• Communications of the Korean Mathematical Society
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• v.26 no.1
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.1
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• pp.128-132
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• 2009

In this paper, we introduce the concept of fuzzy S-weakly (r,s)-continuous mapping on an intuitionistic fuzzy topological space in Sostak's sense and investigate some properties of such mappings.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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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)

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.2
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• pp.254-258
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• 2009

In this paper, we introduce the concepts of fuzzy strongly (r,s)-irresolute mappings and fuzzy strongly (r,s)-irresolute semiopen mappings and investigate some properties of such mappings.

• Kyungpook Mathematical Journal
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• v.54 no.1
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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.

• Bulletin of the Korean Chemical Society
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• v.6 no.4
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.4
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• pp.312-315
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• 2008

In this paper, we investigate some characterizations for fuzzy weakly (r, s)-continuous mapping on an intuitionistic fuzzy topological space in ${\check{S}}ostak's$ sense.

• Korean Journal of Microbiology
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• v.45 no.4
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• pp.430-434
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• 2009

Bacterial 16S rRNA gene sequences have been widely used for the studies on molecular phylogeny, evolutional history, and molecular detections. Bacterial genomes have multiple rRNA operons, of which gene sequences sometimes are variable. In the present study, heterogeneity of the Vibrio 16S rRNA gene sequences were investigated. Vibrio 16S rRNA sequences were obtained from GenBank databases, considering the completion of gene annotation of Vibrio genome sequences. These included V. cholerae, V. harveyi, V. parahaemolyticus, V. splendidus, and V. vulnificus. Chromosome 1 of the studied Vibrio had 7~10 copies of the 16S rRNA gene, and their intragenomic variations were less than 0.9% dissimilarity (more than 99.1% DNA similarity). Chromosome 2 had none or single 16S rRNA gene. Intragenomic 16S rRNA genotypes were detected at least 5 types (V. vulnificus #CMCP6) to 8 types (V. parahaemolyticus #RIMD 2210633, V. harveyi #ATCC BAA-1116). These suggest that Vibrio has high heterogeneity of the 16S rRNA gene sequences.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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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.