• Journal of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.661-678
• /
• 1995

In this paper we will estimate from above and below the values of the Bergman, Caratheodory and Kobayashi metrics for a vector X at z, where z is any point near a given point $z_0$ in the boundary of pseudoconvex domains in $C^n$.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.21 no.12
• /
• pp.3227-3234
• /
• 1996

This paper proposes a new absorbing boundary condition(ABC) for the FDTD simulation of waveguide problems. It is based on the exact analytic expression for the time domain EM wave propatation in the waveguide. The ABC derived from the expression has a convolution form whose kernel (the discrete Green's function) has a simple, closed form formula. Also, it is applicable to the wide variety of waveguide types with conducting boundaries and complex cross-sectional shapes.

• Journal of applied mathematics & informatics
• /
• v.12 no.1_2
• /
• pp.81-105
• /
• 2003

This paper deals with the very interesting problem about the influence of piecewise smooth boundary conditions on the distribution of the eigenvalues of the negative Laplacian in R$^3$. The asymptotic expansion of the trace of the wave operator (equation omitted) for small ｜t｜ and i=√-1, where (equation omitted) are the eigenvalues of the negative Laplacian (equation omitted) in the (x$^1$, x$^2$, x$^3$)-space, is studied for an annular vibrating membrane $\Omega$ in R$^3$together with its smooth inner boundary surface S$_1$and its smooth outer boundary surface S$_2$. In the present paper, a finite number of Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components (equation omitted)(i = 1,...,m) of S$_1$and on the piecewise smooth components (equation omitted)(i = m +1,...,n) of S$_2$such that S$_1$= (equation omitted) and S$_2$= (equation omitted) are considered. The basic problem is to extract information on the geometry of the annular vibrating membrane $\Omega$ from complete knowledge of its eigenvalues by analysing the asymptotic expansions of the spectral function (equation omitted) for small ｜t｜.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.5
• /
• pp.1215-1235
• /
• 2022

In this paper we study Szegö kernel projections for Hardy spaces in quaternionic Clifford analysis. At first we introduce the matrix Szegö projection operator for the Hardy space of quaternionic Hermitean monogenic functions by the characterization of the matrix Hilbert transform in the quaternionic Clifford analysis. Then we establish the Kerzman-Stein formula which closely connects the matrix Szegö projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szegö projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szegö kernel function for the Hardy space on the sphere as an example, and get the solution to a Diriclet boundary value problem for matrix functions.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.4
• /
• pp.631-642
• /
• 2016

This article deals with one-dimension backward heat conduction problem (BHCP). A new approach based on least squares support vector machines (LS-SVM) is proposed for obtaining their approximate solutions. The approximate solution is presented in closed form by means of LS-SVM, whose parameters are adjusted to minimize an appropriate error function. The approximate solution consists of two parts. The first part is a known function that satisfies initial and boundary conditions. The other is a product of two terms. One term is known function which has zero boundary and initial conditions, another term is unknown which is related to kernel functions. This method has been successfully tested on practical examples and has yielded higher accuracy and stable solutions.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.4
• /
• pp.981-989
• /
• 1995

A new weight function approach to determine SIF(stress intensity factor) using single-layer potential has been presented. The crack surface displacement field was represented by one boundary integral term whose kernel was modified from Kelvin's fundamental solution. The proposed method enables the calculation of SIF using only one SIF solution without any modification for the crack geometries symmetric in two-dimensional plane such as a center crack in a plate with or without an internal hole, double edge cracks, circumferential crack or radial cracks in a pipe. The application procedure to those crack problems is very simple and straightforward with only one SIF solution. The necessary information in the analysis is two reference SIFs. The analysis results using present closed-form solution were in good agreement with those of the literature.

• Interaction and multiscale mechanics
• /
• v.2 no.2
• /
• pp.129-151
• /
• 2009

This paper presents a meshfree procedure using a convex generalized meshfree (GMF) approximation for the large deformation analysis of particle-reinforced rubber compounds on microscopic level. The convex GMF approximation possesses the weak-Kronecker-delta property that guarantees the continuity of displacement across the material interface in the rubber compounds. The convex approximation also ensures the positive mass in the discrete system and is less sensitive to the meshfree nodal support size and integration order effects. In this study, the convex approximation is generated in the GMF method by choosing the positive and monotonic increasing basis function. In order to impose the periodic boundary condition in the unit cell method for the microscopic analysis, a singular kernel is introduced on the periodic boundary nodes in the construction of GMF approximation. The periodic boundary condition is solved by the transformation method in both explicit and implicit analyses. To simulate the interface de-bonding phenomena in the rubber compound, the cohesive interface element method is employed in corporation with meshfree method in this study. Several numerical examples are presented to demonstrate the effectiveness of the proposed numerical procedure in the large deformation analysis.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 2003.03a
• /
• pp.232-237
• /
• 2003

A new displacement-based transmitting boundary is developed for the transient analysis of dynamics interactions between flexible dam body and reservoir impounding compressible water The mechanical model is derived analytically in time domain from the kernel function, Bessel function, appearing in the convolution integral and corresponding mechanical model is developed that consists of mass, damping and stiffness matrices. The resulting system of, equations uses displacement degrees of freedom. Hence it can be coupled directly with the displacement-based solid finite element model of dam body, linear of nonlinear. The method was applied to the rigid and flexible dam models. The results showed very good agreement : with the semi-analytic frequency domain solutions.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.31 no.2B
• /
• pp.87-98
• /
• 2011

Recently, occurrence frequency of extreme events like flood and drought is increasing due to climate change by global warming. Especially, a drought is more severer than other hydrologic disasters because it causes continuous damage through long period. But, ironically, it is difficult to recognize the importance and seriousness of droughts because droughts occur for a long stretch of time unlike flood. So as to analyze occurrence of droughts and prepare a countermeasure, this study analyzed a meteorologic drought among many kinds of drought that it is closely related with precipitation. Palmer Drought Severity Index, Standard Precipitation and Effective Drought Index are computed using precipitation and temperature material observed by Korean Meteorological Administration. With the result of comparative analysis of computed drought indices, Effective Drought Index is selected to execute frequency analysis because it is accordant to past droughts and has advantage to compute daily indices. A Frequency analysis of Effective Drought Index was executed using boundary kernel density function. In the result of analysis, occurrence periods of spring showed about between 10 year and 20 year, it implies that droughts of spring are more frequent than other seasons. And severity and occurrence period of droughts varied in different regions as occurrence periods of the Youngnam region and the southern coast of Korea are relatively shorter than other regions.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 2000.10a
• /
• pp.143-150
• /
• 2000

A physical lumped parameter model is proposed for the time domain analysis of dam-reservoir system. The exact solution of transmitting boundary is derived for a semi-infinite 2-D reservoir of constant depth. The characteristics of the solution are examined in both frequency and the domains. Mass and damping coefficient are obtained from asymptotic behavior of the frequency domain solution. Further refinement to the lumped model is made by approximating the kernel function of the convolution integral in the exact solution. Finally a new physical lumped parameter model is proposed that consists of two masses, a spring and two dampers for each mode. It is demonstrated that new lumped parameter model of transmitting boundary can give excellent results.