• Korean Journal of Mathematics
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• 제26권4호
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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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• 제37권3_4호
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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.

• 대한수학회보
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• 제52권6호
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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.

• 충청수학회지
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• 제36권2호
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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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• 제30권3_4호
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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.

• 대한수학회보
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• 제57권3호
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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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• 제60권4호
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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.

• 대한수학회논문집
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• 제38권3호
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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).

• 패션비즈니스
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• 제20권1호
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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.

• 한국음향학회지
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• 제21권2호
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• pp.110-119
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• 2002

수중퇴적물의 투과음향특성을 실험실 조건에서 고찰하였다. 물로 포화된 입자지름 0.5 mm이하의 모래퇴적물을 (재질의 두께가 1 mm이고 부피가100mm×100m×42m인 아크릴상자 안에) 형성시켜 수중모래퇴적물 시료를 제작하였다. 수중 모래퇴적물 시료의 다공율을 조절할 수 있도록 퇴적물 내부에 내경 3 mm, 길이 42 mm인 원통형 관들을 이용하여 물로 채워진 관을 위치시켜서, 원통다공율이 각각 0 %, 5%, 11%, 18%, 26%인 다섯 개의 수중 모래퇴적물 시료를 만들었다. 수중 모래퇴적물 시료의 음향특성을 다공율과 0.3 MHz에서 4 MHz의 구간에서 주파수의 함수로 분석하였다. 수중 모래퇴적물 시료를 투과한 음향신호는 시료 전체로부터 나온 첫번째파 (first-kind wave)와 관을 통하여 나온 두번째파 (second-kind wave)를 구분하여 관측하였다. 중심주파수 1 MHz에서는 첫번째파가 지배적이었으나 중심주파수 2.25 MHz에서는 두번째파가 지배적이었다. 첫번째파의 경우, 다공율이 증가되면 음압투과계수는 작아지고 음속은 물의 음속에 가깝게 낮아지며, 주파수가 증가되면 투과계수는 점차 작아지나 음속의 변화는 없었다. 두번째파의 경우, 다공율이 커지면 투과계수가 커지고 음속은 변화가 없었으며, 주파수가 증가되어도 투과계수와 음속의 변화는 없었다.