• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.185-201
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• 2014

In this paper, we construct a numerical method to solve singularly perturbed one-dimensional parabolic convection-diffusion problems. We use Euler method with uniform step size for temporal discretization and exponential-spline scheme on spatial uniform mesh of Shishkin type for full discretization. We show that the resulting method is uniformly convergent with respect to diffusion parameter. An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. The obtained numerical results show that the method is efficient, stable and reliable for solving convection-diffusion problem accurately even involving diffusion parameter.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 하계종합학술대회 논문집(4)
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• pp.70-73
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• 2000

The error diffusion is good for reproducing continuous image to binary image. However the reproduction of edge characteristics is weak in power spectrum analysis of display error. It is suggested for us an edge-enhanced error-diffusion method that is included pre-processing algorithm for edge characteristic enhancement. Pre-processing algorithm is organized horizontal and vertical directional 2nd order differential values and weighting function of pre-filter. The improved Error diffusion using pre-filter, presents a good results visually which edge characteristics is enhanced. The performance of the proposed algorithm is compared with that of the conventional edge-enhanced error diffusion by measuring the RAPSD of display error, the egde correlation and the local average accordance.

• Communications for Statistical Applications and Methods
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• 제22권1호
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• pp.95-103
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• 2015

We introduce a surplus process which follows a diffusion process with positive drift and is subject to two types of claim. We assume that type I claim occurs more frequently, however, its size is stochastically smaller than type II claim. We obtain the ruin probability that the level of the surplus becomes negative, and then, decompose the ruin probability into three parts, two ruin probabilities caused by each type of claim and the probability that the level of the surplus becomes negative naturally due to the diffusion process. Finally, we illustrate a numerical example, when the sizes of both types of claim are exponentially distributed, to compare the impacts of two types of claim on the ruin probability of the surplus along with that of the diffusion process.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.455-460
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• 2007

In allelic model $X=(x_1,\;x_2,\;{\cdots},\;x_d)$, $$M_f(t)=f(p(t))-{\int}_0^t\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we try to apply diffusion processes for countable-allelic model in population genetic model and we can define a new diffusion operator $L^*$. Since the martingale problem for this operator $L^*$ is related to diffusion processes, we can define a integral which is combined with operator $L^*$ and a bilinar form $<{\cdot},{\cdot}>$. We can find properties for this integral using maximum principle.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권1호
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• pp.436-450
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• 2017

Recently, the method based on fractional order partial differential equation has been used in image processing. Usually, the optional order of fractional differentiation is determined by a lot of experiments. In this paper, a denoising model is proposed based on adaptive fractional order anisotropic diffusion. In the proposed model, the complexity of the local image texture is reflected by the local variance, and the order of the fractional differentiation is determined adaptively. In the process of the adaptive fractional order model, the discrete Fourier transform is applied to compute the fractional order difference as well as the dynamic evolution process. Experimental results show that the peak signal-to-noise ratio (PSNR) and structural similarity index measurement (SSIM) of the proposed image denoising algorithm is better than that of other some algorithms. The proposed algorithm not only can keep the detailed image information and edge information, but also obtain a good visual effect.

• 반도체디스플레이기술학회지
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• 제13권2호
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• pp.37-44
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• 2014

In this study, the performance of dye-sensitized solar cells with different thickness of the photelectrode film was simulated by using the electron-diffusion differential model. Through this simulation, the relationships between the thickness of the photoelectrode film and the performances (open-circuit voltage, short-circuit current density, and overall photoelectric-conversion efficiency) of cells were understood and the performances with different thickness of the photoelectrede film were also examined. For considering the refractive index in the liquid electrolyte and exploring the scattering effect of titanium dioxide particles with different sizes using the Mie light-scattering theory, the highest scattering effect of each particles was found out and the optimal size of the titanium dioxide particle was determined for light scattering in the photoelectrode film of dye-sensitized solar cell. Through experiment, the mixed titanium dioxide cell was better than the single titanium dioxide cell and generated a higher overall conversion efficiency because the optimal titanium dioxide particles in the phoelectrode film as light scattering.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권3호
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

• Communications for Statistical Applications and Methods
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• 제21권6호
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• pp.521-528
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• 2014

A stochastic Gompertz diffusion model for tumor growth is a topic of active interest as cancer is a leading cause of death in Korea. The direct maximum likelihood estimation of stochastic differential equations would be possible based on the continuous path likelihood on condition that a continuous sample path of the process is recorded over the interval. This likelihood is useful in providing a basis for the so-called continuous record or infill likelihood function and infill asymptotic. In practice, we do not have fully continuous data except a few special cases. As a result, the exact ML method is not applicable. In this paper we proposed a method of parameter estimation of stochastic Gompertz differential equation via Markov chain Monte Carlo methods that is applicable for several data structures. We compared a Markov transition data structure with a data structure that have an initial point.

• 한국분무공학회지
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• 제15권4호
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• pp.182-188
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• 2010

Significant real fluid behaviors including rapid property changes take place where high pressure combustion devices such as rocket engines. The flamelet model is the reliable approach to account for the real fluid effects. In the present study, the flamelet equations are extended to treat the general fluids over transcritical and supercritical states. The real fluid flamelet model is carried out for the gaseous hydrogen and cryogenic liquid oxygen flames at the wide range of thermodynamic conditions. Based on numerical results, the precise discussions are made for effects of real fluid, pressure, and differential diffusion on the local flame structure.

• Asian Pacific Journal of Cancer Prevention
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• 제16권14호
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• pp.6135-6140
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• 2015

Background: The aim of this meta-analysis was to assess the efficacy of the apparent diffusion coefficient (ADC) value of diffusion-weighted MRI (DWI) for differentiating biliary tract cancer (BTC) from benign biliary tract diseases in Asians. Materials and Methods: We systematically searched Embase and PubMed prior to December 2014. Eight studies conducted in Asians met our predetermined inclusion criteria. Results: Our meta-analysis results showed that ADC values in BTC tissues were significantly lower than in benign biliary tract tissues (SMD = -1.54, 95%CI: -1.75~-1.33, P<0.001). Subgroup analysis based on the MRI machine type showed that the ADC values were consistent, accurate and reliable in the diagnosis of BTC when comparing cancer tissue vs. benign tissue under the Siemens 1.5 T/3.0 T, Philips 1.5 T/3.0 T, GE 1.5 T, and Toshiba 1.5 T types, respectively (all P<0.05). Further, ADC values were still consistent and accurate in the differential diagnosis of BTC under the b value of 800 and $1000s/mm^2$ (all P<0.05). Conclusions: Our findings supported potential clinical applications of DWI ADC values in differentiating BTC from benign biliary tract diseases in Asians.