• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.731-749
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• 2005

In this paper, we study the two dimensional g-Navier­Stokes equations on some unbounded domain ${\Omega}\;{\subset}\;R^2$. We prove the existence of the global attractor for the two dimensional g-Navier­Stokes equations under suitable conditions. Also, we estimate the dimension of the global attractor. For this purpose, we exploit the concept of asymptotic compactness used by Rosa for the usual Navier-Stokes equations.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.393-404
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• 2003

In general, a differential operator can be used as a tool of treating the local properties of given function. However, when the given function is varied with high frequency and has irregular form with non-stationary evolution it may not act its role sufficiently as in case of nowhere differentiable curves. In this paper we introduce a multi-scale derivative as a form of weakened global derivative so that it may explain its semi global diffusion properties as well as local ones for the various irregular diffusion phenomena.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.205-212
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• 2007

In this paper, we give some properties of the dynamics of quadratic rational maps. Using the properties we present the algorithm for drawing the Julia sets of the quadratic rational maps. We illustrate that they are fractals by computer graphics.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.583-605
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• 2024

This paper discusses the properties of attractors of Type 1 IFS which construct self similar fractals on product spaces. General results like continuity theorem and Collage theorem for Type 1 IFS are established. An algebraic equivalent condition for the open set condition is studied to characterize the points outside a feasible open set. Connectedness properties of Type 1 IFS are mainly discussed. Equivalence condition for connectedness, arc wise connectedness and locally connectedness of a Type 1 IFS is established. A relation connecting separation properties and topological properties of Type 1 IFS attractors is studied using a generalized address system in product spaces. A construction of 3D fractal images is proposed as an application of the Type 1 IFS theory.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.07a
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• pp.369-372
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• 2000

ZnO varistor is studied to sintering condition and mixing condition for the improvement to non linear of electrical characteristics. In this paper, ZnO varistor, ZnO-Bi$_2$O$_3$-Y$_2$O$_3$-MnO-Cr$_2$O$_3$-Sb$_2$O$_3$series, is fabricated with Sb$_2$O$_3$mol ratio(0.5~4[mol%]) and sintered at 1250[$^{\circ}C$] for 2 hours. The grain size to Sb$_2$O$_3$moi ratio was measured by fractal mathematics. The ZnO varistors that Sb$_2$O$_3$mot ratio is 1[mol%] were shown small grain size because of spinel phase. The fractal dimension were increased with increasing of Sb$_2$O$_3$mo ratios. The capacitance of ZnO varistors with increasing of Sb$_2$O$_3$additive in voltage-capacitance characteristics was decreased by small grain size.

• Archives of design research
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• v.17 no.1
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• pp.211-220
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• 2004

The Chaos theory of complexity and Fractal theory which became a prominent figure as a new paradigm of natural science should be understood not as whole, and not into separate elements of nature. Fractal Dimensions are used to measure the complexity of objects. We now have ways of measuring things that were traditionally meaningless or impossible to measure. They are capable of describing many irregularly shaped objects including man and nature. It is compatible method of application to express complexity of nature in the dimension of non-fixed number by placing our point of view to lean toward non-linear, diverse, endless time, and complexity when we look at our world. Fractal Dimension allows us to measure the complexity of an object. Having a wide application of fractal geometry and Chaos theory to the art field is the territory of imagination where art and science encounter each other and yet there has not been much research in this area. The formative word has been extracted in this study by analyzing objective data to grasp formative principle and geometric characteristic of (this)distinct figures of Fractals. With this form of research, it is not so much about fractal in mathematics, but the concept of self-similarity and recursiveness, randomness, devices expressed from unspeakable space, and the formative similarity to graphic design are focused in this study. The fractal figures have characteristics in which the structure doesn't change the nature of things of the figure even in the process if repeated infinitely many times, the limit of the process produces is fractal. Almost all fractals are at least partially self-similar. This means that a part of the fractal is identical to the entire fractal itself even if there is an enlargement to infinitesimal. This means any part has all the information to recompose as whole. Based on this scene, the research is intended to examine possibility of analysis of fractals in geometric characteristics in plasticity toward forms in graphic design. As a result, a beautiful proportion appears in graphic design with calculation of mathematic. It should be an appropriate equation to express nature since the fractal dimension allows us to measure the complexity of an object and the Fractla geometry should pick out high addition in value of peculiarity and characteristics in the complex of art and science. At the stage where the necessity of accepting this demand and adapting ourselves to the change is gathering strength is very significant in this research.

• The Mathematical Education
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• v.37 no.1
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• pp.115-138
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• 1998

We seek the possibility of introduction of Fractals to the high school math. curriculum through identifying Fractals teaching programs appropriate for the scopes and sequences in math. education for the high school students. We presented the contents of Fractal theory suitable for the high school students. The following subjects were chosen to be introduced; self-similarity, Fractal dimension, Cantor set, Sierpinsky triangle, Sierpinsky carpel Koch curve, Koch island, perimeter estimate of rugged profiles drawn on paper, and chaos game. We developed the working papers and the criteria for appraisal. Each working paper focuses on the activities in which students can solve the given problems, understanding the characteristics and ideas of Fractals. The working papers were given to the second year students who take science course, and the degree of achievements were analyzed based on the appraisal criteria. The results show that it is possible to introduce Fractals to the high school students.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.05c
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• pp.217-220
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• 2001

Fractal mathematics is being highlighted as a research method for classification of image. But the application of Fractal dimension(FD) has been required the complicated calculation method because of its complex repetition progressing. In this paper, it has been applied the new approach method to express FD for aging level calculation and investigated the relative degradation processing in outdoor EPDM insulator. As a result after testing, new proposed method has a capability to estimate in case of the field operated EPDM and accelerating test. Therefore, we find the differency of operated EPDM according to field condition.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.405-419
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• 2005

We present some properties characterizing the Mandelbrot set of quadratic rational maps. Any quadratic rational map is conjugate to either $z^2+c$ or ${\lambda}(z+1/z)+b$. For ${\mid}{\lambda}{\mid}=1$, we find the figure of the Mandelbrot set $M_{\lambda}$, the set of parameters b for which the Julia set of ${\lambda}(z+1/z)+b$ is connected. It is seen to be the whole complex plane if ${\lambda}{\neq}1$, but it is intricate fractal if ${\lambda}=1$. This supplements the work already investigated for the case ${\mid}{\lambda}{\mid}>1$.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.05a
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• pp.1-4
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• 2000

Fractal mathematics is being highlighted as a research method for classification of image. But the application of Fractal dimension(FD) has been required the complicated calculation method because of its complex repetition progressing. In this paper, it has been applied the new approach method to express FD for aging level calculation and investigated the relative degradation processing in outside EPDM insulator. As a result after testing, new proposed method has a capability to estimate in case of the field operated EPDM and accelerating test. Therefore, we find the differency of operated EPDM according to field condition.