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Analysis of teaching and learning contents of matrix in German high school mathematics (독일 고등학교 수학에서 행렬 교수·학습 내용 분석)

  • Ahn, Eunkyung;Ko, Ho Kyoung
    • The Mathematical Education
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    • v.62 no.2
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    • pp.269-287
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    • 2023
  • Matrix theory is widely used not only in mathematics, natural sciences, and engineering, but also in social sciences and artificial intelligence. In the 2009 revised mathematics curriculum, matrices were removed from high school math education to reduce the burden on students, but in anticipation of the age of artificial intelligence, they will be reintegrated into the 2022 revised education curriculum. Therefore, there is a need to analyze the matrix content covered in other countries to suggest a meaningful direction for matrix education and to derive implications for textbook composition. In this study, we analyzed the German mathematics curriculum and standard education curriculum, as well as the matrix units in the German Hesse state mathematics curriculum and textbook, and identified the characteristics of their content elements and development methods. As a result of our analysis, it was found that the German textbooks cover matrices in three categories: matrices for solving linear equations, matrices for explaining linear transformations, and matrices for explaining transition processes. It was also found that the emphasis was on mathematical reasoning and modeling when learning matrices. Based on these findings, we suggest that if matrices are to be reintegrated into school mathematics, the curriculum should focus on deep conceptual understanding, mathematical reasoning, and mathematical modeling in textbook composition.

Effect of Fine Content on the Monotonic Shear Behavior of Sand-Clay Mixtures (점토와 모래의 혼합토의 정적 전단거동에 대한 세립분 함유율의 영향)

  • Kim, Uk-Gie;Masayuki, Hyodo;Beak, Won-Jin;Ahn, Tae-Bong
    • Journal of the Korean Geotechnical Society
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    • v.23 no.4
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    • pp.91-100
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    • 2007
  • In most design codes, soils are classified as either sand or clay, and appropriate design equations are used to represent their behavior. For example, the behavior of sandy soils is expressed in terms of the relative density, whereas consistency limits are often used for clays. However, sand-clay mixtures, which are typically referred to as intermediate soils, cannot be easily categorized as either sand or clay and therefore a unified interpretation of how the soil will behave at the transition point, i.e., from sandy behavior when fines are low to clay behavior for high fines content, is necessary. In this study, active natural clays are mixed with sand, and the fines content varied in order to produce different structures, ranging from one state where only sand particles form the soil structure to another where the matrix of fines make-up the structure. While paying attention to the granular void ratio in order to clarify the shear properties of sand-clay mixtures with increasing fines content monotonic, shear tests were performed on isotropically, and anisotropically consolidated specimens. From the test results, it was observed that the monotonic shear strength of sand-clay mixtures is dependent on the granular void ratio.

Horizontal-Axis Screw Turbine as a Micro Hydropower Energy Source: A Design Feasibility Study (마이크로 수력 에너지원의 수평축 스크류 터빈 : 설계 타당성 연구)

  • SHAMSUDDEEN, MOHAMED MURSHID;KIM, SEUNG-JUN;MA, SANG-BUM;KIM, JIN-HYUK
    • Transactions of the Korean hydrogen and new energy society
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    • v.33 no.1
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    • pp.95-104
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    • 2022
  • Micro hydropower is a readily available renewable energy source that can be harvested utilizing hydrokinetic turbines from shallow water canals, irrigation and industrial channel flows, and run-off river stream flows. These sources generally have low head (<1 m) and low velocity which makes it difficult to harvest energy using conventional turbines. A horizontal-axis screw turbine was designed and numerically tested to extract power from such low-head water sources. The 3-bladed screw-type turbine is placed horizontally perpendicular to the incoming flow, partially submerged in a narrow water channel at no-head condition. The turbine hydraulic performances were studied using Computational Fluid Dynamics models. Turbine design parameters such as the shroud diameter, the hub-to-shroud ratios, and the submerged depths were obtained through a steady-state parametric study. The resulting turbine configuration was then tested by solving the unsteady multiphase free-surface equations mimicking an actual open channel flow scenario. The turbine performance in the shallow channel were studied for various Tip Speed Ratios (TSR). The highest power coefficient was obtained at a TSR of 0.3. The turbine was then scaled-up to test its performance on a real site condition at a head of 0.3 m. The highest power coefficient obtained was 0.18. Several losses were observed in the 3-bladed turbine design and to minimize losses, the number of blades were increased to five. The power coefficient improved by 236% for a 5-bladed screw turbine. The fluid losses were minimized by increasing the blade surface area submerged in water. The turbine performance was increased by 74.4% after dipping the turbine to a bottom wall clearance of 30 cm from 60 cm. The final output of the novel horizontal-axis screw turbine showed a 2.83 kW power output at a power coefficient of 0.63. The turbine is expected to produce 18,744 kWh/year of electricity. The design feasibility test of the turbine showed promising results to harvest energy from small hydropower sources.

