iosr-Jm   Volume-13 ~ Issue-6 ~ Nov-Dec 2017

Abstract: In this paper a new one-parameter lifetime distribution named "Improved Second-Degree Lindley Distribution" which is a modification of Lindley Distribution, with an increasing hazard rate for modeling lifetime data has been suggested. Its first four moments about origin and mean have been deduced and expressions for mean, variance, coefficient of variation, skewness, kurtosis and index of dispersion have been obtained. Various mathematical and statistical properties of the proposed distribution including its survival function, hazard rate function, mean deviations, and Bonferroni and Lorenz curves have been discussed. Estimation of its parameter has been obtained using the method of maximum likelihood and the method of moments. The applications and goodness of fit of the distribution have been discussed with three real lifetime data sets and the fit has been compared.........

Keywords: lifetime distributions, Sujatha distribution, Akash distribution, Lindley distribution, mathematical and statistical properties, estimation of parameter, goodness of fit.

[1]. Alkarni, S. (2015) Extended Power Lindley Distribution: A New Statistical Model for Non-Monotone Survival Data. European Journal of Statistics and Probability, 3, 19-34.
[2]. Alkarni, S. (2015) Extended Inverse Lindley Distribution: Properties and Application. SpringerPlus, 4, 1-17.
[3]. Bader, M. G., Priest, A. M., (1982). Statistical aspects of fiber and bundle strength in hybrid composites, In: Hayashi, T., Kawata, K., Umekawa, S. (Eds), Progress in Science and Engineering composites, ICCM-IV, Tokyo, 1129–1136.
[4]. Bonferroni, C. E., (1930). Elementi di Statistcagenerale, Seeber, Firenze
[5]. Ghitany, M. E., Atieh, B., Nadarajah, S., (2008). Lindley distribution and its applications.Mathematics Computing and Simulation, 78, pp. 493–506

Abstract: In this work, the authorexamine the open and closedsets on the non-newtonianrealline, and relationshipbetweenthem.

[1]. Duyar C., Sağır B. 2017. Non-Newtoniancomment of Lebesgue Measure in Real Numbers,Journal of Mathematics, Volume 2017 (2017), Article ID 6507013, 4 pages.
[2]. Duyar C., Erdoğan M. 2016. On Non-Newtonian Real Number Series, IOSR Journal of Mathematics(IOSR JM), Volume 12, Issue 6Ver. IV (Nov.-Dec. 2016), PP 34-48.
[3]. Duyar C., Sağır B., Oğur O. 2015. Some Basic TopologicalProperties on Non-Newtonian Real line, British J. Math. Comput. Sci. 9-4, 300-306.
[4]. Grossman, M. 1972. Non-NewtonianCalculus, Lee Press, PigeonCove (LowellTechnologicalInstitue).
[5]. Natanson, I. P. 1964. Theory of Functions of a Real Variable, Vol. 1, FrederickUngar Publishing Co., New York.

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 etc. In this paper, we established a new special differential equation and its polynomial which we named as Mohammed's equation and polynomial. The Rodrigue formula, generating function and recurrence relations of the polynomial are given. We also presented the orthogonality properties of the polynomials and our results are entering the literature for the first time.

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

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(1998), 98-111
[3]. H. S. P. Srivastava, Some generating function relations of multi-index Hermite polynomials, Math. Comput. Appl. 6(3) (2001), 189-
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Abstract: In this paper the finite Fourier sine transform is presented for obtaining solutions for Klein-Gordan equations. The initial-boundary value problems for the Klein-Gordan equations are solved on the half range, using finite Fourier sine transform. Such problems posed on time-depend domain. The results reveal that the finite Fourier sine transform is very effective, simple, convenient and flexible.

Keywords: differential equations, dispersive, perturbation, decomposition

[1]. S. Abbasbandy. Numerical solutions of nonlinear Klein-Gordon equation by variational iteration method. Internat.
[2]. A.M. Wazwaz. The modified decomposition method for analytic treatment of differential equations. Appl. Math. Comput. 2006, pp. 165-176.
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[4]. J.H. He. Homotopy perturbation technique. Computer Methods in Applied Mechanics and Engineering. 1999.
[5]. J.H. He. Variational iteration method a kind of nonlinear analytical technique: some examples. International Journal of Nonlinear Mechanics. 1999.

Abstract: In this paper, Corwin-Greenleaf multiplicity functions for Symplectic Lie Group have been studied in the light of the Kirillov-Kostant Theory. This was pioneered by the famous mathematician L. Corwin and F. Greenleaf. The major objectives of the proposed research are to design and develop symplectic representation. This paper focused on the geometry of coadjoint orbits, which is predicted by recent results on (infinite dimensional) unitary representation theory, namely, the multiplicity-free theorem of branching laws with respect to reductive symmetric pairs.

