• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.343-357
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• 2002

This paper proposes a method for producing smooth and positive estimates of the intensity function of an inhomogeneous Poisson process based on the shrinkage of wavelet coefficients of the observed counts. The information projection is used in conjunction with the level-dependent thresholds to yield smooth and positive estimates. This work is motivated by and demonstrated within the context of a problem involving gamma-ray burst data in astronomy. Simulation results are also presented in order to show the performance of the information projection estimators.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.5
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• pp.1486-1497
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• 1996

The problem of determining the 3-demensional motion of any two rough bodies after a collision involves some rather long analysis and yet in some points it differs essentially from the corresponding problem in tdwo dimensions. We consider a special problem where two rough ellipsolids moving in any manner collide, and analyze the three dimensional impact process with Coulomb friction and Poisson's hypothesis. The differential equations that describe that process of the impact induce a flow in the tangent velocity space, the flow patterns characterize the possible impact cases. By using the graphic method in impulse space and numerical integration thchnique, we analyzed the impact process inall the possible cases and presented the algorithm for determining the post-impact motion. The principles could be applied to the general problem in three dimensions. We verified the effectiveness of the analysis results by simulating the numerous significant examples.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.661-674
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• 2016

In [15] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution we could get accurate solution just by adding the singular part. This approach works for the case when we have the accurate stress intensity factor. In this paper we consider Poisson equations with mixed boundary conditions and show the method depends the accrucy of the stress intensity factor by considering two algorithms.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.247-262
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• 2016

In this paper, we consider the following $Schr{\ddot{o}}dinger$-Poisson system: $$\{\begin{array}{lll}-{\Delta}u+u+{\lambda}{\phi}u={\mu}f(u)+{\mid}u{\mid}^{p-2}u,\;\text{ in }{\Omega},\\-{\Delta}{\phi}=u^2,\;\text{ in }{\Omega},\\{\phi}=u=0,\;\text{ on }{\partial}{\Omega},\end{array}$$ where ${\Omega}$ is a smooth and bounded domain in $\mathbb{R}^3$, $p{\in}(1,6]$, ${\lambda}$, ${\mu}$ are two parameters and $f:\mathbb{R}{\rightarrow}\mathbb{R}$ is a continuous function. Using some critical point theorems and truncation technique, we obtain three multiplicity results for such a problem with subcritical or critical growth.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.503-515
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• 1998

When a neutral particle beam(NPB) aimed at the object and receive a small number of neutron signals at the detector, it follows approximately Poisson distribution. Under the four assumptions in the presence of errors and uncertainties for the Poisson parameters, an exact probability distribution of neutral particles have been derived. The probability distribution for the neutron signals received by a detector averaged over the three sources of errors is expressed as a four-dimensional integral of certain data. Two of the four integrals can be evaluated analytically and thereby the integral is reduced to a two-dimensional integral. The monotone likelihood ratio(MLR) property of the distribution is proved by using the Cauchy mean value theorem for the univariate distribution and multivariate distribution. Its MLR property can be used to find a criteria for the hypothesis testing problem related to the distribution.

• The Korean Journal of Applied Statistics
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• v.21 no.5
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• pp.755-763
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• 2008

This paper approaches the problem of option pricing in an incomplete market, where the underlying asset price process follows a compound Poisson model. We assume that the price process follows a compound Poisson model under an equivalent martingale measure and it converges weakly to the Black-Scholes model. First, we express the option price as the expectation of the discounted payoff and expand it at the Black-Scholes price to obtain a pricing formula with three unknown parameters. Then we estimate those parameters using the market option data. This method can use the option data on the same stock with different expiration dates and different strike prices.

• East Asian mathematical journal
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• v.33 no.1
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• pp.1-9
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• 2017

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get accurate solution just by adding the singular part. This approach works for the case when we have the reasonably accurate stress intensity factor. In this paper we consider Poisson equations defined on a domain with a concave corner with Neumann boundary conditions. First we compute the stress intensity factor using the extraction formular, then find the regular part of the solution and the solution.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.27-39
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• 1998

We describe a fast numerical method for non-separable elliptic equations in self-adjoin form on irregular adaptive domains. One of the most successful results in numerical PDE is developing rapid elliptic solvers for separable EPDEs, for example, Fourier transformation methods for Poisson problem on a square, however, it is known that there is no rapid elliptic solvers capable of solving a general nonseparable problems. It is the purpose of this paper to present an iterative solver for linear EPDEs in self-adjoint form. The scheme discussed in this paper solves a given non-separable equation using a sequence of solutions of Poisson equations, therefore, the most important key for such a method is having a good Poison solver. High performance is achieved by using a fast high-order adaptive Poisson solver which requires only about 500 floating point operations per gridpoint in order to obtain machine precision for both the computed solution and its partial derivatives. A few numerical examples have been presented.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1269-1284
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• 2022

This paper is concerned with the following Schrödinger-Poisson system $$\{\begin{array}{lll}-{\Delta}u+V(x)u+K(x){\phi}u=a(x){\mid}u{\mid}^{p-2}u&&\text{ in }{\mathbb{R}}^3,\\-{\Delta}{\phi}=K(x)u^2&&\text{ in }{\mathbb{R}}^3,\end{array}$$ where 4 < p < 6. For the case that K is nonnegative, V and a are indefinite, we prove the above problem possesses one ground state sign-changing solution with exactly two nodal domains by constraint variational method and quantitative deformation lemma. Moreover, we show that the energy of sign-changing solutions is larger than that of the ground state solutions. The novelty of this paper is that the potential a is indefinite and allowed to vanish at infinity. In this sense, we complement the existing results obtained by Batista and Furtado [5].