• The Mathematical Education
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• v.49 no.4
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• pp.437-462
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• 2010

The purpose of this research is to analyze the textbook contents about the natural number concepts in the Korean National Elementary Mathematics Curriculum. Understanding a concept of natural number is crucial in school mathematics curriculum planning, since elementary students start their basic learning with natural number system. The concepts of natural number have various meaning from the perspectives of pedagogical research, and the philosophy of mathematics. The natural number concepts in the elementary math curriculum consist of four aspects; counting numbers, cardinal numbers, ordinal numbers, and measuring numbers. Two research questions are addressed; (1) How are the natural number concepts focusing on counting, cardinal, ordinal, measuring numbers are covered in the national math curriculum? ; (2) What suggestions can be made to enhance the teaching and learning about the natural number concepts? Findings reveal that (1) the national mathematics curriculum properly reflects four aspects of natural number concepts, as the curriculum covers 50% of the cardinal number system; (2) In the aspect of the counting number, we hope to add the meaning about 'one, two, three, ......, and so on' in the Korean Mathematics curriculum. In the ordinal number, we want to be rich the related meaning in a set. Further suggestions are made for future research to include them ensuing number in the curriculum.

• Communications for Statistical Applications and Methods
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• v.30 no.1
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• pp.49-63
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• 2023

A lot of studies on the summary measures of predictive strength of categorical response models consider the likelihood ratio index (LRI), also known as the McFadden-R², a better option than many other measures. We propose a simple modification of the LRI that adjusts for the effect of the number of response categories on the measure and that also rescales its values, mimicking an underlying latent measure. The modified measure is applicable to both binary and ordinal response models fitted by maximum likelihood. Results from simulation studies and a real data example on the olfactory perception of boar taint show that the proposed measure outperforms most of the widely used goodness-of-fit measures for binary and ordinal models. The proposed R² interestingly proves quite invariant to an increasing number of response categories of an ordinal model.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1465-1475
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• 2013

The chi-square type test statistic is the most commonly used test in terms of measuring testing goodness-of-fit for multinomial logistic regression model, which has its grouped data (binomial data) and ungrouped (binary) data classified by a covariate pattern. Chi-square type statistic is not a satisfactory gauge, however, because the ungrouped Pearson chi-square statistic does not adhere well to the chi-square statistic and the ungrouped Pearson chi-square statistic is also not a satisfactory form of measurement in itself. Currently, goodness-of-fit in the ordinal setting is often assessed using the Pearson chi-square statistic and deviance tests. These tests involve creating a contingency table in which rows consist of all possible cross-classifications of the model covariates, and columns consist of the levels of the ordinal response. I examined goodness-of-fit tests for a proportional odds logistic regression model-the most commonly used regression model for an ordinal response variable. Using a simulation study, I investigated the distribution and power properties of this test and compared these with those of three other goodness-of-fit tests. The new test had lower power than the existing tests; however, it was able to detect a greater number of the different types of lack of fit considered in this study. I illustrated the ability of the tests to detect lack of fit using a study of aftercare decisions for psychiatrically hospitalized adolescents.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.289-300
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• 1995

Every group G has a unique maximal normal locally nilpotent subgroup $\Phi(G)$, called the Hirsh-Plotkin radical of G [9]. If G is a group, we define the upper Hirsh-Plotkin series of G to be the ascending series $1 = R_0 \leq R_1 \leq \ldots$ in which $R_{\alpha+1}/R_\alpha = \{Phi(G/R_\alpha)$ for each ordinal $\alpha and R_\beta = \cup_{\alpha<\beta}R_\alpha$ for each limit ordinal $\beta$. If $R_r = G$ for some natural number r, then G is said to have locally nilpotent length r. $(LN)^r$ denotes the calss of groups of locally nilpotent length at most r.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.105-127
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• 2022

It is known that the maximal invariant set of a continuous iterative dynamical system in a compact Hausdorff space is equal to the intersection of its forward image sets, which we will call the first minimal image set. In this article, we investigate the corresponding relation for a class of discontinuous self maps that are on the verge of continuity, or topologically almost continuous endomorphisms. We prove that the iterative dynamics of a topologically almost continuous endomorphisms yields a chain of minimal image sets that attains a unique transfinite length, which we call the maximal invariance order, as it stabilizes itself at the maximal invariant set. We prove the converse, too. Given ordinal number ξ, there exists a topologically almost continuous endomorphism f on a compact Hausdorff space X with the maximal invariance order ξ. We also discuss some further results regarding the maximal invariance order as more layers of topological restrictions are added.

