• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.307-316
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• 2021

We provide a gap theorem of Simons' type for free boundary minimal and constant mean curvature surfaces in the unit ball in 3-dimensional Euclidean space.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.321-348
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• 2009

In this paper, we give two lower bounds on the diameter of the boundary slope set of a Montesinos knot. One is described in terms of the minimal crossing numbers of the knots, and the other is related to the Euler characteristics of essential surfaces with the maximal/minimal boundary slopes.

• Journal of the Korean Society for Nondestructive Testing
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• v.17 no.4
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• pp.237-247
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• 1997

A geometrical inverse heat conduction problem is solved for the infrared scanning cavity detection by the boundary element method using minimal energy technique. By minimizing the kinetic energy of temperature field, boundary element equations are converted to the quadratic programming problem. A hypothetical inner boundary is defined such that the actual cavity is located interior to the domain. Temperatures at hypothetical inner boundary are determined to meet the constraints of mea- surement error of surface temperature obtained by infrared scanning, and then boundary element analysis is peformed for the position of an unknown boundary (cavity). Cavity detection algorithm is provided, and the effects of minimal energy technique on the inverse solution method are investigated by means of numerical analysis.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.251-256
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• 2010

In this article, we consider a minimal graph in $R^3$ which is bounded by a Jordan curve and a straight line. Suppose that the boundary is symmetric with the reflection under a plane, then we will prove that the minimal graph is itself symmetric under the reflection through the same plane.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.875-882
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• 2004

Let (M,g) be a compact m dimensional Einstein manifold with smooth boundary. Let $\Delta$$_{p}$,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec($\Delta$$_{p}$,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.ant.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.98-109
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• 2022

In the present paper, we prove the growth and distortion theorems for the spirallike functions class 𝓢_k(λ) related to boundary radius rotation, and by using the distortion result, we get an estimate for the Gaussian curvature of a minimal surface lifted by a harmonic function whose analytic part belongs to the class 𝓢_k(λ). Moreover, we determine and draw the minimal surface corresponding to the harmonic Koebe function.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.21-32
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• 2000

We study theoretical aspects of one-dimensional cellular automata over GF(q), where q is a power of a prime. Some results about the characteristic polynomials of such cellular automata are given. Intermediate boundary cellular automata are defined and related to the more common null boundary cellular automata.

• Korean Institute of Interior Design Journal
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• no.20
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• pp.84-90
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• 1999

This study is on relations between minimalism, which is one of important theme in the contemporary design, and East-oriented speculatiov. Minimalism, one inclination of neo-modernism is characterized by Essentialism. That is connected with East-oriented thinking, especially Taoism. The paradigm of contradiction and paradox replaces the paradigm of rationality and the law of cause and effect. Minimal tendency is appeared at Modernism in 60's and Neo-modernism in 90's. The differences are originated with their manner on simplicity. Minimal tendency in Modernism is characterized by 'less is more' and that in Meo-modernism is by 'more with less'. The minimizing strategy is not considered as means as in modern age but as purpose in neo-modern age. This paper explains minimal architectural space as spatial problem and recognitions on that, not as the figurative problem. Conclusively the relationships between minimalism and eastern ideas are represented through the boundary and extensity of space, void and solid, de-formalization and Essentialism.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.597-605
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• 2015

In this study, linear vibrations of an axially moving beam under non-ideal support conditions have been investigated. The main difference of this study from the other studies; the non-ideal clamped support allow minimal rotations and non-ideal simple support carry moment in minimal orders. Axially moving Euler-Bernoulli beam has simple and clamped support conditions that are discussed as combination of ideal and non-ideal boundary with weighting factor (k). Equations of the motion and boundary conditions have been obtained using Hamilton's Principle. Method of Multiple Scales, a perturbation technique, has been employed for solving the linear equations of motion. Linear equations of motion are solved and effects of different parameters on natural frequencies are investigated.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.335-340
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• 2007

Let M be a hyperbolic 3-manifold such that ${\partial}M$ has at least two boundary tori ${\partial}_oM$ and ${\partial}_1M$. Suppose that M contains an essential orientable surface P of genus $g$ with one outer boundary component ${\partial}_oP$, lying in ${\partial}_oM$ and having slope ${\lambda}$ in ${\partial}_oM$, and $p$ inner boundary components ${\partial}_iP$, $i=1$, ${\cdots}$, $p$, each having slope ${\alpha}$ in ${\partial}_1M$. Let ${\beta}$ be a slope in ${\partial}_1M$ and suppose that $M({\beta})$ is toroidal. Let $\hat{T}$ be a minimal essential torus in $M({\beta})$, which means that $\hat{T}$ is pierced a minimal number of times by the core of the ${\beta}$-Dehn filling, among all essential tori in $M({\beta})$. Let $T=\hat{T}{\cap}M$ and denote by $t$ the number of components of ${\partial}T$. In this paper we prove: (i) if $t{\geq}3$, then ${\Delta}({\alpha},{\beta}){\leq}6+\frac{10g-5}{p}$, (ii) If $t=2$, then ${\Delta}({\alpha},{\beta}){\leq}13+\frac{24g-12}{p}$, (iii) If $t=1$, then ${\Delta}({\alpha},{\beta}){\leq}1$.