• Journal of Korea Society of Industrial Information Systems
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• v.11 no.5
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• pp.62-66
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• 2006

We investigate various $\Phi(t)-stability$ of comparison differential equations and we abtain necessary and/or sufficient conditions for the uniform asymptotic and exponential asymptotic stability of the nonlinear differential equation x'=f(t, x).

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.161-166
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• 1997

We obtained sufficient conditions for $\phi$(t)-stability and uniform $\phi$(t)-stability of the trivial solution of comparison differential system. we also investigated the corresponding stability concepts of the trivial solution of the differential system using the thoery of differential inequlities through cones and the method of conevalued Lyapunov functions.

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.167-173
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• 1997

In this paper, we investigated several asymptotic stability properties of the system for the type of dy/dt = $h(t)^{-1}F(t_1, k(t)y(t))$.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.835-847
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• 2000

We investigate various ${\Phi}$(t)-stability of comparison differential equations and we obtain necessary and/or sufficient conditions for the asymptotic and uniform asymptotic stability of the differential equations x'=f(t, x).

• Journal of Korea Society of Industrial Information Systems
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• v.9 no.4
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• pp.68-74
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• 2004

We investigate various $\phi(t)-stability$ of comparison differential equations and We obtain necessary and/or sufficient conditions for the asymptotic and uniform asymptotic stability of the differential equations x'=f( t, x)

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.45-51
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• 2000

We will investigate some properties of integro-delay-differential equations, $$x^{\prime}(t)=A(t)x(t-g_1(t,x_t))+{\int}_{t_0}^{t}B(t,s)x(s-g_2(s,x_s))ds,\;t_0{\geq}0,\\x(t_0)={\phi}$$,

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.75-81
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• 2002

Lipschitz stability and Lipschitz ø$_{o}$ - equistability of the functional differential equation x'= B(x)f(t, x, $x_{t}$), $x_{to}$ =$\theta$$_{o}$ are discussed. Sufficient conditions are given using the comparison with the corresponding scalar equation.ion.n.

• Journal of Korea Society of Industrial Information Systems
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• v.12 no.5
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• pp.54-59
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• 2007

We abtain some stability results for a very general differential system using the method of cone valued vector Lyapunov functions and conversely some sufficient conditions for existence of such vector Lyapunov functions.

• Magazine of the Korean Society of Agricultural Engineers
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• v.31 no.3
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• pp.57-69
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• 1989

The study was carried out for the strength parameter of coarse grained Soil and slope stability analysis of earth dam. The test samples were taken fifteen kinds of soil from cohesive soil to coarse gravel. The degree of compaction of test samples for shear test and permeability test was chosen 95 percentage of maximum dry density. The results of this study are as follows ; 1.The maximum dry density(Yd) of coarse grained soil increase in proportion to coarse particles(P) with the relation of Y d= 1.609+0.0043P. 2.The coefficients of permeability(k) decrease by the increase of fine particles(n) with the relation of k=0.0426e-0 185n. 3.The cohesions of soil decrease by the increase of coarse particles, but internal friction angles are more increased in same condition. 4.The internal friction angles(${\Phi}$) decrease in inverse proportion to void ratio(e) with the relation of ${\Phi}$ = 73.068 - 69.268e. 5.The strength parameters( Ct ${\Phi}$t) by triaxial compression test are clearly smaller than that (Cd, ${\Phi}$d) by direct shear test in fine grained soil, but the differences between both parameters are a little in coarse grained soil.The relations of both parameters are as follows; Ct = O.544Cd + 0.04 ${\Phi}$t= 1.282${\Phi}$d-2306 6.In cohesive soil, the strength parameters( Cl ${\Phi}$l) by large size shear test apparatus are similar to the strength parameters(Cs , ${\Phi}$s) by small size shear test appratus, but Cs and ${\Phi}$s values are larger than Cl and ${\Phi}$l values from 10 percentage to 20 percentage in coarse grained soil. 7.The fine grained soil is inappropriate to high dam more than 20 meters and it must be taken coarse grained soil with high internal friction angle for high dam.

• Journal of Bio-Environment Control
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• v.16 no.4
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• pp.275-283
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• 2007

This study was carried out to: (1) analyze structural stability of representative rain-sheltering greenhouses for large-grain grapevine cultivation with widths of 3.6 m and 5 m in case of using the existing pipe for agriculture; (2) present the optimum specification of pipes in the greenhouse with a width of 5 m under the condition of using the pipe of which ultimate strength has been above $400N{\cdot}mm^{-2}$; (3) evaluate stability and also present the optimum specification of pipes as eaves height was augmented. The above analyses were done for greenhouses with roof vents and also with a main-column interval of 3 m and a rafter interval of 60 cm. First, the existing 3.6 m greenhouse with a rafter of ${\Phi}25.4{\times}1.5t@600$ was stable far a snow-depth of 35 cm but unstable for a wind velocity of $35m{\cdot}s^{-1}$. Meanwhile the existing 5 m greenhouse with the same rafter was not stable for a wind velocity of $335m{\cdot}s^{-1}$ as well as a snow-depth of 35 cm. This meant that existing greenhouses had to be reinforced to secure stability. Second, the specification of pipes, especially rafter, could be classified as two cases. One had a structural stability at a safe wind velocity of $35m{\cdot}s^{-1}$ and a safe snow-depth of 40 cm for which stability the rafter had to be ${\Phi}31.8{\times}1.5t@600$, and the other had a stability at $30m{\cdot}s^{-1}-35cm$ at the specification of rafter ${\Phi}25.4{\times}1.5t@600$. Finally, eaves height had a significant effect on safe wind velocity. But it had little influence on safe snow-depth. The results showed that the specification of side-wall pipes had to be reinforced for the safe side velocity accord-ing to the increment of eaves height and similarly the specification of fore-end post far the safe fore-end velocity.