• Title/Summary/Keyword: Probability and statistics

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Derivation of Optimal Design Flood by Gamma and Generalized Gamma Distribution Models(I) - On the Gamma Distribution Models - (Gamma 및 Generalized Gamma 분포 모형에 의한 적정 설계홍수량의 유도 (I) -Gamma 분포 모형을 중심으로-)

  • 이순혁;박명근;정연수;맹승진;류경식
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.39 no.3
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    • pp.83-95
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    • 1997
  • This study was conducted to derive optimal design floods by Gamma distribution models of the annual maximum series at eight watersheds along Geum , Yeong San and Seom Jin river Systems, Design floods obtained by different methods for evaluation of parameters and for plotting positions in the Gamma distribution models were compared by the relative mean errors and graphical fit along with 95% confidence interval plotted on Gamma probability paper. The results were analyzed and summarized as follows. 1.Adequacy for the analysis of flood flow data used in this study was confirmed by the tests of Independence, Homogeneity and detection of Outliers. 2.Basic statistics and parameters were calculated by Gamma distribution models using Methods of Moments and Maximum Likelihood. 3.It was found that design floods derived by the method of maximum likelihood and Hazen plotting position formular of two parameter Gamma distribution are much closer to those of the observed data in comparison with those obtained by other methods for parameters and for plotting positions from the viewpoint of relative mean errors. 4.Reliability of derived design floods by both maximum likelihood and method of moments with two parameter Gamma distribution was acknowledged within 95% confidence interval.

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The Case Study of Gender Difference in Mathematical Problem Solving (수학적 문제해결 과정에 대한 성별 사례 연구)

  • Lee, Kwang Sang;Suh, Bo Euk
    • Education of Primary School Mathematics
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    • v.16 no.2
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    • pp.147-162
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    • 2013
  • This is an in-dept case study that extract the problems showing remarkable gender gap in 6th graders and analyze the difference between boys and girls in the process of problem solving. This study can be summarized as the following. First, according to the result of basic study, the parts are divided into measurement, probability and statistics and regularity. And then test problems and face-to-face talk contents are developed. Second, the distinct features between boys and girls, follow-up study and face-to-face talk. As a result, five characteristics of gender gap are selected. Through the results of this study, the improvement of teaching & learning development and evaluation considering gender is expected in the classrooms of elementary schools.

Wind-induced random vibration of saddle membrane structures: Theoretical and experimental study

  • Rongjie Pan;Changjiang Liu;Dong Li;Yuanjun Sun;Weibin Huang;Ziye Chen
    • Wind and Structures
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    • v.36 no.2
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    • pp.133-147
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    • 2023
  • The random vibration of saddle membrane structures under wind load is studied theoretically and experimentally. First, the nonlinear random vibration differential equations of saddle membrane structures under wind loads are established based on von Karman's large deflection theory, thin shell theory and potential flow theory. The probabilistic density function (PDF) and its corresponding statistical parameters of the displacement response of membrane structure are obtained by using the diffusion process theory and the Fokker Planck Kolmogorov equation method (FPK) to solve the equation. Furthermore, a wind tunnel test is carried out to obtain the displacement time history data of the test model under wind load, and the statistical characteristics of the displacement time history of the prototype model are obtained by similarity theory and probability statistics method. Finally, the rationality of the theoretical model is verified by comparing the experimental model with the theoretical model. The results show that the theoretical model agrees with the experimental model, and the random vibration response can be effectively reduced by increasing the initial pretension force and the rise-span ratio within a certain range. The research methods can provide a theoretical reference for the random vibration of the membrane structure, and also be the foundation of structural reliability of membrane structure based on wind-induced response.

A Study of Activity-types in Elementary Mathematics Textbooks (초등 수학 교과서의 학습 활동유형에 대한 분석)

  • Ahn, Byoung-Gon
    • School Mathematics
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    • v.14 no.1
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    • pp.151-163
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    • 2012
  • In 2006 with the revised national curriculum, Elementary mathematics teaching and learning methods are presented in the following ways. Learners explore the way through the operational activities of the teachers and students with learning and learners' active learning activities, etc., and an active learning based on the principle of attention to learning how to maximize the effectiveness are required. In this study, from first grade through sixth grade elementary school mathematics textbooks for all learning activities presented in 10 different types were investigated This result of 5 contents area of number and operation, geometry, probability and statistics, measurement and patterns and problem solving and divided into low, middle, and hight three were intentional. In addition, teachers are looking forward to this result was compared with the type of activity.

