• Honam Mathematical Journal
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• v.32 no.1
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• pp.53-60
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• 2010

The concept of discrete curvature is a discretization of the curvature. Many literatures introduce discrete curvatures derived from arc length of circular arcs. We propose a new concept of discrete curvature of a polygon at each vertex, which is derived from area of fan shapes. We estimate the error of the discrete curvature and compare the discrete curvature with old one.

• The Mathematical Education
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• v.41 no.1
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• pp.127-137
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• 2002

Discrete Mathematics is newly introduced into the 7th Elementary and Secondary School Mathematics Curriculum of Republic of Korea. Every high school can choose Discrete Mathematics as an optional course from year 2002, but mostly from year 2003. According to its characteristics and objectives in the curriculum, we should know how to implement Discrete mathematics. But it is hard to predict whether Discrete Mathematics will be successful or not, since many studies have shown the lack of readiness for the course. In this study, we analyze the Discrete Mathematics text book developed recently in 2002. Then we see how Discrete Mathematics can be implemented. First, we suggest how the contents in the Discrete Mathematics text book are related to the mathematical values. This will clarify instruction and learning methods in Discrete Mathematics classrooms. Secondly, rich and various discrete contents should be taught. Students should appreciate the realistic merits of discrete mathematics. Thirdly, evaluation methods and their examples will be presented based upon the contents of she text. The evaluation that distinguishes individual achievement levels is closely related with implementation of Discrete mathematics in schools. Finally, we point out the weakness of Discrete Mathematics contents in the 7th curriculum to prepare ourselves for the 8th curriculum.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.325-336
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• 2019

In this article we extend the discrete Weibull regression model in the presence of missing data. Discrete Weibull regression models can be adapted to various type of dispersion data however, it is not widely used. Recently Yoo (Journal of the Korean Data and Information Science Society, 30, 11-22, 2019) adapted the discrete Weibull regression model using single imputation. We extend their studies by using multiple imputation also with several various settings and compare the results. The purpose of this study is to address the merit of using multiple imputation in the presence of missing data in discrete count data. We analyzed the seventh Korean National Health and Nutrition Examination Survey (KNHANES VII), from 2016 to assess the factors influencing the variable, 1 month hospital stay, and we compared the results using discrete Weibull regression model with those of Poisson, negative Binomial and zero-inflated Poisson regression models, which are widely used in count data analyses. The results showed that the discrete Weibull regression model using multiple imputation provided the best fit. We also performed simulation studies to show the accuracy of the discrete Weibull regression using multiple imputation given both under- and over-dispersed distribution, as well as varying missing rates and sample size. Sensitivity analysis showed the influence of mis-specification and the robustness of the discrete Weibull model. Using imputation with discrete Weibull regression to analyze discrete data will increase explanatory power and is widely applicable to various types of dispersion data with a unified model.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1555-1565
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• 2013

In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90] and [S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859].

• Journal of Information Processing Systems
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• v.12 no.4
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• pp.754-764
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• 2016

The exhaustive list of sparsification methods for a digital image suffers from achieving an adequate number of zero and near-zero coefficients. The method proposed in this paper, which is known as the Discrete Rajan Transform Sparsification, overcomes this inadequacy. An attempt has been made to compare the simulation results for benchmark images by various popular, existing techniques and analyzing from different aspects. With the help of Discrete Rajan Transform algorithm, both lossless and lossy sparse representations are obtained. We divided an image into $8{\times}8-sized$ blocks and applied the Discrete Rajan Transform algorithm to it to get a more sparsified spectrum. The image was reconstructed from the transformed output of the Discrete Rajan Transform algorithm with an acceptable peak signal-to-noise ratio. The performance of the Discrete Rajan Transform in providing sparsity was compared with the results provided by the Discrete Fourier Transform, Discrete Cosine Transform, and the Discrete Wavelet Transform by means of the Degree of Sparsity. The simulation results proved that the Discrete Rajan Transform provides better sparsification when compared to other methods.

