• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.2
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• pp.120-126
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• 2007

In this paper, we investigate some of characteristic properties of fuzzy strongly (r, s)-semicontinuous, fuzzy strongly (r, s )-semiopen and fuzzy strongly (r, s )-semiclosed mappings on the intuitionistic fuzzy topological space in \check{S}ostak's$ sense.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.337-345
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• 2022

Let R ⊆ T be an extension of a commutative ring and S ⊆ R a multiplicative subset. We say that (R, T) is an S-accr (a commutative ring R is said to be S-accr if every ascending chain of residuals of the form (I : B) ⊆ (I : B²) ⊆ (I : B³) ⊆ ⋯ is S-stationary, where I is an ideal of R and B is a finitely generated ideal of R) pair if every ring A with R ⊆ A ⊆ T satisfies S-accr. Using this concept, we give an S-version of several different known results.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.607-617
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• 2014

Let S = C(r,m), the finite cyclic semigroup with index r and period m. Each subsemigroup of S is cyclic if and only if either r = 1; r = 2; or r = 3 with m odd. For $r{\neq}1$, the maximum value of the minimum number of elements in a (minimal) generating set of a subsemigroup of S is 1 if r = 3 and m is odd; 2 if r = 3 and m is even; (r-1)/2 if r is odd and unequal to 3; and r/2 if r is even. The number of cyclic subsemigroups of S is $r-1+{\tau}(m)$. Formulas are also given for the number of 2-generated subsemigroups of S and the total number of subsemigroups of S. The minimal generating sets of subsemigroups of S are characterized, and the problem of counting them is analyzed.

• Journal of the Korean Chemical Society
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• v.41 no.3
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• pp.150-156
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• 1997

A precursor of bulgecinine, (4S,5R)-1-acetyl-2-formyl-5-benzyloxymethyl-4-pyrrolidinol (15) has been synthesized from diacetone-D-glucose. Barton deoxygenation, conversion to an L-sugar and displacement with $N_3^-$ at C-5, and one-pot reductive cyclization at C-2 produced (6R)-6-Ο-benzyloxymethyl-(3R)-3-methoxy-2-oxa-5-azabicyclo-[2,2,1]heptane(13), a key intermediate for bulgecinine. N-Acetylation and acid hydrolysis of 13 furnished a precursor of bulgecinine, (2S,4S,5R)-pyrrolidinol derivative 15 and its (2R,4S,5R)-diastereomer.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.271-285
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• 2020

In this paper, we have introduced a new type of covering property ${\beta}^t_{({\omega}_r,s)}$-closedness, stronger than $P^t_{({\omega}_r,s)}$-closedness [3] in terms of (r, s)-β-open sets [9] and β-ω_t-closures in bitopological spaces along with its several characterizations via filter bases and grills [15] and various properties. Further grill generalizations of ${\beta}^t_{({\omega}_r,s)}$-closedness (namely, ${\beta}^t_{({\omega}_r,s)}$-closedness modulo grill) and associated concepts have also been investigated.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.121-126
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• 1985

D.K. Harrison [5] has shown that if R and S are fields of characteristic different from 2, then two Witt rings W(R) and W(S) are isomorphic if and only if W(R)/I(R)$^{3}$ and W(S)/I(S)$^{3}$ are isomorphic where I(R) and I(S) denote the fundamental ideals of W(R) and W(S) respectively. In [1], J.K. Arason and A. Pfister proved a corresponding result when the characteristics of R and S are 2, and, in [9], K.I. Mandelberg proved the result when R and S are commutative semi-local rings having 2 a unit. In this paper, we prove the result when R and S are 2-fold full rings. Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is nondegenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$ (V, R) induced by B is an isomorphism), and with a quadratic mapping .phi.:V.rarw.R such that B(x,y)=(.phi.(x+y)-.phi.(x)-.phi.(y))/2 and .phi.(rx)= $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U(R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$, .., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2, we reserve the notation [ $a_{11}$, $a_{22}$] for the space.the space.e.e.e.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1523-1537
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• 2023

Let R be a commutative ring with identity and S a multiplicative subset of R. First, we introduce and study the u-S-projective dimension and u-S-injective dimension of an R-module, and then explore the u-S-global dimension u-S-gl.dim(R) of a commutative ring R, i.e., the supremum of u-S-projective dimensions of all R-modules. Finally, we investigate u-S-global dimensions of factor rings and polynomial rings.

• The Korean Journal of Zoology
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• v.7 no.2
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• pp.13-18
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• 1964

The chromosomes of thirteen wild forms of Drosophila obtained from Kwangnung in Kyunggi Province, Korea were investigated with the ganglion cells of both male and female larvae using the aceto-lactic orcein squashed method. The male chromosome patterns of the species observed in the present study are summarized as follows:

• Journal of the korean academy of Pediatric Dentistry
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• v.24 no.3
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• pp.610-627
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• 1997

The purpose of this study was to compare the caries activity and cariogenic factors in children in different residence areas. The subjects of the study were 268 kindergarten children who were selected from the downtown area(D), apartment area(A), suburban area(S), and rural area(R) in and around the city of Iksan, Korea. Caries activity was measured as past caries experience (dft index and dfs index) and salivary reductase activity (Resazurin Disc Test scores). Cariogenic factors were investigated by a questionnaire. The results were as follows: Reductase activity S > R > D > A dt index R, S > D, A ft index D - the highest dft index A - the lowest ds index R - the highest fs index D - the highest Toothbrushing frequency A - the highest, R - the lowest Toothbrushing before bed D, A > S, R Toothbrushing by parents S, R > A, D Sweets intake freqeuncy A - the highest, S - the lowest Distance to dental office D < A < S < R Dental treatment experience D - the highest, A - the lowest Flouride application rate D > S > R > A Sealant application rate D > A, S > R Birth order A, S > R, D Age D > S > R, A

• Proceedings of the Korean Magnestics Society Conference
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• 2007.05a
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• pp.211.1-211.1
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• 2007