iosr-Jm   Volume-12 ~ Issue-3 ~ May-June 2016

Abstract: In this paper, we availed the opportunity of extending the concepts of Babu.G.V.R, Sarma.K.K.M, and Kumari.V.A [9] by introducing a pair ( f , g) of weak generalized ( , )  contractive maps with rational expressions and prove the existence of common fixed points when ( f , g) is a pair of weakly compatible maps and the range of g is complete in partially ordered patrial b - metric spaces where f is a triangular (, g)  admissible map. Further, we also extend the same conclusions by relaxing........

Keywords: Partially ordered patrial b - metric spaces,   admissible, (, g)  admissible, triangular   admissible, triangular (, g)  admissible, ( , )  contractive mapping, a pair ( f , g) of weak generalized ( , )  contractive maps with rational expressions.

[1]. Arshad.M,Karapinar.E,Ahmad.J, Some unique fixed point theorems for rational contractions in partially ordered metric spaces,
Journal Of Inequalities and Appl., Article ID307234, (2013).
[2]. S. M. A. Aleomraninejad, S. Rezapour, and N. Shahzad, On fixed point generalizations of Suzuki's method , Applied Mathematics
Letters, vol. 24, no. 7, pp. 1037-1040, 2011.
[3]. Aleomraninejad.S.M.A,Rezapour.S,Shahzad.N, Fixed points of hemi-convex multifunctions, Topological Methods in Nonlinear
Analysis, vol. 37, no. 2, pp. 383-389, 2011.
[4]. Aleomraninejad.S.M.A,Rezapour.S,Shahzad.N., Some fixed point results on a metric space with a graph , Topology and its
Applications, vol. 159, no. 3, pp. 659-663, 2012.
[5]. Alghamdi.M.A,Alnafei.S.H,Radenovic.S,Shahzad.N.,Fixed point theorems for convex contraction mappings on cone metric spaces,
Mathematical and Computer Modelling, vol. 54, no. 9-10, pp. 2020-2026, 2011.

Abstract:In this paper we are interested to the estimation of the mean  of a multivariate normal distribution p  p  X N I 2 ~  , in p  , by a shrinkage estimators deduced from the empirical average estimator. We study bounds and limits of risk ratios of some minimax shrinkage estimators in the both cases 2  known and unknown. We show that the limit of risk ratios of polynomial estimator, estimator proposed by T.F. Li and W.H. Kuo [9] and the estimator proposed by D. Benmansour and T. Mourid, [3] to the maximum likelihood estimator X tend to values less than one.
Keywords: James-Stein estimator, multivariate normal distribution, non-central chi-square distribution, quadratic risk, shrinkage estimator.

[1]. A.J. Baranchik, Multiple regression and estimation of the mean of a multivariate normal distribution, Stanford Univ. Technical
Report (51), 1964.
[2]. D. Benmansour and A. Hamdaoui. Limit of the Ratio of Risks of James-Stein Estimators with Unknown Variance. Far East Journal
of Theorical Statistics, 36(1), 2011, 31-53.
[3]. D. Benmansour, T. Mourid, Etude d'une classe d'estimateurs avec rétrécisseur de la moyenne d'une loi gaussienne, Annales de
l.ISUP, Fascicule 51, 2007, 1-2.
[4]. A.C. Brandwein, and W.E. Strawderman, Stein Estimation for Spheri-cally Symmetric Distributions : Recent Developments,
Statistical Science, 27(1), 2012, 11-23.

Abstract:In this paper we introduce the notion of right strongly prime gamma Semiring and study some properties of right strongly prime ternary gamma Semiring. Mathematics Subject Classification: 16Y30.
Keywords: Ternary Γ-Semiring, Prime ternary Γ-ideal, Strongly Prime Ternary Γ-Semiring, Strongly Prime Ternary Γ-Ideal.

