• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.456-459
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• 1999

In this paper, we propose a new neural network based on the DNA coding method. The initial population of the structure information and the weights for the neural network is generated, and then the descendants are chose with the Elitist selection by the genetic algorithm. The evolutionary technique and the suitable fitness measure are used to find a neural network with the fractal number of layers. which represents a good approximation to the given function.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.179-184
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• 2005

Empirical findings on interet rate dynamics imply that short rates show some long memories and non-Markovin. It is well-known that fractional Brownian motion(fBm) is a proper candidate for modelling this empirical phenomena. fBm, however, is not a semimartingale process. For this reason, it is very hard to apply such processes for asset price modelling. With some modifications, this paper investigate the fBm interest rate theory, and obtain a pure discount bond price and Greeks.

• International Journal of Aeronautical and Space Sciences
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• v.15 no.4
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• pp.419-433
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• 2014

The Mars Exploration Rover Opportunity investigated plains at Meridiani Planum, where laminated sedimentary rocks are present. The Opportunity rover's Athena morphological investigation showed microstructures organized in intertwined filaments of microspherules: a texture we have also found on samples of terrestrial (biogenic) stromatolites and other microbialites. We performed a quantitative image analysis to compare images (n=45) of microbialites with the images (n=30) photographed by the rover (corresponding, approximately, to 25,000/15,000 microstructures). Contours were extracted and morphometric indexes were obtained: geometric and algorithmic complexities, entropy, tortuosity, minimum and maximum diameters. Terrestrial and Martian textures present a multifractal aspect. Mean values and confidence intervals from the Martian images overlapped perfectly with those from the terrestrial samples. The probability of this occurring by chance is $1/2^8$, less than p<0.004. Terrestrial abiogenic pseudostromatolites showed a simple fractal structure and different morphometric values from those of the terrestrial biogenic stromatolite images or Martian images with a less ordered texture (p<0.001). Our work shows the presumptive evidence of microbialites in the Martian outcroppings: i.e., the presence of unicellular life on the ancient Mars.

• Korean Journal of Crystallography
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• v.4 no.1
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• pp.36-41
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• 1993

Small angle X-ray scattering was used to study on the oxopolymers of sols derived from BaTiethoxide. The growths of the oxopolymers in tools obtained with NH40H as catalyst and catalystfree sol are similar. Their radii of gyration are 1.66-2.08nm. They exhibit a mass fractal behavior with a dimension of 1.6, which is almost inde pendent with amount of NH40H addition. Sols catalyzed with CHSCOOH have greater radii of gyration of 3.24-4.OOnm. Their scattering curves are similar in the intermediate Q region, showing a mass fractal dimension of 1.8. The oxopolymers of the tools from the base and the neutral hydrolysis conditions may have a short chain structure.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.28 no.3
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• pp.170-176
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• 2017

In this paper, we proposed the miniaturized structure of the Log-Periodic Dipole Array(LPDA) antenna for PS-LTE(Pubic Safety-Long Term Evolution) service. The length of array dipole was shortened by adding a fractal tree element with iteration to the array dipole to miniaturize the LPDA antenna. As the result, the proposed LPDA antenna was reduced up to 25 %, compared a typical LPDA antenna. To validation of the proposed LPDA antenna specification, the proposed LPDA antenna is fabricated using aluminum with 1.5 mm thickness and performances are measured. Comparison between simulation result and experiment shows good agreement.

• Proceedings of the KAIS Fall Conference
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• 2002.05a
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• pp.115-117
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• 2002

