• Journal of Mechanical Science and Technology
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• v.20 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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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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• v.35 no.3_4
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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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• v.29 no.5_6
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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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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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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• 1998.11a
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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.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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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.

• Journal of the Korean Society of Propulsion Engineers
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• v.8 no.1
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• pp.27-37
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• 2004

The convergence characteristics of preconditioned Euler equations were studied. A perturbation analysis was conducted to understand the behavior of the preconditioned Euler equations. Various speed flows in a two-dimensional channel with a 10％ circular arc in the middle of the channel were calculated. Roe's FDS scheme was used for spatial discretization and the LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of pressure and velocity were maintained regardless of the Mach numbers but that the convergence characteristics of temperature were strongly related to the Mach number and became worse as the Mach number decreased. The perturbation analysis well explained the trend of the convergence characteristics and showed that the convergence characteristics are strongly related with the behavior o( the Preconditioning matrix.

• The KIPS Transactions:PartB
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• v.13B no.1 s.104
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• pp.15-20
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• 2006

This paper describes research on intelligent game character through performance enhancements of physics engine in computer games. The algorithm that recognizes the physics situation uses momentum back-propagation neural networks. Also, we present an experiment and its results, integration methods that display optimum performance based on the physics situation. In this experiment on integration methods, the Euler method was shown to produce the best results in terms of fps in a simulation environment with collision detection. Simulation with collision detection was shown similar fps for all three methods and the Runge-kutta method was shown the greatest accuracy. In the experiment on physics situation recognition, a physics situation recognition algorithm where the number of input layers (number of physical parameters) and output layers (destruction value for the master car) is fixed has shown the best performance when the number of hidden layers is 3 and the learning count number is 30,000. Since we tested with rigid bodies only, we are currently studying efficient physics situation recognition for soft body objects.