• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.211-221
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• 2007

In this paper, we define ${\bigwedge}$-structure, ${\bigvee}$-structure to generalize some lattices, and study the conditions that a lattice which has ${\bigwedge}$-structure or ${\bigvee}$-structure to be continuous or algebraic.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.4
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• pp.54-63
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• 2002

In recent years, mechanical systems such as high speed vehicles and railway trains moving on elastic beam structures have become a very important issue to consider. In this paper, a general approach, which can predict the dynamic behavior of a constrained mechanical system moving on a flexible beam structure, is proposed. Various supporting conditions for the foundation support are considered for the elastic beam structure. The elastic structure is assumed to be a non-uniform and linear Bernoulli-Euler beam with a proportional damping effect. Combined differential-algebraic equation of motion is derived using the multi-body dynamics theory and the finite element method. The proposed equations of motion can be solved numerically using the generalized coordinate partitioning method and predictor-corrector algorithm, which is an implicit multi-step integration method.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.4
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• pp.64-71
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• 2002

Recently, mechanical systems such as a high-speed vehicles and railway trains moving on flexible beam structures have become a very important issue to consider. Using the general approach proposed in the first part of this paper, it is possible to predict motion of the constrained mechanical system and the elastic structure, with various kinds of foundation supporting conditions. Combined differential-algebraic equation of motion derived from both multibody dynamics theory and finite element method can be analyzed numerically using a generalized coordinate partitioning algorithm. To verify the validity of this approach, results from the simply supported elastic beam subjected to a moving load are compared with the exact solution from a reference. Finally, parametric study is conducted for a moving vehicle model on a simply supported 3-span bridge.

• Kyungpook Mathematical Journal
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• v.33 no.1
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• pp.61-67
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• 1993

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.443-450
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• 2011

In this paper, we construct a Gorenstein Artinian algebra R/J with non-unimodal Hilbert function h = (1, 13, 12, 13, 1) to investigate the algebraic structure of the ideal J in a polynomial ring R. For this purpose, we use a software system Macaulay 2, which is devoted to supporting research in algebraic geometry and commutative algebra.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1231-1252
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• 2006

In this paper we shall explicitly calculate the formula of the algebraic presentation of an embedding of the Teichmiiller space ${\Im}(M)$ into the Goldman space g(M). From this algebraic presentation, we shall show that the Goldman's length parameter on g(M) is an isometric extension of the Fenchel-Nielsen's length parameter on ${\Im}(M)$.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.451-471
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• 2021

First, we define phase tropical hypersurfaces in terms of a degeneration data of smooth complex algebraic hypersurfaces in (ℂ∗)n. Next, we prove that complex hyperplanes are homeomorphic to their degeneration called phase tropical hyperplanes. More generally, using Mikhalkin's decomposition into pairs-of-pants of smooth algebraic hypersurfaces, we show that a phase tropical hypersurface with smooth tropicalization is naturally a topological manifold. Moreover, we prove that a phase tropical hypersurface is naturally homeomorphic to a symplectic manifold.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.1219-1222
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• 1998

This paper analyzes the dynamic spars algebraic codebook used to model a residual signal and proposes a new algebraic codebook structure as well as a searching process with improved performance. The proposed algorithm improves the disadvantage of algebraic codebook without increased computation. First, this paper makes it possibel to select various pulse amplitudes differently from the conventional method which looks up the sign bit simply. In addition, two pulses are made to be selected on the same track. For speech quality on the telephone line 5.6kbps speech coder using the proposed algorithm was equivalent to the 6.3kbps MP-MLQ in the viewpoint of subjective speech quality. However, speech degradation was caused a little compared to the MP-MLQ where MNRU 1=15dB.

• ETRI Journal
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• v.27 no.2
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• pp.231-234
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• 2005

This letter proposes a new embedded speech coding structure based on the Adaptive Multi-Rate Wideband (AMR-WB) standard codec. The proposed coding scheme consists of three different bitrates where the two lower bitrates are embedded into the highest one. The embedded bitstream was achieved by modifying the algebraic codebook search procedure adopted for the AMR-WB codec. The proposed method provides the advantage of scalability due to the embedded bitstream, while it inevitably requires some additional computational complexity for obtaining two different code vectors of the higher bitrate modes. Compared to the AMR-WB codec, the embedded coder shows improved speech qualities for two higher bitrate modes with a slightly increased bitrate caused by the decreased coding efficiency of the algebraic codebook.

• The Mathematical Education
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• v.62 no.1
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• pp.23-34
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• 2023

The rationalizing denominators presented in the mathematics textbooks is being used in various places of school mathematics curriculum. However, according to some previous research on the rationalizing denominators in school mathematics, it seems that there is no clear explanation as to why rationalizing denominators is necessary and why it should be used. In addition, a previous research insists that most students know how to rationalize denominators but do not understand why it is necessary and important. To confirm this, we examined the rationalizing denominators presented in the 2015 revised mathematics curriculum as school mathematics. Then we also examined the rationalizing denominators algebraically as academic mathematics. In detail, we conducted an analysis on the rationalizing denominators presented in randomly selected three mathematics textbooks and teacher guidebooks for middle school third grade. Then the algebraic meaning of the rationalizing denominators was examined from a proper algebraic structure analysis. Based on this, we present alternative definitions of the rationalizing denominators which is suitable for school mathematics and academic mathematics. Finally, we also present the mathematical contents (irrationals of the special form can be algebraically interpreted as numbers in the standard form) that teachers should know when they teach the rationalizing denominators in school mathematics.