• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.45-50
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• 2000

The modified Hyers-Ulam-Rassias Stability Of the generalized form g(x+p) : $\phi$(x)g(x) for the Gamma functional equation shall be proved. As a consequence we obtain the stability theorems for the gamma functional equation.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.287-303
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• 1999

The general solution of the functional equation f1(pr, qs) + f2(ps, qr) = g(p,q) + h(r,s) for p, q, r, s $\in$] 0, 1[will be investigated without any regularity assumptions on the unknown functions f1, f2, g, h:]0.1[->R.

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.103-114
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• 2008

In this paper, we investigate the superstability problem for the pexiderized cosine functional equations f(x+y) +f(x−y) = 2g(x)h(y), f(x + y) + g(x − y) = 2f(x)g(y), f(x + y) + g(x − y) = 2g(x)f(y). Consequently, we have generalized the results of stability for the cosine($d^{\prime}Alembert$) and the Wilson functional equations by J. Baker, $P.\;G{\check{a}}vruta$, R. Badora and R. Ger, and G.H. Kim.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.297-305
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• 2016

In this paper, by using fixed point theorem, we obtain the stability of the following functional equations $$f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)f(p,q)h(r,s)\\f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)g(p,q)h(r,s)$$, where G is a commutative semigroup, ${\theta}:G^4{\rightarrow}{\mathbb{R}}_k$ a function and f, g, h are functionals on $G^2$.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.295-301
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• 2006

We Investigate the relation between the multi-variable bi-additive functional equation f(x+y+z,u+v+w)=f(x,u)+f(x,v)+f(x,w)+f(y,u)+f(y,v)+f(y,w)+f(z,u)+f(z,v)+f(z,w) and the multi-variable quadratic functional equation g(x+y+z)+g(x-y+z)+g(x+y-z)+g(-x+y+z)=4g(x)+4g(y)+4g(z). Furthermore, we find out the general solution of the above two functional equations.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.539-544
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• 1998

Let (M, g) be a noncompact complete Riemannian manifold of dimension n $\geq$ 3 with scalar curvature S, which is close to O. With conditions on a conformal invariant and scalar curvature of (M, g), we show that there exists a conformal metric (equation omitted), near g, whose scalar curvature (equation omitted) = 0 by gluing solutions of the corresponding partial differential equation on each bounded subsets $K_{i}$ with ∪$K_{i}$ = M.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.801-813
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• 2019

In this paper, using the Baire category theorem we investigate the Hyers-Ulam stability problem of pexiderized Jensen functional equation $$2f(\frac{x+y}{2})-g(x)-h(y)=0$$ and pexiderized Jensen type functional equations $$f(x+y)+g(x-y)-2h(x)=0,\\f(x+y)-g(x-y)-2h(y)=0$$ on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.

• Journal of Community Nutrition
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• v.6 no.2
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• pp.61-66
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• 2004

This study was performed to investigate the nutritional status associated with alcohol consumption in Korean adults men and women. The data was derived from the 2001 Korean National Health and Nutrition Survey. The number of subjects included were 6090 (Men: 2789, Women: 3031) aged 20 (equation omitted) < 65y. Men consuming moderate alcohol ((equation omitted) 24 g/day but < 48g/day) had higher intakes of energy and vitamin B groups than the ones consuming less than 24g/day. Heavy drinking men reporting more than 48g alcohol/day were observed as having 3207.2kcal of energy intake (130% of Korean RDA) and significantly elevated levels in most of the nutrients. For women drinkers, when the alcohol consumption was moderate ((equation omitted) 12g/day but 24g/day) or heavy((equation omitted) 36g/day) the energy intake was 2188.9kcal(100% of RDA) or 2627.5kcal (130% of RDA). The other nutrients protein, fat, calcium, iron and vitamin B group were also higher in women with heavy alcohol consumption. Heavy drinking women showed significantly higher weight, BMI and HDL-C. In contrast, heavy drinking men did not show any significant difference in BMI but showed significantly elevated blood pressure, HDL-C and lower serum cholesterol.

• Journal of Advanced Marine Engineering and Technology
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• v.34 no.8
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• pp.1084-1093
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• 2010

Large eddy simulation of turbulent premixed flame stabilized by the bluff body is performed by using sub-grid scale combustion model based on the G-equation describing the flame front propagation. The basic idea of LES modeling is to evaluate the filtered-front speed, which should be enhanced in the grid scale by the scale fluctuations. The dynamic subgrid scale models newly introduced into the G-equation are validated by the premixed combustion flow behind the triangle flame holder. The calculated results can predict the velocity and temperature of the combustion flow in good agreement with the experiment data.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.11
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• pp.57-64
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• 2005

Large Eddy Simulation (LES) of turbulent premixed combustion flow is performed by using the dynamic subgrid scale model based on -equation describing the flame front propagation. After introducing the LES governing equations with dynamic subgrid scale (DSGS) model newly introduced into the -equation, the turbulent premixed combustion flow over backward facing step is analyzed to validate present formulation. The calculated results can predict the velocity and temperature of the combustion flow in good agreement with the experiment data.