In this paper, the degree-n bifurcation set as well as the Julia sets is defined by extending the concept of the Mandelbrot set to the complex polynomial $z^{n}{\;}+{\;}c(c{\;}\in{\;}C,{\;}n{\;}\geq{\;}2)$. Some properties of the degree-n bifurcation set and the Julia sets have been theoretically investigated including the symmetry, periodicity, boundedness, connectedness and the bifurcation points as well as the governing equation for the component centers. An efficient algorithm constructing both the degree-n bifurcation set and the Julia sets is proposed using theoretical results. The mouse-operated software calico "MANJUL" has been developed for the effective construction of the degree-n bifurcation set and the Julia sets in graphic environments with C++ programming language under the windows operating system. Simple mouse operations can construct and magnify the degree-n bifurcation set as well as the Julia sets. They not only compute the component period, bifurcation points and component centers but also save the images of the degree-n bifurcation set and the Julia sets to visually confirm various properties and the geometrical structure of the sets. A demonstration has verified the useful versatility of MANJUL.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.05b
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• pp.34-38
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• 2000

Recently, the ceramics of high permittivity are applied to DRAM and FRAM. In this study, (Ba, Sr)$TiO_3$ (BST) ceramics thin films were prepared by Sol-Gel method. BST solution was made and spin-coated on Pt/$SiO_2$/Si substrate at 4000 [rpm] for 10 seconds. Coated specimens were dried at $150[^{\circ}C]$ for 5 minutes. Coating process was repeated 3 times and then sintered at $750[^{\circ}C]$ for 30 minutes. Each specimen was analyzed structure and electrical characteristics by Fractal Process. Thickness of BST ceramics thin films are about $2000{\AA}$. Dielectric constant and loss of thin films was little decreased at 1[KHz] - 1[MHz]. Dielectric constant and loss to frequency were 250 and 0.02 in BST3. The property of leakage current as the realation between the current and the voltage was that change of the leakage current was stable when the applied voltage was 0~3[V].

• Tribology and Lubricants
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• v.30 no.6
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• pp.378-383
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• 2014

This study predicts the of the hysteretic friction of a rubber block sliding on an SMA asphalt road. The friction of filled rubber on a rough surface is primarily determined by two elements:the viscoelasticity of the rubber and the multi-scale perspective asperities of the road. The surface asperities of the substrate exert osillating forces on the rubber surface leading to energy dissipation via the internal friction of the rubber when rubber slides on a hard and rough substrate. This study defines the power spectra at different length scales by using a high-resolution surface profilometer, and uses rubber and road surface samples to conduct friction tests. I consider in detail the case when the substrate surface has a self affine fractal structure. The theory developed by Persson is applied to describe these tests through comparison with the hysteretic friction coefficient relevant to the energy dissipation of the viscoelastic rubber attributable to cyclic deformation. The results showed differences in the absolute values of predicted and measured friction, but with high correlation between these values. Hence, the friction prediction model is an appropriate tool for separating the effects of each factor. Therefore, this model will contribute to clearer understanding of the fundamental principles of rubber friction.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.59-76
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• 2006

This research focuses on the relationship between mathematics and visual art from a perspective of chaos theory which emerged under the influence of post-modernism. Culture and history, which transform dynamically with the passing of time, are models of complexity. Especially, when the three periods of Medieval, Renaissance, and 17-18 Centuries are observed, the Renaissance period is phase transition phenomenon era between Medieval and 17-18 Centuries. The transition stage between the late Medieval times and the Renaissance; and the stage between the Renaissance and the Modern times are also phase transitions. These phenomena closely resemble similarity in Fractal theory, which includes the whole in a partial structure. Phase transition must be preceded by fluctuation. In addition to the pioneers' prominent act of creation in the fields of mathematics and visual an serving as drive behind change, other socio-cultural factors also served as motivations, influencing the transformation of the society through interdependency. In particular, this research focuses on the fact that scientific minds of artists in the Renaissance stimulated the birth of Perspective Geometry.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.578-582
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• 2000

When the motion of vibrating structure is restrained due to the adjacent objects, the frequencies and the mode shapes of the structure change and its vibration characteristics becomes unpredictable, in general. Although the importance of the study on this type of vibration model increases in many engineering areas, most studies conducted so far are limited to the theoretical study on dynamic responses of the structure with the separation plate, including some experimental works. In the paper, both numerical analyses and experiments are conducted to study the chaotic vibration characteristics and the dynamic response of a fixed-free beam which has restrained motion at the free end by the separation plates. Results are presented for various magnetic forces and gaps between stops.