• Journal of the Korean Mathematical Society
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• v.29 no.2
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• pp.391-400
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• 1992

• Kyungpook Mathematical Journal
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• v.29 no.2
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• pp.203-236
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• 1989

• Kyungpook Mathematical Journal
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• v.20 no.1
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• pp.11-30
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• 1980

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.409-420
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• 1998

In this paper as a univesal Banach space of the separable Banach spaces we investigate the complemented Banach subspaces of $_wL_{\hat {I}}$. Also, using Peck's theorem and the properties of the envelope norm of $_wL_{\hat {I}}$ we will find a canonical basis of $l_1^n, l_\infty^n$ for each n.

• Korean Institute of Interior Design Journal
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• no.41
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• pp.104-111
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• 2003

Most residential buildings in Korea are preferred to have maximum interior spaces, rather than consider its original design, overall building performance, and any other aspects since early 1990's. Especially in high-rise apartment buildings, balcony has been merged to living room to get more interior spaces and this renovation trends have been producing deep and narrow shapes of living rooms that was not initially intended by architects. On the other hand, the same gross area of each unit does not necessarily mean same width and depth ratio of each residential unit. Generally, we can categorize it to the deep or wide unit based on its width and depth ratio. Under these circumstances, this study analyzes the room usage pattern changes based on the space width and depth ratio and the effect of expansion of room space to the balcony. This study also includes about 180 apartments plan case studies to find out the relationships among w/d ratio changes, furniture arrangement types, and room configurations. In this research, general apartment room w/d ratios are 0.97 ∼ 1.23; 0.7(south facing sitting room), 1.23(south facing bed room), and 0.95(north facing bedroom). But, after expanding room space to balcony w/d ratio increased as follows; sitting room become 1.31, general south facing bedroom become 1.23, and north facing bedroom become 1.45. In addition to user preference of w/d ratio, many people prefer rectangular room shape a little(w/d ratio is 0.9 or 1.2) than square style (w/d ratio is 1.0) or very deep room style (w/d ratio Is more over 1.5). Accordingly, expanding the room space to balcony may make unsatisfactory room w/d ratio. Expanding room space to balcony should be considered by existing room w/d ratio.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.855-866
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• 1995

We prove that if a nals X is reflexive, then $X = W_X + V_X$. We prove also that if an als X has a finite basis, then $X = W_X + V_X$ if and only if X is reflexive.

• Journal of the Korean Institute of Intelligent Systems
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• v.6 no.3
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• pp.94-98
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• 1996

The main goal of this paper is to investigate some properties in close connection with the quotient fuzzy norm $ induced by a fuzzy semi-norm $ on a linear space X and the quotient map $q:X{\rightarrow]X/W, $ where W is a subspace of X.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.9-17
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• 2002

In this Paper, we will show that every basically disconnected space is a projective object in the category $Tych_{\sigma}$ of Tychonoff spaces and $_{\sigma}Z^{#}$ -irreducible maps and that if X is a space such that ${\Beta} {\Lambda} X={\Lambda} {\Beta} X$, then X has a projective cover in $Tych_{\sigma}$. Moreover, observing that for any weakly Linde1of space, ${\Lambda} X : {\Lambda} X\;{\longrightarrow}\;X$ is $_{\sigma}Z^{#}$-irreducible, we will show that the projective objects in $wLind_{\sigma}$/ of weakly Lindelof spaces and $_{\sigma}Z^{#}$-irreducible maps are precisely the basically disconnected spaces.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.95-105
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• 2004

In this paper we will consider the weighted composition operators W = $uC_{\tau}$ between $L^{p}$$(X,\sum,\mu$) spaces and Orlicz spaces $L^{\phi}$$(X,\sum,\mu$) generated by measurable and non-singular transformations $\tau$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\tau$ that induce weighted composition operators between $L^{p}$ -spaces by using some properties of conditional expectation operator, pair (u,${\gamma}$) and the measure space $(X,\sum,\mu$). Also, some other properties of these types of operators will be investigated.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.455-466
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• 2008

In, [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\left\|{\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i{\left\|^2+{\sum\limits_{i=1}^{n}}\right\|}{x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}x_j}}\right\|^2}={\sum\limits_{i=1}^{n}}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\cdots},x_{n}{\in}V$. Let V,W be real vector spaces. It is shown that if a mapping $f:V{\rightarrow}W$ satisfies $$(0.1){\hspace{10}}nf{\left({\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i \right)}+{\sum\limits_{i=1}^{n}}f{\left({x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}}x_i}\right)}\\{\hspace{140}}={\sum\limits_{i=1}^{n}}f(x_i)$$ for all $x_1$, ${\dots}$, $x_{n}{\in}V$ $$(0.2){\hspace{10}}2f\(\frac{x+y}{2}\)+f\(\frac{x-y}{2} \)+f\(\frac{y}{2}-x\)\\{\hspace{185}}=f(x)+f(y)$$ for all $x,y{\in}V$. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.2) in real Banach spaces.