• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1059-1068
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• 2015

The paper is devoted to studying a fourth-order degenerate parabolic equation, which arises in fluid, phase transformation and biology. Based on the existence and uniqueness of one semi-discrete problem, two types of approximate solutions are introduced. By establishing some necessary uniform estimates for those approximate solutions, the existence and uniqueness of the corresponding parabolic problem are obtained. Moreover, the long time asymptotic behavior is established by the entropy functional method.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.165-177
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• 2013

In this paper, we apply Homotopy perturbation transform method (HPTM) for solving singular fourth order parabolic partial differential equations with variable coefficients. This method is the combination of the Laplace transform method and Homotopy perturbation method. The nonlinear terms can be easily handled by the use of He's polynomials. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as Homotopy perturbation method (HPM), Variational iteration method (VIM) and Adomain Decomposition method (ADM). The proposed scheme finds the solutions without any discretization or restrictive assumptions and avoids the round-off errors. The comparison shows a precise agreement between the results and introduces this method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.1
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• pp.69-77
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• 1984

In this paper, the governing differential equations for the free vibration of uniform parabolic arches are derived on the basis of equilibrium equations of a small element of arch rib and the D'Alembert principle. A trial eigen value method is used for determining the natural frequencies and mode shapes. And the Runge-Kutta fourth order integration technique is also used in this method to perform the integration of the differential equations. A detailed study is made of the first mode for the symmetrical and anti-symmetrical vibrations of hinged arches with the Span length equal to 10 m. The effects of the rise of arch, the radius of gyration and the rotary inertia on free vibrations are presented in detail in curves and table.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.3
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• pp.185-194
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• 2012

This paper deals with free vibrations of the tapered Timoshenko beam in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the rectangular cross section whose depth is constant but breadth is varied with the parabolic function. The fourth order ordinary differential equation with respect the vertical deflection governing free vibrations of such beam is derived based on the Timoshenko beam theory. This governing equation is solved for determining the natural frequencies corresponding with their mode shapes. In the numerical examples, three end constraints of the hinged-hinged, hinged-clamped and clamped-clamped ends are considered. The effects of various beam parameters on natural frequencies are extensively discussed. The mode shapes of both the deflections and stress resultants are presented, in which the composing rates due to bending rotation and shear deformation are determined.

• Journal of Astronomy and Space Sciences
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• v.29 no.2
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• pp.151-161
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• 2012

An intensive analysis of 148 timings of V700 Cyg was performed, including our new timings and 59 timings calculated from the super wide angle search for planets (SWASP) observations, and the dynamical evidence of the W UMa W subtype binary was examined. It was found that the orbital period of the system has varied over approximately $66^y$ in two complicated cyclical components superposed on a weak upward parabolic path. The orbital period secularly increased at a rate of $+8.7({\pm}3.4){\times}10^{-9}$ day/year, which is one order of magnitude lower than those obtained by previous investigators. The small secular period increase is interpreted as a combination of both angular momentum loss (due to magnetic braking) and mass-transfer from the less massive component to the more massive component. One cyclical component had a $20.^y3$ period with an amplitude of $0.^d0037$, and the other had a $62.^y8$ period with an amplitude of $0.^d0258$. The components had an approximate 1:3 relation between their periods and a 1:7 ratio between their amplitudes. Two plausible mechanisms (i.e., the light-time effects [LTEs] caused by the presence of additional bodies and the Applegate model) were considered as possible explanations for the cyclical components. Based on the LTE interpretation, the minimum masses of 0.29 $M_{\odot}$ for the shorter period and 0.50 $M_{\odot}$ for the longer one were calculated. The total light contributions were within 5%, which was in agreement with the 3% third-light obtained from the light curve synthesis performed by Yang & Dai (2009). The Applegate model parameters show that the root mean square luminosity variations (relative to the luminosities of the eclipsing components) are 3 times smaller than the nominal value (${\Delta}L/L_{p,s}{\approx}0.1$), indicating that the variations are hardly detectable from the light curves. Presently, the LTE interpretation (due to the third and fourth stars) is preferred as the possible cause of the two cycling period changes. A possible evolutionary implication for the V700 Cyg system is discussed.

• Journal of the Korean Applied Science and Technology
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• v.36 no.2
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• pp.498-506
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• 2019

This study is based on a coating method that provides utilization value as a micronised powder for cosmetic raw materials using natural minerals buried in Bonghwa, Gyeongsangbuk-do in Korea. The mineral powder name is called Buseok, and chemical name is pumice powder. The results of a study on the efficacy of cosmetics are reported by the development of particulate powder to assess the performance of this powder. First of all, in order to coat the surface of this powder with oil, aluminum hydroxide was coated on the particulate surface and then coated with alkylsilan. In addition, it was coated with vegetable oil to prevent condensation of the powder and increase the dispersion in the oil phase. First; the particle size of pumice powder was from 10 to 50mm having porous holes on the surface of the particles. Second; The components of this powder contained $SiO_2$, $Al_2O_3$, $Fe_2O_3$, MgO, CaO, $K_2O_2$, $Na_2O$, $TiO_2$, $TiO_2$, MnO, $Cr_2O_3$, $V_2O_5$. Third: The particles of this powder have a planetary structure and are reddish-brown with porosity through SEM and TEM analysis. Fourth; the far-infrared radiation rate of this parabolic powder was $0.924{\mu}m$, and the radiative energy was $3.72{\times}102W/m^2$ and ${\mu}m$. In addition, the anion emission is 128 ION/cc, which shows that the coating remains unchanged. Based on these results, it is expected to be widely applied to basic cosmetics such as BB cream, cushion foundation, powderfect, and other color-coordinated cosmetics, sunblock cream, wash-off massage pack as an application of cosmetics. (Small and Medium Business Administration: S2601385)