• Journal of KIISE:Computer Systems and Theory
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• v.32 no.4
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• pp.160-167
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• 2005

Among finite filed arithmetic operations, division/inverse is known as a basic operation for public-key cryptosystems over $GF(2^{m})$ and it is computed by performing the repetitive $AB^{2}$ multiplication. This paper presents a digit-serial-in-serial-out systolic architecture for performing the $AB^2$ operation in GF$(2^{m})$. To obtain L×L digit-serial-in-serial-out architecture, new $AB^{2}$ algorithm is proposed and partitioning, index transformation and merging the cell of the architecture, which is derived from the algorithm, are proposed. Based on the area-time product, when the digit-size of digit-serial architecture, L, is selected to be less than about m, the proposed digit-serial architecture is efficient than bit-parallel architecture, and L is selected to be less than about $(1/5)log_{2}(m+1)$, the proposed is efficient than bit-serial. In addition, the area-time product complexity of pipelined digit-serial $AB^{2}$ systolic architecture is approximately $10.9\%$ lower than that of nonpipelined one, when it is assumed that m=160 and L=8. Additionally, since the proposed architecture can be utilized for the basic architecture of crypto-processor and it is well suited to VLSI implementation because of its simplicity, regularity and pipelinability.

• The Mathematical Education
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• v.62 no.2
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• pp.269-287
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• 2023

Matrix theory is widely used not only in mathematics, natural sciences, and engineering, but also in social sciences and artificial intelligence. In the 2009 revised mathematics curriculum, matrices were removed from high school math education to reduce the burden on students, but in anticipation of the age of artificial intelligence, they will be reintegrated into the 2022 revised education curriculum. Therefore, there is a need to analyze the matrix content covered in other countries to suggest a meaningful direction for matrix education and to derive implications for textbook composition. In this study, we analyzed the German mathematics curriculum and standard education curriculum, as well as the matrix units in the German Hesse state mathematics curriculum and textbook, and identified the characteristics of their content elements and development methods. As a result of our analysis, it was found that the German textbooks cover matrices in three categories: matrices for solving linear equations, matrices for explaining linear transformations, and matrices for explaining transition processes. It was also found that the emphasis was on mathematical reasoning and modeling when learning matrices. Based on these findings, we suggest that if matrices are to be reintegrated into school mathematics, the curriculum should focus on deep conceptual understanding, mathematical reasoning, and mathematical modeling in textbook composition.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.1A
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• pp.31-43
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• 2009

In this study, the numerical method is presented, which can consider the various train types and can solve the equations of motion for a vehicle-bridge interaction analysis by non-iteration procedure through formulating the coupled equations of motion. The coupled equations of motion for the vehicle-bridge interaction are solved by the Newmark ${\beta}$ of a direct integration method, and by composing the effective stiffness matrix and the effective force vector according to a analysis step, those can be solved with the same manner of the solving procedure of equilibrium equations in static analysis. Also, the effective stiffness matrix is reconstructed by the Skyline method for increasing the analysis effectiveness. The Cholesky's matrix decomposition scheme is applied to the analysis procedure for minimizing the numerical errors that can be generated in directly calculating the inverse matrix. The equations of motion for the conventional trains are derived, and the numerical models of the conventional trains are idealized by a set of linear springs and dashpots with 16 degrees of freedom. The bridge models are simplified by the 3 dimensional space frame element which is based on the Euler-Bernoulli theory. The rail irregularities of vertical and lateral directions are generated by the PSD functions of the Federal Railroad Administration (FRA). The results of the vehicle-bridge interaction analysis are verified by the experimental results for the railway plate girder bridges of a span length with 12 m, 18 m, and the experimental and analytical data are applied to the low pass filtering scheme, and the basis frequency of the filtering is a 2 times of the 1st fundamental frequency of a bridge bending.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.5_6
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• pp.202-213
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• 2007

A network is an important model widely used in natural and social science as well as engineering. To analyze these networks easily it is necessary that we should layout the features of networks visually. These Graph-Layout researches have been performed recently according to the development of the computer technology. Among them, the Scale-free Network that stands out in these days is widely used in analyzing and understanding the complicated situations in various fields. The Scale-free Network is featured in two points. The first, the number of link(Degree) shows the Power-function distribution. The second, the network has the hub that has multiple links. Consequently, it is important for us to represent the hub visually in Scale-free Network but the existing Graph-layout algorithms only represent clusters for the present. Therefor in this thesis we suggest Graph-layout algorithm that effectively presents the Scale-free network. The Hubity(hub+ity) repulsive force between hubs in suggested algorithm in this thesis is in inverse proportion to the distance, and if the degree of hubs increases in a times the Hubity repulsive force between hubs is ${\alpha}^{\gamma}$ times (${\gamma}$??is a connection line index). Also, if the algorithm has the counter that controls the force in proportion to the total node number and the total link number, The Hubity repulsive force is independent of the scale of a network. The proposed algorithm is compared with Graph-layout algorithm through an experiment. The experimental process is as follows: First of all, make out the hub that exists in the network or not. Check out the connection line index to recognize the existence of hub, and then if the value of connection line index is between 2 and 3, then conclude the Scale-free network that has a hub. And then use the suggested algorithm. In result, We validated that the proposed Graph-layout algorithm showed the Scale-free network more effectively than the existing cluster-centered algorithms[Noack, etc.].

• Economic and Environmental Geology
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• v.27 no.6
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• pp.557-561
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• 1994

Q estimates are made by direct measurements of energy loss per cycle from primary P and S waves, as a function of frequency. Assuming that intrinsic Q is frequency independent and scattering Q is frequency dependent over the frequencies of interest, the relative contributions of each, to a total observed Q, may be estimated. Test examples are produced by computing viscoelastic synthetic seismograms using a pseudo spectral solution with inclusion of relaxation mechanisms (for intrinsic Q) and a fractal distribution of scatterers (for scattering Q). The composite theory implies that when the total Q for S-waves is smaller than that for P-waves (the usual situation), intrinsic Q is dominating; when it is larger, scattering Q is dominating. In the inverse problem, performed by a global least squares search, intrinsic $Q_p$ and $Q_s$ estimates are reliable and unique when their absolute values are sufficiently low that their effects are measurable in the data. Large $Q_p$ and $Q_s$ have no measurable effect and hence are not resolvable. Standard deviation of velocity $({\sigma})$ and scatterer size (A) are less unique as they exhibit a tradeoff as predicted by Blair's equation. For the P-waves, intrinsic and scattering contributions are of approximately the same importance, for S-waves, the intrinsic contributions dominate.