• Korean Journal of Mathematics
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• v.26 no.4
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• pp.675-681
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• 2018

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify three families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind and establish a new family of nonlinear ordinary differential equations in terms of the Stirling numbers of the second kind.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.219-234
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• 2019

We use the definition of Euler polynomials of the second kind with (p, q)-numbers to identify some identities and properties of these polynomials. We also investigate some relationships between (p, q)-Euler polynomials of the second kind, (p, q)-Bernoulli polynomials, and (p, q)-tangent polynomials by using the properties of (p, q)-exponential function.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2001-2010
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• 2015

In this paper, we give explicit and new identities for the Bernoulli numbers of the second kind which are derived from a non-linear differential equation.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.2
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• pp.65-76
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• 2023

With the Stirling matrix S of the second kind and the Pascal matrix T, we study recurrence rules and sequences of certain sums over the matrix ST^k. We find a matrix E satisfying ST = ES and interrelations of S and the Stirling matrix of the first kind.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.463-475
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• 2012

In this work, we investigate solving two-dimensional nonlinear Volterra integral equations of the first kind (2DNVIEF). Here we convert 2DNVIEF to the two-dimensional linear Volterra integral equations of the first kind (2DLVIEF) and then we solve it by using operational approach of the Tau method. But for solving the 2DLVIEF we convert it to an equivalent equation of the second kind and then by giving some theorems we formulate the operational Tau method with standard base for solving the equation of the second kind. Finally, some numerical examples are given to clarify the efficiency and accuracy of presented method.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.623-647
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• 2020

The greatest integer that does not belong to a numerical semigroup S is called the Frobenius number of S. The Frobenius problem, which is also called the coin problem or the money changing problem, is a mathematical problem of finding the Frobenius number. In this paper, we introduce the Frobenius problem for two kinds of numerical semigroups generated by the Thabit numbers of the first kind, and the second kind base b, and by the Cunningham numbers. We provide detailed proofs for the Thabit numbers of the second kind base b and omit the proofs for the Thabit numbers of the first kind base b and Cunningham numbers.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.869-881
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• 2020

Most first kind integral equations are ill-posed, and obtaining their numerical solution often requires solving a linear system of algebraic equations of large condition number, which may be difficult or impossible. This article proposes a regularization-direct method to numerically solve first kind Fredholm integral equations. The vector forms of block-pulse functions and related properties are applied to formulate the direct method and reduce the integral equation to a linear system of algebraic equations. We include a regularization scheme to overcome the ill-posedness of integral equation and obtain a stable numerical solution. Some test problems are solved using the proposed regularization-direct method to illustrate its efficiency for solving first kind Fredholm integral equations.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.755-772
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• 2023

Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) and Fox-Wright function _rΨ_s(z).

• Journal of Fashion Business
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• v.20 no.1
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• pp.17-34
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• 2016

This research is a construct to understand CSR and pro-social consumption behavior of fashion consumers which classifies CSR efforts of fashion company and conducts positive analysis of the relationship between such characteristics and social relationship behaviors(sharing of values, consciousness of kind, consciousness of future expectation) and pro-social consumption behavior. For this path analysis was conducted utilizing a sample of 430 consumers who have experience of CSR efforts of fashion brands. The result is as follows. First, as a result of the path relationship among CSR efforts & sharing of values of fashion brands, consciousness of kind and consciousness of future expectation, economic efforts, relational efforts and cyclical efforts meaningfully affected sharing of values, whereas creative efforts did not. Also, relational and creative efforts meaningfully affected consciousness of kind, whereas economic and cyclical efforts did not. Furthermore, economic, relational and cyclical efforts meaningfully affected consciousness of future expectation, when creative efforts failed. Second, as a result of the analysis of path relationship among sharing of values, consciousness of kind, consciousness of future expectation and pro-social consumption behavior of social relationships, sharing of values had a meaningful impact on consciousness of kind, consciousness of future expectation and pro-social consumption behavior. And finally consciousness of kind and future expectation showed meaningful influence on pro-social consumption behavior.

• The Journal of the Acoustical Society of Korea
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• v.21 no.2
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• pp.110-119
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• 2002

Acoustic characteristics of water sediment were experimentally studied in laboratory. Water saturated sand sediment less than the grain size of 0.5 mm diameter is uniformly distributed in an acryl box (100 mm×100mm×42mm) with material thickness 1 mm. Pores in the acryl box are modeled as the structure of cylindrical pore tubes (diameter 3 mm and length 42 mm) filled with water. Cylindrical pore tubes have porosities 0%, 5%, 11%, 18% and 26 % controlled by the tube numbers. Transmitted acoustic waves through sand sediment specimen are analyzed as the functions of porosity and frequency from 0.3 MHz to 4 MHz. Transmitted acoustic waves are mixed with the first-kind wave from whole specimen and the second-kind wane from cylindrical pore tubes. For the center frequency 1 MHz, the first kind wave is dominant but for the center frequency 2.25 MHz, the second kind wave is dominant. In the case of the first-kind wave, as the porosity increases, the transmission coefficient decreases and the sound speed decreases to the sound speed of water. As the frequency increases, the transmission coefficient decreases but the sound speed is almost constant. In the case of the second-kind wave, as the porosity increases, the transmission coefficient increases but the sound speed is almost constant. The transmission coefficient and the sound speed are almost constant as a function of frequency.