Gender Mechanism of Korean Welfare Politics: Gender Difference in Attitudes and Mediating Effects of Welfare Statuses (한국 복지정치의 젠더메커니즘: 태도의 성별차이와 복지지위 매개효과를 중심으로)

  • Kim, Eun-Ji;Ahn, Sang-Hoon
    • Korean Journal of Social Welfare Studies
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    • v.41 no.2
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    • pp.309-334
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    • 2010
  • This study explores gender mechanism of welfare politics in Korea from the perspective of welfare status theory. In the simplistic analysis, it is found that there is no gender difference in welfare attitudes. In the more sophisticated analysis of welfare-status-beased SEM, however, it is found that Korean welfare politics is to be understood in terms of gender-related politics. Three major findings of this study are as follows. Firstly, Korean women possess less pro-welfare attitudes in terms of the status of welfare beneficiary. This is due to the visible gender segregation in the Korean labor market on the one hand and due to the centrality of social insurance programs in the structure of Korean public welfare system on the other hand. Secondly, Korean women have relatively higher level of pro-welfare attitude when it comes to the status of welfare service provider. Thirdly, Korean women tend to be more supportive to pro-welfare parties as they have less chance to be a higher taxpayer. Based on the above mentioned findings, this study concludes that it is possible to make Korean women be more pro-welfare if the Korean welfare state expands more social services that tend to meet urgent needs of women.

A Study on the Calculation of Load Resistance Factor of over Tension Anchors by Optimization Design (최적화 설계를 통한 과긴장 앵커의 하중-저항계수 산정 연구)

  • Soung-Kyu Lee;Yeong-Jin Lee;Yong-Jae Song;Tae-Jun Cho;Kang-Il Lee
    • Journal of the Korean Geosynthetics Society
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    • v.22 no.4
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    • pp.17-26
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    • 2023
  • To consider the risk of damage and fracture of P.C strands, the existing post-maintenance system alone has the limitations, hence it is necessary to quantitatively evaluate and predict the deterioration, durability and safety of facilities and establish a reasonable maintenance system considering the asset value of facilities. Therefore, it is worth considering a preventive maintenance plan that allows proactive measures to be taken before a major defect occurs in the temporary anchor. This study devised a preventive over tension method, reviewed its effectiveness through design and field tests, by calculating the resistance factors by performing a reliability-based optimization design. At this time, the over tension anchor method was evaluated using the ratio of the residual tension force after the fracture of P.C strands to the effective tension force before the fracture of P.C strand, followed by the resistance factor calculated by the optimal solution for each random variables using Excel solver and applying it to the limit state equations. As a result of the study, if the over tension ratio is 125% to 130%, the remaining strands showed a high resistance effect even after the fracture of P.C strand. As a result of the optimization design, it was found that it is appropriate to apply the load factor (γ) of 1.25, and the resistance factors of Φ1, Φ2, Φ3 as 0.7, 0.5, 0.6.

Evaluation of Vertical Vibration Performance of Tridimensional Hybrid Isolation System for Traffic Loads (교통하중에 대한 3차원 하이브리드 면진시스템의 수직 진동성능 평가)

