iosr-Jm   Volume-13 ~ Issue-1 ~ Jan-Feb 2017

Abstract: Two variable natural cubic spline interpolation formula is derived and illustrated using an example

Keywords: Two variable interpolation, Two variable spline, Natural spline

[1]. Anthony Ralston and Philip Rabinowitz, A first course in Numerical Analysis, Second Edition, Dover publication , INC, New York.
[2]. Ion Lixandru, Algorithm for the calculation of the two variables cubic spline function,AnaleleStiintifice Ale
UniversitatiiMatematica, Tomul Lix,2013,f.1
[3]. Richard L Burden, J. Douglas Faires, Numerical Analysis, Ninth Edition,Brooks/Cole Cengage Learning.
[4]. S.S. Sastry , Introductory Methods Of Numerical Analysis, Fourth Edition, PHI Learning Private Limited

Abstract: In this paper, Volterra - nonlinear quadratic integral equation (V-NQIE) of the second kind with continuous kernels in two-dimensions is considered. Then, under certain conditions, and fixed-point theorem, the existence of a unique solution of V-NQIEis proved. After that, a suitable numerical method is considered to transfer V-NQIE to a system of nonlinear quadratic integral equations (SNQIEs) of the second kind. To solve the nonlinear system, the modified Adomian decomposition method (MADM), with the aid of modified Simpson's rule (MSR) are used and considered, to obtain the nonlinear algebraic system (NAS). Finally, many applications are treated; the numerical results are computed, and the estimated error, in each case, is calculated.

Keywords: Volterra-Quadratic integral equation, continuous kernels, Adomian decomposition method, Simpson's rule, nonlinear algebraic system.

[1]. PopovG.Ya., 'Contact Problems for a Linearly Deformable Base', VishaShkola, Kiev-Odessa, 1982. [2]. Onishchuk O.V., PopovG.Ya.andProtserovYu.S., 'On certain contact problems for reinforced plates', J. Applied Mathematics and Mechanics, 48:2 (1984) 217-223.
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Abstract: Let G = (V, E) be any graph.A dominating set D of a graph G is a nonsplit dominat- ing if < V −D > is connected. The minimum cardinality of a nonsplit dominating set is called nonsplit domination number γns(G). In this paper, we investigate several properties of this parameter.

Keywords: Domination, Domination number, Nonsplit Domination, Nonsplit Domination number. AMS subject classification: 05C 69

[1]. B. D. Acharya, The strong domination number of a graph and related concepts, J.Math. Phys.Sci. 14(1980), No. 5, 471-475.
[2]. S. Arumugam and R. Kala, Domsaturation number of a graph, Indian J. Pure appl. Math., 33(2002), No. 11, 1671-1676.
[3]. G. Chartrand and L. Lesniak, Graphs and Digraphs, Chapman and Hall, Madras (1996).
[4]. E. J. Cockayne, Domination of undirected graphs -A survey. In theory and Applications of Graphs. LNM 642,Springer - Verlag, (1978), 141-147.
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Abstract: In this paper we establish the relation with property (t) and (gt) introduced by M. H. M. RACHID in [1] and sprectrale mapping theorem. We will special establish several sufficient and necessary conditions for which f(T) verify the (t) and (gt) as f an analytic function on the T spectrum and see the validity of these results for the semi- Browder operators. Analogously we ask question about the conditions for which the spectral theory hold for generalized a-weyl's theorem and generalized a-browder's theorem [18].

Keywords: Generalized a-weyl's theorem. Generalized a-browder'stheorem . Semi-Browder operators. Property (t).Property (gt).Spectral theory

[1]. M.H.M. Rachid, Properties (t) and (gt) for Bounded Linear Operators, Mediterr. J. Math. 11 (2014), 729-744.
[2]. P.Aiena, P.Pena, Variations on Weyls theorem. J. Math. Anal. Appl. 324, 566-579 (2006).
[3]. P.Aiena, M.T.Biondi, C.Carpintero, On Drazininvertibility. Proc. Amer. Math. Soc. 136 2839-2848 (2008).
[4]. M.Berkani, Index of B-Fredholm operators and generalization of a Weyl Theorem. Proc. Amer. Math. Soc. 130, 1717-1723 (2001).
[5]. M.Berkani, B-Weyl spectrum and poles of the resolvent, J. Math. Anal. Appl. 272, 596-603 (2002).

Abstract: The receiver operating characteristic (ROC) curve is a graphical representation of the relationship between false positive and true positive rates. It is a widely used statistical tool for describing the accuracy of a diagnostic test and applied in measuring discriminatory ability of diagnostic or prognostic tests. This makes ROC analysis one of the most actively research areas in medical statistics. In this research we used ROC analysis in radiological tests as a method for distinction between the two types of kidney stones (radio opaque and radio lucent).............

