iosr-Jm   Volume-11 ~ Issue-2 ~ Mar-Apr 2015

Abstract: In this paper, the fuzzy variational formulation will be introduced and derived. This paper is about studying variational problems with fuzzy functions, fuzzy condition and fuzzy boundaries by using different approaches for defuzzification, such as centroid method, 𝛼-cut method, centroid point and expected interval in which fuzzy sets have been transformed into crisp sets and finding the necessary conditions for extremizing the fuzzy variational problems with fuzzy function and fuzzy boundaries

[1]. Hsien-Chung Wu, "The improper fuzzy Riemann integral and its numerical integration", Information Sciences, 111(1-4), 109-137, 1998.
[2]. Kandel A., "Fuzzy Mathematical Techniques with Applications", Addison-Wesley Publishing Company, July, 1986.
[3]. Zadeh L. A., "Fuzzy Sets", 1965. In Fuzzy Sets and Applications: Selected Papers by Zadeh L. A., Edited by Yager R. R., Ovchinnikos S., Tong R. M., and Ngnyen W. T., John Wieley and Sons, Inc., 1987.
[4]. Yan J., Ryan, M. and Power, J., "Using Fuzzy Logic: Towards Intelligent Systems", Printice Hall, Inc., 1994.
[5]. Zadeh, L. A.: "Fuzzy Sets", 1965. In Fuzzy Sets and Applications: Selected Papers by L. A. Zadeh, Edited by Yager R. R., Ovchinnikos S., Tong R. M., and Ngnyen W. T., John Wiely and Sons, Inc., 1987.

Abstract: We consider an extension to the lost sale recapture model in a newsvendor framework developed earlier by the authors. As in real practice, we have considered that there may be an opportunity to backlog the lost sales, by offering some incentive for waiting. The back log fill rate is modelled as a log function of adding one to the proportion of rebate relative to the price. The retailer's decision includes selling price, order quantity and the rebate that will maximize its expected profit. Sensitivities of the demand errors in the form of beta distribution rather than the uniform and the normal distribution serve as an extension to the previous work by the authors.
Keywords : newsvendor problem, lost sales, rebates, price dependent demand, beta distribution

[1]. Alford, B.L., Biswas, A. (2002). The effects of discount level, price consciousness and sale proneness on consumers' price
perception and behavioral intentions. Journal of Business Research 55, 775-783.
[2]. Arcelus, F.J, Ravi Gor, Srinivasan, G. (2012): Price, rebate and order quantity decisions in a newsvendor framework with rebate
dependent recapture of lost sales, International Journal of Production Economics, Vol. 140, No. 1. (November 2012), 473-482.
[3]. Arcelus, F.J., Srinivasan, G. (1987). Inventory policies under various optimizing criteria and variable markup rates. Management
Science 33, 756-762.
[4]. Arcelus, F. J., Kumar, S., Srinivasan, G. (2005). Retailer's response to alternate manufacturer's incentives under a single period,
price-dependent, stochastic-demand framework. Decision Sciences 36, 599-626.
[5]. Aydin, G., Porteus, E.L. (2009). Manufacturer-to-Retailer versus Manufacturer-to-Consumer Rebates in a Supply Chain. In N.
with the left-skewed (right-skewed) the next lowest (highest) and the symmetrical, Agrawal & S. Smith (Eds.), Retail Supply Chain
Management. New York: Kluwer.
[6]. Bawa, K., Shoemaker, R.S. (1989). Analyzing Incremental Sales from a Direct Mail Coupon Promotion. Journal of Marketing 53,
66-78.

Abstract: In this paper we define the inequalities for the classes k-USH() and k-HCV() are considered and obtain inequality for G(z). A class k-USH() is the class of k uniformely harmonic starlike function of order ().and the class k-HCV() is the class of k uniformely convex function of order ().These two classes are obtained by the generalization of class k-USH(,,) [8].
Keywords: Harmonic,uniformely starlike, uniformely convex, salagean.

