• 한국수학교육학회지시리즈E:수학교육논문집
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• 제35권4호
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• pp.505-525
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• 2021

본 연구에서는 한국과 일본, 싱가포르, 미국의 초등학교 수학 교과서에서 곱하는 수가 두 자리 수인 자연수 곱셈 계산을 어떻게 제시하는지를 비교·분석하여 곱셈 지도 관련 교육적 시사점을 도출하고자 하였다. 교과서 분석 결과, 우리나라 교과서는 10과 10의 거듭제곱의 곱을 별도로 지도하지 않는 반면, 일본, 싱가포르, 미국 교과서는 관련 내용을 명시하여 제시하고 있음을 확인하였다. '×(몇십)'의 지도에서는 일본과 미국 교과서가 자릿값에 따라 나누어 곱한 부분곱의 계산과정에서 적용되는 곱셈의 결합법칙 지도를 형식적으로 접근하고 있었다. 세로셈 계산 도식은 대체적으로 분배법칙에 따른 부분곱 계산을 자리를 맞추어 표기하는 표준적인 방식을 따르고 있었지만, 지도 모델과 분배법칙의 지도 방법, 끝 자리 '0'의 표기 등에서 차이가 확인되었다. 이상의 분석결과를 토대로 곱셈 지도와 관련한 시사점을 제안하였다.

• Advances in nano research
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• 제9권3호
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• pp.211-220
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• 2020

This paper investigates the effect of linear and non-linear distribution of carbon nanotube volume fraction in the FG-CNTRC beams on the critical buckling by using higher-order shear deformation theories. Here, the material properties of the CNTRC beams are assumed to be graded in the thickness direction according to a new exponential power law distribution in terms of the carbon nanotube volume fractions. The single-walled carbon nanotube is aligned and distributed in the polymeric matrix with different patterns of reinforcement; the material properties of the CNTRC beams are described by using the rule of mixture. The governing equations are derived through using Hamilton's principle. The Navier solution method is used under the specified boundary conditions for simply supported CNTRC beams. The mathematical models provided in this work are numerically validated by comparison with some available results. New results of critical buckling with the non-linear distribution of CNT volume fraction in different patterns are presented and discussed in detail, and compared with the linear distribution. Several aspects of beam types, CNT volume fraction, exponent degree (n), aspect ratio, etc., are taken into this investigation. It is revealed that the influences of non-linearity distribution in the beam play an important role to improve the mechanical properties, especially in buckling behavior. The results show that the X-Beam configuration is the strongest among all different types of CNTRC beams in supporting the buckling loads.

• KIEE International Transactions on Electrophysics and Applications
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• 제2C권5호
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• pp.246-252
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• 2002

Two-dimensional steady state simulations of planar type radio frequency inductively coupled plasma (RFICP) have been performed. The characteristics of RFICP were investigated in terms of power transfer efficiency, equivalent circuit analysis, spatial distribution of plasma density and electron temperature. Plasma density and electron temperature were determined from the equations of ambipolar diffusion and energy conservation. Joule heating, ionization, excitation and elastic collision loss were included as the source terms of the electron energy equation. The electromagnetic field was calculated from the vector potential formulation of ampere's law. The peak electron temperature decreases from about 4eV to 2eV as pressure increases from 5 mTorr to 100 mTorr. The peak density increases with increasing pressure. Electron temperatures at the center of the chamber are almost independent of input power and electron densities linearly increase with power level. The results agree well with theoretical analysis and experimental results. A single turn, edge feeding antenna configuration shows better density uniformity than a four-turn antenna system at relatively low pressure conditions. The thickness of the dielectric window should be minimized to reduce power loss. The equivalent resistance of the system increases with both power and pressure, which reflects the improvement of power transfer efficiency.

• 한국정보과학회논문지:정보통신
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• 제37권3호
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• pp.167-174
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• 2010

최근에 비 구조적 피어투피어 시스템을 위해 분산적으로 재결정위상을 구성하는 위상 제어 프로토콜이 제안되었다[1]. 본 논문에서는 재결정위상이라고 불리는 이러한 계층적 위상이 척도 없는 거듭제곱 법칙 망임을 보인다. 우리는 재결정 위상의 분산된 구성을 위한 알고리즘의 프로세스를 모형화 하고, 평균 장 점근법(Mean field Approximation)과 연속체 이론(Continuum theory)에 근거를 두고 분석하여, 구성된 재결정 망이 척도 없는 망임을 보였다. 위상제어 알고리즘을 따르는 각 노드는 더 선호하는 노드에 대한 연결을 추가하고, 가장 비선호하는 노드에 대한 연결을 제거한다. 다시 말해, 알고리즘에 따라, 각 피어는 자신이 알고 있는 피어들 중에서 최고의 적중률(또는 검색 능력 혹은 선호도)을 가지고 있는 노드들과 연결을 추가하고, 최저의 적중률을 가진 노드들과의 연결을 끊는다. 이것은 비구조적 피어투피어 망에서 재결정 위상을 구성하기 위한 지역적인 프로세스를 실제적으로 표현한다. 우리는 차수의 분포를 분석적으로 유도한다. 분석 결과, 만들어지는 재결정 위상은 척도 없는 망이며, 이것의 거듭제곱 법칙의 지수$\gamma$는 3 이다.

