• 대한수학회보
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• 제54권4호
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• pp.1185-1194
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• 2017

In this paper, we present nonlinear differential equations arising from the generating function of the Eulerian polynomials. In addition, we give explicit formulae for the Eulerian polynomials which are derived from our nonlinear differential equations.

• 충청수학회지
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• 제26권1호
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• pp.191-196
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• 2013

In this paper we derive some identities on Eulerian polynomials of higher order from non-linear ordinary differential equations. We show that the generating functions of Eulerian polynomials are solutions of our non-linear ordinary differential equations.

• 충청수학회지
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• 제26권3호
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• pp.591-599
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• 2013

A large number of sequences of polynomials and numbers have arisen in mathematics. Some of them, for example, Bernoulli polynomials and numbers, have been investigated deeply and widely. Here we aim at presenting certain interesting and (potentially) useful identities involving mainly in the second-order Eulerian numbers and Stirling polynomials, which seem to have not been given so much attention.

• 한국환경과학회지
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• 제11권9호
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• pp.907-914
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• 2002

Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.

• 물과 미래
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• 제27권2호
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• pp.155-166
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• 1994

Eulerian-Lagrangian 방법을 이용하여 1차원 종확산방정식의 수치모형을 비교·분석하였다. 본 연구에서서 비교·분석한 모형은 지배방정식을 연산자 분리방법에 의해서 이송만을 지배하는 이송방정식과 확산만을 지배하는 확산방정식으로 분리한다. 이송방정식은 특성곡선을 따라서 유체입자를 추적하는 특성곡선법을 사용하여 해를 구하고, 그 결과를 고정된 Eulerian 격자상에 보간하였고, 확산방정식은 상기 고정격자상에서 Crank-Nicholson 유한차분법을 사용하여 해를 구하였다. 이송방정식의 풀이에서 다양한 보간방법이 적용되었는데, 일반적으로 Hermite 보간다항식을 사용한 경우가 Lagrange 보간다항식을 사용한 경우보다 수치확산 및 수치진동 등의 오차를 최소화할 수 있어서 더욱 우수한 것으로 밝혀졌다.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.443-450
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• 2016

In this paper we give some properties, explicit formulas, several identities, a connection with tangent numbers and polynomials, and some integral formulas.

• Korean Journal of Hydrosciences
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• 제6권
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• pp.51-66
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• 1995

Various Eulerian-Lagerangian numerical models for the one-dimensional longtudinal dispersion equation are studied comparatively. In the models studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing advection and the other dispersion. The advection equation has been solved using the method of characteristics following flud particles along the characteristic line and the result are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpo;ation po;ynomials are superor to Lagrange interpolation polynomials in reducing both dissipation and dispersion errors.

• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.449-457
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• 2017

In this paper, we shall provide several properties of Dedekind sums with quasi-periodicity Euler functions. In particular, we present a representation of these Dedekind sums in terms of the Eulerian functions and the tangent functions.

• 대한수학회보
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• 제36권1호
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• pp.47-61
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• 1999

In this paper we difine poly-Euler numbers which generalize ordinary Euler numbers. We construct a p-adic poly-Euler measure by the poly-Euler polynomials and derive an integral formula.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2002년도 학술대회지
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• pp.803-806
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• 2002

The dispersion of Lagrangian fluid particles in a turbulent channel flow is studied by a direct numerical simulation. Four points Hermite interpolation in the homogeneous direction and Chebyshev polynomials in the inhomogeneous direction is adopted by assesing the acceleration of fluid particles. In order to characterize the inhomogeneous Lagrangian statistics, accurate single particle Lagrangian statistics are obtained along the wall normal direction. Integral time scales of Lagrangian velocity can be normalized by Eulerian mean shear stresses.