iosr-Jm   Volume-14 ~ Issue-3 ~ May-June 2018

Abstract: This article deals the problem of optimally controlling the perishable inventory with exponential lead time in a finite capacity retrial service facility system. Arrival of demands to the system is assumed as Poisson and service times are assumed to follows an exponential distribution. For the given values of maximum inventory, maximum waiting space and reorder level, we determine the optimal ordering policy at various instants of time. The system is formulated as a Semi-Markov Decision Process and the optimum inventory control to be employed by using linear programming method. Numerical examples are provided to illustrate the
model..

Keywords:Single server, Service facility, Retrial queue, Inventory system, Perishable items, Semi-Markov Decision Process

[1]. Arivudainambi, D., Averbakh, I., and Berman, O., Stationary analysis of a single server retrial queue with priority and vacation, International Journal of Operational Research, 5 (2009) 26 - 47.
[2]. Artalejo, J.R., and Gomez-Corral, A., Retrial Queuing Systems: A Computational Approach, Springer, Berlin, (2008).

[3]. Artalejo, J.R., Rajagopalan, V., and Sivasamy, R., On finite Markovian queues with repeated attempts", Investigación Operativa., 9 (2000) 83 - 94.
[4]. Dragieva, V. I., A finite source retrial queue: number of retrials, Communications in Statistics - Theory and Methods, 42 (2013) 812-829.
[5]. Dudin, A. N., Manzo, R., and Piscopo, R., Single server retrial queue with group admission of customers, Computers & Operations Research, 61 (2015a) 89-99..

Abstract: A new concept of the c-distance in cone metric spaces has been introduced by Cho et al. [2] in 2011. Recently, Dubey, A.K. et al. [13] proved some fixed point results contractive conditions under c- distance in cone metric spaces. The purpose of this paper is to establish, extend and the generalization of fixed point theorems for contractive type mapping on complete cone metric spaces applying under c- distance. Our results generalize and extend some well known results in the literature [8].

Keywords: Cone metric space, complete cone metric space, c-distance, fixed point, contraction mapping..

[1]. Huang and Zhang. Cone metric spaces and fixed point theorems of Contractive Mappings, J. Math. Anal. Appl. 332, 1468-1476,(2007).
[2]. Cho, Y.J. Saadati, R.and Wang, S., common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl.,61, 1254-1260, (2011).
[3]. Kada, O., Suzuki, T. and Takahashi, W. , Non convex minimization theorems and fixed point theorems in complete metric spaces, Mathematica Japonica, 44, 381-391, (1996).
[4]. Situnavarat, W.,. Cho Y. J and Kumam, P., Common fixed point theorems for c- distance in ordered cone metric spaces, Comput. Math. APPL. 62, 1969-1978, (2011).
[5]. Wang, S. and Guo., B., Distance in cone metric spaces and common fixed point theorems, Applied Mathematics Letters, 24(2011), 17-1739.

Abstract: In this paper we introduce the concept of nano 𝑟𝑔∗∗𝑏......

Keywords: nano 𝑟𝑔∗∗𝑏-regular, nano 𝑟𝑔 ∗∗𝑏-normal.

[1]. Dhanis Arul Mary. A. and Arockiarani. I., Note on Nano b normal spaces, Bulletin of Mathematics and Statistics Research, 3(3) (2015), 124-136.
[2]. Maheswari. S.N. and Prasad. R., On s-regular spaces, Glasnik Mat.Ser.III, 10(1975), 347-350.
[3]. Maheswari.S.N. and Prasad. R., On s- normal spaces, Bull. Math. Soc. Sci. Math. R.S. Roumanie, 22(1978), 27-29.
[4]. Munshi. B.M., Separation axioms, Acta Ciencia Indica, 12(1986), 140-144.
[5]. Lellis Thivagar. M. and Carmel Richard, On Nano forms of weakly open sets, International Journal of Mathematics and Statistics Invention, 1(1) (2013), 31 -37...

Abstract: There exist infinite-dimensional extremely non-complex Banach spaces, i.e. spaces 𝑋 such that the norm equality ‖𝐼𝑑+𝑇2‖=1+‖𝑇2‖ holds for every bounded linear operator 𝑇 on 𝑋.show that every extremely non-complex Banach space has positive numerical index Keywords.Banachspace ;numerical index; extremely non-complex; diameter of slices. The concept of numerical index of a Banach space it is a parameter relating the norm and the numerical range of operators on the space. The numerical range was first introduced for matrices, and it was extended in the sixties to bounded linear operators on an arbitrary Banach space [1] , and we defined it for an operator................

