• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.415-420
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• 2014

We give explicit formulas, without using the Poisson integral, for the functions that are C-harmonic on the unit disk and restrict to a prescribed polynomial on the boundary.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.31-38
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• 1996

It is well known that Dirichlet problem of the first-order Hamilton-Jacobi equations $$ (H-J) u(x) + H(\nabla u(x)) = f(x), x \in R^N, $$ does not have a classical solution even though the Hamiltonian H is smooth.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.327-329
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• 1994

The Dirichlet problem (DP) on the upper half plane {z = x ＋ iy : y > 0} is to find a real-valued harmonic function u(x, y) satisfying u(x, 0) = g(x) almost everywhere for some reasonably nice function g defined on the real line, which is called the data on the boundary for (DP).(omitted)

• The Korean Journal of Applied Statistics
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• v.6 no.1
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• pp.173-181
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• 1993

Nonparametric empirical Bayes estimation of a distribution function with respect to dirichlet process prior is considered when sample sizes are varying from component to component. Zehnwirth's estimate of $\alpha$(R) is modified to be used in our empirical Bayes problem with non-identical components.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.495-505
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• 2009

By means of Green function and fixed point theorem related with cone theoretic method we show that there exist multiple nonnegative solutions of a Dirichlet problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\lambda}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x(0)=0=x(T)}$$, and a mixed problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\mu}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x^{\prime}(0)=0=x(T)}$$, where ${\lambda}$ and ${\mu}$ are positive parameters.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.681-715
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• 2004

Mathematical formulation and numerical solutions of an optimal Dirichlet boundary control problem for the Boussinesq equations are considered. The solution of the optimal control problem is obtained by adjusting of the temperature on the boundary. We analyze finite element approximations. A gradient method for the solution of the discrete optimal control problem is presented and analyzed. Finally, the results of some computational experiments are presented.

• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.165-169
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• 2009

The effect of the Dirichlet boundary condition for the redistance equation of level set method on the solutionof sloshing problem is investigated by adopting four Dirichlet boundary conditions. For the solution of the incompressible Navier-Stokes equations, P1P1 four-step fractional finite element method is employed and a least-square finite element method is used for the solutions of the two hyperbolic type equations of level set method; advection and redistance equation. ALE (Arbitrary Lagrangian Eulerian) method is used to deal with a moving computational domain. It has been shown that the free surface motion in a sloshing tank is strongly dependent on the type of the Dirichlet boundary condition and the results of broken dam and sloshing problems using various Dirichlet boundary conditions are discussed and compared with the existing experimental results.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.405-413
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• 2001

The inverse boundary value problem for the steady state heat equation with convection term is considered in a simply connected bounded domain with smooth boundary. Taking the Dirichlet to Neumann map which maps the temperature on the boundary to the that flux on the boundary as an observation data, the global uniqueness for identifying the convection term from the Dirichlet to Neumann map is proved.

• Communications for Statistical Applications and Methods
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• v.17 no.6
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• pp.791-801
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• 2010

This study reviews the concept of disclosure, disclosure risks, and uniqueness. The number of uniqueness in the population is of great importance in evaluating the disclosure risk of micro data files. We approach this problem by considering some basic superpopulation models including the Multinomial-Dirichlet model, the Poisson- Gamma model of Bethlehem et al. (1990) and Takemura (1997), and the Modified Multinomial-Dirichlet model. We decided the critical population size of each superpopulation model for four different superpopulation models.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.201-211
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• 2010

We investigate the number of the nontrivial solutions of the nonlinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the nonlinear biharmonic problem. We prove this result by the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.