iosr-Jm   Volume-7 ~ Issue-5

Abstract: In this paper we established Boundedness and Compositions of the Operator 𝐺𝜌 ,𝜂 ,𝛾 ,𝜔 ;𝑎+𝛹 (𝑥) and the Inversion Formulae on the space L(a,b) and C[a,b] , given by Hartely and Lorenzo[5]

Key words -𝐺𝜌 ,𝜂 ,𝑟 [𝑎, 𝑧] function, Riemann liouville fractional integral, Riemann liouville fractional derivative , beta-integral.

[1]. Carl F. Lorenzo, Tom T. Hartley: Generalized Functions for the Fractional Calculus, NASA/TP—1999-209424/REV1(1999)
[2]. Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G. : Tables of Integral Transforms, Vol.-II, McGraw-Hill, New York
Toronto & London (1954).
[3]. H.Nagar and A.K.Menaria, J. Comp. & Math. Sci. Vol.3 (5), 536-541 (2012)
[4]. Kober, H.: On fractional integrals and derivatives. Quart. J. Math. Oxford 11,193(1940)
[5]. Lorenzo, C.F. and Hartely, T.T. : R-function relationships for application in the fractional calculus, NASA Tech. Mem. 210361, 1-22,
(2000)

Abstract: Neighbour Balanced Block Designs, permitting the estimation of direct and neighbour effects, are used when the treatment applied to one experimental plot may affect the response on neighbouring plots as well as the response on the plot to which it is applied. The allocation of treatments in these designs is such that every treatment occurs equally often with every other treatment as neighbours. Neighbour Balanced Block Designs for observations correlated within a block have been investigated for the estimation of direct as well as left and right neighbour effects of treatments. It is observed that efficiency for direct as well as neighbour effects is high, in case of Complete block designs i.e., m  0 for Nearest Neighbour correlation structure with  in the interval 0.1 to 0.4. In case of incomplete block designs m 1,2,, v  4 for Nearest Neighbour correlation structure turns out to be more efficient as compared to others models with  in the interval 0.1 to 0.4. The performance of Nearest neighbour balanced block designs is satisfactory for ARMA(1,1) models. The gain in efficiency of NNBD and NNBIBD over regular block design is high under MA(1) models for direct and neighbour effects of treatments.

Keywords: Neighbour Balanced Block Design; Correlated observations; Generalized least squares; AutoRegressive; Moving Average; Nearest neighbour; Efficiency; Regular Block Design.

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Abstract: In this paper we have established a theorem on k   |C,, , , | -summability factor, which gives some new results.

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Abstract: In this paper, a general analysis of one dimensional non-steady state temperature distribution and stresses under thermal load in a solid sphere subjected to different types of heat sources is developed. The article deals with comparative study of the effect of varying heat generation on displacement and thermal stresses. The heat conduction equation solved by integral transforms technique with convective thermal boundary condition and arbitrary initial and surrounding temperature. The results are obtained in a trigonometric series and are studied numerically and are illustrated graphically.

Keywords: Thermal stresses, heat sources, integral transform.

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Abstract: In this Paper, we extend the idea of collocation of linear multistep methods to develop an eight-point Continuous Block method of order (7, 7, 7, 7, 7, 7, 7, 7) T for direct solution of the second order ordinary differential equations. The methods are derived by interpolating the continuous formulation at 𝑥=𝑥𝑛+𝑗 ,𝑗=𝑘 and collocating the first and second derivative of the continuous interpolant at 𝑥𝑛+𝑗 ,𝑗=0,1,2,(𝑘) and 𝑗=2,3,(𝑘) respectively. This approach yielded the multi discrete schemes that form a self-starting uniform order 7 block methods. The convergence analysis of the methods were discussed and the absolute stability regions shown. Two numerical experiments were used to demonstrate the efficiency of the new methods.

Keywords: Linear multistep methods (LMM), zero-stable, block method, interpolation and collocation.

