• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.725-741
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• 1997

This paper considers the problem of deriving exponential probability inequalities for product symmetric Poisson processes. As an application they are used to show the existence of regular version of some product process derived from L$\acute{e}$vy process.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.25-42
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• 2007

A direct solver for the Legendre tau approximation for the two-dimensional Poisson problem is proposed. Using the factorization of symmetric eigenvalue problem, the algorithm overcomes the weak points of the Schur decomposition and the conventional diagonalization techniques for the Legendre tau approximation. The convergence of the method is proved and numerical results are presented.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.489-496
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• 2006

The aim of this paper is to use the Stein-Chen method to obtain a non-uniform bound on Poisson approximation in matching problem.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.3
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• pp.62-71
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• 1995

In the numerical analysis of incompressible unsteady Navier-stokes equation, large time is required for solving the pressure Poisson equation of the elliptic type at each time step. In this paper, a numerical analysis by the direct method is carried out to solve the pressure Poisson equation and the computing time is analyzed as mesh size increases. The pressure Poisson equation can be transformed to the boundary value problem by the Green theorem. The computing time for the convolution type of the domain integral can be reduced by using F.F.T. and the computing time in the direct method depends entirely on obtaining the solution of the boundary value problem. The numerical analysis on the known solutions is carried out and compared for the verification of the direct method. And the numerical analysis on the body boundary and domain decomposition problem are carried out with the computing time less than O($n^{3}$) in the (n.n) mesh.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.2
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• pp.117-123
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• 2018

In this study, we suggest a fast image reconstruction scheme using Poisson equation from image gradient domain. In this approach, using the Poisson equation, a guided vector field is created by employing source and target images within a selected region at the first step. Next, the guided vector is used in generating the result image. We analyze the problem of reconstructing a two-dimensional function that approximates a set of desired gradients and a data term. The joined data and gradients are able to work like modifying the image gradients while staying close to the original image. Starting with this formulation, we have a screened Poisson equation known in physics. This equation leads to an efficient solution to the problem in FFT domain. It represents the spatial filters that solve the two-dimensional screened Poisson model and shows gradient scaling to be a well-defined sharpen filter that generalizes Laplace sharpening. We demonstrate the results using a discrete cosine transformation based this Poisson model.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.511-527
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• 2014

This paper provides a new application similar to the Local Defect Correction (LDC) technique to solve Poisson problem -u"(x) = f(x) with Dirichlet boundary conditions. The exact solution is supposed to have high activity in some region of the domain. LDC is combined with a fourth order compact scheme which is recently developed in Abbas (Num. Meth. Partial differential equations, 2013). Numerical tests illustrate the interest of this application.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.49
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• pp.23-31
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• 1999

Bayesian approach using nonhomogeneous Poisson process is considered for modelling software reliability problem. The usefulness of the iterative sampling-based method increases greatly as the dimension of a problem increases. Maximum likelihood estimator and Gibbs estimator are derived. Model selection based on a predictive likelihood is studied. A numerical example is given.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.27-44
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• 2001

A fast Poisson solver on irregular domains, based on bound-ary methods, is presented. The harmonic polynomial approximation of the solution of the associated homogeneous problem provides a good practical boundary method which allows a trivial parallel processing for solution evaluation or straightfoward computations of the interface values for domain decomposition/embedding. AMS Mathematics Subject Classification : 65N35, 65N55, 65Y05.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.427-434
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• 2001

In this paper, we consider the nonparametric Bayesian approach to the multiple comparisons problem for I Poisson populations using Dirichlet process priors. We describe Gibbs sampling algorithm for calculating posterior probabilities for the hypotheses and calculate posterior probabilities for the hypotheses using Markov chain Monte Carlo. Also we provide a numerical example to illustrate the developed numerical technique.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.96-101
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• 1998

Various discretiation methods of Laplacian operator in the Pressure-Poisson equation are investigated for the solution of incompressible Navier-Stokes equations using the non-staggered grid. Laplacian operators previously proposed by other researchers are applied to a Driven-Cavity problem. The computational results are compared with those of Ghia. The results show the characteristics of the discrete Laplacian operators.