• Honam Mathematical Journal
• /
• v.34 no.1
• /
• pp.35-44
• /
• 2012

Motivated by the extension of classical Dixon's summation theorem for the series $_3F_2$ given by Lavoie, Grondin, Rathie and Arora, the authors aim at deriving four generalized summation formulas, which, upon specializing their parameters, give many summation identities including, especially, the four very interesting summation formulas due to Ramanujan.

• Communications of the Korean Mathematical Society
• /
• v.30 no.3
• /
• pp.227-237
• /
• 2015

By employing certain extended classical summation theorems, several surprising ${\pi}$ and other formulae are displayed.

• Communications of the Korean Mathematical Society
• /
• v.25 no.3
• /
• pp.385-389
• /
• 2010

In 1997, Exton, by mainly employing a widely-used process of resolving hypergeometric series into odd and even parts, obtained some new and interesting summation formulas with arguments 1 and -1. We aim at showing how easily many summation formulas can be obtained by simply combining some known summation formulas. Indeed, we present 22 results in the form of two generalized summation formulas for the generalized hypergeometric series $_4F_3$, including two Exton's summation formulas for $_4F_3$ as special cases.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.3
• /
• pp.469-475
• /
• 2005

The authors aim at deriving four generalized summation formulas, which, upon specializing their parameters, give many summation identities including, especially, the four very interesting summation formulas due to Ramanujan. The results are derived with the help of generalized Dixon's theorem obtained earlier by Lavoie, Grondin, Rathie, and Arora.

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

• The Korean Journal of Pain
• /
• v.21 no.2
• /
• pp.126-130
• /
• 2008

Background: Females generally have a lower pain and temporal summation threshold than men. However, the results of studies designed to evaluate gender differences in the thresholds of heat pain and the temporal summation have been inconsistent. Newly developed device, CHEPS (Contact Heat Evoked Potential Stimulation) model of PATHWAY, have superiority on its fast rise and return time in temperature. Therefore we investigated gender differences in heat pain and temporal summation threshold. Methods: Forty healthy volunteers (20 males and 20 females) were enrolled in this study. A thermode was applied to the volar side of each volunteer's left forearm and heat pain and the temporal summation threshold was then measured. The heat pain threshold was estimated using the staircase method by starting from $36^{\circ}C$ and then increasing the temperature in $0.5^{\circ}C$ increments. The temporal summation threshold was estimated by applying five successive stimulation of the same temperature starting at $2^{\circ}C$ lower than the heat pain threshold and then increasing the temperature in $0.5^{\circ}C$ increments. Results: The mean heat pain thresholds was found to be $41.63{\pm}1.63^{\circ}C$ for males and $41.60{\pm}1.84^{\circ}C$ for females and the temporal summation thresholds were found to be $40.83{\pm}1.64^{\circ}C$ for males and $40.77{\pm}1.93^{\circ}C$ for females. The differences between males and females were not statistically significant. Conclusions: The result of this study suggested that there are no gender differences in heat pain and temporal summation threshold.

• Communications of the Korean Mathematical Society
• /
• v.30 no.2
• /
• pp.103-108
• /
• 2015

Fox [2] presented an interesting identity for $_pF_q$ which is expressed in terms of a finite summation of $_pF_q$'s whose involved numerator and denominator parameters are different from those in the starting one. Moreover Fox [2] found a very interesting and general summation formula for $_3F_2(1/2)$ as a special case of his above-mentioned general identity with the help of Kummer's second summation theorem for $_2F_1(1/2)$. Here, in this paper, we show how two general summation formulas for $$_3F_2\[\array{\hspace{110}{\alpha},{\beta},{\gamma};\\{\alpha}-m,\;\frac{1}{2}({\beta}+{\gamma}+i+1);}\;{\frac{1}{2}}\]$$, m being a nonnegative integer and i any integer, can be easily established by suitably specializing the above-mentioned Fox's general identity with, here, the aid of generalizations of Kummer's second summation theorem for $_2F_1(1/2)$ obtained recently by Rakha and Rathie [7]. Several known results are also seen to be certain special cases of our main identities.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.14 no.1
• /
• pp.71-77
• /
• 2004

It was proved that Hen is an algebraic ,elation of degree [n(l+1]/2] for an (n, 1)-combine. which consists of n LFSRs and l memory bits. For the summation generator with $2^k$ LFSRs which uses k memory bits, we show that there is a non-trivial relation of degree at most $2^k$ using k+1 consecutive outputs. In general, for the summation generator with n LFSRs, we can construct a non-trivial algebraic relation of degree at most 2$^{{2^{[${log}_2$}n]}}$ using [${log}_2$＋1 consecutive outputs.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.16 no.1
• /
• pp.65-70
• /
• 2006

It is hewn that we can apply algebraic attacks on combiners with memory such as summation generators. [1,8] To apply algebraic attacks on combiners with memory, we need to construct algebraic relations between the keystream bits and the initial bits of the LFSRs. Until now, all known methods produce algebraic relations involving several consecutive bits of keystream. [l.4.8] In this paper, we show that algebraic relations involving only one keystream bit can be constructed for summation generators. We also show that there is an algebraic relation involving only one keystream bit for ISG (9) proposed by Lee and Moon. Using this fact, we analyze the keystream generators which generate the keystreams by combining summation generators.

• East Asian mathematical journal
• /
• v.33 no.5
• /
• pp.527-531
• /
• 2017

We aim to prove a known summation formula for the series $_4F_3(1)$ by mainly using a similar method as in [2], which is different from that in [3]. The method of proof here as well as that in [2] is potentially useful in getting some other summation formulas for $_pF_q$.