R.P., and Philip, G.C.,( 1973), An EOQ Model for Item with Weibull Distribution Deterioration, AIIE Transactions, 5, (4), 323-326,

Abstract: The i(G) -graph is defined as a graph whose vertex set correspond 1 to 1 with the i(G) -sets of G . Two i(G) - sets say 1 S and 2 S are adjacent in i(G) if there exists a vertex 1 vS , and a vertex 2 wS such that v is adjacent to w and = { } { } 1 2 S S  w  v or equivalently = { } { } 2 1 S S  v  w . In this paper we obtain i(G) -graph of some special graphs.

[1]. Acharya B.D, Walikar, H.B and sampath Kumar, E, Recent developments in the theory of domination in graphs, Mehta Research
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Abstract: In this short article alpha-skew-generalized logistic distribution of type III has been introduced as an extension of the alpha-skew-logistic distribution [Hazarika and Chakraborty (2014). Alpha Skew Logistic Distribution, IOSR Journal of Mathematics 10 (4) Ver. VI: 36-46] by considering the generalized logistic distribution of type III as the base distribution. Cumulative distribution function, moment generating function and a few moments have been derived. AMS Subject Classification: 60E05; 62E15; 62H10
Key Words: Skew logistic distribution, moment generating function, generalized Hurwitz–Lerch Zeta function

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