• 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.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.731-742
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• 2009

In this paper, by introducing parameters ${\lambda}$, ${\alpha}$and two pairs of conjugate exponents (p, q), (r, s) and applying the improved Euler-Maclaurin's summation formula, we establish a reverse of the slightly sharper Hilbert-type inequality. As applications, the strengthened version and the equivalent form are given.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.597-614
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• 2015

In this paper, we study some properties of the generalized Apostol type Hermite-based polynomials. which extend some known results. We also deduce some properties of the generalized Apostol-Bernoulli polynomials, the generalized Apostol-Euler polynomials and the generalized Apostol-Genocchi polynomials of high order. Numerous properties of these polynomials and some relationships between $F_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ and $_HF_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.

• Proceedings of the Korean Society of Computer Information Conference
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• 2014.01a
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• pp.273-274
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• 2014

4-2 압축기는 곱셈기의 부분 곱 합 트리(partial product summation tree)의 기본적인 구성요소이다. 본 논문은 고속 연산이 가능한 4-2 압축기의 구조를 제안한다. 제안한 구조는 최적화된 XOR-XNOR와 MUX로 구성된다 이 구조는 기존의 구조에 비해 신호 전달시간이 감소하여 고속 연산이 가능한 장점을 갖는다.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.21-24
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• 2003

In the recent papers by Harris and Park (1994) and by Hui and Park (2000), a family of lattice distributions derived from a sum of independent identically distributed random variables is examined. In this paper we generalize a result of Hui and Park (2000) on lattice distributions on the torus using the Poisson summation formula.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.5-12
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• 1998

We evaluate the sum of certain class of generalized hypergeometric series of unit argument. Summation formulas, contiguous to Watson's, Whipple's, Lavoie's and Choi's theorems in the theory of the generalized hypergeometric series, are obtained. Certain limiting cases of these results are given.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.473-496
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• 2022

In 2014, Liu and Wang established a large number of interesting reduction, transformation and summation formulas for the Kampé de Fériet function. Inspired by the work, we aim to find further several transformation and reduction formulas for the Kampé de Fériet function. Theses formulas are mainly based on the formulas given by Liu and Wang [33].

• 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.

• Investigative Magnetic Resonance Imaging
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• v.22 no.1
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• pp.18-25
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• 2018

Purpose: To investigate the various imaging factors associated with aggravation of lumbar disc herniation (LDH) and develop a scoring system for prediction of LDH aggravation. Materials and Methods: From 2015 to 2017, we retrospectively reviewed the magnetic resonance imaging (MRI) findings of 60 patients (30 patients with aggravated LDH and 30 patients without any altered LDH). Imaging factors for MRI evaluation included the level of LDH, disc degeneration, back muscle atrophy, facet joint degeneration, ligamentum flavum thickness and interspinous ligament degeneration. Flexion-extension difference was measured with simple radiography. The scoring system was analyzed using receiver operating characteristic (ROC) analysis. Results: The aggravated group manifested a higher grade of disc degeneration, back muscle atrophy and facet degeneration than the control group. The ligamentum flavum thickness in the aggravated group was thicker than in the group with unaltered LDH. The summation score was defined as the sum of the grade of disc degeneration, back muscle atrophy and facet joint degeneration. The area under the ROC curve showing the threshold value of the summation score for prediction of aggravation of LDH was 0.832 and the threshold value corresponded to 6.5. Conclusion: Disc degeneration, facet degeneration, back muscle atrophy and ligamentum flavum thickness are important factors in predicting aggravation of LDH and may facilitate the determination of treatment strategy in patients with LDH. The summation score is available as supplemental data.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.7C
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• pp.640-648
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• 2009

Summation generator with high period and high linear complexity can be easily implemented by a simple hardware or software and it is proper to apply in mobile security system for ubiquitous environments. However the generator has been some weaknesses from Dawson's divided-and-conquer attack, Golic's correlation attack and Meier's fast correlation attack. In this paper, we propose an improved version($2^{128}$security level) of $E_0$algorithm, CVC-NSG(Circular-Clock-Controlled - Nonlinear Summation Generator), which partially replaces LFSRs with nonlinear FSRs and controls the irregular clock to reinforce it's own weaknesses. Finally, we analyze our proposed design in terms of security and performance.