• School Mathematics
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• v.7 no.1
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• pp.77-101
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• 2005

This study is a discussion of the teaching and learning of discrete mathematics in school mathematics. In this study, we summarized the importance of discrete mathematics m school mathematics. And we examined instruction methods of discrete mathematics expressed in the 7th mathematics curriculum. On the basis of analysis for teaching cases in previous studies, we proposed four suggestions to organize discrete mathematics classroom. That is as follows. First, discrete mathematics needs to be introduced as a mathematical modeling of real-world problem. Second, algorithm learning in discrete mathematics have to be accomplished with computer experiments. Third, when we solve a problem with discrete data, we need to consider discrete property of given data. Forth, discrete mathematics class must be full of investigation and discussion among students. In each suggestion, we dealt with detailed examples including educational ideas in order to helping mathematics teacher orgainzing discrete mathematics classroom.

• Proceedings of the KOSOMBE Conference
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• v.1997 no.05
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• pp.150-155
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• 1997

Modelling and Simulation of the activation process for the myocardium is meaningful to understand special excitation conduction system in the heart and to study cardiac functions. In this paper, we propose two dimensional cellular automata model for the activation process of the myocardium and simulated by means of discrete time and discrete event algorithm. In the model, cells are classified into anatomically similar characteristic parts of heart; SA node, internodal tracks, AV node, His bundle, bundle branch and four layers of the ventricular muscle, each of which has a set of cells with preassigned properties, that is, activation time, refractory duration and conduction time between neighbor cell. Each cell in this model has state variables to represent the state of the cell and has some simple state transition rules to change values of state variables executed by state transition function. Simulation results are as follows. First, simulation of the normal and abnormal activation process for the myocardium has been done with discrete time and discrete event formalism. Next, we show that the simulation results of discrete time and discrete event cell space model is the same. Finally, we compare the simulation time of discrete event myocardium model with discrete time myocardium models and show that the discrete event myocardium model spends much less simulation time than discrete time myocardium model and conclude the discrete event simulation method Is excellent in the simulation time aspect if the interval deviation of event time is large.

• The Journal of the Acoustical Society of Korea
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• v.19 no.8
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• pp.54-62
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• 2000

Adaptive filtering method is one of signal processing area which is frequently used in the case of statistical characteristic change in time-varing situation. The performance of adaptive filter is usually evaluated with complexity of its structure, convergence speed and misadjustment. The structure of adaptive filter must be simple and its speed of adaptation must be fast for real-time implementation. In this paper, we propose chirp discrete cosine transform (CDCT), which has the characteristics of CZT (chrip z-transform) and DCT (discrete cosine transform), and then CDCTLMS (chirp discrete cosine transform LMS) using the above mentioned algorithm for the improvement of its speed of adaptation. Using loaming curve, we prove that the proposed method is superior to the conventional US (normalized LMS) algorithm and DCTLMS (discrete cosine transform LMS) algorithm. Also, we show the real application for the ultrasonic signal processing.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.2
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• pp.248-257
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• 2010

In this study, a discrete event and dynamic-based discrete time combined simulation modeling architecture, which can be used to calculate equations of motions among discrete events, is developed. This is composed of a command model, which is in charge of discrete event simulation, a numerical integration model, which finds motions by numerically integrating equations of motions, and an external force and control force model, which calculates the force and transmits it to the equations. Using this architecture, we can develop dynamic-based simulation by simply connecting and combining models, and handle simultaneously discrete event and discrete time simulation. To verify the efficiency of the architecture, it is applied to the submarine diving and surfacing simulation.

• Journal of Power Electronics
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• v.11 no.3
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• pp.304-310
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• 2011

The power series approximation method is proposed for real time implementations of a discrete flux observer. The proposed method improves the performance of the discrete flux observer in the case of a low sampling rate and high speed range, where the simple discrete flux observer converted by the Euler method cannot estimate the actual flux precisely. The performance of discrete flux observers with different orders of approximation is compared to find out the proper order of approximation. The validity of the proposed method is verified through simulation and experiment.