[1]. Dutta. T. K. and Kar. S., On Regular Ternary Semiring, Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics, World Scientific (2003), 343-355.
[2]. Dutta. T. K and Das. M. L., On Strongly Prime Semiring, Bull. Malays. Math. Sci. Soc. (2) 30 (2) (2007), 135-141.
[3]. Handelman. D. and Lawrence. J., Strongly Prime Rings, Trans. Amer. Mat. Soc. 211 (1975), 209-223.
[4]. Lister, W. G., Ternary Rings, Trans. Amer. Math. Soc. 154 (1971), 37-55.
[5]. Sajani Lavanya. M, Madhusudhana Rao. D.and Syam Julius Rajendra. V., On Lateral Ternary Γ-Ideals of Ternary Γ-Semirings, American International Journal of Research in Science, Technology, Engineering & Mathematics, 12(1), September-November, 2015, 11-14.

Abstract: A New method of evaluation of Numerical integration by using Harmonic Mean derivative - based closed Newton cotes quadrature rule (HMDCNC) is presented, in which the Harmonic mean value is used for Computing the function derivative. It has shown that the proposed rule gives increase of single order of precision over the existing closed Newton cotes rule. The error terms are also obtained by using the concept of precision and are compared with the existing methods. Finally, the accuracy of the proposed rule is analyzed using Numerical Examples and the results are compared with the existing methods.
Keywords: Closed Newton-Cotes formula, Error terms, Harmonic Mean Derivative, Numerical Examples, Numerical Integration .

[1] M.Evan and T.Swartz, "Methods for approximating integrals in statistics with special Emphasis on Bayesian integration problem",Statistical Science, vol.10 , pp. 254 - 272, 1995.
[2] M.K.Jain,S.R.K.Iyengar and R.K.Jain, Numerical methods for Scientific and Computation, New Age International (P) limited, Fifth Edition ,2007.
[3] M.Dehghan, M.Masjed-Jamei, and M.R.Eslahchi, "On numerical improvement of closed Newton-Cotes quadrature rules", Applied Mathematics and Computations, vol.165, pp. 251-260 , 2005.
[4] M.Dehghan, M.Masjed-Jamei, and M.R.Eslahchi, "On numerical improvement of open Newton-Cotes quadrature rules", Applied Mathematics and Computations, vol.175, pp. 618-627 , 2006.
[5] M.Dehghan, M.Masjed-Jamei, and M.R.Eslahchi, "The semi-open Newton-Cotes quadrature rule and its numerical improvement", Applied Mathematics and Computations, vol.171, pp. 1129-1140 , 2005.

Abstract:The paper studies the degree of approximation of Fourier series of functions in Besove space by Riesz Means and this generalizes many known results.
Keywords: Besove space,Holders space,Lipschitz space, Riesz mean, Fourier series, modulus of smoothness.

[1]. Das, G., Ghosh, T. and Ray, B.K: Degree of Approximation of function by their Fourier series in the generalized Holder metric, proc.
Indian Acad. Sci. (Math.Sci) 106(2)(1996) 139-153.
[2]. Devore Ronald A. Lorentz, G.: Constructive approximation, Springler- Verlay, Berlin Heidelberg New York, 1993.
[3]. Prossdorf, S.: Zur Konvergenz der Fourier richen Holder stetiger Funktionen math.Nachar, 69(1975),7-14.
[4]. Wojtaszczyk, P.: A Mathematical Introduction to Wevlets, London Mathematical Society students texts 37, Cambridge University
Press, New York, 1997.
[5]. Zygmund, A .: Smooth fuctions, Duke math. Jounal 12(1945), 47-56.
[6]. Zygmund,A.: Trigonometric series vols I & II combined, Cambridge Univ. Press, New York, 1993.

Abstract: In this paper, we study the inventory model for deteriorating items with triangular type demand rate, that is, the demand rate is a piecewise linear function. The inventory system consists of several replenishments and all the ordering cycles are of fixed length. We have considered two cases in first case we have considered that 0<𝑡1<𝜆 and in the other we have taken 𝜆≤𝑡1<𝑇; Where t1 is the time when the inventory level reaches zero and 𝜆 is time point changing from the increasing linearly demand to decreasing linearly demand
Keywords: ....................

