• 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.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1193-1204
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• 2011

In the present paper we consider a differential-algebraic prey-predator model with stage structure for prey and harvesting of predator species. Stability and instability of the equilibrium points are discussed and it is observed that the model exhibits a singular induced bifurcation when the economic profit is zero. It indicates that the zero economic profit brings impulse, i.e. rapid expansion of the population and the system collapses. For the purpose of stabilizing the system around the positive equilibrium, a state feedback controller is designed. Finally, numerical simulations are given to show the consistency with theoretical analysis.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.723-731
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• 2020

The purpose of this paper is to study the structure of quotient rings R/P where R is an arbitrary ring and P is a prime ideal of R. Especially, we will establish a relationship between the structure of this class of rings and the behavior of derivations satisfying algebraic identities involving prime ideals. Furthermore, the characteristic of the quotient ring R/P has been determined in some situations.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.1 no.1
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• pp.77-83
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• 1997

In this paper, we present a comparison between QCELP(Qualcomm Code Excited Linear Predictor) speech coder that is operating in digital mobile communication system and CS-ACELP(Conjugate Structure Algebraic Code Excited Linear Prediction) speech coder that is scheduled to use for IMT-2000 (International Mobile Telecommunications 2000) system. The performance comparison might give help to design of the speech coding algorithms so that the robustness of the algorithms to channel errors engaged by mobile communication system be optimized.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.19-25
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• 1996

A multiblock grid generation has been developed to be reliably used for a Navier-Stokes simulation of the turbomachinery flow-fields A multiblock structure simplifies the creation of structured H-grids about complex turbomachinery geometries and facilitate the creation of a grid in the tip flow region. The numerical algorithm adopts the combination of the algebraic and elliptic method to create the internal grids efficiently and quickly. The grid refinement process is enhanced by developing strategies to utilized Bezier curves and splines along with weighted transfinite interpolation technique and by formulating the grid-imbedding method for the viscous boundary-layer meshes. For purposes of illustration, the grid generator is applied to the high turning turbine rotor blades. Two different types of computational grids are provided to be compared with respect to the grid adaptation to the flow simulations. Extension to three-dimensions was done to show the possibility of its application to the tip-flow simulations. The grid quality of the multiblock structure is good in the passages, with gloval orthogonality and adequate smoothness.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.14 no.4
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• pp.49-59
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• 2004

Boolean function synthesize problem is to find a boolean expression with in/outputs of original function. This problem can be modeled into a 0-1 integer programming. In this paper, we find a boolean expressions of S-boxes of DES for an example, whose algebraic structure has been unknown for many years. The results of this paper can be used for efficient hardware implementation of a function and cryptanalysis using algebraic structure of a block cipher.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.223-245
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• 2024

We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots emphasize a biomolecule's entanglement while ignoring their intrachain interactions. We remedy this by using stuck knots and links, which provide a way to emphasize both their entanglement and intrachain interactions. We first give a generating set of the oriented stuck Reidemeister moves for oriented stuck links. We then introduce an algebraic structure to axiomatize the oriented stuck Reidemeister moves. Using this algebraic structure, we define a coloring counting invariant of stuck links and provide explicit computations of the invariant. Lastly, we compute the counting invariant for arc diagrams of RNA foldings through the use of stuck link diagrams.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.11
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• pp.176-184
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• 2000

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

• Journal of the Korean Society for Precision Engineering
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• v.17 no.11
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• pp.165-175
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• 2000

In recent years, it becomes a very important issue to consider the mechanical systems such as high-speed vehicles and railway trains moving on elastic beam structures. In this paper, a general approach, which can predict the dynamic behavior of constrained mechanical system and elastic beam structure, is proposed. Also, various supporting conditions of a foundation support are considered for the elastic beam structures. The elastic structure is assumed to be a nonuniform and linear Bernoulli-Euler beam with proportional damping effect. Combined Differential-Algebraic Equations of motion are derived using multibody dynamics theory and Finite Element Method. The proposed equations of motion can be solved numerically using generalizd coordinate partitioning method and Predictor-Corrector algorithm, which is an implicit multi-step integration method.

• The Journal of the Acoustical Society of Korea
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• v.18 no.7
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• pp.33-38
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• 1999

In this paper, we combine a generalized analysis-by-synthesis (AbS) structure and an algebraic excitation scheme to propose a new 4kb/s speech codec. This codec partly uses the structure of G.729. We design a line spectrum pair (LSP) quantizer, an adaptive codebook, and an excitation codebook to fit the 4 kb/s bit rate. The codec has a 25㎳ algorithmic delay, which corresponds to a 20㎳ frame size and a 5㎳ lookahead. At the bit rates below 4kb/s, most CELP speech codecs using the AbS principle have a drawback that results a rapid degradation of speech quality. To overcome this drawback we use the generalized AbS structure which is efficient for the low bit rate speech codec. LP coefficients are converted to LSP and quantized using a predictive 2-stage VQ. A low complexity algebraic codebook which uses shifting method is used for the fixed codebook excitation, and gains of the adaptive codebook and the fixed codebook are quantized using the VQ. To evaluate the performance of the proposed codec A-B preference tests are done with the fixed rate 8kb/s QCELP. As the result of the test, the performance of the codec is similar to that of the fixed rate 8kb/s QCELP.