• Journal of Korean Academy of Nursing
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• v.44 no.5
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• pp.542-551
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• 2014

Purpose: This study was done to examine the incidence of oral mucositis in hematopoietic stem cell transplantation patients and to identify factors influencing oral mucositis and patient outcomes according to severity. Methods: In this retrospective study, data were collected from electronic medical records of 222 patients who had received hematopoietic stem cell transplantation. Oral mucositis was evaluated using WHO's assessment scale. Data were analyzed using Chi-square test, Fisher exact test, Spearman's correlation, Ordinal logistic regression, ANOVA and Kruskal-Wallis test. Results: A total of 69.8% of the patients evaluated developed oral mucositis (grade II and over). As a results of ordinal regression, factors influencing oral mucositis severity were found to be diagnosis, type of transplantation, oxygen inhalation and the number of antiemetics administration before transplantation. The severity of oral mucositis was found to increase the days of hospitalization, days of TPN administration, days of using antibiotics and the number and dosage of analgesics. Conclusion: The results would help predict severity of oral mucositis in hematopoietic stem cell transplantation patients and suggest that provision of appropriate nursing assessment and oral care would improve patient outcomes.

• Health Policy and Management
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• v.30 no.3
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• pp.399-408
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• 2020

Background: The purpose of this study was to examine the impact of the regional characteristics on the accessibility of emergency care and the impact of emergency medical accessibility on the patients' prognosis and the emergency medical expenditure. Methods: This study used the 13th beta version 1.6 annual data of Korea Health Panel and the statistics from the Korean Statistical Information Service. The sample included 8,119 patients who visited the emergency centers between year 2013 and 2017. The arrival time, which indicated medical access, was used as dependent variable for multi-level analysis. For ordinal logistic regression and multiple regression, the arrival time was used as independent variable while patients' prognosis and emergency medical expenditure were used as dependent variables. Results: The results for the multi-level analysis in both the individual and regional variables showed that as the number of emergency medical institutions per 100 km² area increased, the time required to reach emergency centers significantly decreased. Ordinal logistic regression and multiple regression results showed that as the arrival time increased, the patients' prognosis significantly worsened and the emergency medical expenses significantly increased. Conclusion: In conclusion, the access to emergency care was affected by regional characteristics and affected patient outcomes and emergency medical expenditure.

• Journal for History of Mathematics
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• v.25 no.1
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• pp.29-43
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• 2012

In this paper, we survey the history of search for axiomatic set theory and show that ${\exists}U(0{\in}U{\wedge}{\forall}x(x{\in}U{\leftrightarrow}{\exists}z(z{\in}U{\wedge}{\forall}y(y{\in}x{\rightarrow}y{\subseteq}z))){\rightarrow}$ ZR.

• Journal of the Korea Safety Management & Science
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• v.9 no.3
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• pp.165-171
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• 2007

Dependent models in quality statistics are classified as serially autocorrelated model, multivariate model and dependent sample model. Dependent sample model is most efficient in time and cost to obtain samples among the above models. This paper proposes to implement parametric and nonparametric models into production system depended on demand pattern. Nonparametric models have distribution free and asymptotic distribution free techniques. Quality statistical models are classified into two categories ; the number of dependent sample and the type of data. The type of data consists of nominal, ordinal, interval and ratio data. The number of dependent sample divides into 2 samples and more than 3 samples.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.358-363
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• 1998

An algorithm for representing the cubic spline interpolation of differentiable functions by a fuzzy system is presented in this paper. The cubic B-spline functions which form a basis for the interpolation function are used as the fuzzy sets for input fuzzification. The ordinal number of the coefficient cKL in the list of the coefficient cij's as sorted in increasing order, is taken to be the output fuzzy set number in the (k, l) th entry of the fuzzy rule table. Spike functions are used for the output fuzzy sets, with cij's as support boundaries after they are sorted. An algorithm to compute the support boundaries explicitly without solving the matrix equation involved is included, along with a few properties of the fuzzy rule matrix for the designed fuzzy system.