• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.321-341
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• 2013

In this paper, we discuss the a posteriori error estimates of the semidiscrete mixed finite element methods for quadratic optimal control problems governed by linear hyperbolic equations. The state and the co-state are discretized by the order $k$ Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order $k(k{\geq}0)$. Using mixed elliptic reconstruction method, a posterior $L^{\infty}(L^2)$-error estimates for both the state and the control approximation are derived. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.643-653
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• 2012

Let $f\;:\;M\;{\rightarrow}\;M$ be a diffeomorphism on a closed $C^{\infty}$ manifold. Let $\Lambda$ be a transitive set. In this paper, we show that (i) $C^1$-generically, $f$ has the shadowing property on a locally maximal $\Lambda$ if and only if $\Lambda$ is hyperbolic, (ii) f has the $C^1$-stably shadowing property on $\Lambda$ if and only if $\Lambda$ is hyperbolic.

• The Pure and Applied Mathematics
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• v.13 no.2 s.32
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• pp.151-155
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• 2006

Let $\gamma$ be a $C_2$ curve in the open unit disk $\mathbb{D}. Flinn and Osgood proved that $K_{\mathbb{D}}(z,\gamma){\geq}1$ for all $z{\in}{\gamma}$ if and only if the curve ${\Large f}o{\gamma}$ is convex for every convex conformal mapping $\Large f$ of $\mathbb{D}, where $K_{\mathbb{D}}(z,\;\gamma)$ denotes the hyperbolic curvature of $\gamma$ at the point z. In this paper we establish a generalization of the Flinn-Osgood characterization for a curve with the hyperbolic curvature at least 1.

• Proceedings of the KIEE Conference
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• 2008.11a
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• pp.53-55
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• 2008

본 논문에서는, 기존의 문헌에 사용되어 온 $\Gamma$형을 대체할 수 있는 새로운 T형 장거리 송전선로 모델을 제시한다. 특히, T-모델은 선로 양단의 병렬 어드미턴스와의 중복이 없다. 또한, 기존 문헌에 제시된 hyperbolic solution을 이용한 간단한 장거리 송전선로 A,B,C,D 파라미터 유도방법을 소개한다. hyperbolic solution으로 장거리 송전선로 파라미터를 유도할 경우, exponential solution보다 수식의 양을 줄일 수 있고, 초기값도 간단하게 구할 수 있다.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.209-219
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• 2015

In this article, we first give metric version of an iteration scheme of Agarwal et al. [1] and approximate fixed points of two finite families of nonexpansive mappings in hyperbolic spaces through this iteration scheme which is independent of but faster than Mann and Ishikawa scheme. Also we consider case of three finite families of nonexpansive mappings. But, we need an extra condition to get convergence. Our convergence theorems generalize and refine many know results in the current literature.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.543-558
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• 2013

Let ${\Gamma}$ be a graph which contains two vertices $a$, $b$ with the same link. For the case where the link has less than 3 vertices, we prove that if the right-angled Artin group A(${\Gamma}$) contains a hyperbolic surface subgroup, then A(${\Gamma}$-{a}) contains a hyperbolic surface subgroup. Moreover, we also show that the same result holds with certain restrictions for the case where the link has more than or equal to 3 vertices.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1103-1107
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• 2018

Let M be a complete spacelike hypersurface in the (n + 1)-dimensional Minkowski space ${\mathbb{L}}^{n+1}$. Suppose that every unit speed curve X(s) on M satisfies ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}{\geq}-1/r^2$ and there exists a point $p{\in}M$ such that for every unit speed geodesic X(s) of M through the point p, ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}=-1/r^2$ holds. Then, we show that up to isometries of ${\mathbb{L}}^{n+1}$, M is the hyperbolic space $H^n(r)$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1127-1142
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• 2020

In 2016, the Hurwitz metric was introduced by D. Minda in arbitrary proper subdomains of the complex plane and he proved that this metric coincides with the Poincaré's hyperbolic metric when the domains are simply connected. In this paper, we provide an alternate definition of the Hurwitz metric through which we could define a generalized Hurwitz metric in arbitrary subdomains of the complex plane. This paper mainly highlights various important properties of the Hurwitz metric and the generalized metric including the situations where they coincide with each other.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.149-165
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• 2007

We investigate the existence of multiple nontrivial solutions $u(x,t)$ for a perturbation $b[({\xi}-{\eta}+2)^+-2]$ of the hyperbolic system with Dirichlet boundary condition $$(0.1)\;L{\xi}={\mu}[({\xi}-{\eta}+2)^+-2]\;in\;({-{\frac{{\pi}}{2}}},{\frac{{\pi}}{2}}){\times}\mathbb{R},\\L{\eta}={\nu}[({\xi}-{\eta}+2)^+-2]\;in\;({-{\frac{{\pi}}{2}}},{\frac{{\pi}}{2}}){\times}\mathbb{R},$$, where $u^+$=max{u,o}, ${\mu}$, ${\nu}$ are nonzero constants. Here L is the wave operator in $\mathbb{R}^2$ and the nonlinearity $({\mu}-{\nu})[({\xi}-{\eta}+2)^+-2]$ crosses the eigenvalues of the wave operator.

• Transactions of the Korean Society of Automotive Engineers
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• v.11 no.5
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• pp.156-162
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• 2003

The shock absorber is a part having a direct influence on the ride comfort, stability and dynamic load prediction of a vehicle. Thus, a rationally modeled shock absorber should be required in the dynamic analysis of vehicles. This thesis presents a modified model, based on Worden's hyperbolic tangent function, in order to fit experimental data on the velocity-damping force of a shock absorber. The hyperbolic tangent function correctly indicates the characteristics of a shock absorber, and has the advantage of containing physical causality. To evaluate the method, comparative evaluations of the linear model, the 5th polynomial model and Worden's model were carried out. The function presented in this paper is not only simple but also makes it possible to estimate the function coefficients easily and visually. In addition, it has the advantage of containing physical causality. Lastly, it effectively models the damping force of a shock absorber.