• Applied Chemistry for Engineering
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• v.35 no.3
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• pp.200-208
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• 2024

Chung's equations-IX and Chung's equation-XII were utilized to predict the fire risk and evaluate fire risk ratings for four types of wood: camphor, cherry, rubber, and elm trees. The combustion tests were conducted using a cone calorimeter test method by ISO 5660-1 standards. The fire risk and fire risk rating (FRR) were compared for Fire Risk Index-IX (FRI-IX) and Fire Risk Index-XII (FRI-XII). The results yielded Fire Performance Index-XI (FPI-XI) ranging from 0.08 to 11.48 and Fire Growth Index-XI (FGI-XI) ranging from 0.67 to 111.89. The Fire Risk Index-XII (FRI-XII), indicating fire risk rating, exhibited an increasing order of cherry (0.45): Grade A (Ranking 5) < PMMA (1): Grade A (Ranking 4) < elm (1.23): Grade A (Ranking 3) < rubber (1.56): Grade A (Ranking 2) << camphor (148.23): Grade G (Ranking 1). Additionally, the fire risk index-IX (FRI-IX) was cherry (0): Grade A (Ranking 3) ≈ rubber (0): Grade A (Ranking 3) ≈ elm tree (0): Grade A (Ranking 3) < PMMA (1): Grade A (Ranking 2) << camphor tree (66.67): Grade G (Ranking 1). In general, camphor was found to have the highest fire risk. In conclusion, although the expression of the index is different as shown based on the standards of FRI-IX and FRI-XII, predictions based on fire risk assessment of combustible materials showed similar trends.

• Membrane Journal
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• v.13 no.4
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• pp.291-299
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• 2003

Polymer membranes such as poly(1-trimethylsilyl-1-propyne)-polyetherimide (PTMSP-PEI) and poly(dimethylsiloxane)- polyetherimide (PDMS-PEI) composite membrane were prepared by solution casting method. To investigate the characteristics of these membranes, the analytical methods such as FT-IR, $^1H-NMR,$ DSC, TGA, GPC, and SEM have been utilized. The number-average (equation omitted) and weight-average (equation omitted) molecular weight of PTMSP were 477,920 and 673,329 respectively. The glass transition temperature ($T_g$) of PTMSP was $224^{\circ}C.$ The separation of the gas mixture ($H_2/N_2$) through the composite membranes were studied as a function of pressure. The separation factor (${\alpha}, {\beta},$ quation omitted) of the composite membranes used in this work increased as the pressure of permeation cell increased. The real separation factor (${\alpha}$), head separation factor (${\beta}$), and tail separation factor (equation omitted) of PTMSP-PEI composite membrane were 2.28, 1.17, and 1.96 respectively at ${\Delta}P$ 30psi and $25^{\circ}C.$ (${\alpha}, {\beta}$ and equation omitted of PDMS-PEI composite membrane were 3.70, 1.53, and 2.42 respectively at ${\Delta}P$ 30psi and $25^{\circ}C$.

• The Pure and Applied Mathematics
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• v.27 no.3
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• pp.109-124
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• 2020

We establish coincidence point theorem for S-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. With the help of obtain result, we derive two dimensional results for generalized compatible pair of mappings F, G : X² → X. As an application, we obtain the solution of integral equation and also give an example to show the usefulness of our results. Our results improve, sharpen, enrich and generalize various known results.

• 한국연소학회:학술대회논문집
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• 2015.12a
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• pp.49-51
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• 2015

In this research, engine performance and emission variation according to equivalence ratio and ignition time is calculated by validated analysis model. LNG engine ignite by spark plug and spark ignition modeled using DPIK model and G-equation that modeled initial flame surface called kernel and velocity and position of flame front. Engine pressure and emission was validated with experimental data.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.321-338
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• 2005

In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(X))\;=\;\phi(X)f(X)$, where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers, Ulam, Rassias, and Gavruta for many other equations such as the gamma, beta, Schroder, iterative, and G-function type's equations.

