• Korean Journal of Mathematics
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• v.10 no.1
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• pp.19-23
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• 2002

Let X be a Banach space satisfying Opial's condition, C a weakly compact convex subset of $X,F:C{\rightarrow}X$ a nonexpansive map, and let $G:C{\rightarrow}X$ be a compact and demiclosed map. We prove that F + G has a fixed point in C if $F+G:C{\rightarrow}X$ is a weakly inward map.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.1137-1159
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• 2024

In the paper, we prove that if a continuous map of a compact uniform space is equicontinuous and pointwise topologically stable, then it is persistent. We also show that if a sequence of uniformly expansive continuous maps of a compact uniform space has a uniform limit and the uniform shadowing property, then the limit is topologically stable. In addition, we introduce the concepts of shadowable points and topologically stable points for a continuous map of a compact topological space and obtain that every shadowable point of an expansive continuous map of a compact topological space is topologically stable.

• Progress in Medical Physics
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• v.31 no.4
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• pp.189-193
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• 2020

An MR-based attenuation correction (MRAC) map plays an important role in quantitative positron emission tomography (PET) image evaluation in PET/magnetic resonance imaging (MRI) systems. However, the MRAC map is affected by the magnetic field inhomogeneity of MRIs. This study aims to evaluate the characteristics of MRAC maps of physical phantoms on PET/MRI images. Phantom measurements were performed using the Siemens Biograph mMR. The modular type physical phantoms that provide assembly versatility for phantom construction were scanned in a four-channel Body Matrix coil. The MRAC map was generated using the two-point Dixon-based segmentation method for whole-body imaging. The modular phantoms were scanned in compact and non-compact assembly configurations. In addition, the phantoms were scanned repeatedly to generate MRAC maps. The acquired MRAC maps show differently assigned values for void areas. An incorrect assignment of a void area was shown on a locally compact space between phantoms. The assigned MRAC values were distorted using a wide field-of-view (FOV). The MRAC values also differed after repeated scans. However, the erroneous MRAC values appeared outside of phantom, except for a large FOV. The MRAC map of the phantom was affected by phantom configuration and the number of scans. A quantitative study using a phantom in a PET/MRI system should be performed after evaluation of the MRAC map characteristics.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.791-801
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• 2005

In this paper, we introduce the concepts of closure and interior defined by an intuitionistic gradation of openness. We also introduce the concepts of weakly gp-maps, gp-open maps and several types of compactness, and obtain some characterizations.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.197-204
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• 2008

We study diameter preserving linear maps from C(X) into C(Y) where X and Y are compact Hausdorff spaces. By using the extreme points of $C(X)^*\;and\;C(Y)^*$ and a linear condition on them, we obtain that there exists a diameter preserving linear map from C(X) into C(Y) if and only if X is homeomorphic to a subspace of Y. We also consider the case when X and Y are noncompact but locally compact spaces.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.183-189
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• 2013

Let W be a parallelizable compact oriented manifold of dimension $n$ with boundary ${\partial}W=M$. We define the so-called Gauss map $f:M{\rightarrow}S^{n-1}$ using a framing of TW and show that the degree of $f$ is equal to Euler-Poincar$\acute{e}$ number ${\chi}(W)$, regardless of the specific framing. As a special case, we get a Hopf theorem.

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.115-119
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• 1997

We show that if $f_{i}$:$X_{i}$ longrightarrow Y is strongly continuous(resp. weakly continuous, set connected, compact, feebly continuous, almost-continuous, strongly $\theta$-continuous, $\theta$-continuous, g-continuous, V-map), then F : $X_1 \bigoplus X_2$longrightarrow Y is strongly continuous(resp.weakly continuous, set connected, compact, feebly continuous, almost-continuous, strongly $\theta$-continuous, $\theta$-continuous, g-continuous, V-map).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.905-910
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• 2005

Increasing population in the cities, it has been demanded that urban planner should consider environmental problem. In this regard compact city has been strongly suggested as an environmental urban form which can reduce energy consumption. However, compact city can also cause noise problem, because residential buildings have to be located near roads and railways. In order to solve this problem, it is necessary for urban planner to examine the types of roads and railways before they are established. Noise map is able to be useful tool for the task.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.4
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• pp.1266-1285
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• 2022

Compact E-cash is the first scheme which can withdraw 2^l coins within 𝒪(1) operations and then store them in 𝒪(𝑙) bits. Because of its high efficiency, a lot of research has been carried out on its basis, but no previous research pay attention to the privacy of payees and in some cases, payees have the same privacy requirement as payers. We propose a double-blind compact E-cash scheme, which means that both the payer and the payee can keep anonymous while spending. In our scheme, the payer and the bank cannot determine whether the payees of two different transactions are the same one and connect the payee with transactions related to him, in this way, the privacy of the payee is protected. And our protocols disconnect the received coin from previous transaction, then, the coin can be transferred into an unspent coin which belongs to the payee. The proposed e-cash scheme is secure within y-DDHI and LRSW assumption.

• Journal of the Korea Society of Computer and Information
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• v.12 no.4
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• pp.11-19
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• 2007

This paper proposes RCB(Reduced Compact Binary) tie to correct faults of both CB(Compact Binary) tie and HCB(Hierarchical Compact Binary) trie. First, in the case of CB trie, a compact structure was tried for the first time, but as the amount of data was increasing, that of inputted data gained and much difficulty was experienced in insertion due to the dummy nods used in balancing trees. On the other hand, if the HCB trie realized hierarchically, given certain depth to prevent the map from increasing on the right, reached the depth, the method for making new trees and connecting to them was used. Eventually, fast progress could be made in the inputting and searching speed, but this had a disadvantage of the storage space becoming bigger because of the use of dummy nods like CB trie and of many tree links. In the case of RCB trie in this thesis, the tree-map could be reduced by about 35% by completely cutting down dummy nods and the whole size by half, compared with the HCB trie.