• Proceedings of the Korean Nuclear Society Conference
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• 2001.10a
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• pp.87.2-87
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• 2001

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.87-93
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• 1999

A holomorphic function f on D = {z : │z│ ＜ 1} is called uniformly locally univalent if there exists a positive constant $\rho$ such that f is univalent in every hyperbolic disk of hyperbolic radius $\rho$. We establish a characterization of uniformly locally univalent functions and investigate uniform local univalence of holomorphic universal covering projections.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.45-52
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• 2013

We show that a nontrivial transitive set is $C^1$-stably limit shadowable if and only if the transitive set is hyperbolic.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.83-90
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• 2000

We establish a sufficient condition for a simple closed curve in the Euclidean plain $\mathbb{R}^2$, the unit sphere $S^2$ or the hyperbolic plane $H^2$ to be the boundary of a metric ball.

• East Asian mathematical journal
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• v.16 no.2
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• pp.169-174
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• 2000

We give an easy proof that ${\phi}(z)=\frac{z^2_1}{1-z^2_2}$ induces the bounded composition operator $C_{\phi}:\mathcal{B}{\rightarrow}{\bigcap}H^p(B_2)$ defined by $C_{\phi}f=f\;o\;{\phi}$.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.549-555
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• 2021

We show the solvability of the ordinary differential equations describing curves on sphere or hyperbolic space. Making use of the geometric properties of the equations, we derive explicit solution formulae.

• East Asian mathematical journal
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• v.39 no.1
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• pp.87-92
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• 2023

In this paper, we study the nonlinear hyperbolic system with epsilon perturbation s_tt - div[c(x)∇s] + (ε - 1)s_t = |s|^γs. Under the conditions of c, γ and other assumptions, we prove the exponential behavior rates of the modified energy perturbation.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.619-634
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• 2023

This paper considers a parabolic-hyperbolic-hyperbolic type chemotaxis system in ℝ^d, d ≥ 3, describing tumor-induced angiogenesis. The global existence result and temporal decay estimate for a unique mild solution are established under the assumption that some Sobolev norms of initial data are sufficiently small.

• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.495-513
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• 2024

In the paper, we show that for a generic C¹ vector field X on a closed three dimensional manifold M, any isolated transitive set of X is singular hyperbolic. It is a partial answer of the conjecture in [13].

• The Journal of Engineering Geology
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• v.32 no.4
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• pp.513-523
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• 2022

The purpose of settlement management when treating soft ground through preloading is to determine the amount of settlement, check the progression of consolidation, and compare the settlement with the target settlement amount. Of the various methods available for predicting settlement based on measured data, the hyperbolic method was used in this study to analyze the settlement behavior of soft ground considering the creep behavior resulting from staged fill. Two versions of the method were used: the existing hyperbolic method, and a modified hyperbolic method. The existing hyperbolic method predicts the settlement amount using data for the final settlement section only during soft ground treatment through staged fill, for which the coefficient of consolidation behavior (k) was computed to give a predicted final consolidation settlement amount of S_r = 1.05 cm. In comparison, using the modified method, a predicted final consolidation settlement of S_r = 0.50 cm is obtained by considering the data for each staged fill section. These results show that the modified method considering data from the staged settlement was more accurate than the existing method considering data only from the final settlement section. This modification to the hyperbolic method therefore represents an improvement in performance over the existing method.