iosr-Jm   Volume-13 ~ Issue-2 ~ Mar-Apr 2017

Abstract: This paper analyses a discrete time Geo/G/1 retrial queuing system with general retrial times, multiple vacations and state dependent arrivals. Here the arrival rates are different when the system is idle and busy or on vacation. If the server is busy or on vacation at the arrival epoch, the customers joins the orbit to repeat the request later. On the other hand, if the server is idle, then the arriving customer begins its service immediately. The customers in the orbit try for service when the server is idle...............

Keywords: Discrete time retrial queues, general retrial times, state dependent arrivals, multiple vacation, Markov chain.

[1]. J.R. Artalejo, Accessible bibliography on retrial queues, Math. Computer Model. 30, 1999, 1–6.
[2]. J.R. Artalejo, A classified bibliography of research on retrial queues: Progress in 1990–1999, Top 7, 1999, 187–211.
[3]. J.R. Artalejo, Accessible bibliography on retrial queues: progress in 2000–2009, Math. Computer. Model, 51, 2010, 1071–1081.
[4]. J.R. Artalejo, A. Gomez-Corral, Retrial Queueing Systems: A Computational Approach, (Springer, Berlin, 2008).
[5]. J.R. Artalejo, Analysis of an M/G/1 queue with constant repeated attempts and server vacations, Computers and Operations Research, 1997, 24, 493-504.

Abstract: Levine [7] introduced the notion of g-closed sets and further proper ties of g-closed sets are investigated. In 1982, the notions of 𝜔-open and 𝜔-closed sets were introduced and studied by Hdeib [5]. Khalid Y. Al-Zoubi [6] introduced the notion of g𝜔-closed sets and further properties of g𝜔-closed sets are investigated. In this paper, we introduce the notion of mg𝜔-closed sets and obtain the unified characterizations for certain families of subsets between closed sets and g𝜔-closed sets.

Keywords: gw𝜔-closed set, m-structure, m-space, mg𝜔 -closed set..

[1] Al-Omari. A and Noorani. M. S. M., Regular Generalized 𝜔-Closed sets, International Journal of Mathematics and
Mathematical Scoences, Volume 2007, 1-11
[2] Arockiarani. I, Balachandran. K and Janaki. C, On Contra-𝜋g𝛼 -Continuous Functions, Kochi J. Math., 3(2008), 201-209.
[3] Dhanasekaran. V, Nagalakshmi. K. T and Ravi. O, Locally Closed Sets in 𝜔-Topological Spaces, Submitted.
[4] Dontchev. J and Noiri. T, Quasi-Normal Spaces and 𝜋 g-Closed Sets, Acta Math. Hungar., 89(3), (2000), 211-219.
[5] Hdeib. H. Z, 𝜔-Closed Mappings, Revista Colomb. De Matem., 16(1-2), (1982), 65-78.

Abstract: The properties of the families F of finite subsets of n element set S are considered in the situation, where subsets of F are incomparable on the binary relation of inclusion and a)for any A F there exists some set A'F such that either A  A' or A' A; b)for any AF is place.......

Keywords: maximal Sperner family, typical property.

[1]. Gilbert E. N. Lattice theoretic properties of frontal switching functions, J. Math. Phys., 33, №1 (1954), pp. 57-67.
[2]. Sperner E. Ein Satz über Untermengen einer edlichen Menge, Math. Z. 27 (1928), 544-548.
[3]. Kochkarev B. S. Structural properties of a class of maximal Sperner families of the finite set, Logika I prilogeniya, Tez. Megdunar.
konf. posv. 60-letiju so dnya rogd. acad. Ju. L. Ershova, Novosibirsk, 2000, pp. 60-61.
[4]. Kochkarev B.S. Structural properties of a class of maximal Sperner families of subsets, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, 7,
pp. 37-42.
[5]. Kochkarev B.S. On a class of maximal Sperner families of subsets of a finite set, Proceedings of Mathematical Center named after
N.I. Lobachevskii. Vol. 11, Unipress, 2001, pp. 160-162

Abstract: We consider the non-linear partial differential equation of time-fractional type describing the spontaneous imbibition of water by an oil-saturated rock (double phase flow through porous media). The fact that oil and water form two immiscible liquid phases and water represents preferentially wet-ting phase are the basic assumption of this work. The Elzaki Transform Decomposition Method is used to obtain the saturation of injected water. We obtain the graphical representation of solution using MATLAB R2007b and Microsoft Excel 2010 with different fractional order (α > 0)................

