• Journal of the Korean Ceramic Society
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• v.44 no.6 s.301
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• pp.319-324
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• 2007

The structural properties of $SiO_2$ liquid at finite temperatures have been investigated by molecular dynamics (MD) simulations utilizing the Tersoff interatomic potential. During cooling process, the $SiO_2$ liquid structure quenched with a cooling rate of $1.0{\times}10^{11}K/sec$ shows the traditional properties observed in the experiments. The coordination defects of system decrease with decreasing temperature up to 17%. The $SiO_2$ glass quenched up to 1600 K contains defects consisting of the fivefold coordination of Si, and the threefold coordination of O atoms. The calculated diffusion coefficients which are calculated by monitoring. the mean-square displacement of atoms drop to almost zero below 3000 K ($<10^{-6}\;cm^2/sec$) but has a fluctuations at low temperature. The structure properties of $SiO_2$ liquid shows a significant dependence on the temperature during cooling process. Bond-angle distribution at around $120^{\circ}$ originate from the O and Si atoms consisting of the over-coordinated O atoms.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.977-992
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• 2019

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.36 no.5 s.108
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• pp.78-84
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• 2004

Lignin precipitated from black liquor of soda pulping of bagasse was used to prepare cation-exchange resin. The effect of sulfuric acid treatment, concentration of phenol and formaldehyde on the properties of the prepared cation-exchange resin was investigated. It was found that sulfonated resinified phenolated lignin gave a resin with an ion-exchange capacity higher than that of resin, which resulted from sulfonation of resinified lignin at zero phenol concentration. Infrared spectroscopy of the prepared ion-exchange resin shows anew bands at 1060, 1160, 1280 and $1330\;cm^{-1}$ which indicated to the presence of $SO_{3}$.

• Journal of the military operations research society of Korea
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• v.8 no.2
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• pp.57-68
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• 1982

Bimatrix games are the two-person non-zero-sum non-cooperative games. These games were studied by Mills, Lemke, Howson, Millham, Winkels, and others. This paper is a systematic and synthetic survey relevant to bimatrix games. Among the many aspects of researches on bimatrix games, emphasis in this paper is placed on the relation of the equilibrium set to Nash subsets. Topics discussed are as follows: Properties of equilibrium point; The structure of equilibrium set; Relation of Nash subsets to equilibrium set; Algorithm for finding the equilibrium points; Concepts of solutions on bimatrix games.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.317-330
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• 2017

In this paper we introduce some new kinds of injectivities, namely, LC (resp. Ind, PInd) injectivity and investigate the relation among various kinds of injectivities. Some classifications of monoids by properties of these kinds of injective acts are presented. Among other results, it is shown that over a principal right ideal monoid, right completely LC-injectivity implies right completely injectivity. Also over a monoid with a zero Ind-injective (resp. PInd-injective) acts are injective.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.125-142
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• 2004

We analyze the convergence properties of Powell's UOBYQA method. A distinguished feature of the method is its use of two trust region radii. We first study the convergence of the method when the objective function is quadratic. We then prove that it is globally convergent for general objective functions when the second trust region radius p converges to zero. This gives a justification for the use of p as a stopping criterion. Finally, we show that a variant of this method is superlinearly convergent when the objective function is strictly convex at the solution.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.591-601
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• 2011

In this paper, we deal with the discrete p-Laplacian operators with a potential term having the smallest nonnegative eigenvalue. Such operators are classified as its smallest eigenvalue is positive or zero. We discuss differences between them such as an existence of solutions of p-Laplacian equations on networks and properties of the energy functional. Also, we give some examples of Poisson equations which suggest a difference between linear types and nonlinear types. Finally, we study characteristics of the set of a potential those involving operator has the smallest positive eigenvalue.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.559-580
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• 2017

Let G be an arbitrary group with identity e and let R be a G-graded ring. In this paper, we define the concept of graded 2-absorbing and graded weakly 2-absorbing primary ideals of commutative G-graded rings with non-zero identity. A number of results and basic properties of graded 2-absorbing primary and graded weakly 2-absorbing primary ideals are given.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.659-670
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• 2008

We denote by $\mathcal{Q}$(A) the set of all real matrices with the same sign pattern as a real matrix A. A matrix A is an SN-matrix provided there exists a set S of sign pattern such that the set of sign patterns of vectors in the -space of $\tilde{A}$ is S, for each ${\tilde{A}}{\in}\mathcal{Q}(A)$. Some properties of SN-matrices arc investigated.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.779-787
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• 2019

In this paper, we study two functional equations with two unknown functions from an Abelian group into a commutative ring without zero divisors. The two equations are generalizations of Swiatak's functional equations with an involution. We determine the general solutions of the two functional equations and the properties of the general solutions of the two functional equations under three different hypotheses, respectively. For one of the functional equations, we establish the Hyers-Ulam stability in the case that the unknown functions are complex valued.