• 한국수학사학회지
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• 제24권2호
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• pp.1-15
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• 2011

인간 인식의 한계상 무한적 대상에 접근하거 위한 방법이 근사이고 그때 오차는 필수적이다. 동 서양의 근사적 접근 방식은 고유의 수학하는 방식을 반영하여 차이가 있다. 본 논문에서는 중국 및 조선의 산학서에서 발견되는 근사적 접근에서 나타나는 특정을 다섯 가지로 구분하고, 이를 통해 당시 수학자들의 근삿값에 대한 인식을 추론한다. 결과적으로, 동양 수학에서는 파악이 불가능한 대상을 다루기 위해 실제로 다룰 수 있는 근삿값을 구하여 사용한 필연성과 동시에, 오차와 관련된 근삿값의 정확도에 있어 고려된 편리성이 주목된다. 수학적 방법론으로서 근사적 원리가 구현되는 사례뿐만 아니라, 비록 근거가 원리에 대한 명시적 설명이 없다는 한계는 있지만 근삿값에 대한 인식과 정확도의 제고에 대한 의지도 여러 문맥을 통해 확인할 수 있었다. 거기에는 근삿값을 구하는 계산의 역 계산을 통해 근삿값의 정확도를 확인하는 과정도 포함된다. 그러나 선조들이 전해준 방법에 대한 고수나 편리함의 추구라는 입장에서 상당한 오차를 지닌 근삿값이 18세기까지도 상용되었다는 사실 또한 흥미롭다.

• 대한기계학회논문집A
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• 제29권1호
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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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• 제8권1호
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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.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 2002년도 제35회 춘계학술대회
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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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• 제20권1호
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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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• 제28권5_6호
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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.

• 한국경영과학회지
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• 제32권1호
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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.

• 대한기계학회논문집A
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• 제29권6호
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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.

• 한국해양공학회지
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• 제11권1호
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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.

• 대한수학교육학회지:수학교육학연구
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• 제27권4호
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• pp.811-831
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• 2017

본 연구의 목적은 원주율과 관련되는 조선산학의 내용을 교수학적 차원에서 분석하는 것이며, 분석 내용을 바탕으로 원주율에 대한 심화된 이해를 돕는 교수 학습활동을 조직화하는 것이다. 이를 위해 먼저 조선산학서 <묵사집산법>, <구수략>, <구일집>에 대한 상세 분석을 수행하였다. 분석 결과, 조선에서 사용한 고법, 휘율, 밀률을 비롯한 다양한 원주율의 근삿값이 지름과 원주의 비라는 원주율의 의미가 잘 드러나는 형태로 제시되었다는 것과 문제의 상황에 맞게 원주율을 적절히 선택하게 함으로써 계산의 정확도를 조정할 수 있었다는 것을 확인하였다. 이상의 분석 결과를 종합하여, 원주율에 대한 심화학습 자료로 활용 가능한 구체적인 교수 학습활동으로 조직화하였다. 교수 학습활동은 원주율의 뜻과 원주율의 근삿값 설명하기, 원주 또는 원의 넓이 계산 방법에 대해서 교과서 방법과 비교 설명하기, 원의 넓이와 정사각형의 넓이의 비의 관계 설명하기 등 총 4가지 활동으로 구성하여 제시하였다.