Keywords:Fractional derivative, Fingero-imbibition, Double phase flow in porous media, immiscible fluid, Elzaki Transform Decomposition Method.

[1]. T.M.Elzaki and S.M.Elzaki and E.A.Elnour , On the New Integral Transform " Elzaki Transform" Fundamental Properties Investigations and Applications, Glo.J.Math. Sci.,4, (2012), 1-13.
[2]. O. Abdulaziz, I. Hashim, M. S. H. Chowdhury, and A. K. Zulkifle. Assessment of decomposition method for linear and nonlinear fractional differential equations, Far East Journal of Applied Mathematics, vol. 28, no. 1, pp. 95-112, 2007.
[3]. O. Abdulaziz, I. Hashim, and A. Saif. Series Solution of Time-Fractional PDEs by Homotopy Analysis Method, Hindawi Publishing Corporation, Differential Equations and Nonlinear Mechanics, pps. 16, 2008. REFERENCES 228
[4]. T.M.Elzaki and E.M.A. Hilal, Homotopy Perturbation and Elzaki Transform for Solving Nonlinear Partial Differential Equations, Math. Theor. Mod., 2, (2012), 33-42.
[5]. A. S. Bataineh, M. S. M. Noorani, and I. Hashim. Approximate solutions of singular twopoint BVPs by modified homotopy analysis method, Physics Letters A, vol. 372, no. 22, pp. 4062-4066, 2008.

Abstract: Nonlinear phenomena play a major role in applied mathematics and engineering. The Burger-Fisher equation which is a mixed hyperbolic-parabolic non-linear partial differential equation occurs in various areas of applied sciences and physical applications, such as modeling of gas dynamics and fluid mechanics. In this paper, Haar wavelet method was implemented efficiently in finding the numerical solution of Burger-Fisher equation. This method shows rather rapid convergence than other existing methods. Illustrative examples suggest that using wavelet based method providing a powerful approach to find numerical solutions of Burger-Fisher equation............

Keywords: Burger's-Fisher equation, Haar wavelet method, Variational iteration method.

[1]. Mittal RC, Jiwar R (2009) Differential Quadrature Method for Two Dimensional Burgers' Equations. International Journal of Computational Methods in Engineering Science and Mechanics 10: 450–459.
[2]. Mittal RC, Tripathi A (2014) Numerical solutions of generalized Burgers—Fisher and generalized Burgers— Huxley equations using collocation of cubic B-splines.International Journal of Computer Mathematics http://dx.doi. org/10. 1080/00207160.2014.920834.
[3]. Kheiri H, Ebadi DG (2010) Application of the (G0/G)-expansion method for the Burgers, Fisher, and Burgers- Fisher equations, Acta Universitatis Apulensis 24: 35–44.
[4]. Nawaz R, Ullah H, Islam S, Idrees M (2013) Application of optimal homotopy asymptotic method to Burger equations. Journal of Applied Mathematics http://dx.doi.org/10.1155/2013/387478 doi: 10.1155/ 2013/935154 PMID: 24415902
[5]. J. Lu, G. Yu-Cui, X. Shu-Jiang, ―Some new exact solutions to the Burger-Fisher equation and generalized Burgers-Fisher equation‖, Chinese Physics, vol. 16, no. 9, pp. 1009-1963, 2007.

Abstract: In this paper we have deal with the role of a dual space of a function space . In dealing so we will try to observe that the behavior of the dual space is the same as for the function space or not . That is why if a result holds good for a function space then same type of result also holds good for it dual space in case of convergences .

Keywords: Linear space, Sequence space, Function space, Dual Space, Perfect space, Parametric limit and parametric convergent, projective limit and projective convergent.

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Abstract: We started looking for a formula to simplify the calculation of the difference of two k–Fibonacci numbers depending on the kind of subscripts. Then we study the value of the determinant of circulant matrices whose entries are k–Fibonacci numbers. We continue calculating their eigenvalues and finish with the calculation of the eigenvalues of the matrix obtained multiplying the k–Fibonacci

Keywords: k–Fibonacci and k–Lucas numbers, Eigenvalues, Circulant matrix.

