• Journal of the Korean School Mathematics Society
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• v.23 no.4
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• pp.509-521
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• 2020

This study began with the discovery of the concept of frequency density in Singapore textbooks and in a set of subject contents of the UK's General Certificate of Secondary Education. To understand the mathematical meaning of frequency density, the mathematical connection of frequency density was considered in terms of mathematics internal connections and mathematics external connections. In addition, the teaching method of frequency density was introduced. In terms of mathematical internal connections, the connections among the probability density function, relative frequency density, and frequency density in high school statistics were examined. Regarding mathematical external connections, the connection with the density concept in middle school science was analyzed. Based on the mathematical connection, the study suggested the need to introduce the frequency density concept. For the teaching method of frequency density, the Singapore secondary mathematics textbook was introduced. The Singapore textbook introduces frequency density to correctly represent and accurately interpret data in histograms with unequal class intervals. Therefore, by introducing frequency density, Korea can consistently teach probability density function, relative frequency density, and frequency density, emphasizing the mathematical internal connections among them and considering the external connections with the science subject. Furthermore, as a teaching method of frequency density, we can consider the method provided in the Singapore textbook.

• Geomechanics and Engineering
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• v.38 no.2
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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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• v.3 no.2
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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.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.20 no.5
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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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• v.37 no.2
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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.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2003.10a
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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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• v.13 no.2
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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.

• Geotechnical Engineering
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• v.4 no.3
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• pp.5-18
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• 1988

This study aims at scrutinizing the relationships among the frequency distribution of voids the relative density and the shear strength for the three types of different granular materials. The main results summarized are as follows: (1) The frequency distribution of void ratio of glass beads can be approximated by the negative exponential distribution proposed by Shahinpoor (1981), while as the particle shape changes from spherical to angular the frequency of the denser voids decreases and the distributions are well presented by the beta distribution. (2) For all materials, the standard deviation of void ratio increases with decreasing both the relative density of the material and sphericity of particle. (3) It was found that shear strength of the material was a function of not only the mean void ratio and its standard deviation, but also of the shape of the probability density function of the distribution of void ratio. The more the frequency distribution of void inclines towards the denser voids, the higher the shear strength of the material and vice versa.

• Proceedings of the Acoustical Society of Korea Conference
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• spring
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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.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.07a
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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.