• 한국학교수학회논문집
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• 제23권4호
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• pp.509-521
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• 2020

본 연구는 싱가포르 교과서와 영국의 중등 졸업 자격시험 항목에서 도수밀도(frequency density)라는 개념을 발견하면서 시작되었다. 도수밀도의 수학적 의미를 파악하기 위해 도수밀도 개념의 수학적 연결성을 수학 내적 연결성과 수학 외적 연결성 측면에서 고찰하고, 이에 관한 지도 방안을 소개하고자 하였다. 수학 내적 연결성 측면에서는 고등학교 연속확률분포 단원의 연속확률변수와 확률밀도함수와의 연계성을 탐구하였고, 수학 외적 연결성 측면에서는 중학교 과학 교과의 밀도 개념과의 연계성을 탐구하였다. 연구 결과, 수학적 연결성을 바탕으로 도수밀도 개념의 도입 필요성을 제시했다. 도수밀도의 도입과 지도 방안에 대해서는 싱가포르의 중등 2학년 수학 교과서를 소개하였다. 싱가포르 교과서에서는 비균등 구간의 자료를 히스토그램으로 올바르게 표현하고 정확하게 해석하기 위한 방법으로 도수밀도를 도입하고 있다. 따라서 우리나라도 도수밀도를 도입함으로써 확률밀도함수와 상대도수밀도, 그리고 도수밀도 사이의 수학 내적 연결성을 강조하여 일관성 있게 지도하고, 도수밀도의 과학 교과와의 외적 연결성을 고려하며, 도수밀도 도입 방법으로 싱가포르의 지도 방안을 고려해 볼 수 있겠다.

• Geomechanics and Engineering
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• 제38권2호
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• pp.165-177
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• 2024

Liquefaction phenomenon refers to a phenomenon in which excess pore water pressure occurs when a dynamic load such as an earthquake is rapidly applied to a loose sandy soil ground where the ground is saturated, and the ground loses effective stress and becomes liquid. The laboratory repetition test for liquefaction evaluation can be performed through a repeated triaxial compression test and a repeated shear test. In this regard, this study attempted to evaluate the effects of the relative density of sand on the liquefaction resistance strength according to particle size distribution using repeated triaxial compression tests, and additional experimental verification using numerical analysis was conducted to overcome the limitations of experimental equipment. As a result of the experiment, it was confirmed that the liquefaction resistance strength increased as the relative density increased regardless of the classification of soil, and the liquefaction resistance strength of the SP sample close to SW was quite high. As a result of numerical analysis, it was confirmed that the liquefaction resistance strength increased as the confining pressure increased under the same relative density, and the liquefaction resistance strength did not decrease below a certain limit even though the confining pressure was significantly reduced at a relatively low relative density. This is judged to be due to a change in confining pressure according to the depth of the ground. As a result of analyzing the liquefaction resistance strength according to the frequency range, it was confirmed that there was no significant difference from the laboratory experiment results in the basic range of 0.1 to 1.0 Hz.

• Geomechanics and Engineering
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• 제3권2호
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• pp.83-108
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• 2011

The effect of non-plastic fines (silt) on liquefaction and pore pressure generation characteristics of saturated sands was studied through undrained stress controlled cyclic triaxial tests using cylindrical specimens of size 50 mm diameter and height 100 mm at different cyclic stress ratios and at a frequency of 0.1 Hz. The tests were carried out in the laboratory adopting various measures of sample density through various approaches namely gross void ratio approach, relative density approach, sand skeleton void ratio approach, and interfine void ratio approach. The limiting silt content and the relative density of a specimen were found to influence the undrained cyclic response of sand-silt mixtures to a great extent. Undrained cyclic response was observed to be independent of silt content at very high relative densities. However, the presence of fines significantly influenced this response of loose to medium dense specimens. Combined analyses of cyclic resistance have been done using the entire data collected from all the approaches.

• 한국전기전자재료학회논문지
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• 제20권5호
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• pp.430-435
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• 2007

This paper describes the results of electrical characteristics assessment for organic insulations of polyethylene(PE) series insulations and acrylonitrile butadiene styrene copolymer(ABS). In the experiment, 4 kinds of specimens by composition density were tested in relative permittivity, specific resistance and tracking duration. A WinDETA system and a tracking test set manufactured for this assessment were used to measure the dielectric parameters and tracking duration, respectively. In measuring the tracking duration, the time from testing voltage application to testing circuit breaking due to the tracking current was measured. As a result, dielectric dispersion was observed in measuring the relative permittivity of ABS. It was confirmed that the relative permittivity decreased with the density of the PE series insulations and it depends rather on the temperature than frequency. In most specimens, specific resistance exponentially decreased with frequency and the result for each specimen was almost similar. By the way, in the tracking test, all the PE series insulations showed more excellent performance than ABS and especially in the case of HDPE, its tracking withstand performance was the best.

