• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.4
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• pp.329-350
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• 2019

This paper examines individual and social strategies to form profitable cooperation networks. These two types of strategies measure network stability and efficiency that may not meet in a single network. We apply restrictions on knowledge flows (R&D spillovers) and links formation to integrate these benefits into structures that ensure high outcomes for both strategies. The results suggest that linking the spillovers to the firms' positions and restricting cooperation contribute to reducing the conflict between the individual and social strategies in the development of cooperative networks.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.1
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• pp.25-31
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• 2003

The concepts of stability of algorithms for solving the symmetric and generalized symmetric-definite eigenproblems are discussed. An algorithm for solving the symmetric eigenproblem $Ax={\lambda}x$ is stable if the computed solution z is the exact solution of some slightly perturbed system $(A+E)z={\lambda}z$. We use both normwise approach and componentwise way of measuring the size of the perturbations in data. If E preserves symmetry we say that an algorithm is strongly stable (in a normwise or componentwise sense, respectively). The relations between the stability and strong stability are investigated for some classes of matrices.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.1
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• pp.63-77
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• 2003

Some inequalities for the $Csisz{\acute{a}}r\;{\Phi}-divergence$ and applications for the Kullback-Leibler, $R{\acute{e}}nyi$, Hellinger and Bhattacharyya distances in Information Theory are given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.1
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• pp.1-5
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• 2003

We suggest Bisection method, Fixed point method and Newton's method for finding the intersection point of a nonparametric surface and a line in $R^3$ and apply ray-tracing in Color Picture Tube or Color Display Tube.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.77-84
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• 2000

Black-Scholes equation arising from option pricing in the presence of cost in trading the underlying asset is derived. The transaction cost is chosen precisely and generalized to reflect the trade in the real world. Furthermore the concept of the bandwidth is introduced to obtain the better rehedging. The model with bandwidth derived in this paper can be used to calculate the more accurate option price numerically even if it is nonlinear and more complicated than the models shown before.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.33-39
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• 2000

Well known is the directed self-avoiding walk model on the square lattice with reflecting and absorbing barriers. We consider two models, namely, a pyramid self-avoiding polygon model and a top and bottom pyramid polygon model, as subcollections of the model. We derive explicit formulas for the number of 2N-step polygons in these models.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.215-227
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• 2020

A new multiscale finite element method for elliptic problems with highly oscillating coefficients are introduced. A hybridization yields a locally flux-conserving numerical scheme for multiscale problems. Our approach naturally induces a homogenized equation which facilitates error analysis. Complete convergence analysis is given and numerical examples are presented to validate our analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.65-73
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• 2003

In this work, we use a numerical method to solve the nonlinear integral equation of the second kind when the kernel of the integral equation in the logarithmic function form or in Carleman function form. The solution has a computing time requirement of $0(N^2)$, where (2N +1) is the number of discretization points used. Also, the error estimate is computed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.95-111
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• 2003

BDM mixed methods are obtained for a good approximation of velocity for flow equations. In this paper, we study an implementation issue of solving the algebraic system arising from the BDM mixed finite elements. First we discuss post-processing based on the use of Lagrange multipliers to enforce interelement continuity. Furthermore, we establish an equivalence between given mixed methods and projection finite element methods developed by Chen. Finally, we present the implementation of the first order BDM on rectangular grids and show it is as simple as solving the pressure equation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.17-23
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• 2001

The evaluation of a few of the smallest eigenpairs of large symmetric eigenvalue problem is of great interest in many physical and engineering applications. A deflation-preconditioned conjugate gradient(PCG) scheme for a such problem has been shown to be very efficient. In the present paper we provide the numerical stability of a deflation-PCG with partial shifts.