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[7] Ixaru L.Gr., Paternoster B., Function fitting two–step BDF algorithms for ODEs, Part IV, p.443-450 in Computational Science - ICCS 2004, Lecture Notes in Computer Science 3039,M.Bubak, G.D. van Albada, P.M.A.Sloot, J.J.Dongarra Eds., Springer Verlag, 2004.

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[10] Paternoster B., Two step Runge-Kutta-Nystrom methods for y = f(x, y) and P-stability, Part III, p. 459-466 in Computational Science - ICCS 2002, Lecture Notes in Computer Science 2331, P.M.A.Sloot, C.J.K.Tan, J.J.Dongarra, A.G.Hoekstra Eds., Springer Verlag, Amsterdam, 2002.

Abstract: Ideal in topological space have been considered since 1930 by Kuratowski[9] and Vaidyanathaswamy[14]. After several decades, in 1990, Jankovic and Hamlett[6] investigated the topological ideals which is the generalization of general topology. Where as in 2010, Khan and Noiri[7] introduced and studied the concept of semi-local functions. The notion of semi-open sets and semi-continuity was first introduced and investigated by Levine [10] in 1963. Finally in 2005, Hatir and Noiri [4] introduced the notion of semi- -open sets and semi- -continuity in ideal topological spaces. Recently we introduced semi- -open sets and semi- -continuity to obtain decomposition of continuity. In this paper, we obtain several characterizations of semi- -open sets and semi- -continuous functions. Also we introduce new functions semi- -open and semi- -closed functions

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Abstract: In this paper optimal solution of unconstrained single variable problems has been proposed using Newton's interval analysis method. Usually unconstrained single variable problems are solved in differential calculus using elementary theory of maxima and minima. Here nonlinear unconstrained problems have been taken whose derivatives are also non linear.

Keywords: Interval analysis, Interval expansion, Newton's method, Optimization , Unconstrained single variable problems.

[1] Karl Nickel, On the Newton method in Interval Analysis. Technical report 1136,Mathematical Research Centre,University of Wisconsion,Dec 1971.

[2] Louis B. Rall, A Theory of interval iteration, proceeding of the American Mathematics Society, 86z: 625-631, 1982.

[3] Hansen E.R (1978a), "Interval forms of Newton's method, Computing 20,153-163

Abstract: multiset is a collection of objects in which repetition of elements is significant. In this paper an attempt to define a symmetric group under multiset context is presented and the analogous to Cayley's theorem is derived.

Key words: Multiset, group, symmetric group, Cayley's theorem

[1]. Y. Tella and S. Daniel; The Study of Group Theory in the context of Multiset Theory, International journal of Science and Technology, 8(2) (2013)

[2]. SK Nazamul, P. Majumdar, and S.K. Samanta, On Multisets and Multigroups, Anals of Fuzzy Mathematics and Informatics (2013)

[3]. K. P. Girisha,_, Sunil Jacob John, On Multiset Topologies,Theory and Applications of Mathematics & Computer Science 2 (1) (2012) .

[4]. Y.Tella and S.Daniel; Functions in Multiset Context International Journal of Physical science, 4(2). 2010

[5]. K.P. Girish and Sunil Jacob John, General Relations between partially ordered multisets and their chains and antichains, Math. Commun. , 14 (2) (2009). [6]. K.P. Girish and Sunil Jacob John, Relations and Functions in Multiset Context, Information Sciences 179 (2009)

. [7]. R.R. Yager, On the theory of bags, International Journal of General System 13 (1986) . [8]. W. D. Blizard, Multiset Theory, Notre Dame Journal of Logic 30 (1989).

[9]. W. D. Blizard , Dedeking Multisets and Functions shells, Theoret. Comput. Sci. 110 (1993)

[10]. W. D. Blizard, The development of Multiset Theory, Modern Logic (1991)

Abstract: In this paper a two dimensional non linear map is taken whose period doubling dynamical behavior has been analyzed. The bifurcation points have been calculated numerically and have been observed that the map follows a universal behavior that has been proposed by Feigenbaum. With the help of experimental bifurcation points the accumulation point where chaos starts has been calculated.

