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

• Honam Mathematical Journal
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• v.43 no.2
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• pp.221-237
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• 2021

B. C. Berndt has found modular transformation formulae for a large class of functions coming from generalized Eisenstein series. Using those formulae, he established a lot of infinite series identities, some of which explain many infinite series identities given by Ramanujan. Continuing his work, the author proved a lot of new infinite series identities. Moreover, recently the author found transformation formulae for a class of functions coming from generalized non-holomorphic Eisenstein series. In this paper, using those formulae, we evaluate a few new infinite series identities which generalize the author's previous results.

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

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.209-222
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• 2015

Time series are used in many studies for model building and analysis. We must be very careful to understand the kind of time series data used in the analysis. In this review article, we will begin with some issues related to the use of aggregate and systematic sampling time series. Since several time series are often used in a study of the relationship of variables, we will also consider vector time series modeling and analysis. Although the basic procedures of model building between univariate time series and vector time series are the same, there are some important phenomena which are unique to vector time series. Therefore, we will also discuss some issues related to vector time models. Understanding these issues is important when we use time series data in modeling and analysis, regardless of whether it is a univariate or multivariate time series.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1511-1528
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• 2020

A skew generalized power series ring R[[S, 𝜔]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action 𝜔 of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are skew polynomial rings, skew Laurent polynomial rings, skew power series rings, skew Laurent series rings, skew monoid rings, skew group rings, skew Mal'cev-Neumann series rings, the "untwisted" versions of all of these, and generalized power series rings. In this paper we obtain some necessary conditions on R, S and 𝜔 such that the skew generalized power series ring R[[S, 𝜔]] is (uniquely) clean. As particular cases of our general results we obtain new theorems on skew Mal'cev-Neumann series rings, skew Laurent series rings, and generalized power series rings.

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

• Journal for History of Mathematics
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• v.27 no.4
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• pp.285-297
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• 2014

G. H. Hardy laid the foundation of classical studies on double Fourier series at the beginning of the 20th century. In this paper we are concerned not only with Fourier series but more generally with trigonometric series. We consider Norlund means and Cesaro summation method for double Fourier Series. In section 2, we investigate the classical results on the summability and the convergence of double Fourier series from G. H. Hardy to P. Sjolin in the mid-20th century. This study concerns with the $L^1(T^2)$-convergence of double Fourier series fundamentally. In conclusion, there are the features of the classical results by comparing and reinterpreting the theorems about double Fourier series mutually.

• Proceedings of the SAREK Conference
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• 2009.06a
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• pp.1332-1336
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• 2009

If water-chillers are arranged in series-series counterflow, compressor lift of each chiller will be decreased in comparison with water-chillers in parallel. That means that compressor power of the chillers in series will be lower than that of chillers in parallel. However, the pressure drop of the water flow through the chillers in series will increase, and thus increase the power of water pumps. This disadvantage will be made good by increasing the temperature difference of water flow through evaporator and condenser, but the water flow rates will decrease. This paper explores the optimal parameters in system of series-series counterflow for central chilled water plants such as the leaving chilled water temperature, the leaving condenser water temperature, condenser water flow rate and number of chillers in series.

• Industrial Engineering and Management Systems
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• v.7 no.1
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• pp.9-22
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• 2008

As an extension of a previous work by the authors (Song and Esogbue, 2006), a new algorithm for automated modeling of nonstationary seasonal time series is presented in this paper. Issues relative to the methodology for building automatically seasonal time series models and periodic time series models are addressed. This is achieved by inspecting the trend, estimating the seasonality, determining the orders of the model, and estimating the parameters. As in our previous work, the major instruments used in the model identification process are correlograms of the modeling errors while the least square method is used for parameter estimation. We provide numerical illustrations of the performance of the new algorithms with respect to building both seasonal time series and periodic time series models. Additionally, we consider forecasting and exercise the models on some sample time series problems found in the literature as well as real life problems drawn from the retail industry. In each instance, the models are built automatically avoiding the necessity of any human intervention.

• The korean journal of orthodontics
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• v.53 no.3
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• pp.163-174
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• 2023

Objective: This study evaluated the influence of various gingival displays on the esthetic perception in the presence of upper dental midline discrepancy. Methods: A smiling image of a male subject was altered digitally to produce five image series: normal smile (series A), decreased tooth show (series B), increased gingival show (series C), maxillary cant (series D), and asymmetric upper lip elevation (series E). In each image series, the midline was deviated to the right and left incrementally. A total of 210 raters (four professional groups and laypersons, n = 42 in each group) determined the midline deviation threshold and the attractiveness of midline position in each series. Results: The right and left thresholds were statistically similar for the symmetrical series (A, B, and C), while for series D, the right threshold was significantly lower. In most rater groups, the mean threshold order was: B > A > E > C > D. In all the series, the raters selected the coincident midline as the most attractive series except for series D, for which 1-2-mm deviations to the left were selected as the most attractive by almost all the groups. Conclusions: It is crucial to establish the coincident midline position in a symmetrical smile, especially when a gummy smile exists. In the asymmetrical gingival show, a coincident midline might not be the most esthetic midline position.