• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.133-144
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• 2020

In this paper, we discuss generalized q-poly-Euler numbers and polynomials. To do so, we define generalized q-poly-Euler polynomials with variable a and investigate its identities. We also represent generalized q-poly-Euler polynomials E^(k)_n,q(x; a) using Stirling numbers of the second kind. So we explore the relation between generalized q-poly-Euler polynomials and Stirling numbers of the second kind through it. At the end, we provide symmetric properties related to generalized q-poly-Euler polynomials using alternating power sum.

• 대한수학회지
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• 제56권2호
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• pp.485-505
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• 2019

In 1935, D. H. Lehmer introduced and investigated generalized Euler numbers $W_n$, defined by $${\frac{3}{e^t+e^{wt}e^{w^2t}}}={\sum\limits_{n=0}^{\infty}}W_n{\frac{t^n}{n!}}$$, where ${\omega}$ is a complex root of $x^2+x+1=0$. In 1875, Glaisher gave several interesting determinant expressions of numbers, including Bernoulli and Euler numbers. These concepts can be generalized to the hypergeometric Bernoulli and Euler numbers by several authors, including Ohno and the second author. In this paper, we study more general numbers in terms of determinants, which involve Bernoulli, Euler and Lehmer's generalized Euler numbers. The motivations and backgrounds of the definition are in an operator related to Graph theory. We also give several expressions and identities by Trudi's and inversion formulae.

• 충청수학회지
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• 제29권2호
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• pp.283-286
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• 2016

In this paper, we find a new recurrence formula of the Euler zeta functions.

• Structural Engineering and Mechanics
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• 제72권5호
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• pp.617-629
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• 2019

Based on the finite element method of traditional straight Euler-Bernoulli beams and the coupled relations between linear displacement and angular displacement of a pre-twisted Euler-Bernoulli beam, the shape functions and stiffness matrix are deduced. Firstly, the stiffness of pre-twisted Euler-Bernoulli beam is developed based on the traditional straight Euler-Bernoulli beam. Then, a new finite element model is proposed based on the displacement general solution of a pre-twisted Euler-Bernoulli beam. Finally, comparison analyses are made among the proposed Euler-Bernoulli model, the new numerical model based on displacement general solution and the ANSYS solution by Beam188 element based on infinite approach. The results show that developed numerical models are available for the pre-twisted Euler-Bernoulli beam, and which provide more accurate finite element model for the numerical analysis. The effects of pre-twisted angle and flexural stiffness ratio on the mechanical property are investigated.

• 한국수학사학회지
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• 제19권1호
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• pp.17-32
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• 2006

위상수학은 기하학, 대수학, 해석학 등 수학의 다른 분야에 비하여 비교적 늦게 연구되기 시작하였고 Euler는 위상수학의 시조로 알려져 있다. 우리는 먼저 위상수학의 기원과 발달에 대해 살피고 Euler의 삶과 업적에 대해 알아본다.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.611-623
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• 2020

In this paper, we define a q-analogue of the poly-Euler numbers and polynomials which is generalization of the poly Euler numbers and polynomials including q-analogue of polylogarithm function. We also give the relations between generalized poly-Euler polynomials. Furthermore, we introduce zeta fuctions of Arakawa-Kaneko type and talk their properties and the relation with q-analogue of poly-Euler polynomials.

• 전산구조공학
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• 제9권3호
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• pp.187-197
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• 1996

Explicit 직접적분법 알고리듬을 사용하여 Euler기둥의 동적 좌굴거동을 해석할 수 있는 수치해석법을 제시하였다. 평면뼈대 유한요소를 기하학적 비선형 거동과 전체좌굴의 영향을 고려할 수 있도록 보의 대변위 이론으로부터 유도하였고, central difference method를 바탕으로 해석 알고리듬을 개발하였다. 다양한 형상, 크기, 재하시간을 갖는 충격하중에 대하여 Euler기둥의 동적좌굴거동과 고유치 문제를 해석하였다. 수치해석 예제를 통하여 본 연구의 결과를 검증하였다.

• 제어로봇시스템학회논문지
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• 제7권12호
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• pp.1044-1050
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• 2001

This paper presents firstly the method of Euler angle matching designing the transfer alignment using the attitude matching. In this method, the observation directly uses Euler angle difference between MINS and SINS so it needs to describe the rotation vector error to the Euler angle error. The rotation vector error related to the Euler angle error is derive from the direction cosine matrix error equation. The feasibility of the Kalman filter designed for the transfer alignment by Euler angle matching is analyzed by the alignment error results with respect to the roll angle the pitch angle, and the yaw angle matching.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2003년도 춘계학술대회 논문집
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• pp.163-167
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• 2003

A novel method for 3-dimensional dynamic analysis of marine slender structure gas been developed by using Euler parameters. The Euler parameter rotation, which is being widely used in aerospace vehicle dynamics and multi-body dynamics, has been applied to elastic structure analysis. Large deformation of flexible slender structures is described by means of Euler parameters. Euler parameter method is implemented effectively in incremental-iterative algorithm for 3D dynamic analysis. The normalization constraint of Euler parameters is efficiently satisfied by means of a sequential updating method.

• 대한수학회지
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• 제52권3호
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• pp.537-565
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• 2015

In this paper, we give relationship between Bernoulli-Euler polynomials and convolution sums of divisor functions. First, we establish two explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli and Euler polynomials. Second, as applications, we show five identities concerning the third and fourth-order convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli or Euler polynomials.