• 제목/요약/키워드: $R_s$

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Ptr,s)-CLOSED SPACES AND PRE-(ωr,s)t-θf-CLUSTER SETS

  • Afsan, Bin Mostakim Uzzal;Basu, Chanchal Kumar
    • 대한수학회논문집
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    • 제26권1호
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    • pp.135-149
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    • 2011
  • Using (r, s)-preopen sets [14] and pre-${\omega}_t$-closures [6], a new kind of covering property $P^t_{({\omega}_r,s)}$-closedness is introduced in a bitopological space and several characterizations via filter bases, nets and grills [30] along with various properties of such concept are investigated. Two new types of cluster sets, namely pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets and (r, s)t-${\theta}_f$-precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets are investigated and using the degeneracy of such cluster sets, some new characterizations of some separation axioms in topological spaces or in bitopological spaces are obtained. A sufficient condition for $P^t_{({\omega}_r,s)}$-closedness has also been established in terms of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets.

UPPER BOUNDS FOR ASSIGNMENT FUNCTIONS

  • Lee, Gwang-Yeon
    • 대한수학회논문집
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    • 제9권2호
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    • pp.279-284
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    • 1994
  • Let R = ($r_1$, $r_2$, …, $r_{m}$) and S = ($s_1$, $s_2$, …, $s_{n}$ ) be positive integral vectors satisfying $r_1$$r_2$+…+ $r_{m}$ = $s_1$$s_2$+ㆍㆍㆍ+ $s_{n}$ , and let U(R, S) denote the class of all m $\times$ n matrices A = [$_a{ij}$ ] where $a_{ij}$ = 0 or 1 such that (equation omitted) = $r_{i}$ , (equation omitted) = $s_{j}$ , i = 1, ㆍㆍㆍ, m, j = 1, ㆍㆍㆍ, n.(omitted)

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DOUBLE PAIRWISE (r, s)(u, v)-SEMICONTINUOUS MAPPINGS

  • Lee, Eun Pyo;Lee, Seung On
    • 충청수학회지
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    • 제27권4호
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    • pp.603-614
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    • 2014
  • We introduce the concepts of ($\mathcal{T}^{{\mu}{\gamma}}$, $\mathcal{U}^{{\mu}{\gamma}}$)-double (r, s) (u, v)-semiclosures and ($\mathcal{T}^{{\mu}{\gamma}}$, $\mathcal{U}^{{\mu}{\gamma}}$)-double (r, s)(u, v)-semiinteriors. Using the notions, we investigate some of characteristic properties of double pairwise (r, s)(u, v)-semicontinuous, double pairwise (r, s)(u, v)-semiopen and double pairwise (r, s)(u, v)-semiclosed mappings.

The Line n-sigraph of a Symmetric n-sigraph-V

  • Reddy, P. Siva Kota;Nagaraja, K.M.;Geetha, M.C.
    • Kyungpook Mathematical Journal
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    • 제54권1호
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    • pp.95-101
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    • 2014
  • An n-tuple ($a_1,a_2,{\ldots},a_n$) is symmetric, if $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$. Let $H_n$ = {$(a_1,a_2,{\ldots},a_n)$ ; $a_k$ ${\in}$ {+,-}, $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair $S_n$ = (G,${\sigma}$) ($S_n$ = (G,${\mu}$)), where G = (V,E) is a graph called the underlying graph of $S_n$ and ${\sigma}$:E ${\rightarrow}H_n({\mu}:V{\rightarrow}H_n)$ is a function. The restricted super line graph of index r of a graph G, denoted by $\mathcal{R}\mathcal{L}_r$(G). The vertices of $\mathcal{R}\mathcal{L}_r$(G) are the r-subsets of E(G) and two vertices P = ${p_1,p_2,{\ldots},p_r}$ and Q = ${q_1,q_2,{\ldots},q_r}$ are adjacent if there exists exactly one pair of edges, say $p_i$ and $q_j$, where $1{\leq}i$, $j{\leq}r$, that are adjacent edges in G. Analogously, one can define the restricted super line symmetric n-sigraph of index r of a symmetric n-sigraph $S_n$ = (G,${\sigma}$) as a symmetric n-sigraph $\mathcal{R}\mathcal{L}_r$($S_n$) = ($\mathcal{R}\mathcal{L}_r(G)$, ${\sigma}$'), where $\mathcal{R}\mathcal{L}_r(G)$ is the underlying graph of $\mathcal{R}\mathcal{L}_r(S_n)$, where for any edge PQ in $\mathcal{R}\mathcal{L}_r(S_n)$, ${\sigma}^{\prime}(PQ)$=${\sigma}(P){\sigma}(Q)$. It is shown that for any symmetric n-sigraph $S_n$, its $\mathcal{R}\mathcal{L}_r(S_n)$ is i-balanced and we offer a structural characterization of super line symmetric n-sigraphs of index r. Further, we characterize symmetric n-sigraphs $S_n$ for which $\mathcal{R}\mathcal{L}_r(S_n)$~$\mathcal{L}_r(S_n)$ and $$\mathcal{R}\mathcal{L}_r(S_n){\sim_=}\mathcal{L}_r(S_n)$$, where ~ and $$\sim_=$$ denotes switching equivalence and isomorphism and $\mathcal{R}\mathcal{L}_r(S_n)$ and $\mathcal{L}_r(S_n)$ are denotes the restricted super line symmetric n-sigraph of index r and super line symmetric n-sigraph of index r of $S_n$ respectively.