• Structural Engineering and Mechanics
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• v.4 no.3
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• pp.227-242
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• 1996

An important class of problems in the field of geotechnical engineering may be analyzed with the aid of a simple integro-differential equation. Behavior of "rigid" piles(say concrete piles), "deformable" piles(say gravel piles), pile groups, pile-raft foundations, heavily reinforced earth, flow within circular silos and down drag on cylindrical structures (for example the crusher unit of a mineral processing complex) are the type of situations that can be handled by this type of equation. The equation under consideration has the form; $$\frac{{\partial}w(r,\;z)}{{\partial}z}+f(z){\int}^z_0g({\xi})(\frac{{\partial}^2w(r,\;{\xi})}{{\partial}r^2}+\frac{1}{r}\frac{{\partial}w(r,\;{\xi})}{{\partial}r})d{\xi}+h(r,\;z)=0$$ where w(r, z) is the vertical displacement of a soil particle expressed as a function of the polar cylindrical space coordinates (r, z) and the symbols f, g and h represent soil properties and the loading conditions. The merit of the analysis is its simplicity (both in concept and in application) and the ease with which it can be expressed in a computer code. In the present paper the analysis is applied to investigate the behavior of a single rigid pile to bedrock. The emphasis, however, is placed on developing the equation, the numerical techique used in its evaluation and validation of the technique, hereafter called the ID technique, against a formal program, CRISP, which uses the FEM.

• Journal of the Korean Society of Propulsion Engineers
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• v.16 no.5
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• pp.47-57
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• 2012

A modified ignition and growth(I&G) model which is necessary to simulate the combustion phenomena of energetic materials and an analytical model determining the unknown parameters of the reaction rate equation are proposed. The modified I&G model sustains important physical implications with overcoming some problems of previous rate equations. This rate model consists of ignition term which represents the formation of the hotspot due to void collapse and growth term which means the shock to detonation transition phenomena. Also, the theoretical model is used to investigate the combustion characteristics of certain energetic materials before running Hydrocode by pre-determination of unknown parameter, $b,\;G,\;x,\;I$. The analytical model provides efficient and highly accurate results rather than previous method which simulated the unconfined-rate-stick via the numerical means.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2012.05a
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• pp.331-341
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• 2012

A modified Ignition and Growth(I&G) model which is necessary to simulate the combustion phenomena of energetic materials and an analytical model determining the unknown parameters of the reaction rate equation are proposed. The modified I&G model sustains important physical implications with overcoming some problems of previous rate equations. This rate model consist of Ignition term which represent the formation of the hotspot due to void collapse and Growth term which means the shock to detonation transition phenomena. Also, the theoretical model is used to investigate the combustion characteristics of certain energetic materials before running Hydrocode by pre-determination of unknown parameter, b, G, x, I. The analytical model provides efficient and highly accurate results rather than previous method which simulated the unconfined-rate-stick via the numerical means.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.271-279
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• 1995

In 1986, Fabry, Mawhin and Nkashama [1] have considered periodic solutios for Lienard equation $$ (1_s) x" + f(x)x' + g(t,x) = s, $$ where s is a real parameter, f and g are continuous functions, and g is $2\pi$-periodic in t and have proved that if $$ (H) lim_{$\mid$x$\mid$\to\infty} g(t,x) = \infty uniformly in t \in [0,2\pi], $$ there exists $s_1 \in R$ such that $(1_s)$ has no $2\pi$periodic solution if $s< s_1$, and at least one $2\pi$-periodic solution if $s = s_1$, and at least two $2\pi$-periodic solutions if $s > s_1$.s_1$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.4
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• pp.309-321
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• 1988

This paper proposes on the algorithm of axis equation & radius function for the G.C representation which describes the curved objects with circular cross section. Object combined with linear and nonlinear parts is detached by clustering from depth data & axis points is extracted by normal vecter of the surface mask patches. In ths case of nonlinear axis point, axis equation is described by Hermite curve & the effectiveness of this paper is demonstrated by serveral experiments.