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

• Honam Mathematical Journal
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• v.38 no.3
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• pp.479-494
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• 2016

In this paper, using a transformation formula for a certain series which comes from the generalized non-analytic Eisenstein series, we obtained some infinite series identities which contain Ramanujan's formula and author's previous results.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.391-401
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• 2012

B. C. Berndt has found a transformation formula for a large class of functions, which comes from a transformation formula for a more general class of Eisenstein series. In this paper, using his formula which is 'twisted' by change of variables, we find a class of infinite series identities.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.285-292
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• 2013

B. C. Berndt computed the Fourier series of a class of generalized Eisenstein series, which gives an analytic continuation to the generalized Eisenstein series. In this paper, continuing his work, we consider generalized non-holomorphic Eisenstein series and give an analytic continuation to the $s$-plane.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.451-461
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• 2012

B.C. Berndt has established many relations between various infinite series using a transformation formula for a large class of functions, which comes from a more general class of Eisenstein series. In this paper, continuing his study, we find some infinite series identities.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.481-502
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• 2011

B. C. Berndt [4, 5] evaluated several classes of infinite series and established many relations between various infinite series. In this paper, continuing his work, we derive new relations between infinite series.

• East Asian mathematical journal
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• v.39 no.3
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• pp.299-303
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• 2023

The aim of this note is to provide three derivations of the well-known Gregory-Leibniz series for π via a hypergeometric series approach.

• Journal of Advanced Marine Engineering and Technology
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• v.8 no.1
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• pp.100-111
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• 1984

The methods solving the 2nd order linear ordinary differential equations of the form y"+H(x)y'+G(x)y=P(x) using Fourier series are presented in this paper. These methods are applied to the differential equations of which the exact solutions are known, and the solutions by Fourier series are compared with the exact solutions. The main results obtained in these studies are summarized as follows; 1) The product and the quotient of two functions expressed in Fourier series can be expressed also in Fourier series and the relations between the Fourier coefficients of the series are obtained by multiplying term by term. 2) If the solution of the 2nd order lindar ordinary differential equation exists in a certain interval, the solution can be obtained using Fourier series and can be expressed in Fourier series. 3) The absolute errors of Fourier series solutions are generally less in the center of the interval than in the end of the interval. 4) The more terms are considered in Fourier series solutions, the less the absolute errors.rors.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.377-381
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• 2005

We present a convenient recursive formula for the sums of alternating harmonic series of odd order. The recursion is obtained by expanding in Fourier series certain elementary functions.

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