• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.719-736
• /
• 2005

An understanding of Fourier series and their generalization is important for physics and engineering students, as much for mathematical and physical insight as for applications. Students are usually confused by the so-called Gibbs' phenomenon, an overshoot between a discontinuous function and its approximation by a Fourier series as the number of terms in the series becomes indefinitely large. In this paper we give short story of Gibbs phenomenon in chronological order.

• Korean Journal of Soil Science and Fertilizer
• /
• v.48 no.4
• /
• pp.255-261
• /
• 2015

Soil catena can be characterized by some properties, such as drainage levels and soil textures. Characteristics of soil catena are different drainage levels from a summit to the direction of gravity and similar soil textures. Therefore this study was performed GIS (Geographic information system) and statistical analyses using perimeters from soil series in order to characterize quantitatively and objectively soil distributional properties in Korea. The total of 16 soil series from representative granite and granite gneiss originated soils were selected among inland soils from detailed soil maps (1:25,000 scale) in Rural Development Administration (RDA) and analyzed. After the detailed soil maps were merged by soil series unit, perimeters were measured from one soil series to neighboring soil series using functions of table join, merge, dissolve, buffer, and clip in ArcGIS (10.1). The covering ratio of each soil series unit was calculated from neighboring perimeters by soil series and applied to clustering analysis. Soils that were analyzed were the total of 16 soil series; 7 of sandy loam and 9 of clay loam. As a result, analyzed soil series adjoined complicatedly such as Hyocheon series adjoined 26 series and Jisan did 276 series. The results of the clustering analysis showed that soils were clustered by soil textures except a few soil series. This study applied only one property that was a length of neighboring soil series to GIS and statistical analyses. These results were compared to existing soil groups that were classified by new-soil taxonomy, texture, soil type and drainage level. It showed that these analyses can provide soil characteristics by soil texture. Based on this study, there is a need to investigate further objectively and quantitatively in statistical analyses of soil series.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.12 no.7
• /
• pp.3112-3127
• /
• 2018

Since time series clustering is performed without prior information, it is used for exploratory data analysis. In particular, clusters of time series with similar shapes can be used in various fields, such as business, medicine, finance, and communications. However, existing time series clustering algorithms have a problem in that time series with different shapes are included in the clusters. The reason for such a problem is that the existing algorithms do not consider the limitations on the size of the generated clusters, and use a dimension reduction method in which the information loss is large. In this paper, we propose a method to alleviate the disadvantages of existing methods and to find a better quality of cluster containing similarly shaped time series. In the data preprocessing step, we normalize the time series using z-transformation. Then, we use piecewise aggregate approximation (PAA) to reduce the dimension of the time series. In the clustering step, we use density-based spatial clustering of applications with noise (DBSCAN) to create a precluster. We then use a modified K-means algorithm to refine the preclusters containing differently shaped time series into subclusters containing only similarly shaped time series. In our experiments, our method showed better results than the existing method.

• Journal of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.785-802
• /
• 1995

It is well known that every periodic function $f \in L^p([0,2\pi]), p > 1$, can be represented by a convergent trigonometric series called the Fourier series of f. Uniqueness of the representing series is very important, and we know that the Fourier series of a periodic function $f \in L^p([0,2\pi])$ is unique.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.4
• /
• pp.421-440
• /
• 2019

We establish a few class of infinite series identities from modular transformation formulas for certain series which originally come from generalized non-holomorphic Eisenstein series.

• International Journal of Reliability and Applications
• /
• v.12 no.2
• /
• pp.103-116
• /
• 2011

A series-parallel system with independent but non-identical components is considered. The expressions have been derived for the joint reliability importance (JRI) of m (${\geq}2$) components, chosen from a series-parallel system. JRIs of components of two different series-parallel systems are studied analytically and graphically.