Keywords: Sensitivity; Specificity; ROC analysis; Medical decision making; Radiology

[1] Bamber, D. The Area above the Ordinal Dominance Graph and the Area below the Receiver Operating Characteristic Graph. J. Math Psychol, 12:387-415,1975
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Abstract: Based on an approximate formula of factoring an odd composite number, the article deduces a distribution for factors in big odd composite number and designs an algorithm to pick up the factors. Mathematical deduction is presented in detail and numerical experiment is made on some big numbers. Experiment shows that the algorithm is as efficient as the Pullard's Rho algorithm for conventional numbers.

Keywords: Integer factorization, Algorithm design, numerical experiments

[1] Sonal Sarnaik, Dinesh Gadekarand Umesh Gaikwad, "An overview to Integer factorization and RSA in Cryptography", INTERNATIONAL JOURNAL FOR ADVANCE RESEARCH IN ENGINEERING AND TECHNOLOGY,2(9),21-26(2014)
[2] Jongsoo Park,Mathology Sys, "Prime Sieve and Factorization Using Multiplication Table", Journal of Mathematics Research,4(3):7-12(2012)
[3] W Aldrin, Wanambisi Shem Aywa, Cleophas Maende and Geoffrey Muchiri Muketha, "Factorization of Large Integers". International Journal of Mathematics and Statistics Studies,1(1):39-44(2013)
[4] Xingbo WANG. "Seed and Sieve of Odd Composite Numbers with Applications In Factorization of Integers", OSR Journal of Mathematics (IOSR-JM), 12(5, Ver. VIII), 01-07(2016)
[5] Xingbo WANG, "Factorization of Large Numbers via Factorization of Small Numbers", Global Journal of Pure and Applied Mathematics, 12( 6), 5157-5173 (2016)

Abstract: In this paper, we presented a new scheme which is a combination of Standard and nonstandard finite difference method. The scheme is a one step method which can be used to solve ordinary differential equations that arises from the dynamics of drug infusion and dissemination in human beings. We applied the scheme to the solubility component of the deterministic model of drug diffusion. The numerical experiment has shown that the scheme can be used for the simulation of drug dissemination in human beings.

Keywords: Drug Dissemination, Interpolating function, Nonstandard schemes, Solubility, Drug Infusion, Deterministic Model, Dynamic system

[1]. Anguelov, R. and Lubuma, J. M. S. (2000). On Mathematical Foundation of the Nonstandard Finite Differential Method, Proceeding of the International Conference on Differential Equations, EQUADIFF' 99 Word Scientific, 1401-1403, Singapore.
[2]. Anguelov, R. and Lubuma, J.M.S (2003). Nonstandard Finite Difference Method by Nonlocal Approximation. Mathematics and Computers in Simulation 6, 465-475.
[3]. Ibijola, E.A., Obayomi A.A and Olabode B. T. (2013). New Nonstandard Finite Difference Schemes for Ordinary Differential Equations whose Solutions can be expressed as Quotient of Two Polynomials, Journal of Emerging Trends in Engineering and Applied Sciences 4(3), 478 – 484.
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Abstract: The steady, two dimensional, laminar flow of a power - law fluid over a permeable a stretching sheet with constant heat flux in the presence of MHD, viscous dissipation and heat generation/absorption. Using the similarity transformations, the governing equations have been transformed into a system of ordinary differential equations. These differential equations are highly nonlinear which cannot be solved analytically. Therefore, bvp4c MATLAB solver has been used for solving it. Numerical results are obtained for the skin-friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for different values of the governing parameters, namely suction parameter, power-law index parameter, Eckert number, heat generation/absorption parameter, Prandtl number.

Keywords: Power-law fluid, viscous dissipation, stretching sheet, heat generation/absorption, constant heat flux.

[1]. Schowalter, W. R., (1960), The application of boundary-layer theory to power-law pseudo plastic fluids: similar solutions, AIChE
Journal, Vol. 6, pp. 24–28.
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Biorheology, Vol.24, pp.22-28.
[5]. Mahmoud M.A.A., (2011), Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat
generation, Mathematical and Computer Modelling, Vol. 54, Pp. 1228–1237.

Abstract: In this work, the rectangular Kirchhoff plate on Winkler foundation problem was solved using the finite Fourier Sine transform method. The plate considered was assumed homogeneous and isotropic and simply supported at the four edges x = 0, x = a, y = 0 and y = b. Application of the double finite Fourier sine transformation to the governing fourth order partial differential equation simplified the boundary value problem to an algebraic equation in terms of the deflection in the transform space variables, m, n. The deflection obtained in the transform space variables was inverted............

Keywords: Double finite Fourier sine transform method, Kirchhoff plate, Winkler foundations

[1] Timoshenko S. and Woinowsky-Krieger S.: Theory of Plates and Shells, Second Edition, McGraw Hill Book Company, Tokyo 580pp., 1959.

[2] Ventsel E. and Krauthammer T.: Thin Plates and Shells: Theory, Analysis and Applications. Marcel Dekker Inc USA, 666pp., 2001.

[3] Winkler E. Die Lehre vonder elastizitat und festigkeit, Prague, 1867.

[4] Pasternak P.L.: On a new method of analysis of an elastic foundation by means of two foundation constants (in Russian) Gosud.Izd.Lit po Stroitelstvu, Arkhitekture, Moscow, 1954.

