• 대한수학회보
• /
• 제50권5호
• /
• pp.1673-1681
• /
• 2013

The main objective of this paper is to show how one can obtain eleven new and interesting hypergeometric identities in the form of a single result from the old ones by mainly employing the known beta integral method which was recently introduced and used in a systematic manner by Krattenthaler and Rao [6]. The results are derived with the help of a generalization of a well-known hypergeometric transformation formula due to Kummer. Several identities including one obtained earlier by Krattenthaler and Rao [6] follow as special cases of our main results.

• 대한수학회지
• /
• 제53권6호
• /
• pp.1261-1273
• /
• 2016

In this paper, we analyze the necessary and sufficient condition introduced in [5]: that a functional F in $L^2(C_{a,b}[0,T])$ has an integral transform ${\mathcal{F}}_{{\gamma},{\beta}}F$, also belonging to $L^2(C_{a,b}[0,T])$. We then establish the inverse integral transforms of the functionals in $L^2(C_{a,b}[0,T])$ and then examine various properties with respect to the inverse integral transforms via the translation theorem. Several possible outcomes are presented as remarks. Our approach is a new method to solve some difficulties with respect to the inverse integral transform.

• 대한수학회논문집
• /
• 제28권2호
• /
• pp.297-301
• /
• 2013

When certain general single or multiple hypergeometric functions were introduced, their reduction formulas have naturally been investigated. Here, in this paper, we aim at presenting a very interesting reduction formula for the Srivastava's triple hypergeometric function $F^{(3)}[x,y,z]$ by applying the so-called Beta integral method to the Henrici's triple product formula for hypergeometric series.

• Kyungpook Mathematical Journal
• /
• 제55권2호
• /
• pp.439-447
• /
• 2015

Very recently the authors have obtained a very interesting reduction formula for the Srivastava's triple hypergeometric series $F^{(3)}$(x, y, z) by applying the so-called Beta integral method to the Henrici's triple product formula for the hypergeometric series. In this sequel, we also present three more interesting reduction formulas for the function $F^{(3)}$(x, y, z) by using the well known identities due to Bailey and Ramanujan. The results established here are simple, easily derived and (potentially) useful.

• 한국해양공학회:학술대회논문집
• /
• 한국해양공학회 2001년도 추계학술대회 논문집
• /
• pp.164-168
• /
• 2001

The motion of a ship advancing in regular waves is analyzed in the time-domain using the convolution integral of the radiation forces. The memory effect functions and infinite frequency added masses are obtained from the solution of the three dimensional improved Green integral equation in the frequency domain by making use of the Fourier transformation. The ship motions in regular waves have been calculated by both the time and frequency domain methods. It has been shown that they agree very well with each other. The present time-domain method can be used to predict the time histories of unsteady motions in irregular waves. It can also be used to calculate the hydrostatic and Froude-Krylov forces over the instantaneous wetted surface of the ship hull to predict large ship motions, in a practical sense, advancing in large amplitude waves.

• 대한화학회지
• /
• 제13권4호
• /
• pp.281-287
• /
• 1969

Arymethychloride의 교환반응에 대한 반응속도 상수를 측정하고 또한 활성화 파라메터를 결정하였다.Substrate의 반응도를 섭동분자궤도(PMO)법으로 설명하였으며 HSAB원리를 이에 적용하였다. 또한 전이상태에서의 탄소-염소공명적분값이 탄소-탄소 공명자분값이 약 67%임을 밝혔다.

• 대한수학회논문집
• /
• 제29권3호
• /
• pp.429-437
• /
• 2014

Motivated by the recent investigations of several authors, in this paper we present a generalization of a result obtained recently by Choi et al. ([3]) involving hypergeometric identities. The result is obtained by suitably applying fractional calculus method to a generalization of the hypergeometric transformation formula due to Kummer.

• Biomolecules & Therapeutics
• /
• 제1권2호
• /
• pp.188-195
• /
• 1993

In order to understand the machanism of action and regulation of ${\beta}$-adrenergic receptor in terms of molecular level, the purification of receptor protein has a fundamental importance. Moreover, species differences among avian, amphibian and mammalian ${\beta}$-adrenergic receptors make it more important to purify mammalian ${\beta}$-adrenergic receptor. Because ${\beta}$-adrenergic receptor is an integral membrane protein, it must be solubilized from the membrane for the purification. The purpose of the present study was to solubilize and characterize the mammalian $\beta$-adrenergic receptor from guinea pig lung in quantities by more efficient and practical method eventually to purify receptor. Guinea pig lung membrane preparation was solubilized by sequential treatment of buffers containing low and high concentration of digitonin which are 0.2 and 1.2% respectively. About 50% of the total receptor pool was released by this double extraction procedure. The $\beta$-adrenoceptors in the digitonin extract were identified using the ${\beta}$-adrenergic antagonist, (-)-[$^3H$]-dihydroalprenolol ([$^3H$]DHA). The solubilized receptor retained all of the essential characteristics of membrane-bound receptor, namely saturability; stereoselectivity; high affinity to ${\beta}$-adrenergic drugs. For the measurement of soluble receptor activity, Sephadex G-50 chromatography method has been widely used. Inspite of its accuracy and wide acceptance, this technique employed troublesome column work which required long time to assay the activity of receptor. We employed another methods to measure receptor activity. When using 0.5% polyethylenimine pretreated GF/B glass fiber filter, filtration technique could be used to measure soluble receptor activity. This technique enabled us to reduce the total amount of time to assay by a factor of 4 as well as to detect soluble receptor. In the present study, we could establish more efficient and practical solubilization method of mammalian $\beta$-adrenergic receptor. The rapidity and high yield of this solubilization scheme, together with the favorable recovery of the receptor activity, are significant steps toward the ultimate purification of the mammalian $\beta$-adrenergic receptor. The result of this study together with more convenient purification method could provide large amount of purified receptor with ease for various research purposes.

• 대한수학회논문집
• /
• 제22권4호
• /
• pp.509-512
• /
• 2007

We aim at deriving Gauss's second summation theorem for the series $_2F_1(1/2)$ by using Euler's integral representation for $_2F_1$. It seems that this method of proof has not been tried.

• Journal of Mechanical Science and Technology
• /
• 제16권8호
• /
• pp.1053-1063
• /
• 2002

This paper presents a robust nonlinear controller for a f degree of freedom (DOF) parallel manipulator in the task space coordinates. The proposed control strategy requires information on orientations and translations in the task space unlike the joint space or link space control scheme. Although a 6 DOF sensor may provide such information in a straightforward manner, its cost calls for a more economical alternative. A novel indirect method based on the readily available length information engages as a potential candidate to replace a 6 DOF sensor. The indirect approach generates the necessary information by solving the forward kinematics and subsequently applying alpha-beta-gamma tracker With the 6 DOF signals available, a robust nonlinear task space control (RNTC) scheme is proposed based on the Lyapunov redesign method, whose stability is rigorously proved. The performance of the proposed RNTC with the new estimation scheme is evaluated via experiments. First, the results of the estimator are compared with the rate-gyro signals, which indicates excellent agreement. Then, the RNTC with on-line estimated 6 DOF data is shown to achieve excellent control performance to sinusoidal inputs, which is superior to those of a commonly used proportional-plus-integral-plus-derivative controller with a feedforward friction compensation under joint space coordinates and the nonlinear controller under task space coordinates.