• Kyungpook Mathematical Journal
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• 제21권1호
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• pp.39-47
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• 1981

• Journal of the Korean Statistical Society
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• 제7권1호
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• pp.3-10
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• 1978

Let $X_i,...,X_n$ be a random sample from a distribution with cumulants $K_1, K_2,...$. The statistic $t = \frac{\sqrt{x}(\bar{X}-K_1)}{S}$ has the well-known 'student' distribution with $\nu = n-1$ degrees of freedom if the $X_i$ are normally distributed (i.e., $K_i = 0$ for $i \geq 3$). An Edgeworth series expansion for the distribution of t when the $X_i$ are not normally distributed is obtained. The form of this expansion is Prob $(t

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1998년도 추계종합학술대회 논문집
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• pp.679-682
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• 1998

This paper presents the VLSI implementation of RS(reed-solomon) decoder using the Modified Euclidean Algorithm(hereafter MEA) for DVD(Digital Versatile Disc) and CD(Compact Disc). The decoder has a capability of correcting 8-error or 16-erasure for DVD and 2-error or 4-erasure for CD. The technique of polynomial evaluation is introduced to realize syndrome calculation and a polynomial expansion circuit is developed to calculate the Forney syndrome polynomial and the erasure locator polynomial. Due to the property of our system with buffer memory, the MEA architecture can have a recursive structure which the number of basic operating cells can be reduced to one. We also proposed five criteria to determine an uncorrectable codeword in using the MEA. The overall architecture is a simple and regular and has a 4-stage pipelined structure.

• Nuclear Engineering and Technology
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• 제31권2호
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• pp.172-181
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• 1999

Series expansion methods to compute the exponential of a matrix have been compared by applying them to fuel depletion calculations. Specifically, Taylor, Pade, Chebyshev, and rational Chebyshev approximations have been investigated by approximating the exponentials of bum matrices by truncated series of each method with the scaling and squaring algorithm. The accuracy and efficiency of these methods have been tested by performing various numerical tests using one thermal reactor and two fast reactor depletion problems. The results indicate that all the four series methods are accurate enough to be used for fuel depletion calculations although the rational Chebyshev approximation is relatively less accurate. They also show that the rational approximations are more efficient than the polynomial approximations. Considering the computational accuracy and efficiency, the Pade approximation appears to be better than the other methods. Its accuracy is better than the rational Chebyshev approximation, while being comparable to the polynomial approximations. On the other hand, its efficiency is better than the polynomial approximations and is similar to the rational Chebyshev approximation. In particular, for fast reactor depletion calculations, it is faster than the polynomial approximations by a factor of ∼ 1.7.

• 대한전자공학회논문지
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• 제24권6호
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• pp.948-955
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• 1987

The model reduction method of the high order linear time invariant systems is proposed. The continuous fraction expansion of Auxiliary denominator polynomial is used to obtain denominator polynomial of the reduced order model, and the numerator polynomial of the reduced order model is obtained by equating the first some moments of the original and the reduced order model, using simplified moment function. This methiod does not require the calculation of the reciprocal transformation which should be calculated in Routh approximation, furthemore the stability of the reduced order model is guaranted if original system is stable. Responses of this method showed us good characteristics.

• 한국수학교육학회지시리즈A:수학교육
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• 제54권4호
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• pp.365-383
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• 2015

Factorization asks the recognition of the structure of polynomials, compared to polynomial expansion with process characteristic. Therefore it makes students experience a lot of difficulties. This study aims to figure out causes of the difficulties by identifying students' cognitive characteristics in factorizing in the perspective of 'structure sense'. To do this, we gave six factorizing problems of three types to middle school students and selected six participants as interviewees based on the test results. They were classified into two categories, structure sense and non-structure sense. Through this interview, we figured out the interviewee's cognitive characteristics and the causes of difficulty in the perspective of structure sense. Furthermore, we suggested some didactical implications for encouraging structure sense in factorizing by identifying assistances and obstacles for recognition of structures.

• 전기학회논문지
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• 제62권3호
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• pp.407-413
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• 2013

This paper proposes anti-swing control of overhead crane system using sum of squares method. The dynamic equations of overhead crane include nonlinear terms, which are transformed into polynomials by using Taylor series expansion. Therefore the dynamic equation of overhead crane can be changed to the system of polynomial equation. On the basis of polynomial dynamics of crane system, we propose the Sum of Squares (SOS) conditions considering the input constraints. In addition, control gains are obtained by numerical tool which is called by SOSTOOL. The effectiveness of the proposed method is demonstrated by numerical simulation.

• 대한수학회지
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• 제51권3호
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• pp.443-462
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• 2014

Using a simple recurrence relation, we give a new method to compute the Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for the Jones polynomials. The method is used to estimate the degree of the Jones polynomials for some families of braids and to obtain general qualitative results.

• Kyungpook Mathematical Journal
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• 제12권1호
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• pp.115-117
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• 1972

The purpose of the present paper is to evaluate certain integrals involving Laguerre, Jacobi and Hermite polynomials. These integrals are very useful in case of expansion of any polynomial in a series of Orthogonal polynomials [1, Theo. 56].

• Smart Structures and Systems
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• 제31권2호
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• pp.113-130
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• 2023

Hybrid simulation (HS) has attracted community attention in recent years as an efficient and effective experimental technique for structural performance evaluation in size-limited laboratories. Traditional hybrid simulations usually take deterministic properties for their numerical substructures therefore could not account for inherent uncertainties within the engineering structures to provide probabilistic performance assessment. Reliable structural performance evaluation, therefore, calls for stochastic hybrid simulation (SHS) to explicitly account for substructure uncertainties. The experimental design of SHS is explored in this study to account for uncertainties within analytical substructures. Both computational simulation and laboratory experiments are conducted to evaluate the pseudo-random Sobol sequence for the experimental design of SHS. Meta-modeling through polynomial chaos expansion (PCE) is established from a computational simulation of a nonlinear single-degree-of-freedom (SDOF) structure to evaluate the influence of nonlinear behavior and ground motions uncertainties. A series of hybrid simulations are further conducted in the laboratory to validate the findings from computational analysis. It is shown that the Sobol sequence provides a good starting point for the experimental design of stochastic hybrid simulation. However, nonlinear structural behavior involving stiffness and strength degradation could significantly increase the number of hybrid simulations to acquire accurate statistical estimation for the structural response of interests. Compared with the statistical moments calculated directly from hybrid simulations in the laboratory, the meta-model through PCE gives more accurate estimation, therefore, providing a more effective way for uncertainty quantification.