• Journal of the Korea Society of Computer and Information
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• v.20 no.3
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• pp.69-74
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• 2015

This paper offers solutions to unresolved $43{\leq}R(5,5){\leq}49$ and $102{\leq}R(6,6){\leq}165$ problems of Ramsey's number. The Ramsey's number R(s,t) of a complete graph $k_n$ dictates that n-1 number of incidental edges of a arbitrary vertex ${\upsilon}$ is dichotomized into two colors: (n-1)/2=R and (n-1)/2=B. Therefore, if one introduces the concept of distance to the vertex ${\upsilon}$, one may construct a partite graph $K_n=K_L+{\upsilon}+K_R$, to satisfy (n-1)/2=R of {$K_L,{\upsilon}$} and (n-1)/2=B of {${\upsilon},K_R$}. Subsequently, given that $K_L$ forms the color R of $K_{s-1)$, $K_S$ is attainable. Likewise, given that $K_R$ forms the color B of $K_{t-1}$, $K_t$ is obtained. By following the above-mentioned steps, $R(s,t)=K_n$ was obtained, satisfying necessary and sufficient conditions where, for $K_L$ and $K_R$, the maximum distance should be even and incidental edges of all vertices should be equal are satisfied. This paper accordingly proves R(5,5)=43 and R(6,6)=91.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.2
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• pp.234-238
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• 2004

We introduce the concepts of fuzzy (r, s)-semiopen sets and fuzzy (r, s)-semicontinuous mappings on intuitionistic fuzzy topological spaces in Sostak's sense and then we investigate some of their characteristic properties.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1059-1066
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• 2011

We introduce the concept of fuzzy S-weakly r-M-continuous functions on fuzzy r-minimal spaces, and investigate some characterizations of such functions and the relations between the continuity and fuzzy r-minimal compactness on fuzzy r-minimal spaces.

• Proceedings of the KSCN Conference
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• 2000.11a
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• pp.62-62
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• 2000

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.463-472
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• 2014

Let R be a ring with identity 1, I(R) be the set of all nonunit idempotents in R and $S_{\ell}$(R) (resp. $S_r$(R)) be the set of all left (resp. right) semicentral idempotents in R. In this paper, the following are investigated: (1) $e{\in}S_{\ell}(R)$ (resp. $e{\in}S_r(R)$) if and only if re=ere (resp. er=ere) for all nilpotent elements $r{\in}R$ if and only if $fe{\in}I(R)$ (resp. $ef{\in}I(R)$) for all $f{\in}I(R)$ if and only if fe=efe (resp. ef=efe) for all $f{\in}I(R)$ if and only if fe=efe (resp. ef=efe) for all $f{\in}I(R)$ which are isomorphic to e if and only if $(fe)^n=(efe)^n$ (resp. $(ef)^n=(efe)^n$) for all $f{\in}I(R)$ which are isomorphic to e where n is some positive integer; (2) For a ring R having a complete set of centrally primitive idempotents, every nonzero left (resp. right) semicentral idempotent is a finite sum of orthogonal left (resp. right) semicentral primitive idempotents, and eRe has also a complete set of primitive idempotents for any $0{\neq}e{\in}S_{\ell}(R)$ (resp. 0$0{\neq}e{\in}S_r(R)$).

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.71-77
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• 1993

Every ring considered in the paper will be assumed to be commutative and have a unit element. An ideal A of a ring R will be called primal if the elements of R which are zero divisors modulo A, form an ideal of R, say pp. If A is a primal ideal of R, P is called the adjoint ideal of A. The adjoint ideal of a primal ideal is prime [2]. The definition of primal ideals may also be formulated as follows: An ideal A of a ring R is primal if in the residue class ring R/A the zero divisors form an ideal of R/A. If Q is a primary idel of a ring R then every zero divisor of R/Q is nilpotent; therefore, Q is a primal ideal of R. That a primal ideal need not be primary, is shown by an example in [2]. Let R[X], and R[[X]] denote the polynomial ring and formal power series ring in an indeterminate X over a ring R, respectively. Let S be a multiplicative system in a ring R and S$^{-1}$ R the quotient ring of R. Let Q be a P-primary ideal of a ring R. Then Q[X] is a P[X]-primary ideal of R[X], and S$^{-1}$ Q is a S$^{-1}$ P-primary ideal of a ring S$^{-1}$ R if S.cap.P=.phi., and Q[[X]] is a P[[X]]-primary ideal of R[[X]] if R is Noetherian [1]. We search for analogous results when primary ideals are replaced with primal ideals. To show an ideal A of a ring R to be primal, it sufficies to show that a-b is a zero divisor modulo A whenever a and b are zero divisors modulo A.

