iosr-Jm   Volume-15 ~ Issue-1 ~ Jan-Feb 2019

Abstract: In this paper, we proposed a three step method for approximating roots of non-linear equations. This method has three evaluations of function and first derivative which is modified from McDougall and Wotherspoon [1]. Numerical examples are tested to compare the method with other methods and demonstrate the efficiency of the proposed method.

Key Word: Non-linear equation, Iterative method, Newton's method, Multiple roots, Order of convergence

[1]. T.J. McDougall, and S.J. Wotherspoon, A simple modification of Newton's method to achieve convergence of order, Journal of
Applied and Mathematical letters, 29, 2014, 20-25.
[2]. A. Cordero, and J. R. Torregrosa, Low-complexity root-finding iteration functions with no derivatives of any order of convergence,
Journal of Computational and Applied Mathematics, 275, 2015, 502–515.
[3]. H. T. Kung, and J. F. Traub, Optimal order of one-point and multipoint iteration, Journal of the Association for Computing
Machinery, 21, 1974, 643–651.
[4]. F. Zafar, N. Yasmin, S. Akram, and M. D. Junjua, A general class of derivative free optimal root finding methods based on rational
interpolation, Science World Journal, 2015.

[5]. N.A. Mir, K. Bibi, and N. Rafiq, Three-step Method for Finding Multiple Root of Non-linear Equation, Life Science Journal, 11(7), 2014, 287-289.

Abstract: In this paper, some new types of separation axioms in topological spaces by using 𝛽g*-open sets are formulated. In particular the concept of 𝛽g*-R0 and 𝛽g*-R1 axioms are introduced. Several properties of these spaces are investigated using these axioms.

Key Word: 𝛽g*-open set, 𝛽g*-R0, 𝛽g*-R1, 𝛽g*-Ti(i= 0,1,2)

[1]. D.Andrijevic, semi preopen sets, Mat.Vesnik, 38(1) (1986), 24-32
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[3]. C.Dhanapakyam ,K.ndirani,On 𝛽g*closed sets in topological spaces, Int. J. App. Research (2016),388
391
[4]. N.Levine, Generalized Closed sets in Topology, rend.Cir.Mat.palermo,2(1970),89-96. N.Levine, Semiopen sets and semi continuity in topological spaces.,Amer.Math.Monthly, 70(1963),36-41.
[5]. M.K.R.S Veerakumar, Between closed sets and g-closed sets, Mem. Fac. Sci.Kochi Univ.Ser.A,Math., 21 (2000) 1-19..

Abstract: This paper is devoted to define a new class of life distribution, named new better than used in increasing convex in Laplace transform order (NBUCL). A new test statistic for testing exponentiality against (NBUCL) class based on U-statistic is introduced. For the proposed test, the asymptotic properties are studied andselected critical values for sample size 5(5)50 are tabulated. The powers of this test are also estimated by using a simulation study for commonly used distributions in reliability. Pitman's asymptotic efficiencies of the test are calculated and compared with some old tests. The problem in the case of right censored data is also touched. Finally, our proposed test is applied to some real data sets in different areas.

Key Word: NBUCL class; Testing Exponentiality; U-statistic; Pitman asymptotic efficiency; censored data; Laplace transform.

[1]. Bryson MC, Siddiqui M. Some criteria for aging. Journal of the American Statistical Association. 1969;64:1472-83.
[2]. Marshall AW, Proschan F. Classes of distributions applicable in replacement with renewal theory implications. University of Rochester Rochester United States; 1972.
[3]. Cao J, Wang Y. The NBUC and NWUC classes of life distributions. Journal of Applied Probability. 1991;28:473-9.
[4]. Alzaid A, Kim JS, Proschan F. Laplace ordering and its applications. Journal of Applied Probability. 1991;28:116-30.
[5]. Denuit M. Laplace transform ordering of actuarial quantities. Insurance: Mathematics and Economics. 2001;29:83-102.

Abstract: Many longitudinal studies generate a dataset having two or more longitudinal repeated biomarkers measurement, which often depend on each other. In Gestational hypertension study the two important markers are gestational systolic blood pressure (GSBP) and diastolic blood pressure (GDBP) are collected simultaneously from a pregnant woman every visit. In such studies, evolution of the biomarkers over time and the association between them are commonly of interest. The aim of the analysis was to determine joint evolution and association of pregnancy induced systolic and diastolic blood pressure over time and determining their associated risk factors. The association among the two sequences is captured............

