• 대한수학회보
• /
• 제49권3호
• /
• pp.621-633
• /
• 2012

By establishing a new summation formula for the series $_3F_2(\frac{1}{2})$, recently Rathie and Pogany have obtained an interesting result known as Kummer type II transformation for the generalized hypergeometric function $_2F_2$. Here we aim at deriving their result by using a very elementary method and presenting two elegant results for certain terminating series $_3F_2(2)$. Furthermore two interesting applications of our new results are demonstrated.

• Kyungpook Mathematical Journal
• /
• 제47권3호
• /
• pp.449-454
• /
• 2007

InIn this paper we consider generalizations of the classical Dixon's theorem and the classical Whipple's theorem on the sum of a $_3F_2$. The results are derived with the help of generalized Watson's theorem obtained earlier by Mitra. A large number of results contiguous to Dixon's and Whipple's theorems obtained earlier by Lavoie, Grondin and Rathie, and Lavoie, Grondin, Rathie and Arora follow special cases of our main findings.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제25권1호
• /
• pp.7-16
• /
• 2018

The main objective of this paper is to demonstrate how one can obtain very quickly so far unknown Laplace transforms of rather general cases of the generalized hypergeometric function $_3F_3$ by employing generalizations of classical summation theorems for the series $_3F_2$ available in the literature. Several new as well known results obtained earlier by Kim et al. follow special cases of main findings.

• 호남수학학술지
• /
• 제37권3호
• /
• pp.339-352
• /
• 2015

We aim at giving explicit expressions of $${\sum_{m,n=0}^{{\infty}}}{\frac{{\Delta}_{m+n}(-1)^nx^{m+n}}{({\rho})_m({\rho}+i)_nm!n!}$$, where i = 0, ${\pm}1$, ${\ldots}$, ${\pm}9$ and $\{{\Delta}_n\}$ is a bounded sequence of complex numbers. The main result is derived with the help of the generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Choi. Further some special cases of the main result considered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.

• 한국공간구조학회논문집
• /
• 제13권2호
• /
• pp.75-82
• /
• 2013

For each cable component in a cable dome structure, pre-tension is needed for stability of whole the structure. The summation of these pre-tension at each joint should be zero to achieve the self equilibrium structure. The first step in cable dome structure analysis is to find the ratio of pre-tension in each member which can produce a stable and structure on self-equilibrium. In this paper, a new method based on the basic principle of closed force polygon for equilibrium system is proposed for the determination of self-equilibrium mode of cable dome structure. A single layer cable dome and two multi layer type domes have been analyzed. The ratios of cable members are determined by the presented method, and check the validation of the results by numerical calculation.

• Smart Structures and Systems
• /
• 제17권1호
• /
• pp.59-72
• /
• 2016

The Impact Echo method can be used to measure the thickness of concrete plate like structures. Measurements are based on the identification of a clear thickness resonance frequency which can be difficult in very thick or highly attenuative plates. In this study the detectability of the measured resonant frequency is enhanced by time domain summation of signals with different source receiver spacing. The proposed method is based on the spatial and temporal properties of the first higher symmetric zero group velocity Lamb mode (S1-ZGV) which are described in detail. No application dependent tuning or filtering is needed which makes the method robust and suitable for implementation in automatic IE thickness measurements. The proposed technique is exemplified with numerical data and field data from a thick concrete wall and a highly attenuative asphalt concrete layer.

• 한국광학회지
• /
• 제2권2호
• /
• pp.83-88
• /
• 1991

공간불변(space-invariant) 패턴인식에 대한 연구는 여러 접근방식에서 많은 시도가 이루어지고 있다. 학습 이미지의 가중치 선형조합(weighted linear summation)에 의한 SDF(synthetic discriminant function) 필터를 이용한 패턴인식은 그 중의 한 방식으로서 꾸준히 많은 관심을 받고 있다. 본 논문에서는 off-axis 평면기준파의 각분할(angular multiplexing) 방식과 pseude-inverse 알고리듬에 의한 pSDF 필터를 결합하여 상관기를 구성하고 상관면에서의 상관반응을 관측하여, off-axis pSDF 공간정합필터가 유형분류에 유용함을 입증하고, 광상관기로의 적용가능성을 보여주고자 한다.

• Journal of the Korean Data and Information Science Society
• /
• 제25권6호
• /
• pp.1521-1530
• /
• 2014

The ROC analysis is considered for multiple class diagnosis. There exist many criteria to find optimal thresholds and measure the accuracy of diagnostic tests for k dimensional ROC analysis. In this paper, we proposed a diagnostic accuracy measure called the correct classification simple rate, which is defined as the summation of true rates for each classification distribution and expressed as a function of summation of sequential true rates for two consecutive distributions. This measure does not weight accuracy across categories by the category prevalence and is comparable across populations for multiple class diagnosis. It is found that this accuracy measure does not only have a relationship with Kolmogorov - Smirnov statistics, but also can be represented as a linear function of some optimal threshold criteria. With these facts, the suggested measure could be applied to test for comparing multiple distributions.

• 한국정보과학회:학술대회논문집
• /
• 한국정보과학회 2003년도 가을 학술발표논문집 Vol.30 No.2 (2)
• /
• pp.568-570
• /
• 2003

비월주사(interlaced)에서 순차주사(progressive)로의 변환을 디인터레이싱(de-interlacing)이라 한다. 제안하는 방식은 움직임 검출을 통해 움직임이 없는 영역에서는 앞선 필드정보를 이용하여 별도의 계산량 없이 디인터레이싱을 하게 되며, 움직임이 있는 영역에서는 공간정보(spatial information)를 이용하여 디인터레이싱하는 ELA(Edge based line average) 방식과 양방향 움직임 추정(bi-directional motion estimation)을 통한 시간정보(temporal information)를 이용하여 디인터레이싱하는 움직임 보상방법 간의 가중합산(weighted summation)을 이용하여 디인터레이싱을 수행하는 방법을 제안한다. 이 때 가중치(weight)는 공간 및 시간 정보 모두를 사용하여 결정되어지며, 이렇게 결정되어진 가중치를 통해 각 방식의 단점을 극복하게 된다. 이러한 가중합산을 이용한 방법은 높은 계산복잡도 없이 단순한 구현을 통해 다양한 조건에서 높은 성능의 디인터레이싱이 가능토록 해주며, 그 하드웨어 구현을 용이하게 해준다.

• 대한수학회논문집
• /
• 제16권2호
• /
• pp.319-332
• /
• 2001

The main object of this paper is first to give tow contiguous analogues of a well-known hypergeometric summation formula for $_2$F$_1$(1/2). We then apply each of these analogues with a view to evaluating the sums of several classes of series in terms of Psi(or Digamma) and the Zeta functions. Relevant connections of the series identities presented here with those given elsewhere are also pointed out.