• Journal of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.337-348
• /
• 2001

The unitary Lie-Trotter-Kato product formula gives in a simplest way a meaning to the Feynman path integral for the Schroding-er equation. In this note we want to survey some of recent results on the norm convergence of the selfadjoint Lie-Trotter Kato product formula for the Schrodinger operator -1/2Δ + V(x) and for the sum of two selfadjoint operators A and B. As one of the applications, a remark is mentioned about an approximation therewith to the fundamental solution for the imaginary-time Schrodinger equation.

• Journal of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.867-885
• /
• 2011

We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.1
• /
• pp.13-27
• /
• 2014

The purpose of this paper is to derive a perturbation theory of evolution systems of the hyperbolic second order hyperbolic equations. We give an example of a partial functional equation as an application of the preceding result in case of the mixed problems for hyperbolic equations of second order with unbounded principal operators.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 1995.11a
• /
• pp.324-327
• /
• 1995

In this research, FEM solution to analysis near field of high Tc superconductor microstrip antenna is presented. This method uses the interpolation function with vector edge triangular element. The advantage of this element is elimination of spurious solutions which are attributed to the lack of enforcement of the divergence condition. The solutions of this method will be used to have a good fundamental data for next reaserch about analysis of HTS microstrip array antenna etc.

• Proceedings of the Korea Concrete Institute Conference
• /
• 1999.04a
• /
• pp.799-806
• /
• 1999

This study describes the results of experiment and numerical analysis for heating image by thermographic method when the size of void in concrete are changed. By comparing analytical solution by finite element method with measured image by thermography, the relationships between the surface temperature which can be confirmed by this method, the size of void and optimum time for detection of void and the difference of temperature are cleared.

• Proceedings of the Korea Concrete Institute Conference
• /
• 1998.04a
• /
• pp.267-270
• /
• 1998

Recently, underwater concrete constructions are increasing. Therefore it is considered important to control the quality of underwater concrete. In this paper, we have an intention of evaluating fundamental properties of underwater concrete using the anti-washout admixtures. Thus, it has been investigated that the setting slump flow of the concrete, pH value and suspended solids in solution, compressive strength on both of specimens made above and under water. Also the percentage of fine aggregate has been found to alter the compressive strength in underwater concrete.

• Journal of the Korean Mathematical Society
• /
• v.45 no.5
• /
• pp.1361-1378
• /
• 2008

This paper deals with the study of dichotomy and conditioning for two-point boundary value problems associated with first order matrix Lyapunov systems, with the help of Kronecker product of matrices. Further, we obtain close relationship between the stability bounds of the problem on one hand, and the growth behaviour of the fundamental matrix solution on the other hand.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1411-1425
• /
• 2016

We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).

• 한국전산유체공학회:학술대회논문집
• /
• 1997.10a
• /
• pp.10-15
• /
• 1997

Unsteady natural convection of an enclosed fluid has been one of the fundamental thermo-fluid problems, of which dynamic relevance is found in many engineering applications. Together with the inherent coupling between the boundary layers and the interior core, and strong interaction between flow and temperature fields, the unsteadiness poses serious hurdles for analytical and experimental approaches. With the recent development of computers and solution algorithms, computational fluid dynamics has become the prevailing tool to tackle the underlying problems. In this presentation, a few examples of numerical studies are introduced. The usefulness and potential of numerical simulations in investigating unsteady natural convection are elaborated.

• Journal of the Chungcheong Mathematical Society
• /
• v.7 no.1
• /
• pp.141-152
• /
• 1994

We consider a numerical scheme for solving a nonlinear boundary integral equation (BIE) obtained by reformulation the nonlinear boundary value problem (BVP). We give a simple alternative to the standard collocation method for the nonlinear BIE. This method consists of one conventional linear system and another coupled linear system resulting from an auxiliary BIE which is obtained by differentiating both side of the nonlinear interior integral equations. We obtain an analogue BIE through the perturbation of the fundamental solution of Laplace's equation. We procure the super-convergence of approximate solutions.