• The Korean Journal of Applied Statistics
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• v.19 no.2
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• pp.339-347
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• 2006

In mixture experiments, performing experiments in highly constrained regions causes collinearity problems. We can use the ridge regression as a means for stabilizing the coefficient estimators in the fitted model. But there is no theory available on which to base statistical inference of ridge estimators. The bootstrap technique could be used to seek the confidence intervals for ridge estimators.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.7
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• pp.885-895
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• 2004

Generally, automatic design is carried out with computer simulation and the simulation models are established by investigating the correlations between the simulation and real experiments. Therefore, the experiment results are utilized as complimentary data although they are considered to be precise. Orthogonal arrays have been adopted for discrete design. A method is proposed to directly exploit the experiment results in the design process with orthogonal arrays. Experiments are allocated to some rows of an orthogonal array and computer simulations are allocated to the others. A rule for the allocation is found to keep the orthogonality. Error analysis of the design results is performed. Mathematical examples are made to verify the validity of the proposed method. Error models are defined with the examples and the design solutions from the examples are discussed.

• Journal of Biosystems Engineering
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• v.42 no.3
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• pp.127-135
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• 2017

Purpose: Purpose: The usability of a mathematical model modified for analysis of the static stability of an asymmetric tractor-harvester system was investigated. Method: The modified asynchronous mathematical model was validated through empirical experiments, and the effects of movements of the center of gravity (CG) coordinates on the stability against lateral overturning were analyzed through simulations. Results: Changes in the lateral overturning angle of the system were investigated when the coordinates of the CG of the system were moved within the variable range. The errors between simulation results and empirical experiments were compared, and the results were -4.7% at the left side overturning and -0.1% at the right side overturning. The asymmetric system was characterized in such a way that the right side overturning had an increase in overturning angle in the (+) variable range, while it had a decrease in overturning angle in the (-) variable range. In addition, the left side overturning showed an opposite result to that of the right side. At the declination angle (296<${\gamma}$<76), the right side overturning had an increase in the maximum overturning angle of 3.6%, in the minimum overturning angle of 20.3%, and in the mean overturning angle of 15.9%. Furthermore, at the declination angle (284<${\gamma}$<64), the left side overturning had a decrease in the maximum overturning angle of 29.2%, in the minimum overturning angle of 44%, and in a mean overturning angle of 39.7%. Conclusion: The modified mathematical model was useful for predicting the overturning angle of the asymmetric tractor-harvester system, and verified that a movement of the CG coordinates had a critical effect on its stability. In particular, the left side overturning was the most vulnerable to stability, regardless of the direction of declination angle.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.395-395
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• 2000

Optimization of existing processes becomes more important than the past as environmental problems and concerns about energy savings stand out. When we can model a process mathematically, we can easily optimize it by using the model as constraints. However, modeling is very difficult for most chemical processes as they include numerous units together with their correlation and we can hardly obtain parameters. Therefore, optimization that is based on the process models is, in turn, hard to perform. Especially, f3r unknown processes, such as bioprocess or microelectronics materials process, optimization using mathematical model (first principle model) is nearly impossible, as we cannot understand the inside mechanism. Consequently, we propose a few optimization method using empirical model evolutionarily instead of mathematical model. In this method, firstly, designing experiments is executed fur removing unecessary experiments. D-optimal DOE is the most developed one among DOEs. It calculates design points so as to minimize the parameters variances of empirical model. Experiments must be performed in order to see the causation between input variables and output variables as only correlation structure can be detected in historical data. And then, using data generated by experiments, empirical model, i.e. response surface is built by PLS or MLR. Now, as process model is constructed, it is used as objective function for optimization. As the optimum point is a local one. above procedures are repeated while moving to a new experiment region fur finding the global optimum point. As a result of application to the pulp digester benchmark model, kappa number that is an indication fur impurity contents decreased to very low value, 3.0394 from 29.7091. From the result, we can see that the proposed methodology has sufficient good performance fur optimization, and is also applicable to real processes.

• The Mathematical Education
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• v.50 no.1
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• pp.69-87
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• 2011

The aim of this research is to develop a 'program which improves critical thinking' to improve elementary school students' mathematical thinking, and investigate the effect of program by applying and verifying the program. In order to achieve the objective, the author determined the factors of critical thinking capabilities matched to the discipline of mathematics, and accordingly designed relevant programs and test questions for critical thinking skills which contributes to improving the critical thinking of elementary school students, and thus applied the program the developed program of improving the critical thinking to both preliminary and main experiments, which verified the effects of the test method. The following results have been acquired through this research : In the preliminary inspection that this researcher has developed, it was able to predict that 'the program which improves critical thinking' would have a positive influence on the students' critical thinking. In the main experiment which was performed after modifying and supplementing it, the result showed that the program had a positive influence on the students' critical thinking.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.12
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• pp.1752-1755
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• 2016

In this letter, to determine how mathematical morphology operators can be best used to enhance the accuracy of background subtraction for "soccer videos", we conducted an experimental comparative study. We investigated six different mathematical morphology operators under the same experimental setup. We found that the closing by reconstruction-opening by reconstruction is optimal through the experiments using the F-measure. We believe that this comprehensive comparative study serves as a reference point and guide for developers and practitioners in choosing an appropriate mathematical morphology operator adopted for building intelligent soccer video analysis systems.

• The Journal of the Korea institute of electronic communication sciences
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• v.15 no.4
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• pp.773-778
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• 2020

In this paper, we analyzed the effects of musical stimuli on humans in performing mathematical tasks through EEG measurements. The musical stimuli were divided into preferred music and non-preferred music, and mathematical tasks were divided into memorization task and procedure task. The data measured in the EEG experiments was divided into frequency bands of Theta, SMR, and Mid-beta because of the concentration. In our results, preferred music causes more positive emotional response than no music and non-preferred music regardless of the type of mathematical task.

• IE interfaces
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• v.21 no.1
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• pp.1-7
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• 2008

In this paper we study the Minimum Edge Addition Problem(MEAP) to decrease the diameter of a graph. MEAP can be used for improving the serviceability of telecommunication networks with a minimum investment. MEAP is an NP-hard optimization problem. We present two mathematical programming models : One is a multi-commodity flow formulation and the other is a path partition formulation. We propose a branch-and-price algorithm to solve the path partition formulation to the optimality. We develop a polynomial time column generation sub-routine conserving the mathematical structure of a sub problem for the path partition formulation. Computational experiments show that the path partition formulation is better than the multi-commodity flow formulation. The branch-and-price algorithm can find the optimal solutions for the immediate size graphs within reasonable time.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.349-372
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• 2015

This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.

• Journal of Korean Institute of Industrial Engineers
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• v.35 no.2
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• pp.129-140
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• 2009

This paper introduces the planar storage location assignment problem (PSLAP) that no research has attempted to mathematically solve. The PSLAP can be defined as the assignment of the inbound and outbound objects to the storage yard with aim of minimizing the number of obstructive object moves. The storage yard allows only planar moves of objects. The PSLAP usually occurs in the assembly block stockyard operations at a shipyard. This paper formulates the PSLAP using a mathematical programming model, but which belongs to the NP-hard problems category. Thus this paper utilizes an efficient genetic algorithm (GA) to solve the PSLAP for real-sized instances. The performance of the proposed mathematical programming model and developed GA is verified by a number of numerical experiments.