• 충청수학회지
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• 제28권1호
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• pp.151-159
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• 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 $1{\leq}p{\leq}d$.

• 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.

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

• 한국수학사학회지
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• 제20권3호
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• pp.27-42
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• 2007

오일러의 탄생 300주년을 기념하여 2007년에 세계 각국에서는 각종 학술행사가 계획되고, 미국에는 오일러의 업적을 온라인상에 모아놓은 Euler Archive가 생겼다. 본 글에서는 Euler Archive의 활용을 제안하는 한편, 현재에 이르기까지 수학사상 가장 많은 업적을 일궈낸 오일러의 삶을 간단히 돌아보고, 그가 증명한 수학 정리들 중에서 가장 대표적인 10개의 정리들에 대한 배경과 수학 지식세계에 미친 영향을 살펴봄으로써 오일러의 탄생 300주년을 축하하고자 한다.

• 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.

• 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.

• Kyungpook Mathematical Journal
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• 제57권2호
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• pp.327-329
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• 2017

For any even integer n, we show that there exists a log Calabi-Yau threefold (Y, D) such that the Euler characteristic of Y is n. Furthermore Y is smooth and D is smooth anticanonical section of Y that is a K3 surface.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2004년도 추계학술대회 논문집
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• pp.382-387
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• 2004

As the increasing needs in the industrial filed, many studies for the 3D CAD system are carried out. There are two types of 3D CAD system. One is manifold modeler, the other is non-manifold modeler. In the manifold modeler only 3D objects can be modeled. In the non-manifold modeler 3D, 2D, 1D, and 0D objects can be modeled in a unified data structure. Recently there are many studies on the non-manifold modeler. Most of them are focused on finding unknown topological entities and representing all kinds of topological entities found. In this paper, efficient data structure is selected. The boundary information on a face and an edge is included in this data structure. The boundary information on a vertex is excluded considering the frequency of usage. Because the disk cycle information is not required in most case of modeling. It is compact. It stores essential non-manifold information such as loop cycle and radial cycle. A suitable Euler-Poincare equation is studied and selected. Using the efficient data structure and the selected Euler-Poincare equation, 18 basic Euler operators are implemented. Several 3D models are created using the implemented modeler. A non-manifold modeling can be carried out using the implemented 3D CAD system. The results of this paper could be used in the further studies such as an implementation of Boolean operators, and a translation of 2D CAD drawings to 3D models.

• 한국전산유체공학회지
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• 제17권4호
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• pp.103-109
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• 2012

Sound scattering in 3D complex geometry is difficult to model with body-fitted grid. Thus Brinkman Penalization method is used to compute sound scattering in 3D complex geometry. Sound propagation of monitor/TV is studied. The sound field for monitor/TV is simulated by applying Brinkman Penalization method to Linearized Euler Equation. Solid Structure and ambient air are represented as penalty terms in Linearized Euler Equation.

• 지구물리와물리탐사
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• 제10권1호
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• pp.44-49
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• 2007

고해상도를 가지는 지하 밀도 영상을 얻기 위한 3 차원 중력 역산은 모델 변수들이 급격하게 많아지는 문제가 발생한다. 이 논문에서는 모델 변수들의 수를 줄이기 위해서 오일러 디컨벌루션의 해를 사전정보로 활용하는 3 차원 중력역산을 제안하였다. 이 논문에서 고안한 역산 알고리즘의 핵심은 오일러 디컨벌루션의 해가 얻어진 주위로 역산 공간을 제한하여 역산 해의 비유일성을 줄인 점이다. 먼저 중력 자료에 대한 3 차원 오일러 디컨별루션의 해를 구하고, 오일러 디컨벌루션의 해가 나타나는 주위에서만 3 차원 확장 탐색 역산을 수행하여 지하 밀도 영상을 구하였다. 이 3 차원 중력 역산 방법은 합성 모델에 적용하여 그 성능을 검증하였고, 석회암 지대에 존재하는 공동의 분포를 밝히기 위한 고정밀 중력탐사 자료 역산에도 적용하였다. 결과적으로, 오일러 디컨벌루션의 해를 사전정보로 이용한 역산을 이용하여 분해능이 향상된 고해상도의 지하 멸도 영상을 구할 수 있었다.