• Bulletin of the Korean Mathematical Society
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• v.21 no.1
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• pp.27-30
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• 1984

The concepts of the numerical range of an operator on a Hillbert space and on a Banach space were introduced by Toeplitz in 1918 and Bauer in 1962 respectively. Bauer's paper was concerned only with finite dimensional Banach spaces, but the concept of numerical range that he introduced is available without restriction of the dimension [1, 2]. In this paper, we define a C-algebra spatial numerical range of an operator on C-algebra valued inner product modules introduced by Paschke [4], and give analogous results on these modules as those on Banach spaces.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.399-406
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• 2019

Let n be the spatial dimension. For d, $0<d{\leq}n$, let $H^d$ be the d-dimensional Hausdorff content. The purpose of this paper is to prove the boundedness of the dyadic strong maximal operator on the Choquet space $L^p(H^d,{\mathbb{R}}^n)$ for min(1, d) < p. We also show that our result is sharp.

• Journal of Korean Society for Geospatial Information Science
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• v.4 no.1 s.6
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• pp.67-73
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• 1996

The objective of this research is to investigate the behavior of the $F\"{o}rstner$ interest operator, which has been widely used for detecting distinct points in the field of digital photogrammetry and computer vision, in scale space. Considering the hugh volume of digital image utilized in digital photogrammetry, the scale space (image pyramid) approach which appears to be a solution for enhancing image processing, began to gain its attention. The investigation of the $F\"{o}rstner$ interest operator in scale space generated by the Gaussian kernel shows its behavior and feasibility for being used in practice.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.1
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• pp.139-144
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• 2017

As technologies related to sensor network are currently emerging and the use of GeoSensor is increasing along with the development of IoT technology, spatial query processing systems to efficiently process spatial sensor data are being actively studied. However, existing spatial query processing systems do not support a spatial-temporal data type and a spatial-temporal operator for processing spatial-temporal sensor data. Therefore, they are inadequate for processing spatial-temporal sensor data like GeoSensor. Accordingly, this paper developed a spatial-temporal query processing system, for efficient spatial-temporal query processing of spatial-temporal sensor data in a sensor network. Lastly, this paper verified the utility of System through a scenario, and proved that this system's performance is better than existing systems through performance assessment of performance time and memory usage.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.31-37
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• 2002

In this paper, we find explicitly the eigenvalues and the eigenfunctions of Laplace operator on a triangle domain with a mixed boundary condition. We also show that a weaker form of the principle of spatial averaging holds for this domain under suitable boundary condition.

• The Journal of the Acoustical Society of Korea
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• v.31 no.4
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• pp.214-224
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• 2012

The objective of this paper is to design multichannel spherical loudspeaker array by considering various positioning methods such as Gaussian grid, Lebedev grid and packing method. For the spatial sound manipulation, which is to make desired sound field by controling multiple sound sources, the Kirchhoff- Helmholtz integral states that sound fields can be reproduced in terms of infinite control sources on the integral surface. But since we cannot control infinite number of sources for the implementation, we have to allocate finite number of sound sources which can approximately act as infinite number of sources. To manipulate sound field inside of a sphere (which is typical example of three dimensional array) by controlling sound sources on the surface, three methods of allocating sound sources, which are Gaussian grid, Lebedev grid and packing method, are reviewed. For each geometry, the performances of manipulation rendered by time-reversal operator and higher-order ambisonics are compared.

• ETRI Journal
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• v.24 no.3
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• pp.226-238
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• 2002

A spatial object changes its states over time. However, existing spatial and temporal database systems cannot fully manage time-varying data with both spatial and non-spatial attributes. To overcome this limitation, we present a framework for spatio-temporal databases that can manage all time-varying historical information and integrate spatial and temporal relationship operators into the select statement in SQL3. For the purpose of our framework, we define three referencing macros and a history aggregate operator and classify the existing spatial and temporal relationship operators into three groups: exclusively spatial relationship operators, exclusively temporal relationship operators, and spatio-temporal common relationship operators. Finally, we believe the integration of spatial and temporal relationship operators into SQL3 will provide a useful framework for the history management of time-varying spatial objects in a uniform manner.

• Journal of KIISE:Computing Practices and Letters
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• v.5 no.5
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• pp.543-552
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• 1999

The iterator technique which is used for implementing physical operators of the query executor is known for its efficiency and extensibility. The most widely used technique for processing an operator on spatial objects is to process by dividing it into the filter step and the refinement step. Recently, there was a research for an optimizer which can generate more efficient query execution plans than those of traditional methods by separating a spatial operator into filter and refinement steps in the level of the object algebra. But, traditional query executors were not designed considering such query execution plans. So they have no function of transmitting the result of the filter operation between operators. We propose two methods, the probe technique and the tag technique, which transmit the result of the filter operator when using the iterator in the query execution plan in which operators are separated by filter/refinement steps and other operators can be allowed between the steps. Whereas the probe technique extends the state record within an operator, the tag technique stores the result of a filter step in an intermediate result in the form of the tag. Based on the comparison of these methods, we design and implement a query executor using the tag technique that is superior in extensibility. The implemented query executor can execute operations defined in the Spatial Object Algebra(SOA) to process an extended OQL for spatial queries.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.119-126
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• 1989

Throughout this paper, X will always denote a Banach space over the complex numbers C, and L(X) will denote the Banach algebra of all continuous linear operators on X. Operator will always mean continuous linear operator. An n-tuple of operators T$_{1}$,..,T$_{n}$ on X will be denoted by over ^ T=(T$_{1}$,..,T$_{n}$ ). Let L$^{n}$ (X) be the set of all n-tuples of operators on X. X' will denote the dual space of X, S(X) its unit sphere and .PI.(X) the subset of X*X' defined by .PI.(X)={(x,f).mem.X*X': ∥x∥=∥f∥=f(x)=1}.

• Journal of Korean Society for Geospatial Information Science
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• v.14 no.3 s.37
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• pp.13-22
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• 2006

Realistic 3D building construction in urban area has become an important issue because of increasing demand of 3D geo-spatial information in many application. Contrary to the conventional 3D building model construction approach using aerial images and high-resolution satellite imagery, it has been researched widely in building reconstruction using high-accuracy aerial LIDAR data in the latest. This paper presents a method for 3D building construction through building outlines extraction by LoG operator's Zero-crossing and line generation and refinement by Douglas-Peucker algorithm.