• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.281-298
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• 2023

A class of systems of Caputo fractional differential equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a uniform mesh is proposed. Supremum norm is used to derive an error estimate which is of order κ − 1, 1 < κ < 2. Numerical examples are given which validate our theoretical results.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2001.01a
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• pp.486-495
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• 2001

This paper describes an implementation of the interval based expert system for syndrome differential diagnosis of Oriental Traditional Medicine (OTM). An approximate reasoning model using fuzzy logic for syndrome differential diagnosis is proposed. Based on this model, we implemented the system for diagnosing Eight rule diagnosis, organ diagnosis and then final differential syndrome of OTM. After carrying out inference process, the system will provide patient\`s syndromes differentiation diagnosis in the intervals and will give the explanation, which helps the user to understand the obtained conclusions.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.28 no.6
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• pp.99-105
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• 2014

Power transformers are applied throughout the power system to connect systems of different voltage to one another. Since a ratio differential relay offers high sensitivity in detection of internal faults in power transformers, it is widely used in the main protection system. The use of nonlinear devices such as rectifiers and other devices utilizing solid state switching have been increased in industry during recent years. For nonlinear loads, the load current is not proportional to the instantaneous voltage. This situation creates harmonic distortion on the system. The harmonic could differential relay misoperation if not recognized. This paper aims at analyzing and probing into the influences of harmonics on a ratio differential relay for power transformer protection.

• 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 Korean Mathematical Society
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• v.42 no.4
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• pp.749-759
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• 2005

We apply a cone theoretic fixed point theorem and obtain conditions for the existence of positive periodic solutions of the system of functional differential equations $$x'(t)\;=\;A(t)x(t)+{\lambda}f(t,\;x(t-\tau(t))$$.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.757-771
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• 1999

We consider a system of functional differential equations x'(t)=F(t, $x_t$) and obtain conditions on a Liapunov functional and a Liapunov function to ensure the instability of the zero solution.

• 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.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.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.415-427
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• 2015

In this paper, we investigate bounds for solutions of the non-linear functional differential systems.

• Computers and Concrete
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• v.7 no.4
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• pp.317-329
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• 2010

The paper describes localization of deformation in a bar under tensile loading. The material of the bar is considered as non-linear viscous elastic and the bar consists of two symmetric halves. It is assumed that the model represents behavior of the quasi-brittle viscous material under uniaxial tension with different loading rates. Besides that, the bar could represent uniaxial stress-strain law on a single plane of a microplane material model. Non-linear material property is taken from the microplane material model and it is coupled with the viscous damper producing non-linear Maxwell material model. Mathematically, the problem is described with a system of two partial differential equations with a non-linear algebraic constraint. In order to obtain solution, the system of differential algebraic equations is transformed into a system of three partial differential equations. System is subjected to loadings of different rate and it is shown that localization occurs only for high loading rates. Mathematically, in such a case two solutions are possible: one without the localization (unstable) and one with the localization (stable one). Furthermore, mass is added to the bar and in that case the problem is described with a system of four differential equations. It is demonstrated that for high enough loading rates, it is the added mass that dominates the response, in contrast to the viscous and elastic material parameters that dominated in the case without mass. This is demonstrated by several numerical examples.