• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.289-317
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• 2002

We associate binary codes to polynomials over fields of characteristic two and show that the binary Golay codes are associated to the Mathieu group polynomials in characteristics two. We give two more polynomials whose Galois group in $M_{12}$ but different self-orthogonal binary codes are associated. Also, we find a family of $M_{24}$-coverings which includes previous ones.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.199-210
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• 2007

Given a field K and a finite group G, it is a very interesting problem, although very difficult, to find all Galois extensions over K whose Galois group is isomorphic to G. In this paper, we prepare a theoretical background to study this type of problem when G is the Mathieu group $M_{24}$ and K is a field of characteristic two.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.45-64
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• 2024

Let G be a finite group, K a split field for G, and L a linear map from K[G] to K. In our paper, we first give sufficient and necessary conditions for Ker L and Ker L ∩ Z(K[G]), respectively, to be Mathieu-Zhao spaces for some linear maps L. Then we give equivalent conditions for Ker L to be Mathieu-Zhao spaces of K[G] in term of the degrees of irreducible representations of G over K if G is a finite Abelian group or G has a normal Sylow p-subgroup H and L are class functions of G/H. In particular, we classify all Mathieu-Zhao spaces of the finite Abelian group algebras if K is a split field for G.

• Journal of Microbiology and Biotechnology
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• v.24 no.1
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• pp.26-35
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• 2014

Saccharothrix algeriensis NRRL B-24137 produces naturally different dithiolopyrrolone derivatives. The enzymatic activity of pyrrothine N-acyltransferase was determined to be responsible for the transfer of an acyl group from acyl-CoA to pyrrothine core. This activity was also reported to be responsible for the diversity of the dithiolopyrrolone derivatives. Based on this fact, nine dithiolopyrrolone derivatives were produced in vitro via the crude extract of Sa. algeriensis. Three of them have never been obtained before by natural fermentation: acetoacetyl-pyrrothine, hydroxybutyryl-pyrrothine, and dimethyl thiolutin (holomycin). Two acyltransferase activities, acetyltransferase and benzoyltransferase catalyzing the incorporation of linear and cyclic acyl groups to the pyrrothine core, respectively, were biochemically characterized in this crude extract. The first one is responsible for formation of acetyl-pyrrothine and the second for benzoyl-pyrrothine. Both enzymes were sensitive to temperature changes: For example, the loss of acetyltransferase and benzoyltransferase activity was 53% and 80% respectively after pre-incubation of crude extract for 60 min at $20^{\circ}C$. The two enzymes were more active in neutral and basal media (pH 7-10) than in the acidic one (pH 3-6). The optimum temperature and pH of acetyltransferase were $40^{\circ}C$ and 7, with a $K_m$ value of $7.9{\mu}M$ and a $V_{max}$ of $0.63{\mu}M/min$ when acetyl-CoA was used as limited substrate. Benzoyltransferase had a temperature and a pH optimum at $55^{\circ}C$and 9, a $K_m$ value of $14.7{\mu}M$, and a $V_{max}$ of $0.67{\mu}M/min$ when benzoyl-CoA was used as limited substrate.