Keywords: Branching laws, Corwin-Greenleaf multiplicity functions, orbit method, Symplectic Lie Groups.

[1]. Kirillov A.A., Lectures on the Orbit Method, ISBN-10: 0-8218-3530-0; ISBN-13: 978-0-8218-3530-2, Graduate Studies in Mathematics, vol. 64, American Mathematical Society, Providence, Rhode Island, 2004.
[2]. Kobayashi, T., Harmonic analysis on homogeneous manifolds of reductive type and unitary representation theory, Translations, Series II, Selected Papers on Harmonic Analysis, Groups, and Invariants (K. Nomizu, ed.), vol. 183, American Mathematical Society, pp. 1-31, 1998.
[3]. Kobayashi, T., Discrete decomposability of the restrictions of A_q (λ) with respect to reduce subgroups and its applications, Inventiones Mathematicae, vol. 117, Issue 1, pp. 181–205, 1994.
[4]. Nasrin, S., Corwin-Greenleaf Multiplicity Functions for Hermitian Symmetric Spaces, Proceedings of the Japan Academy, Series A, Mathematical Sciences, vol. 84, Number 7, pp. 97-100. 2008.
[5]. Kobayashi, T., Multiplicity-free branching laws for unitary highest weight modules, Proceedings of the Symposium on Representation theory held at Saga, Kyushu (K. Mimachi, ed.), pp. 9-17, 1997.

Abstract: Graph Theory is the fast growing area of research in Mathematics. Recently, dominating functions in domination theory have received much attention. In this paper we discuss some results on minimal signed dominating functions and minimal total signed dominating functions of corona product graph of a cycle with a star.

Keywords: Corona Product, Signed Dominating Function, Total Dominating Function

[1]. Allan R.B and Laskar, R.C – On domination, independent domination numbers of a graph, Discrete Math, 23(1978), 73-76.
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[3]. Cockayne C.J, Dawes, R.M amd Hedentiemi, S.T – Total domination in graphs, Networks, 10(1980), 211-219.
[4]. Cockayne, E.J, Mynhardt, C.M and Yu, B-Total dominating functions in trees: Minimality and convexity, Journal of Graph Thoery, 19(1995), 83-92.
[5]. Frutch R and Harary F – on the corona of two graphs, Aequationes Mathematicae,Volume 4, Issue 3 (1970), 322-325.

Abstract: Maternal weight gain and wait size is one of the most important independent predictors of birth weight. This study was conducted to observe the weight gained and waist size increase by pregnant women and the correlation between the weight gain, waist size increase and the birth weight of baby. In this study women who delivered full term single baby at Webuye sub-county hospital were included after their verbal consent. Baby weights after birth, mothers' weights and their waist sizes before birth were recorded and the data obtained was analysed using general least square method to estimate the parameters of the model.........

Keywords: Gestational weight gain, Birth weight, Regression

[1]. Abrams, B. (1995).Factors associated with pattern of maternal weight gain. Journal of obstetric gynecology 86,170-176.
[2]. Bajracharya, J. Shreshtha , N.S, Karki, C. (2012). Accuracy of prediction of birth weight by fetal ultrasound. Kathmandu University
medical Journal 10 (38), 74-76.
[3]. Chang, T.C Robson, S.C (1992). Prediction of the small for gestational age infant. Journal of obstetric gynecology.80, 1030-1037.
[4]. Ekele,B.Otubu,A.M.(2006). Maternal and perinatal mortality.Textbook of obstetrics and Gynaecology for medical students. Ibadan
Nigeria 2 526-531.
[5]. Fawzia, A. (2002).prediction of low birth weight infants from ultra sound measurements of placental diameter and thickness. King
Khalid university. Journal of obstetrics and gynecololgy. 5, 312-314.

Abstract: This report contains the analysis of queuing systems of Neuro-Trauma Centre at the National Hospital in Sri Lanka. There are several clinics held by Neuro-Trauma Centre and in most of them, a waiting queue may form when the doctors or the serving persons are too busy to meet the requirements of the arriving patients immediately as a result of the demand exceeds the supply. The main purpose of this study is to apply the queuing theory and to evaluate the parameters involved in the service unit for the consultations and pharmacy of Neuro-Trauma Centre at the National Hospital in Sri Lanka. Therefore, a mathematical model is developed based on queuing theory by collecting data through an observational study at the clinic and analyzing them through computations to optimize the queues.

