• Proceedings of the Korea Concrete Institute Conference
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• 2001.11a
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• pp.803-808
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• 2001

Mathematical basis of interpretation of data from nondestructive evaluation (NDE) methods in bridge inspection is presented. In bridge inspection with NDE methods, NDE data are not assessments. NDE data must be interpreted as condition of element. Interpretation is then assessment. Correct assessments of conditions of bridge elements depend on the accuracy and variability in test data as well as on the uncertainty of correlations between attributes (what is measured) and conditions (what is sought in the inspection). Inaccuracy and variability in test data defines the qualify or NDE test. The qualify or test itself is important, but in view of condition assessment, the significance of uncertainty in correlations of attributes and conditions must be combined. NDE methods that are accurate in their measurements may still be found to be poor methods if attributes are uncertain indicators of condition of bridge elements. This paper reports mathematical presentation of inaccuracy and variability in test data and of uncertainty in correlation of attributes to element conditions with three examples of NDE methods.

• Journal of Physiology & Pathology in Korean Medicine
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• v.36 no.5
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• pp.193-208
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• 2022

In this study, we proposed a mathematical model that can explain the source of the observed variability of repeated measurement data collected in Korean medicine clinical practice, and conducted a pilot analysis to infer the source of these variability based on our model. Mathematical model was constructed by dividing the observed variations into three components: common time-dependent variations, signal shift, and measurement error. To show the applicability of our model in real data, we analyzed 20 repeated measurement data of Korean clinical indicators in graduate students of Pusan National University Graduate School of Korean Medicine. We showed how to infer each source of variations based on our model and also showed the limitation of inference given the acquired the dataset. On the basis of objective recognition of these source of the variability, we hope that quantitative investigations on these sources for each Korean medicine clinical indicator are made in the future, so that they can be used in the clinical and educational areas of Korean medicine.

• The Mathematical Education
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• v.57 no.4
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• pp.413-431
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• 2018

In this study, I developed an activity oriented lesson to support the understanding of probabilistic and quantitative estimating population ratios according to the standard statistical principles and discussed its implications in didactical respects. The developed activity lesson, as an efficient physical simulation activity by sampling with replacement, simulates unknown populations and real problem situations through completely closed 'Closed Box' in which we can not see nor take out the inside balls, and provides teaching and learning devices which highlight the representativeness of sample ratios and the sampling variability. I applied this activity lesson to the gifted students who did not learn estimating population ratios and collected the research data such as the activity sheets and recording and transcribing data of students' presenting, and analyzed them by Qualitative Content Analysis. As a result of an application, this activity lesson was effective in recognizing and reflecting on the representativeness of sample ratios and recognizing the random sampling variability. On the other hand, in order to show the sampling variability clearer, I discussed appropriately increasing the total number of the inside balls put in 'Closed Box' and the active involvement of the teachers to make students pay attention to controlling possible selection bias in sampling processes.

• 보존과학연구
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• s.6
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• pp.111-120
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• 1985

Data on the concentration of Na, K, Sc, Cr, Fe, Co, Cu, Ga, Rb, Cs, Ba, La,Ce, Sm, Eu, Tb, Lu, Hf, Ta and Th obtained by Neutron Activation Analysishave been used to characterise Korean porcelainsherds by multivariate analysis. The mathematical approaches employed is Principal Component Analysis(PCA).PCA was found to be helpful for dimensionality reduction and for obtaining information regarding (a) the number of independent causal variables required to account for the variability in the overall data set, (b) the extent to which agiven variable contributes to a component and(c) the number of causalvariables required to explain the total variability of each measured variable.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.435-454
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• 2016

