• Honam Mathematical Journal
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• v.40 no.1
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• pp.163-186
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• 2018

The objective of this paper is to present 87 recurrence relations for the Jacobi polynomials $P_n^{({\alpha},{\beta})}(x)$. The results presented here most of which are presumably new are obtained with the help of Gauss's fifteen contiguous function relations and some other identities recently recorded in the literature.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.185-199
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• 2011

In this paper, we present a new extended Jacobi method for computing eigenvalues and eigenvectors of Hermitian matrices which does not use any complex arithmetics. This method can be readily applied to skew-Hermitian and real skew-symmetric matrices as well. An example illustrating its computational efficiency is given.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.279-294
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• 2005

We study a real hypersurface M satisfying $L_{\xi}S=0\;and\;R_{\xi}S=SR_{\xi}$ in a complex hyperbolic space $H_n\mathbb{C}$, where S is the Ricci tensor of type (1,1) on M, $L_{\xi}\;and\;R_{\xi}$ denotes the operator of the Lie derivative and the Jacobi operator with respect to the structure vector field e respectively.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.43-49
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• 1997

In this paper, we study an error of vanishing viscosity method for the first-order Hamilton-Jacobi equations.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.495-507
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• 2008

In this paper we give a complete classification of real hyper-surfaces in complex two-plane Grassmannians $G_2({\mathbb{C}}^{m+2})$ with commuting structure Jacobi operator $R_{\xi}$ and another geometric condition.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.99-112
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• 2012

This paper attempts to present a numerical method for solving optimal control problems. The method is based upon constructing the n-th degree Jacobi polynomials to approximate the control vector and use differentiation matrix to approximate derivative term in the state system. The system dynamics are then converted into system of algebraic equations and hence the optimal control problem is reduced to constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.343-355
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• 2007

Using the modulus of smoothness ${\omega}^2_{{\varphi}^{\lambda}(f,t)_{\omega}$ Stechkin-Marchaud-Type inequalities with Jacobi weights of Bernstein Operators is established.

• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.245-261
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• 2015

The notion of a parabolically semistandard tableau is a generalisation of Young tableau, which explains combinatorial aspect of various Howe dualities of type A. We prove a Jacobi-Trudi type formula for the character of parabolically semistandard tableaux of a given generalised partition shape by using non-intersecting lattice paths.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.993-1002
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• 2016

In this paper we give some non-existence theorems for parallel normal Jacobi operator of real hypersurfaces in real, complex and quaternionic space forms, respectively.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.359-370
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• 2011

In this work, we obtain new solitary wave solutions for some nonlinear partial differential equations. The Jacobi elliptic function rational expansion method is used to establish new solitary wave solutions for the combined KdV-mKdV and Klein-Gordon equations. The results reveal that Jacobi elliptic function rational expansion method is very effective and powerful tool for solving nonlinear evolution equations arising in mathematical physics.