• 대한수학회논문집
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• 제37권4호
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• pp.1259-1267
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• 2022

In this paper we present a full circle approximation method using parametric polynomial curves with algebraic coefficients which are curvature continuous at both endpoints. Our method yields the n-th degree parametric polynomial curves which have a total number of 2n contacts with the full circle at both endpoints and the midpoint. The parametric polynomial approximants have algebraic coefficients involving rational numbers and radicals for degree higher than four. We obtain the exact Hausdorff distances between the circle and the approximation curves.

• 대한수학회지
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• 제42권4호
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• pp.695-708
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• 2005

Certain observations about formal Dirichlet series whose coefficients are arithmetic functions are made. These include for example algebraic independence and representation as infinite series of logarithms.

• 대한기계학회논문집
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• 제17권6호
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• pp.1596-1608
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• 1993

본 연구에서는 좀더 정량적인 이론에 바탕하여 제레이놀즈수 2차모멘트 난류모형을 유도하려 한다.

• Korean Journal of Mathematics
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• 제17권4호
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• pp.375-383
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• 2009

In this note, we determine the properties of the coefficients of Bell domains in the plane and find some coefficients to consist of Bell domain.

• 대한전기학회논문지:시스템및제어부문D
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• 제50권6호
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• pp.259-265
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• 2001

In the last two decades, many researchers proposed various usages of the orthogonal functions such as Walsh, Haar and BPF to solve the system analysis, optimal control, and identification problems from and algebraic form. In this paper, a simple procedure to design and algerbraic observer for the descriptor system is presented by using block pulse function expansions. The main characteristic of this technique is that it converts differential observer equation into an algerbraic equation. And furthermore, a simple recursive algorithm is proposed to obtain BPFs coefficients of the observer equation.

• 한국소음진동공학회논문집
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• 제13권4호
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• pp.247-257
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• 2003

This paper presents an analytical method to Investigate the stability of a hydrodynamic journal bearing with rotating herringbone grooves. The dynamic coefficients of the hydrodynamic Journal bearing are calculated using the FEM and the perturbation method. The linear equations of motion can be represented as a parametrically excited system because the dynamic coefficients have time-varying components due to the rotating grooves, even in the steady state. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill's infinite determinant of these algebraic equations. The validity of this research is proved by the comparison of the stability chart with the time response of the whirl radius obtained from the equations of motion. This research shows that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing eccentricity and with decreasing groove number, which play the major roles in increasing the average and variation of stiffness coefficients, respectively. It also shows that a high rotational speed is another source of instability by increasing the stiffness coefficients without changing the damping coefficients.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 춘계학술대회논문집
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• pp.166-174
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• 2002

This paper presents an analytical method to Investigate the stability of a hydrodynamic journal bearing with rotating herringbone grooves. The dynamic coefficients of the hydrodynamic journal bearing are calculated using the FEM and the perturbation method. The linear equations of motion can be represented as a parametrically excited system because the dynamic coefficients have time-varying components due to the rotating grooves, even in the steady state. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill's infinite determinant of these algebraic equations. The validity of this research is proved by the comparison of the stability chart with the time response of the whirl radius obtained from the equations of motion. This research shows that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing eccentricity and with decreasing groove number, which play the major roles in increasing the average and variation of stiffness coefficients, respectively. It also shows that a high rotational speed is another source of instability by increasing the stiffness coefficients without changing the damping coefficients.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제29권4호
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• pp.699-722
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• 2015

본 연구의 목적은 라그랑주의 방정식론을 바탕으로 한 방정식의 해법을 고등학교 1학년 수업에 적용하여 방정식의 해법과 관련한 근과 계수의 관계와 대칭성의 의의를 인식하게 하는 것이다. 대칭성은 라그랑주의 방정식론의 핵심 아이디어이며, 근과 계수의 관계는 그의 해법에 있어 중요한 수단이다. 학생들은 수업을 통해 근과 계수의 관계에 대한 학습 의의를 인식하였고, 대칭성의 아이디어를 이해하였으며, 새로운 해법에 흥미를 나타내었다. 이러한 연구는 학교수학에서 다루는 국소적인 방정식의 해법만이 아닌 교수학적 조직화에 의한 체계적인 방정식론에 대한 경험을 주며, 방정식의 해법과 관련한 지식들의 연결성을 이해하게 한다.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제2권2호
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• pp.115-121
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• 2002

This paper presents an evolutionary design of digital IIR filters using the genetic algorithm (GA) with modified genetic operators and real-valued encoding. Conventional digital IIR filter design methods involve algebraic transformations of the transfer function of an analog low-pass filter (LPF) that satisfies prescribed filter specifications. Other types of frequency-selective digital fillers as high-pass (HPF), band-pass (BPF), and band-stop (BSF) filters are obtained by appropriate transformations of a prototype low-pass filter. In the GA-based digital IIR filter design scheme, filter coefficients are represented as a set of real-valued genes in a chromosome. Each chromosome represents the structure and weights of an individual filter. GA directly finds the coefficients of the desired filter transfer function through genetic search fur given filter specifications of minimum filter order. Crossover and mutation operators are selected to ensure the stability of resulting IIR filters. Other types of filters can be found independently from the filter specifications, not from algebraic transformations.

• 대한수학회보
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• 제53권4호
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• pp.1005-1015
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• 2016

It is a surprising but now well-known fact that there exist algebraic power series of degree higher than two with partial quotients of bounded degrees in their continued fraction expansions, while there is no single algebraic real number known with bounded partial quotients. However, it seems that these special algebraic power series are quite rare and it is hard to determine their continued fraction expansions explicitly. To the short list of known examples, we add a new family of cubic power series with bounded partial quotients.