[1]. KostyantynBoyko, Vladimir Kadets , Numerical index of Banach spaces and duality,Under consideration for publication in MathProc. Camb. Phil. Soc. 1
[2]. Miguel Martin, Javier Meri, Angel Rodriguez-Palacios , Finite-Dimensional Banach Spaces with Numerical Index Zero , extractamathematicaeVol. 19, Num. 1, 151–153 (2004)
[3]. Miguel Martin, Javier Meri, Extermely non-complex Banach Spaces, Central European Journal of Mathematics · DOI: 10.2478/s11533-011-0040-0 ( 2011)
[4]. PiotrKoszmider, Miguel Martin, AND Javier Mer ,ISOMETRIES ON EXTREMELY NON-COMPLEX BANACH SPACES ,Mathematics Subject Classification. Primary: 46B04. Secondary: 46B10, 46B20, 46E15, 47A99 (2010)...

Abstract: A four-point quadrature rule with degree of precision four for numerical integration of complex Cauchy principal value integrals has been constructed. An asymptotic error estimate and an error bound of the rule constructed have been derived. At the end, the rule constructed has been numerically verified.

Keywords: Cauchy Principal Value integrals, analytic function, quadrature rules, asymptotic error estimate, error bound and error constant. 2000 mathematical subject classification: No: 65D30

[1]. Acharya, B.P. And Das, R.N., Numerical evaluation of singular integrals of complex valued function, Journal of mathematical sciences 14-15, 40-44, 1979-1980.
[2]. Acharya, B.P., Mahapatra, T., A numerical computation of Complex Cauchy Principal Value Integral, Int. Journal of Computer Mathematics, 43, 147-151, 1992.
[3]. Acharya, B.P. and Das, R.N., Numerical determination of Cauchy Principal value integrals, Computing, vol.27, pp. 373-378 (1981).
[4]. Birckhoff, G., Young, D., Numerical quadrature of analytic and harmonic functions, J. math. Phy, 29, 217-221, 1950.
[5]. Conway, J.B., Functions of one complex variable, 2nd edition, Narosa Publishing house, New York, 1980.

Abstract: Special differential equations and polynomials are very popular in the field of mathematics and serve as important tools in the solution of some engineering problems. Examples of these equations are Legendre, Hermite, Laguerre, Bessel, Gegenbaur differential equations. In this paper, we established a new special differential equation and its polynomial which we called Legendre subsidiary equation and polynomial. The Rodrigue formula, generating function and recurrence relations of the polynomial are given. We also gave the orthogonality properties of the polynomials, and our results are entering the literature for the first time.

Keywords: Rodrigue formula, generating function, recurrence relations and orthogonality.

[1]. E. D. Rainville, Special Functions, Macmillan, New York, 1960; Reprinted by Chelsea Publ. Co., Bronx, New York, 1971.
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Abstract: Our aim of this paper is to find some more common fixed point theorems satisfying rational type contractive mappings in 2-metric spaces, which are generalizations of various known results.

Keywords: fixed point theorem , metric space, contraction.

[1]. Aage, C. T. and Salunke, J. N., "On Fixed Point Theorems in Fuzzy Metric Spaces." Int. J. Open Problems Compt. Math., 3 (2), (2010), 123-131.
[2]. Banach, S. "Surles Operation Dansles Ensembles Abstraites Etleur Application Integrals." Fund. Math., 3, (1922), 133-181.
[3]. Cho, Y.J, "Fixed Points for Compatible Mappings of Type (A)." Math. Japonica, 38(3), (1993), 497-508.
[4]. Cho Y.J, Khan M.S. and Singh S.L., Common Fixed Points of Weakly Commutating Mappings." Univ. Novom Sadu, Sb.Rd. Prirod-Mat. Fak. Ser. Mat., 18(1), (1988), 129-142.
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Abstract: A real representation of the split quaternion matrix is defined and its properties are studied. The differences between three representations are discussed. Then the split quaternionic least squares problem is studied in detail from norm, definition to computation, and an algebraic method is obtained for finding solutions of the problem in split quaternionic mechanics. Numerical examples show that our method is effective and better than that of the paper[Z. Zhang, Z. Jiang, T. Jiang, Algebraic methods for least squares problem in split quaternionic mechanics, Applied Mathematics and Computation, 269 (2015), 618-625.]

