• 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.

• Journal of Korean Society for Quality Management
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• v.12 no.2
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• pp.15-24
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• 1984

Since W.A. Shewhart (1931) developed the quality control method using the control chart, many theoretical and empirical works about such an analytical method have been done. However there are two major methods relating to the control chart analysis; the conventional 3 sigma control method and the warning limit method which has been suggested as a modification of the former. The conventional 3 sigma method requires to take a remedial action only when a quality characteristic is beyond the control limit (3 sigma). However, once a quality characteristic is over the control limit, searching and repairing an assignable cause requires time consuming job and high costs. Therefore if we set the warning limit between the central line and the control limit, we will be able to take remedial measures before too late. In spite of its advantage, much attention has not been paid to use the control chart with warning limit in Korean industries. The main object of this study is to examine improvement of quality and productivity when the control chart with warning limit is used.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.675-690
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• 1998

A role of singletons in quantum central limit theorems is studied. A common feature of quantum central limit distributions, the singleton condition which guarantees the symmetry of the limit distributions, is revisited in the category of discrete groups and monoids. Introducing a general notion of quantum independence, the singleton independence which include the singleton condition as an extremal case, we clarify the role of singletons and investigate the mechanism of arising non-symmetric limit distributions.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.207-218
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• 2021

In this paper, the notion of two-sided limit shadowing property is considered for a positively expansive open map. More precisely, let f be a positively expansive open map of a compact metric space X. It is proved that if f is topologically mixing, then it has the two-sided limit shadowing property. As a corollary, we have that if X is connected, then the notions of the two-sided limit shadowing property and the average-shadowing property are equivalent.

• Journal of the Korean Geotechnical Society
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• v.29 no.11
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• pp.73-84
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• 2013

When a slope failure or a debris flow occurs, a shear strength on failure plane becomes nearly zero and soil begins to flow like a non-cohesive liquid. A consistency of cohesive soils changes as a water content increases. Even a cohesive soil existing at liquid limit state has a small amount of shear strength. In this study, a water content, at which a shear strength of cohesive soils is zero and then cohesive soils will start to flow, was proposed. Three types of clays (kaolinite, bentonite and kaolinite (50%)+bentonite (50%)) were mixed with three different solutions (distilled water, sea water and microbial solution) at liquid limit state and then their water contents were increased step by step. Then, their undrained shear strength was measured using a portable vane shear device called Torvane. The ranges of undrained shear strength at liquid and plastic limits are 3.6-9.2 kPa and 24-45 kPa, respectively. On the other hand, the water content that corresponds to the value of the undrained shear strength changing most rapidly is called flow water content. The flow limit refers to the water content when undrained shear strength of cohesive soils is zero. In order to investigate the relationship between liquid limit and flow limit, the cohesive index was defined as a value of the difference between flow limit and liquid limit. The new plasticity index was defined as the value of difference between flow limit and plastic limit. The new liquidity index was also defined using flow limit. The values of flow limit are 1.5-2 times higher than those of liquid limit. At the same time, the values of new plasticity index are 2-5.5 times higher than those of original plasticity index.

• Journal of the Korean Society of Industry Convergence
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• v.25 no.2_2
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• pp.233-238
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• 2022

This study evaluated the fatigue limit depending on microcracks using 0.57 wt.% carbon steel with different Vickers hardness. The fatigue limit was almost constant up to a certain limit regardless of the carbon content. However, the fatigue limit decreased rapidly as the size of the crack increased. As the crack aspect ratio was smaller, the fatigue limit of the depth (point A) a lot decreased. The fatigue limit ratio of the depth decreased significantly because the crack propagation in the depth direction was fast as the crack aspect ratio became smaller. On the other hand, the fatigue limit ratio of surface cracks increased as the crack aspect ratio decreased.

• The Mathematical Education
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• v.42 no.5
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• pp.707-723
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• 2003

Teaching the notion of limit of the sequence in high school mathematics needs special attention and accurate teaching methods, for it is one of the most important bases of the advanced mathematics. Therefore it is necessary for high school students to have the right understanding of the notion of limit of the sequence. In this paper, we survey several teaching methods of the notion of limit of the sequence in high school mathematics and introduce a new method using Excell program. Also through questionnaire survey we discuss and analyse students' reaction when they learn the notion of limit of the sequence. And based on that, we suggest a method that would be believed to improve the students' understanding for the notion of limit It should be also notified that questionnaire survey was performed in order to find out which method would be appropriate to teach the notion of limit of the sequence, and that the survey result was fully reflected in the guideline that suggested.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1334-1338
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• 2005

A limit switch box is used for an indicator of a valve actuator. This device indicates an opening and closing of a valve or a throttle in the valve actuator. In a ship, equipments require safety and robustness because of a rough environment and a specific condition during a voyage. However, the limit switch box has been used in an indoor environment generally. This study developed a new limit switch box which can be used at an outdoor environment. This study designed the new limit switch box. The housing of the limit switch box was made by an aluminum die cast method with surface painting after anodizing or chromate coating. In order to evaluate the endurance of the housing, the endurance tests against salt water have been conducted. Experiment results showed that the proposed device provides a reliable performance against salt water.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.5 s.248
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• pp.568-575
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• 2006

The present paper provides plastic limit load solutions of axial and circumferential through-wall cracked pipes based on detailed three-dimensional (3-D) finite element (FE) limit analysis using elastic-perfectly-plastic behavior. As a loading condition, axial tension, global bending moment, internal pressure, combined tension and bending and combined internal pressure and bending are considered for circumferential through-wall cracked pipes, while only internal pressure is considered for axial through-wall cracked pipes. Especially, more emphasis is given for through-wall cracked pipes subject to combined loading. Comparisons with existing solutions show a large discrepancy in short through-wall crack (both axial and circumferential) for internal pressure. In the case of combined loading, the FE limit analyses results show thickness effect on limit load solutions. Furthermore, the plastic limit load solution for circumferential through-wall cracked pipes under bending is applied to derive plastic $\eta\;and\;{\gamma}$-factor of testing circumferential through-wall cracked pipes to estimate fracture toughness. Being based on detailed 3-D FE limit analysis, the present solutions are believed to be meaningful fur structural integrity assessment of through-wall cracked pipes.

• Nuclear Engineering and Technology
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• v.53 no.3
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• pp.901-910
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• 2021

KHNP recently has obtained the approval for the commercialization of the modified 37-element (or 37 M) fuel bundle and now is loading the 37 M fuel bundles in CANDU-6 reactors in KOREA. One of the main issues for approval was the burnup limit. Due to CANDU design and neutronic characteristics, there was no specific burnup restriction of a fuel bundle. The absence of a burnup limit does not mean that a fuel bundle can stay in the CANDU reactor without a time limit. However, the regulator requested traditional design values as well as the burnup limit reflecting the computer code uncertainty. The method for the PWR burnup limit was not applied to the CANDU fuel bundle. Since there was no approved methodology to build the burnup limit with uncertainties, KHNP introduced a Monte-Carlo method coupled with a 95/95 approach to determine the conservative burnup limit from the viewpoint of the centerline temperature, internal pressure, strain measurement deviation. Moreover, to consider the uncertainties of various computing models, a converted power uncertainty was introduced. This paper presents the methodology and puts forward the limits on burnup, evaluated for each of the existing and modified fuel bundles, in consideration of the pressure tube aging condition.