• 호남수학학술지
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• 제41권1호
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• pp.135-152
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• 2019

In the last decades, various integral formulas associated with Bessel functions of different kinds as well as Bessel functions themselves, have been studied and a noteworthy amount of work can be found in the literature. Following up, we present two definite integral formulas involving the product of generalized Bessel function associated with orthogonal polynomials. Also, some intriguing special cases of our main results have been discussed.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.513-530
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• 2021

The purpose of this paper is to introduce and study a class of coupled systems of fuzzy delay differential equations involving fuzzy initial values and fuzzy source functions of triangular type. We assume that these initial values and source functions are triangular fuzzy functions and define solutions of the coupled systems as a triangular fuzzy function matrix consisting of real functional matrices. The method of triangular fuzzy function, fractional steps and fuzzy terms separation are used to solve the problems. Furthermore, we prove existence and uniqueness of solution for the considered systems, and then a solution algorithm is proposed. Finally, we present an example to illustrate our main results and give some work that can be done later.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권2호
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• pp.159-168
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• 2015

Abstract. We propose a fast and robust finite difference method for Merton's jump diffusion model, which is a partial integro-differential equation. To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. Also, we use non-uniform grids to increase efficiency. We present numerical experiments such as evaluation of the option prices and Greeks to demonstrate a performance of the proposed numerical method. The computational results are in good agreements with the exact solutions of the jump-diffusion model.

• Advances in concrete construction
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• 제15권3호
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• pp.171-178
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• 2023

Cytoskeleton components play key role in maintaining cell structure and in giving shape to the cell. These components include microtubules, microfilaments and intermediate filaments. Among these filaments intermediate filaments are the most rigid and bear large compressive force. Actually, these filaments are surrounded by other filaments like microtubules and microfilaments. This network of filaments makes a layer as a surface on intermediate filaments that have great impact on buckling behavior of intermediate filaments. In the present article, buckling behavior of intermediate filaments is studied by taking into account the effects of surface by using Euler Bernoulli and Timoshenko beam theories. It is found that effects of surface greatly affect the critical buckling force of intermediate filaments. Further, it is observed that the critical buckling force is inversely proportional to the length of filament. Such types of observations are helpful for further analysis of nanofibrous in their actual environments within the cell.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1257-1274
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• 2023

Rotating machines heavily rely on an intricate network of interconnected sub-components, with bearing failures accounting for a substantial proportion (40% to 90%) of all such failures. To address this issue, intelligent algorithms have been developed to evaluate vibrational signals and accurately detect faults, thereby reducing the reliance on expert knowledge and lowering maintenance costs. Within the field of machine learning, Artificial Immune Systems (AIS) have exhibited notable potential, with applications ranging from malware detection in computer systems to fault detection in bearings, which is the primary focus of this study. In pursuit of this objective, we propose a novel procedure for detecting novel instances of anomalies in varying operating conditions, utilizing only the signals derived from the healthy state of the analyzed machine. Our approach incorporates AIS augmented by Dynamic Time Warping (DTW). The experimental outcomes demonstrate that the AIS-DTW method yields a considerable improvement in anomaly detection rates (up to 53.83%) compared to the conventional AIS. In summary, our findings indicate that our method represents a significant advancement in enhancing the resilience of AIS-based novelty detection, thereby bolstering the reliability of rotating machines and reducing the need for expertise in bearing fault detection.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제28권3호
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• pp.88-95
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• 2024

In this article, we propose an efficient and accurate adaptive time-stepping numerical method for the Black-Scholes (BS) equations. The numerical scheme used is the finite difference method (FDM). The proposed adaptive time-stepping computational scheme is based on the maximum norm of the discrete Laplacian values of option values on a discrete domain. Most numerical solvers for the BS equations require a small time step when there are large variations in the solutions. To resolve this problem, we propose an adaptive time-stepping algorithm that uses a small time step size when the maximum norm of the discrete Laplacian values on a discrete domain is large; otherwise, a larger time step size is used to speed up the computation. To demonstrate the high performance of the proposed adaptive time-stepping methodology, we conduct several computational experiments. The numerical tests confirm that the proposed adaptive time-stepping method improves both the efficiency and accuracy of computations for the BS equations.

