• Korean Journal of Mathematics
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• v.25 no.2
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• pp.181-199
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• 2017

In this paper we consider the orthogonal polynomials with weights ${\omega}_{\alpha}(x)=x^{\alpha}{\exp}(-x^3+tx)$ and $W_{\alpha}(x)={\mid}x{\mid}^{2{\alpha}+1}{\exp}(-x^6+tx^2)$. Using the compatibility conditions for the ladder operators for these orthogonal polynomials, we derive several difference equations satisfied by the recurrence coefficients of these orthogonal polynomials. We also derive differential-difference equations and second order linear ordinary differential equations satisfied by these orthogonal polynomials.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1239-1243
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• 2005

A multipath mitigation method using the fault detection and isolation technique is proposed for the CDGPS. The base station is assumed to be immune to the effect of the multipath. With this reasonable assumption, the effect of multipath in moving station is mitigated. For that, the double difference measurement is produced, and then another additional difference between code pseudorange and acclumulated carrier phase is calculated. The test statistic is constituted with those differences. The hypothesis testing is applied to that test statistic. The proposed test statistic makes use of the effect of multipath in code pseudoranges and it does not use time differences. Therefore the detection ability for multipath is improved in most environments. However, the increased number of differences makes the measurement noises larger. The performance of the method is compared with that of the conventional parity space method with code pseudorange.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.715-725
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• 2013

In this paper, a finite difference scheme for a two-point boundary value problem of 2nth-order ordinary differential equations is presented. The convergence and uniqueness of the solution for the scheme are proved by means of theories on matrix eigenvalues and norm. Numerical examples show that our method is very simple and effective, and that this method can be used effectively for other types of boundary value problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.15-29
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• 2007

In this paper, we explore some interesting models of the quasi-negative-binomial distribution based on difference differential equations applicable to theory of microorganisms and the situations like that. Some characterizations based on conditional distributions and damage process have been obtained. Further, the distribution of number of accidents as the quasi-negative-binomial distribution in the light of Irwin's theory of ";proneness-liability"; model has been derived. Finally, the proposed model (QNBD) has been applied to study the Shunting accidents, home injuries, and strikes in industries.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.10
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• pp.4108-4125
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• 2015

This paper presents a scalable coding method for depth images by considering the quality of synthesized images in virtual views. First, we design a new edge detection algorithm that is based on calculating the depth difference between two neighboring pixels within the depth map. By choosing different thresholds, this algorithm generates a scalable bit stream that puts larger depth differences in front, followed by smaller depth differences. A scalable scheme is also designed for coding depth pixels through a layered sampling structure. At the receiver side, the full-resolution depth image is reconstructed from the received bits by solving a partial-differential-equation (PDE). Experimental results show that the proposed method improves the rate-distortion performance of synthesized images at virtual views and achieves better visual quality.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.939-955
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• 2022

In this paper, we study a first-order non-linear singularly perturbed Volterra integro-differential equation (SPVIDE). We discretize the problem by a uniform difference scheme on a Bakhvalov-Shishkin mesh. The scheme is constructed by the method of integral identities with exponential basis functions and integral terms are handled with interpolating quadrature rules with remainder terms. An effective quasi-linearization technique is employed for the algorithm. We establish the error estimates and demonstrate that the scheme on Bakhvalov-Shishkin mesh is O(N^-1) uniformly convergent, where N is the mesh parameter. The numerical results on a couple of examples are also provided to confirm the theoretical analysis.

• Proceedings of the Korean Institute of Building Construction Conference
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• 2023.05a
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• pp.227-228
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• 2023

This study is tocompare and analyze the results of hydration heat analysis and on-field measurements using the method with hydration heat difference and insulation curing method for controlling hydration heat in mass concrete. As a result of the analysis, the temperature difference between the center and the surface was predicted very similarly, and the mass concrete surface was controlled to a safe level when evaluating with a temperature crack index, and after being finished, it was confirmed that there was no hydration crack.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.269-282
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• 2007

In this paper, we consider a two-dimensional fractional space-time diffusion equation (2DFSTDE) on a finite domain. We examine an implicit difference approximation to solve the 2DFSTDE. Stability and convergence of the method are discussed. Some numerical examples are presented to show the application of the present technique.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.753-762
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• 2012

We study the BS-stability and the $\rho$-stability for functional difference equations with infinite delay as a discretization of Murakami and Yoshizawa's results [6] for functional differential equation with infinite delay.