• Water Engineering Research
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• v.1 no.4
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• pp.279-291
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• 2000

A mathematical model using dynamic programming approach is applied to an optimal unit commitment problem. In this study, the units are treated as stages instead of as state dimension, and the time dimension corresponds to the state dimension instead of stages. A considerable amount of computer time is saved as compared to the normal approach if there are many units in the basin. A case study on the Lower Colorado River Basin System is presented to demonstrate the capabilities of the optimal scheduling of hydropower units.

• Journal of the Korean housing association
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• v.19 no.6
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• pp.1-8
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• 2008

A fitness facility in an apartment complex is not a simple sports facility. It has important roles in improving the residents' physical and mental health, and in forming a sense of community. This study analyzed the number of users in the fitness facility of the apartment complex, which is a significant criterion in determining the dimension. A comparative analysis between the past and the present function and dimension was performed in finding out the optimal solutions. In conclusion, the number of users in the fitness facility is influenced not by the number of households in the complex but by the facility's size and creating a desired environment. The users' favorite sports equipments were figured out to meet those needs. Moreover, comparing the facilities' size, user satisfaction, area per person, an optimal dimension for the facility, and rates of equipments were found out.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.107-115
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• 2012

Yoo and Cook (2007) developed an optimal sufficient dimension reduction methodology for the conditional mean in multivariate regression and it is known that their method is asymptotically optimal and its test statistic has a chi-squared distribution asymptotically under the null hypothesis. To check the effect of dimension used in estimation on regression coefficients and the explanatory power of the conditional mean model in multivariate regression, we applied their method to several simulated data sets with various dimensions. A small simulation study showed that it is quite helpful to search for an appropriate dimension for a given data set if we use the asymptotic test for the dimension as well as results from the estimation with several dimensions simultaneously.

• Communications for Statistical Applications and Methods
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• v.24 no.3
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• pp.303-315
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• 2017

Yoo (2015, Statistics and Probability Letters, 99, 109-113) derives theoretical results in an optimal sufficient dimension reduction with singular inner-product matrix. The results are promising, but Yoo (2015) only presents one simulation study. So, an evaluation of its practical usefulness is necessary based on numerical studies. This paper studies the asymptotic behaviors of Yoo (2015) through various simulation models and presents a real data example that focuses on ordinary least squares. Intensive numerical studies show that the $x^2$ test by Yoo (2015) outperforms the existing optimal sufficient dimension reduction method. The basis estimation by the former can be theoretically sub-optimal; however, there are no notable differences from that by the latter. This investigation confirms the practical usefulness of Yoo (2015).

• Journal of the Korean Society for Precision Engineering
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• v.15 no.6
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• pp.33-39
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• 1998

This paper is related to economic design of tool-resetting period in NC machining. In NC lathe machining, the mean and variance of components dimension fluctuate in slow time and we should reset tool program to compensate the variation from the fluctuation. In this paper. we propose the procedure determining the optimal resetting period based on the total expected operating cost which consists of resetting cost and the quality cost related to dimension variation. As a case study, using experimental data about dimension changes of a lathe machining, we obtain the regression equations of mean and variance of the dimension fluctuation, total expected operating cost, and optimal resetting period.

• The Korean Journal of Applied Statistics
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• v.23 no.5
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• pp.977-985
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• 2010

In this paper, we propose an approach to conduct partial sufficient dimension reduction with heavily unbalanced categorical predictors. For this, we consider integrated categorical predictors and investigate certain conditions that the integrated categorical predictor is fully informative to partial sufficient dimension reduction. For illustration, the proposed approach is implemented on optimal partial sliced inverse regression in simulation and data analysis.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.13 no.4
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• pp.79-86
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• 2004

Tooth errors inevitable in the manufacturing process have large effect on the strength/durability and vibration performances of gear drives. We show that the manufacturing errors affect the overall gear performances, especially vibration performance, and propose a robust optimal design method for gear dimension and its tooth flank form that guarantees reliable performances to the variation of manufacturing errors. This method begins with a search of optimal design candidates by using the previously developed gear optimal design method for the strength/durability and vibration performances. Then, the statistical analysis method is applied to find a robust design solution for the vibration performance which is generally very sensitive to the manufacturing variations.

• Journal of the Korean Statistical Society
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• v.33 no.4
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• pp.435-447
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• 2004

In additive nonparametric regression, Linton and Nielsen (1995) showed that the marginal integration when applied to the local linear smoother produces a rate-optimal estimator of each univariate component function for the case where the dimension of the predictor is two. In this paper we give new formulas for the bias and variance of the marginal integration regression estimators which are valid for boundary areas as well as fixed interior points, and show the local linear marginal integration estimator is in fact rate-optimal when the dimension of the predictor is less than or equal to four. We extend the results to the case of the local polynomial smoother, too.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.431-450
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• 2023

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n-means and the nth quantization errors for different values of n with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise [2], which says that for a Borel probability measure P with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.17 no.4
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• pp.408-417
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• 1988

This study optimized the condenser dimension of heat pump system with the heat sources which are solar irradiation and ambient air. At first, the author selected the principal design factors influencing the performance of heat pump system. And the author considered the variation of condenser dimension according to the variation of the selected design factors, that is, ambient air temperature, condenser temperature, degree of superheating, degree of sub-cooling and irradiation. As a result this study, among refrigerants R12, R22 and R500, refrigerant R22 has more heating output than R12 and R500, and the coefficient of performance on this heat pump system is not greatly influenced by the degree of superheating and degree of sub cooling. The ambient air temperature is below $5^{\circ}C$ at balance point and the optimal tube length of condenser dimension is about 3.8 m. Also the author gained the optimal design diagram for the optimization of condenser dimension according to various design factors.