• Human Ecology Research
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• v.52 no.2
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• pp.165-173
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• 2014

The study was conducted to analyze whether the recent trends in preference toward small and medium-sized housing in Korea represent changes in space norms. To accomplish this, the existing data from Statistics Korea and two different empirical data sets collected in 2007 and 2012 from Ulsan, Korea, were statistically analyzed through descriptive statistics, cross-tabulation analysis with a chi-squared test and multiple regression analysis. In the analyses, the space norms of households were compared and any changes in the space norms and the related factors were determined. The space norms were mainly investigated in terms of the housing size and the number of rooms. The results are as follows: 1) since 2010, there have been changes in the housing stock distribution in terms of size. Stocks of small housing increased, while those of medium and large housing decreased. Nevertheless, the overall conditions of spatial density have improved considerably in the recent 30 years. 2) It was found that there were statistically significant differences between 2007 and 2012 in space norms. The norms for housing sized less than 99 m2 and with one or two rooms were found to have increased, while that for housing sized more than 132 m2 decreased. 3) Household size, education of the head, monthly household income, housing type and the number of bedrooms in the current dwelling were the significant explanatory variables of space norms.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.175-178
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• 2005

In the present paper, we observe a relation between fuzzy norms and induced crisp norms on a linear space. We first prove that if $\rho_1,\;\rho_2$ are equivalent fuzzy norms on a linear space, then for every $\varepsilon\in(0.1)$, the induced crisp norms $P_\varepsilon^1,\;and\;P_\varepsilon^2$, respectively are equivalent. Since the converse does not hold, we prove it under some strict conditions. And consider the following theorem proved in [8]: Let $\rho$ be a lower semicontinuous fuzzy norm on a normed linear space X, and have the bounded support. Then $\rho$ is equivalent to the fuzzy norm $\chi_B$ where B is the closed unit ball of X. The lower semi-continuity of $\rho$ is an essential condition which guarantees the continuity of $P_\varepsilon$, where 0 < e < 1. As the last result, we prove that : if $\rho$ is a fuzzy norm on a finite dimensional vector space, then $\rho$ is equivalent to $\chi_B$ if and only if the support of $\rho$ is bounded.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.937-958
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• 1996

On the setting of product of balls we consider Toeplitz operators, with symbols satisfying a certain condition, on the Bergman space. Norms and essential norms of such operators are estimated by means of certain integral quantities.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.223-232
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• 2017

We classify the extreme and exposed symmetric bilinear forms of the unit ball of the space of symmetric bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms. We also show that every extreme symmetric bilinear forms of the unit ball of the space of symmetric bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms is exposed.

• Journal of the Korean housing association
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• v.17 no.4
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• pp.93-100
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• 2006

The purpose of the study was to analyze the appropriateness of space in multi-family housing by examining the current conditions of space, space norms and deficits, satisfaction with and needs for the spaces of individual rooms. The data came from the survey with 412 households living in Haeundae New Town, Busan and were analyzed with descriptive statistics. The appropriateness of space were mainly investigated in terms of housing size, number of bedrooms, and number of bathrooms. In terms of current space conditions, the highest portion of the households live in apartments with $20\sim30s$ pyong, 3 bedrooms, and 2 bathrooms. It was found that the space norms included housing with $30\sim40s$ pyong, 3 bedrooms, and 2 bathrooms. Households in current study tended to have some space deficits, especially in housing size and number or bathrooms. In general, the satisfaction with the current space of individual rooms were generally low except living room and master bedroom. It was also found that the households were more likely to make the second biggest bedroom bigger than now. The stages of family life cycle has significant effects on needs for the spaces of several rooms, such as dining room, room2, and room3.

• East Asian mathematical journal
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• v.28 no.1
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• pp.73-79
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• 2012

It is well-known that the BMO norm is equivalent to the Garsia norm. In this paper, we characterize mean-Lipschitz spaces by using Garsia-type norms on the upper half space $\mathbb{R}_+^{n+1}$.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1387-1401
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• 2019

Consider a finite measure space (${\Omega}$, ${\Sigma}$, ${\mu}$) and a Banach space $X({\mu})$ consisting of (equivalence classes of) real measurable functions defined on ${\Omega}$ such that $f{\chi}_A{\in}X({\mu})$ and ${\parallel}f{\chi}_A{\parallel}{\leq}{\parallel}f{\parallel}$, ${\forall}f{\in}({\mu})$, $A{\in}{\Sigma}$. We prove that if it satisfies the subsequence property, then it is an ideal of measurable functions and has an equivalent norm under which it is a Banach function space. As an application we characterize norms that are equivalent to a Banach function space norm.

• Journal of Aerospace System Engineering
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• v.8 no.2
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• pp.1-6
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• 2014

Currently outer space become more and more congested and contested, according to the increase of satellites, nations and government consortia that operate satellites, and commercial and academic satellite operators. Therefore, international community, including the United Nations has been making a greater effort to adopt non-legally binding international documents capable of regulating space activities for the purpose of the security, safety and long-term sustainability of space activities. These are a draft International Code of Conduct for Outer Space Activities(ICoC) and UN Group of Governmental Experts on Transparency and Confidence-Building Measures in Outer Space Activities(UNGGE).

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.417-428
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• 2017

We classify the extreme bilinear forms of the unit ball of the space of bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.855-861
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• 2007

Let A and B be commuting bounded linear operators on a Hilbert space. In this paper, we study spectral area estimates for norms of $A^*B-BA^*$ when A is subnormal or p-hyponormal.