[1]. G.S. Salagean, Subclass of Univalent Functions, Lecture Notes in Math. Springer – Verlag 1013(1983), 362-372.
[2]. J.M. Jahangiri, Harmonic Functions starlike in the unit disc, J. Math. Anal. Appl., 235 (2) (1999), 470-477.
[3]. J.M, Jahangiri, Coefficient bounds and univalence criteria for harmonic functions with negative coefficient, Ann. Univ. Mariae,
Curie –Skledowska Sect. A, 52(2) (1998), 57-66.
[4]. JahangiriJ.M, Murugusundarmoorthy,G. and Vijaya,K., Salagean type Harmonic Univalent Functions, South. J. Pure and Appl.
Math., Issue 2(2002), 77-82.

Abstract: The aim of this paper is to introduce two new classes of functions, namely slightly continuous functions and totally 𝑆𝑔
continuous functions and study its properties. Mathematics Subject Classification: 54A05

[1]. Baker.C.W., Slightly pre continuous functions, Acta Math. Hungar., 94(1-2)(2002), 45-52.
[2]. Dontchev J, Contra - continuous functions and strongly s - closed spaces, Internat. J Mat. Sci 19(1996), 303 - 310.
[3]. Jain R.C. and Singal A.R., Slightly continuous mappings, Indian Math. Soc., 64(1997),195-203
[4]. Levine, N., Semi-Open Sets and Semi-Continuity in Topological Spaces, Amer. Math. Monthly. 70 (1963), 36-41.
[5]. Nour T.M, Slightly semi continuous functions, Bull. Cal. Math. Soc., 87(1995), 187-191.
[6]. Pious Missier.S and Arul Jesti.J. , A new notion of open sets in topological spaces, Int.J.Math.Arc., 3(11), 2012, 3990-3996.

Abstract: Fractional Calculus and generalized hypergeometric functions have contributed a lot to the theory of science and engineering. In view of importance and usefulness of fractional-calculus operators in different directions, we present a number of key results for the product of two 𝐼-functions involving the Riemann-iouville, the Weyl and such other fractional-calculus operators as those based upon the Cauchy-Goursat Integral Formula. The results discussed here can be used to investigate a wide class of new and known results.

[1] Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations to Methods of their Solutions and Some of Their Applications, Mathematics in Science and Engineering 198, Academic Press, New York, (1999).

[2] Saxena, V.P.: Proc. Nat. Acad. Sci. India 52A (1982): 366.

[3] Sharma, C.K. and Shrivastava, S.: Proc. Nat. Acad. Sci. India, 62 (A) (1992) : 235.

[4] Srivastava, H.M., Owa, S. and Nishimoto, K.: Some Fractional Differential Equations, J. Math. Anal. Appl. 106, (1985), 360-366.

[5] Vaishya, G.D., Jain, R. & Verma, R.C.: Proc. Nat. Acad. Sci. India 59A (1989): 329.

Abstract: T-norms are generalization of the usual two-valued logical conjunction, studied by classical logic, for fuzzy logics. T-norms are also used to construct the intersection of fuzzy sets or as a basis for aggregation operators. In probabilistic metric spaces, T-norms are used to generalize triangle inequality of ordinary metric spaces. Individual T-norms may of course frequently occur in further disciplines of mathematics, since the class contains many familiar functions. Firstly, we select some continuous function. Then we try to generate T-norms by using those functions.

Keywords: Algebraic Product 𝑇𝑃, Hamacher Product 𝑇𝐻, Lukasiewicz 𝑇𝐿

[1]. George J Klir, Yuan Bo, Fuzzy Sets And Fuzzy Logic, Theory And Applications, Prentice-Hall Inc. N.J. U.S.A. 1995.
[2]. Mirko Navara(2007), "Triangular Norms And Conforms" Scholarpedia.
[3]. Peter J Crickmore, Fuzzy Sets And System, Centre For Environmental Investigation Inc.
[4]. Peter Vicenik, A Note On Generators Of T-Norms; Department Of Mathematics, Slovak Technical University, Radlinskeho 11, 813 68 Bratislava, Slovak Republic.
[5]. Peter Vicenik, A Note To Construction Of T-Norms Based On Pseudo-Inverse Of Monotone Functions; Department Of Mathematics, Slovak Technical University, Radlinskeho 11, 813 68 Bratislava, Slovak Republic Received June 1998.

