• Journal of the Society of Naval Architects of Korea
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• v.41 no.1
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• pp.1-7
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• 2004

GUI program for analyzing directional spectrum waves is introduced in this paper Basically, MLM (Maximum Likelihood Method) was used for this program which was additionally consisted of performing spectral and time domain analysis for two dimensional irregular waves. Moreover, the directionality of directional spectrum waves generated by single summation and double summation method was investigated based on MLM. The directionality from each summation method has good agreement compared with that of target wave spreading function in the case of single wide directional spectrum waves. In addition to this, the resolution of directionality in double summation method was investigated as introducing coherence function between each wave component

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.979-990
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• 2017

Inspired by the results obtained by Brychkov ([2]), the authors evaluate a large number of new and interesting double definite integrals. The results are obtained with the use of classical hypergeometric summation theorems and a well-known double finite integral due to Edwards ([3]). The results are given in terms of Psi and Hurwitz zeta functions suitable for numerical computations.

• 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.

• Kyungpook Mathematical Journal
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• v.18 no.2
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• pp.245-249
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• 1978

• Journal of Information Processing Systems
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• v.13 no.3
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• pp.573-589
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• 2017

Cloud computing is an attractive solution that can provide low cost storage and powerful processing capabilities for government agencies or enterprises of small and medium size. Yet the confidentiality of information should be considered by any organization migrating to cloud, which makes the research on relational database system based on encryption schemes to preserve the integrity and confidentiality of data in cloud be an interesting subject. So far there have been various solutions for realizing SQL queries on encrypted data in cloud without decryption in advance, where generally homomorphic encryption algorithm is applied to support queries with aggregate functions or numerical computation. But the existing homomorphic encryption algorithms cannot encrypt floating-point numbers. So in this paper, we present a mechanism to enable the trusted party to encrypt the floating-points by homomorphic encryption algorithm and partial trusty server to perform summation on their ciphertexts without revealing the data itself. In the first step, we encode floating-point numbers to hide the decimal points and the positive or negative signs. Then, the codes of floating-point numbers are encrypted by homomorphic encryption algorithm and stored as sequences in cloud. Finally, we use the data structure of DoubleListTree to implement the aggregate function of SUM and later do some extra processes to accomplish the summation.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.809-816
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• 2018

The aim of this research paper is to evaluate fifty double integrals invoving generalized hypergeometric function (25 each) in the form of $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c-1}(1-x)^{c-1}(1-y)^{c+{\ell}}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{(1-x)y}{1-xy}}\]dxdy$$ and $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c+{\ell}}(1-x)^{c+{\ell}}(1-y)^{c-1}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{1-y}{1-xy}}\]dxdy$$ in the most general form for any ${\ell}{\in}{\mathbb{Z}}$ and i, j = 0, ${\pm}1$, ${\pm}2$. The results are derived with the help of generalization of Edwards's well known double integral due to Kim, et al. and generalized classical Watson's summation theorem obtained earlier by Lavoie, et al. More than one hundred ineteresting special cases have also been obtained.

• 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.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.271-289
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• 2018

Let 0 < q < ${\infty}$. In this study, we introduce the spaces ${\mathcal{BV}}_q$ and ${\mathcal{LS}}_q$ of q-bounded variation double sequences and q-summable double series as the domain of four-dimensional backward difference matrix ${\Delta}$ and summation matrix S in the space ${\mathcal{L}}_q$ of absolutely q-summable double sequences, respectively. Also, we determine their ${\alpha}$- and ${\beta}-duals$ and give the characterizations of some classes of four-dimensional matrix transformations in the case 0 < q ${\leq}$ 1.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.26-34
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• 2021

In this paper two interesting double integrals involving product of two generalized hypergeometric functions have been evaluated in terms of gamma function. The results are derived with the help of known integrals involving hypergeometric functions recorded in the paper of Rathie et al. [6]. We also give several very interesting special cases.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.111-117
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• 2021

In this paper we aim to establish a new class of six definite double integrals in terms of gamma functions. The results are obtained with the help of some definite integrals obtained recently by Kim and Edward equality. The results established in this paper are simple, interesting, easily established and may be useful potentially.