• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.235-246
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• 2005

We present an interpolating, univariate subdivision scheme which preserves the discrete curvature and tangent direction at each step of subdivision. Since the polygon have a geometric information of some original(in some sense) curve as a discrete curvature, we can expect that the limit curve has the same curvature at each vertex as the control polygon. We estimate the curvature bound of odd vertices and give an error estimate for restoring a curve from sampled vertices on curves.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.4
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• pp.253-287
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• 2018

This paper studies the global stability of a class of discrete-time pathogen infection models with latently infected cells. The rate of pathogens infect the susceptible cells is taken as bilinear, saturation and general. The continuous-time models are discretized by using nonstandard finite difference scheme. The basic and global properties of the models are established. The global stability analysis of the equilibria is performed using Lyapunov method. The theoretical results are illustrated by numerical simulations.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.529-548
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• 2007

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

• Journal of the Korea Society of Computer and Information
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• v.16 no.2
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• pp.235-242
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• 2011

The industry of computer has been changed quickly by developing and growing info-communications industry and by supplying new technologies. The importance of software field which is based on this change is gradually emphasized. Nowadays more people tend to have realization of mathematics and statistics that are basic theory of software study, moreover, discrete mathematics is especially getting more important in whole mathematics field. It's essential to understand discrete mathematics in order to understand existing knowledge about software field in computer engineering and develop new technologies in different areas in the future. The way people get education about discrete mathematics, however, is improper as a result of massive materials and uncertain standard. This study subdivides discrete mathematics according to different tracks in the computer software study. In addition, the research which is suitable to individuality in different fields is able to be efficiently carried out by selecting related parts and the method of mathematics education is provided to deal with rapidly changed applications in related fields.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.31-40
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• 1998

Spectral analysis by energy method is given for a fully discrete methods for hyperbolic integro-differential equations with a weakly singular kernel. Stability and error estimates in $H^1$-norm are derived.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1033-1046
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• 1999

This paper is devoted to the point wise error estimate up to boundary for the standard finite element solution of Poisson equation with Dirichlet boundary condition. Our new approach used the discrete maximum principle for the discrete harmonic solution. once the mesh in our domain satisfies the $\beta$-condition defined by us, the discrete harmonic solution with dirichlet boundary condition has the discrete maximum principle and the pointwise error should be bounded by L-errors newly obtained.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.321-325
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• 2007

We prove the Medina's results about the existence and uniqueness of solutions of discrete Volterra equations of convolution type in weighted spaces, by using the well-known Contraction Mapping Principle.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.127-133
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• 2018

We look at Toeplitz arrays on ${\mathbb{Z}}^d$ and study a characterizing property for pure discrete spectrum in terms of the periodic structures of the Toeplitz arrays.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.363-374
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• 2007

In this paper, we consider the discrete nonlinear delay model which describe the control of a single population of cells. We establish a sufficient condition for oscillation of all positive solutions about the positive equilibrium point and give a sufficient condition for the global attractivity of the equilibrium point. The oscillation condition guarantees the prevalence of the population about the positive steady sate and the global attractivity condition guarantees the nonexistence of dynamical diseases on the population.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.387-396
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• 1997

For given discrete derivative data in a rectangular re-gion we propose a method to generate an approximated surface which fits the given derivative data in the region and extends smoothly to a sufficiently large rectangular region. Such an extension in nec-essary in the generation of the surface in NC(numerical control) ma-chine.