• Journal for History of Mathematics
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• v.24 no.2
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• pp.1-15
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• 2011

Approximation is a very useful approach in mathematics research. It was the same in traditional Chinese and Chosun mathematics. This study derived five characteristics from approximation approaches which were found in Chinese and Chosun mathematical books: improvement of approximate values, common and inevitable use of approximate values, recognition of approximate values and their reasons, comparison of their exactness, application of approximate principles. Through these characteristics, we can infer what Chinese and Chosun mathematicians recognized approximate values and how they manipulated them. They took approximate approaches by necessity or for the sake of convenience in mathematical study and its applications. Also, they tried to improve the degree of exactness of approximate values and use the inverse calculations to check them.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.1 s.232
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• pp.45-52
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• 2005

A general approximate optimization technique by sequential design domain(SDD) did not save response values for getting an approximate function in each step. It has a disadvantage at aspect of an expense. In this paper, previous response values are recycled for constructing an approximate function. For this reason, approximation function is more accurate. Accordingly, even if we did not determine move limit, a system is converged to the optimal design. Size and shape optimization using approximate optimization technique is carried out with SDD. Algorithm executing Pro/Engineer and ANSYS are automatically adopted in the approximate optimization program by SDD. Convergence criterion is defined such that optimal point must be located within SDD during the three steps. The PLBA(Pshenichny-Lim-Belegundu-Arora) algorithm is used to solve approximate optimization problems. This algorithm uses the second-order information in the direction finding problem and uses the active set strategy.

• International Journal of Reliability and Applications
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• v.8 no.1
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• pp.1-16
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• 2007

In this paper, we derive exact explicit expressions for the triple and quadruple moments of the lower record values from inverse the Weibull (IW) distribution. Next, we present and calculate the coefficients of the best linear unbiased estimates of the location and scale parameters of IW distribution (BLUEs) for different choices of the shape parameter and records size. We then use the higher order moments and the calculated BLUEs to compute the mean, variance, and the coefficients of skewness and kurtosis of certain linear functions of lower record values. By using the coefficients of the skewness and kurtosis, we develop approximate confidence intervals for the location and scale parameters of the IW distribution using Edgeworth approximate values and then compare them with the corresponding intervals constructed through Monte Carlo simulations. Finally, we apply the findings of the paper to some simulated data.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2002.05a
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• pp.80-87
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• 2002

We predict the unknown cannon tube erosion rate by using observed values of the standard cannon, 155mm Howitzer Ml85. We know the standard cannon's ten erosion observation values each 400 rounds. An approximate formula fitting the erosion values of the standard cannon has been derived. Numerical simulation applying this formula to the Rauf Imam's erosion equations is presented.

• Communications for Statistical Applications and Methods
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• v.20 no.1
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• pp.29-39
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• 2013

This paper derives maximum likelihood estimators (MLEs) and some approximate MLEs (AMLEs) of unknown parameters of the generalized exponential distribution when data are lower record values. We derive approximate Bayes estimators through importance sampling and obtain corresponding Bayes predictive intervals for unknown parameters for lower record values from the generalized exponential distribution. For illustrative purposes, we examine the validity of the proposed estimation method by using real and simulated data.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1239-1248
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• 2010

In this paper, an implementable BFGS bundle algorithm for solving a nonsmooth convex optimization problem is presented. The typical method minimizes an approximate Moreau-Yosida regularization using a BFGS algorithm with inexact function and the approximate gradient values which are generated by a finite inner bundle algorithm. The approximate subgradient of the objective function is used in the algorithm, which can make the algorithm easier to implement. The convergence property of the algorithm is proved under some additional assumptions.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.1
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• pp.125-136
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• 2007

The study on query relaxation which provides approximate answers has received attention. In recent years, some arguments have been made that semantic relationships are useful to present the relationships among data values and calculating the semantic distance between two data values can be used as a quantitative measure to express relative distance. The aim of this article is a hierarchical metricized knowledge abstraction (HiMKA) with an emphasis on combining data abstraction hierarchy and distance measure among data values. We propose the operations and the query relaxation algorithm appropriate to the HiMKA. With various experiments and comparison with other method, we show that the HiMKA is very useful for the quantified approximate query answering and our result is to offer a new methodological framework for query relaxation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.6 s.237
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• pp.842-851
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• 2005

In this paper, a new method for constrained optimization of noisy functions is proposed. In approximate optimization using response surface methods, if constraints have severe noise, the approximate feasible region defined by approximate constraints is apt to include some of the infeasible region defined by actual constraints. This can cause the approximate optimum to converge into the infeasible region. In the proposed method, the approximate optimization is performed with the approximate constraints shifted by their deviations, which are calculated using a diagonal quadratic response surface method. This can prevent the approximate optimum from converging into the infeasible region. To fit the objective and constraints into diagonal quadratic models, we select the center and 4 additional points along each axis of design variables as experimental points. The deviation of each function is calculated using the differences between the real and approximate function values at the experimental points. A sequential approximate optimization technique based on the trust region algorithm is adopted to manage approximate models. The proposed approach is validated by solving some design problems. The results of the problems show the effectiveness of the proposed method.

• Journal of Ocean Engineering and Technology
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• v.11 no.1
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• pp.36-43
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• 1997

Weld bead shape is an important measure for evaluation of weld quality. Many welding parameters have influence on the weld bead shape. The quantitative relationship between welding parameters and bead shape, however, is not determined yet because of their high complexity and many unknown factors. Fuzzy expert system is an advanced expert system which uses fuzzy rules and approximate reasoning. It is a vert useful tool for welding technology because is can process rationally the uncertain and inexact information such as the welding information. In this paper, the empirical and the qualitative relationship between welding parameters and bead shape are analyzed and represented by fuzzy rules. They are converted to the quantitative relationship by use of approximate reasoning of fuzzy expert system. Weld bead shape is estimated from the welding parameters using fuzzy expert system. The result of comparison between measured values of weld bead by welding experiments and the estimates values by fuzzy expert system shows a good consistancy.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.811-831
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• 2017

The purpose of this study is to analyze the contents of pi of Chosun-sanhak and organize the teaching and learning activities to help to understand the concept of pi deeply using the analysis results. The results of this study are as follows. First, Chosun-sanhak used various approximate values of pi and those were represented as the form to reveal the meaning of the ratio of radius and circumference. Second, There were the freedom of selection of the approximate values of pi suitably. Lastly, the enriched leaning about pi need to draw a distinction pi from approximate values of pi, choose the suitable approximate values of pi and compare the method of calculation of circumference and the area of circle of Chosun-sanhak and today's mathematics. In conclusion, I proposed several issues which is worth exploring further in relation to pi and Chosun-Sanhak.