• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.697-711
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• 2017

Let X, Y be real normed vector spaces. We exhibit all the solutions $f:X{\rightarrow}Y$ of the functional equation f(rx + sy) + rsf(x - y) = rf(x) + sf(y) for all $x,y{\in}X$, where r, s are nonzero real numbers satisfying r + s = 1. In particular, if Y is a Banach space, we investigate the Hyers-Ulam stability problem of the equation. We also investigate the Hyers-Ulam stability problem on a restricted domain of the following form ${\Omega}{\cap}\{(x,y){\in}X^2:{\parallel}x{\parallel}+{\parallel}y{\parallel}{\geq}d\}$, where ${\Omega}$ is a rotation of $H{\times}H{\subset}X^2$ and $H^c$ is of the first category. As a consequence, we obtain a measure zero Hyers-Ulam stability of the above equation when $f:\mathbb{R}{\rightarrow}Y$.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.331-336
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• 1994

Let $P_{0}$ be a $\delta$-ring (a ring closed with respect to the forming of countable intersections) of subsets of a nonempty set $\Omega$. Let X and Y be Banach spaces and L(X, Y) the Banach space of all bounded linear operators from X to Y. A set function m : $P_{0}$ longrightarrow L(X, Y) is called an operator valued measure countably additive in the strong operator topology if for every x $\epsilon$ X the set function E longrightarrow m(E)x is a countably additive vector measure. From now on, m will denote an operator valued measure countably additive in the strong operator topology.(omitted)

• Journal of the Korean Institute of Landscape Architecture
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• v.24 no.3
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• pp.133-149
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• 1996

The aim of this study is to compare open space planning between Australia and Korea by Local Governments Areas. Open space planning is carried out at the state and municipal level in Australia, but by metropolitan city government in Korea. This study is structured by reviewing the presemt phenomena of provision of open space in Sydney and Seoul, By measuring disparity in terms of open spaces by L. G. A. s an by comparing planning approaches between two cities, for example policy, government standards, government administration system in open space management. In this paper, the provision of parks in Sydney and Seoul are comparatively examined and geographically mapped, and multiple repression analysis is applied to measure the residuals from the line of equality. The results of this study show that, 1) During the last 1 dacade from '80 and '90. Sydney has increased the quantity of open spaces from ratio of 19.11ha/1000 to 22.33ha/1000 of parks, however Seoul decreased it by the ratio of 12.21$m^2$/person to 1012$m^2$ per person. 2) Sydney has more programs, such as Greenspace program, Metropolitan open space program etc. to increase and to distribute open spaces equally rather than Seoul which has less open spaces. 3) There exists patterned inequality in terms of open space provision in inner city and suburb between Sydney and Seoul. 4) Seoul requires more active polices to increase open spaces like Greenacre Program of New Jerrsey State, Double Open Space Pland of Tokyo or Green Space Program of Sydney.

• Journal of Korean Society of Environmental Engineers
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• v.32 no.4
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• pp.311-322
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• 2010

The common life with modern urban residence, spending more than 80~90% of daily life in indoor environment, makes the importance of indoor air quality (IAQ) even higher. Many efforts have made to improve indoor air quality (IAQ), which requires those systematic approaches for field practice. A recent study reported that no general approach cannot be made for IAQ improvement due to the great deal of variety in different indoor environments. Those indoor spaces included in Korean IAQ regulation were classified based on their characteristics and the IAQ guideline was suggested for each group of indoor spaces. Apart from those indoor spaces, the classroom in elementary school has different characteristics. By introducing the systematic approaches, the elementary classroom was surveyed and analyzed to understand its characteristics in due IAQ consideration. Based on the characteristics, there are several IAQ control measures suggested, including ventilation operation, dust mat installation, and white board. $CO_2$ and airborne dust were monitored and analyzed in order to evaluate the effectiveness of each control measure to IAQ. It was found that the general level of $CO_2$ concentration was managed under the IAQ guideline by applying the ventilator operation. The ventilation was also effective to the fugitive airborne particulate in elementary classroom environment.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.285-295
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• 2013

In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.25-31
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• 1999

Let $\nu$ be a positive Borel measure on a space of homogeneous type (X, d, $\mu$), satisfying the doubling property. A condition on a weight $\omega$ for whixh a maximal operator $M\nu f$(x) defined by M$mu$f(x)=supr>0{{{{ { 1} over {ν(B(x,r)) } INT _{ B(x,r)} │f(y)│d mu (y)}}}}, is of weak type (p,p) with respect to (ν, $omega$), is that there exists a constant C such that C $omega$(y) for a.e. y$\in$B(x, r) if p=1, and {{{{( { 1} over { upsilon (B(x,r) } INT _{ B(x,r)}omega(y) ^ (-1/p-1) d mu (y))^(p-1)}}}} C, if 1$infty$.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.319-357
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• 2017

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such that uniformly bounded sequences of functions that converge pointwise in the weak (or norm) topology of E are sent to sequences that converge in the weak, norm or weak* topology of the target space. As an application, a new description of uniform closures of convex subsets of C(X, E) is given. Also new and strong results on integral representations of continuous linear operators defined on C(X, E) are presented. A new classes of vector measures are introduced and various bounded convergence theorems for them are proved.

• Proceedings of the Korea Multimedia Society Conference
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• 2012.05a
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• pp.284-286
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• 2012

There has been increasing attention about the prevention and counter-measure of disasters. Particularly, for the case of fire disaster, early detection reduces the damage caused by fire significantly and effective detection method is important. Since most existing detectors need to be located at a close distance to fire, analyzing camera images to find fire becomes active research topic. In this paper, we analyze the color characteristics of fire images in various color spaces and report the experimental detection results. The best result is 77.8% success rate in YIQ space.

• Journal of the Korean housing association
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• v.11 no.2
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• pp.63-73
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• 2000

The purpose of this study was to find a suitable standard height of the lavatory in public spaces through the review of relevant regulations, questionnaire survey, lab works, and experiment to measure lavatory heights. The results of the study were as follows: First, the heights of the current public lavatory were ranged from 68cm to 89cm, and the heights to the faucet were from 71cm to 91cm. The recent lavatory was more likely to be higher in heights. Secondly, the suitable height for public lavatory was ranged from 55% to 65% of the heights of the participants put on shoes. Thirdly, 90cm lavatory in height was considered to be more suitable to use for the majority than was 83cm lavatory. Fourth, the author suggest that the suitable y(lavatory height)=77.818 + 0.117x(put on shoes heights). This study suggested that adopting 95% range, the most suitable height of public lavatory is more than 90cm high for the people whose heights are more than 150cm.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.809-822
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• 2007

Certain weak type endpoint estimates are established for maximal commutators generated by $Calder\acute{o}n-Zygmund$ operators and $Osc_{exp}L^{\gamma}({\mu})$ functions for ${\gamma}{\ge}1$ under the condition that the underlying measure only satisfies some growth condition, where the kernels of $Calder\acute{o}n-Zygmund$ operators only satisfy the standard size condition and some $H\ddot{o}rmander$ type regularity condition, and $Osc_{exp}L^{\gamma}({\mu})$ are the spaces of Orlicz type satisfying that $Osc_{exp}L^{\gamma}({\mu})$ = RBMO(${\mu}$) if ${\gamma}$ = 1 and $Osc_{exp}L^{\gamma}({\mu}){\subset}RBMO({\mu})$ if ${\gamma}$ > 1.