• The Transactions of the Korean Institute of Electrical Engineers C
• /
• v.48 no.9
• /
• pp.641-647
• /
• 1999

The paper provides the results of microstructure analysis and dielectricproperties of porcelain suspension insulators. The evaluation of characteristics was also made as a function of the manufacturers and fabricated years for the experimental specimens which had been used in real distribution lines. Even though the series A contained higher alumina contents than the series B, the densification of series A was lower than that of series B, resulting from much porosity. The microstructure investigation confirmed that series A had much porosity than series B. The series A contained quartz $(SiO_2),\; mullite\; (Al_6Si_2O_{13}),\; corundum(Al_2O_3),\; and cristobalite\; (SiO_2)$ phases. However, the series B had no cristobalite phase which had very high thermal expansion coefficient. Also, the tan$\delta$of series A was more abruptly increased than that of series B as increasing temperature. The elevated temperature may make much expansion of cristobalite crystal than other crystals, resulting in crack and puncture inside cap during the summer days.

• Journal for History of Mathematics
• /
• v.30 no.4
• /
• pp.233-246
• /
• 2017

$Ces{\grave{a}}ro$ summability is a generalized convergence criterion for infinite series. We have investigated the classical results of summability for Fourier series from 1897 to 1957. In this paper, we are concerned with the summability and summation methods for Fourier Series from 1960 to 2010. Many authors have studied the subject during this period. Especially, G.M. Petersen,$K{\hat{o}}si$ Kanno, S.R. Sinha, Fu Cheng Hsiang, Prem Chandra, G. D. Dikshit, B. E. Rhoades and others had studied neoclassical results on the summability of Fourier series from 1960 to 1989. We investigate the results on the summability for Fourier series from 1990 to 2010 in section 3. In conclusion, we present the research minor lineage on summability for Fourier series from 1960 to 2010. $H{\ddot{u}}seyin$ Bor is the earliest researcher on ${\mid}{\bar{N}},p_n{\mid}_k$-summability. Thus we consider his research results and achievements on ${\mid}{\bar{N}},p_n{\mid}_k$-summability and ${\mid}{\bar{N}},p_n,{\gamma}{\mid}_k$-summability.

• Journal of the Korean Society of Fashion and Beauty
• /
• v.1 no.1 s.1
• /
• pp.27-47
• /
• 2003

This research is to build the foundation of systematic application of color in cosmetology by analyzing color attributes in women's makeup presentation. The result were as follows. 1. The most popular color series in make up were R then RP and YR. The most popular color tone is 'd' and 'lt'. 2. Colors in make up according to age was as follows. For eye shadow, people aged 18 to 24 used 'lt' tone of the R color series; people aged 25 to 34 used 'lt', 's', 'sf tone of the R color series, 'lt' tone of the PB color series, 'lt' tone of the YR color series; people over 35 'g' tone of the YR color series, 'sf' tone of the P color series. For lipstick, people aged 18 to 24 used 'd' tone of the R color series; people aged 25 to 34 used 'd', 'sf' tone of the R color series; people over 35 used 'd' tone of the R color series. For lip-gloss, people aged 18 to 24 used 'v', 'lt', 'b', 's' tone of the R color series; people aged 25 to 34 used 's' 'd' 'dp' 'sf' tone of the R color series; people over 35 used 'b' tone of the R color series. 3. Make up colors according to marital status was as follows. For eye shadow, while married interviewees used 's', 'dk' tone of the R color series, single interviewees used 'lt', 'sf' tone of the R color series. For lipstick, while married interviewees used 'd', 'g' tone of the R color series, single interviewees preferred to use madder 'd', 'sf' tone of the R color series. For lip-gross, while married interviewees used 'd' tone of the R color series, single interviewees used 'b' tone of the R color series the most.

• East Asian mathematical journal
• /
• v.16 no.1
• /
• pp.81-87
• /
• 2000

Bose and Mitra obtained certain interesting tansformations of the generalized hypergeometric series by using some known summation formulas and employing suitable contour integrations in complex function theory. The authors aim at providing another transformation of the generalized hypergeometric series by making use of the technique as those of Bose and Mitra and a known summation formula, which Bose and Mitra did not use, for the Gaussian hypergeometric series.