• Honam Mathematical Journal
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• v.27 no.3
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• pp.477-485
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• 2005

Let ($M^n$, g) be a compact oriented Riemannian manifold. It has been conjectured that every solution of the equation $z_g=D_gdf-{\Delta}_gfg-fr_g$ is an Einstein metric. In this article, we deal with the 3 dimensional case of the equation. In dimension 3, if the conjecture fails, there should be a stable minimal hypersurface in ($M^3$, g). We study some necessary conditions to guarantee that a stable minimal hypersurface exists in $M^3$.

• Journal of the Korean Society of Tobacco Science
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• v.27 no.1 s.53
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• pp.94-99
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• 2005

To correct the difference of filling volumn for various cut tobacco and puffed stem according to moisture contents, correction equation was estamated by a simple regression analysis. The $R^2$(coefficient of determination) of correction equation was above 0.95. To verify the precision of correction equation, we predicted correction equation of other samples. The filling volumns by the difference of $1\%$ moisture content were $0.018\;~\;0.022cc/g$ (cut tobacco) and 0.060cc/g (puffed stem). The precision of correction equation for various cut tobacco was very high, but that of puffed stem was low due to quality deviation of row stem according to a season.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.375-379
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• 2012

We find a general solution $f:G{\rightarrow}G$ of the symmetric functional equation $$x+f(y+f(x))=y+f(x+f(y)),\;f(0)=0$$ where G is a 2-divisible abelian group. We also prove that there exists no measurable solution $f:\mathbb{R}{\rightarrow}\mathbb{R}$ of the equation. We also find the continuous solutions $f:\mathbb{C}{\rightarrow}\mathbb{C}$ of the equation.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1431-1437
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• 2010

We use the (G'/G)-expansion method to seek the traveling wave solution of the Seventh-order Sawada-Kotera Equation. The solutions that we get are more general than the solutions given in literature. It is shown that the (G'/G)-expansion method provides a very effective and powerful mathematical tool for solving nonlinear equations in mathematical physics.

• Journal of Advanced Marine Engineering and Technology
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• v.29 no.8
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• pp.849-854
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• 2005

The laminar flame concept in turbulent reacting flow is considered applicable to many practical combustion systems For turbulent premixed combustion under widely used flamelet concept, the flame surface is described as an infinitely thin propagating surface that such a Propagating front can be represented as a level contour of a continuous function G. In this study, for the Purpose of validating the LES of G-equation combustion model. LES of turbulent Premixed combustion with dynamic SGS model of G-equation in turbulent channel flow are carried out A constant density assumption is used. The Predicted flame propagating speed is goof agreement with the DNS result of G. Bruneaux et al.

• Journal of Mechanical Science and Technology
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• v.18 no.10
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• pp.1869-1879
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• 2004

The present study has numerically investigated two-dimensional flow over three circular cylinders in an equidistant side-by-side arrangement at a low Reynolds number. For the study, numerical simulations are performed, using the immersed boundary method, in the range of g* < 5 at Re= 100, where g* is the spacing between two adjacent cylinder surfaces divided by the cylinder diameter. Results show that the flow characteristics significantly depend on the gap spacing and a total of five kinds of wake patterns are observed over the range: modulation-synchronized (g* (equation omitted) 2), inphase-synchronized (g* (equation omitted) 1.5) , flip-flopping (0.3 < g* (equation omitted) 1.2) , deflected (g* (equation omitted) 0.3), and single bluff-body patterns (g* < 0.3). Moreover, the parallel and symmetric modes are also observed depending on g* in the regime of the flip-flopping pattern. The corresponding flow fields and statistics are presented to verify the observations.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.357-369
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• 2008

We obtain the superstability of a generalized exponential functional equation f(x+y)=E(x,y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: $$|\frac{f(x+y)}{(E(x,y)g(x)f(y)}-1|{\leq}{\varphi}(x,y)$$ where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.801-812
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• 2023

In this paper, we investigate the superstability for the p-power-radical sine functional equation $$f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=f(x)f(y)$$ from an approximation of the p-power-radical functional equation: $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)h(y),$$ where p is an odd positive integer and f, g, h are complex valued functions. Furthermore, the obtained results are extended to Banach algebras.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.213-223
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• 2012

In this paper, we will prove the superstability of the following generalized Pexider type exponential equation $${f(x+y)}^m=g(x)h(y)$$, where $f,g,h\;:\;G{\rightarrow}\mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here G is an Abelian group (G, +), and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G$\check{a}$vruta's result in 1994 and G. H. Kim's results in 2011.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.261-272
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• 2001

In this paper we prove the stability of the generalized quadratic equation f(x+y)+g(x-y)-2f(x)-2g(y)=0 in the spirit of Hyers, Ulam and Rassias.