• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.53-59
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• 2001

In this paper, we introduce the notion of positive implicative BH-algebras and study some relations between R - (L-) maps and positive implicativity in BH-algebras.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.561-570
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• 2005

In this paper, we introduce the notion of positive implicative subtraction algebras and study some relations between R(L)-maps and positive implicativity in subtraction algebras.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1171-1187
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• 2011

Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly regular pair. In this paper, we provide the same improvement for a jointly regular family: let h : ${\mathbb{P}}_{\mathbb{Q}}^n{\rightarrow}{{\mathbb{R}}$ be the logarithmic absolute height on the projective space, let r(f) be the D-ratio of a rational map f which is de ned in [10] and let {$f_1,{\ldots},f_k|f_l:\mathbb{A}^n{\rightarrow}\mathbb{A}^n$} bbe finite set of polynomial maps which is defined over a number field K. If the intersection of the indeterminacy loci of $f_1,{\ldots},f_k$ is empty, then there is a constant C such that $ \sum\limits_{l=1}^k\frac{1}{def\;f_\iota}h(f_\iota(P))>(1+\frac{1}{r})f(P)-C$ for all $P{\in}\mathbb{A}^n$ where r= $max_{\iota=1},{\ldots},k(r(f_l))$.

• The Pure and Applied Mathematics
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• v.10 no.3
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• pp.145-161
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• 2003

Weak commutativity of a pair of maps was introduced by Sessa [On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) (N.S.) 32(40) (1982),149-153] in fixed point considerations. Thereafter a number of generalizations of this notion has been obtained. The purpose of this paper is to present a brief development of weaker forms of commuting maps, and to obtain two fixed point theorems for noncommuting and noncontinuous maps on noncomplete metric spaces.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.101-113
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• 2005

We define and study a concept of $T_A$-space which is closely related to the generalized Gottlieb group. We know that X is a $T_A$-space if and only if there is a map $r:L(A,\;X){\rightarrow}L_0(A,\;X)$ called a $T_A$-structure such that $ri{\sim}1_{L_0(A,\;X)}$. The concepts of $T_{{\Sigma}B}$-spaces are preserved by retraction and product. We also introduce and study a dual concept of $T_A$-space.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.1-7
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• 2001

In this paper, we show that for a homotopically periodic (i.e., $fk{\simeq}id$, for some $k{\geq}1$) self map f of a Seifert 3-manifold with $P{\widetilde{SL(2,}}\mathbb{R})$-geometry, N(f) = L(f) = 0.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.31-49
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• 2002

An R$^{n}$ -geometry (P$^{n}$ , L) is a generalization of the Euclidean geometry on R$^{n}$ (see Def. 1.1). We can consider some topologies (see Def. 2.2) on the line set L such that the join operation V : P$^{n}$ $\times$ P$^{n}$ \ $\Delta$ longrightarrow L is continuous. It is a notable fact that in the case n = 2 the introduced topologies on L are same and the join operation V : P$^2$ $\times$ P$^2$ \ $\Delta$ longrightarrow L is continuous and open [10, 11]. It is a fundamental topological property of plane geometry, but in the cases n $\geq$ 3, it is no longer true. There are counter examples [2]. Hence, it is a fundamental problem to find suitable topologies on the line set L in an R$^{n}$ -geometry (P$^{n}$ , L) such that these topologies are compatible with the incidence structure of (P$^{n}$ , L). Therefore, we need to study the topologies of the line set L in an R$^{n}$ -geometry (P$^{n}$ , L). In this paper, the relations of such topologies on the line set L are studied.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.507-517
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• 2004

Let (2,2,2,2) be ramification indices for the Riemann sphere. It is well known that the regular branched covering map corresponding to this, is the Weierstrass P function. Lattes [7] gives a rational function R(z)= ${\frac{z^4+{\frac{1}{2}}g2^{z}^2+{\frac{1}{16}}g{\frac{2}{2}}$ which is chaotic on ${\bar{C}}$ and is induced by the Weierstrass P function and the linear map L(z) = 2z on complex plane C. It is also known that there exist regular branched covering maps from $T^2$ onto ${\bar{C}}$ if and only if the ramification indices are (2,2,2,2), (2,4,4), (2,3,6) and (3,3,3), by the Riemann-Hurwitz formula. In this paper we will construct regular branched covering maps corresponding to the ramification indices (2,4,4), (2,3,6) and (3,3,3), as well as chaotic maps induced by these regular branched covering maps.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.45-52
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• 2006

Every non-associative algebra L corresponds to its symmetric semi-Lie algebra $L_{[,]}$ with respect to its commutator. It is an interesting problem whether the equality $Aut{non}(L)=Aut_{semi-Lie}(L)$ holds or not [2], [13]. We find the non-associative algebra automorphism groups $Aut_{non}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ and $Aut_{non-Lie}\; \frac\;{(WN_{0,0,1}_{[0,1,r_1...,r_p])}$ where every automorphism of the automorphism groups is the composition of elementary maps [3], [4], [7], [8], [9], [10], [11]. The results of the paper show that the F-algebra automorphism groups of a polynomial ring and its Laurent extension make easy to find the automorphism groups of the algebras in the paper.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.14 no.9
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• pp.756-765
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• 2002

Experimental work was performed on the flow characteristics of R-22 and R-l34a in small diameter tubes. The experimental apparatus was made up of liquid pump, pre-heater, sight-glass, condenser and measurement instruments. The sight-glass for flow pattern observations was located at the outlet of the pre-heater. The experiment was carried out to show the flow characteristics of R-22 and R-l34a. Data were taken with test conditions in the following ranges; the mass flux was ranged from 100 to 1,000 kg/$m^2s$, the saturation temperature was $30^{\circ}C$ and the vapor quality was ranged from 0.1 to 0.9. The main results were summarized as follows; In the flow patterns during evaporation, the annular flow in a 2 mm inner diameter tube occurred at a relatively lower quality and mass velocity, compared to the flow in a 8mm inner diameter tube. The evaporation flow in small diameter tubes has been shown major deviations with the Mandhane, Taitel-Dukler's and Wambs-ganss' flow pattern maps but it was similar to the Dobson's flow pattern map.