• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.35-56
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• 2015

In this paper, we classify all nonconstant smooth CR maps from a sphere $S_{n,1}{\subset}\mathbb{C}^n$ with n > 3 to the Shilov boundary $S_{p,q}{\subset}\mathbb{C}^{p{\times}q}$ of a bounded symmetric domain of Cartan type I under the condition that p - q < 3n - 4. We show that they are either linear maps up to automorphisms of $S_{n,1}$ and $S_{p,q}$ or D'Angelo maps. This is the first classification of CR maps into the Shilov boundary of bounded symmetric domains other than sphere that includes nonlinear maps.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.481-506
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• 2022

This paper is concerned with the study of various notions of shadowing of dynamical systems induced by a sequence of maps, so-called time varying maps, on a metric space. We define and study the shadowing, h-shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties of these dynamical systems. We show that h-shadowing, limit shadowing and s-limit shadowing properties are conjugacy invariant. Also, we investigate the relationships between these notions of shadowing for time varying maps and examine the role that expansivity plays in shadowing properties of such dynamical systems. Specially, we prove some results linking s-limit shadowing property to limit shadowing property, and h-shadowing property to s-limit shadowing and limit shadowing properties. Moreover, under the assumption of expansivity, we show that the shadowing property implies the h-shadowing, s-limit shadowing and limit shadowing properties. Finally, it is proved that the uniformly contracting and uniformly expanding time varying maps exhibit the shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties.

• Korean Journal of Radiology
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• v.21 no.8
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• pp.978-986
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• 2020

Objective: To compare native and post-contrast T1 mapping with late gadolinium enhancement (LGE) imaging for detecting and measuring the microvascular obstruction (MVO) area in reperfused acute myocardial infarction (MI). Materials and Methods: This study included 20 patients with acute MI who had undergone 1.5T cardiovascular magnetic resonance imaging (CMR) after reperfusion therapy. CMR included cine imaging, LGE, and T1 mapping (modified look-locker inversion recovery). MI size was calculated from LGE by full-width at half-maximum technique. MVO was defined as an area with low signal intensity (LGE) or as a region of visually distinguishable T1 values (T1 maps) within infarcted myocardium. Regional T1 values were measured in MVO, infarcted, and remote myocardium on T1 maps. MVO area was measured on and compared among LGE, native, and post-contrast T1 maps. Results: The mean MI size was 27.1 ± 9.7% of the left ventricular mass. Of the 20 identified MVOs, 18 (90%) were detected on native T1 maps, while 10 (50%) were recognized on post-contrast T1 maps. The mean native T1 values of MVO, infarcted, and remote myocardium were 1013.5 ± 58.5, 1240.9 ± 55.8 (p < 0.001), and 1062.2 ± 55.8 ms (p = 0.169), respectively, while the mean post-contrast T1 values were 466.7 ± 26.8, 399.1 ± 21.3, and 585.2 ± 21.3 ms, respectively (p < 0.001). The mean MVO areas on LGE, native, and post-contrast T1 maps were 134.1 ± 81.2, 133.7 ± 80.4, and 117.1 ± 53.3 mm², respectively. The median (interquartile range) MVO areas on LGE, native, and post-contrast T1 maps were 128.0 (58.1-215.4), 110.5 (67.7-227.9), and 143.0 (76.7-155.3) mm², respectively (p = 0.002). Concordance correlation coefficients for the MVO area between LGE and native T1 maps, LGE and post-contrast T1 maps, and native and post-contrast T1 maps were 0.770, 0.375, and 0.565, respectively. Conclusion: MVO areas were accurately delineated on native T1 maps and showed high concordance with the areas measured on LGE. However, post-contrast T1 maps had low detection rates and underestimated MVO areas. Collectively, native T1 mapping is a useful tool for detecting MVO within the infarcted myocardium.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.961-971
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• 2018

We determine the sets of homotopy minimal periods of all self-maps on the Klein bottle by using a single formula for homotopy minimal periods of maps on the infra-solvmanifolds of type (R). This provides an alternate but an easy proof for the main results of [12].

