• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.185-191
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• 2010

Srivastava noticed the existence of three additional complete triple hypergeometric functions $H_A$, $H_B$ and $H_C$ of the second order in the course of an extensive investigation of Lauricella's fourteen hypergeometric functions of three variables. In 2004, Rathie and Kim obtained four summation formulas containing a large number of very interesting reducible cases of Srivastava's triple hypergeometric series $H_A$ and $H_C$. Here we are also aiming at presenting two unified summation formulas (actually, including 62 ones) for some reducible cases of Srivastava's $H_C$ with the help of generalized Dixon's theorem and generalized Whipple's theorem on the sum of a $_3F_2$ obtained earlier by Lavoie et al.. Some special cases of our results are also considered.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.277-290
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• 2020

We propose and analyze a chord summation algorithm, which combines the ideas of Viète and Archimedes to calculate the value of π. The error of the algorithm decreases exponentially per iteration and becomes pinched at a critical iteration, depending on the accuracy of the first input value, ${\sqrt{2}}$. The critical iteration is also analyzed.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.865-874
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• 2017

In the theory of hypergeometric and generalized hypergeometric series, classical summation theorems have been found interesting applications in obtaining various series identities for ${\Pi}$, ${\Pi}^2$ and ${\frac{1}{\Pi}}$. The aim of this research paper is to provide twelve general formulas for ${\frac{1}{\Pi}}$. On specializing the parameters, a large number of very interesting series identities for ${\frac{1}{\Pi}}$ not previously appeared in the literature have been obtained. Also, several other results for multiples of ${\Pi}$, ${\Pi}^2$, ${\frac{1}{{\Pi}^2}}$, ${\frac{1}{{\Pi}^3}}$ and ${\frac{1}{\sqrt{\Pi}}}$ have been obtained. The results are established with the help of the extensions of classical Gauss's summation theorem available in the literature.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.151-156
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• 2011

In this research paper, motivated by the extension of the Euler type I transformation obtained very recently by Rathie and Paris, the authors aim at presenting the extensions of Euler type II transformation. In addition to this, a natural extension of the classical Saalsch$\ddot{u}$tz's summation theorem for the series $_3F_2$ has been investigated. Two interesting applications of the newly obtained extension of classical Saalsch$\ddot{u}$tz's summation theorem are given.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.6
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• pp.267-271
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• 2002

The Hotelling transform is based on statistical properties of an image. The principal uses of this transform are in data compression. The basic concept of the Hotelling transform is that the choice of basis vectors pointing the direction of maximum variance of the data. This property can be used for rotation normalization. Many objects of interest in pattern recognition applications can be easily standardized by performing a rotation normalization that aligns the coordinate axes with the axes of maximum variance of the pixels in the object. However, this transform can not be used to rotation normalization of color images directly. In this paper, we propose a new method for rotation normalization of color images based on the Hotelling transform. The Hotelling transform is performed to calculate basis vectors of each channel. Then the summation of vectors of all channels are processed. Rotation normalization is performed using the result of summation of vectors. Experimental results showed the proposed method can be used for rotation normalization of color images effectively.

• Journal of Digital Convergence
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• v.3 no.1
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• pp.115-148
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• 2005

This study is intended to suggest a more reasonable and practical method of estimating discount & capitalization rate for valuation of closely-held culture content business, that is, to modify the Buildup Summation Model(which is recommended for the closely-held business by the NACVA) by adopting the weighted ratings in the CT Project Investment Evaluation of the Korea Culture Contents Association to risk factors of the Buildup Summation Model. This method is ease to apply for closely-held culture content business and has advantages in applying the weighted rates based on the characteristics of respective culture contents. And it can make up for the Weighted Average Cost of Capital (WACC) which shows generally low discount rates.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.395-403
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• 2005

The authors aim mainly at giving fifteen three-term contiguous relations for the basic hypergeometric series $series\;_2{\phi}_1$ corresponding to Gauss's contiguous relations for the hypergeometric series $series\;_2F_1$ given in Rainville([6], p.71). They also apply them to obtain two summation formulas closely related to a known q-analogue of Kummer's theorem.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.439-446
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• 2015

The main objective of this paper is to establish certain explicit expressions for the Humbert functions ${\Phi}_2$(a, a + i ; c ; x, -x) and ${\Psi}_2$(a ; c, c + i ; x, -x) for i = 0, ${\pm}1$, ${\pm}2$, ..., ${\pm}5$. Several new and known summation formulas for ${\Phi}_2$ and ${\Psi}_2$ are considered as special cases of our main identities.

• East Asian mathematical journal
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• v.25 no.4
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• pp.481-486
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• 2009

The first object of this note is to show that a summation formula due to Padmanabham for three-variables hypergeometric function $X_8$ introduced by Exton can be proved in a different (from Padmanabham's and his observation) yet, in a sense, conventional method, which has been employed in obtaining a variety of identities associated with hypergeometric series. The second purpose is to point out that one of two seemingly new hypergeometric identities due to Exton was already recorded and the other one is easily derivable from the first one. A corrected and a little more compact form of a general transform involving hypergeometric functions due to Exton is also given.

• Journal of Digital Contents Society
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• v.1 no.1
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• pp.53-64
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• 2000

This paper is related to color image segmentation scheme which makes it possible to achieve the excellent segmented results by block-based segmentation using Y/C bit-plane summation image. First, normalized chrominance summation image is obtained by normalizing the image which is summed up the absolutes of color-differential values between R, G, B images. Secondly, upper 2 bits of the luminance image and upper 6bits of and the normalized chrominance summation image are bitwise operated by the pixel to generate the Y/C bit-plane summation image. Next, the Y/C bit-plane summation image divided into predetermined block size, is classified into monotone blocks, texture blocks and edge blocks, and then each classified block is merged to the regions including one more blocks in the individual block type, and each region is selectively allocated to unique marker according to predetermined marker allocation rules. Finally, fine segmented results are obtained by applying the watershed algorithm to each pixel in the unmarked blocks. As shown in computer simulation, the main advantage of the proposed method is that it suppresses the over-segmentation in the texture regions and reduces computational load. Furthermore, it is able to apply global parameters to various images with different pixel distribution properties because they are nonsensitive for pixel distribution. Especially, the proposed method offers reasonable segmentation results in edge areas with lower contrast owing to the regional characteristics of the color components reflected in the Y/C bit-plane summation image.