• Korean Journal of Mathematics
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• v.22 no.1
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• pp.57-69
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• 2014

We obtain a formula for the conditional Wiener integral of the first variation of functionals and establish several integration by parts formulas of conditional Wiener integrals of functionals on a function space. We then apply these results to obtain various integration by parts formulas involving conditional integral transforms and conditional convolution products on the function space.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.443-451
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• 2017

Very recently, Agarwal gave remakably a scads of fractional integral formulas involving various special functions. Using the same technique, we obtain certain(presumably) new fractional integral formulas involving the product of confluent hypergeometric functions. Some interesting special cases of our two main results are considered.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1179-1192
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• 2018

Several addition formulas for a general class of q-Appell sequences are proved. The q-addition formulas, which are derived, involved not only the generalized q-Bernoulli, the generalized q-Euler and the generalized q-Genocchi polynomials, but also the q-Stirling numbers of the second kind and several general families of hypergeometric polynomials. Some q-umbral calculus generalizations of the addition formulas are also investigated.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.1-16
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• 2010

By using the generalized operator method given by Burchnall and Chaundy in 1940, the authors present one-dimensional inverse pairs of symbolic operators. Many operator identities involving these pairs of symbolic operators are rst constructed. By means of these operator identities, 11 decomposition formulas for the generalized hypergeometric $_4F_3$ function are then given. Furthermore, the integral representations associated with generalized hypergeometric functions are also presented.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.809-818
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• 2016

Chaudhary and Choi [7] presented 14 identities which reveal certain interesting interrelations among character formulas, combinatorial partition identities and continued partition identities. In this sequel, we aim to give slightly modified versions for 8 identities which are chosen among the above-mentioned 14 formulas.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.421-435
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• 2001

In this paper we use a general Fubini theorem established in [13] to obtain several Feynman integration formulas involving analytic Fourier-Feynman transforms. Included in these formulas is a general Parseval's relation.

• Journal of KSNVE
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• v.9 no.2
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• pp.331-339
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• 1999

This paper presents the simplified formulas for calculating the fundamental frequencies of the cantilevered bellows in the axial and lateral directions. The frequencies of the bellow are evaluated based on analogies with those of the beam. It is shown that the results calculated by the simplified formulas are in good agreement with those obtained from FEM analysis and the experiment.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.495-513
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• 2021

The hypergeometric series of four variables are introduced and studied by Bin-Saad and Younis recently. In this line, we derive several fractional derivative formulas, integral representations and operational formulas for new quadruple hypergeometric series.

• Journal of Korean Society of Water and Wastewater
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• v.12 no.3
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• pp.99-106
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• 1998

This paper presents a procedure for determining the design rainfall depth and the design rainfall intensity at Incheon city area in Korea. In this study the eight probability distributions are considered to estimate the probable rainfall depths for 11 different durations. The Kolmogorov - Smirnov test and the Chi-square test are adopted to test each distribution. The probable rainfall intensity formulas are then determined by i) the least squares (LS) method, ii) the least median squares (LMS) method, iii) the reweighted least squares method based on the LMS (RLS), and iv) the constrained regression (CR) model. The Talbot, the Sherman, the Japanese, and the Unified type are considered to determine the best type for the Incheon station. The root mean squared (RMS) errors are computed to test the formulas derived by four methods. It is found that the Unified type is the most reliable and that all methods presented herein are acceptable for determining the coefficients of rainfall intensity formulas from an engineering point of view.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.581-592
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• 2010

With the help of some techniques based upon certain inverse pairs of symbolic operators initiated by Burchnall-Chaundy, the authors investigate decomposition formulas associated with Saran's function $F_E$ in three variables. Many operator identities involving these pairs of symbolic operators are first constructed for this purpose. By employing their decomposition formulas, we also present a new group of integral representations for the Saran function $F_E$.