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SCHUR CONVEXITY AND CONCAVITY OF GNAN MEAN
K. M. Nagaraja,MURALI K,V. Lokesha 장전수학회 2014 Proceedings of the Jangjeon mathematical society Vol.17 No.3
In this paper, the Schur convexity and Schur concavity of the Gnan mean and its dual form in two variables are discussed using strong mathematical induction by grouping of terms.
OPTIMAL SUBPARAMETRIC FINITE ELEMENT METHOD FOR ELLIPTIC PDE OVER CIRCULAR DOMAIN
V. KESAVULU NAIDU,DIPAYAN BANERJEE,K. V. NAGARAJA 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.1
This paper gives us an insight into the usefulness of the proposed method in Finite Element Analysis (FEM) for solving an el- liptic Partial Dierential Equation (PDE) over circular domain. We are using quadratic and cubic order curved triangular elements to solve the problem of stress concentration on a circular plate, which is governed by Poisson's equation. The proposed FEM solution matches very well with the exact solution. This shows the eciency and effectiveness of the method in various mechanical applications.
A simple proof strengthening and extension of inequalities
K. M. Nagaraja,V. Lokesha,S. Padmanabhan 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.17 No.1
In this short note, using Weighted Arithmetic and Geometric means We deduce Contra Harmonic mean and Power exponential mean. Also we established some new inequalities involving important means.
INEQUALITIES FOR THE ARGUMENTS LYING ON LINEAR AND CURVED PATH
( K. M. Nagaraja ),( Serkan Araci ),( V. Lokesha ),( R. Sampathkumar ),( T. Vimala ) 호남수학회 2020 호남수학학술지 Vol.42 No.4
The mathematical proof for establishing some new in- equalities involving arithmetic, geometric, harmonic means for the arguments lying on the paths of triangular wave function (linear) and new parabolic function (curved) over the interval (0; 1) are dis- cussed. The results representing an extension as well as strength-ening of Ky Fan Type inequalities.
V. Lokesha,Naveen Kumar B.,K. M. Nagaraja,M. Saraj,Abdelmejid Bayad 장전수학회 2010 Proceedings of the Jangjeon mathematical society Vol.13 No.2
The object of this paper is to introduce three new means on the basis of proportions and its dual forms, study certain properties, monotonicities and new inequalities involving them. Further, we dened weighted three new means and its dual form, its properties are stated and deduced the ten Neo-Pythagorean means, weighted rth Oscillatory mean, weighted rth Oscillatory mean, also some familiar means and various other means.
V. Kesavulu Naidu,K.V. Nagaraja 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.3
This paper is concerned with curved boundary triangular element having one curved side and two straight sides. The curved element considered here is the 36-node (septic) triangular ele-ment. On using the isoparametric coordinate transformation, the curved triangle in the global (x; y) coordinate system is mapped into a standard triangle: f{ξ, Ƞ)/0≤ξ, Ƞ≤1,ξ+Ƞ≤1}in the local coordinate system (ξ, Ƞ). Under this transformation curved boundary of this triangular element is implicitly replaced by septic arc. The equation of this arc involves parameters, which are the coordinates of points on the curved side. This paper deduces rela-tions for choosing the parameters in septic arc in such a way that the arc is always a parabola which passes through four points of the original curve, thus ensuring a good approximation. The point transformations which are thus determined with the above choice of parameters on the curved boundary and also in turn the other parameters inthe interior of curved triangle will serve as a powerful subparametric coordinate transformation for higher order curved triangular elements with one curved side and two straight sides. We have considered an ap-plication example, which consists of the quarter ellipse: { n(x, y)/x = 0, y = 0, x2/36 + y2/4 = 1}We take this as a curved triangle in the physical coordinate system (x, y). We have demon-strated the use of point transformations to determine the points along the curved boundary of the triangle and also the points in the interior of the curved triangle. We have next demon-strated the use of point transformation to determine the arc length of the curved boundary. An additional demonstration which uses the point transformation and the Jacobian is con-sidered. We have thus evaluated certain integrals, for example, ∬Atαdxdy, (t = x, y, α= 0, 1)and found the physical quantities like area and centroid of the curved triangular elements. We hope that this study gives us the required impetus in the use of higher order curved triangular elements under the subparametric coordinate transformation.
AN OPTIMAL NUMERICAL INTEGRATION METHOD OVER A LUNE BY USING AN EFFICIENT TRANSFORMATION TECHNIQUE
SARADA JAYAN,K. V. NAGARAJA 장전수학회 2016 Proceedings of the Jangjeon mathematical society Vol.19 No.3
In this paper, we derive an optimal numerical integration method to integrate functions over a lunar model, a closed region bounded by two different circular boundaries. The region is discretized into two and suitable efficient transformations are used to transform the regions to a zeroone square. After the transformation, a product formula is applied to derive the proposed numerical integration method. The generalized Gaussian quadrature nodes and weights for one dimension are used in the derived integration formula for evaluating the results. The results obtained for seven different functions are tabulated along with a comparative study in order to show that the proposed method gives more accurate results using less number of quadrature points and is the optimal one.
NUMERICAL INTEGRATION OVER IRREGULAR DOMAINS USING GENERALIZED GAUSSIAN QUADRATURE
S. Jayan,K. V. Nagaraja 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.1
A numerical integration formula is derived in this paper to evaluate integrals over a two, three and n-dimensional closed irregular region, the boundary of which is given in polar coordinates. In each case the region is transformed to a square, cube and an n-cube respec- tively, using transformation of variables. Generalized Gaussian quad- rature nodes and weights for one-dimension are applied in the product formula derived. Numerical results over selected domains are tabulated.
Numerical integration over n-dimensional cubes using generalized Gaussian quadrature
S. Jayan,K.V. Nagaraja 장전수학회 2014 Proceedings of the Jangjeon mathematical society Vol.17 No.1
Numerical integration over n-dimensional cubes using generalized Gaussian quadrature