[5] Hetenyi M.: Beams on Elastic Foundation. The University of Michigan Press, Ann Arbor, Michigan, 1946.

Abstract: To select a suitable model for the gold rate data To predicts the nature of gold rate next some years Data collected: The data is secondary data collected the data shows trend in the Price History of Gold (10gms) over the given period of time. Given below is year wise Price of Gold in India in last 88 year. the data is collected year wise in1925-2012

Keywords: Statistical tools: Trend line, Forecasting with auto regressive model, ARIMA model Software: SPSS (Statistical packages for social science)

[1]. Fundamentals of applied statistics ,S.C.GUPTA,V.K.KAPOOR
[2]. Statistics for management Richard I.LEVIN, David S.RUBUN, The university of north Carolina chapel hill.
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Abstract: The public transit system are essential services to the sustainability and livability of any city. Transit agencies are consistently trying to improve service reliability and attract passengers by applying various strategies. In this paper, we present an approach to mining the temporal behavior of the passengers in a public transportation system, which may help the transport operators to know the demand of the passengers, which may be helpful in redesigning the existing transport system. In our model, the choices between alternatives are based on the factors like cheaper cost.............

Keywords: Passenger behavior, Decision Making Soft set, Choice Matrix

[1]. P. K. Maji, R. Biswas and A. R. Roy, An application of soft sets in a decision making problem, Comput Math Appl. 44(2002),
1077‐ 1083.
[2]. P. K. Maji, R. Biswas and A. R. Roy, Soft Set Theory, ComputMath Appl. 45 (2003), 555‐562.
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[4]. D. Molodtsov, Soft set theory-First results, Comput. Math. Appl. 37 (1999) 19–31.
[5]. Naim Cagman, Serdar Enginoglu, Soft Matrix Theory and It's Decision Making, Comput Math Appl., 59(2010), 3308‐3314

Abstract: The aim of this paper is to introduce Nano generalized β continuous function in Nano topological spaces and also we introduce and study the relation between Nano generalized β irresolute function and Nano generalized β continuous function

Keywords: Nano β continuous, Nano generalized β continuous and Nano generalized β irresolute functions

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Abstract: In this paper, through the establishment of a new space, we discuss the existence of sign-changing solution of a fourth-order nonlinear elliptic equation with Hardy potential in the new Hilbert space. The existence of sign-changing solution for fourth-order nonlinear elliptic equation are obtained under a linking theorem.

Keywords: sign-changing solution; nonlinear elliptic problem; (PS) condition

[1]. A.M Micheletti............

Abstract: This paper investigates Magneto hydrodynamics of fluid flow of unsteady free convection between a pair of infinite vertical Couette plates embedded in a porous medium. Temperatures of the plates and concentration of the fluid vary with time. The free convection between plates with the inclusion of thermal radiation and chemical reaction is considered. The Couette plates are immersed vertically in a porous medium. We use regular perturbation technique to convert the governing nonlinear partial differential equations into a system of ordinary differential equations. The effects of various parameters viz. permeability of porous medium, thermal Grashof number, frequency parameter...........

Keywords: MHD, Permeability of porous medium, thermal radiation, frequency parameter and Chemical reaction parameter.

[1]. Nield, D. A. and Bejan, A. 1998: Convection in porous media. 2nd edition, Springer Verlag, Berlin.
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Abstract: Following the recent generalization of the recently introduced summability...........

Keywords: Statistical convergence of double sequence.........

[1]. S. Bhunia, P. Das, S. Pal, Restricting statistical convergence, Acta Math. Hungar. 134 (2012), no. 1-2, 153-161.
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[4]. L. Cheng, G. Lin, Y. Lan and H. Liu, Measure Theory of Statistical Convergence. Science in China Series A-Math. (2008) 51: 2285.

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Abstract: This research applies the concept of game theory under optimizationtechniques to determine the behavioural factor that affects the choice of soft drinks of residence of Port Harcourt city , Nigeria using its different market strategies. It summarised how best to use marketing strategies to analyse the desirabilityand sales of beverage known as soft drink, using responses from the distributed questionnaires to the residence of PortHarcourt, Nigeria.A case study of Coca-Cola Group of Companies and Seven-up bottling Company were examined and analysed. The payoff matrix was calculated from the harvested data from the distributed questionnaire in eight major populated areasin port Harcourt.........

Keywords: Optimization, marketing strategies,Two-person zero sum game, pay off matrix, questionnaire, minimax principle

[1] Ekanem O. T, Iyoha M.A (2000). Mathematical Economic: An Introduction. Benin City: Mareh Publishers.
[2] Jingjing Liu and YuqiZou(2013) game theory based research on profit distribution among stakeholders in urban renewal project.

[3] Mlvin Dresher (1961)Games of Strategy: Theory and Applications, Prentice Hall, Inc. N.J

[4] Carmichael F.: A Guide to Game Theory, Prentice Hall, Yew Jersey, USA, 2005.
[5] Rapoport and Chammah (1966) pp. 10–14 and 23–28. GAME OF CHICKEN