• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.929-937
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• 2003

Kernel type estimations of discontinuity point at an unknown location in regression function or its derivatives have been developed. It is known that the discontinuity point estimator based on $Gasser-M\ddot{u}ller$ regression estimator with a one-sided kernel function which has a zero value at the point 0 makes a poor asymptotic behavior. Further, the asymptotic variance of $Gasser-M\ddot{u}ller$ regression estimator in the random design case is 1.5 times larger that the one in the corresponding fixed design case, while those two are identical for the local polynomial regression estimator. Although $Gasser-M\ddot{u}ller$ regression estimator with a one-sided kernel function which has a non-zero value at the point 0 for the modification is used, computer simulation show that this phenomenon is also appeared in the discontinuity point estimation.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1485-1502
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• 2014

The explicit formula for the hyperbolic metric ${\lambda}_{{\alpha},{\beta},{\gamma}}(z){\mid}dz{\mid}$ on the thrice-punctured sphere $\mathbb{P}{\backslash}\{0,1,{\infty}\}$ with singularities of order 0 < ${\alpha}$, ${\beta}$ < 1, ${\gamma}{\leq}1$, ${\alpha}+{\beta}+{\gamma}$ > 2 at 0, 1, ${\infty}$ was given by Kraus, Roth and Sugawa in [9]. In this article we investigate the asymptotic properties of the higher order derivatives of ${\lambda}_{{\alpha},{\beta},{\gamma}}(z)$ near the origin and give more precise descriptions for the asymptotic behavior of ${\lambda}_{{\alpha},{\beta},{\gamma}}(z)$.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.125-140
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• 2006

Let $g(n,\;l_1,\;l_2,\;d,\;t,\;q)$ be the number of general4-regular graphs on n labelled vertices with $l_1+2l_2$ loops, d double edges, t triple edges and q quartet edges. We use inclusion and exclusion with five types of properties to determine the asymptotic behavior of $g(n,\;l_1,\;l_2,\;d,\;t,\;q)$ and hence that of g(2n), the total number of general 4-regular graphs where $l_1,\;l_2,\;d,\;t\;and\;q\;=\;o(\sqrt{n})$, respectively. We show that almost all general 4-regular graphs are 2-connected. Moreover, we determine the asymptotic numbers of general 4-regular graphs with given connectivities.

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.345-355
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• 2018

This paper looks into phase plane behavior of the solution near the positive steady-state for the system with prey density dependent response functions. The positive invariance and boundedness property of the solution to the objective model are proved. The existence result of a positive steady-state and asymptotic analysis near the positive constant equilibrium for the objective system are of interest. The results of phase plane analysis for the system are proved by observing the asymptotic properties of the solutions. Also some numerical analysis results for the behaviors of the solutions in time are provided.

• Journal of the Korean Geotechnical Society
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• v.21 no.6
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• pp.93-100
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• 2005

The occurrence of multi-segmented hydraulic fractures that show different behavior from the single fracture is common phenomenon. However, it is not easy to evaluate the behavior of multiple fractures computed by most numerical techniques because of complicated process computation. This study presents how to efficiently calculate the displacement of the multi-segmented hydraulic fractures using the boundary collocation method (BCM). First of all, asymptotic solutions are obtained for the closely spaced overlapping fractures and are compared with those by the BCM where the number of collocation points is varied. As a result, the BCM provides an excellent agreement with the asymptotic solutions even when the number of collocation points is reduced ten times as many as that of conventional implementations. Accordingly, the numerical simulation of more realistic and, hence, more complex fracture geometries by the BCM would be valid with such a significant reduction of the number of collocation points.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.157-167
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• 2008

A mapping f : $M{\rightarrow}N$ between Hilbert $C^*$-modules approximately preserves the inner product if $$\parallel<f(x),\;f(y)>-<x,y>\parallel\leq\varphi(x,y)$$ for an appropriate control function $\varphi(x,y)$ and all x, y $\in$ M. In this paper, we extend some results concerning the stability of the orthogonality equation to the framework of Hilbert $C^*$-modules on more general restricted domains. In particular, we investigate some asymptotic behavior and the Hyers-Ulam-Rassias stability of the orthogonality equation.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.731-743
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• 2002

Let M be a Riemannian manifold with asymptotically non-negative curvature. We study the asymptotic behavior of the energy densities of a harmonic map and an exponentially harmonic function on M. We prove that the energy density of a bounded harmonic map vanishes at infinity when the target is a Cartan-Hadamard manifold. Also we prove that the energy density of a bounded exponentially harmonic function vanishes at infinity.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.820-823
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• 2002

The asymptotic problem of a semi-infinite conducting crack parallel to the poling direction in ferroelectric ceramics subjected to electric fields is analyzed. The main mechanism for the conducting crack growth behavior is thought to be ferroelectric domain switching leading to the development of a process zone around the crack. The shape and size of the switching zone is shown to depend strongly on the relative magnitude on the ratio of the coercive electric field to the yield electric field. It is shown that the crack growth can be either enhanced or retarded depending on the ratio of the coercive electric field to yield electric field.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.8
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• pp.75-83
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• 2005

A steady transonic dilute premixed combustion in a diverging channel is investigated by using asymptotic analysis. This model explores the nonlinear interactions between the near-sonic speed of the flow, the small changes in geometry from a straight channel, and the small heat release due to the one-step first-order Arrhenius chemical reaction. The reactive flow is described by a nonhomogeneous transonic small-disturbance (TSD) equation coupled with an ordinary differential equation for the calculation of the reactant mass fraction in the combustible gas. Also the asymptotic analysis reveals the similarity parameters that govern the reacting flow problem. The results show the complicated nonlinear interaction between the convection, reaction, and geometry effects and its effect on the flow behavior.

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.115-119
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• 1991

In this paper we obtain the asymptotic behavior of solutions of the perturbed system x' = (A(t) + B(t))x of x' = A(t)x by using the Floquet theorem.