• Geomechanics and Engineering
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• 제37권2호
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• pp.167-178
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• 2024

The natural frequency shift under cyclic environmental loads is a key issue in the design of monopile-based offshore wind power turbines because of their dynamic sensitivity. Existing evidence reveals that the natural frequency shift of the turbine system in sand is related to the varying foundation stiffness, which is caused by soil deformation around the monopile under cyclic loads. Therefore, it is an urgent need to investigate the effect of soil deformation on the system frequency. In the present paper, three generalized geometric models that can describe soil deformation under two-way cyclic loads are proposed. On this basis, the cycling-induced changes in soil parameters around the monopile are quantified. A theoretical approach considering three-spring foundation stiffness is employed to calculate the natural frequency during cycling. Further, a parametric study is conducted to describe and evaluate the frequency shift characteristics of the system under different conditions of sand relative density, pile slenderness ratio and pile-soil relative stiffness. The results indicate that the frequency shift trends are mainly affected by the pile-soil relative stiffness. Following the relevant conclusions, a design optimization is proposed to avoid resonance of the monopile-based wind turbines during their service life.

• 한국분말야금학회:학술대회논문집
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• 한국분말야금학회 2003년도 international symposium on advanced powder metallurgy
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• pp.39-40
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• 2003

1) Using a developed high-frequency induction heated sintering method, the rapid densification of WC-Co hard materials was accomplished using ultra fine powders with 260 nm size within 1 minute. 2) The relative density of the composite was 99.5% for the applide pressure of 60MPa and the induced current for 90% output of total capacity. 3) The grain size of WC-Co hard materials is about 260nm and the average thickness of the binder phase determined is about 11nm. The fracture toughness and the hardness of this work 12 $MPa{\cdot}nm^2$, respectively. 4) Using pressureless sintering, we produced dense WC-Co hard materials with a relative density of 97% without applying pressure.

• Communications for Statistical Applications and Methods
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• 제13권2호
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• pp.243-254
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• 2006

The relative frequency of order statistics is investigated for independent and identically distributed (i.i.d.) random variables. Specifically, it is shown that the probability $Pr\{X_{[s]}=x\}$ is no less than the probability $Pr\{X_{[r]}=x\}$ at any point $x{\geqq}x_0$ when r$X_{[r]}$ denotes the r-th order statistic of an i.i.d. discrete random vector and $x_0$ depends on the population probability distribution. A similar result for i.i.d. continuous random vectors is also presented.

• 한국지반공학회지:지반
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• 제4권3호
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• pp.5-18
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• 1988

3종의 입상체시료를 대상으로 공극비의 빈도분포, 상대밀도 전단강도 등에 대한 시험연구결과 (1) 유리알의 경우 공극비의 빈도분포는 Shahinpoorl가 제안한 음의 지수분포에 접근하며 입자의 모양은 구형에서 각형의 순으로 변화되는 반면에 조밀한 공극의 빈도는 감소하며 Beta분포로서 잘 나타냈다. (2) 전 시료에서 공극비의 표준편차는 시료의 상대밀도와 입자의 구형성이 감소함에 따라 증가하였다. (3) 전단강도는 평균공극비와 표준편차의 함수일 뿐만 아니라 공극비 분포의 확율밀도함수이다. (4) 공극비는 정도분포가 조밀한 공극쪽으로 기울수록 시료의 전단강도는 더 크며 이의 역도 또한 같다.

• 한국음향학회:학술대회논문집
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• 한국음향학회 2002년도 하계학술발표대회 논문집 제21권 1호
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• pp.373-376
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• 2002

Most previous studies using ultrasound for osteoporosis diagnosis have employed ultrasound in a frequency range of 0.2-1 MHz. In this study, acoustic properties of the 12 defatted bovine cancellous bone specimens were investigated in vitro. Speed of sound (SOS) and broadband ultrasonic attenuation (BUA) were measured using three matched pairs of transducers with the center frequencies of 1, 2.25, and 3.5 MHz, respectively, in order to cover a broad frequency range of 0.5-2 MHz. The relative orientation between ultrasonic beam and bone specimens was the mediolateral (ML) direction of the bovine tibia. SOS showed significant linear positive correlations with apparent density for all three pairs of transducers of 1 MHz, 2.25 MHz, and 3.5 MHz, respectively. BUA showed relatively weak correlations with apparent density for the pairs of transducers of 1 MHz and 2.25 MHz. Furthermore, in the measurement with the pair of 3.5 MHz transducers, BUA was independent of apparent density. SOS and BUA were only weakly correlated with each other. The linear combination of SOS and BUA showed significant correlations with apparent density. These results suggest that the frequency range up to 1.5 MHz may be also useful in the osteoporosis diagnosis.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2000년도 하계학술대회 논문집
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• pp.636-639
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• 2000

Effects of sintering temperature and time on relative permittivity $\varepsilon$$\_$r/, unloaded quality factor Q$.$f and temperature coefficient of resonant frequency $\tau$$\_$f/ of dielectric resonator materials produced from commercial ZST powder were investigated in some detail. Q$.$f values, as determined from cavity perturbation method at 1.6 GHz, gradually increased with sintering temperature reaching the maximum at 1420$^{\circ}C$. However, bulk density and relative permittivity values, which increased with temperature, started to decrease above 1380$^{\circ}C$. In addition, Q$.$f values slightly increased with sintering time at the sintering temperature of 1300$^{\circ}C$∼1380$^{\circ}C$, while bulk density and relative permittivity values were approximately constant. It was also found that $\tau$$\_$f/ values were not affected by sintering temperature and time within the experimental conditions used.