• 대한수학회지
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• 제51권4호
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• pp.665-678
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• 2014

We present a new space-time discontinuous Galerkin (DG) method for solving the time dependent, positive symmetric hyperbolic systems. The main feature of this DG method is that the discrete equations can be solved semi-explicitly, layer by layer, in time direction. For the partition made of triangle or rectangular meshes, we give the stability analysis of this DG method and derive the optimal error estimates in the DG-norm which is stronger than the $L_2$-norm. As application, the wave equation is considered and some numerical experiments are provided to illustrate the validity of this DG method.

• 수학
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• 제4권1호
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• pp.18-24
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• 1967

• 대한수학회지
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• 제61권3호
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• pp.547-564
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• 2024

We study totally real and complex subsets of a right quarternionic vector space of dimension n + 1 with a Hermitian form of signature (n, 1) and extend these notions to right quaternionic projective space. Then we give a necessary and sufficient condition for a subset of a right quaternionic projective space to be totally real or complex in terms of the quaternionic Hermitian triple product. As an application, we show that the limit set of a non-elementary quaternionic Kleinian group 𝚪 is totally real (resp. commutative) with respect to the quaternionic Hermitian triple product if and only if 𝚪 leaves a real (resp. complex) hyperbolic subspace invariant.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.1043-1048
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• 1990

The degenerate case of multivariable hyperbolic distributed-parameter systems (systems of hyperbolic partial differential equations) in time coordinate t and space coordinate x is characterized by a property that all the characteristic curves of the state equations are parallel to the coordinate axes of independent variables. It is a disturbing fact, although not well known, that the so-called maximum principle as applied to these systems does not exist for the control that depend on time alone. In this paper, however, it is shown that a set of necessary conditions in the small can exist for unconstrained as well as magnitude constrained controls in a locally convex set. The necessary conditions thus derived can be used conveniently to find the optimal control for degenerate hyperbolic distributed-parameter control systems.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권4호
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• pp.269-276
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• 2013

We find an explicit $C^{\infty}$-continuous path of Riemannian metrics $g_t$ on the 4-d hyperbolic space $\mathbb{H}^4$, for $0{\leq}t{\leq}{\varepsilon}$ for some number ${\varepsilon}$ > 0 with the following property: $g_0$ is the hyperbolic metric on $\mathbb{H}^4$, the scalar curvatures of $g_t$ are strictly decreasing in t in an open ball and $g_t$ is isometric to the hyperbolic metric in the complement of the ball.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.623-646
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• 2023

In this article, we introduce the hyperbolic space version of a faster iterative algorithm. The proposed iterative algorithm is used to approximate the common fixed point of three multi-valued almost contraction mappings and three multi-valued mappings satisfying condition (E) in hyperbolic spaces. The concepts weak w²-stability involving three multi-valued almost contraction mappings are considered. Several strong and △-convergence theorems of the suggested algorithm are proved in hyperbolic spaces. We provide an example to compare the performance of the proposed method with some well-known methods in the literature.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.13-20
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• 2015

As a vector space provides a fundamental tool for the study of Euclidean geometry, a gyrovector space provides an algebraic tool for the study of hyperbolic geometry. In general, the gyrovector spaces do not satisfy the distributivity with scalar multiplication. In this article, we see under what condition the distributivity with scalar multiplication is satisfied.

• 대한수학회지
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• 제25권2호
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• pp.227-243
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• 1988

• East Asian mathematical journal
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• 제13권1호
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• pp.11-22
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• 1997

• Kyungpook Mathematical Journal
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• 제25권2호
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• pp.155-160
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• 1985