• Proceedings of the Botanical Society of Korea Conference
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• 1987.07a
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• pp.323-347
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• 1987

The R locus of maize in one of several genes that regulate the anthocyanin pigments throughout the body of the plant and seed. The R gene product may regulate pigment deposition by controlling the expression of the flavonoid biosynthetic gene pathway in a tissue-specific manner. To understand the basis for tissue specific regulation and allelic variation at R, the molecular study has been done by cloning a portion of the R complex by transposon tagging with Ac. R specific probe were cloned from the R-nj mutant induced by Ac insertion mutagenesis. From southern analysis of R-r complex using the R-nj probe, the structure of R-r was proposed that R-r containes the three elements, (P)(Q)(S). These elements may organize as the inversion triplication model which (S) sequence was inverted in relation to (P) and (Q). The R-sc derivated from R-mb or R-nj was cloned with R-nj probe, and molecular genetical data showed that R-sc containes tissue specific and tissue nonspecific area, and the sequencing of R-sc are progressed now.

• Animal cells and systems
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• v.6 no.2
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• pp.145-151
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• 2002

Phylogenetic signal present in the mitochondrial 16S ribosomal RNA gene (16S rDNA) and the nuclear large subunit ribosomal RNA gene (28S rDNA) was explored to assess their utility in resolving family level relationships of the superfamily Tephritoidea. These two genes were chosen because they appear to evolve at different rates, and might contribute to resolve both shallow and deeper phylogenetic branches within a highly diversified group. For the 16S rDNA data set, the number of aligned sites was 1,258 bp, but 1,204 bp were used for analysis after excluding sites of ambiguous alignment. Among these 1,204 sites, 662 sites were variable and 450 sites were informative for parsimony analysis. For the 28S rDNA data set, the number of aligned sites was 1,102 bp, but 1,000 bp were used for analysis after excluding sites of ambiguous alignment. Among these 1000 sites, 235 sites were variable and 95 sites were informative for parsimony analysis. Our analyses suggest that: (1) while 16S rDNA is useful for resolving more recent phylogenetic divergences, 28S rDNA can be used to define much deeper phylogenetic branches; (2) the combined analysis of the 16S and 28S rDNAs enhances the overall resolution without losing phylogenetic signal from either single gene analysis; and (3) additional genes that evolve at intermediate rates between the 16S and 28S rDNAs are needed to further resolve relationships among the tephritoid families.

• Journal of the Korean Chemical Society
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• v.26 no.5
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• pp.310-319
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• 1982

Cobalt(III) complexes with sexidentate ligands, N,N,N',N'-tetrakis(2-amino-ethyl)-1,2-ethanediamine (ten), -1,3-propanediamine (ttn), -1,4-butanediamine (ttmd), -(R,R)-and -(R,S)-2,4-pentanediamine (tptn) were prepared, and the characterization of d-d absorption band on the variation of chelate ring size and conformation of these complexes were studied by means of electronic spectra. The first d-d absorption bands of $[Co(L)]^{3+}$ complexes are shifted to smaller wave numbers in the order. ttn > (R,R)-tptn > ten > ttmd${\simeq}$(R,S)-tptn for (L). The UV, $^{13}C$ NMR, and Circular Dichroism studies indicate that the R,S-tptn ligand of $[Co(R,S-tptn)]^{3+}$ complex coodinates to cobalt(Ⅲ) ion as a sexidentate with one methyl group in axial position.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.149-157
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• 2003

Let M be an exponentially bounded o-minimal expansion of the standard structure R = (R ,＋,.,<) of the field of real numbers. We prove that if r is a non-negative integer, then every definable $C^{r}$ manifold is affine. Let f : X ${\longrightarrow}$ Y be a definable $C^1$ map between definable $C^1$ manifolds. We show that the set S of critical points of f and f(S) are definable and dim f(S) < dim Y. Moreover we prove that if 1 < s < ${\gamma}$ < $\infty$, then every definable $C^{s}$ manifold admits a unique definable $C^{r}$ manifold structure up to definable $C^{r}$ diffeomorphism.