• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.147-157
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• 2006

In this paper, we study complete maximal space-like hypersurfaces with constant Gauss-Kronecker curvature in an antide Sitter space $H_1^4(-1)$. It is proved that complete maximal spacelike hypersurfaces with constant Gauss-Kronecker curvature in an anti-de Sitter space $H_1^4(-1)$ are isometric to the hyperbolic cylinder $H^2(c1){\times}H^1(c2)$ with S = 3 or they satisfy $S{\leq}2$, where S denotes the squared norm of the second fundamental form.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.249-266
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• 2024

In this work, we study time-like and space-like surfaces invariant by a group of translation isometries of the half-space model ℋ³₁ of the anti-de Sitter space ℍ³₁ . We determine all such surfaces with constant mean curvature and constant Gaussian curvature. We also obtain umbilical surfaces of ℋ³₁.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.603-614
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• 2022

The main intent of this paper is to prove an existence and uniqueness fixed point result under Geraghty contractions in b-metric-like spaces, which remains an extended version of corresponding results in b-metric spaces and metriclike spaces. Using two types of Geraghty contractions, an approach is adopted to verify some fixed point results in b-metric-like spaces. Our main result is an extension of an earlier result given by Geraghty in b-metric-like-space. An example is also provided to demonstrate the validity of our main result. Moreover, as an application of our main result, the existence of solution of a Fredholm integral equation is established which may further be utilized to study the seismic response of dams during earthquakes.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.47-55
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• 2008

Local convergence results for three Newton-like methods in Banach space are provided. A comparison is given between the three convergence radii. Then we show that using the largest convergence radius we can pick an initial guess from with we start the corresponding iteration. It turns out that after a finite number of steps we can always use the iterate found as the starting guess for a faster method, since this iterate will be inside the convergence domain of the new method.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.35-45
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• 2008

In cases sufficient conditions for the semilocal convergence of Newtonlike methods are violated, we start with a modified Newton-like method (whose weaker convergence conditions hold) until we stop at a certain finite step. Then using as a starting guess the point found above we show convergence of the Newtonlike method to a locally unique solution of a nonlinear operator equation in a Banach space setting. A numerical example is also provided.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.41-50
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• 2002

We provide local and semilocal theorems for the convergence of Newton-like methods to a locally unique solution of an equation in a Banach space. The analytic property of the operator involved replaces the usual domain condition for Newton-like methods. In the case of the local results we show that the radius of convergence can be enlarged. A numerical example is given to justify our claim . This observation is important and finds applications in steplength selection in predictor-corrector continuation procedures.

• Journal of the Architectural Institute of Korea Planning & Design
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• v.34 no.6
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• pp.23-30
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• 2018

Gordon Cullen, who tried to understand urban landscapes in terms of visual attention, introduced a concept called 'Space and Infinity' in his book 'Townscape'. According to him, urban images like infinity spreading across the sky are more effectively created when we happen to see an open space while walking along a ground-level street than when we look at the sky. This study aims to quantitatively examine if urban observers pay more attention to spaces like pilotis on the bottom of a building. Thus, this study collected observers on actual urban landscape images and partially-edited images and conducted an experiment by adopting Eye-movement Tracking to find out if they actually pay more visual attention to a space like pilotis. This study selected a total of 50 people as research subjects and divided them into two groups. Image 1 was shown to one group, and Image 2 with the pilotis space edited was shown to the other group. As an experiment to find objective evidences on Gordon Cullen's 'Space and Infinity', this study analyzed difference between Image 1 and Image 2, and it was found that the domain of pilotis showed a value five times higher than the average visual attention since it attracted much visual attention although it was very small in area. That is, it has objectively clarified that people get most fascinated with a place with infinite images in the background like a pilotis space out of all the urban landscapes as Gordon Cullen's theory. In addition, the differences in visual concentration of pilotis space by sex, by subject was examined, and there was no significant difference in visual concentration of pilotis space by gender. As a result of examining the difference of visual concentration by classifying the subjects into architectural related major, the major group showed higher frequency of viewing than the non - major group.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1569-1578
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• 2015

We study helicoidal surfaces with the non-degenerate third fundamental form in Minkowski 3-space. In particular, we mainly focus on the study of helicoidal surfaces with light-like axis in Minkowski 3-space. As a result, we classify helicoidal surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form on the surface.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.135-146
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• 2001

Let M(sup)n be a space-ike submanifold in a de Sitter space M(sub)p(sup)n+p (c) with constant scalar curvature. We firstly extend Cheng-Yau's Technique to higher codimensional cases. Then we study the rigidity problem for M(sup)n with parallel normalized mean curvature vector field.

• Applied Microscopy
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• v.45 no.3
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• pp.115-118
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• 2015

In this review paper, I'd like to introduce the basics of angle-resolved photoemission spectroscopy (ARPES) and some of my results taken at the Pohang Accelerator Laboratory (PAL), the only synchrotron radiation in South Korea. The results show that ARPES is very useful, in particular, for studying two-dimensional materials. It looks like a microscope in momentum space similar to transmission electron microscope imaging atoms in real space.