Platinum(Ⅱ) Complexes of 2,2$^\prime$-Diaminobinaphthyl

  • 전무진;최성락
    • Bulletin of the Korean Chemical Society
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    • 제6권4호
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    • pp.214-217
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    • 1985
  • Platinum(II) complexes of R-2,2'-diaminobinaphthyl (R-dabn), [Pt(R-dabn)(H2O)2]Cl2, [Pt(R-dabn)(R-Pn)]Cl2, [Pt(R-dabn)(R-bn)]Cl2, and platinum(II) complexes of S-2,2'-diaminobinaphthyl (S-dabn), [Pt(S-dabn)(H2O)2]Cl2, [Pt(S-dabn)(S-Pn)]Cl2, and [(Pt(S-dabn)(S-bn)]Cl2 have been prepared. (R-Pn and S-Pn are, respectively R- and S isomer of 2,3-diaminobutane). R-Pn and S-bn are, respectively R and S isomer of 2,3-diaminopropane). In the vicinity of the B-absorption band region of dabn, the circular dichroism spectra of platinum(Ⅱ) complexes of R-dabn series show a positive B-band followed by a negative higher energy A-band, which is generally understood as the splitting pattern for a ${\lambda}$ conformation, while the circular dichroism spectra of platinum(Ⅱ) complexes of S-dabn series show a negative B-band followed by a positive higher energy A-band in the long-axis polarized absorption region as expected for a $\delta$ conformation.

Vibrio 속 16S rRNA 유전자 염기서열의 이질성 분석 (Heterogeneity Analysis of the 16S rRNA Gene Sequences of the Genus Vibrio)

  • 기장서
    • 미생물학회지
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    • 제45권4호
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    • pp.430-434
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    • 2009
  • 세균 16S rRNA 유전자 염기서열은 분자계통분류, 진화역사 규명, 미생물 검출 등 다양한 목적으로 이용되어 왔다. 세균 제놈(genome)은 multiple rRNA 오페론을 갖고 있으며, 이들 유전자 염기서열은 일부 변이가 있는 것으로 알려져 있다. 본 연구에서는 Vibrio 속의 16S rRNA 유전자 염기서열을 이용하여 세포 내 16S rRNA의 이질성을 규명하였다. 분석은 GenBank 자료 중에서 제놈 염기서열 annotation이 완료된 V. cholerae, V. harveyi, V. parahaemolyticus, V. splendidus, V. vulnificus를 이용하여 실시하였다. Vibrio 속은 1번 염색체에 7~10개의 16S rRNA 유전자 copy를 갖고 있으며, 이들의 세포 내 유전자 변이는 0.9% 이하 상이성(99.1%이상 DNA 상동성)을 보였다. 2번 염색체에서는 16S rRNA 유전자가 1개 이하로 존재하였다. 유전체내 16S rRNA 유전형은 최소 5개(V. vulnificus #CMCP6)에서 최대 8개(V. parahaemolyticus #RIMD 2210633, V. harveyi #ATCC BAA-1116)로 조사되었다. 본 결과는 Vibrio 속의 16S rRNA 유전자 염기서열이 높은 이질성을 갖는 것을 제시해 준다.

THE SOURCE OF SEMIPRIMENESS OF RINGS

  • Aydin, Neset;Demir, Cagri;Camci, Didem Karalarlioglu
    • 대한수학회논문집
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    • 제33권4호
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    • pp.1083-1096
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    • 2018
  • Let R be an associative ring. We define a subset $S_R$ of R as $S_R=\{a{\in}R{\mid}aRa=(0)\}$ and call it the source of semiprimeness of R. We first examine some basic properties of the subset $S_R$ in any ring R, and then define the notions such as R being a ${\mid}S_R{\mid}$-reduced ring, a ${\mid}S_R{\mid}$-domain and a ${\mid}S_R{\mid}$-division ring which are slight generalizations of their classical versions. Beside others, we for instance prove that a finite ${\mid}S_R{\mid}$-domain is necessarily unitary, and is in fact a ${\mid}S_R{\mid}$-division ring. However, we provide an example showing that a finite ${\mid}S_R{\mid}$-division ring does not need to be commutative. All possible values for characteristics of unitary ${\mid}S_R{\mid}$-reduced rings and ${\mid}S_R{\mid}$-domains are also determined.