• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.831-836
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• 1994

In this paper we characterize the quasiaffine transforms of quasisubscalar operators. Let H and K be separable, complex Hilbert spaces and L(H,K) denote the space of all linear, bounded operators from H to K. If H = K, we write L(H) in place of L(H,K). A linear bounded operators S on H is called scalar of order m if there is a continuous unital morphism of topological algebras $$ \Phi : C^m_0(C) \to L(H) $$ such that $\Phi(z) = S$, where as usual z stands for identity function on C, and $C^m_0(C)$ stands for the space of compactly supproted functions on C, continuously differentiable of order m, $0 \leq m \leq \infty$.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.967-979
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• 2019

Chaotic dynamical systems, preferably on a Cantor-like space with some arithmetic operations are considered as good pseudo-random number generators. There are many definitions of chaos, of which Devaney-chaos and pos itive topological entropy seem to be the strongest. Let $A=\{0,1,{\dots},p-1\}$. We define a continuous map on $A^{\mathbb{Z}}$ using addition with a carry, in combination with the shift map. We show that this map gives rise to a dynamical system with positive entropy, which is also Devaney-chaotic: i.e., it is transitive, sensitive and has a dense set of periodic points.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.25-40
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• 2021

In this article we introduce tribonacci sequence spaces c0(T) and c(T) derived by the domain of a newly defined regular tribonacci matrix T. We give some topological properties, inclusion relations, obtain the Schauder basis and determine ��-, ��- and ��- duals of the spaces c0(T) and c(T). We characterize certain matrix classes (c0(T), Y) and (c(T), Y), where Y is any of the spaces c0, c or ℓ∞. Finally, using Hausdorff measure of non-compactness we characterize certain class of compact operators on the space c0(T).

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.105-127
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• 2022

It is known that the maximal invariant set of a continuous iterative dynamical system in a compact Hausdorff space is equal to the intersection of its forward image sets, which we will call the first minimal image set. In this article, we investigate the corresponding relation for a class of discontinuous self maps that are on the verge of continuity, or topologically almost continuous endomorphisms. We prove that the iterative dynamics of a topologically almost continuous endomorphisms yields a chain of minimal image sets that attains a unique transfinite length, which we call the maximal invariance order, as it stabilizes itself at the maximal invariant set. We prove the converse, too. Given ordinal number ξ, there exists a topologically almost continuous endomorphism f on a compact Hausdorff space X with the maximal invariance order ξ. We also discuss some further results regarding the maximal invariance order as more layers of topological restrictions are added.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.17-22
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• 1985

B.M. Munshi and D.S. Bassan defined and developed the concept of super continuity in [5]. The concept has been investigated further by I. L. Reilly and M. K. Vamanamurthy in [6] where super continuity is characterized in terms of the semi-regularization topology. Super continuity is related to the concepts of .delta.-continuity and strong .theta.-continuity developed by T. Noiri in [7]. The purpose of this note is to derive relationships between super continuity and other strong continuity conditions and to develop additional properties of super continuous functions. Super continuity implies continuity, but the converse implication is false [5]. Super continuity is strictly between strong .theta.-continuity and .delta.-continuity and strictly between complete continuity and .delta.-continuity. The symbols X and Y will denote topological spaces with no separation axioms assumed unless explicity stated. The closure and interior of a subset U of a space X will be denoted by Cl(U) and Int(U) respectively and U is said to be regular open (resp. regular closed) if U=Int[Cl(U) (resp. U=Cl(Int(U)]. If necessary, a subscript will be added to denote the space in which the closure or interior is taken.

• Journal of KIISE:Software and Applications
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• v.37 no.3
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• pp.194-204
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• 2010

A space, real or virtual, comprises regions as its parts and physical objects residing in them. A coherent and sophisticated representaion scheme for their spatial relations premises the precision and plausibility in its associated agents' inferencing on the spatial relations and the development of events occurring in such a space. The existing spatial models are not suitable for a comprehensive representation of the general spatial relations in that they have limited expressive powers based on the dichotomy between the large and small scales, or support only a small set of topological relations. The representaion model we propose has the following distinctive chracteristics: firstly, our model provides a comprehensive representation scheme to accommodate large and small scale spaces in an integrated fashion; secondly, our model greatly elaborated the spatial relations among the small-scale objects based on their contact relations and the compositional relations among their respective components objects beyond the basic topological relations like disjoint and touch; thirdly, our model further diversifies the types of supported relations by adding the container property besides the soildness together with considering the gravity direction. The resulting integrated spatial knowledge representation scheme considering the gravity allows the diverse spatial relations in the real world to be simulated in a precise manner in relation to the associated spatial events and provides an expression measure for the agents in such a cyber-world to capture the spatial knowledge to be used for recognizing the situations in the spatial aspects.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.34 no.3
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• pp.329-338
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• 2016

