• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.19-23
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• 1995

We will estimate the lower bound of the first nonzero Neumann and Dirichlet eigenvalue of Laplacian equation on compact Riemannian manifold M with boundary. In case that the boundary of M has positive second fundamental form elements, Ly-Yau[3] gave the lower bound of the first nonzero neumann eigenvalue $\eta_1$. In case that the second fundamental form elements of $\partial$M is bounded below by negative constant, Roger Chen[4] investigated the lower bound of $\eta_1$. In [1], [2], we obtained the lower bound of the first nonzero Neumann eigenvalue is estimated under the condtion that the second fundamental form elements of boundary is bounded below by zero. Moreover, I realize that "the interior rolling $\varepsilon$ - ball condition" is not necessary when the first Dirichlet eigenvalue was estimated in [1].ed in [1].

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.12
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• pp.91-100
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• 1995

This paper represents the lateral first-order mode characteristics for the semiconductor laser diodes using a two-dimensional numerical simulator. In order to analyze the lateral first-order mode characteristics, Helmholtz wave equation is solved twice for the lateral fundamental and the first-order mode considering the mode gain, total losses, and the recombination rate due to the stimulated emission radiation for the each mode independantly. Through this procedure, we find that the lateral first-order mode was easily guided as increasing the stripe width for the index-guiding structures, and that the lateral first-order mode seems to be dominated in the distribution of total light intensity when its output power reaches nearly half of that of the lateral fundamental mode. This results may be used to design the device structure which guides only the lateral fundamental mode.

• Structural Monitoring and Maintenance
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• v.4 no.4
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• pp.351-364
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• 2017

In this study effects of various parameters like a number of bays, the stiffness of the structure along with the height of the structure was examined. The fundamental period of vibration T of the building is an important parameter for evaluation of seismic base shear. Empirical equations which are given in the Indian seismic code for the calculation of the fundamental period of a framed structure, primarily as a function of height, and do not consider the effect of number of bays and stiffness of the structure. Building periods predicted by these expressions are widely used in practice, although it has been observed that there is scope for further improvement in these equations since the height alone is inadequate to explain the period variability. The aim of this study is to find the effects of a number of bays in both the directions, the stiffness of the structure and propose a new period equation which incorporates a number of bays, plan area, stiffness along with the height of the structure.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.3
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• pp.301-312
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• 2009

This paper presents a theoretical approach to calculate the resonant frequency of a thickness vibration mode in the radial direction for a 1-3 piezoelectric composite transducer of circular arch shape. For the composite transducer composed of a piezoelectric ceramic and a polymer, vibration parameters were derived according to the volume ratio of a ceramic, and a vibration characteristic equation was derived from the piezoelectric governing equations with adequate boundary conditions. The fundamental resonant frequencies were calculated numerically and verified by comparing them with those obtained from the finite element analysis and the experiment. The volume ratio and the thickness are more substantial than the curvature radius to determine the fundamental resonant characteristics, and the fundamental resonant frequency becomes higher for the larger volume ratio of the piezoelectric ceramic and for the smaller thickness.

• Advances in aircraft and spacecraft science
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• v.3 no.1
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• pp.45-59
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• 2016

In this paper, the condensation method which is based on the Rayleigh-Ritz method, is described for the free vibration analysis of axially loaded slightly curved beams subject to partial axial restraints. If the longitudinal inertia is neglected, some of the Rayleigh-Ritz minimization equations are independent of the frequency. These equations can be used to formulate a relationship between the weighting coefficients associated with the lateral and longitudinal displacements, which leads to "connection coefficient matrix". Once this matrix is formed, it is then substituted into the remaining Rayleigh-Ritz equations to obtain an eigenvalue equation with a reduced matrix size. This method has been applied to simply supported and partially clamped beams with three different shapes of imperfection. The results indicate that for small imperfections resembling the fundamental vibration mode, the sum of the square of the fundamental natural and a non-dimensional axial load ratio normalized with respect to the fundamental critical load is approximately proportional to the square of the central displacement.

• Journal of Bio-Environment Control
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• v.23 no.3
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• pp.192-198
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• 2014

To establish the design criteria for seasonal heating load calculation in greenhouses, standard weather data are required. However, they are being provided only at seven regions in Korea. So, instead of using standard weather data, in order to find the method to build design weather data for seasonal heating load calculation, heating degree-hour and heating degree-day were analyzed and compared by methods of fundamental equation, Mihara's equation and modified Mihara's equation using normal and thirty years from 1981 to 2010 hourly weather data provided by KMA and standard weather data provided by KSES. Average heating degree-hours calculated by fundamental equation using thirty years hourly weather data showed a good agreement with them using standard weather data. The 24 times of heating degree-day showed relatively big differences with heating degree-hour at the low setting temperature. Therefore, the heating degree-hour was considered more appropriate method to estimate the seasonal heating load. And to conclude, in regions which are not available standard weather data, we suggest that design weather data should be analyzed using thirty years hourly weather data. Average of heating degree-hours derived from every year hourly weather data during the whole period can be established as environmental design standards, and also minimum and maximum of them can be used as reference data for energy estimation.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.15 no.1
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• pp.79-84
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• 2002

An accurate cross sections set is necessary for the quantitatively understanding and modeling of plasma phenomena. By using the electron swarm method, we determine an accurate electron cross sections set for objective atoms or molecule at low electron energy range. It is general calculation that used in this method to an two-term approximation of Boltzmann equation. But it may give erroneous transport coefficients for CF$_4$ molecule treated in this paper having \`C2v symmetry\`, therefore, multi-term approximation of the Boltzmann equation analysis which can consider anisotropic scattering exactly is carried out. It is necessary to require understanding of the fundamental principle of analysis method. Therefore, in this paper, we compared the electron transport coefficients(W and ND$\_$L/) in pure Ar, O$_2$, and CF$_4$ gas calculated by using two-term approximation of the Boltzmann equation analysis code uses the algorithm proposed by Tagashira et al. with those by multi-term approximation by Rubson and Ness which was developed at James-Cook university, and discussed an application and/or validity of the calculation method by comparing these calculated results.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.31-36
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• 2003

Using a short time expansion of the fundamental solution of heat equation by analysis of Wiener functional with the help of Malliavin calculus, we obtain the asymptotic expansion of the mean distance of Brownian motion on Riemannian manifolds.