Keywords: Arrival rate; service rate; number of channels

[1]. Dilrukshi, PDA, Nirmanamali, HDIM, Lanel, GHJ &Samarakoon, MASC 2016 , 'AStrategy to reduce the waiting time at the outpatient department of the national hospitalin Sri Lanka', International Journal of Scientific and Research Publications, vol. 6, no.2, pp. 2250-3153.
[2]. Ferdinandes, MGRUK, Lanel, GHJ, Samrarakoon, MASC 2017, 'A queuing model tooptimize the performance of surgical units', International Journal of Advanced EngineeringResearch and Science (IJAERS), vol. 4, no.5, pp. 119-123.

Abstract: In this paper, the methodof Zedan (1990)for computation of the lift coefficientand surface pressure coefficient distribution on arbitrary airfoils in potential flows is applied to the NACA 4412 airfoil and the results compared with NACA experimental data in order to verify its performance for a real cambered airfoil since nosuch airfoilwas considered in Zedan (1990). Comparison of results between theory and experiment for both the NACA 4412 and modified NACA 4412 airfoils has shown that the method can be made to agree more closely with experiment when the airfoil is modified by adjusting one of the coefficients in the formula for thickness that results in the least overall change in the airfoil contour when compared with similar modifications as shown in Nico (2010).

Keywords And Phrases: Airfoil,NACA airfoil, Angle of attack, Lift coefficient, Pressure coefficient

[1]. Abbot, I.H. and Von Doenhoff,A.E. (1959).Theory of Wing Sections Including a Summary of Airfoil Data. Dover Publications Inc, New York, pp. 31-123
[2]. Anderson, J. K. (1991). Fundamentals of Aerodynamics. McGraw-Hill, New York, pp. 112-229
[3]. Björn, R. (2006).Conformal Mapping Potential Flow around a Wing SectionUsed as a Test Case for the Inviscid Part of Rans Solvers. Paper presented at the European Conference on Computational Fluid Dynamics, TU Delft, The Netherlands.
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[5]. Deglaire, P., Ågren, O., Bernhoff, H. and Leijon, M. (2008). Conformal Mapping and Efficient Boundary Element Method without Boundary Elements for Fast Vortex Particle Simulations.European Journal of Mechanics B/Fluids 27: 150-176..

Abstract: In this paper, we introduced the concept of the Modified Adomian Decomposition (MADM) in solving third-order ordinary differential equations. Some test problems were considered and the results are compared with the existing methods in the literature. The convergent of the MADM was so rapid and involved only few terms of the series and by far better than the Seven-Step Block method, Variation Iteration Method and Differential Transform method.

Keywords: Ordinary differential equations, Modified Adomian Decomposition method, Initial value problems (IVP)

[1]. Kiymaz, O., and Cetinkaya, A., 2010, "VariationalIteration method for a class of nonlinear differential equations,"Int. J. Contemp. Math. Science, 5(37), pp. 1819-1826.
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[3]. Biazar, J., and Ghazvini, H., 2008,"Homotopy perturbation method for solvinghyperbolic partial differential equations,"Computers and Mathematics withApplications, 56, pp. 453-458.Okuboye,J. O., and Omar, Z., 2015,"Numericalsolution ofthird orderordinary differential equations using a seven-step block method,"International Journal of MathematicaAnalysis, 9(15),pp.743-745doi.org/10.12988/ijma.2015.5125
[4]. Zhou, J.DifferentialK., transformation1986,"and its application for electrical circuits,"HarjungUniversity press, Wuuhan, China, (in Chinese).
[5]. Biazar, J., and Eslami, M., 2010 ,"Differentialtransform method for quadratic Riccati differential equations,"International Journal of Nonlinear Science, 9(4), pp. 444-447

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[1]. J.M.A.M. van Neerven ,The Norm of a Complex Banach Lattice,Department of Mathematics TU Delft .
[2]. JAMES S. HOWLAND ,Analyticity of Determinants of operators on a Ba- nach Space

Abstract: The main goal of this paper is to demonstrate the use of multiple exp-function method for Boussinesq equation and Kudryashov–Sinelshchikov equation (KSE). With the help of Maple, applying the approach to these equations yields some new exact explicit travelling one wave solutions. The significance of obtained solutions gives credence to the explanation and understanding of related physical phenomena.

Keywords: The Boussinesq equation and the Kudryashov–Sinelshchikov equations, Multiple exp-function
method, One Wave Solution.

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Commun. Theor. Phys. 35 (2001) 7–10.
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(2002) 265–268.
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Scr. 82 (2010) 065003.
[5]. W.X. Ma, A. Abdeljabbar, M.G. Asaad, Wronskian and Grammian solutions to a (3+1)-dimensional generalized KP equation, Appl.
Math. Comput. 217 (2011) 10016–10023

Abstract: In this paper we consider the incidence coloring of Sierpiński graphs .............

Keywords: Sierpiński graphs, incidence graph, incidence chromatic number

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