Keywords: split quaternion matrix; real presentation; split quaternionic least squares

[1]. Y. Alagoz, K.H. Oral, S. Yuce, Split quaternion matrices, Miskolc Math. Notes,13(2012)223–232
[2]. D.C. Brody, E.M. Graefe, On complexified mechanics and coquaternions, J. Phys. A: Math. Theor., 44 (2011) 072001.
[3]. N. Moiseyev, Non-Hermitian Quantum Mechanics, Cambridge University Press, 2011.
[4]. Z. Zhang, Z. Jiang, T. Jiang, Algebraic methods for least squares problem in split quaternionic mechanics, Applied Mathematics and Computation, 269 (2015), 618-625.
[5]. Z.-Z. Bai, G.H. Golub and M.K. Ng, Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, SIAM Journal on Matrix Analysis and Applications, 24(2003), 603-626..

Abstract: This paper attempts to perform an appropriate ARIMA model for forecasting Sudanese pound against USA dollar exchange rate. Both The Augmented Dickey Fuller (ADF) and correlogram tests were applied to exchange rate data. It is found that exchange rate series showed a unit roots (i.e. exchange rate series level is non stationary) however the first difference of exchange rate series is seristationary.Box-Jenkins approach through the stages of identification, estimation and diagnostic checking were applied to data representing exchange rate in the Sudan. The ACF and PACF indicates that ARIMA(1,1,0) an appropriate however, the diagnostic checking concluded that the error term of the model does not follow normal distribution. ARIMA(2,1,1) also estimated and checked however the error terms seems not normal, numerous ARIMA (p,d,q) models have been suggested with the objective of deciding which of these models is adequate to fit exchange rate data in the Sudan, ARIMA(1,1,0) model is selected as a greatest one according to corresponding AIC, SBC of model selection criteria.

Keywords: Time series, exchange rate ADF test, Correlogram, Box-Jenkins, ARIMA models, AIC, SBC.

[1]. Anderas, S. and Reou, "Exchange Rates Forecasting: A Hybrid Algorithm Based on Genetically Optimized Adaptive Neural
Networks", Computational Economics, 2002, pp.191-210.
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Economics, 23(8), 1377-1384.
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monetary policies. Applied Economics, 22(7), 917-925.
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Abstract: This paper discusses maximum likelihood estimation (M L) approach to derive availability measures of a two unit system with common cause shocks (CCS) as well as Human errors. Availability estimates for timedependent and steady-state availability were developed in the case of series and parallel systems. The purpose of this investigation is to incorporate the possibility of Human errors in reliability analysis. We developed empirical evidence to establish the validity of the proposed estimates by Monte Carlo Simulation

Keywords: Availability, Common cause shock failures, Human errors, M L Estimation, Simulation.

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2770, EGG-Ea-5485, 1983.
[2]. Billinton, R and Allan, R. N, Reliability evaluation of engineering systems; concepts and techniques, (Plenum Press, 1983, New
York).
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[4]. B. S. Dhillon, On common cause failures, Bibliography, Microelectronics and Reliability, 18(6), 533-534.
[5]. G. Y. Sagar, S. M. Verma, A.A. Chari, Y.R. Reddy and G.S.S.Raju, Availability and Frequency Measures of a Two Unit System
with CCS Failures and Human Errors, International Journal of Agricultural and Statistical Sciences, 3(2), 2007, 507 – 516.

Abstract: A conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. In particular, any change in such a conserved quantity can only occur as a result of an "influx" or an "outflow" of this quantity into or out of the system. In this paper, we study a class of first order PDEs that may serve as mathematical descriptions of physical conservation laws, such as the laws of gas dynamics and the laws of electromagnetism. We show how the viscosity method, known as the vanishing viscosity method, can be used to construct the entropy solution of the scalar conservation law as the limit of solutions of the parabolic equations with viscous term.

Keywords: Partial differential equations, Conservation laws, jump condition, vanishing viscosity method, entropy solution.

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(AMiTaNS’11), (St Constantine and Helena, Bulgaria), American Institute of Physics AIP Conference Proceedings 1487, 2012,
151-158.