• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.81-87
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• 1992

Wellknown invariance of domain theorems are Brower's invariance of domain theorem for continuous mappings defined on a finite dimensional space and Schauder-Leray's invariance of domain theorem for the class of mappings I+C defined on a infinite dimensional Banach space with I the identity and C compact. The two classical invariance of domain theorems were proved by applying the homotopy invariance of Brower's degree and Leray-Schauder's degree respectively. Degree theory for some class of mappings is a useful tool for mapping theorems. And mapping theorems (or surjectivity theorems of mappings) are closely related with invariance of domain theorems for mappings. In[4, 5], Browder and Petryshyn constructed a multi-valued degree theory for A-proper mappings. From this degree Petryshyn [9] obtained some invariance of domain theorems for locally A-proper mappings. Recently Browder [6] has developed a degree theory for demicontinuous mapings of type ( $S_{+}$) from a reflexive Banach space X to its dual $X^{*}$. By applying this degree we obtain some invariance of domain theorems for demicontinuous mappings of type ( $S_{+}$). ( $S_{+}$).

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.2
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• pp.16-30
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• 1990

The microwave imaging technique which is mostly analyzed in the spectral domain has been exploited the image reconstruction of object using the 2-dimensional inverse Fourier transform so far. In this paper, a new method of microwave imaging corresponding to a coherent tomographic scheme in the space domain is presented for the conducting objects. Also, it is shown that image reconstruction for lines targets and conducting circular cylinder is per-formed by computer simulation using the filtered-backprojection which is the reconstruction algorithm widely used in X-ray CT. The proposed method analyzed in the space domain can reconstruct the image without any problems such as interpolation and image artifact which results from the reconstruction in the spectral domain for the symmetric conducting objects located in the origin. The image reconstructed by the filtered-backprojection in the space domain has given the superior quality compared with that produced by 2-dimensional IFFT using the interpolation scheme in the spectral domain. Finally, the image of line targets using the moment-method in the space domain which does not require the wide-band signal as the spectral domain has shown a possibility of super-resolution in the microwave imaging.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.589-606
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• 2002

We introduce and analyze a frequency-domain method for parabolic partial differential equations. The method is naturally parallelizable. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we propose to solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time domain. Existence and uniqueness as well as error estimates are given. Fourier invertibility is also examined. Numerical experiments are presented.

• Proceedings of the Korean Institute of Interior Design Conference
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• 2001.05a
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• pp.64-68
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• 2001

As Dutch structuralism discovered a possibility that can improve the problem of modem architecture through study on non-western area. Dutch structuralism had tremendous impact on Philosophy, psychology, art history and the style of a dress and many other cultural trend. In architecture, Aldo van Eyck embodied that theory and succeeded to Herman Hertzberger and Piet Blom. As result Structuralism related with architecture has dealt with the participation and domain of residents, namely public domain and private domain, the approach property of public space, middle domain which shows the harmony between public domain and private one, and the structuralism discovered that each element of public space and private space has been developed as an architectural type that makes a group by repetitive arrangement and it found out a possibility that can make up problems overlooked in modem architecture through development and change.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.3
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• pp.342-349
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• 1999

The metric defined on the domain deformation space better measures the similarity between bounded and continuous signals for the purpose of classification via the metric distances between signals. In this paper, a modified domain deformation theory is introduced for one-dimensional signal classification. A new metric defined on a modified domain deformation for measuring the distance between signals is employed. By introducing a newly defined metric space via the newly defined Integra-Normalizer, the assumption that domain deformation is applicable only to continuous signals is removed such that any kind of integrable signal can be classified. The metric on the modified domain deformation has an advantage over the $L^2$ metric as well as the previously introduced domain deformation does.

• Journal of The Korea Institute of Healthcare Architecture
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• v.27 no.2
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• pp.25-37
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• 2021

Purpose: The main purpose of this study is to develop an evaluation system using the weighted-values of various users and experts for the public space to apply Universal Design, and additionally to find out the commonalities and differences by comparing the importance of evaluation indicators between users and expert groups. Method: A one-sample t-test was conducted to verify that the components of the public space to universal design application are suitable as evaluation indicators, and AHP(analytic hierarchy process) was performed to derive weight-values for the evaluation system. Results: The importance-values for the total 23 facilities to be used as evaluation indicators were derived by multiplying the weighted-values of each sector, domain, and facility by the disabled, non-disabled, and experts. To summarize the results of overall importance-values derived from the AHP, The disabled showed high-rank weighted-values in facilities of building sector > park & recreation sector > cross domain and low-rank weighted-values for sidewalk and roadway domain. The non-disabled showed high-rank weighted-values in facilities of park & recreation sector > roadway domain > building sector > cross domain and low-rank weighted-values for sidewalk domain. Experts mainly showed high-rank weighted-values in the cross domain and in facilities related to entry and movement to the target space in all sectors and domains. However, it showed moderate importance-values in the sanitary space. The disabled who are restricted to movement have a high demand for universal design in buildings consisting of vertical moving line, and non-disabled people who are not limited to physical movement have a high demand for universal design in parks and recreation sector for increased leisure time. It means that experts are important to recognize the principles of making space because they value cross domain and the key spaces and facilities for suitable the purpose of use. In addition, it can be inferred that non-disabled people have a higher demand for safety than disabled people due to their high importance in roadway domain and facilities of safety and disaster prevention. Implications: The significance of this study is the establishment of a quantitative universal design evaluation system for public spaces considering the different perspectives of the disabled and the non-disabled.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1143-1158
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• 2006

We consider the projectivization of Minkowski space with the analytic continuation of the hyperbolic metric and call this an extended hyperbolic space. We can measure the volume of a domain lying across the boundary of the hyperbolic space using an analytic continuation argument. In this paper we show this method can be further generalized to find the volume of a domain with smooth boundary with suitable regularity in dimension 2 and 3. We also discuss that this volume is invariant under the group of hyperbolic isometries and that this regularity condition is sharp.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.705-707
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• 2004

In this paper, we propose a robust control technique against parameter uncertainties as well as external disturbances. It is robust control scheme using discrete-time state space disturbance observer. It does not require disturbance modeling, plant inverse modeling and/or Q filter. In frequency domain, its performance is evaluated in terms of sensitivity and complementary sensitivity as well as gain and phase margin. Finally we discuss design criterion of state space disturbance observer considering its performance in frequency domain.

• Journal of electromagnetic engineering and science
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• v.18 no.1
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• pp.58-62
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• 2018

In this study, we propose a software-defined radio-based frequency interference emulator in the space-time domain. This emulator can easily model actual interference environments because of the versatile programming capability of the universal software radio peripheral and LabVIEW. As an example of an interfering network using the contention-based multiple access scheme in the time domain, we emulate a coordinated Wi-Fi network that consists of one access point and two Wi-Fi nodes. Results show that our emulator can successfully model multiple interfering signals in the Wi-Fi network and easily adjust various space-time domain parameters.