• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.29-41
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• 2022

We study the concept of a quasi-ideal and a generalized bi-ideal of an n-ary semigroup; give a construction of the quasi-ideal of an n-ary semigroup generated by its nonempty subset; and introduce the notions of regularities, namely, a left regularity and a left weakly regularity. Moreover, the notions of a right regularity, a right weak regularity and a complete regularity are given. Finally, characterizations of these regularities are presented.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.287-302
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• 2008

The vertex set of a digraph D is denoted by V (D). A c-partite tournament is an orientation of a complete c-partite graph. A digraph D is called cycle complementary if there exist two vertex disjoint cycles $C_1$ and $C_2$ such that V(D) = $V(C_1)\;{\cup}\;V(C_2)$, and a multipartite tournament D is called weakly cycle complementary if there exist two vertex disjoint cycles $C_1$ and $C_2$ such that $V(C_1)\;{\cup}\;V(C_2)$ contains vertices of all partite sets of D. The problem of complementary cycles in 2-connected tournaments was completely solved by Reid [4] in 1985 and Z. Song [5] in 1993. They proved that every 2-connected tournament T on at least 8 vertices has complementary cycles of length t and ${\mid}V(T)\mid$ - t for all $3\;{\leq}\;t\;{\leq}\;{\mid}V(T)\mid/2$. Recently, Volkmann [8] proved that each regular multipartite tournament D of order ${\mid}V(D)\mid\;\geq\;8$ is cycle complementary. In this article, we analyze multipartite tournaments that are weakly cycle complementary. Especially, we will characterize all 3-connected c-partite tournaments with $c\;\geq\;3$ that are weakly cycle complementary.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.809-820
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• 2012

We establish a coincidence and a common fixed point result for four mappings involving a (${\psi}$, ${\varphi}$)-weak contractive condition type on a complete metric space. We take on ${\psi}$ and ${\varphi}$ the same conditions given by Popescu [Fixed points for (${\psi}$, ${\varphi}$)-weak contractions, Appl. Math. Lett. 24 (2011), 1-4].

• Honam Mathematical Journal
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• v.32 no.1
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• pp.167-176
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• 2010

Let (B, $\check{g}$) and (N, $\hat{g}$) be Einstein manifolds. Then, we get a complete (necessary and sufficient) condition for the warped product manifold $B\;{\times}_f\;N\;:=\;(B\;{\times}\;N,\;\check{g}\;+\;f{\hat{g}}$) to be Einstein, and obtain a complete condition for the Einstein warped product manifold $B\;{\times}_f\;N$ to be weakly stable. Moreover, we get a complete condition for the map i : ($B,\;\check{g})\;{\times}\;(N,\;\hat{g})\;{\rightarrow}\;B\;{\times}_f\;N$, which is the identity map as a map, to be harmonic. Under the assumption that i is harmonic, we obtain a complete condition for $B\;{\times}_f\;N$ to be Einstein.

• East Asian mathematical journal
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• v.14 no.2
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• pp.371-375
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• 1998

• The Pure and Applied Mathematics
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• v.21 no.2
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• pp.113-120
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• 2014

In this paper, we first show that for any space X, there is a ${\sigma}$-complete Boolean subalgebra of $\mathcal{R}$(X) and that the subspace {${\alpha}{\mid}{\alpha}$ is a fixed ${\sigma}Z(X)^{\sharp}$-ultrafilter} of the Stone-space $S(Z({\Lambda}_X)^{\sharp})$ is the minimal basically disconnected cover of X. Using this, we will show that for any countably locally weakly Lindel$\ddot{o}$f space X, the set {$M{\mid}M$ is a ${\sigma}$-complete Boolean subalgebra of $\mathcal{R}$(X) containing $Z(X)^{\sharp}$ and $s_M^{-1}(X)$ is basically disconnected}, when partially ordered by inclusion, becomes a complete lattice.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1613-1615
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• 2016

It is proved that $k[X_1,{\ldots},X_v ]$ localized at the ideal ($X_1,{\ldots},X_v$ ), where k is a field and $X_1,{\ldots},X_v$ indeterminates, is not weakly quasi-complete for $v{\geq}2$, thus proving a conjecture of D. D. Anderson and solving a problem from "Open Problems in Commutative Ring Theory" by Cahen, Fontana, Frisch, and Glaz.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.1-22
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• 2005

The object of this paper is to introduce the concept of a pair of semi-compatible self-maps in a fuzzy metric space to establish a fixed point theorem for four self-maps. It offers an extension of Vasuki [10] to four self-maps under the assumption of semi-compatibility and compatibility, repsectively. At the same time, these results give the alternate results of Grebiec [5] and Vasuki [9] as well.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.265-278
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• 2012

In this work we have considered several common fixed point results in metric spaces for weak compatible mappings. By applications of these results we establish some fixed point theorems in fuzzy metric spaces.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.2
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• pp.149-157
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• 2001

From the weakly nonlinear mild-slope wave equations introduced by Nadaoka et al.(1994, 1997), a set of weakly nonlinear wave equations for rapidly varying topography are derived by including the bottom curvature and slope-squared tenns ignored in the original equations ofNadaoka et al. To solve the linear version of extended wave equations derived in this study one-dimensional finite difference numerical model is con¬structed. The perfonnance of the model is tested for the case of wave reflection from a plane slope with various inclination. The numerical results are compared with the results calculated using other numerical models reported earlier. The comparison shows that the accuracy of the numerical model is improved significantly in comparison with that of the original equations ofNadaoka et al. by including a complete set of bottom curva1w'e and slope¬squared terms for a rapidly varying topography.