Abstract: A production and sale system is considered. During the operation time a machine produces random number of products. After operation time, sale time starts, and it has one among two distinct distributions depending on the magnitude of production time is within or exceeding a random threshold magnitude. Two models are treated. In model I, the machine operation time has exponential distribution and the life time of the machine is governed by SCBZ property; repair, recruitment, production and sale times have general distributions. In model II, when the operation time is more than a threshold, the sales are done altogether and when it is less than the threshold, the sales are done one by one. Joint transforms of the variables, their means and Co-variances with numerical results are presented. Mathematics Subject Classification: 91B70

Keywords: Storage system, Production and Sale, Repair and Recruitment, Joint transform.siewicz 𝑇𝐿

[1]. Arrow.K, Karlin.S and Scarf.H, Studies in Mathematical Theory of Inventory and Production, Stanford University Press, Stanford,
California (1958).
[2]. Danial.J.K and Ramanarayanan.R, an (S, s) inventory system with rest periods to the server, Naval Research Logistics, 35, (1988),
119-123.
[3]. Kun- Shan Wu, Ouyang and Liang -Yuh, (Q, r, L) inventory model with defective items, Computer and Industrial Engineering,
39(2001), 173-185.
[4]. Harikumar.K, General manpower and machine system with Markovian production and general sales, IOSR Journal of
Mathematics[IOSR-JM],e-ISSN,2278-5728,p-ISSN;2319-765X, volume10 Issue 6 Ver. VI(Nov-Dec2014)pp54-62.
[5]. Murthy.S and Ramanarayanan.R, Two ordering levels inventory system with different lead times and rest time to the server,
Inter.J.of Applied Math., 21(2), (2008) 265-280.

Abstract: We consider a global supply chain consisting of one retailer and one manufacturer, both from different countries. As there is a time lag between the payments made while placing the order and the time when the order is realized, risk in the form of the exchange rate fluctuation affects the optimal pricing and order quantity decisions. We explore the derivations of analytic expressions involving the transaction exposure when the retailer or manufacturer undertakes to share the exchange rate risk and the demand error is modelled in the
additive form in the news vendor framework.

Keywords: transaction exposure, exchange rate, global supply chain, newsvendor problem, optimal pricing and quantitywicz 𝑇𝐿

[1] F.J. Arcelus, Ravi Gor, G. Srinivasan, Foreign exchange transaction exposure in a newsvendor setting, European Journal of
Operational Research, 227(2013) 552-557
[2] Goel, M., 2012. Management of transaction exposure: a comparative analysis of MNCs in India. International Journal of Service
Science, Management, Engineering and Technology 3, 37–54.
[3] Eitemann, D.K., Stonehill, A.I., Moffett, M.H., 2010. Multinational Business Finance,12th ed. Prentice Hall, Boston.
[4] Shubita, M.F., Harris, P., Malindretos, J., Bobb, L.M., 2011. Foreign exchange exposure: an overview. International Research
Journal of Finance and Economics 78, 171–177.
[5] Petruzzi, N.C., Dada, M., 1999. Pricing and the newsboy problem: a review with extensions. Operations Research 47, 183–194.

Abstract: We consider a global supply chain consisting of one retailer and one manufacturer, both from different countries. As there is a time lag between the payments made while placing the order and the time when the order is realized, risk in the form of the exchange rate fluctuation affects the optimal pricing and order quantity decisions. We explore the derivations of analytic expressions involving the transaction exposure when the retailer or manufacturer undertakes to share the exchange rate risk and the demand error is modelled in the
multiplicative form in the news vendor framework.