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Health Pattern of Elderly According to Age Group Who Living Alone in an Urban Area (일 도시 독거노인의 연령 군별 건강양상)

  • Kang Hae-Young;Seo Nam-Sook;Kim Young-Hee
    • Journal of Korean Academy of Nursing
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    • v.34 no.6
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    • pp.1057-1068
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    • 2004
  • Purpose: This study was conducted to identify the differences of health patterns; health-related characteristics, health behaviors, health problems, and self-care levels of elderly, living alone in an urban area according to age roup. Method: The study design was a descriptive survey and the subjects were 1,800 elderly consisting of 937 young old, 704 middle old, and 159 old old. Data was collected from May to July 2003 using the structured questionnaire and analyzed by descriptive statistics, $\chi$$^2$-test, Fisher's exact probability test, ANOVA and Scheffe test using SPSS/PC. Result: The health related characteristics which involved body mass index, mental status, use of assistant devices, perceived health, concern of health, and social support were different among the groups and more aggravated by aging. Health behaviors and health problems were also significantly aggravated in the old old group. The self-care levels measured by ADL, physical activity, and self-care ability scores were also significantly decreased in the old old group. Conclusion: For the level of health status, health behaviors and self-care ability were significantly decreased by aging, health care services for the elderly should be planned considering the difference in the health pattern by age group.

Chronic Obstructive Pulmonary Disease in Korea: Prevalence, Risk Factors, and Quality of Life (한국성인의 만성 폐쇄성 폐질환 유병률, 위험요인 및 삶의 질)

  • Jung, Young-Mi;Lee, Hee-Young
    • Journal of Korean Academy of Nursing
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    • v.41 no.2
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    • pp.149-156
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    • 2011
  • Purpose: This study seeks to examine prevalence, risk factors, and quality of life of Korean adults with Chronic Obstructive Pulmonary Disease (COPD). Methods: From the database of the Fourth Korean National Health and Nutrition Examination Survey (KNHANES IV-1, 2008), the researchers selected 1,458 adults over the age of 45. The original study was a population-based epidemiological survey of health and nutrition with a stratified multistage clustered probability design. Prevalence of COPD was computed on the basis of the sampling weight. Data were analyzed using descriptive statistics, ${\chi}^2$ test, t-test and multiple logistic regression with the SPSS WIN 18.0 and SAS Ver. 9.1 program. Results: The prevalence of COPD was 18.0% among people older than 45 yr. The prevalence of current smokers was 19.7% in this population and 26.3% in individuals with COPD. Age, gender, education, and smoking levels were found to be risk factors for COPD. Significant difference in quality of life was founded between adults with COPD and the healthy controls. Conclusion: The results of this study indicate that COPD is a highly prevalent disease in Korea. To reduce the prevalence of COPD and improve health-related quality of life in patients with COPD, nursing interventions must focus on prevention of risk factors.

Stochastic characteristics of reinforcement corrosion in concrete beams under sustained loads

  • Huang, Le;Jin, Xianyu;Fu, Chuanqing;Ye, Hailong;Dong, Xiaoyu
    • Computers and Concrete
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    • v.25 no.5
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    • pp.447-460
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    • 2020
  • This paper deals with the characteristics of reinforcement corrosion in concrete beams under the influence of sustained loads. The evolution and distribution laws of the reinforcement corrosion were measured periodically over time. The results show that sustained load exhibits a pronounced exacerbating effect on the reinforcement corrosion, and enlarges the nonuniformity level of corrosion as the load level increases. Accompanied with the continuous formation of the rust, the corrosion rate was also observed to be highly nonlinear and time-dependent. Moreover, to visually and quantitatively analyze the distribution of reinforcement corrosion, the 3D scanning technology combined with the probability statistics analysis was adopted, and the observed nonuniformity can be well described by the Gumbel distribution. Finally, an approach based on the three-phase spherical model was proposed to estimate the reinforcement corrosion, taking account of the effects of sustained load on the changes of concrete porosity and oxygen diffusivity.