• Structural Engineering and Mechanics
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• 제34권1호
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• pp.135-138
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• 2010

• 한국과학교육학회지
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• 제32권6호
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• pp.1072-1086
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• 2012

Science, Technology, Engineering, and Mathematics (STEM) education in the U.S. has been identified as a significant national reform in K-16 education and curriculum in order to prepare students for the global economy of the 21st century. Korea has been facing very similar challenges to improve science, technology and mathematics education, in particular, the affective aspect of learning science and mathematics. Science, Technology, Engineering, Arts, and Mathematics (STEAM) education has become a crucial issue in Korean education system. The major purpose of this exploratory study is to inform the exemplary framework of STEAM education in the U.S. for Korea and to provide descriptive and analytical accounts on STEAM teaching and learning as an innovative integrated convergence education. This study integrates the outcomes of research papers on STEM education and recent literature. It employs content analysis methodology qualitatively by analyzing and synthesizing the findings, conclusions, discussions, and recommendations of accumulated research works related to STEM/STEAM education. This study will help gain a stronger sense of the STEAM framework and will guide to develop the educational programs for Korea.

• 한국학교수학회논문집
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• 제22권4호
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• pp.395-413
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• 2019

본 연구는 블렌디드 이러닝이 공과대학 학생들의 공학수학 교수·학습에 미치는 영향을 알아보기 위하여 M대학교 기계공학과 3학년 42명을 연구대상자로 선정하였다. 본 연구에서 공학수학 교과목에 블렌디드 이러닝을 적용한 수업은 오프라인에서는 전체 수강생을 대상으로 강의실에서 면대면 수업의 형태로 진행되었고, 수업이 진행되는 동안 수업의 전 과정을 녹화한 후 녹화된 동영상을 LMS에 탑재하여 온라인 상에서 개별 학습이 이루어지도록 하였다. 한 학기 동안 오프라인과 온라인을 혼합한 형태로 수업을 진행하면서 학습자들의 온라인 자료의 활용 실태 및 오프라인 수업에서의 학생들의 태도의 변화 등을 조사하였다. 그 결과 다음과 같은 결론을 얻었다. 첫째, 공학수학에 적용한 블렌디드 이러닝은 학생들의 자기주도적이고 개별화된 학습에 긍정적인 영향을 준다. 둘째, 블렌디드 이러닝은 공학수학 교수·학습에 긍정적인 영향을 준다. 셋째, 블렌디드 이러닝은 학생들의 수업 만족도에 긍정적인 영향을 준다.

• 디지털융복합연구
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• 제17권12호
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• pp.67-75
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• 2019

본 연구는 중학교 1학년 기본도형과 작도 단원을 중심으로 공학적 도구를 활용한 수학 수업이 학생들의 수학 학업 성취도와 수학 학습 태도에 미치는 효과를 분석하기 위하여 수행되었다. 이를 위해 경남 소재 H중학교 1학년 학생 80명을 두 집단으로 구분하여 공학적 도구(Algeomath)를 활용한 수업과 전통적인 교구를 사용한 판서 수업을 총 6주간에 걸쳐 진행하였으며, 학생들의 수학 학업 성취도와 수학적 성향 변화를 분석하기 위해 공변량분석(ANCOVA)을 활용하였다. 분석 결과, 공학적 도구를 활용한 수업이 학생들의 수학 학업 성취도와 수학 학습 태도에 효과가 있는 것으로 밝혀졌으며, 연구 결과를 바탕으로 향후 중등학교 수학 수업에서 다양한 공학적 도구 활용의 필요성과 수업의 전망 및 시사점을 논의하였다.