Key Words: Period-Doubling Bifurcation/ Periodic orbits / Feigenbaum Universal Constant / Accumulation point

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Abstract: In the recent past, different variants of Newton's method with cubic convergence have become popular iterative methods to find the roots of non-linear equations. In this paper, a new class of Newton's method for solving a single nonlinear equation is proposed. This method is the generalization of Simpson's integration rule applied on the Newton' theorem. Some of the existing methods become special cases of this method. Third order convergence of the proposed methods is established. Numerical examples are provided. A comparison study is done to show the efficiency of this method for different parameters in the method.

Keywords: Iterative Method, Newton's Method, Non-linear equation, Third order convergence, Simpson integration method.

[1] M.K.Jain, S.R.K. Iyengar, R.K.Jain, Numerical Methods for Scientific and Engineering Computation, New Age International,6th edition, 2012.

[2] S. Weerakoon. T.G.I. Fernando, A Variant of Newton's method with accelerated third-order convergence, Applied Mathematics Letters 13 (8) (2000) 87-93.

[3] V. I. Hasanov, I. G. Ivanov, G. Nedjibov, A new modification of Newton's method, Applied Mathematics andEngineering 27 (2002) 278 -286.

[4] G. Nedzhibov, On a few iterative methods for solving nonlinear equations. Application of Mathematics in Engineering and Economics'28, in: Proceeding of the XXVIII Summer school Sozopol' 02, pp.1-8, Heron press, Sofia, 2002.

[5] M. Frontini, E. Sormoni, Some variants of Newton's method with third order convergence, Applied Mathematics and Computation 140 (2003) 419-426.

[6] A.Y. Ozban, Some new variants of Newton's method, Applied Mathematics Letters 17 (2004) 677-682.

[7] H.H.H. Homeier, On Newton-type methods with cubic convergence, Journal of Computational and AppliedMathematics 176 (2005) 425-432

[8] D.K.R. Babajee, M.Z. Dauhoo, An analysis of the properties of the variants of Newton's method with third order convergence, Applied Mathematics and Computation 183 (2006) 659–684.

[9] K. Jisheng, L.Yitian, W. Xiuhua, Third-order modification of Newton's method, Journal of Computational and Applied Mathematics 205 (2007) 1 – 5.

[10] T. Lukic, N. M. Ralevic, Geometric mean Newton's method for simple and multiple roots, Applied Mathematics Letters 21 (2008) 30–36.

Abstract: The transcendental equation with five unknowns given 2 2 2 3 2 2 2 2 5 y  2x  X Y  (k 1)z is analysed for its non-zero distinct integral solutions.Various different patterns of integral solutions are illustrated and some interesting relations between the solutions and special numbers are exhibited.

Keywords: Surd,transcendental equation,integral points,figurative numbers.

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Abstract: A study has been carried out to analyze the effect of Magnetic field flow in a porous medium with consider thermal radiation and suction/injection over a permeable stretching wall. We consider wall boundary conditions are distribution of wall temperature, in addition to momentum, both first and second laws of the thermodynamics analyses of the problem are investigated. A set of solution to the non-linear equations is presented using the shooting method. A parametric study showing the effects of magnetic parameter M; thermal radiation parameter R and the injection parameter fw .The effect of various parameter on the fluid flow and heat transfer profile on the velocity and temperature profile as well as the wall heat transfer are presented graphically and in tabulated.

Keyword: Magnetic Field, Thermal Radiation, Stretching wall, Porous Medium.

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Mass Transfer, 3, (1961) 267–274.
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Management 42, (2001) 917–931
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Heat and Mass Transfer Past a Vertical Surface Embedded in a Porous Medium, Transport in Porous Media, 66, (2007) 391-401.
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stretching sheet, Nonlinear Analysis: Real World Applications, 10 (2009) 966–973