[1] Cheng, Mingbao, Wang, Guoqing (2009). A note on the inventory model for deteriorating items with trapezoidal type demand rate Computers & Industrial Engineering 56, 1296–1300.
[2] Benkherouf, L. (1995). On an inventory model with deteriorating items and decreasing time-varying demand and shortages. European Journal of Operational Research, 86, 293–299.
[3] Deng, Peter Shaohua, Lin, Robert H.-J., & Chu, Peter (2007). A note on the inventory models for deteriorating items with ramp type demand rate. European Journal of Operational Research, 178, 112–120.
[4] Giri, B. C., Jalan, A. K., & Chaudhuri, K. S. (2003). Economic order quantity model with Weibull deterioration distribution, shortage and ramp-type demand. International Journal of Systems Science, 34, 237–243.

Abstract: The method of median polish with covariate is use for verifying the relationship between before and after treatment data. The relationship is base on the yield of grain crops for both before and after data in a classification of contingency table. The main effects such as grand, column and row effects were estimated using median polish algorithm..............
Keywords: Before and after data, Robustness, Exploratory data analysis, Median polish with covariate, Logarithmic transformation

[1]. Emerson, J. D. & Hoaglin, D. C. (1983).Analysis of two-way tables by medians. Understanding Robust and Exploratory Data Analysis 165–210.
[2]. Fitrianto A. et al. (2014). Median Polish for final Grades of MTH3000 and MTH 4000- Level courses. .Journal of Applied of Mathematical Science Vol. 3:126, 6295-6302
[3]. Freeman, G.H. (1973). Analysis of Interaction in Incomplete Two-way Tables, National Vegetable Research Station, Wellesbourne, Warwick, 1973 Green, R.H. (1979). Sampling design &statistical methods for environmental biologists.
[4]. John Wiley & Sons Goodall C. (1983). Examining Residuals; Understanding Robust and Exploratory Data Analysis, New York: John Wiley & Sons 211-246

Abstract: This paper reflects the present, past & future of Sudan domestic airline services. It is an attempt to identify the extent of aviation development in Sudan, particularly domestic flight services; by estimating the function of total cost. The data were obtained from the Planning Directorate of Sudan Civil Aviation Authority, Air Transport Directorate, Sudan Airways Directorate of Central Planning and some other currently active Sudanese airlines. The data were statistically analyzed determine the annual cost function of six Sudan airlines companies for the period from 2004 to 2013...........
Keywords: Classical Linear Regression Model, Cost Function, Fuel Price, Load Factor.

[1]. Sultan, A.M. (2012). Aviation Prospect in Sudan, Unpublished, Khartoum, Sudan, Issue 3, 1-15.
[2]. D.G.,C.A.A.(2002). Khartoum New International Airport (KNIA) Feasibility Study, Civil Aviation Khartoum, Sudan, 6-12.
[3]. Sultan, A.M., Siddig, M.K. (2006). Air Transport Company Feasibility Study, Civil Aviation, Khartoum, Sudan, 5-12.
[4]. Director S.A.C. planning (2012). Sudan Airways Central Planning Directorate, Khartoum, Sudan.
[5]. Director S.A.C. Planning (2012). Sudan Airways Research Study Directorate, Unpublished Manuscript, Khartoum, Sudan.
[6]. S.C.A.A. (2012). Sudan Civil Aviation Integrated Statistics Centre, Khartoum, Sudan.

