• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.61-72
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• 1998

It has been known that if T and S are even Kakutani equivalent, then there exists U such that T and U are $\alpha$-equivalent and S and U are $\beta$-equivalent where $\alpha$ and $\beta$ are irrationally related. In this paper we give a complete discrete proof of this theorem without using R-actions.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.705-710
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• 2018

Let T(X) be the full transformation semigroup on a set X and ${\sigma}$ be an equivalence relation on X. Denote $$E(X,{\sigma})=\{{\alpha}{\in}T(X):{\forall}x,\;y{\in}X,\;(x,y){\in}{\sigma}\;\text{implies}\;x{\alpha}=y{\alpha}\}.$$. Then $E(X,{\sigma})$ is a subsemigroup of T(X). In this paper, we characterize two semigroups of type $E(X,{\sigma})$ when they are isomorphic.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.611-624
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• 2010

Several methods were suggested for constructing a fuzzy relationship between fuzzy independent and dependent variables. This paper reviews the use of the method by minimizing the square of the difference between an observed and a predicted fuzzy number in an ${\alpha}$-level linear regression model. We introduce a new distance between fuzzy numbers on the basis of a mode, a core point and a radius of an ${\alpha}$-level set of a fuzzy number an construct the fuzzy regression model using the proposed fuzzy distance. We also investigate sufficient condition for an equivalence in the ${\alpha}$-level regression model.

• The Korean Journal of Applied Statistics
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• v.21 no.5
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• pp.867-873
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• 2008

It is a convention to use 5% significance level when a statistical test is employed for clinical data. But when a confidence interval is used for testing equivalence, 90% confidence interval has often been used. When $1-{\alpha}$ confidence interval is used for hypothesis testing, its significance level is often ${\alpha}$. So it makes a confusion that the significance level is 10% if 90% confidence interval is employed for testing equivalence. In this paper I will clarify this issue by reviewing relevant papers and conducting simulation studies. I hope that it will be beneficial to statisticians in pharmaceutical companies, CROs, university hospitals.

• International Journal of Reliability and Applications
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• v.10 no.1
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• pp.17-32
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• 2009

The aim of this work is to generalize reliability equivalence technique to apply it to a system consists of n independent and non-identical components connected in series system, that have mixing constant failure rates. We shall improve the system by using some reliability techniques: (i) reducing some failure rates; (ii) add hot reduncy components; (iii) add cold reduncy components; (iv) add cold reduncy components with imperfect switches. We start by establishing two different types of reliability equivalence factors, the survival equivalence (SRE), and mean reliability equivalence (MRE) factors. Also, we introduced some numerical results.

• Journal of the Korean Society of Combustion
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• v.8 no.3
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• pp.38-48
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• 2003

OH, CH and NO radical distributions have been measured and compared with the numerical analysis results in methane/air partially premixed laminar flames using 2-D LIF technique. The pick intensity of OH LIF signal is insensitive to fuel equivalence ratio: however, CH LIF intensity decreases as equivalence ratio increases and the NO concentration increases with equivalence ratio. The contribution of the prompt NO, formed near premixed reaction zone, to the total NO formation is evident from the OH, CH, and NO PLIF images in which the dilution effect of nitrogen is minimal for the highest equivalence ratio. Measured OH and NO LIF signals in counterflow flames agree with the computed concentration distributions. Both numerical and experimental results indicate that the structural change in a flame alters the NO formation characteristics of a partially premixed counterflow flame. The nitrogen dilution also changes flame structure, temperature and OH radical distributions and results in the decreased NO concentrations in a flame. The levels of decrease in NO concentrations, however, depends on the premixedness(${\alpha}$) of a flame. The larger change in the flame structure and NO concentrations have been observed in a premixed flame(${\alpha}=1.0$), which implies that the premixedness is likely to be a factor in the dilution effect on NO formation of a flame.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1121-1136
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• 2005

Nonstandard finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with periodic boundary conditions, which are of the type $$U_t\;+\;\frac{{\partial}^2}{{\partial}x^2} g(u,\;U_x,\;U_{xx})\;=\;\frac{{\partial}^{\alpha}}{{\partial}x^{\alpha}}f(u,\;u_x),\;{\alpha}\;=\;0,\;1,\;2$$. Stability and error estimate of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem. Three examples are provided to apply the nonstandard finite difference schemes.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.281-288
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• 2012

In this paper, the author defines a new generalized ${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.

• Journal of Korean Academy of Nursing Administration
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• v.13 no.4
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• pp.509-515
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• 2007

Purpose: The purpose of this study was to translate and validate the Korean version of Hall's Professional Inventory(HPI) scale to assess levels of professionalism among Korean registered nurses. Method: The 25 item HPI scale was translated and content review was done by translation panel. After the content review, a bilingual nursing scholar performed the back-translation into English. A semantic equivalence test was conducted with 5 American nursing professors. A pilot study was conducted with a sample of 164 registered nurses in Korea to test the validity and reliability of the translated HPI. Result: The content equivalence for translated version of HPI was validated by a translation panel. The finding of the semantic equivalence test of back-translated version was 72.8%. The Cronbach's alpha for the Korean version of HPI was .820. Conclusions: This study provides information about the issues of translating an instrument such as the HPI. The Korean version of the HPI is a valid and reliable instrument and can have psychometric properties equivalent to those of the original HPI. The translated version could be used for assessing levels of professionalism for other health care professionalism as well as nurses.

• The Mathematical Education
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• v.57 no.2
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• pp.179-196
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• 2018

The purpose of this study was to investigate the measurement equivalence and to suggest application ways in teaching aptitude and personality test results for pre-service mathematics teachers between a graduate school of education and a college of education. This study analyzed the scores of the teaching aptitude and personality test of 36 pre-service mathematics teachers enrolled in a graduate school of education and 111 pre-service mathematics teachers in a college of education by performing a multivariate generalizability analysis. The main results were as follows. First, graduate's pre-service mathematics teachers had a higher level of teaching aptitude and personality than that of college's pre-service mathematics teachers based on the total scores. In addition, graduate's pre-service mathematics teachers had higher levels of teaching aptitude and personality than those of college's pre-service mathematics teachers except for a creativity application domain based on the sub-domain scores. Second, cognitive domains were measured more precisely but affective domains were measured less precisely for graduate's pre-service mathematics teachers than for college's pre-service mathematics teachers. Third, regardless of school levels, Cronbach's ${\alpha}$ values, which might be overestimated by applying the classical test theory, were higher than dependability coefficients. Fourth, this study showed a somewhat negative result in ensuring the measurement equivalence for a problem solving exploration domain. However, regardless of school levels, this study indicated that the overall measurement was generally reliable on composite scores. Based on these results, it was confirmed that multivariate generalizability methodologies' approach can be useful for exploring the measurement equivalence issues. Finally, this study suggests how to utilize the results of the test, how to apply a multivariate generalizability analysis for detecting the measurement equivalence, and how to develop future research based on limitations.