• 대한수학회지
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• 제31권4호
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• pp.539-544
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• 1994

We [1] investigated the Hausdorff dimension and the packing dimension of a certain perturbed Cantor set whose ratios are unformly bounded. In this paper, we consider a specific Cantor set whose ratios are not necessarily uniformly bounded but satisfy some other conditions. In fact, in the hypothesis, only the condition of the unform boundedness of ratios on the set is substituted by a "*-condition". We use energy theory related to Hausdorff dimension in this study while we [1] used Hausdorff density theorem to find the Hausdorff dimension of some perturbed Cantor set. In the end, we given an example which explains aformentioned facts.ned facts.

• 한국멀티미디어학회논문지
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• 제19권1호
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• pp.80-85
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• 2016

It costs high in both memory usage and time consuming to sample the space to compute charge density and calculate electric field on that with large size of plasma data. In real-time and interactive application, accelerating the compute time is critical problem. In this paper, we suggest new method to visualize electric field by using convolution theorem, and the parallel computing to accelerate computing time by using GPGPU. We conduct a simulation that compare running time between the methods with convolution and without convolution. We discussed the method of visualization of multivariate data in three dimensional space using colored volume rendering and surface construction.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1101-1121
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• 2008

One proposes an approach to fractional Fourier's transform, or Fourier's transform of fractional order, which applies to functions which are fractional differentiable but are not necessarily differentiable, in such a manner that they cannot be analyzed by using the so-called Caputo-Djrbashian fractional derivative. Firstly, as a preliminary, one defines fractional sine and cosine functions, therefore one obtains Fourier's series of fractional order. Then one defines the fractional Fourier's transform. The main properties of this fractal transformation are exhibited, the Parseval equation is obtained as well as the fractional Fourier inversion theorem. The prospect of application for this new tool is the spectral density analysis of signals, in signal processing, and the analysis of some partial differential equations of fractional order.

• 한국멀티미디어학회논문지
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• 제20권7호
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• pp.1004-1013
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• 2017

This paper presents a relationship between the number of curves and geometric parameters of a 3D object. Once the relationship is established, the number of closed curves that can reliably represent 3D object is derived. Inspired by Shannon-Nyquist Sampling Theorem, in this paper, approach for sampling rate (defined as the minimum number of curves) for 3D reconstruction is proposed. The relationship is straightforward, is suitable for application to 3D object overlaid with closed-continuous curves, and can achieve efficient 3D reconstruction system in practice. To substantiate the proposed approach, simulation results are provided and the results show that the number of curves can be decreased without loss of generality of characteristics of a target 3D object.

• EDISON SW 활용 경진대회 논문집
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• 제6회(2017년)
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• pp.376-382
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• 2017

Graphene nanoribbons with zigzag-shaped edge (zGNRs) are predicted to be magnetic insulator at the ground state, attracting significant interest in view of spintronic applications [1]. On the other hand, although they are energetically and thermodynamically more favored than zGNRs [2], graphene nanoribbons with armchair-shaped edge (aGNRs) have been less spotlighted than zGNRs due to the absence of magnetism. Herein, based on the combined density functional theory (DFT) and matrix Green's function (MGF) approach, we consider aGNRs functionalized with various molecular groups, and show that the spin polarizations develop for some of the considered aGNR edge functionalization cases. The origin of the induced magnetism will be discussed within the Lieb's theorem [3]. This work will provide a novel guidance for the development of graphene-based spintronic devices.

• 대한조선학회논문집
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• 제41권4호
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• pp.17-29
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• 2004

Internal waves are computed using a ghost fluid method on an unstructured grid. Discontinuities in density and dynamic pressure are captured in one cell without smearing or oscillations along a multimaterial interface. A time-accurate incompressible Navier-Stokes/Euler solver is developed based on a three-point backward difference formula for the physical time marching. Artificial compressibility is introduced with respect to pseudotime and an implicit method is used for the pseudotime iteration. To track evolution of an interface, a level set function is coupled with the governing equations. Roe's flux difference splitting method is used to calculate numerical fluxes of the coupled equations. To get higher order accuracy, dependent variables are reconstructed based on gradients which are calculated using Gauss theorem. For each edge crossing an interface, dynamic pressure is assigned for a ghost node to enforce the continuity of total pressure along the interface. Solitary internal waves are computed and the results are compared with other computational and experimental results.

• ETRI Journal
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• 제36권4호
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• pp.635-642
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• 2014

Three-dimensional integrated circuits (3D ICs) implement heterogeneous systems in the same platform by stacking several planar chips vertically with through-silicon via (TSV) technology. 3D ICs have some advantages, including shorter interconnect lengths, higher integration density, and improved performance. Thermal-aware design would enhance the reliability and performance of the interconnects and devices. In this paper, we propose thermal-aware floorplanning with min-cut die partitioning for 3D ICs. The proposed min-cut die partition methodology minimizes the number of connections between partitions based on the min-cut theorem and minimizes the number of TSVs by considering a complementary set from the set of connections between two partitions when assigning the partitions to dies. Also, thermal-aware floorplanning methodology ensures a more even power distribution in the dies and reduces the peak temperature of the chip. The simulation results show that the proposed methodologies reduced the number of TSVs and the peak temperature effectively while also reducing the run-time.

• Structural Engineering and Mechanics
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• 제82권4호
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• pp.469-476
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• 2022

A mathematical model of Lord-Shulman photo-thermal theorem induced by pulse heat flux is presented to study the propagations waves for plasma, thermal and elastic in two-dimensional semiconductor materials. The medium is assumed initially quiescent. By using Laplace-Fourier transforms with the eigenvalue method, the variables are obtained analytically. A semiconductor medium such as silicon is investigated. The displacements, stresses, the carrier density and temperature distributions are calculated numerically and clarified graphically. The outcomes show that thermal relaxation time has varying degrees of effects on the studying fields.

• 대한수학회보
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• 제61권3호
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• pp.611-619
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• 2024

For a finite group G, let 𝜓(G) denote the sum of element orders of G. If ${\psi}^{{\prime}{\prime}}(G)\,=\,{\frac{\psi(G)}{{\mid}G{\mid}^2}}$, we show here that the image of 𝜓'' on the class of all Dihedral groups whose order is twice a composite number greater than 4 is dense in $[0,\,{\frac{1}{4}}]$. We also derive some properties of 𝜓'' on the class of all dihedral groups whose order is twice a prime number.

• 천문학회지
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• 제24권1호
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• pp.71-94
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• 1991

With the 14 m radio telescope at DRAO and the 4 m at Nagoya University, we have made detailed maps of $^{12}CO$ and $^{13}CO$ emissions from two Barnard objects B133 and B134 in the $J=1{\rightarrow}O$ rotational transition lines. Usual LTE analyses of the CO observations led us to determine the distribution of column densities over an entire area encompassing both globules. Total gas masses estimated from the column density map are $90\;M_{\odot}$ and $20\;M_{\odot}$ for B133 and B134, respectively. The radial velocity of B133 is red shifted with respect to B134 by $0.8\;km\;s^{-1}$, which is too lagre to bind the two clouds as a binary system. We have shown that the usual stability analysis based on the simplified version of virial theorem with the second time-derivative of the moment of inertia term $\ddot{I}$ being ignored could mislead us in determining whether a given cloud eventually collapses or not. The lull version of the scalar virial theorem with the $\ddot{I}$ term is shown to be useful in following up the time-dependent variations of the cloud size R and its streaming velocity $\dot{R}$ as functions of time. Results of our stability analysis suggest that B133 will eventually collapse in $(2{\sim}4){\times}10^6$ years.