Abstract: Let 𝑆 be a 2-torsion free semiprime semiring and 𝑇:𝑆→𝑆 𝑏𝑒 an additive mapping. Then we prove that every Jordan left centralizer on 𝑆 is a left centralizer on 𝑆. We also prove that every Jordan centralizer of a 2-torsion free Semiprime Semiring is a centralizer
Keywords: Semiring, Semiprime Semiring , left(right)centralizer,Centralizer, Jordan centralizer

[1] Jonathan S.Golan, Semirings and their Applications, Kluwer Academic Press(1969).
[2] Chandramouleeswaran, Thiruveni, On Derivations of Semirings, Advances in Algebra, 3(1) (2010), 123-131
[3] Herstein I.N., Topics in ring theory, University of Chicago Press, 1969.
[4] BorutZalar , On centralizers of Semiprime rings. Commentationes Mathematicae Universitatis Carolinae, Vol, 32(1991), N0.4,609-614
[5] Joso. Vukman, Centralizers on semiprime rings, Comment,Math.Univ.Carolinae 42,2(2001),237-245..

Abstract:In this article we found the numerical solution of singularly perturbed one dimensional convection diffusion equation using Non-Standard finite difference method by following the Mickens Rules. To compare the results with the known methods we also found solution of one dimensional convection diffusion equation using standard backward and central finite difference schemes. The work has been illustrated through the examples for different values of small parameter ϵ, with different step lengths.....
Keywords: Convection diffusion problem; Non-standard finite difference method; Perturbation problem; Absolute error.

[1]. R. E. Mickens, Difference equation models of differential equations having zero local truncation errors, in: I. W. Knowles and R. T. Lewis (Editors), Differential Equations, North-Holland, Amsterdam, 1984, 445-449.
[2]. R. E.Mickens, Exact solutions to difference equation models of Burgers'equation, Numerical Methods for Partial Differential Equations 2, 123-129(1986).
[3]. R.E. Mickens, Exact solution to a finite-difference model of a nonlinear reaction Advection equation: implications for numerical analysis, Numerical Methods for Partial Differential Equations, 313-325.5 (1989).
[4]. Deepti Shakti. Numerics of Singularly perturbed Differential Equations. Dept. of Mathematics, NIT- Rourkela, May 2014.
[5]. Kadalbajoo, M. K. and Vikas Gupta, A brief survey on numerical methods for solving singularly perturbed problems, Applied Mathematics and Computation, vol.217, pp. 3641-3716(2010).

Abstract: In this paper we have considered the population dynamics of dogs subjected to rabies disease. A new mathematical model 𝑆𝐸𝐼𝑃𝐼𝐹𝑅 is presented which is designed and developed with some reasonable modifications to the corresponding epidemic 𝑆𝐸𝐼𝑅 model. Disease spread controlling technique called vaccination is included in the present model and studied its impact. Vaccine can be given to both susceptible and exposed individuals so as to control the spread of epidemic. The basic reproduction number is derived using the next generation matrix method......
Keywords: Rabies, 𝑆𝐸𝐼𝑃𝐼𝐹𝑅 model, Vaccination, Simulation, Reproductive number

[1]. Wilkinson L. Introduction in Rabies. Edited by J. B. Campbell and K. M. Charlton. Boston: Kluwer Academic Publishers, 1988: 1–23.
[2]. Anderson R. M. May R. M. Infectious diseases of humans: Dynamics and Control. Oxford: University Press, 1991.
[3]. WHO expert consultation on rabies, Second report in WHO technical report series. Geneva: World Health Organization, 2013.
[4]. H. W. Heathcoat. The basic epidemiology models: Models expressions for 𝑅0, parameter estimation and applications, 2006.
[5]. Harris G. Where streets are thronged with strays baring fangs. The New York Times, August 6, 2012.

Abstract:The major purpose in this paper is to demonstrate on Differential equations, Types of differential equations, ordinary differential equations, partial differential equations , order and degree of a differential equation, Linear differential equation, Bernoulli's equation.

[1]. ENGINEERING MATHEMATICS, By Srimanta Pal.
[2]. ENGINEERING MATHEMATICS - I, By E.Rukmangadachari.
[3]. ENGINEERING MATHEMATICS , By Dr. T.K.V.Iyengar.
[4]. HIGHER ENGINEERING MATHEMATICS , By Dr.B.S.Grewal

Abstract: We consider four Conjectures for 𝐺 𝑥 . An attempt has been made to obtain the value of 𝑥 for which the corresponding value of 𝐺 𝑥 is nearest to the actual gap while calculating the Sums of Squares of Consecutive Primes. In this paper we calculate sums of squares of consecutive primes using four conjectures and compare it with actual sums of squares of consecutive primes. Keywords: Sums of Squares, Maximal gap.

