• Journal of Mechanical Science and Technology
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• 제20권4호
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• pp.467-472
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• 2006

A study of the natural vibrations of beam resting on elastic foundation with finite number of transverse open cracks is presented. Frequency equations are derived for beams with different end restraints. Euler-Bernoulli beam on Pasternak foundation and Euler-Bernoulli beam on Pasternak foundation are investigated. The cracks are modeled by massless substitute spring. The effects of the crack location, size and its number and the foundation constants, on the natural frequencies of the beam, are investigated.

• 대한수학회논문집
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• 제33권1호
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• pp.13-36
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• 2018

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several quadratic and cubic Euler sums through zeta values and linear sums. Furthermore, some relationships between harmonic numbers and Stirling numbers of the first kind are established.

• 대한수학회보
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• 제61권2호
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• pp.557-584
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• 2024

An almost complex torus manifold is a 2n-dimensional compact connected almost complex manifold equipped with an effective action of a real n-dimensional torus Tⁿ ≃ (S¹)ⁿ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let M be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for M, and for each type of graph we construct such a manifold M, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch χ_y-genus of M.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.413-421
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• 2017

In this paper, we study the generalizations of Euler numbers and polynomials by using the q-extension with p-adic integral on $\mathbb{Z}_p$. We call these: the generalized q-${\omega}$-Euler numbers $E^{({\alpha})}_{n,q,{{\omega}}(a)$ and polynomials $E^{({\alpha})}_{n,q,{\omega}}(x;a)$. We investigate some elementary properties and relations for $E^{({\alpha})}_{n,q,{{\omega}}(a)$ and $E^{({\alpha})}_{n,q,{\omega}}(x;a)$.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1221-1228
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• 2011

Recently, several mathematicians have studied some interesting relations between extended q-Euler number and Bernstein polynomials(see [3, 5, 7, 8, 10]). In this paper, we give some interesting identities on the Genocchi polynomials and Bernstein polynomials.

• 대한수학회보
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• 제54권4호
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• pp.1255-1280
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• 2017

In this paper we present a new family of identities for parametric Euler sums which generalize a result of David Borwein et al. [2]. We then apply it to obtain a family of identities relating quadratic and cubic sums to linear sums and zeta values. Furthermore, we also evaluate several other series involving harmonic numbers and alternating harmonic numbers, and give explicit formulas.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1998년도 추계 학술대회논문집
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• pp.141-146
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• 1998

An Euler/Navier Stokes solver has been developed for the analysis of steady and unsteady flows. The $q-{\omega}$ turbulent model has been incorporated into the solver in strongly coupled manner for stability and robustness. A new Chimera hole cutting algorithm, Cut-paste algorithm, has been devised for automatic Chimera hole cutting. Number of viscous/inviscid numerical computations demonstrate the accuracy and the versatility of the solver.

• 대한수학회지
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• 제44권5호
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• pp.1163-1184
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• 2007

In this presentation dedicated to the tricentennial birth anniversary of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707-1783), we begin by remarking about the so-called Basler problem of evaluating the Zeta function ${\zeta}(s)$ [in the much later notation of Georg Friedrich Bernhard Riemann (1826-1866)] when s=2, which was then of vital importance to Euler and to many other contemporary mathematicians including especially the Bernoulli brothers [Jakob Bernoulli (1654-1705) and Johann Bernoulli (1667-1748)], and for which a fascinatingly large number of seemingly independent solutions have appeared in the mathematical literature ever since Euler first solved this problem in the year 1736. We then investigate various recent developments on the evaluations and representations of ${\zeta}(s)$ when $s{\in}{\mathbb{N}}{\backslash}\;[1],\;{\mathbb{N}}$ being the set of natural numbers. We emphasize upon several interesting classes of rapidly convergent series representations for ${\zeta}(2n+1)(n{\in}{\mathbb{N}})$ which have been developed in recent years. In two of many computationally useful special cases considered here, it is observed that ${\zeta}(3)$ can be represented by means of series which converge much more rapidly than that in Euler's celebrated formula as well as the series used recently by Roger $Ap\'{e}ry$ (1916-1994) in his proof of the irrationality of ${\zeta}(3)$. Symbolic and numerical computations using Mathematica (Version 4.0) for Linux show, among other things, that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places.

• 한국추진공학회지
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• 제8권1호
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• pp.27-37
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• 2004

예조건화된 오일러 방정식의 수렴특성에 대한 연구를 수행하였다. 지배방정식의 거동을 이해하기 위하여 섭동 해석을 수행하였다. 중앙부에 10％ 원호를 가진 2차원 관을 통과하는 다양한 마하수의 비점성 유동장에 대해 수치 계산을 수행하였다. 공간차분은 Roe의 FDS를 사용하고 시간적분은 LU-SGS 기법을 사용하였다. 압력 및 속도의 수렴특성은 마하수와 상관없이 일정하게 유지되었으나, 온도의 수렴성은 마하수가 작아질수록 악화되는 것으로 나타났다. 섭동 해석을 통해 이러한 지배방정식의 수렴특성을 설명할 수 있었으며, 수렴특성이 예조건화 행렬의 거동 특성에 의해 결정된다는 사실을 알 수 있었다.

• 정보처리학회논문지B
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• 제13B권1호
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• pp.15-20
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• 2006

이 논문은 컴퓨터 게임을 위한 물리 엔진의 성능 향상 및 이를 적용한 지능적인 게임 캐릭터에 관한 연구를 서술한다. 물리적 상황을 자동으로 인식하는 알고리즘으로는 Momentum back-propagation을 적용하였다. 또한 우리는 각 상황에 따른 적분 방식의 실험 결과를 제시한다. 실험을 위하여 Euler Method, Improved Euler Method, 및 Runge-kutta Method의 세 가지의 적분 방식을 적용하였다. 각 적분 방식의 실험 결과에서 충돌이 없는 상황에서는 Euler Method가 최적의 성능을 보여주었다. 또한 충돌 상황에서는 세 가지 방식이 모두 비슷한 성능을 보여주었지만, Runge-kutta Method가 최적의 정확도를 보여주었다. 물리 상황인식에 대한 실험결과에서는 입력 층과 출력 층이 고정된 상태에서 은닉 층이 3일 때 가장 좋은 성능을 보여주었고, 또한 학습횟수가 30000일 때 최적의 성능을 보여주었다. 앞으로 우리는 다른 장르의 게임에 이러한 물리적 컨텍스트(context)를 인식하는 연구를 진행할 것이며 또한 전체 게임의 성능을 증가할 수 있도록 M-BP이외의 인식 알고리즘을 적용할 것이다.