Key Word: pregnancy induced hypertension; gestational hypertension; joint modeling; joint evolution; mixed model; systolic blood pressure; diastolic blood pressure

[1]. Abate, M. & Lakew, Z. (2006). Eclampsia a 5 years retrospective review of 216 cases managed in two teaching hospitals in Addis Ababa. Ethiop Med J, 44(1):27-31.
[2]. Al-Ghamdi, S. M., Al-Harbi, A. S., Khalil, A., & El-Yahyia, A. R. (1999). Hypertensive disorders of pregnancy: Prevalence, classification and adverse outcomes in northwestern Saudi Arabia. Annals of Saudi medicine, 19(6):557-560
[3]. Bergstrom, S. (2001). Preeclampsia and Eclampsia in Lawson JB, Harrison KA, Bergstrom S. eds. Maternity Care in Developing Countries. London. RCOG Press, 146-159.
[4]. Cnossen, J.S., van der Post, J.A., Mol, B.W., Khan, K.S., Meads, C.A., ter Riet, G. (2006). Prediction of pre-eclampsia: a protocol for systematic reviews of test accuracy. BMC Pregnancy Childbirth, 6: 29
[5]. Fieuws, S. and Verbeke, G. (2004). Joint Modeling of Multivariate Longitudinal Profiles: Pitfalls of the Random-Effects Approach. Statistics in Medicine, 23; 3093-3104.

Abstract: We study commutativity in Rings R with the property that for fixed positive integers k,m,n, xkSm = Smxk for all x∈𝑅 and for all n-subsets S of R.

[1]. H.E.Bell: A.Setwise commutativity Property for Rings, Comm.Algebra 25 No.3,(1997),989-998.
[2]. H.E.Bell: A.A.Klein: A Combinatorial commutativity Property for Rings,VMMS 29-9,(2002),525-530.
[3]. B.Corbas: Rings With Few ZeroDivisors, Math.Ann.181,(1969),1-7.
[4]. Dr.G.Gopalakrishnamoorthy:S.Anitha,On Commutativity Property of 𝑄𝑘,𝑛, 𝑄𝑘,,∞ ,𝑃𝑘,𝑛,𝑃∞ and 𝑄,∞ Rings ,Jour.of.Inst.Of Mathematics and computer Science(Mathematics Series) Vol.23,No.2(2010)63-70.
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Abstract: In this article, the boundary value problem for singularly perturbed nonlinear reaction diffussion equations are treated. The exponentially fitted difference schemes on a uniform mesh which is accomplished by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form are presented. The stability and convergence analysis of the method is discussed. The fully discrete scheme is shown to be convergent of order 1 in independent variable, independently of the perturbation parameter. Some numerical experiments have been carried out to validate the predicted theory.

Keywords: Difference schemes, Differential equation, Singular perturbation, Uniform mesh. 2010 Mathematical Subject Classification: 65L10, 65L11, 65L12

[1]. Amiraliyev, G., Duru H., 2002. "Nümerik Analiz", Pegem Yayıncılık.
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[3]. Auchmutyi, J. F. G., Nicolis, G., 1976. Bulletin of Mathematical Biology. Bifurcation analysis of reaction-diffusion equations, 8:325-350.
[4]. Boglaev, I. P., 1984. Approximate solution of a nonlinear boundary value problem with a small parameter fort he highest-order differential. U.S.S.R. Comput. Maths. Math. Phys., 24(6):30-35.
[5]. Cantrell, R. S., Cosner, C., 2003. Spatial Ecology via Reaction-Diffusion Equations, Department of Mathematics, University of Miami, U.S.A.

Abstract: Let B= (Q, *, Ʃ, δ, q0, F) be a Finite Monoid Automaton. Let S= (R, *, E, γ, qs, T) be a Finite Sub-Binary Automaton such that 0 ϵR. Then S= (R, *, E, γ, qs, T) is a Finite Sub-Monoid Automaton. Let B= (Q, *, Ʃ, δ, q0, F) be a Finite Group Automaton. Let S= (R, *, E, γ, qs, T) be a Finite Sub-Binary Automaton of B (as a Finite Binary Automaton). Then S= (R, *, E, γ, qs, T) is a Finite Sub-group Automaton.

