• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1067-1076
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• 2006

Although the proportional hazards model is the most common approach used for studying the relationship of event times and covariates, alternative models are needed for occasions when it does not fit data. In the two-sample case, proportional odds models are useful for fitting data whose hazard rates converge asymptotically. In this thesis, we propose a new estimator of the relative odds ratio of the proportional odds model when two independent random samples are observed under uncensorship. We prove the asymptotic normality and consistency of the estimator by using martingale-representation. The efficiency of the proposed is assessed through a simulation study.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.11
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• pp.1065-1070
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• 2004

Optimal collision avoidance algorithm for unmanned aerial vehicles based on proportional navigation guidance law is investigated this paper. Although proportional navigation guidance law is widely used in missile guidance problems, it can be used in collision avoidance problem by guiding the relative velocity vector to collision avoidance vector. The optimal navigation coefficient can be obtained if an obstacle if an obstacle moves at constant velocity vector. The stability of the proposed algorithm is also investigated. The stability can be obtained by choosing a proper navigation coefficient.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.613-618
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• 2011

The proposed method is based on a penalized log partial likelihood of Cox proportional hazard model with L1-penalty. We use the iteratively reweighted least squares procedure to solve L1 penalized log partial likelihood function of Cox proportional hazard model. It provide the ecient computation including variable selection and leads to the generalized cross validation function for the model selection. Experimental results are then presented to indicate the performance of the proposed procedure.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.965-971
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• 2004

In this paper we consider several nonparametric estimators for the mean residual life by using the partial moment approximation under the proportional hazard model. Also we compare the magnitude of mean square error of the proposed nonparametric estimators for mean residual life under the proportional hazard model.

• Journal of the Korean School Mathematics Society
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• v.11 no.4
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• pp.609-627
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• 2008

The purpose of this research was to investigate the relationship between the students' strategy types and the recognition for proportional situations. The students' strategy types which were based on the results of ratio and proportion tests were divided into an additive type, a multiplicative type, and a formal type. This research analyzed the students' activities of categorization when were given the proportional problems and nonproportional problems to the students. And it also explored how to develop students' recognizing for the discrimination between the proportional situations and nonproportional situations. The results was the following. First, the students didn't discriminate the proportional situations and the nonproportional situations in the initial state but they came to discriminate little by little. Secondly, the students didn't discriminate the direct proportions and the inverse proportions until the last stage. Third, the multiplicative type was outperformed more than the formal type in solving the ratio and proportion problems but the formal type was outperformed more than the multiplicative type in discriminating between proportional situations and nonproportional situations. These results are interpreted as showing that solving ratio and proportion tasks and recognizing proportional situations are different aspects of proportional reasoning and it is necessary to understand multiplicative strategy with formal strategy in recognizing proportional situations.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.21-58
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• 2015

The aim of this study is to look into the didactical background for teaching proportional reasoning in elementary school mathematics and offer suggestions to improve teaching proportional reasoning in the future. In order to attain these purposes, this study extracted and examined key ideas with respect to the didactical background on teaching proportional reasoning through a theoretical consideration regarding various studies on proportional reasoning. Based on such examination, this study compared and analyzed textbooks used in the United States, the United Kingdom, and South Korea. In the light of such theoretical consideration and analytical results, this study provided suggestions for improving teaching proportional reasoning in elementary schools in Korea as follows: giving much weight on proportional reasoning, emphasizing multiplicative comparison and discerning between additive comparison and multiplicative comparison, underlining the ratio concept as an equivalent relation, balancing between comparisons tasks and missing value tasks inclusive of quantitative and qualitative, algebraic and geometrical aspects, emphasizing informal strategies of students before teaching cross-product method, and utilizing informal and pre-formal models actively.

• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.505-516
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• 2013

The purpose of this paper is to analyse the essence of proportional reasoning and to analyse the contents of the textbooks according to the mathematics curriculum revised in 2007, and to seek the direction for developing the proportional reasoning in the elementary school mathematics focused the task variables. As a result of analysis, it is found out that proportional reasoning is one form of qualitative and quantitative reasoning which is related to ratio, rate, proportion and involves a sense of covariation, multiple comparison. Mathematics textbooks according to the mathematics curriculum revised in 2007 are mainly examined by the characteristics of the proportional reasoning. It is found out that some tasks related the proportional reasoning were decreased and deleted and were numerically and algorithmically approached. It should be recognized that mechanical methods, such as the cross-product algorithm, for solving proportions do not develop proportional reasoning and should be required to provide tasks in a wide range of context including visual models.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.225-236
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• 2002

By means of the method of majorant series, sufficient conditions are obtained for the existence of analytic solutions of a functional differential equation with proportional delays.

• Journal of Power System Engineering
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• v.16 no.3
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• pp.64-68
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• 2012

Because the magnetic bearing supports levitating body without contact, wear, noise and vibration are very small comparing with mechanical bearings, it is very useful to high revolution machinery. In general, the magnetic attractive force function that is proportional to square of control current(x), and inversely proportional to square of an air gap(i) has been widely used. This paper proposed the new magnetic attractive force function that is proportional to cube of the control current, and inversely proportional to square of the air gap. The function was optimized to minimize the cost function that is the percentage of deviation about the change of a proportional constant(k), using the experimental data, ie, control currents and air gaps.

• Transactions of The Korea Fluid Power Systems Society
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• v.8 no.4
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• pp.9-16
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• 2011

Because of the increasing demand on the high precision and high response of a machinery, proportional control valves are widely adopted at various application fields. This paper studies on the static and dynamic characteristics of a pilot proportional pressure control valve. An experimental apparatus including hydraulic pump, variable speed inverter, pressure and flow sensors and data aquisition system was set up. And various experiments such as P-Q-V curves, step responses due to input voltage and flow rate, hysteresis, frequency response of the proportional valve was carried out and the results are discussed.