  • Yonghun Lee;Sang-Hyun Lee;Moo-Won Hur
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.28 no.1
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    • pp.70-81
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    • 2024
  • In this study, Tridimensional Hybrid Isolation System(THIS) was proposed as a vibration isolator for traffic loads, combining vertical and horizontal isolation systems. Its efficacy in improving serviceability for vertical vibration was analytically evaluated. Firstly, for the analysis, the major vibration modes of the existing apartment were identified through eigenvalue analysis for the system and pulse response analysis for the bedroom slab using commercial structural analysis software. Subsequently, a 16-story model with horizontal, vertical and rotational degrees of freedom for each slab was numerically organized to represent the achieved modes. The dynamic analysis for the measured acceleration from an adjacent ground to high-speed railway was performed by state-space equations with the stiffness and damping ratio of THIS as variables. The result indicated that as the vertical period ratio increased, the threshold period ratio where the slab response started to be suppressed varied. Specifically, when the period ratio is greater than or equal to 5, the acceleration levels of all slabs decreased to approximately 70% or less compared to the non-isolated condition. On the other hand, it was ascertained that the influence of damping ratios on the response control of THIS is inconsequential in the analysis. Finally, the improvement in vertical vibration performance of THIS was evaluated according to design guidelines for floor vibration of AIJ, SCI and AISC. It was confirmed that, after the application of THIS, the residential performance criteria were met, whereas the non-isolated structure failed to satisfy them.

A Study on the Calculation of Consolidation Constants using Moisture Content of Sedimentary Clay in Busan and Gyeongnam Regions (부산·경남지역 퇴적 점토의 함수비를 이용한 압밀정수 산정 연구)

  • Sung-Uk Kang;Dae-Hwan Kim;Tae-hyung Kim;Chin-Gyo Chung;In-Gon Joo
    • Journal of the Korean Geosynthetics Society
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    • v.23 no.1
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    • pp.39-47
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    • 2024
  • In this study, physical property tests and standard consolidation tests were conducted on the marine clay of Busan New Port and North Port, the middle and lower reaches of the Nakdong River including Gimhae and Yangsan, and Ulsan regions. The moisture content, a property unrelated to sample disturbance with small individual test errors, was used for regression analysis with the compression index, virgin compression index, consolidation coefficient, expansion index, and secondary compression index, among others. Subsequently, the correlation and accuracy were evaluated. Upon analyzing the correlation between the moisture content, void ratio, and liquid limit commonly used physical properties for calculating compression indexes, it was confirmed that the liquid limit had the lowest correlation. Through a linear regression analysis of the consolidation constants using the current moisture content in the natural state, a high correlation was demonstrated. Relationship equations were then presented to determine settlement and settlement time. This study suggests that moisture content can be utilized as an alternative for evaluating and calculating consolidation constants when examining ground settlement in sedimentary clays distributed in the Busan and Gyeongnam regions.

Studies on the Mechanical Properties of Weathered Granitic Soil -On the Elements of Shear Strength and Hardness- (화강암질풍화토(花崗岩質風化土)의 역학적(力學的) 성질(性質)에 관(關)한 연구(硏究) -전단강도(剪斷强度)의 영향요소(影響要素)와 견밀도(堅密度)에 대(對)하여-)

