• Journal of the Korean Statistical Society
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• v.29 no.4
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• pp.489-499
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• 2000

We propose a new instrumental variable estimator of the complex parameter of a class of univariate complex-valued diffusion processes defined by the possibly non-stationary and/or nonlinear stochastic differential equations. On the basis of the exact finite sample distribution of the pivotal quantity, we construct the exact confidence intervals and the exact tests for the parameter. Monte-Carlo simulation suggests that the new estimator seems to provide a viable alternative to the maximum likelihood estimator (MLE) for nonlinear and/or non-stationary processes.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.49-58
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• 2010

In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain $\mathbb{R}$. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.383-398
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• 2006

We consider a geometric Levy process for an underlying asset. We prove first that the option price is the unique solution of certain integro-differential equation without assuming differentiability and boundedness of derivatives of the payoff function. Second result is to provide convergence rate for option prices when the small jumps are removed from the Levy process.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.393-404
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• 2003

In general, a differential operator can be used as a tool of treating the local properties of given function. However, when the given function is varied with high frequency and has irregular form with non-stationary evolution it may not act its role sufficiently as in case of nowhere differentiable curves. In this paper we introduce a multi-scale derivative as a form of weakened global derivative so that it may explain its semi global diffusion properties as well as local ones for the various irregular diffusion phenomena.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1817-1828
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• 2017

We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05b
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• pp.160-165
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• 1998

Under the heavy irradiation, when the production and the recombination of interstitials and vacancies are included, the diffusion equations become nonlinear. An effort has been made to arrange an appropriated transformation of these nonlinear differential equations to soluble Poisson's equations, so that analytical solutions for simultaneously calculating the concentrations of interstitials and vacancies in the angular dependent Cottrell's potential of the edge dislocation have been derived from the well-known Green's theorem and perturbation theory.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.149-159
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• 2005

We study an age-dependent s-i-s epidemic model with spatial diffusion. The model equations are described by a nonlinear and nonlocal system of integro-differential equations. Finite difference methods along the characteristics in age-time domain combined with finite elements in the spatial variable are applied to approximate the solution of the model. Stability of the discrete periodic solution is investigated.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.71-96
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• 2024

In this paper we present many interesting results such as completeness and composition theorems in the 𝛼 norm. Moreover, under some conditions, we establish the existence and uniqueness of Cⁿ-(𝜇, 𝜈) pseudo-almost automorphic solutions of class r in the 𝛼-norm for some partial functional differential equations in Banach space when the delay is distributed. An example is given to illustrate our results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.5C
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• pp.542-549
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• 2007

Recently, many research activities in the image processing area are concentrated on developing new algorithms by finding the solution of the 'diffusion equation'. The diffusion algorithms are expected to be utilized in numerous applications including noise removal and image restoration, edge detection, segmentation, etc. In this paper, at first, it will be shown that the anisotropic diffusion algorithms have the similar structure with the adaptive FIR filters with cross-shaped 5-tap kernel, and this relatively small-sized kernel causes many iterating procedure for satisfactory filtering effects. Moreover, it will also be shown that lots of modifications which are adopted to the conventional Gaussian diffusion method in order to weaken the edge blurring nature of the linear filtering process increases another computational burden. We propose a new Median diffusion scheme by replacing the adaptive linear filters in the diffusion process with the AWM (Adaptive Weighted Median) filters. A diffusion-equation-based adaptation scheme is also proposed. With the proposed scheme, the size of the diffusion kernel can be increased, and thus diffusion speed greatly increases. Simulation results shows that the proposed Median diffusion scheme outperforms in noise removal (especially impulsive noise), and edge preservation.

• Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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• v.10 no.S_3
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• pp.121-126
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• 2001

The techniques of pulse and cyclic voltammetry were applied to the determination of (E$_{1}$2)$_2$-(E$_{1}$2)$_1$ for two-step electrochemical charge transfers. In addition, a simple amplitude was derived far the dependence of the differential pulse response on (E$_{l}$ 2/)$_1$ and (E$_{1}$2/)$_2$. and the use of peak to peak separation in cyclic voltammetry and differential pulse methods was evaluated. A comparison of the comproportionation constants(Ke) from differential pulse and cyclic voltammetry methods exhibited a good agreement within 5%.