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.4
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• pp.514-519
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• 2005

We define extensional spaces. Moreover, we investigate the relations among T-upper-approximation spaces, T-quasi -equivalence relations and extensional spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.2
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• pp.113-120
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• 2012

In this paper we study various properties of the fuzzy linear maps over the fuzzy quotient spaces. In particular we obtain some exact sequences of the fuzzy linear maps over the fuzzy quotient spaces.

• Journal of the Korean Association of Geographic Information Studies
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• v.8 no.2
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• pp.95-102
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• 2005

Currently, the government has been established GIS DB related to river as a part of the river map digitization projects such as RIMGIS and flood map. This study was aimed to demonstrate the generation of thematic maps related to river space and their management system, the one of the major river thematic maps proposed from the precedent study "Establishment of River Thematic Map Project" in an effort to maximize the utilization of river related database, the major product of the project for digitization of river maps. This study includes amending database model for building river thematic maps. Also, metadata were amended and built for efficient management and distribution of the river related data based on the national standard metadata proposed from "Establishing Standard Metadata" sponsored by National Geography Institute in 2003 for more effective management of river thematic maps. In addition, this study analyzed the method for utilizing existing data from RIMGIS and WAMIS as well as digital topographic maps to produce 25 river thematic maps in accordance of defined building procedure. Management system of the river thematic maps for Kyungan watershed has been generated for effective managing river thematic maps based on the design and pilot generation of river thematic maps, and metadata management function has been added into the management system.

• Proceedings of the KSRS Conference
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• v.2
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• pp.551-554
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• 2006

House management is very important in water resource protection in order to provide sustainable drinking water for about four millions population in northern Taiwan. House management can be a simple job that can be done without any ingredient of remote sensing or geographic information systems. Remote sensing and GIS integration for house management can provide more efficient management prescription when land use enforcement, soil and water conservation, sewage management, garbage collection, and reforestation have to be managed simultaneously. The objective of this paper was to integrate remote sensing and GIS to manage houses in a water resource protection district. More than four thousand houses have been surveyed and created as a house data base. Site map of every single house and very detail information consisting of address, ownership, date of creation, building materials, acreages floor by floor, parcel information, and types of house condition. Some houses have their photos in different directions. One house has its own card consists these information and these attributes were created into a house data base. Site maps of all houses were created with the same coordinates system as parcel maps, topographic maps, sewage maps, and city planning maps. Visual Basic.NET, Visual C#.NET have been implemented to develop computer programs for house information inquiry and maps overlay among house maps and other GIS map layers. Remote sensing techniques have been implemented to generate the background information of a single house in the past 15 years. Digital orthophoto maps at a scale of 1:5000 overlay with house site maps are very useful in determination of a house was there or not for a given year. Satellite images if their resolutions good enough are also very useful in this type of daily government operations. The developed house management systems can work with commercial GIS software such as ArcView and ArcPad. Remote sensing provided image information of a single house whether it was there or not in a given year. GIS provided overlay and inquiry functions to automatically extract attributes of a given house by ownership, address, and so on when certain house management prescriptions have to be made by government agency. File format is the key component that makes remote sensing and GIS integration smoothly. The developed house management systems are user friendly and can be modified to meet needs encountered in a single task of a government technician.

• East Asian mathematical journal
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• v.24 no.4
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• pp.359-368
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• 2008

The object of this paper is to establish a unique common fixed point theorem through weak compatibility for a sequence of self-maps satisfying a generalized contractive condition in a generalized Menger space. It improves and generalizes the result of Milovanovic-Arandelovic [2], Vasuki [10] and Sehgal and Bharucha-Reid [8]. All the results presented in this paper are new.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.51-64
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• 2005

The object of this paper is to prove two unique common fixed point theorems for a pair of a set-valued map and a self map satisfying a general contractive condition using orbital concept and weak-compatibility of the pair. One of these results generalizes substantially, the result of Dhage, Jennifer and Kang [4]. Simultaneously, its implications for two maps and one map improves and generalizes the results of Dhage [3], and Rhoades [11]. All the results of this paper are new.