• Communications of Mathematical Education
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• v.20 no.4 s.28
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• pp.603-619
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• 2006

One of the most important aims in mathematics education is to enhance students' problem-solving abilities. To achieve this aim, in real school classrooms, many educators have examined and developed effective teaching methods, learning strategies, and practical problem-solving techniques. Among those trials, it is noticeable that Engel, Zeits, Shapiro and other not a few mathematicians emphasized 'Invariance Principle' as a mean of solving problems. This study is to consider the basic concept of 'Invariance Principle', analyze 'Invariance' concept in secondary Mathematics contents on the basis of framework of 'Invariance Principle' shown by Shapiro and discuss some instructional issues to occur in the process of it.

• Journal of Distribution Science
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• v.21 no.5
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• pp.75-82
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• 2023

Purpose: This research aims to test the measurement invariance of the consumer-based brand equity scale on Turkish and Syrian university students who live together but are from different cultural groups. Research design, data, and methodology: The consumer-based brand equity scale developed by Buil et al. (2008) is applied to the participants. In testing the consumer-based brand equity scale, the Netflix brand, which is considered well-known by both cultural groups, is preferred. It is thought that choosing an internationally recognized brand would facilitate the conduct of this research. Structural invariance and measurement invariance are tested using structural equation modeling. Results: The consumer-based brand equity scale has measurement invariance on Turkish and Syrian university students. Therefore, it has been revealed that the responses of participants from both cultures regarding the Netflix brand are comparable. Conclusion: The findings of the study provide clues for practitioners to review their distribution strategies. As a matter of fact, cultural studies conducted in different countries are common. Still, the originality of this study is ensured by the profile of participants who live in the same country but come from different countries.

• Journal of Korea Water Resources Association
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• v.49 no.12
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• pp.995-1006
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• 2016

According to 5th IPCC Climate Change Report, there is a very high likelihood that the frequency and intensity of extreme rainfall events will increase. In reality, flood damage has increased, and it is necessary to estimate the future probabilistic design rainfall amount that climate change is reflected. In this study, the future probabilistic design precipitation amount is estimated by analyzing trends of future annual maximum daily rainfall derived by RCP 8.5 scenarios and using the scale-invariance technique. In the first step, after reviewing the time-scale characteristics of annual maximum rainfall amounts for each duration observed from 60 sites operating in Korea Meterological Administration, the feasibility of the scale-invariance technique are examined using annual daily maximum rainfall time series simulated under the present climate condition. Then future probabilistic design rainfall amounts for several durations reflecting the effects of climate change are estimated by applying future annual maximum daily rainfall time series in the IDF curve equation derived by scale-invariance properties. It is shown that the increasing trend on the probabilistic design rainfall amount has resulted on most sites, but the decreasing trend in some regions has been projected.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.11C
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• pp.1060-1067
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• 2005

In this paper, we generalize the shift-invariance properties of linear time-frequency distributions to the fractional Fourier domains that interpolate between the time and frequency domains. Magnitude-wise shift invariance in arbitrary fractional Fourier domains distinguishes the short-time Fourier transform (STFT) among all linear time-frequency distributions and simplifies the interpretation of the resultant distribution. We prove that the STFT is the only linear distribution that satisfies the magnitude-wise shift-invariance property in the fractional Fourier domains.

• Child Health Nursing Research
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• v.25 no.3
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• pp.333-343
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• 2019

Purpose: This study sought to develop the Breastfeeding Adaptation Scale-Short Form (BFAS-SF) for use at 4 weeks postpartum, to test its validity and reliability, and to examine its measurement invariance. The latent mean score of the BFAS-SF across multiple groups was also compared. Methods: This methodological research study was conducted to develop a short form of the BFAS and to test its psychometric properties and measurement invariance. Data were collected twice for measurement invariance testing. The sample included 431 and 272 breastfeeding mothers at 2 weeks and 4 weeks postpartum, respectively. Results: Confirmatory factor analysis supported six dimensions of the BFAS-SF at 4 weeks postpartum. Multi-group confirmatory factor analysis revealed evidence for invariance of the BFAS-SF according to employment status, parity, delivery mode, and the postpartum period. There were statistically significant latent mean differences. Mothers who were unemployed and who had a vaginal delivery showed significantly higher scores for breastfeeding confidence, sufficient breast milk, and baby's satisfaction with breastfeeding. Conclusion: The BFAS-SF is valid, reliable, and an appropriate instrument for assessing mothers' breastfeeding adaptation. It can be used to compare mean scores according to employment status and delivery mode.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.127-137
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• 1992

In this paper we investigate scaling limits for associated random measures satisfying some moment conditions. No stationarity is required. Our results imply an improvement of a central limit theorem of Cox and Grimmett to associated random measure and an extension to the nonstationary case of scaling limits of Burton and Waymire. Also we prove an invariance principle for associated random measures which is an extension of the Birkel's invariance principle for associated process.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.249-256
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• 1995

In this note we prove an invariance principle for strictly stationary linear positive quadrant dependent sequences, satifying some assumption on the covariance structure, $0 < \sum Cov(X_1,X_j) < \infty$. This result is an extension of Burton, Dabrowski and Dehlings' invariance principle for weakly associated sequences to LPQD sequences as well as an improvement of Newman's central limit theorem for LPQD sequences.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1539-1554
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• 2013

In this paper, we extend Donsker's invariance principle to the case of random partial sums processes based on a double sequence of row-wise i.i.d. random variables.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.706-709
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• 2005

We study the adaptive stabilization of the Van der Pol equation. A parameter update law is designed by the immersion and invariance method, and is used in conjunction with both the feedback linearization and backstepping control laws. Simulation results show that the responses obtained in the adaptive case are very similar to the known parameter case, and the parameter estimator converges to the true value.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.321-328
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• 1995

Ibragimov(1975) showed the central limit theorem and the invariance principle for $\rho$-mixing random variables satisfying $\sigma^2(n) = nh(n) \longrightarrow \infty$ and $E$\mid$\zeta_0$\mid$^{2+\delta} < \infty$ for some $\delta > 0$ where $\sigma^2(n)$ denotes the variance of the partial sum $S_n$ and h(n) is a slowly varying function.