• Proceedings of the Korean Geotechical Society Conference
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• 1997.10a
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• pp.65-72
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• 1997

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.653-658
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• 1998

In this paper, we investigate the Hyers-Ulam stability of the (p,k)-MP functional equation.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.60-64
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• 1997

In a fuzzy relation equation R=U=T, we find the bounde by U* and U* of the equation where U* is lower bound and U* is upper bound.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.301-310
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• 1999

This paper is concerned with the existence of positive solution of a semilinear elliptic equation with homogeneous Dirichlet boundary condition.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.7
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• pp.2367-2374
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• 1996

A generalized Scheil equation for the solute redistribution in the absence of the back diffusion during the dendritic solidification of binary alloys is derived, in which coarsening of the secondary dendrite arms is taken into account. The obtained equation essentially includes the original Scheil equation as a subset. Calculated results for typical cases show that the coarsening affects the microsegregation significantly. The eutectic fraction predicted for coarsening is considerably smaller than that for fixed arm spacing. The most important feature of the present equation in comparison with the Scheil equation lies in the fact that there exists a lower limit of the initial composition below which the eutectic is not formed. Based on the generalized Scheil equation and the lever rule, a new regime map of the eutectic formation on the initial composition-equilibrium partition coefficient plane is proposed. The map consists of three regimes: the eutectic not formed, conditionally formed and unconditionally formed, bounded by the solubility and diffusion controlled limit lines.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2165-2182
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• 2017

Let G be a group and $\mathbb{C}$ the field of complex numbers. Suppose ${\sigma}:G{\rightarrow}G$ is an endomorphism satisfying ${{\sigma}}({{\sigma}}(x))=x$ for all x in G. In this paper, we first determine the central solution, f : G or $G{\times}G{\rightarrow}\mathbb{C}$, of the functional equation $f(xy)+f({\sigma}(y)x)=2f(x)+2f(y)$ for all $x,y{\in}G$, which is a variant of the quadratic functional equation. Using the central solution of this functional equation, we determine the general solution of the functional equation f(pr, qs) + f(sp, rq) = 2f(p, q) + 2f(r, s) for all $p,q,r,s{\in}G$, which is a variant of the equation f(pr, qs) + f(ps, qr) = 2f(p, q) + 2f(r, s) studied by Chung, Kannappan, Ng and Sahoo in [3] (see also [16]). Finally, we determine the solutions of this equation on the free groups generated by one element, the cyclic groups of order m, the symmetric groups of order m, and the dihedral groups of order 2m for $m{\geq}2$.

• Korean Chemical Engineering Research
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• v.62 no.1
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• pp.53-69
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• 2024

The solubility of Cloxacillin sodium in ethanol, 1-propanol, isopropanol, and acetone solutions was measured at different temperatures. The melting property was also tested by using a differential scanning calorimeter (DSC). Then, the solubility data were fitted using Apelblat equation and λh equation, respectively. The Wilson model and NRTL model were not utilized to correlate the test data, since Cloxacillin sodium will decompose directly after melting. For comparison purposes, the four empirical models, i.e., Apelblat equation, λh equation, Wilson model and NRTL Model, were evaluated by using 1155 solubility curves of 103 solutes tested under different monosolvents and temperatures. The comparison results indicate that the Apelblat equation is superior to the others. Furthermore, a new method (named the calculation method) for determining the Apelblat equation using only three data points was proposed to solve the problem that there may not be enough solute in the determination of solubility. The log-logistic distribution function was used to further capture the trend of the correlation and to make better quantitative comparison between predicted data and the experimental ones for the Apelblat equation determined by different methods (fitting method or calculation method). It is found that the proposed calculation method not only greatly reduces the number of test data points, but also has satisfactory prediction accuracy.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.487-500
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• 1997

In this paper we introduce a multigrid method for solving the nonliear Urysohn integral equation. The algorithm is derived from a discrete resolvent equation which approximates the continuous resolvent equation of the nonlinear Urysohn integral equa-tion. The algorithm is mathematically equivalent to Atkinson's adap-tive twogrid iteration. But the two are different computationally. We show the convergence of the algorithm and its equivalence to Atkinson's adaptive twogrid iteration. in our numerical example we compare our algorithm to other multigrid methods for solving the nonliear Urysohn integral equation including the nonlinear multigrid nethod introduced by hackbush.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.545-558
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• 2013

In this paper, the formulas for calculating the extremal ranks and inertias of the Hermitian least squares solutions to matrix equation AX = B are established. In particular, the necessary and sufficient conditions for the existences of the positive and nonnegative definite solutions to this matrix equation are given. Meanwhile, the least squares problem of the above matrix equation with Hermitian R-symmetric and R-skew symmetric constraints are also investigated.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.435-446
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• 2004

In this paper, we obtain the general solution of a quadratic functional equation $b^2f(\frac{x+y+z}{b})+f(x-y)+f(x-z)=\;a^2[f(\frac{x-y-z}{a})+f(\frac{x+y}{a})+f(\frac{x+z}{a})]$ and prove the stability of this equation.