Keywords: transaction exposure, exchange rate, global supply chain, newsvendor problem, optimal pricing and quantity𝑇𝐿

[1] F.J. Arcelus, Ravi Gor, G. Srinivasan, Foreign exchange transaction exposure in a newsvendor setting, European Journal of Operational Research, 227(2013) 552-557
[2] Goel, M., 2012. Management of transaction exposure: a comparative analysis of MNCs in India. International Journal of Service Science,
Management, Engineering and Technology 3, 37–54.
[3] Eitemann, D.K., Stonehill, A.I., Moffett, M.H., 2010. Multinational Business Finance,12th ed. Prentice Hall, Boston.
[4] Shubita, M.F., Harris, P., Malindretos, J., Bobb, L.M., 2011. Foreign exchange exposure: an overview. International Research Journal of Finance and Economics 78, 171–177.
[5] Petruzzi, N.C., Dada, M., 1999. Pricing and the newsboy problem: a review with extensions. Operations Research 47, 183–194.
[6] Mills, E.S., 1958. Uncertainty and price theory. Quarterly Journal of Economics 73, 116–130.

Abstract: In recent papers solution Two â€"Dimensional Diffusion Equations of partial differential equations with nonlocal boundary conditions was introduced using iterative laplace transform method. This method which combines two method iterative method and laplace transform method is successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases of the important equation comparsion with Special Class of Pade Approximants ,the numerical results of ILTM show that based numerical schemes are quite accurate and easily implemented

Keywords: Partial Differential Equations, Laplace Transform Method, Iterative Method.

[1]. A. B. Gumel, W. T. Ang and E. H. Twizell, Efficient Parallel Algorithm for the Two Dimensional Diffusion Equation Subject to
Specification of Mass, Intern. J. Computer Math, Vol.(64), p.(153 â€" 163) ,1997
[2]. Manoj K,Garima M, An Introduction to Numerical Methods for the Solutions of Partial Differential Equations,Applied Mathematics,
vol (2), no(4), pp (1327-1338), 2011.
[3]. Mohammad S,Solving Two â€"Dimensional Diffusion Equations with Nonlocal Boundary Conditions by a Special Class of Padé
Approximants,SYSTEMICS, CYBERNETICS AND INFORMATICS, vol (8), pp (1690-4524), 2010.
[4]. V.Daftardar-Gejji andH. Jafari, â€oeAn iterativemethod for solving nonlinear functional equations,― Journal of Mathematical
Analysis and Applications, vol(316), no(2), pp (753-763), 2006.
[5]. H. Jafari, Iterative Methods for solving system of fractional differential equations [Ph.D. thesis], Pune University, 2006.

Abstract: Aim of the paper is to investigate unsteady oscillatory free convective flow of a viscous incompressible electrically conducting fluid through a non-homogenous porous medium between two vertical parallel plates in slip flow regime in the presence of radiation, chemical reaction and temperature gradient dependent heat source. A uniform magnetic field is applied in the direction normal to the plate. The effect of free convection and chemical reaction on unsteady MHD oscillatory flow of fluid in vertical media is encountered in a wide range of engineering and industrial applications. The oscillatory time-dependent coupled non-linear equations are solved for the fluid velocity, temperature and concentration by using regular perturbation technique. Numerical results for the velocity, temperature, concentration profiles, local skin friction coefficient, local Nusselt number and Sherwood number for various physical parameters are discussed numerically and presented graphically.

Keywords: Unsteady, MHD, porous medium, chemical reaction, free-convection, temperature gradient dependant heat source, suction, radiation, skin-friction coefficient, Nusselt number and Sherwood number.

[1]. Acharya, M; Dash, G. C. and Singh, L. P., "Magnetic field effects on the free convection and mass transfer flow through porous medium with constant suction and constant heat flux". Indian J. Pure Appl. Math., Vol. 31, 2000, pp. 1-8.
[2]. Ajadi, S. O.; Adegoke, A. and Aziz, A., "Slip boundary layer flow of non-Newtonian fluid over a flat plate with convective thermal boundary condition". Int. J. of Nonlinear Sci., Vol. 8, 2009, pp. 300-306.
[3]. Attia, H. A. and Kotb, N. A., "MHD flow between two parallel plates with heat transfer". ACTA Mechanica, Vol. 117, 1996, pp. 215-220.
[4]. Chung, T. J., "Computational Fluid Dynamics". Cambridge University Press, 2002.
[5]. Devika, B.; Satyanarayana, P. V. And Venkataramana, S., "MHD oscillatory flow of a visco elastic fluid in a porous channel with chemical reaction". Int. J. of Engg. Sci. Invention, Vol. 2, 2013, pp. 26-35..
[6]. Ganesh, S. and Krishnambal, S., "Magnetohydrodynamic flow of viscous fluid between two parallel porous plates". J. of Appl. Sci., Vol. 6, 2006, pp. 2450-2425.

