iosr-Jm   Volume-15 ~ Issue-5 ~ Sep-Oct 2019

Abstract: Quasi Newton's methods are promising schemes for solving systems of nonlinear equations. In this paper, we continue in the spirit of quasi-Newton update and present an accelerated Broyden's-like method with improved Jacobian approximation for solving large-scale systems of nonlinear equations. The anticipation has been to further improve the performance of Broyden's update as well as reducing function values. The effectiveness of our proposed scheme is appraised through numerical comparison with some well known
Newton's like methods..

Key Word: Approximation, Broyden's, Equations, iterative, Single-point.

[1]. J. E. Dennis, Numerical methods for unconstrained optimization and nonlinear equations (Englewood Cliffs, New Jersey: Prince-Hall Inc., 1983)
[2]. I. D. L.Bogle, and J. D. Perkins, A New Sparsity Preserving Quasi-Newton Update for Solving Nonlinear Equations, SIAM Journal on Scientific and Statistical Computing, 1990 Vol. 11, No. 4 : 621-630 https://epubs.siam.org/doi/abs/10.1137/0911036
[3]. W. J.Leong, M. A. Hassan, and , M. Y. Waziri., A matrix-free quasi- Newton method for solving large-scale nonlinear systems, Computers and Mathematics with Applications 62(2011) 2354- 2363.
[4]. D.H. Li and M. Fukushima, A modified BFGS method and its global convergence in nonconvex minimization, Journal of Computational and Applied Mathematics, Vol. 129 (2001) 15-35.
[5]. M.Y. Waziri, W.J. Leong, M. Mamat, A Two-Step Matrix-Free Secant Method for Solving Large-scale Systems of Nonlinear Equations, Journal of Applied Mathematics: Vol. (2012), Article ID 348654, 9 pages doi:10.1155/2012/348654.

Abstract: In this paper we present a circuit network in the concept of application of graph theory and circuit models of graph are represented in logical connection by using truth table. We formulate the matrix method of adjacency and incidence of matrix followed by application of truth table.

Key Word: Adjacent Matrix, Network Circuit, Electrical Circuit, Representations of Graph Models

[1]. B. Bollobas, Modern Graph Theory, Springer 1998.
[2]. Introductory graph theory for Electrical and Electronics Engineers, IEEE Multidisciplinary Engineering education magazine.
[3]. Narasih Deo, Graph Theory and its Applications to Computer Science..

Abstract: In this paper the authors carried some self-standing studies to examinethe game of chess and its counting techniques associatedwith non-attacking bishop positions. The authors studied the chess boardfor bishop placement with forbidden positions and varied the diagonal movement to the direction𝜃𝑟=450(to the right) and 𝜃𝑙=1350(to the left). We discussed the general movement of a bishopas generating function of two diagonal sums. Furthermore, weconstructed the movement techniques of a bishop placements in the game of chess that generates a finite sum of terms 𝒳𝜃𝑟𝜇𝛽𝑢 𝑎𝑛𝑑 𝒳𝜃𝑙 𝜑𝛿𝑣 respectively. Finally, we applied it to combinatorial problems that generates' the diagonal movement of a bishop to give the sum of two algebraic expansion.

Key Word: Chess movements; Laurent series;Permutation;Puiseux expansion; Rings

[1]. Abigail, M. (2004). A block decomposition algorithm for computing rook polynomials,.
[2]. Artin, M. (1991). Algebra. Massachusetts Institute of Technology: Prentice Hall Upper Saddle River New Jersey 07458.
[3]. Barbeau, E. J. (2003). Polynomials. Springer, New York.
[4]. Berge, C. (1971). Principles of Combinatorics; vol. 72 in Mathematics in . New York: Science and Engineering a series of monographs and textbooks, Academic press, vol. 72.
[5]. Butler, F. (1985). Rook theory and cycle-counting permutation statistics. Advances in Applied Mathematics, 124-135.

Abstract: In this paper, we find the necessary and sufficient conditions for a Finsler space with the metric 𝐿=𝛼−𝛽2𝛼 to be a Berwald space and also to be a Berwald space, where 𝛼 is a Riemannian metric and 𝛽 is a differential one-form. Further, we study the conformal change of Berwald space with the above mentioned special 𝛼,𝛽 −𝑚𝑒𝑡𝑟𝑖𝑐.

Key Word: FinslerSpace, Berwald Space, Conformal change

[1]. Benling Li, Yibing Shen and Zhongmin Shen, On a class of Douglas metrics, Comm. Korean Math. Soc., 14(3)(1999), 535-544. B.N Prasad. B.N Gupta and D.D. Singh, Conformal transformation in Finsler spaces with α,β −metric, Indian J. Pure and Appl. Math., 18(4)(1961), 290-301.
[2]. Hong-Suh Park and Eun-Seo Choi, Finsler spaces with an approximate Matsumoto metric of Douglas type, Comm. Korean Math. Soc., 14(3)(1999), 535-544.
[3]. M. Hashiguchi, S. Hojo and Matsumoto, On Landsberg spaces of dimension two with α,β −metric,Tensor, N.S., 57(1996), 145-153.
[4]. M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha press, Otsu, Saikawa, Japan, (1986).
[5]. M. Matsumoto, The Berwald connection of a Finsler space with an α,β −metric, Tensor, N.S., 50(1991),18-21.