Research Trends in Elementary Mathematics Education: Focused on the Papers Published in Domestic Journals During the Recent 5 Years (초등수학교육 연구동향 - 최근 5년간 게재된 국내 학술지 논문을 중심으로 -)

  • Ha, Su-Hyun;Pang, Jeong-Suk;Ju, Mi-Kyung
    • The Mathematical Education
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    • v.49 no.1
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    • pp.67-83
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    • 2010
  • The purpose of this study was to analyze the research trends of elementary mathematics education with regard to the topics, methods, subjects, and mathematical contents of such research. For this purpose, the papers published in domestic journals during the recent 5 years (2004-2009) were analyzed. A total of 383 papers from 8 professional journals were analyzed with the 4 criteria. First, the frequent research topics included instructional design and methods, learners' perspectives and abilities, and analysis of curriculum and textbooks in order. Second, qualitative research methodology was used twice as many as quantitative one. Whereas a survey was the most frequent quantitative research method, content analysis and case study were for qualitative methods. Third, research subjects included mainly typical students, specifically fifth and sixth graders. Papers dealing with lower graders or low-achievers as well as pre-service teachers were rare. Lastly, whereas the research on geometry as well as number and operations was active, that of measurement as well as probability and statistics was not. On the basis of these results, this paper includes several implications for the future research direction in elementary mathematics education.

Fragility curves for woodframe structures subjected to lateral wind loads

  • Lee, Kyung Ho;Rosowsky, David V.
    • Wind and Structures
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    • v.9 no.3
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    • pp.217-230
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    • 2006
  • This paper describes a procedure to develop fragility curves for woodframe structures subjected to lateral wind loads. The fragilities are cast in terms of horizontal displacement criteria (maximum drift at the top of the shearwalls). The procedure is illustrated through the development of fragility curves for one and two-story residential woodframe buildings in high wind regions. The structures were analyzed using a monotonic pushover analysis to develop the relationship between displacement and base shear. The base shear values were then transformed to equivalent nominal wind speeds using information on the geometry of the baseline buildings and the wind load equations (and associated parameters) in ASCE 7-02. Displacement vs. equivalent nominal wind speed curves were used to determine the critical wind direction, and Monte Carlo simulation was used along with wind load parameter statistics provided by Ellingwood and Tekie (1999) to construct displacement vs. wind speed curves. Wind speeds corresponding to a presumed limit displacement were used to construct fragility curves. Since the fragilities were fit well using a lognormal CDF and had similar logarithmic standard deviations (${\xi}$), a quick analysis to develop approximate fragilities is possible, and this also is illustrated. Finally, a compound fragility curve, defined as a weighted combination of individual fragilities, is developed.

Derivation of Optimal Design Flood by Gamma and Generalized Gamma Distribution Models(II) -On the Generalized Gamma Distribution Model- (Gamma 및 Generalized Gamma 분포 모형에 의한 적정 설계홍수량의 유도(II) -Generalized Gamma 분포모형을 중심으로-)

  • 이순혁;박명근;맹승진;정연수;류경선
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.40 no.2
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    • pp.59-68
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    • 1998
  • This study was conducted to derive optimal design floods by generalized gamma distribution model of the annual maximum series at eight watersheds along Geum, Yeongsan and Seomjin river systems. Design floods obtained by different methods for evaluation of parameters and for plotting positions in the generalized gamma distribution model were compared by the relative mean errors and graphical fit along with 95% confidence limits plotted on gamma probability paper. The results were analyzed and summarized as follows. 1. Basic statistics and parameters were calculated by the generalized gamma distribution model using different methods for parameters. 2. Design floods according to the return periods were obtained by different methods for evaluation of parameters and for plotting positions in the generalized gamma distribution model. 3. It was found that design floods derived by sundry averages method for parameters and Cunnane method for plotting position in the generalized gamma distribution are much closer to those of the observed data in comparison with those obtained by the other methods for parameters and for plotting positions from the viewpoint of relative mean errors. 4. Reliability of design floods derived by sundry averages method in the generalized gamma distribution was acknowledged within 95% confidence interval.

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