• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.475-491
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• 2012

In 1950 a class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of $I$-graphs mentioned in 1988 by Bouwer et al. represents a slight further albeit important generalization of the renowned Petersen graph. We show that each $I$-graph $I(n,j,k)$ admits a unit-distance representation in the Euclidean plane. This implies that each generalized Petersen graph admits a unit-distance representation in the Euclidean plane. In particular, we show that every $I$-graph $I(n,j,k)$ has an isomorphic $I$-graph that admits a unit-distance representation in the Euclidean plane with a $n$-fold rotational symmetry, with the exception of the families $I(n,j,j)$ and $I(12m,m,5m)$, $m{\geq}1$. We also provide unit-distance representations for these graphs.

• Geomechanics and Engineering
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• v.3 no.1
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• pp.17-28
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• 2011

This paper presents an analytical solution for steady state flow into a close-ended cylindrical permeameter. The soil medium is considered to be uniform, isotropic, and of infinite thickness. Laplace equation is solved by considering rotational symmetry and by using curvilinear coordinates obtained from conformal mapping. The deduced shape factors, which are compared to approximate relationships obtained from both numerical and physical modelling, and idealizations involving ellipsoidal cavities, are proposed for use in field measurements. It is shown that some of the shape factors obtained are significantly different from published values and show a much higher dependence of the rate of flow on the aspect ratio, than deduced from approximate solutions.

• Journal of the Korean Home Economics Association
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• v.50 no.3
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• pp.15-24
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• 2012

This study examined the formative beauty found in daenggi, which is a traditional feminine hair ornament. For research methods, both Adobe's Illustrator CS3 and Photoshop CS3 were used as designing tools and literatures on daenggi. Sixteen pieces of work were prepared by applying rotations of up, down, right, and left, repeat, symmetry, and overlap from the basic motif. For the scarf design, the rotational or diagonally symmetrical arrangement was repeated in order to maximize the outstanding features for each textile expression or was designed freely using one repetition unit (a whole scarf). Diverse images were expressed for the pendant design via usage of a basic motif and its variation. In addition, this work would suggest another alternative for apparel application by using the textile design for a simple one-piece dress.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.9
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• pp.84-93
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• 1996

This paper describes the development of new feature positioning method which embedded into the top-down assembly modeling system supporting conceptual design. In this work, the user provides the geometric constraints representing the position and size of features, then the system calculates their proper solution. The use of geometric constraints which are easy to understand intuitively enables the user to represent his design intents about geometric shapes, and enables the system to propagate the changes automatically when some editing occurs. To find the proper solution of given constraints, the Selective Solving Method in which the redundant or conflict equations are detected and discarded is devised. The validity of feature shapes satisfying the constraints can be maintained by this technique, and under or over constrained user-defined constraints can also be estimated. The problems such as getting the initial guess, controlling the multiple solutions, and dealing with objects of rotational symmetry are also resolved. Through this work, the feature based modeling system can support more general and convenient modeling method, and keeps the model being valid during modifying models.

• Journal of KIISE:Software and Applications
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• v.31 no.5
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• pp.563-569
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• 2004

A set of Zernike moments has been successfully used for object recognition or content-based image retrieval systems. Real time applications using Zernike moments, however, have been limited due to its complicated definition. Conventional methods to compute Zernike moments fast have focused mainly on the radial components of the moments. In this paper, utilizing symmetric/anti-symmetric properties of Zernike basis functions, we propose a fast and efficient method for Zernike moments. By reducing the number of operations to one quarter of the conventional methods in the proposed method, the computation time to generate Zernike basis functions was reduced to about 20% compared with conventional methods. In addition, the amount of memory required for efficient computation of the moments is also reduced to a quarter. We also showed that the algorithm can be extended to compute the similar classes of rotational moments, such as pseudo-Zernike moments, and ART descriptors in same manner.

• Wind and Structures
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• v.34 no.5
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• pp.407-419
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• 2022

Many factors should be considered by architects and designers for designing a tall building. Wind load is one of these important factors that govern the design of tall building structures and can become a serious challenge when buildings tend to be built very tall and slender. On the other hand, through the initial stages of a design process, choosing the design geometry greatly affects the wind-induced forces on a tall building. With this respect, geometric shapes with 3-fold rotational symmetry are one of the applied plan shapes in tall buildings. This study, therefore, aims to investigate the aerodynamic characteristics of 8 different geometrical shapes using Computational Fluid Dynamics (CFD) by measuring the drag and lift forces. A case study approach was conducted in which different building shape models have the same total gross area and the same height of 300 meters. The simulation was an incompressible transient flow that ran 1700 timesteps (85 seconds on the real-time scale). The results show a great difference between wind-induced force performance of buildings with different plan shapes. Generally, it is stated that the shapes with the same area, but with smaller perimeters, are better choices for reducing the drag force on buildings. Applying the lift force, the results show that the buildings with plan shapes that have rounded corners act better in crosswind flow while, those with sharp corners induce larger forces in the same direction. This study delivers more analytical understanding of building shapes and their behavior against the wind force through the parametric modelling.

