• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.111-118
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• 1996

Throughout this paper Z and C will respectively denote the ring of rational integers and the complex number field.

• Journal of Integrative Natural Science
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• v.12 no.2
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• pp.44-46
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• 2019

In this paper, we study a ratio variation of Nicomachus' theorem by computing ${\sum\limits_{k=1}^{n}}[rk]$ and ${\sum\limits_{k=1}^{n}}[rk]^3$, where r is a rational number.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.72-77
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• 2001

The computational efficiency of an shape optimization procedure is highly dependent upon the proper selection of shape representation methods and design variables. In this study, shape functions, Bezier and NURBS(non-uniform rational B-splines) curves are selected as configuration generation methods and their efficiencies on the nose shape design of high-speed air vehicles, are compared. The effects of the number of control points, weighting factors and the optimization methods when utilizing the NURBS curves, are investigated. By implementing Bezier and NURBS curves, shapes having lower drag than the optimization case utilizing the shape functions, were obtained, hence it was demonstrated that these curves have better capability in representing the configuration. Efforts will be given to improve the convergence behavior when utilizing the NURBS, hence to reduce the number of Navier-Stokes analysis calculations.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.39-44
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• 1996

Throughout this paper $Z^p, Q_p$ and C_p$ will denote the ring of p-adic rational integers, the field of p-adic rational numbers and the completion of the algebraic closure of $Q_p$, respectively. Let $v_p$ be the normalized exponential valuation of $C_p$ with $$\mid$p$\mid$_p = p^{-v_p (p)} = p^{-1}$. We set $p^* = p$ for any prime p > 2 $p^* = 4 for p = 2$.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.923-937
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• 2014

The rational finite element method is different from the standard finite element method, which is constructed using basic solutions of the governing differential equations as interpolation functions in the elements. Therefore, it is superior to the isoparametric approach because of its obvious physical meaning and accuracy; it has successfully been applied to the isotropic elasticity problem. In this paper, the formulation of rational finite elements for plane orthotropic elasticity problems is deduced. This method is formulated directly in the physical domain with full consideration of the requirements of the patch test. Based on the number of element nodes and the interpolation functions, different approaches are applied with complete polynomial interpolation functions. Then, two special stiffness matrixes of elements with four and five nodes are deduced as a representative application. In addition, some typical numerical examples are considered to evaluate the performance of the elements. The numerical results demonstrate that the present method has a high level of accuracy and is an effective technique for solving plane orthotropic elasticity problems.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.21 no.2
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• pp.165-172
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• 2003

IKONOS satellite images are particularly well suited for stereo feature extraction. But, because IKONOS doesn't offer information about the satellite ephemeris and attitude, we have to use IKONOS RPC(Rational Polynomial Coefficients) data for 3-D feature extraction. In this study, it was intended to increase the accuracy and the efficiency in application of high resolution satellite images. Therefore, this study develop the program to extract 3-D feature information and have analyzed the geometric accuracy of the IKONOS satellite images by means of the change with the number, distribution and height of GCPs. This study will provide basic information for luther studies of the accuracy correction in IKONOS and high resolution satellite images.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.765-773
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• 2002

Let $textsc{k}$＝$F_{q}$(T) be a rational function field. Let $\ell$ be a prime number with ($\ell$, q-1) ＝ 1. Let K/$textsc{k}$ be an elmentary abelian $\ell$-extension which is contained in some cyclotomic function field. In this paper, we study the $\ell$-divisibility of ideal class number $h_{K}$ of K by using cyclotomic units.s.s.

• Journal for History of Mathematics
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• v.13 no.2
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• pp.151-160
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• 2000

In this paper we prove that for all irreducible complex characters of a finite group, there exist F-representations and a finite degree field extension F ⊇ Q, where Q is the rational number field.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.517-534
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• 2012

As observing the learning of middle school mathematics students for three years, I examined the relationship between students' procedural knowledge and their conceptual knowledge as they develop those knowledges in the rational number domain. In particular, I explored the implications of an unbalanced development in a student's conceptual knowledge and procedural knowledge by considering two conditions: (a) the case of a student who has relatively strong conceptual knowledge and weak procedural knowledge, and (b) the case of a student who has relatively weak conceptual knowledge and strong procedural knowledge. Results suggest that conceptual knowledge and procedural knowledge are most productive when they develop in a balanced fashion (i.e., closely iterative or simultaneously), which calls into question the assumption that one has primacy over the other.

• Proceedings of the Safety Management and Science Conference
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• 2004.05a
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• pp.283-289
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• 2004

The number of pixel defects including bright and black dots on a panel is one of the critical factors determining the quality of TFT-LCD. Since pixel defects on the TFT-LCD panels are sometimes unavoidable, manufacturers have to inspect the panels so that any panel with an unacceptable number of defects will not be delivered to the buyers. However, the buyers demand for the manufacturers to meet different pixel defects tolerances (acceptable number of pixel defects on a TFT-LCD panel) around central(tight) and peripheral(loose) inspection zones. The disagreement in quality standard among different buyers also cause confusions in screening non-confirmative products and unstable yield of production. Few research has focused on the effects of defect locations on a TFT-LCD panel on their detection probabilities and the rational division of defect inspection zones. In this research, experiments were conducted to find the detection probabilities of black dot defects with respect to their varying locations on a TFT-LCD. It is proposed a rational division of inspection zone on a TFT-LCD panel on the basis of detection probabilities of the defects. With these division of inspection zones and the mean defect detection probability within each zone, it is expected to establish a more reasonable pixel defects tolerances.