• Applied Chemistry for Engineering
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• v.34 no.4
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• pp.388-396
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• 2023

The evaluation of fire risk for combustible materials was carried out using Chung's equations-X, Chung's equations-XI, and Chung's equation-XII, which were newly established. The fire risk index-XII (FRI-XII) and fire risk rating (FRR) were calculated for specimens including camphor tree, cherry, rubber tree, and elm. The combustion characteristics were determined using a cone calorimeter according to ISO 5660-1. Chung's equations caculated the fire performance index-X (FPI-X) and fire growth index-X (FGI-X) values ranged from 89.34 to 1696.75 s² /kW and from 0.0006 to 0.0107 kW/s² , respectively. In addition, the fire performance index-XI (FPI-XI) and fire growth index-XI (FGI-XI) varied from 0.08 to 1.48 and from 0.67 to 11.89, respectively. The fire risk index-XII (FRI-XII), which is an indicator of fire risk, showed that camphor tree had a value of 148.63 (fire risk rating: G), indicating a very high fire risk. This suggests that combustible materials with a high concentration of volatile organic compounds have lower FPI-X and FPI-XI values, higher FGI-X and FGI-XI values, and consequently higher FRI-XII values, indicating an increased fire risk.

• Applied Chemistry for Engineering
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• v.34 no.2
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• pp.144-152
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• 2023

To evaluate the fire risk of combustible materials, Chung's equations VII, VIII, and IX were newly established. The fire risk index-IX (FRI-IX) and fire risk rating (FRR) were calculated. Ginkgo, dawn redwood, toona, lime, walnut, and polymethylmethacrylate (PMMA) were selected as test specimens. The combustion characteristics were evaluated using a cone calorimeter according to ISO 5660-1. After combustion, the fire performance index-VII (FPI-VII) of the specimens, varied between 15.15 and 182.53 s²/kW, as determined by Chung's equations, and the fire growth index-VII (FGI-VII) varied between 0.0023 and 0.0165 kW/s². The fire performance index-VIII (FPI-VIII) based on PMMA varied between 0.29 and 3.45, and the fire growth index-VIII (FGI-VIII) varied between 2.88 and 20.63. The FRI-IX, which is the fire risk rating, showed dawn redwood has a very high fire risk, with FRI-IX values of 71.14 (fire risk rating: G). Therefore, wood with a large amount of volatile organic compounds and a low bulk density showed a high value of FRI-IX by lowering FPI-VII and FPI-VIII and increasing FGI-VII and FGI-VIII.

• Applied Chemistry for Engineering
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• v.32 no.4
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• pp.417-422
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• 2021

In this study, poly isocyanurate foam (PIR), poly urethane foam (PUR), and phenol foam (PF) of organic insulation materials were selected, and investigated using a cone calorimeter, as per ISO 5660-1. Standard materials (PMMA) were used to standardize the fire hazard assessment, and the fire risk was classified and evaluated by Chung's equations-III and IV. The fire performance index-II value of Chung's equations-II was the highest value with PF of 14.77 s²/kW. And the PUR was 0.08 s²/kW, the lowest value of fire performance index-II value. The fire growth index-II value was the lowest value with PF of 0.01 kW/s². And the PUR was 1.14 kW/s², the highest value of fire growth index-II value. The fire performance index-III (FPI-III) of Chung's equations-III had the lowest value for PUR (0.11) and the highest for PF (20.23). The PUR showed the highest value of the fire growth index-III (FGI-III) as 14.25, while the PF exhibited 0.13 regarded as the safest materials. The fire risk index-IV (FRI-IV) value of Chung's equation-IV was in the following order: PUR (130.03) >> PIR (19.13) > PMMA (1.00) > PF (0.01). Therefore, it was concluded that the fire risk associated with PF is the lowest, whereas that associated with PUR is the highest.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.538-544
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• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

• Applied Chemistry for Engineering
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• v.33 no.4
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• pp.373-380
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• 2022

In this study, Chung's equations 1, 2, and 3 were extended to standardize smoke safety rating evaluation in case of fire, and Chung's equations-V, smoke performance index-V, and smoke growth index-V were calculated. Five types of wood were selected and their smoke indices were measured using the cone calorimeter method according to ISO 5660-1. The smoke risk was graded by the smoke risk index-VI according to Chung's equation-VI. Smoke risk index-VI increased in the order of PMMA (1) ≈ maple (1.01) < ash (1.57) < needle fir (4.98) < paulownia (46.15) < western red cedar (106.26). It was predicted that maple and ash had the lowest smoke risk, and paulownia and western red cedar had the highest. The five samples' CO mean production rate (COP_mean) was 0.0009~0.0024 g/s, indicating that these woods were incompletely burned than the polymethyl methacrylate (PMMA) reference material. Regarding the smoke properties of the chosen woods, the smoke performance index-V (SPI-V) increased as the bulk density increased, and the smoke risk index-VI (SRI-VI) decreased.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1047-1053
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• 1996

In this paper, we obtain a solution of Einstein's unified field equations on a generalized n-dimensional Riemannian manifold $X_n$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.31-40
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• 1998

Spectral analysis by energy method is given for a fully discrete methods for hyperbolic integro-differential equations with a weakly singular kernel. Stability and error estimates in $H^1$-norm are derived.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1157-1169
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• 2016

We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

• Journal of the Korean Mathematical Society
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• v.31 no.1
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• pp.57-67
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• 1994

• 유체기계공업학회:학술대회논문집
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• 2000.12a
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• pp.169-175
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• 2000

A design method for transonic turbine blades is developed based on Navier-Stokes equations. The present computing process is done on the four separate steps, 1.e., determination of the blade profile, generation of the computational grids, cascade flow simulation and analysis of the computed results in the sense of the aerodynamic performance. The blade shapes are designed using the cubic polynomials under the control of the design parameters. Numerical methods for the flow equations are based on Van-Leer's FVS with an upwind TVD scheme on the finite volume. Applications are made to the VKI transonic rotor blades. Computed results are analyzed with respect to the aerodynamic performance and are compared with the experimental data.