• Proceedings of the Korean Vacuum Society Conference
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• 2014.02a
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• pp.327.1-327.1
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• 2014

Nitrides-on-silicon structures are considered to be an excellent candidate for unique design architectures and creating devices for high-power applications. Therefore, a lot of effort has been concentrating on growing high-quality III-nitrides on Si substrates, mostly Si(111) and Si(001) substrates. However, there are several fundamental problems in the growth of nitride compound semiconductors on silicon. First, the large difference in lattice constants and thermal expansion coefficients will lead to misfit dislocation and stress in the epitaxial films. Second, the growth of polar compounds on a non-polar substrate can lead to antiphase domains or other defective structures. Even though the lattice mismatches are reached to 16.9 % to GaN and 19 % to AlN and a number of dislocations are originated, Si(111) has been selected as the substrate for the epitaxial growth of nitrides because it is always favored due to its three-fold symmetry at the surface, which gives a good rotational matching for the six-fold symmetry of the wurtzite structure of nitrides. Also, Si(001) has been used for the growth of nitrides due to a possible integration of nitride devices with silicon technology despite a four-fold symmetry and a surface reconstruction. Moreover, Si(110), one of surface orientations used in the silicon technology, begins to attract attention as a substrate for the epitaxial growth of nitrides due to an interesting interface structure. In this system, the close lattice match along the [-1100]AlN/[001]Si direction promotes the faster growth along a particular crystal orientation. However, there are insufficient until now on the studies for the growth of nitride compound semiconductors on Si(110) substrate from a microstructural point of view. In this work, the microstructural properties of nitride thin layers grown on Si(110) have been characterized using various TEM techniques. The main purpose of this study was to understand the atomic structure and the strain behavior of III-nitrides grown on Si(110) substrate by molecular beam epitaxy (MBE). Insight gained at the microscopic level regarding how thin layer grows at the interface is essential for the growth of high quality thin films for various applications.

• Journal of Korea Entertainment Industry Association
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• v.15 no.1
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• pp.171-180
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• 2021

The present study investigated the effects of dynamic tubing gait (DTG II) program on the balancing ability for the promotion of life care of patients with chronic stroke. In the study, 25 sessions of DTG II program (30 minutes per session, 5 sessions per week, for a total of 5 weeks) were applied to 10 patients with chronic stroke. To determine the effects of DTG II program for improving balance, surface electromyography(external oblique, erector spinae, iliopsoas, gluteus maximus), symmetry index test on three pelvic axes, and dynamic gait index test were performed before and after the intervention. The results showed statistically significant differences between preand post-intervention measurements of the gluteus maximus muscle at early and mid-stance phases(p<.05). The pelvic symmetry index differed significantly between pre- and post-intervention measurements of diagonal and rotational movement(p<.05). Comparison of dynamic gait index also showed statistically significant differences between pre- and post-intervention measurements(p<.05). Based on these findings, it was determined that the DTG II program was able to improve the balancing ability of patients with chronic stroke by activating their trunk muscles and improving the symmetry of diagonal pelvic movement and rotation. Therefore, DTG II program is recommended as an interventional method to improve life-care through improving the balancing ability of patients with chronic stroke.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.834-839
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• 2007

This paper investigates the distortion of magnetic field of a brushless DC (BLDC) motor due to deformed rubber magnet. Global or local deformation of rubber magnet in the BLDC motor is mathematically modeled by using the Fourier series. Distorted magnetic field is calculated by using the finite element method, and unbalanced magnetic force are calculated by using the Maxwell stress tensor. The first harmonic deformation in the global deformation of rubber magnet generates the first harmonic driving frequency of the unbalanced magnetic force, and the rest harmonic deformations of rubber magnet except the harmonic deformation with multiple of common divisor of pole and slot introduces the driving frequencies with multiple of slot number ${\pm}1$ to the unbalanced magnetic force. However, the harmonic deformation with multiple of common divisor of pole and slot does not generate unbalanced magnetic force due to the rotational symmetry. When the rubber magnet is locally deformed, the unbalanced magnetic force has the first harmonic driving frequency and the driving frequencies with multiples of slot number ${\pm}1$.

• Proceedings of the Korean Vacuum Society Conference
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• 2013.02a
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• pp.153-153
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• 2013

Turbomolecular pump (TMP) is widely used to obtain and maintain high vacuum by spinning turbine rotors to migrate gas molecules to the exhaust of the pump. However, performance of the TMP has not been well observed when it is influenced by strong magnetic field. Such study may give useful information about magnetic field tolerance of TMP, development of magnetic shielding technique for key components of TMP, etc. For this purpose, magnetic field induced by a circular current source was firstly designed and investigated. Using spherical coordinates and vector potential, magnetic field throughout the space including axis of rotation was calculated. Due to the rotational symmetry of the circular current source, induced magnetic field is azimuthally symmetric and, thus, is analyzed by radial and polar components of the magnetic fields. In order to enhance the numerical accuracy for the calculation, magnetic field was expressed by complete elliptic integrals of first and second kinds. According to the calculation, when 1 A of DC-current passes through a 1 turned circular wire with 50 cm of diameter, overall magnitude of the inducedmagnetic field was about 0.02 Gauss, which was used to the determination of the current and the number of turns of wires to fabricate the coil for the study on the magnetic field tolerance of TMP.