As the need of indoor spatial information has grown, many applications have been developed. Nevertheless, the major representations of indoor spatial information are on the 2D or 3D, recently, the service based on omni-directional image has increased. Current service based on omni-directional image is used just for viewer. To provide various applications which can serve the identifying the attribute of indoor space, query based services and so on, topological data which can define the spatial relationships between spaces is required. For developing diverse applications based on omni-directional image, this study proposes the method to generate IndoorGML data which is the international standard of indoor topological data model. The proposed method is consist of 3 step to generate IndoorGML data; 1) Analysis the core elements to adopt IndoorGML concept to image, 2) Propose the method to identify the element of ‘Space’ which is the core element of IndoorGML concept, 3) Define the connectivity of indoor spaces. The proposed method is implemented at the 6-floor of 21centurybuilding of the University of Seoul to generate IndoorGML data and the demo service is implemented based on the generated data. This study has the significance to propose a method to generate the indoor topological data for the indoor spatial information services based on the IndoorGML.

• Spatial Information Research
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• v.19 no.5
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• pp.75-86
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• 2011

Three-dimensional modeling of cities in the real-world is an essential task for city planning and decision-making. And many three-dimensional city models are being developed with the development of wireless Internet and location-based services that identify the location of users and provide the information increases for consumers. Especially, in case of urban areas of Korea, indoor space modeling as well as outdoor is needed due to the high-rise buildings densities. Also location-based services should be provided through spatial analysis such as the shortest path based on a space model. Many studies of three-dimensional city models are feature models. In a feature model, space is represented by combining primitives, and relationships among spaces are represented only if shared primitives are detected. So relationships between complex three-dimensional objects in space is difficult to be defined through the feature models. In this study, Navigable space-relation model(NSRM) is developed, which is topological data model for efficient representation of spatial relationships between objects based on the network structure.

• Korean Institute of Interior Design Journal
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• v.15 no.6 s.59
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• pp.205-212
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• 2006

The premise of this study is that an ultimate objective in planning an exhibition space is spectators' experiences shaped by a result of their first-hand experiences and responses within an exhibition space, and this result can be recognized in the spectators' movement. Thus, the sign system that can directly affects viewers' main line of flow and movement patterns was examined vis--vis a mutually complementary relation in a triangular composition with the structure of exhibition space and the exhibition contents. Based on the findings, predictive values before and after a complementary application of the sign system to the structure of exhibition space was analyzed and its validity was assessed. The results of this research analysis were drawn as follows. It was shown that an understanding of the locations of direction signs and the degree of recognition can function as an important factor to predict viewers' movement, along with an understanding of topological characteristics of an exhibition space. In terms of the connection and disconnection of space units that form the space structure, it suggests that the distribution of signs and the degree of recognition can adjust the degree of connection and disconnection. Even though exhibition spaces for research subjects were selected from a relatively large number of museums, but the research was limited with a focus on the structure of exhibition space and sign systems. Thus, it is proposed that future studies should be conducted by including varieties of exhibition and environmental factors.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.38 no.5
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• pp.467-476
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• 2020

Indoor space has been one of the focal points for geospatial research as various factors such as increasing demands for application and demand for adaptive response in emergencies have arisen. IndoorGML (Indoor Geography Markup Language) has provided a standardized method of representing the topological aspect of micro-scale environments, with its extensive specifications and flexible applicability. However, as more real-world problems and needs demand attention, suggestions to improve this standard, such as representing IndoorPOI (Indoor Points of Interest), have arisen. Hence, existing algorithms and functionalities that we use on perceiving these indoor spaces must also adapt to accommodate said improvements. In this study, we explore how to define spatial neighborhoods in indoor spaces represented by an integrated IndoorGML and IndoorPOI data. We revisit existing approaches to combine the aforementioned datasets and refine previous approaches to perform neighborhood spatial queries in 3D. We implement the proposed algorithm in three use cases using sample datasets representing a real-world structure to demonstrate its effectiveness for performing indoor spatial analysis.