• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.999-1008
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• 2017

By mainly using certain properties arising from the semisimple Lie group SO(2, 1), we aim to show how a family of some interesting formulas for bilateral series and integrals involving Whittaker, Bessel functions, and their product can be obtained.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.357-385
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• 2014

Recently several authors have extended the Gamma function, Beta function, the hypergeometric function, and the confluent hypergeometric function by using their integral representations and provided many interesting properties of their extended functions. Here we aim at giving further extensions of the abovementioned extended functions and investigating various formulas for the further extended functions in a systematic manner. Moreover, our extension of the Beta function is shown to be applied to Statistics and also our extensions find some connections with other special functions and polynomials such as Laguerre polynomials, Macdonald and Whittaker functions.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.1-17
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• 2008

Here, we consider the existence and uniqueness solution of nonlinear integral equation of the second kind of type Volterra-Hammerstein. Also, the normality and continuity of the integral operator are discussed. A numerical method is used to obtain a system of nonlinear integral equations in position. The solution is obtained, and many applications in one, two and three dimensionals are considered.

• Corrosion Science and Technology
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• v.4 no.3
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• pp.75-80
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• 2005

This work dealt with the evaluation of galvanic corrosion rate in a corrosion cell having annular gap of 0.5 mm between carbon steel 1018 and alloy 600 as a function of temperature and boron concentration. Temperature and boron concentration were ranged from 110 to 300 $^{\circ}C$ and 2000~10000 ppm, respectively. After the operating temperature of the corrosion cell where the electrolyte was injected was attained at setting temperature, galvanic coupling was made and at the same time galvanic current was measured. The galvanic corrosion rate decreased with time, which was described by corrosion product such as protective film as well as boric acid deposit formed on the carbon steel with time. From the galvanic current obtained as a function of temperature and boron concentration, it was found that the galvanic corrosion rate decreased with temperaturewhilethe corrosionrate increasedwith boronconcentration. The experimental resultsobtained from galvanic corrosion measurement were explained by adhesive property of corrosion product such as protective film, boric acid deposit formed on the carbon steel wall and dehydration of boric acid to be slightlysolubleboric acid phase.Moreoverthe galvaniccorrosionrate calculatedusing initialgalvaniccoupling current instead of steady state coupling current was remarked, which could give us relatively closer galvanic corrosion rate to real pressurized water reactor.