This paper investigates the effect of dual-phase-lags on a thermoviscoelastic orthotropic solid with a cylindrical cavity. The cylindrical cavity is subjected to a thermal shock varying heat and its material is taken to be of Kelvin-Voigt type. The phase-lag thermoelastic model, Lord and Shulman's model and the coupled thermoelasticity model are employed to study the thermomechanical coupling, thermal and mechanical relaxation (viscous) effects. Numerical solutions for temperature, displacement and thermal stresses are obtained by using the method of Laplace transforms. Numerical results are plotted to illustrate the effect phase-lags, viscoelasticity, and the variability thermal conductivity parameter on the studied fields. The variations of all field quantities in the context of dual-phase-lags and coupled thermoelasticity models follow similar trends while the Lord and Shulman's model may be different. The influence of viscosity parameter and variability of thermal conductivity is very pronounced on temperature and thermal stresses of the thermoviscoelastic solids.

• The Mathematical Education
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• v.56 no.1
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• pp.19-39
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• 2017

Taking samples of data and using samples to make inferences about unknown populations are at the core of statistical investigations. So, an understanding of the nature of sample as statistical thinking is involved in the area of statistical literacy, since the process of a statistical investigation can turn out to be totally useless if we don't appreciate the part sampling plays. However, the conception of sampling is a scheme of interrelated ideas entailing many statistical notions such as repeatability, representativeness, randomness, variability, and distribution. This complexity makes many people, teachers as well as students, reason about statistical inference relying on their incorrect intuitions without understanding sample comprehensively. Some research investigated how the concept of a sample is understood by not only students but also teachers or preservice teachers, but we want to identify preservice secondary mathematics teachers' understanding of sample as the statistical literacy by a qualitative analysis. We designed four items which asked preservice teachers to write their understanding for sampling tasks including representativeness and variability. Then, we categorized the similar responses and compared these categories with Watson's statistical literacy hierarchy. As a result, many preservice teachers turned out to be lie in the low level of statistical literacy as they ignore contexts and critical thinking, expecially about sampling variability rather than sample representativeness. Moreover, the experience of taking statistics courses in university did not seem to make a contribution to development of their statistical literacy. These findings should be considered when design preservice teacher education program to promote statistics education.

• School Mathematics
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• v.8 no.1
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• pp.45-68
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• 2006

Singaporean students have demonstrated their superior mathematical achievement and positive mathematical dispositions. Against this background, this study compared Korean elementary mathematics textbooks with Singaporean counterparts focusing on the geometry and measurement strand. The analysis was conducted in many aspects, including an overall unit structure, the contents to be covered in each grade, and the methods of introducing essential learning themes. The textbooks were also compared and contrasted with regard to the main characteristics of constructing mathematical contents. Whereas Korean textbooks used block teaming, Singaporean textbooks used repeated teaming. The latter also employed the activity of classifying multiple figures as the main method of introducing concepts. Whereas Korean textbooks consist of typical examples of figures, Singaporean counterparts include various examples consistent with the principle of mathematical variability.

• Research in Mathematical Education
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• v.15 no.4
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• pp.311-325
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• 2011

In this paper I propose that teaching students the most efficient method of problem solving may curtail students' creativity. Instead it is important to arm students with a variety of problem solving heuristics. It is the students' responsibility to decide which heuristic will solve the problem. The chosen heuristic is the one which is meaningful to the students.

• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.191-202
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• 2009

In this study, we drive the one dimensional marginal transform function, probability density function and probability distribution function for the random variables $T_{{\xi}N}$ (Time taken by the servers during the vacations), ${\xi}_N$(Number of vacations taken by the servers) and ${\eta}_N$(Number of customers or units arrive in the system) by controlling the variability of two random variables simultaneously.

• Korean Management Science Review
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• v.13 no.1
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• pp.47-55
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• 1996

Rapid globalization of production and marketing functions makes choice of international transportation mode of great importance. In this paper, transportation mode is characterized by two factors, mean and variability of transportation lead time. We developed a simple mathematical model to estimate the relative impact of mean lead time, lead time variance and demand variance on the required average inventory level under specified service rates.