• Korean Journal of Mathematics
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• v.27 no.3
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• pp.707-722
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• 2019

For any non-negative real number ${\epsilon}_0$, we shall introduce a concept of the ${\epsilon}_0$-Cauchy sequence in a normed linear space V and also introduce a concept of the ${\epsilon}_0$-completeness in those spaces. Finally we introduce a concept of the generalized Banach spaces with these concepts.

• Journal of the Korean Institute of Landscape Architecture
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• v.34 no.1 s.114
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• pp.69-80
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• 2006

The purposes of this study are to analyze the meanings of urban spaces which are the background of the Korean films, and to capture the interactions of ordinary culture and urban spaces. By reading urban spaces through films, it is possible to understand the variety of experiences that are hardly captured with direct eyes, specific and vivid urban images, and various events formed by the interactions of spaces and people. The scope of the study is the urban spaces revealed in Korean films portraying cities after the 1960's as their settings, and the total of 18 films was selected with every $4{\sim}5$ films for each time stage. With the selected films, analytical meanings were developed with considering three aspects; 1) phylogenetic meaning that simply reflects social-cultural and historical background, 2) the outer strum meaning that concerns the situation of special background and film scene, and 3) metaphorical and metanymic meaning on films. According to the appearance frequency, spatial backgrounds of film scenes are mainly alleys, main streets, railroad, loft, and riverside. And then the connection between spaces and meaning clusters was grasped, and reflected meanings were derived for every spaces. And the meaning of urban space in films was analyzed based on the meaning of developments and outer stratum. The fundamental characteristics and feelings of people in media such as films are more emphasized than in real world. Urban space is not considered as a simple visible shell, but is recognized as 'a real situation' created by people. The intension of this study was to open the possibility of the various views of urban spaces. The construction of the urban space should be approached from a perspective of creating new places at where the space and human beings interact with considerations of stories of various human lives. I hope new vistas can be opened up for the research subjects and methodologies about the hereafter study of urban spaces through the mutual communications with various adjacent regions including films.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.309-318
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• 2006

Let X and Y be real Banach spaces and ${\varepsilon}\;>\;0$, p > 1. Let f : $X\;{\to}\;Y$ be a bijective mapping with f(0) = 0 satisfying $$|\;{\parallel}f(x)-f(y){\parallel}-{\parallel}{x}-y{\parallel}\;|\;{\leq}{\varepsilon}{\parallel}{x}-y{\parallel}^p$$ for all $x\;{\in}\;X$ and, let $f^{-1}\;:\;Y\;{\to}\;X$ be uniformly continuous. Then there exist a constant ${\delta}\;>\;0$ and N(${\varepsilon},p$) such that lim N(${\varepsilon},p$)=0 and a unique surjective isometry I : X ${\to}$ Y satisfying ${\parallel}f(x)-I(x){\parallel}{\leq}N({\varepsilon,p}){\parallel}x{\parallel}^p$ for all $x\;{\in}\;X\;with\;{\parallel}x{\parallel}{\leq}{\delta}$.

• Proceedings of the Korean Institute of Interior Design Conference
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• 2004.11a
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• pp.40-45
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• 2004

From 20th century, the perception of the problem on self-loss originated from philosophy and emerged in the pursuit of study on humans in real life, not from metaphysical questions. In particular, Phenomenon theory originating from Husserl has been unfolding around, above all, body concepts about human experiences. This is the part where Phenomenon theory finds its meaning as an analytical method of real space concepts. In addition, subjects' perception of situation is done through sense organs not only with sight but also with space-sensible aspects. And since these perceptions are done in consecutive and procedural times, they are done in the experience which shows transitional attributes. The experience elements of transitional senses in situation should be considered more about perception experience of human beings than other spaces, and classify into physical and program elements the introductory parts of eating and drinking spaces where the movements of active perceptionists and the flow of spaces can be felt. And this grants experimental, not usual, characteristics

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.59-69
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• 2010

The main aim of this article is to introduce a new class of sequence spaces using the concept of n-norm and to investigate these spaces for some linear topological structures as well as examine these spaces with respect to derived (n-1)-norm. We use an Orlicz function, a bounded sequence of positive real numbers and some difference operators to construct these spaces so that they become more generalized and some other spaces can be derived under special cases. These investigations will enhance the acceptability of the notion of n-norm by giving a way to construct different sequence spaces with elements in n-normed spaces.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2021.05a
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• pp.541-543
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• 2021

Recently, the number of cars owned in Jeju Island and the use of tourist rental cars have been increasing rapidly. Therefore, parking problems are getting worse in residential and commercial areas. As a result, a system is required to secure parking spaces and utilize existing parking spaces. Therefore, this paper proposes a system for real-time sharing of free public and paid parking spaces by introducing services that provide information on nearby restaurants, tourist information, and real-time parking status. The system analyzes infrared sensors and CCTV images installed in the actual parking lot and provides convenience for service users by analyzing the space currently in use and the number of unused parking spaces in real time.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.623-633
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• 2009

The classical Mazur-Ulam theorem states that every surjective isometry between real normed spaces is affine. In this paper, we study 2-isometries in probabilistic 2-normed spaces.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.201-212
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• 1993

It is our purpose in this paper to first establish an inequality in real uniformly smooth Banach spaces with modulus of smoothness of power type q > 1 that generalizes a well known Hilbert space inequality. Using our inequality, we shall then extend the above result of Qihou [15] on the Ishikawa iteration process from Hilbert spaces to these much more general Banach spaces. Furthermore, we shall prove that the Mann iteration process converges strongly to the unique fixed point of a quasi-contractive map in this general setting. No compactness assumption on K is required in our theorems.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1265-1283
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• 2019

We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces $X^{\mathbb{R}}$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of $X^{\mathbb{R}}$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1003-1013
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• 1996

The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).