• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.751-762
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• 2020

We define the average of a set of continuous functions of two variables (surfaces) using the structure of the two-parameter Wiener space that constitutes a probability space. The average of a sample set in the two-parameter Wiener space is defined employing the two-parameter Wiener process, which provides the concept of distribution over the two-parameter Wiener space. The average defined in our work, called an average function, also turns out to be a continuous function which is very desirable. It is proved that the average function also lies within the range of the sample set. The average function can be applied to model 3D shapes, which are regarded as their boundaries (surfaces), and serve as the average shape of them.

• Proceedings of the KSRS Conference
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• 2005.10a
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• pp.482-484
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• 2005

The Modulation Transfer Function (MTF) is commonly used to characterize the spatial quality of imaging systems. This work is the attempt to measure the MTF at Nyquist frequency of the satellite imaging system what has 1m spatial resolution for KOMPSAT-2 image using the edge function. Artificial tarp targets are used in this study. A type of this tarp edge consists of two adjacent uniform bright and dark sides commonly used to test the performance of an optical system in edge function. The results from this work demonstrate the potential applicability of this method to estimate the response characteristics for KOMPSAT-2 that is scheduled to be launched.

• Journal of the Korean housing association
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• v.18 no.3
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• pp.41-49
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• 2007

The purpose of this study was to investigate the using behavior of the balcony space in apartment housing for improving apartment balcony as dwelling space. For that, it is needed to identify the practical meaning of balcony space as function so balcony expansion and the using behavior of balcony space were investigated and analyzed. For this study, survey and depth-interview methods were used for data collection. The major findings were as followings: 1) Balcony expansion mainly occurred in balcony of livingroom and bedroom. Balcony expansion showed several phases according to the type of plan and function of balcony space and few residents chose expansion of all balconies. 2) The using behavior of balcony space was categorized by these various functions of balconies. It was also related to unit-plan type of apartment housing. These results can provide improvement guidelines for the balcony with the differentiation of design factors for residents.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.375-415
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• 2019

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1299-1307
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• 2023

In this paper, we attempt to study several topological properties for the function space H(X), space of self-homeomorphisms on a metric space endowed with the regular topology. We investigate its metrizability and countability and prove their coincidence at X compact. Furthermore, we prove that the space H(X) endowed with the regular topology is a topological group when X is a metric, almost P-space. Moreover, we prove that the homeomorphism spaces of increasing and decreasing functions on ℝ under regular topology are open subspaces of H(ℝ) and are homeomorphic.

• International Journal of High-Rise Buildings
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• v.5 no.2
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• pp.95-103
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• 2016

One of the key problems in the design of high-rise commercial complex is how to guide reasonable pedestrian distribution in commercial space. In this study, pedestrian distribution in three high-rise commercial complexes in Shanghai and Hong Kong was studied using spatial configuration analysis software Space Syntax and quantification of physical elements in commercial spaces, such as functional attractiveness, entrances, escalators, level variations and passage width. Additionally, in an attempt to integrate functions with spatial integration and spatial depth, two combination variables, the spatial coefficient of function (IF) and spatial depth coefficient of function (F/D), were proposed. The results of the correlation analysis and multiple regression analyses reflected the following: (1) Regarding the influence on pedestrian distribution, there was a synergistic and complementary relationship between function and space; (2) The comprehensive flow distribution analytic model could successfully interpret flow distribution in high-rise commercial complexes and its R Square ranged up to about 70% in the three cases; (3) The spatial coefficient of function (IF) and spatial depth coefficient (F/D) could effectively integrate functions and spatial configuration, which could help close the gap between over-emphasis on function in commercial research and the lack of consideration of function in space-syntax analysis.

• Design Convergence Study
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• v.16 no.6
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• pp.59-74
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• 2017

Louis Sullivan insisted, "Form follows function." Functionality is one of the most fundamental elements for users to use product or space, and "function" in space and architecture has the meaning of the most important factor in determining its form. In this way, from the viewpoint of "Functionalism," the research selected Toyo Ito to see how important elements pursued by Functionalism are related to his forms of creation. Small residential space projects of Toyo Ito from the early 1970s to the present are selected, so that the structure, material and space type of space and architecture can easily grasped and analyzed. Space and architectural structures and surfaces were classified into the characteristics of materials and classified according to the strength of openness of space. As a result, the space and architecture that pursue the function use a method that can maximize the efficiency of the function while excluding the whole decoration in order to highlight the function. The characteristics found in Toyo Ito's small-scale residential space can be defined as the formalization and simplification of the form, the openness of space, and the versatility of each element.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.659-668
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• 2001

Let S(z) be a power series with operator coefficients such that multiplication by S(z) is an everywhere defined transformation in the square summable power series C(z). In this paper we show that there exists a reproducing kernel Krein space which is state space of extended canonical linear system with transfer function S(z). Also we characterize the reproducing kernel function of the state space of a linear system.

• The Pure and Applied Mathematics
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• v.27 no.1
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• pp.1-11
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• 2020

In this paper we determine conditions which a function a(t) must satisfy to insure that the function a'(t) is an element of the separable Hilbert space L²_a,b[0, T]. We then proceed to illustrate our results with several pertinent examples and counter-examples.

• Proceedings of the Korean Institute of Interior Design Conference
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• 1999.04a
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• pp.145-148
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• 1999

The contemporary society needs complex space for multiple function. Interior space plan should suggest the solution of the narrow site and process for multiple function through showing the examples of other functional spaces. The purpose of this study is choosing an express station which has wide site and cultural exchange function, while it is not used for specific function and then the waiting room of station adapted for cultural and multiple functional space.