  • Cho, Hi Doo
    • Journal of Korean Society of Forest Science
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    • v.66 no.1
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    • pp.16-36
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    • 1984
  • It is very important in forestry to study the shear strength of weathered granitic soil, because the soil covers 66% of our country, and because the majority of land slides have been occured in the soil. In general, the causes of land slide can be classified both the external and internal factors. The external factors are known as vegetations, geography and climate, but internal factors are known as engineering properties originated from parent rocks and weathering. Soil engineering properties are controlled by the skeleton structure, texture, consistency, cohesion, permeability, water content, mineral components, porosity and density etc. of soils. And the effects of these internal factors on sliding down summarize as resistance, shear strength, against silding of soil mass. Shear strength basically depends upon effective stress, kinds of soils, density (void ratio), water content, the structure and arrangement of soil particles, among the properties. But these elements of shear strength work not all alone, but together. The purpose of this thesis is to clarify the characteristics of shear strength and the related elements, such as water content ($w_o$), void ratio($e_o$), dry density (${\gamma}_d$) and specific gravity ($G_s$), and the interrelationship among related elements in order to decide the dominant element chiefly influencing on shear strength in natural/undisturbed state of weathered granitic soil, in addition to the characteristics of soil hardness of weathered granitic soil and root distribution of Pinus rigida Mill and Pinus rigida ${\times}$ taeda planted in erosion-controlled lands. For the characteristics of shear strength of weathered granitic soil and the related elements of shear strength, three sites were selected from Kwangju district. The outlines of sampling sites in the district were: average specific gravity, 2.63 ~ 2.79; average natural water content, 24.3 ~ 28.3%; average dry density, $1.31{\sim}1.43g/cm^3$, average void ratio, 0.93 ~ 1.001 ; cohesion, $ 0.2{\sim}0.75kg/cm^2$ ; angle of internal friction, $29^{\circ}{\sim}45^{\circ}$ ; soil texture, SL. The shear strength of the soil in different sites was measured by a direct shear apparatus (type B; shear box size, $62.5{\times}20mm$; ${\sigma}$, $1.434kg/cm^2$; speed, 1/100mm/min.). For the related element analyses, water content was moderated through a series of drainage experiments with 4 levels of drainage period, specific gravity was measured by KS F 308, analysis of particle size distribution, by KS F 2302 and soil samples were dried at $110{\pm}5^{\circ}C$ for more than 12 hours in dry oven. Soil hardness represents physical properties, such as particle size distribution, porosity, bulk density and water content of soil, and test of the hardness by soil hardness tester is the simplest approach and totally indicative method to grasp the mechanical properties of soil. It is important to understand the mechanical properties of soil as well as the chemical in order to realize the fundamental phenomena in the growth and the distribution of tree roots. The writer intended to study the correlation between the soil hardness and the distribution of tree roots of Pinus rigida Mill. planted in 1966 and Pinus rigida ${\times}$ taeda in 199 to 1960 in the denuded forest lands with and after several erosion control works. The soil texture of the sites investigated was SL originated from weathered granitic soil. The former is situated at Py$\ddot{o}$ngchangri, Ky$\ddot{o}$m-my$\ddot{o}$n, Kogs$\ddot{o}$ng-gun, Ch$\ddot{o}$llanam-do (3.63 ha; slope, $17^{\circ}{\sim}41^{\circ}$ soil depth, thin or medium; humidity, dry or optimum; height, 5.66/3.73 ~ 7.63 m; D.B.H., 9.7/8.00 ~ 12.00 cm) and the Latter at changun-long Kwangju-shi (3.50 ha; slope, $12^{\circ}{\sim}23^{\circ}$; soil depth, thin; humidity, dry; height, 10.47/7.3 ~ 12.79 m; D.B.H., 16.94/14.3 ~ 19.4 cm).The sampling areas were 24quadrats ($10m{\times}10m$) in the former area and 12 in the latter expanding from summit to foot. Each sampling trees for hardness test and investigation of root distribution were selected by purposive selection and soil profiles of these trees were made at the downward distance of 50 cm from the trees, at each quadrat. Soil layers of the profile were separated by the distance of 10 cm from the surface (layer I, II, ... ...). Soil hardness was measured with Yamanaka soil hardness tester and indicated as indicated soil hardness at the different soil layers. The distribution of tree root number per unit area in different soil depth was investigated, and the relationship between the soil hardness and the number of tree roots was discussed. The results obtained from the experiments are summarized as follows. 1. Analyses of simple relationship between shear strength and elements of shear strength, water content ($w_o$), void ratio ($e_o$), dry density (${\gamma}_d$) and specific gravity ($G_s$). 1) Negative correlation coefficients were recognized between shear strength and water content. and shear strength and void ratio. 2) Positive correlation coefficients were recognized between shear strength and dry density. 3) The correlation coefficients between shear strength and specific gravity were not significant. 2. Analyses of partial and multiple correlation coefficients between shear strength and the related elements: 1) From the analyses of the partial correlation coefficients among water content ($x_1$), void ratio ($x_2$), and dry density ($x_3$), the direct effect of the water content on shear strength was the highest, and effect on shear strength was in order of void ratio and dry density. Similar trend was recognized from the results of multiple correlation coefficient analyses. 2) Multiple linear regression equations derived from two independent variables, water content ($x_1$ and dry density ($x_2$) were found to be ineffective in estimating shear strength ($\hat{Y}$). However, the simple linear regression equations with an independent variable, water content (x) were highly efficient to estimate shear strength ($\hat{Y}$) with relatively high fitness. 3. A relationship between soil hardness and the distribution of root number: 1) The soil hardness increased proportionally to the soil depth. Negative correlation coefficients were recognized between indicated soil hardness and the number of tree roots in both plantations. 2) The majority of tree roots of Pinus rigida Mill and Pinus rigida ${\times}$ taeda planted in erosion-controlled lands distributed at 20 cm deep from the surface. 3) Simple linear regression equations were derived from indicated hardness (x) and the number of tree roots (Y) to estimate root numbers in both plantations.

