• Journal of The Korean Astronomical Society
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• v.37 no.5
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• pp.477-482
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• 2004

Shock waves form in the intergalactic space as an ubiquitous consequence of cosmic structure formation. Using N-body/hydrodynamic simulation data of a ACDM universe, we examined the properties of cosmological shock waves including their morphological distribution. Adopting a diffusive shock acceleration model, we then calculated the amount of cosmic ray energy as well as that of gas thermal energy dissipated at the shocks. Finally, the dynamical consequence of those cosmic rays on cluster properties is discussed.

• Journal of The Korean Astronomical Society
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• v.28 no.1
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• pp.67-70
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• 1995

In contrast to conventional belief that extended inflation ends when the Universe percolates, we find inflation may continue at least many Hubble times even after the Universe percolates. What is observed is that inflation will not stop unless the global equation of state changes from inflationary one into radiation one. Thus the energy density of shorter wavelength gravitational waves induced by bubble collision at near the end of inflation should be at least Order $(10^2)\~O(10^3)$ times greater than previous estimation of Turner and Wilcek(TW).

• Honam Mathematical Journal
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• v.32 no.2
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• pp.333-362
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• 2010

We define H*H-fuzzy set and form a new category Set(H*H) consisting of H*H-fuzzy sets and morphisms between them. First, we study it in the sense of topological universe and obtain an exponential objects of Set(H*H). Second, we investigate some relationships among the categories Set(H*H), Set(H) and ISet(H).

• Publications of The Korean Astronomical Society
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• v.22 no.1
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• pp.1-20
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• 2007

Quasars at cosmological distances can be gravitationally lensed by galaxies into two or more images. The probability of this lensing and the angular separation between the images depend on the geometry and the expansion history of the universe as well as the lensing galaxies. The time delay between lensed images is also a direct indicator of the size of the universe. I review these cosmological applications of multiple-image gravitationally lensed quasars to determine or constrain the cosmological parameters.

• Publications of The Korean Astronomical Society
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• v.7 no.1
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• pp.79-87
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• 1992

New and improved data on the gravitational lens systems discovered so far are compared with the theoretical predictions of Gott, Park, and Lee (1989, GPL). Systems lensed by a single galaxy, compatible with assumptions of GPL, support flat or near-flat geometry for the universe. But the statistical uncertainty is too large to draw any definite conclusion. We need more lens systems. Also, the probability of multiple image lensing and mean separation of the images averaged over the source distribution are calculated for various cosmological models. Multiple-image lens systems and radio ring systems are compared with the predictions. Although the data reject exotic cosmological models, it cannot discriminate among conventional Friedmann models yet.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.2
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• pp.134-141
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• 2010

We introduce the category IVSet(H) of interval-valued H-fuzzy sets and show that IVSet(H) satisfies all the conditions of a topological universe except the terminal separator property. And we study some relations among IVSet (H), ISet (H) and Set (H).

• Journal for History of Mathematics
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• v.25 no.1
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• pp.29-43
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• 2012

In this paper, we survey the history of search for axiomatic set theory and show that ${\exists}U(0{\in}U{\wedge}{\forall}x(x{\in}U{\leftrightarrow}{\exists}z(z{\in}U{\wedge}{\forall}y(y{\in}x{\rightarrow}y{\subseteq}z))){\rightarrow}$ ZR.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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• pp.389-394
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• 2005

The purpose of this paper is to introduce the notions of L-fuzzy topological towers by using a completely distributive lattic L and show that the category L-FPrTR of L-fuzzy pretopoplogical tower spaces and the category L-FPsTR of L-fuzzy pseudotopological tower spaces are extensional topological constructs. And we show that L-FPsTR is the cartesian closed topological extension of L-FPrTR. Hence we show that L-FPsTR is a topological universe.

• Publications of The Korean Astronomical Society
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• v.28 no.1
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• pp.15-15
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• 2013

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.1
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• pp.73-81
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• 2010

We introduce the new category VSet(H) consisting of H-fuzzy spaces and H-fuzzy mappings between them satisfying a certain condition, and investigate VSet(H) in the sense of a topological universe. Moreover, we show that VSet(H) is Cartesian closed over Set.