[1] V.E. Hoggat, Fibonacci and Lucas numbers, Palo Alto, CA: Houghton-Mifflin; 1969.
[2] A.F. Horadam, A generalized Fibonacci sequence, Math. Mag., Vol. 68, 1961, 455–459.
[3] Sergio Falcon, A. Plaza, On the Fibonacci k-numbers, Chaos, Solit. & Fract., Vol. 32(5), 2007, 1615–24.
[4] Sergio Falcon, A. Plaza, The k-Fibonacci sequence and the Pascal 2-triangle, Chaos, Solit. & Fract., Vol. 33(1), 2007, 38–49.
[5] Sergio Falcon, On the k–Lucas numbers, Int. J. Contemp. Math. Sciences, Vol. 6(21), 2011, 1039–1050.

Abstract: In this paper, a numerical algorithm for solving hybrid fuzzy initial value problem using the Fourth Order Runge-Kutta method based on Geometric Mean (RK4GM) is proposed. The algorithm is illustrated by solving hybrid fuzzy initial value problems using triangular fuzzy number. It is compared with the classical fourth order Runge – Kutta method. The results show that the proposed fourth order Runge-Kutta method based on Geometric Mean works well for solving hybrid fuzzy initial value problems.

Keywords: Numerical solution, Hybrid Fuzzy Initial Value Problems, Triangular fuzzy number, Fourth order Runge-Kutta method, Geometric Mean

[1]. Abbasbandy. S, Allah Viranloo. T, Numerical solution of fuzzy differential equations by Runge-Kutta method, Nonlinear studies.11(2004)N0.1,117-129.
[2]. Abbasbandy. S, Allahviranloo. T, Numerical solution of fuzzy differential equations by Taylor method, Journal of Computational Methods and Applied Mathematics, 2(2002)113-124.
[3]. Abdul-Majid Wazwaz, A comparision of modified Runge-Kutta formulas based on a variety of means, International Journal of Computer Mathematics, vol.50,pp-105-112.
[4]. Balachandran. K, Prakash. P, Existence of solutions of fuzzy delay differential equations with nonlocal condition, Journal of the Korea Society for Industrial and Applied Mathematics, 6(2002)81-89.
[5]. Balachandran. K, Kanagarajan. K, Existence of solutions of fuzzy delay integrodifferential equations with nonlocal condition, Journal of the Korea Society for Industrial and Applied Mathematics, 9(2005)65-74.

Abstract: Let 𝑓: 𝑉(𝐺) → 𝑁 be a labeling of the vertices of a graph 𝐺 by positive integers. Define 𝑆 𝑣 = 𝑢∈𝑁(𝑣) 𝑓(𝑢), as the sum of neighborhood of vertex 𝑣, where 𝑁(𝑣) denotes the open neighborhood of 𝑣 ∈ 𝑉. A labeling 𝑓 is lucky if 𝑆(𝑢) ≠ 𝑆(𝑣) for every pair of adjacent vertices 𝑢 and 𝑣. The lucky number of a graph 𝐺, denoted by 𝜂(𝐺) , is the least positive integer 𝑘 such that 𝐺 has a lucky labeling with {1,2, … , 𝑘} as the set of labels. A Lucky labeling is proper lucky labeling if the labeling 𝑓 is proper as well as lucky, i.e. if 𝑢 and 𝑣 are adjacent in 𝐺 then 𝑓(𝑢) ≠ 𝑓(𝑣)and 𝑆(𝑢) ............

Keywords: Lucky labeling, Proper Lucky labeling, Bloom Graph.

[1]. A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Inter-nat. Symposium, Rome, July 1966), Gordon and
Breach, N. Y. and Dunod Paris 349-355, 1967.
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157, 2004.
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Abstract: Behaviour pattern of degradation of plastic material is very important in industrial applications. Activation energy is hindering factor in the degradation process of plastic materials. This is the very important in the selecting the plastic materials. In this study objective is activation energy could be predicted as the function of temperature and time. Experiment results of heated polypropylene plastic pieces (3×15cm) for 0-8 hours have presented the effect of isothermal temperature..................

