• 대한수학회보
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• 제38권3호
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• pp.505-516
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• 2001

We show the existence and uniqueness of solutions for the Cauchy problem for nonlinear evolution equations with the strong damping: ${\upsilon}"(t)-M(｜{\nablauu}(t)｜^2){\triangle}u(t)-{\delta}{\triangle}u'(t)=f(t)$. As an application, a Kirchhoff model with viscosity is given.

• 대한수학회보
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• 제49권5호
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• pp.1057-1065
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• 2012

We prove that if $\widehat{\Gamma}$ is a co-contraction of ${\Gamma}$, then the right-angled Coxeter group $C(\widehat{\Gamma})$ embeds into $C({\Gamma})$. Further, we provide a graph ${\Gamma}$ without an induced long cycle while $C({\Gamma})$ does not contain a hyperbolic surface group.

• 대한수학회지
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• 제46권6호
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• pp.1119-1137
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• 2009

We construct a family of hyperbolic 3-manifolds by pairwise identifications of faces in the boundary of certain polyhedral 3-balls and prove that all these manifolds are cyclic branched coverings of the 3-sphere over certain family of links with two components. These extend some results from [5] and [10] concerning with the branched coverings of the whitehead link.

• 대한수학회보
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• 제55권2호
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• pp.359-366
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• 2018

We extend Jung's result about the relations among bi-closing, open and constant-to-one codes between general shift spaces to closing codes. We also show that any closing factor code ${\varphi}:X{\rightarrow}Y$ has a degree d, and it is proved that d is the minimal number of preimages of points in Y. Some other properties of closing codes are provided. Then, we show that any closing factor code is hyperbolic. This enables us to determine some shift spaces which preserved by closing codes.

• 충청수학회지
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• 제22권4호
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• pp.771-776
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• 2009

Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.46.3-46
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• 2002

Most of the process control algorithms in practice are based on the finite dimensional control theory. However, many chemical processes are described by partial differential equations (PDE's) and are infinite dimensional in nature due to spatial variation. Especially when the convection is dominant and thus diffusion can be ignored, chemical processes that are described by a system of first order hyperbolic PDE's. Such processes include tubular reactors, fixed bed reactors and pressure swinging adsorption. Conventionally such infinite dimensional systems described by PDE's are controlled by finite dimensional controllers that are designed through finite dimensional reduction of the process m...

• 충청수학회지
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• 제28권2호
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• pp.243-249
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• 2015

Let X be a closed surface for which the Euler characteristic $_{\mathcal{X}}(X)$ is negative, and let $f:X{\rightarrow}X$ be a self-map that is not surjective. In this short paper, we prove that we can compute the Nielsen number of f, N(f), under some algebraic conditions.

• 전자공학회논문지S
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• 제35S권1호
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• pp.23-28
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• 1998

A linearly-chirped fiber grating for the dispersion compensation over 520km of 1.3.mu.m single mode fiber is designed. The compensation characteristics of the gratings apodized each with Gaussian and hyperbolic tangent function are studied. the ripples in reflection and delay curves are coniderably reduced for both cases, but the reflection bandwidth for the hyperbolic tangent apodization is much less shrinked than that of the Gaussian apodization.

• 대한수학회논문집
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• 제31권3호
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• pp.575-583
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• 2016

In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.

• 대한수학회보
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• 제47권5호
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• pp.1067-1076
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• 2010

In this paper we investigate complete spacelike (r - 1)-maximal (i.e., $H_r\;{\equiv}\;0$) hypersurfaces with two distinct principal curvatures in the anti-de Sitter space $\mathbb{H}_1^{n+1}$(-1). We give a characterization of the hyperbolic cylinder.