• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.87-94
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• 1997

The circular plate resting on Boussinesq's half-space model under axisymmetric loading is studied by a finite element procedure to evaluate the distribution of contact pressure between plate and elastic half-space. The displacement of half-space due to axisymmetric surface loading can be evaluated by double integration of Boussinesq's solution. On that case the analytical integration can be executed for the radial direction but the analytical integration for the circumferential direction is impossible and the numerical integration should be considered. With the radial integration we can get non-dimensional function. Then the numerical integration for the formula is executed for the circumferential direction and the results are approximated 5th order Polynomials by using the least square method. With these 5th order approximate formula, the flexibility matrix of half-space is constructed as the coefficient matrix of nodal contact pressure by the finite element procedures. Iteration procedures are attempted by using this method to determine the separated region.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.535-540
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• 2003

The objective of this paper is to assess the variability of modal properties caused by temperature effects and to adjust modal data used for frequency-based damage detection in plate-girder bridges. First, experiments on model plate-girder bridges are described. Next, the relationship between temperature and natural frequencies is assessed and a set of empirical frequency-correction formula are analyzed for the test structure. Finally, a frequency-based method is used to locate and estimate severity of damage in the test structure using experimental modal data which are adjusted by the frequency-correction formula. Here, local damage in beam-type structures is detected by using measured frequencies and analytical mode shapes.

• Journal of computational fluids engineering
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• v.14 no.4
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• pp.86-92
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• 2009

Nowadays, the development of microfluidic chip [i.e. biochip, micro-total analysis system ($\mu$-TAS) and LOC (lab-on-a-chip)] becomes more active, and the microchannels to deliver fluid by pressure or electroosmotic forces tend to be more complex like electronic circuits or networks. For a simple network of channels, we may calculate the pressure and the flow rate easily by using suitable formula. However, for complex network it is not handy to obtain such information with that simple way. For this reason, Graphic User Interface (GUI) program which can rapidly give required information should be necessary for microchip designers. In this paper, we present a GUI program developed in our laboratory and the simple theoretical formula used in the program. We applied our program to simple case and could get results compared well with other numerical results. Further, we applied our program to several complex cases and obtained reasonable results.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.541-549
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• 2010

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere $S^{2m+1}$. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.623-635
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• 2006

In this paper, we derive an elementary formula for the linearization coefficients of the product of two Legendre polynomials. Our main purpose is to study the method which can be used to derive the formula, which is straightforward from the integration and their orthogonality.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.305-315
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• 2015

Recently, Jianxin Liu, Hao Pan and Yong Zhang in [On the integral of the product of the Appell polynomials, Integral Transforms Spec. Funct. 25 (2014), no. 9, 680-685] established an explicit formula for the integral of the product of several Appell polynomials. Their work generalizes all the known results by previous authors on the integral of the product of Bernoulli and Euler polynomials. In this note, by using a special case of their formula for Euler polynomials, we shall provide several reciprocity relations between the special values of Tornheim's multiple series.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.33-55
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• 2005

The temporal discretisation of a moderate semilinear parabolic problem in an abstract setting by the two-step backward differentiation formula with variable step sizes is analysed. Stability as well as optimal smooth data error estimates are derived if the ratios of adjacent step sizes are bounded from above by 1.91.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.256-258
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• 2011

Using the axial Green's function method for Steady Stokes flows, we introduce a new pressure correction formula to satisfy the incompressibility condition, in which the pressure is related to the integral of the second order derivatives of the velocity. Based on this formula, we propose the iterative method for solving the Stokes flows in complicated domains. Even if the domain is complex, this method maintains the second order of convergence for the velocity.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.289-309
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• 2014

A combinatorial description of the crystal $\mathcal{B}({\infty})$ for finite-dimensional simple Lie algebras in terms of certain Young tableaux was developed by J. Hong and H. Lee. We establish an explicit bijection between these Young tableaux and canonical bases indexed by Lusztig's parametrization, and obtain a combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum over the set of Young tableaux.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.679-689
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• 2021

The first author suggested an exact volume formula of the hypercubes [0, 1]ⁿ clipped by several hyperplanes expressed directly in terms of linear coefficients of the hyperplanes. However, it requires awkward assumptions to apply the formula to various situations. We suggest a concrete method to overcome those restrictions for two or three hyperplanes using 𝜖-perturbation, which gives an exact value applicable for any kind of arrangement of hyperplanes with no consideration.