• Communications of Mathematical Education
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• v.35 no.4
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• pp.413-423
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• 2021

This study investigated the empty set which is one of the mathematical objects. We inquired some misconceptions about empty set and the background of imposing empty set. Also we studied historical background of the introduction of empty set and the axiomatic system of Set theory. We investigated the nature of mathematical object through studying empty set, pure conceptual entity. In this study we study about the existence of empty set by investigating Alian Badiou's ontology known as based on the axiomatic set theory. we attempted to explain the relation between simultaneous equations and sets. Thus we pondered the meaning of the existence of empty set. Finally we commented about the thoughts of sets from a different standpoint and presented the meaning of axiomatic and philosophical aspect of mathematics.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.93-104
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• 2005

The present article discusses the number of empty convex 4-gons and empty convex 5-gons in a finite planar point set. New proofs are provided for the two related important results.

• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.337-352
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• 2022

We consider the set of points with historic behavior (which is also called the irregular set) for continuous flows and suspension flows. In this paper under the hypothesis that (X_t)_t is a continuous flow on a d-dimensional Riemaniann closed manifold M (d ≥ 2) with gluing orbit property, we prove that the set of points with historic behavior in a compact and invariant subset ∆ of M is either empty or is a Baire residual subset on ∆. We also prove that the set of points with historic behavior of a suspension flows over a homeomorphism satisfyng the gluing orbit property is either empty or Baire residual and carries full topological entropy.

• Journal of Mechanical Science and Technology
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• v.16 no.6
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• pp.776-784
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• 2002

We have performed experimental studies for the improvements of pneumatic brake systems of freight trains. Currently, most of the freight trains operated by the Korean National Railroad have either empty-load or diaphragm type brake systems. In this study, appropriate methods that the air pressure characteristics in both type of brake systems are in accordance with each other have been investigated. We have also performed running tests using a 30 car-train set to design optimum capacity of a quick release valve. The test results show that the quick release valve is considerably effective in shortening the release time of the diaphragm type brake system. In the case of a normal brake application, the diaphragm type brake system with the quick release valve reduces the release time to 34% of that of the system without the quick release valve. This release time is almost equivalent to that of the empty-load type brake system. Accordance of braking performance in different types of brake systems in a train set is expected to prevent wheel flats and to reduce maintenance costs.

• Journal of the Architectural Institute of Korea Planning & Design
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• v.34 no.6
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• pp.127-134
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• 2018

The purpose of this study is to derive a model of urban regeneration business using idle facilities in the old city center. The scope of the study was set as empty houses and empty stores owned by private companies, and analyzed the 50 central city revitalization projects using idle facilities in 14 local cities in Japan. The results of this study are follows; First, as an urban regeneration strategy using idle facilities in the old town, it was a combination of other functions centering on commercial functions or introducing new functions required in the city center. Second, various financial supports have been provided to induce the utilization of idle facilities by the private sector, and different strategies have been implemented for businesses that need maintenance first. Third, based on the analysis results, it was possible to derive urban regeneration business model. Fourth, in order to operate smooth business, it is a need for an organization that is in charge of reviewing the consistency of upper-level planning and urban guiding functions such as urban revitalization plan, balance review of expenditure and revenues by cost subsidy and loan repayment, consultation among the business partners.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.593-598
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• 2000

Experimental study is conducted to clarify the pneumatic characteristics of brake system for freight train. Empty-load and diaphragm brake systems are mainly installed in the freight trains owned by KNR(Korean National Railroad). Experimental train set is composed of sixteen freight train and one diesel locomotive that are now in use. From the experimental results, in case of commercial brake, empty-load brake system responds to the brake command more slowly than the diaphragm brake system. But, in case of release command, the response time of diaphragm brake system is shorter than that of empty-load one. In the emergency brake test, the decreasing rate of brake pipe pressure of tenth car is almost same that of decreasing rate of commercial brake service.

• Structural Engineering and Mechanics
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• v.74 no.4
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• pp.559-565
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• 2020

This paper intends to progress models to accurately estimate the behavior of fresh concrete under vibration using artificial neural networks (ANNs). To this end, behavior of a full scale precast concrete mold was investigated numerically. Experimental study was carried out under vibration with the use of a computer-based data acquisition system. In this study measurements were taken at three points using two vibrators. Transducers were used to measure time-dependent lateral displacements at these points on mold while both mold is empty and full of fresh concrete. Modeling of empty and full mold was made using ANNs. Benefiting ANNs used in this study for modeling fresh concrete, mold design can be performed. For the modeling of ANNs: Experimental data were divided randomly into two parts such as training set and testing set. Training set was used for ANN's learning stage. And the remaining part was used for testing the ANNs. Finally, ANN modeling was compared with measured data. The comparisons show that the experimental data and ANN results are compatible.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.1
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• pp.9-11
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• 2023

Intuitionistic Zermelo-Fraenkel (IZF) set theory is a set theory without the axiom of choice and the law of excluded middle (LEM). The weak excluded middle law (WEM) states that ¬𝜑∨¬¬𝜑 for any formula 𝜑. In IZF we show that LEM is equivalent to WEM plus the condition that any set not equal to the empty set has an element.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.161-169
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• 2024

A semi-well ordered set is a partially ordered set in which every non-empty subset of it contains a least element or a greatest element. It is defined as an extension of the concept of well ordered sets. An attempt is made to identify the properties of a semi-well ordered set equipped with the order topology.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.315-321
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• 2009

Erd$\"{o}$s posed the problem of determining the minimum number g(n) such that any set of g(n) points in general position in the plane contains an empty convex n-gon. In 1978, Harborth proved that g(5) = 10. We reprove the result in a geometric approach.