• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1077-1100
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• 2016

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1539-1550
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• 2019

We classify minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles and ruled constant mean curvature (cmc) surfaces in ${\mathbb{S}}^3$. First we show that minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles are either ruled (that is, foliated by geodesics) or rotationally symmetric (that is, invariant under an isometric ${\mathbb{S}}^1$-action which fixes a geodesic). Secondly, we show that, locally, there is only one ruled cmc surface in ${\mathbb{S}}^3$ up to isometry for each nonnegative mean curvature. We give a parametrization of the ruled cmc surface in ${\mathbb{S}}^3$(cf. Theorem 3).

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.403-404
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• 2014

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.523-535
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• 2015

We study surfaces in Euclidean space which are obtained as the sum of two curves or that are graphs of the product of two functions. We consider the problem of finding all these surfaces with constant Gauss curvature. We extend the results to non-degenerate surfaces in Lorentz-Minkowski space.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.693-708
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• 2002

The warped product L$\times$$_{f}$ F of a line L and a Kaehler manifold F is a typical example of Kenmotsu manifold. In this paper we determine submanifolds of L$\times$$_{f}$ F which are tangent to the structure vector field and satisfy certain conditions concerning with Ricci curvature and mean curvature.ure.

• Communications for Statistical Applications and Methods
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• v.18 no.1
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• pp.131-136
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• 2011

The original Bates-Watts framework applies only to the complete parameter vector. Thus, guidelines developed in that framework can be misleading when the adequacy of the linear approximation is very different for different subsets. The subset curvature measures appear to be reliable indicators of the adequacy of linear approximation for an arbitrary subset of parameters in nonlinear models. Given the specific mean shift outlier model, the standard approaches to obtaining test statistics for outliers are discussed. The accuracy of outlier tests is investigated using subset curvatures.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5B
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• pp.463-472
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• 2009

The aim of this study is to examine the effect of beach curvature on wave fields in coastal area with Submerged Breakwaters using the 3D numerical model that is able to simulate directly interaction of WAve Structure Sandy beach (LES-WASS-3D). At first, the adopted model was validated through the comparison with an existing experimental data and showed fairly nice agreement. And then, the numerical simulations have been performed to investigate the effect of according to the variation of beach curvature. Based on the numerical results, the wave height, mean surface elevation, mean flow around submerged breakwaters and longshore distributions of run-up height have been discussed in relation to the variation of beach curvature.

• Journal of the HCI Society of Korea
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• v.10 no.2
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• pp.13-19
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• 2015

Display technology has recently made enormous progress. In particular, display companies are competing each other to develop flexible display. Curved display, as a precursor of flexible display, are now used for smart phones and TVs. Curved monitors have been just introduced in the market, and are used for office work or entertainment. The aim of the current study was to investigate whether the curvature of a 42" multi-monitor affects postural control when it is used for entertainment purpose. The current study used two curvature levels (flat and 600mm). Ten college students [mean(SD) age = 20.9 (1.5)] with at least 20/25 visual acuity, and without color blindness and musculoskeletal disorders participated in this study. In a typical VDT environment, each participant played a car racing video game using a steering wheel and pedals for 30 minutes at each curvature level. During the video game, a pressure mat on the seat pan measured the participant's COP (Center of Pressure), and from which four measures (Mean Velocity, Median Power Frequency, Root-Mean-Square Distance, and 95% Confidence Ellipse Area) were derived. A larger AP (Anterior-Posterior) RMS distance was observed in the flat condition, indicating more forward-backward upper body movements. It can be partly due to more variability in visual distance across display, and hence longer ocular accommodation time in the case of the flat display. In addition, a different level of presence or attention between two curvature conditions can lead to such a difference. Any potential effect of such a behavioral change by display curvature on musculoskeletal disorders should be further investigated.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.979-998
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• 2009

Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for a submanifold of an S-space form tangent to structure vector fields. Equality cases are also discussed. As applications we find corresponding results for almost semi-invariant submanifolds, $\theta$-slant submanifolds, anti-invariant submanifold and invariant submanifolds. A necessary and sufficient condition for a totally umbilical invariant submanifold of an S-space form to be Einstein is obtained. The inequalities for scalar curvature and a Riemannian invariant $\Theta_k$ of different kind of submanifolds of a S-space form $\tilde{M}(c)$ are obtained.

• Structural Engineering and Mechanics
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• v.28 no.5
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• pp.495-514
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• 2008

In this paper, experimental and theoretical investigations of the effect of the mean moment on the response and collapse of circular thin-walled tubes subjected to cyclic bending are discussed. To highlight the influence of the mean moment effect, three different moment ratios r (minimum moment/ maximum moment) of -1, -0.5 and 0, respectively, were experimentally investigated. It has been found that the moment-curvature loop gradually shrinks with the number of cycles, and becomes stable after a few cycles for symmetric cyclic bending (r = -1). However, the moment-curvature loop exhibits ratcheting and increases with the number of cycles for unsymmetric cyclic bending (r = -0.5 or 0). In addition, although the three groups of tested specimens had three different moment ratios, when plotted in a log-log scale, three parallel straight lines describe the relationship between the controlled moment range and the number of cycles necessary to produce buckling. Finally, the endochronic theory combined with the principle of virtual work was used to simulate the relationship among the moment, curvature and ovalization of thin-walled tubes under cyclic bending. An empirical formulation was proposed for simulating the relationship between the moment range and the number of cycles necessary to produce buckling for thin-walled tubes subjected to cyclic bending with different moment ratios. The results of the experimental investigation and the simulation are in good agreement with each other.