Abstract: In this paper, we introduced a new model called the geometric inverse burr distribution. Statistical measures and their properties are derived and discussed. In particular, explicit expression for the density, rth moment and entropy are obtained. The method of maximum likelihood estimator is used to obtain the estimate values of the parameters and provide the information matrix. Simulation studies are performed for different parameter values and sample sizes to assess the finite sample behavior of the MLEs.

Key Words: probability density function(pdf), probability mass function(pmf), geometric inverse burr(GIB) hazard function, cumulative distribution function(cdf), moments, maximum likelihood estimation(MLEs) and quartile.

[1]. Adamidis K, Dimitrakopoulou, T, Loukas S (2005) on a generalization of the exponential-geometric distribution. Statist. And Probab. Lett. 73:259-269
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[6]. Erdelyi A, Magnus W, Oberhettinger F, Tricomi FG (1953) Higher Transcendental function, McGraw-hill, New York

Abstract: We consider an extension to the lost sale recapture model in a newsvendor framework developed earlier by the authors. As in real practice, we have considered that there may be an opportunity to backlog the lost sales, by offering some incentive for waiting. The back log fill rate is modeled as a function of proportion of rebate relative to the price. The retailer's decision includes selling price, order quantity and the rebate that will maximize its expected profit. Sensitivities of the demand errors in the form of beta distribution rather than the uniform and the normal distribution serve as an extension to the previous work by the authors.
Keywords: newsvendor problem, lost sales, rebates, price dependent demand, beta distribution.

[1]. Alford, B.L., Biswas, A. (2002). The effects of discount level, price consciousness and sale proneness on consumers' price perception and behavioral intentions. Journal of Business Research 55, 775-783.
[2]. Arcelus, F.J, Ravi Gor, Srinivasan, G. (2012): Price, rebate and order quantity decisions in a newsvendor framework with rebate dependent recapture of lost sales, International Journal of Production Economics, Vol. 140, No. 1. (November 2012), 473-482.
[3]. Arcelus, F.J., Srinivasan, G. (1987). Inventory policies under various optimizing criteria and variable markup rates. Management Science 33, 756-762.
[4]. Arcelus, F. J., Kumar, S., Srinivasan, G. (2005). Retailer's response to alternate manufacturer's incentives under a single period, price-dependent, stochastic-demand framework. Decision Sciences 36, 599-626.
[5]. Aydin, G., Porteus, E.L. (2009). Manufacturer-to-Retailer versus Manufacturer-to-Consumer Rebates in a Supply Chain. In N. with the left-skewed (right-skewed) the next lowest (highest) and the symmetrical, Agrawal & S. Smith (Eds.), Retail Supply Chain Management. New York: Kluwer.
[6]. Bawa, K., Shoemaker, R.S. (1989). Analyzing Incremental Sales from a Direct Mail Coupon Promotion. Journal of Marketing 53, 66-78.

Abstract: In this paper, the study of evolution equations with two independent variables which are related to pseudospherical surfaces in 𝑅3, is extended to evolution equations with more than two independent variables. Equations of the type 𝑢𝑡=𝜓(𝑢,𝑢𝑥,……..,𝜕𝑘𝑢𝜕 𝑥𝑘 ,𝑢𝑦,………,𝜕𝑘ʹ𝑢𝜕 𝑦𝑘ʹ) are studied and characterized. Some features and results on properties of these equations are given via this study.
Keywords: Evolution equations, Pseudospherical surfaces, Riemannian manifold, Solitons and differential equations.

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Abstract: Our goal in this work, is to obtain sufficient conditions for the instability of the zero solution for a
certain fourth-order vector delay differential equation on the following form

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