• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.297-314
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• 2021

This manuscript is divided into three segments. In the first segment, we formulate a unique common fixed point theorem satisfying generalized Meir-Keeler contraction on partially ordered metric spaces and also give an example to demonstrate the usability of our result. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of some periodic boundary value problems. Our results generalize, extend and improve several well-known results of the existing literature.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.3
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• pp.33-38
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• 2002

To establish the national standard of capacitance, four main electrodes of the cross capacitor which were evaluated to linearity and roundness less the $\pm 1 \mu m$ respectively have to be adjusted symmetrically in an inner cylinder. Four LM shafts with diameter of 5 mm were installed between main electrodes of the cross capacitor, and the electrodes were adjusted, as the first step, by means of the measured capacitance. In the second step, the symmetrical adjustment up to $\pm 1.2\mu m$ was performed by using a ball sensor, ball-type movable sensor, non-contacting capacitive sensor and upper guard sensor which were developed in this project.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.2
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• pp.43-53
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• 1993

There exist two difficulties in the nonlinear wave-body problems. First is the abrupt behavior near the intersection point between the body and the free surface, and second is the far field treatment. In this paper, the far field treatment is considered. The main idea is the Taylor series expansion of free-surface geometry and the application of F.F.T. algorithm. The numerical step is as follows. The velocity potential is expressed by the Green's theorem. and the solution is obtained by iteration method. In the iteration stage, the expressions by the Green's theorem are transformed to the convolution forts with the expansion of free surface by the wave slope. Here F.F.T. is applied, so the computing time can be of O(Nlog N) where N is the number of unknowns. The numerical analysis is carried out and the results are compared with other results in linear floating body problem and nonlinear moving pressure patch problem, and good agreements are obtained. Finally nonlinear floating body radiation problem is carried out with computing time of O(Nlog N).

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.137-162
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• 2024

This paper consists of two significant aims. The first aim of this paper is to establish the criteria for the existence of solutions to nonlinear Volterra-Fredholm (V-F) fractional integral equations on [0, L], where 0 < L < ∞. The fractional integral is described here in the sense of the Katugampola fractional integral of order λ > 0 and with the parameter β > 0. The concepts of the fixed point theorem and the measure of noncompactness are used as the main tools to prove the existence of solutions. The second aim of this paper is to introduce a computational method to obtain approximate numerical solutions to the considered problem. This method is based on the Fibonacci wavelets with collocation technique. Besides, the results of the error analysis and discussions of the accuracy of the solutions are also presented. To the best knowledge of the authors, this is the first computational method for this generalized problem to obtain approximate solutions. Finally, two examples are discussed with the computational tables and convergence graphs to interpret the efficiency and applicability of the presented method.

• The KIPS Transactions:PartC
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• v.18C no.5
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• pp.331-338
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• 2011

The RFID system includes a section of wireless communication between the readers and the tags. Because of its vulnerability in terms of security, this part is always targeted by attackers and causes various security problems including the leakage of secret and the invasion of privacy. In response to these problems, various protocols have been proposed, but because many of them have been hardly implementable they have been limited to theoretical description and theorem proving without the accurate verification of their safety. Thus, this study tested whether the protocol proposed by Kenji et al. satisfies security requirements, and identified its vulnerabilities such as the exposure of IDs and messages. In addition, we proposed an improved RFID security protocol that reduced the number of public keys and random numbers. As one of its main characteristics, the proposed protocol was designed to avoid unnecessary calculations and to remove vulnerabilities in terms of security. In order to develop and verify a safe protocol, we tested the protocol using Casper and FDR(Failure Divergence Refinements) and confirmed that the proposed protocol is safe in terms of security. Furthermore, the academic contributions of this study are summarized as follows. First, this study tested the safety of a security protocol through model checking, going beyond theorem proving. Second, this study suggested a more effective method for protocol development through verification using FDR.

• The Journal of Korean Association of Computer Education
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• v.4 no.1
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• pp.99-107
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• 2001

One of the main objects of geometry in mathematics education is to improve students' geometric intuition capability and logical reasoning capability based on them. A visual element related to intuition plays an important role in teaching and learning of geometry. Therefore, in this research, we focus on the development of multimedia title available to dynamic operation about visual elements and verify of effect of its application. This title for the learning of "the Pythagorean theorem and its practical use" in the third grade of middle school is designed and implemented by an authoring tool, Toolbook. And it enables learners to study mathematics individually and can be applied to the educational field, too. And we taught two groups, the applied group and the compared one of the second grade of middle school and surveyed Questions and evaluated study achievement. We calculated study achievement of two groups on t-test using SPSS. As the result, we knew that the applied group is higher than the compared one in the study achievement and provision of dynamic operation possibility on visual elements make students know very high learning effect and help improvement of intelligent capability.