• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.1-14
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• 1998

Multiplicity results of doubly-periodic solution for semilinear heat equations having coercive nonlinearity are discussed. Our proofs rely on Mawhin's continuation theorem.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.873-894
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• 2021

In this paper, we consider the Gudnason model of 𝒩 = 2 supersymmetric field theory, where the gauge field dynamics is governed by two Chern-Simons terms. Recently, it was shown by Han et al. that for a prescribed configuration of vortex points, there exist at least two distinct solutions for the Gudnason model in a flat two-torus, where a sufficient condition was obtained for the existence. Furthermore, one of these solutions has the asymptotic behavior of topological type. In this paper, we prove that such doubly periodic topological solutions are uniquely determined by the location of their vortex points in a weak-coupling regime.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.153-164
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• 2012

In this paper, we study the existence, non-existence, and multiplicity of positive solutions for a coupled telegraph system using the xed-point theorem of cone expansion/compression type, the upper-lowe solutions method, and xed point index theory.

• Korean Journal of Microbiology
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• v.53 no.3
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• pp.200-207
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• 2017

A new approach to the solubilization of waste activated sludge (WAS) using alginate-quaternary ammonium complex beads was investigated under controlled mild alkaline conditions. The complex beads were prepared by the reaction of sodium alginate (SA) with 3-(trimethoxysilyl)propyl-octadecyldimethylammonium chloride (TSA) in acid solution, followed by crosslinking with $CaCl_2$. Treatment of WAS with SA-TSA complex beads was effective for enhancing the efficacy of WAS solubilization. The highest value of soluble chemical oxygen demand (SCOD) concentration (3,900 mg/L) was achieved after 10 days of treatment with 30% (v/v) SA-TSA complex beads. The WAS solubilization efficacy of the complex beads was also evaluated by estimating the concentrations of volatile fatty acids (VFAs). The maximum value of VFAs was 2,961 mg/L, and the overall proportions of VFAs were more than 75% of SCOD. The main components of VFAs were acetic, propionic, iso-butyric, and butyric acids. These results suggest that SA-TSA complex beads might be useful for enhancing the solubilization of WAS. The potential use of VFAs as the external carbon substrate for the production of polyhydroxyalkanoate (PHA) by a mixed microbial culture (MMC) was also examined. The enrichment of PHA-accumulating MMC could be achieved by periodic feeding of VFAs generated from WAS in a sequencing batch reactor. The composition of PHA synthesized from VFAs mainly consisted of 3-hydroxybutyrate. The maximum PHA content accounted for 25.9% of dry cell weight. PHA production by this process is considered to be promising since it has a doubly beneficial effect on the environment by reducing the amount of WAS and concomitantly producing an eco-friendly biopolymer.