• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.215-227
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• 2015

In this paper, we investigate bounds for solutions of nonlinear functional differential systems using the notion of t_∞-similarity.

• Nuclear Engineering and Technology
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• v.54 no.8
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• pp.2898-2914
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• 2022

When evaluating energy balance and temperature in reduced-scale fire experiments, which are conducted as an alternative to full-scale fire experiments, it is important to consider the similarity in the scale among these experiments. In this paper, a method considering the similarity of energy balance is proposed for setting the conditions for reduced-scale experiments of mechanically ventilated compartment fires. A small-scale fire experiment consisting of various cases with different compartment geometries (aspect ratios between 0.2 and 4.7) and heights of vents and fire sources was conducted under mechanical ventilation, and the energy balance in the quasi-steady state was evaluated. The results indicate the following: (1) although the compartment geometry varies the energy balance in a mechanically ventilated compartment, the variation in the energy balance can be evaluated irrespective of the compartment size and geometry by considering scaling factor F (∝h_effA_wR_T, where h_eff is the effective heat transfer coefficient, A_w is the total wall area, and R_T is the ratio of the spatial mean gas temperature to the exhaust temperature); (2) the value of R_T, which is a part of F, reflects the effects of the compartment geometry and corresponds to the distributions of the gas temperature and wall heat loss.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.383-389
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• 2010

In this paper, we investigate h-stability of the nonlinear differential systems using the notion of $t_{\infty}$-similarity.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.447-457
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• 2015

In this paper, we investigate bounds for solutions of the nonlinear perturbed functional differential systems using the notion of t_∞-similarity.

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.269-282
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• 2015

In this paper, we investigate bounds for solutions of perturbed functional differential systems using the notion of $t_{\infty}$-similarity.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.695-702
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• 2011

In this paper, we investigate h-stability of the non-linear perturbed differential systems using the the notion of $t_{\infty}$-similarity.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.347-359
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• 2016

In this paper, we show that the solutions to perturbed functional differential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$, have a bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of $t_{\infty}$-similarity.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.105-117
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• 2016

This paper shows that the solutions to the nonlinear perturbed differential system $y{\prime}=f(t,y)+\int_{t_0}^{t}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$, have the bounded property by imposing conditions on the perturbed part $\int_{t_0}^{t}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$, and on the fundamental matrix of the unperturbed system y′ = f(t, y) using the notion of h-stability.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.723-736
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• 2016

This paper shows that the solutions to nonlinear perturbed differential system $$y^{\prime}= f(t,y)+{\int_{t_{0}}^{t}g(s,y(s))ds+h(t,y(t),Ty(t))$$ have bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_{0}}^{t}g(s,y(s))ds,\;h(t, y(t),\;Ty(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.

• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.145-158
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• 2015

In this paper, we investigate h-stability and boundedness for solutions of the functional perturbed differential systems using the notion of t_∞-similarity.