• 대한수학회논문집
• /
• 제36권1호
• /
• pp.19-26
• /
• 2021

Degenerate versions of the special polynomials and numbers since they have many applications in analytic number theory, combinatorial analysis and p-adic analysis. In this paper, we define the degenerate poly-Euler numbers and polynomials arising from the modified polyexponential functions. We derive explicit relations for these numbers and polynomials. Also, we obtain some identities involving these polynomials and some other special numbers and polynomials.

• 대한수학회논문집
• /
• 제39권3호
• /
• pp.673-692
• /
• 2024

In this work, an alternative fashion of the multi-Jensen is introduced. The structures of the multi-Jensen and the multi-Euler-Lagrange-Jensen mappings are described. In other words, the system of n equations defining each of the mentioned mappings is unified as a single equation. Furthermore, by applying a fixed point theorem, the Hyers-Ulam stability for the multi-Euler-Lagrange-Jensen mappings in the setting of Banach spaces is established. An appropriate counterexample is supplied to invalidate the results in the case of singularity for multiadditive mappings.

• 한국전산유체공학회지
• /
• 제10권3호
• /
• pp.1-8
• /
• 2005

In this study, unsteady aerodynamic analyses of a wedge-type airfoil based on nonlinear piston theory and Euler equations have been performed in supersonic and hypersonic flows. The third-order nonlinear piston theory (NPT) to calculate unsteady lift and moment coefficients is derived and applied in the time-domain. Also, unsteady flow quantities are obtained from the two-dimensional time-dependent Euler equations. For the CFD based unsteady aerodynamic analyses, an arbitrary Lagrangean-Eulerian (ALE) formulation for the Euler equations is used to calculate flow fluxes in the computational flow field with moving boundaries. Numerical comparisons for unsteady lift and moment coefficients are presented between NPT and Euler approaches. The results show very good agreements in the high supersonic and hypersonic flows. It means that the present NPT can be efficiently used to predict unsteady aerodynamic forces ol wedge type airfoils with dynamic motions in the high supersonic and hypersonic flow regimes.

• Journal of applied mathematics & informatics
• /
• 제7권3호
• /
• pp.941-958
• /
• 2000

Euler method is generalized to solve the system of nonlinear differential equations. The generalization is carried out by taking a special constant matrix S so that exp(tS) can be exactly computed. Such a matrix S is extracted from the Jacobian matrix of the given problem. Stability of the generalized Euler process is discussed. It is shown that the generalized Euler process is comparable to the fourth order Runge-Kutta method. We also exemplify that the important qualitative and geometric features of the underlying dynamical system can be recovered by the generalized Euler process.

• Journal of applied mathematics & informatics
• /
• 제29권1_2호
• /
• pp.511-516
• /
• 2011

In this paper we prove a generalized symmetry relation between the generalized Euler polynomials and the generalized higher-order (attached to Dirichlet character) Euler polynomials. Indeed, we prove a relation between the power sum polynomials and the generalized higher-order Euler polynomials..

• 대한토목학회논문집
• /
• 제29권5B호
• /
• pp.493-496
• /
• 2009

본 연구에서 Euler-Lagrange 식을 사용하여 속도포텐셜로 표현되는 확장형 완경사방정식을 유도하였다. 먼저, Euler-Lagrange 식을 사용하여 흐름함수로 표현된 확장형 완경사방정식을 유도한 Kim과 Bai(2004)의 유도과정을 따라가면서 속도 표텐셜로 표현된 확장형 완경사방정식과의 관계를 찾았다. 속도포텐셜로 표현된 Euler-Lagrange 식을 찾아낸 다음 고차의 수심변화 항을 유도하였다. 본 연구에서 유도된 확장형 완경사방정식은 기존의 식인 Massel(1993)의 식과 Chamberlain과 Porter(1995)의 식과 정확히 일치하였다. 본 연구의 연구 성과는 확장형 완경사방정식의 유도 방법을 새로 제시하여 해안공학의 영역을 넓히는데 의의가 있다.

• 충청수학회지
• /
• 제28권1호
• /
• pp.151-159
• /
• 2015

This paper investigates temporal regularity of solutions for the incompressible Euler equations in a critical Besov space $B^{\frac{d}{p}+1}_{p,1}(\mathbb{R}^d)$ for $1{\leq}p{\leq}d$.

• 대한수학회논문집
• /
• 제16권4호
• /
• pp.607-619
• /
• 2001

Rassias obtained the Hyers-Ulam stability of the gen-eral Euler-Lagrange functional equation. In this paper we general-ized this stability in the spirit of Hyers, Ulam, Rassias and Gavruta.

• 호남수학학술지
• /
• 제33권4호
• /
• pp.529-534
• /
• 2011

In this paper, we consider the q-analogues of Euler numbers and polynomials using the fermionic p-adic invariant integral on $\mathbb{Z}_p$. From these numbers and polynomials, we derive some interesting identities and properties on the q-analogues of Euler numbers and polynomials.

• Journal of applied mathematics & informatics
• /
• 제31권5_6호
• /
• pp.623-630
• /
• 2013

In this paper, our aim is finding the term of generalized Eule polynomials. We also obtain some identities and relations involving the Bernoulli numbers, the Euler numbers and the Stirling numbers.