Keywords: Weight loss, polypropylene, Activation Energy

[1]. Moinuddin., S , Mohammad M,R, Muhammad., S. R , Mohammad, M., Polypropylene Waste Plastic into Light Fractional Gasoline Grade Fuel for Vehicle by using Two Step Thermal Processes, Int. J. Forest, Soil and Erosion, 2012 2 (4): 186-191,
[2]. Al-Furhood, J. A., Alsewailem, F. D. , Almutabaqani, L. A., Activation Energy for the pyrolysis of polymer wastes., Eur. Chem. Bull., 2014, 3(1), 93-97
[3]. Gersten J, Fainberg V, Hetsroni G, Shindler Y. Kinetic study of the thermaldecomposition of polypropylene. oil shale and their mixture. Fuel 2000;79(13):1679-1686.
[4]. Arao Y, Nakamura S, Tomita Y, Takakuwa K, Umemura T, Tanaka T. Improvement on fire retardancy of wood flour/polypropylene composites using various fire retardants. Polym Degrad Stab 2014;100(1):79-85.
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Abstract: In this paper some criteria for the oscillation of mixed type third order neutral difference equation of the form..................

Keywords: Mixed neutral difference equation, Nonlinear, Non-oscillation, Oscillation.

[1]. R. P. Agarwal, P. J. Y. Wong, Advanced Topics in Difference Equations, Kluwer Academic Publishers, Dordrecht, 1997.
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Abstract: In the apparel industry Cut Order Planning (COP) considered as the most important procedure in the production process. Cutting large number of pieces with different shapes and sizes should be well planned to increase the utilization of fabric while reducing the wastage. Therefore cut planners pay great deal of attention to the number of plies, size ratios, length of the fabric, the cost of labour and they highly concerned about fabric wastage. This procedure is carried out manually in most of the factories. Due to that, high cost of labour, time and the fabric wastage have become more crucial problems in this industry...................

Keywords: Cut Order Plan, Dockets, Size Ratios

[1]. J.C. Ammons and C. J. Blecha "Cut Order Planning –Short Term Task, Final Report" 1991.
[2]. R. P. Abeysooriya, T.G.I. Fernando "Canonical Genetic Algorithm To Optimize Cut Order Plan Solutions in Apparel Manufacturing", Journal of Emerging Trends in Computing and Information Sciences, vol. 3, no. 2, 2012.
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[4]. K. Puasakul and P. Chaovalitwongse - "The Review of Mark Planning Problem", Engineering Journal, vol. 20 issue 3, 2016.
[5]. W.K. Wong, C.K Chan, C.K. Kwong, P.Y. Mok, and W.H. Ip " Optimization of manual fabric-cutting process in apparel manufacture using genetic algorithms" The International Journal of Advanced Manufacturing Technology, vol 27, issue 1, pp. 152-158, 2005.

Abstract: This paper introduce two different definitions of fractional derivatives, namely Riemann-Liouville and Caputo derivatives , and some basics properties of these derivatives are discussed, conformable fractional derivative are addressed . The paper focuses on the conditions needed in order to guarantee the general solution when we have the particular solution by applied some theorems . illustrated some examples...................

Keywords: Gamma Function, Beta Function, Mittag-Leffler Function, Complementary Error Function, Fractional Integration, Riemann-Liouville derivative, fractional Caputo operator, conformable fractional derivative.

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Abstract: The concept of scalar commutativity defined in an algebra over a ring is mixed with the concept of pseudo commutativity defined in a near – ring to define the new concept of scalar pseudo commutativity in an algebra over a ring and many interesting results are obtained.

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Abstract: The aim of this study is to propose the use of the fuzzy systematic technique as aunifying format for analyzing diverse input data sources using both triangular fuzzy numbers (TFNs) and intuitionistic fuzzy numbers (IFNs). It focuses on converting three different data sources into the unifying format which consists of crisp values, interval values as well as linguistic expressions. This study utilizedthe experience of experts in order to construct the membership functions for the crisp datasets, while the advantages of both the TFNs and IFNs based onthe cost-benefitcriterion were employed respectively for datasets whichoccurred naturally in interval and linguistic forms..............

Keywords: Fuzzy unifying format, input data sources, Intuitionistic Fuzzy Numbers (IFNs), multi-criteria decision-making (MCDM), Triangular Fuzzy Numbers (TFNs)

[1] Suwelack, K., & Dominik W. An approach to unify the appraisal framework for biomass conversion systems. Biomass and Bioenergy, 83, 2015, 354-365.
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