• 대한기계학회논문집A
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• 제39권6호
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• pp.625-629
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• 2015

본 연구에서는 수냉식 발전기 고정자 권선의 건전성 예지 방법에 대해 연구하였다. 권선의 데이터를 흡습 데이터와 정상 데이터로 분류 하였으며 각각의 데이터 군을 다른 방법으로 예측 하였다. 흡습 데이터를 예측하기 위해 픽의 제 2 법칙(Fick's second law)를 이용하여 건전성 감소 모델링을 하였고 픽의 제 2법칙의 해를 이용하여 흡습 모델식을 만들었다. 정상 데이터는 데이터의 분포가 정규분포를 따른다는 가설을 세운 후 카이제곱 검정을 통해 이를 입증하였다. 예측된 흡습 데이터와 정상 데이터를 이용하여 건전성 인자인 방향성 마할라노비스 거리(Directional mahalanobis distance; DMD)의 예측값을 산출하였고 흡습 권선의 고장 예상시점을 계산했다.

• 한국신뢰성학회지:신뢰성응용연구
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• 제14권1호
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• pp.45-51
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• 2014

Thermal shock tests at two stress levels were performed to see the life (cycles) of LPF ASSY (low pass filter assembly) at normal stress level. In this case Coffin-Manson relationship is generally used to describe the relationship between the temperature difference and the life, together with the Weibull distribution describing the life at each stress level. So for given data Coffin-Manson is fitted to predict the life at normal stress level. However, different types of models are appropriate for this type of test. Hence, a more appropriate model such as General log-linear model which can also incorporate the duration at the highest and lowest temperatures and acceleration time will be introduced.

• 대한산업공학회지
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• 제19권2호
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• pp.15-21
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• 1993

This paper considers the optimal design of accelerated life test in which the stress is linearly increased. It discusses the special case when the life distribution under constant stress follows an exponential distribution and the accelerated equation satisfies the inverse power law. It is assumed that cumulative damage is linear, that is, the remaining life of test units depends only on the current cumulative fraction failed and current stress(cumulative exposure model). The optimization criterion is the asymptotic variance of the maximum likelihood estimator of the log mean life at a design stress. The optimal increasing rate is obtained to minimize the asymptotic variance. Table of sensitivity analysis is given for the prior estimators of model parameters.

• Advances in aircraft and spacecraft science
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• 제7권4호
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• pp.335-351
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• 2020

Thermal buckling of functionally graded sandwich cylindrical shells is presented in this study. Material properties and thermal expansion coefficient of FGM layers are assumed to vary continuously through the thickness according to a sigmoid function and simple power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FGM sandwich cylindrical shells with simply supported boundary conditions are derived according to the Donnell theory. The influences of cylindrical shell geometry and the gradient index on the critical buckling temperature of several kinds of FGM sandwich cylindrical shells are investigated. The thermal loads are assumed to be uniform, linear and nonlinear distribution across the thickness direction. An exact simple form of nonlinear temperature rise through its thickness taking into account the thermal conductivity and the inhomogeneity parameter is presented.

• 천문학회보
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• 제39권2호
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• pp.60.2-60.2
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• 2014

Hierarchical structure of star-forming regions is widespread and may be characteristic of all star formation. We studied the hierarchical structure of star-forming regions in the Local Group galaxies (M31, M33, Phoenix, Pegasus, Sextans A, Sextans B, WLM). The star-forming regions were selected from Galaxy Evolution Explorer (GALEX) far-UV imaging in various detection thresholds for investigating hierarchical structure. We examined the spatial distribution of the hot massive stars within star-forming regions from Hubble Space Telescope (HST) multi-band photometry. Small compact groups arranged within large complexes. The cumulative mass distribution follows a power law. The results allow us to understand the hierarchical structure of star formation and recent evolution of the Local Group galaxies.

• Smart Structures and Systems
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• 제19권4호
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• pp.441-448
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• 2017

This paper uses the four-variable refined plate theory for the free vibration analysis of functionally graded material (FGM) rectangular plates. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Equations of motion are derived from the Hamilton's principle. The closed-form solutions of functionally graded plates are obtained using Navier solution. Numerical results of the refined plate theory are presented to show the effect of the material distribution, the aspect and side-to-thickness ratio on the fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of functionally graded plates.