• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1007-1019
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• 2000

In this paper, we discuss a uniqueness problem for the Cauchy problem of the Euler equation. W give a sufficient condition on the vorticity to show the uniqueness of a class of generalized solution in terms of the generalized solution in terms o the generalized Besov space. The condition allows the iterated logarithmic singularity to the vorticity of the solution. We also discuss the break down (or blow up) condition for a smooth solution to the Euler equation under the related assumption.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.225-231
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• 1995

An eventual uniform equicontinuity condition is investigated in the context of the uniform central limit theorem (UCLT) for continuous martingales. We assume the usual intergrability condition on metric entropy. We establish an exponential inequality for a martingales. Then we use the chaining lemma of Pollard (1984) to prove an eventual uniform equicontinuity which is a sufficient condition of UCLT. We apply the result to approximate a stochastic integral with respect to a martingale to that of a Brownian motion.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.343-356
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• 2019

In this paper, we introduce metallic maps between metallic Riemannian manifolds, provide an example and obtain certain conditions for such maps to be totally geodesic. We also give a sufficient condition for a map between metallic Riemannian manifolds to be harmonic map. Then we investigate the constancy of certain maps between metallic Riemannian manifolds and various manifolds by imposing the holomorphic-like condition. Moreover, we check the reverse case and show that some such maps are constant if there is a condition for this.

• Journal of Advanced Navigation Technology
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• v.20 no.5
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• pp.475-481
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• 2016

In this paper, the new stability condition of linear discrete interval time-varying systems with time-varying delay time is proposed. The considered system has interval time-varying system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. The restricted stability issue on the interval time-invariant system is expanded to interval time-varying system and a powerful stability condition which is more comprehensive than the previous is proposed. As a results, it is possible to avoid the introduction of complex linear matrix inequality (LMI) or upper solution bound of Lyapunov equation in the derivation of sufficient condition. Also, it is shown that the proposed result can include the many existing stability conditions in the previous literatures. A numerical example in the pe revious works is modified to more general interval system and shows the expandability and effectiveness of the new stability condition.

• Journal of Environmental Science International
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• v.21 no.12
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• pp.1455-1462
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• 2012

The vertical distributions of nitrifying bacteria in aerobic fixed biofilm were investigated to evaluate the relationship between nitrification performance and microbial community at different HRT. Fluorescent in situ hybridization (FISH) and portable ion selective microelectrode system were adopted to analyze microbial communities and ions profiles according to the biofilm depth. Cilia media packed MLE (Modified Ludzack-Ettinger) like reactor composed of anoxic, aerobic I/II was operated with synthetic wastewater having COD 200 mg/L and $NH_4{^+}$-N mg/L at HRT of 6 hrs and 4 hrs. Total biofilm thickness of aerobic I, II reactor at 4 hrs condition was over two times than that of 6 hrs condition due to the sufficient substrate supply at 4 hrs condition (6 hrs; aerobic I 380 ${\mu}m$ and II 400 ${\mu}m$, 4 hrs; aerobic I 830 ${\mu}m$ and II 1040 ${\mu}m$). As deepen the biofilm detection point, the ratio of ammonia oxidizing bacteria (AOB) was decreased while the ratio of nitrite oxidizing bacteria (NOB) was maintained similar distribution at both HRT condition. The ratio of AOB was higher at 4 hrs than 6 hrs condition and $NH_4{^+}$-N removal efficiency was also higher at 4 hrs with 89.2% than 65.4% of 6 hrs. However, the ratio of NOB was decreased when HRT was reduced from 6 hrs to 4 hrs and $NO_2{^-}$-N accumulation was observed at 4 hrs condition. Therefore, it is considered that insufficient HRT condition could supply sufficient substrate and enrichment of AOB in all depth of fixed biofilm but cause decrease of NOB and nitrite accumulation.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.71-77
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• 1995

In this paper, we define a subgroup S(X, ${\gamma}$) of the group of automorphisms of universal minimal sets and give a necessary and sufficient condition for a minimal transformation group to be regular.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1879-1886
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• 2016

In this paper, we investigate domains having a flat piece in the boundary and find a sufficient condition for such a domain to be a cone.

• Communications of the Korean Mathematical Society
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• v.8 no.1
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• pp.47-54
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• 1993

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.81-97
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• 1999

A sufficient condition for pseudo-Laplacian equations involving critical Sobolev exponents to have positive solutions is established.

• Proceedings of the Korean Reliability Society Conference
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• 2002.06a
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• pp.303-303
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• 2002

We obtain the necessary and sufficient condition of tightness for a sequence of random variables in the space of fuzzy sets with compact support in R.