• Title/Summary/Keyword: K^+\

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REMARKS ON DIGITAL HOMOTOPY EQUIVALENCE

  • Han, Sang-Eon
    • Honam Mathematical Journal
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    • v.29 no.1
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    • pp.101-118
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    • 2007
  • The notions of digital k-homotopy equivalence and digital ($k_0,k_1$)-homotopy equivalence were developed in [13, 16]. By the use of the digital k-homotopy equivalence, we can investigate digital k-homotopy equivalent properties of Cartesian products constructed by the minimal simple closed 4- and 8-curves in $\mathbf{Z}^2$.

GREEN'S ADDITIVE COMPLEMENT PROBLEM FOR k-TH POWERS

  • Ding, Yuchen;Wang, Li-Yuan
    • Journal of the Korean Mathematical Society
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    • v.59 no.2
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    • pp.299-309
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    • 2022
  • Let k ⩾ 2 be an integer, Sk = {1k, 2k, 3k, …} and B = {b1, b2, b3, …} be an additive complement of Sk, which means all sufficiently large integers can be written as the sum of an element of Sk and an element of B. In this paper we prove that $${{\lim}\;{\sup}}\limits_{n{\rightarrow}{\infty}}\;{\frac{{\Gamma}(2-{\frac{1}{k}})^{\frac{k}{k-1}}{\Gamma}(1+{\frac{1}{k}})^{\frac{k}{k-1}}n^{\frac{k}{k-1}}-b_n}{n}}\;{\geqslant}\;{\frac{k}{2(k-1)}}\;{\frac{{\Gamma}(2-{\frac{1}{k}})^2}{{\Gamma}(2-{\frac{2}{k}})}},$$ where 𝚪(·) is Euler's Gamma function.

The Purfication and Characterization of Macrolide-Phosphotransferase K of Escherichia coli 209K Highly Resistant to Erythromycin (에리스로마이신 고도내성 대장균 209K 유래 마크로라이드-포스포트란스페라제 K의 정제 및 특성)

  • Kim, Sook-Kyung;Oh, Tae-Gwon;Baek, Moon-Chang;Hong, Jong-Soo;Kim, Byong-Kak;Choi, Eung-Chil
    • YAKHAK HOEJI
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    • v.41 no.3
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    • pp.359-364
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    • 1997
  • Resistance gene mphK was cloned from Escherichia coli 209K strain which is highly resistant to erythromycin (EM). By using the cloned plasmid pGE64, E. coli NM522 was transformed. The comparison of macrolide-phosphotransferase K [MPH(K)] activity between E. coli 209K and E. coli NM522(pGE64) showed that the total enzyme activity of MN522(pGE64) was fifty-fole higher than that of 209K. To identify characteristics of MPH(K) more precisely. MPH(K) was isolated and purified from the NM522 (pGE64). The final purification f MPH(K) through several stages of purification process was 89 fole and the overall recovery was 11%. This enzyme was monomer with the molecular weight of 34 kDa and its isoelectric point (pI) was 5.0. The optimal pH and temperature for activity were 8.0 and $40^{\circ}C$, respectively.

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