• Bulletin of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.481-506
• /
• 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 the Korean Society of Marine Environment & Safety
• /
• v.21 no.3
• /
• pp.274-282
• /
• 2015

This research is the result on calculating the logical speed limit through certain process which some elements must be considered on selecting the speed limit of harbour and waterway. The suggested speed limit select model on this research is processed from 1~6 steps by forming a professional group of experts. Each step has its information which 1st step(water division), 2nd step(selecting the model vessel and vessel applied with speed limit.), 3rd step(selecting the maximum and minimum speed range on each section), 4th step(evaluation on the safeness of traffic), 5th step(suggesting the appropriate speed limit), 6th step(execution and evaluation.). The appropriate speed limit was decided on consideration of the safety of maritime traffic on the range of the maximum speed and the minimum speed. This model was used to derive the appropriate speed limit on the harbour water and Busan harbour entrance waterway. As the result, the harbour water was calculated to be 6.9 knots, the appropriate speed limit of Busan entrance harbour was 9.3 knots. The present calculation of the speed limit on the approaching channel area is 10 knots, inner harbour area is 7 knots, which are similar to the result of the speed limit. This research is the first research on selecting the speed limit model and has its limits on finding the perfect speed limit result. More detailed standards on the safeness of traffic evaluation must be found and additional study is necessary on discriminating consideration of the elements. This research has its value which it provides instances of aboard cases on guidelines of selecting the speed limit.

• Proceedings of the KSR Conference
• /
• 2011.10a
• /
• pp.1092-1099
• /
• 2011

This paper is concerned with the ATO speed profile generation method in the moving block system. The ATO speed profile is calculated using the acceleration limit and the jerk limit to improve ride comfort. In addition, the speed limit and stop distance provided from ATP profile should be considered to ensure safety. In the moving block system, the speed limit and the stop position are frequently changed in real-time. Therefore, the ATO speed profile should be regenerated immediately according to change of the speed limit and the stop position, within the acceleration limit and the jerk limit. In this paper, the ATO speed profile generation method is proposed, which considers not only frequent changes of the speed limit and the stop position but also acceleration limit and jerk limit. Futhermore the simulation result is presented to verify usefulness of this method.

• Steel and Composite Structures
• /
• v.22 no.6
• /
• pp.1391-1415
• /
• 2016

Limit load of pressure bearing structures was reviewed in this article. By means of the finite element analysis, limit load of pressurized cylinder with nozzle was taken as an example. Stress classification method and Elastic-plastic finite element analysis combining with limit load determination methods were used to determine limit load of cylinder with nozzle. Comparison of limit load determined by different methods, the results indicated that limit load determined by linearization method was the smallest. Limit load determined by twice elastic slope criterion was the nearest than experimental results. Elastic-plastic finite element analysis had comparably computational precision, but required time consuming. And then the requirements of computer processing and storage capacity by power system became higher and higher. Most of criteria for limit load estimation included any human factors based on a certain substantive characteristics of experimental results. The reasonable criterion should be objective and operational.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2003.03a
• /
• pp.375-382
• /
• 2003

This study, Using Pusan clay, examined a relationship between Dynamic and Static Liquid Tests. The Static Liquid Tests wow carried out based on BS and JIS. The results of the study are summarized as follows. (1) The result of the Dynamic Liquid Limit Test showed that the liquid limit values of air-dried soil were greater than those of oven-dried soil by 4%~15% (2) The liquid limit value of the Static Liquid Limit Test was greater than that of the Dynamic Liquid Limit Test by 2%~9%. The following equations show the relationship between the two values WL,Fall(JIS) = 0.961ㆍWL,Cas. + 4.209 WL,Fall(BS) = 0.969ㆍWL,Cas + 5.024 (3) The liquid limit value of BS was greater than that of JIS by 1%~6%. The following equation shows the relationship between the two values.

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

• Proceedings of the KSR Conference
• /
• 2008.06a
• /
• pp.80-85
• /
• 2008

In general, deflection limit criteria of bridge design specifications have been considered based on static serviceability and structural stability. Dynamic serviceability induced from bridge vibration actually has not been included in the criteria. Thus, it is necessary for comfort limit to be considered in order to check dynamic serviceability on bridge vibration. In this study, the comfort limit of bridge structures based on the RMQ and VDV considering the signal fluctuation effectively and the time duration exposed has been constructed. The comfort limit developed in time domain was verified by using vibration signals directly measured from the existing bridges. Comparing the developed comfort limit with the conventional ones defined in frequency domain, it is shown that the comfort limit developed in time domain would be more feasible for evaluating quantitatively the serviceability due to bridge vibration. Using the Bridge-train interaction analysis program, dynamic response of the bridge by the stiffness change were obtained for several railway bridges. And, a stiffness limit satisfying the bridge vibration serviceability was estimated by compared with comport limit. From the results, a new deflection limit on bridge structures satisfying the vibration serviceability could be proposed by comparing with the conventional deflection limit criteria.

• Communications of the Korean Mathematical Society
• /
• v.15 no.3
• /
• pp.549-553
• /
• 2000

For a continuous map of the circle to itself, we give necessary and sufficient conditions for the $\omega$-limit set of each nonwandering point to be minimal.

• Journal of Educational Research in Mathematics
• /
• v.12 no.4
• /
• pp.557-579
• /
• 2002

The purpose of this study is to find out the problems which are caused when the limit concept of sequences is learned through an intuitive definition and to suggest a way of solving those problems. Students in Korea study the limit concept of sequences through an intuitive definition. They fail to apply the intuitive definition properly to the problems and they are apt to have misconception even though the Intuitive definition is applied properly. To solve these problems, this study examined the develop- mental process of the limit concept of sequences from the Intuitive definition to the formal definition, and looked into the way of students' internalization of the process through a field study. In this study, the levels of the limit concept of sequences possessed by the students at ZPD are as follows; level 0 : Students understand the limit concept of sequences through the intuitive definition. level 1 : Students understand the limit concept of sequences as 'The difference between $\alpha$$_{n}$ and $\alpha$ approaches 0' rather than 'The sequence approaches $\alpha$ infinitely.' level 2 : Students understand the limit concept of sequences through the formal definition. The levels of students' limit concept development were analysed by those criteria. Almost of the students who studied the limit concept of sequences through the intuitive defition stayed at level 0, whereas almost of the students who studied through the formal definition stayed at level 1. Through the study, I found that it was difficult for the students to develop the higher level of understanding for themselves but the teachers and peers could help the students to progress to the higher level. Students' learning ability was one of major factors that make the students progress to the higher level of understanding as the concept was developed hierarchically from Level 0 to Level 2. If you want to see your students get to the higher level of understanding in the limit concept, you need to facilitate them to fully develop understanding in lower levels through enough experiences so that they can be promoted to the highest level.

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