• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.209-222
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• 2006

Estimation of the spectral measure, covariance and spectral density functions of a strictly stationary r-vector valued time series is considered, under the assumption that some of the observations are missed. The modified periodograms are calculated using data window. The asymptotic normality is studied.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.93-100
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• 2008

In this paper, by introducing some parameters and estimating the weight function, we give a new Hilbert-type integral inequality with a best constant factor. The equivalent inequality and the reverse forms are considered.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.141-153
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• 2006

In this paper, we present the U-Statistic test for testing exponentiality against new renewal better than used (NRBU) based on a goodness of fit approach. Selected critical values are tabulated for sample sizes n=5(1)30(10)50. The asymptotic Pitman relative efficiency relative to (NRBU) test given in the work of Mahmoud et all (2003) is studied. The power estimates of this test for some commonly used life distributions in reliability are also calculated. Some of real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. The problem in case of right censored data is also handled.

• International Journal of Reliability and Applications
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• v.4 no.3
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• pp.113-129
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• 2003

Based on moments inequalities new testing procedures are derived for testing exponentiality against new renewal better than used (NRBU) and renewal new better than used (RNBU). These classes play an important role in formulating repair or replacement policies. The asymptotic Pitman efficiency of (NRBU) and (RNBU) testes are studied. Selected critical values are tabulated for sample sizes n=5(1) 50. The power estimates for some commonly used life distributions in reliability are also calculated. Some set of real data is used as an example to elucidate the use of the proposed test statistic for practical reliability analysis. The problem in case of right-censored data is also handled.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.1023-1041
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• 2009

The importance of the mathematical education on the ICT environment has been increased as the educational environment has been changed in 21st century. In Korea, many researches on ICT tools have appeared over the last 10 years. But most of researches are depending on the foreign tools, that was one major obstacle on adapting them in our mathematics curriculum. But we found the new open source tool which is called Sage-Math can be in effective solution to resolve those problems. Now we produce what we have done in linear algebra with this Sage-Math and mobile modules.

• Communications of Mathematical Education
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• v.31 no.3
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• pp.241-255
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• 2017

The 4th industrial revolution is coming. In order to prepare for the new learning environment with it, we may need digital mathematics textbooks that fully utilize all possible technologies. So various attempts have been made in elementary and middle school mathematics education. However, despite the importance of higher mathematics, we haven't seen a best possible math digital textbooks yet in Korea. In this paper, we introduce our new model of interactive math digital textbook about Linear Algebra/ Calculus/ Differential Equations/ Statistics/ Engineering Math. Especially, this manuscript focuses on our experience of using digital contents and interactive labs for developing a new model for linear algebra digital textbook. We introduce our works on linear algebra digital textbooks which include pdf e-book, web contents, video clips of lectures, interactive lab. Using this linear algebra digital textbook, students can freely use any mobile devices to access diverse learning materials, lessons, and hands-on exercises without any limitations. Also, times saved in the computation, coding, and typing process can be used to have more discussions for deeper understanding of mathematical concepts. This type of linear algebra digital textbook, which contains all interactive free cyber-lab with codes and all lectures for each sections, can be considered as a new model for the next generation of math digital textbook.

• Journal of Information Processing Systems
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• v.14 no.3
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• pp.590-599
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• 2018

Multivariate finite mixture model is becoming more and more popular in image processing. Performing image denoising from image patches to the whole image has been widely studied and applied. However, there remains a problem that the structure information is always ignored when transforming the patch into the vector form. In this paper, we study the operator which extracts patches from image and then transforms them to the vector form. Then, we find that some pixels which should be continuous in the image patches are discontinuous in the vector. Due to the poor anti-noise and the loss of structure information, we propose a new operator which may keep more information when extracting image patches. We compare the new operator with the old one by performing image denoising in Expected Patch Log Likelihood (EPLL) method, and we obtain better results in both visual effect and the value of PSNR.

• International Journal of Reliability and Applications
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• v.8 no.1
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• pp.27-39
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• 2007

Based on goodness of fit new testing procedures are derived for testing exponentiality against harmonic new renewal better than used in expectation (HNRBUE). For this aging properties, a nonparametric procedure (U-statistic) is proposed. The percentiles of this test statistic are tabulated for sample sizes n=5(1)30(10)50. The Pitman asymptotic efficiency (PAE) of the test is calculated and compared with, the (PAE) of the test for new renewal better than used (NRBU) class of life distribution [see Mahmoud et al (2003)]. The power of this test is also calculated for some commonly used life distributions in reliability. The right censored data case is also studied. Finally, real examples are given to elucidate the use of the proposed test statistic in the reliability analysis.

• Journal of the Korean Society for information Management
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• v.19 no.4
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• pp.96-111
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• 2002

A lot of accumulated data of many quantity exist within a institution or an organization, but most data is remained in form of standardization as each institution or organization. There are difficulty in exchange and share of information. New concept of knowledge information resource management to overcome this disadvantage was introduced, and the digitization of knowledge information resources to share and manage accumulated data is been doing. Specially, in science technic or education scholarship it, the tendency that importing XML to process necessary data to exchange and share of knowledge information resources structurally, and limitation of back for search and indexing or reusability is happened according as expression of great many mathematics used inside electron document of these sphere is processed to nonstructural data of image or text and so on. There is interest converged in processing of mathematics that use MathML to overcome this, and we require the solution to be able to process MathML easily and efficiently on structural document. In this paper, designed and implemented of XML document editing system which easy structural process of electronic document for knowledge information resources, and create and express MathML easily on structural document without expert knowledge about MathML.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.933-943
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• 2008

Spectral analysis of a strictly stationary r-vector valued time series is considered under the assumption that some of the observations are missed due to some random failure. Statistical properties and asymptotic moments are derived. Asymptotic normality is discussed.