Keywords: Finite Binary Automaton, Finite Monoid Automaton Finite Group Automaton Finite Automaton

[1]. Dr.K.Muthukumaran And S.Shanmugavadivoo , " Finite Abelian Automata" Accepted In "Iosr Journal Of Mathematics", A Journal Of "International Organization Of Scientific Research"
[2]. S.Shanmugavadivoo And Dr.K.Muthukumaran , "Ac Finite Binary Automata" "Iosr Journal Of Mathematics", A Journal Of "International Organization Of Scientific Research"
[3]. S.Shanmugavadivoo And Dr. M.Kamaraj, "Finite Binary Automata" "International Journal Of Mathematical Archive", 7(4),2016, Pages 217-223.
[4]. S.Shanmugavadivoo And Dr. M.Kamaraj, "An Efficient Algorithm To Design Dfa That Accept Strings Over The Input Symbol A,B,C Having Atmost X Number Of A, Y Number Of B, & Z Number Of C" "Shanlax International Journal Of Arts, Science And Humanities" Volume 3, No. 1, July 2015,Pages 13-18
[5]. John E. Hopcroft , Jeffery D.Ullman, Introduction To Automata Theory, Languages, And Computation, Narosa Publising House.

Abstract: Using the expansion of the log of the ξ and the ζ functions in terms of the Pochammer's Polynomials, we obtain a fast convergence sequence for thefirst two Li-Keiper coefficients. The sequences are of oscillatory type. Then we study the oscillating part of the Li-Keiper coefficient (the "tiny" oscillations) and following some analytical calculations we pose a new conjecture in the form of a kind of "stability bound" for the maximum strength of the fluctuations around the mean staircase.

Keywords: Pochammer's Polynomials, ξ function (Xi), Li-Keiper coefficients, Baez-Duarte and Maslanka expansions, trend and "tiny" fluctuations

[1]. Yu.V. Matiyasevich: "Yet another representation for the sum ofreciprocals of the non trivial zeros of the Riemann zeta-function", Arxiv:1400.7036v1 [math . NT ] (2014).
[2]. G. Vacca: "A new series for the Eulerian constant γ =0.577... ",Quart. J. Pure Appl.Math. 41(1909-1910) (363-366).
[3]. J.Sondow: "New Vacca-typerational Series for Euler'sconstantγ and its "alternating" analog log(4/π)",Additive number-theory, Springer NY,2010,(331-340). ArXiv.Org/abs/math/0508042.

Abstract: In this article, we offer an easy and active computational technique for finding the solution of the fractional order Sturm-Liouville problems (FOSLPs) with variable coefficients using operational matrices of (BPs). The fractional order derivatives (FODs) are characterized in the Caputo sense. The proposed technique transform the fractional order differential equations (FDEs) into a linear system of algebraic equations, then the eigenvalues can be computed by finding the roots of the characteristics polynomials. Some tested problems are given in order to illustrate the effectiveness and efficiency of the method.

Keywords: Fractional order eigen-value problems, Sturm-Liouville problems, Bernstein polynomials

[1]. Mohammed. OH., ―A Direct Method for Solving Fractional Order Variational Problems by Hat Basis Functions‖, Ain Shams Eng. J. http://dx.doi.org/10.1016/j.asej.2016.11.006. (2016).
[2]. Momani. S, and Shawagfeh. N, ―Decomposition Method for Solving Fractional Riccati Differential Equations‖, Appl. Math. Comput; 182: 1083- 92, (2006).
[3]. Sweilam. NH, Khader. MM. and Al-Bar. RF, ―Numerical Studies for a Multi-Order Fractional Differential Equation‖, Phys. Lett. A; 371: 26-33. (2007).
[4]. Tan. Y, Abbasbandy. S, ―Homotopy Analysis Method for Quadratic Riccati Differential Equation‖, Commun. Nonlinear Sci. Num. Simul.; 13(3): 539- 46, (2008).
[5]. Khader, MM, Introducing an efficient modification of the homotopy perturbation method by using Chebyshev polynomials, Arab J. Math. Sci. 18, 61−71. (2012).

A95 Theoretical bases definition of practical loss the got production in a trunk of oil and gas wells. – B.: Azerbaijan State University of Oil and Industry, 2018. - 15 pages. ISBN 978-5-9982-1493-10 For the first time in oil and gas industry practice special issues on the loss of extracted products are considered, which is a mixture of two and multi component phase systems in the wellbore, during its ascent to the wellhead in a turbulent regime, due to the formation and impact of negative pressure and the gravitational force of the earth. The technological process is described in terms of the frequency of its change, physicochemical and thermodynamic properties, the main technological parameters of the products produced in the wellbore, and theoretical methods for..........

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