• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.661-667
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• 2013

In this paper we propose the iterated projection method for the approximate solution of an integro-differential equations with Cauchy kernel in $L^2([-1,1],\mathbb{C})$ using Legendre polynomials. We prove the convergence of the method. A system of linear equations is to be solved. Numerical examples illustrate the theoretical results.

• Journal of Korean Society for Atmospheric Environment
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• v.23 no.E1
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• pp.10-15
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• 2007

The gas hydrates are probably most sensitive to climate change since they are stable only under specific conditions of high pressure and low temperature. One of the main factors responsible for formation of gas hydrates is the saturation of the gases with water vapor. Quantitative phase equilibrium data and understanding of the roles of water component in the phase behavior of the heterogeneous water-hydrocarbon-hydrate mixture are of importance and of engineering value. In this study, the water content of ethylene gas in equilibrium with hydrate and water phases were analyzed by theoretical and experimental methods at temperatures between 274.15 up to 291.75 K and pressures between 593.99 to 8,443.18 kPa. The experimental and theoretical enhancement factors (EF) for the water content of ethylene gas and the fugacity coefficients of water and ethylene in gas phase were determined and compared with each other over the entire range of pressure carried out in this experiment. In order to get the theoretical enhancement factors, the modified Redlich-Kwong equation of state was used. The Peng-Robinson equations and modified Redlich-Kwong equations of state were used to get the fugacity coefficients for ethylene and water in the gas phase. The results predicted by both equations agree very well with the experimental values for the fugacity coefficients of the compressed ethylene gas containing small amount of water, whereas, those of water vapor do not in the ethylene rich gas at high temperature for hydrate formation locus.

• Steel and Composite Structures
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• v.39 no.2
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• pp.189-200
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• 2021

The compressive strength of circular concrete filled steel tubular (C-CFST) stubs strengthened with carbon fiber reinforced polymer (CFRP) is studied theoretically. According to previous experimental results, the failure process and mechanism of circular CFRP-concrete filled steel tubular (C-CFRP-CFST) stubs is analyzed, and the loading process is divided into 3 stages, i.e., elastic stage, elasto-plastic stage and failure stage. Based on continuum mechanics, the theoretical model of C-CFRP-CFST stubs under axial compression is established based on the assumptions that steel tube and concrete are both in three-dimensional stress state and CFRP is in uniaxial tensile stress state. Equations for calculating the yield strength and the ultimate strength of C-CFRP-CFST stubs are deduced. Theoretical predictions from the presented equations are compared with existing experimental results. There are a total of 49 tested specimens, including 15 ones for comparison of yield strength and 44 ones for comparison of ultimate strength. It is found that the predicted results of most specimens are within an error limit of 10%. Finally, simplified equations for calculating both yield strength and ultimate strength of C-CFRP-CFST stubs are proposed.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.645-658
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• 2014

Many projection methods have been progressively constructed to find more accurate and efficient solution of the Navier-Stokes equations. In this paper, we consider most recently constructed projection methods: the pressure correction method, the gauge method, the consistent splitting method, the Gauge-Uzawa method, and the stabilized Gauge-Uzawa method. Each method has different background and theoretical proof. We prove equivalentness of the pressure correction method and the stabilized Gauge-Uzawa method. Also we will obtain that the Gauge-Uzawa method is equivalent to the gauge method and the consistent splitting method. We gather theoretical results of them and conclude that the results are also valid on other equivalent methods.

• Journal of Ocean Engineering and Technology
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• v.16 no.6
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• pp.44-48
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• 2002

In lateral ground flow, slope stability, and land slide problems, H-piles have often been used, on a horizontally deforming ground, to prevent the failure of mass of soil in a downward and outward movement of a slope. Here, theoretical equations are derived to estimate the lateral force, assuming that the Mohr-Coulomb's plastic states occur in the ground, just around H-piles. In this study, some model experiments were performed to check the lateral forces determined from theoretical equations, using several pile widths, heights and various interval ratios between H-piles for sand specimens. The solution of the theoretical equation, derived from previous studies, showed reasonable characteristics for constants of soil, as well as for the interval, widths, and heights of H-Pile.

• Proceedings of the SAREK Conference
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• 2008.06a
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• pp.603-608
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• 2008

A simple equation to find a optimum speed of desiccant rotor is presented in this theoretical study. Usually the determination of optimum speed of desiccant rotor requires tedious and lengthy procedures by solving governing differential equations with many complicated parameters. The determining equation of optimal rotating speed is derivated from governing differential equations with three linearization assumptions, which simplify temperature profile linear along the desiccant rotor depth, psychrometric chart within a proper range, and relative humidity-sorption capacity relation. This study shows that the dominant parameters of optimal rotating speed of desiccant rotor are NTU, flow velocity, desiccant rotor depth, and temperature different between dehumidification and regeneration. The comparison shows the good agreement between complicated calculation results and simple theoretical equation prediction.

• Proceedings of the Korean Fiber Society Conference
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• 1988.06a
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• pp.35-37
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• 1988

This paper shows the possibility of the application of the orientation density function of fibers to the mechanics of fibrous assembly. As an example, the orientation density function of a single yarn was theoretically derived in consideration of the idealized helical yarn. And the theoretical derivation of the tensile modulus of the fibrous assembly was performed in view of the fiber orientation. Application of this orientation density function to the obtained tensile modulus and to the contraction factor of the yarn was also performed so that the theoretical equations of the tensile modulus and the contraction factor of the yarn were obtained. Close agreement was shown between the theoretical and the existing equations. Consequently it was confirmed that the application of the orientation density function to the mechanics of the fibrous assembly is sufficiently possible.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.565-573
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• 2007

This paper is concerned with the dynamic modeling, active vibration controller design and experiments for a cylindrical shell equipped with MFC actuators. The dynamic model was derived by using Rayleigh-Ritz method based on Donnel-Mushtari shell theory. The actuator and sensors for the MFC actuator equations were derived based on pin-force model. The equations of motion were then reduced to modal equations of motion by considering the modes of interest. The sensor equations were also converted to a reduced form. An aluminum shell was fabricated to demonstrate the effectiveness of modeling and control techniques. The boundary conditions at both ends of the shell were assumed to be shear diaphragm. Theoretical natural frequencies were calculated and compared to experimental result. It was observed that the theoretical result is in good agreement with experimental result for the first two modes. The multi-input and multi-output positive position feedback controller, which can cope with first two modes, was then designed based on the blockinverse theory and implemented using DSP. It was found from experiment that vibrations can be successfully suppressed.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.247-262
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• 2016

We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.667-677
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• 2002

In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach.