• 한국수학교육학회지시리즈E:수학교육논문집
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• 제29권1호
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• pp.91-110
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• 2015

본 연구는 초등수학 영재교육 대상자들이 원주율 개념에 대해서 어떻게 이해하고 있는지를 살펴보고자 하였다. 이를 위해 원주율 계산 방법의 역사 발달 단계를 토대로 세 가지 과제를 개발한 후 6학년 영재교육 대상자 12명을 대상으로 적용하여 그 반응을 분석하였다. 연구결과, 학생들은 '원주율 = 3.14'라는 사고의 고착화로 인하여 원주율의 개념, 근사성, 무한성을 제대로 이해하지 못하였으며, 원주율과 원주율의 근삿값을 혼동하는 오류를 보였다. 또한 학생들은 원주율을 '(원주) ${\div}$ (지름)'의 대수적인 식으로 이해하려는 성향이 강하였으며, 원주율의 상수성과 무한성을 깊이 있게 이해하고 있는 학생은 극히 적었다. 반면에 과제에 대한 토론 활동은 학생들이 원주율의 근사성에 대한 아이디어를 발견할 수 있는 기회를 제공하였다. 이상의 결과를 종합하여, 초등학교에서의 원주율 지도와 관련하여 원주율을 원의 지름을 단위길이로 원의 둘레를 측정하여 얻을 수 있는 값으로 도입할 것과 공학적 도구 등을 이용하여 직관적인 방법을 통해 이해하도록 할 것, 원주율 개념이 가지는 본질적인 의미를 이해할 수 있도록 다양한 상황을 통해 도입할 것을 제안하였다.

• The Journal of the Acoustical Society of Korea
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• 제16권2E호
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• pp.47-54
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• 1997

This paper presents two results on intersymbol interferences in baseband digital communication over an additive white Gaussian noise channel-the interferences due to mismatched square-root raised-cosine filters, in which the filters have different roll-off factors, and / or due to sampling-time jitter. The result for the mismatched filters is that even the jitter-free sampling causes intersymbol interference and it is negligibly small for a wide range of signal-to-noise ratio up to 10dB, for the roll-off factor ranging from 0.2 to 0.5, the mismatch loss being within 0.1dB from the optimum at around 10-6 .For jitter interference an approximation formula for the bit error probability is derived in case of the matched filters, which shows how the roll-off factors and the amount of jitter affect the system performance. The formula is reasonably accurate.

• ETRI Journal
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• 제35권2호
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• pp.218-225
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• 2013

The pull-out frequency of a second-order phase lock loop (PLL) is an important parameter that quantifies the loop's ability to stay frequency locked under abrupt changes in the reference input frequency. In most cases, this must be determined numerically or approximated using asymptotic techniques, both of which require special knowledge, skills, and tools. An approximating formula is derived analytically for computing the pull-out frequency for a second-order Type II PLL that employs a sinusoidal characteristic phase detector. The pull-out frequency of such PLLs can be easily approximated to satisfactory accuracy with this formula using a modern scientific calculator.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권4호
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• pp.275-287
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• 2005

Geometric invariants are basic tools for geometric processing and computer vision. In this paper, we give a linear approximation for the differentiation of the binormal vector field of a space curve by using the forward and backward differences of discrete binormal vectors. Two kind of discrete torsion, say, back-ward torsion $T_b$ and forward torsion $T_f$ can be defined by the dot product of the (backward and forward) discrete differentiation of binormal vectors that are linear approximations of torsion. Using Frenet formula and Taylor series expansion, we give error estimations for the discrete torsions. We also give numerical tests for a curve. Notably the average of $T_b$ and $T_f$ looks more stable in errors.

• 대한수학회논문집
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• 제37권3호
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• pp.765-800
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• 2022

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.

• 대한수학회지
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• 제57권5호
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• pp.1167-1186
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• 2020

This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure imposed among the state variables. This full correlation structure possesses the limitation to have fully analytical pricing formula for hybrid models of variance swaps, due to the non-affinity property embedded in the model itself. We address this issue by obtaining an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions. Subsequently, we implement numerical experiments to evaluate the accuracy of our pricing formula. Our findings confirm that the impact of the correlation between the underlying and the interest rate is significant for pricing discretely-sampled variance swaps.

• 대한수학회보
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• 제41권1호
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• pp.27-43
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• 2004

Let he(x) and $h_{o}(x)$ denote the limits of the sequences $\{^{2n}x\}\;and\;\{^{2n+1}x\}$, respectively. Asymptotic formulas for the functions E\$h_e\;and\;h_o$ at the points $e^{-e}$ and 0 are established.

• Communications for Statistical Applications and Methods
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• 제21권3호
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• pp.253-260
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• 2014

The intraclass correlation model has a long history of applications in several fields of research. Case deletion diagnostic methods for the intraclass correlation model are proposed. Based on the likelihood equations, we derive a formula for a case deletion diagnostic method which enables us to investigate the influence of observations on the maximum likelihood estimates of the model parameters. Using the Taylor series expansion we develop an approximation to the likelihood distance. Numerical examples are provided for illustration.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2001년도 가을 학술발표회 논문집
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• pp.689-694
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• 2001

Until now, various period formulas Pre proposed, but those of have a little difficult procedure and variation according to structural system. This paper presents an analysis of the uncoupled vibration of symmetric in RC structures. A generalized approximate method is developed using the Southwell-Dunkerley approximation and characteristics of structural deformation. The results of the proposed method for the example structure show good agreement with those of the Midas Genw4.2.2.

• 충청수학회지
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• 제27권3호
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• pp.405-411
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• 2014

Queueing systems with retrials are widely used to model many problems in call centers, telecommunication networks, and in daily life. We present a very accurate but simple approximate formula for the distribution of the number of retrying customers in the M/G/1 retrial queue.