• Honam Mathematical Journal
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• v.32 no.1
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• pp.85-89
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• 2010

In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on space-times M = $({\alpha},{\infty}){\times}_fN$ with prescribed scalar curvature functions.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.629-632
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• 1994

Let (M, g) be a Riemannian manifold. The relation between a (pointwise) conformal metric of the metric g and the scalar curvature of this new metrics is investigated by Kazdan, Warner and Schoen (cf. [1, 4]).

• Honam Mathematical Journal
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• v.30 no.4
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• pp.693-701
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• 2008

In this paper, when N is a compact Riemannian manifold of class (A), we consider the nonexistence of some warping functions on space-times M = $[a,{\infty}){\times}_fN$ with prescribed scalar curvatures.

• Journal of The Korean Astronomical Society
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• v.29 no.spc1
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• pp.283-284
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• 1996

Wormhole solutions of general theory of relativity are known to violate energy conditions. We have considered the possibility of having wormhole solutions in Brans-Dicke theory which is the prototype of scalar-tensor theories of gravity.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.317-336
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• 2000

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future (or past) complete Lorentzian metrics on $M=(-{\infty},{\;}\infty){\;}{\times}f^N$ with specific scalar curvatures.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.13-20
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• 2015

As a vector space provides a fundamental tool for the study of Euclidean geometry, a gyrovector space provides an algebraic tool for the study of hyperbolic geometry. In general, the gyrovector spaces do not satisfy the distributivity with scalar multiplication. In this article, we see under what condition the distributivity with scalar multiplication is satisfied.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.171-185
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• 2011

In this paper, when N is a compact Riemannian manifold of class (C), we consider the nonexistence of some warping functions on Riemannian warped product manifolds $M=[a,\;{\infty}){\times}_fN$ with prescribed scalar curvatures.

• East Asian mathematical journal
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• v.39 no.5
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• pp.529-536
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• 2023

This paper introduces the Frobenius endomophisms on the binary Hessian curves. It provides an efficient and computable homomorphism for computing point multiplication on binary Hessian curves. As an application, it is possible to construct the GLV method combined with the Frobenius endomorphism to accelerate scalar multiplication over the curve.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.10
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• pp.1409-1416
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• 2000

In this study, turbulent flows in a planar combustor which has a square rib-type flame holder are numerically investigated by Large Eddy Simulation(LES). Firstly, the flow fields with or without jet injection downstream of the flame-holder are examined using uniform inlet velocity. Comparison of the present LES results with experimental one shows a good agreement. Secondly, to investigate mixing of oxidizer(air) and fuel injected behind the flame holder, the scalar-transport equation is introduced and solved. From the instantaneous flow and scalar fields, complex and intense mixing phenomena between fuel and jet are observed. It is shown that the ratio of jet to blocked air velocity is an important factor to determine the flow structure. Especially, when the ratio is large enough, the fuel jet penetrates the main vortices shed from the flame holder, resulting in significant changes in the flow and scalar fields.

• Journal of Korea Multimedia Society
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• v.6 no.4
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• pp.698-706
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• 2003

The primary goal of surface approximation is to reduce the degree of deviation of the simplified surface from the original surface. However it is difficult to define the metric that can measure the amount of deviation quantitatively. Many of the existing studies analogize it by using the change of the scalar quantity before and after simplification. This approach makes a lot of sense in the point that the local surfaces with small scalar are relatively less important since they make a low impact on the adjacent areas and thus can be removed from the current surface. However using scalar value alone there can exist many cases that cannot compute the degree of geometric importance of local surface. Especially the perceptual geometric features providing important clues to understand an object, in our observation, are generally constructed with small scalar value. This means that the distinguishing features can be removed in the earlier stage of the simplification process. In this paper, to resolve this problem, we present various factors and their combination as the metric for calculating the deviation error by introducing the orientation of local surfaces. Experimental results indicate that the surface orientation has an important influence on measuring deviation error and the proposed combined error metric works well retaining the relatively high curvature regions on the object's surface constructed with various and complex curvatures.