• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.327-338
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• 2021

In this paper, we have introduced a new notion of recurrent structure Jacobi of real hypersurfaces in complex hyperbolic two-plane Grassmannians G^*₂(ℂ^m+2). Next, we show a non-existence property of real hypersurfaces in G^*₂(ℂ^m+2) satisfying such a curvature condition.

• East Asian mathematical journal
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• v.37 no.1
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• pp.97-107
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• 2021

Let M be a real hypersurface with almost contact metric structure (��, ξ, ��, g) in a nonflat complex space form Mn(c). We denote S and Rξ by the Ricci tensor of M and by the structure Jacobi operator with respect to the vector field ξ respectively. In this paper, we prove that M is a Hopf hypersurface of type (A) in Mn(c) if it satisfies Rξ�� = ��Rξ and at the same time satisfies $({\nabla}_{{\phi}{\nabla}_{\xi}{\xi}}R_{\xi}){\xi}=0$ or Rξ��S = S��Rξ.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.287-311
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• 2023

In this paper, we introduce the notion of cyclic structure Jacobi semi-symmetric real hypersurfaces in the complex hyperbolic quadric Q^m* = SO⁰_2,m/SO₂SO_m. We give a classifiction of when real hypersurfaces in the complex hyperbolic quadric Q^m* having 𝔄-principal or 𝔄-isotropic unit normal vector fields have cyclic structure Jacobi semi-symmetric tensor.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.569-582
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• 2010

The following "Periodic Jacobi Procrustes" problem is studied: find the Periodic Jacobi matrix X which minimizes the Frobenius (or Euclidean) norm of AX - B, with A and B as given rectangular matrices. The class of Procrustes problems has many application in the biological, physical and social sciences just as in the investigation of elastic structures. The different problems are obtained varying the structure of the matrices belonging to the feasible set. Higham has solved the orthogonal, the symmetric and the positive definite cases. Andersson and Elfving have studied the symmetric positive semidefinite case and the (symmetric) elementwise nonnegative case. In this contribution, we extend and develop these research, however, in a relatively simple way. Numerical difficulties are discussed and illustrated by examples.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.67-75
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• 2004

Paul Turan observed that the Legendre polynomials satisfy the inequality $P_n(x)^2-P_{n-1}(x)P_{n+1}(x)$ > 0, $-1{\leq}x{\leq}1$. And G. Gasper(ref. [6], ref. [7]) proved such an inequality for Jacobi polynomials and J. Bustoz and N. Savage (ref. [2]) proved $P^{\alpha}_n(x)P^{\beta}_{n+1}(x)-P^{\alpha}_{n+1}(x)P{\beta}_n(x)$ > 0, $\frac{1}{2}{\leq}{\alpha}$ < ${\beta}{\leq}{\alpha}+2.0$ < $x$ < 1, for the ultraspherical polynomials (respectively, Laguerre ploynomials). The Bustoz-Savage inequalities hold for Laguerre and ultraspherical polynomials which are symmetric. In this paper, we prove some similar inequalities for non-symmetric Jacobi polynomials.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.307-326
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• 2007

We know that there are no real hypersurfaces with parallel Ricci tensor or parallel structure Jacobi operator in a nonflat complex space form (See [4], [6], [10] and [11]). In this paper we investigate real hypersurfaces M in a nonflat complex space form $M_n(c)$ under the condition that ${\nabla}_{\varepsilon}S=0\;and\;{\nabla}_{\varepsilon}R_{\varepsilon}=0,\;where\;S\;and\;R_{\varepsilon}$ respectively denote the Ricci tensor and the structure Jacobi operator of M in $M_n(c)$.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.547-566
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• 2003

In this paper, we introduce the notion of Maass-Jacobi forms and investigate some properties of these new automorphic forms. We also characterize these automorphic forms in several ways.

• Kyungpook Mathematical Journal
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• v.12 no.1
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• pp.115-117
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• 1972

The purpose of the present paper is to evaluate certain integrals involving Laguerre, Jacobi and Hermite polynomials. These integrals are very useful in case of expansion of any polynomial in a series of Orthogonal polynomials [1, Theo. 56].

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.385-391
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• 1994

In this report, given a Riemannian foliation F on a Riemannian manifold, we introduce the concept of F-Jacobi fields along normal geodesics to investigate geometric properties of the leaves of F.(omitted)

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.119-136
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• 2007

Block Jacobi and Gauss-Seidel iterative methods are studied for solving $n{\times}n$ fuzzy linear systems. A new splitting method is considered as well. These methods are accompanied with some convergence theorems. Numerical examples are presented to illustrate the theory.