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Transformation of Nitrogen Derived from Solid Piggery Manure in Soil under Aerobic or Anaerobic Incubation Condition (혐기(嫌氣) 및 호기조건하(好氣條件下)에서 토양처리(土壤處理)된 돈분(豚糞) 중(中) 질소형태변화(窒素形態變化))

  • Yun, Sun-Gang;Jung, Kwang-Yong;Yoo, Sun-Ho
    • Korean Journal of Soil Science and Fertilizer
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    • v.26 no.2
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    • pp.121-126
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    • 1993
  • The behaviors of inorganic nitrogen derived from solid animal waste in soil has been received too much concern partly because nitrate which occurred from nitrification can act as a pollutant to soil and groundwater and partly because the loss of nitrogen from surface soil by downward movement of water is disadvantageous in the view of plant nutrient. This present study was conducted to get fundamental imformations on nitrogen behavior and to provide improved basical concepts on the management of animal waste. Fresh or fermented pig manure was mixed with a sandy loam soil in the ratio of 2:1(soil:pig manure), packed into test tube and incubated at $30^+/-1^{\circ}C$ for 8 weeks under aerobic- or anaerobic condition. Sample tubes were taken at the one week interval and analyzed on pH, the amount of $CH_4$ produced under anaerobic condition and inorganic nitrogen. The pH of soil treated with fresh pig manure under anaerobic condition was lowered by 1.87 unit compared to that of under aerobic condition, but at the treatment with fermented pig manure, pH change was very little between aerobic and anaerobic condition. The coefficients of regressional equations which were obtained from pH and incubation time were -0.114 in fresh pig manure and -0.089 in fermented pig manure, and the extent of pH decrease due to incubation was greater in fresh pig manure than that of fermented pig waste. No differences in the amounts of $CH_4$ produced under anaerobic condition between fresh and fermented pig manure was observed until 3 weeks of incubation, however, after that the amount of $CH_4$ produced in fresh pig manure was abruptly increased and cumulative amont of $CH_4$ was reached 8.6 mole/g. K values on $CH_4$ production in fresh and fermented pig manure was 0.211 mole/g/day and 0.046 mole/g/day, respectively, for 5 weeks from the 3rd to the 8th week. $NH_4-N$ concentration at aerobic condition with fresh pig manure treatment was lowered by passing time of incubation, but $NO_3-N$ concentration was elevated from 11.2 ppm at initial state to 67.3 ppm after incubation and this trend on $NH_4-N$, $NO_3-N$ concentration was very similar to the treatment of fermented pig manure. While $NH_4-N$ concentration under anaerobic condition was greatly increased. $NO_3-N$ concentartion was not only very low but also no great changes, that was ranged from 4 to 8 ppm.

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Reliability Based Stability Analysis and Design Criteria for Reinforced Concrete Retaining Wall (신뢰성(信賴性) 이론(理論)에 의한 R.C.옹벽(擁壁)의 안정해석(安定解析) 및 설계규준(設計規準))

  • Cho, Tae Song;Cho, Hyo Nam;Chun, Chai Myung
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.3 no.3
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    • pp.71-86
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    • 1983
  • Current R.C. retaining wall design is bared on WSD, but the reliability based design method is more rational than the WSD. For this reason, this study proposes a reliability based design criteria for the cantilever retaining wall, which is most common type of retaining wall, and also proposes the theoretical bases of nominal safety factors of stability analysis by introducing the reliability theory. The limit state equations of stability analysis and design of each part of cantilever retaining wall are derived and the uncertainty measuring algorithms of each equation are also derived by MFOSM using Coulomb's coefficient of the active earth pressure and Hansen's bearing capacity formula. The levels of uncertainties corresponding to these algorithms are proposed appropriate values considering our actuality. The target reliability indices (overturning: ${\beta}_0$=4.0, sliding: ${\beta}_0$=3.5, bearing capacity: [${\beta}_0$=3.0, design for flexure: [${\beta}_0$=3.0, design for shear: ${\beta}_0$=3.2) are selected as optimal values considering our practice based on the calibration with the current R.C. retaining wall design safety provisions. Load and resistance factors are measured by using the proposed uncertainties and the selected target reliability indices. Furthermore, a set of nominal safety factors, allowable stresses, and allowable shear stresses are proposed for the current WSD design provisions. It may be asserted that the proposed LRFD reliability based design criteria for the R.C. retaining wall may have to be incorporated into the current R.C. design codes as a design provision corresponding to the USD provisions of the current R.C. design code.

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