[1]. Cadwell. J.H, Large Intervals Between Consecutive Primes, Mathematics of computation,vol 2,Number 116, Oct 1971
[2]. Cramer. H, On the order of magnitude of the difference between consecutive primes numbers,Acta Arith 2(1936),396-403.
[3]. Erdos.P, On the difference of consecutive Primes,Quart.J.Math.Oxford 6 (1935),124-128.
[4]. Granville.A,Harald Cramer and the distribution of prime numbers,scandanavian Actuarial J 1:12- 28,1995.
[5]. Heath Brown. D.R, Differences between consecutive primes,Jahresber,Deutsch math-verein 90:71-89.1988

Abstract: The aim of this paper is to investigate the high influential factors of pipe breaks in water distribution systems by using various statistical models such as multiple linear regression model (MLRM), Time exponential model (TEM), Poisson generalized linear model (PGLM), Negative Binomial generalized linear model (NBGLM) and Proportional hazard model (PHM). This paper discusses the effect of different types of covariates with the assumption that each of the covariates has linear effect on the number of pipe breaks. The study focuses on comparing statistical models, parameter estimate of pipe breaks and to determine the.....
Keywords: Pipe break, Water distribution system, Infrastructure, and Generalized linear models.

[1]. Achim D., Ghotb F. and McManus, K. (2011) Prediction of water pipe asset life using neural networks. Journal of Infrastructure System, 131, 26-30.
[2]. Andreou, S.A., (1996). "Predictive models for pipe break failures and their implications on maintenance planning strategies for water distribution systems," PhD Thesis, Department of Civil Engineering, Massachusetts Institute of Technology, and Cambridge MA.
[3]. Ayunanda Melliana, Yeni Setyorini, Haris Eko, Sistya Rosi, Purhadi (2013), The Comparison Of Generalized Poisson Regression And Negative Binomial Regression Methods In Overcoming Over dispersion, International journal of scientific and Technology research 2, 8.
[4]. Clark, R. M. Stafford, C. L. and Goodrich, J. A. (2002), Water distribution systems: A spatial and cost evaluation., Journal of Water Resources Planning and Management, 108(3), 243-256.
[5]. Jon Rostum. Norway (2000), Statistical Modeling of pipe failure in water networks, Norwegian University of Science and Technology NTNU, Department of Hydraulic and Environmental Engineering.

Abstract: The Indian govt. celebrated 125𝑡ℎ anniversary of the great Mathematician of Indian soil Srinivasa Ramanujan on 22 December in the year2012. Without any formal education and extreme poverty conditions, he emerged as one of great mathematician of India.His mathematical ideas transformed and reshaped 20𝑡ℎ century mathematics and their ideas are inspiration for 21𝑠𝑡 century mathematicians. His excellence can be realized from the fact that he discovered some results which are supposed to be true but have not been proved till date. His foresightedness was so scintillating that he gave those ideas in Mathematics that no one can imagine to invent them.
Keywords: G.H. Hardy, Highly composite numbers, Partition function, Ramanujan.

[1]. Ramanujan, S. (1921). "Congruence properties of partitions".Mathematische_Zeitschrift9: 147–153.
[2]. The Man Who Knew Infinity: A Life of the Genius Ramanujan, Little, Brown Book Group (10 December 1992), ISBN-10: 0349104522
[3]. Mathematical Legacy of Srinivasa Ramanujan, Ram Murty.
[4]. Ramanujan, S.: The Lost Notebook and Other Unpublished Papers. Intro.by G.E. Andrews. Narosa, New Delhi (1997)
[5]. Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks,George E. Andrews, Inventionesmathematicae, 05/23/2007.