• The Mathematical Education
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• v.51 no.1
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• pp.47-61
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• 2012

Students can infer mathematical principles in a very natural way by connecting mutual relations between mathematical fields. These process can be revealed by taking tasks that can derive mathematical connections. The task of this study is to make expression and design it and derive mathematical principles from the design. This study classifies the mathematical field of expression for design and analyzes mathematical thinking process by connecting mathematical fields. To complete this study, 40 gifted students from 5 to 8 grade were divided into two classes and given 4 hours of instruction. This study analyzes their personal worksheets and e-mail interview. The students make expressions using a functional formula, remainder and figure. While investing mathematical principles, they generalized design by mathematical guesses, generalized principles by inference and accurized concept and design rules. This study proposes the class that can give the chance to infer mathematical principles by connecting mathematical fields by designing.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.6
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• pp.607-613
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• 2009

In this paper, we made a simple paper feeding system which is one of MTS (media transport system) and controllers. The plant has a flexible paper and two driving rollers and two driven rollers. The control system has two conventional PID controllers. Skew angle and feeding speed of MTS deteriorate the quality of feeding system. In order to control a feeding speed and skew of feeding paper, we control rotational velocity of two driving rollers. Therefore, this controller has two inputs and two outputs as MIMO (multi-input and multi-output) system. The control inputs were the feeding speed and the skew displacement of the paper. The control outputs were the rotational velocity to each driving roller. To find appropriate PID gains of two controllers, we proposed an optimization technique. We assume the system variables and performance of a whole system as follows. PID gains of two controllers for skew and feeding speed are system variables. System performance is both skew and feeding speed. We simulates to making mathematical correlation using global Kriging interpolation. To find appropriate value of system variables, optimization method is simulation in sequence as following method. First, the optimization solver simulates with DOE (design of experiment) tables to find correlation equation of both system variable and performances. Then, the solver guesses the appropriate values and simulates if the system variables are appropriate or not. If the result of validation doesn't satisfy the convergence and iteration tolerance, the solver makes a new Kriging models and iterates this sequence until satisfy the tolerances.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.8
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• pp.1468-1484
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• 1992

In the present paper forward projection is proposed as a new approach to determine the preform shape in rib-web type forging. In the forward projection technique an optimal billet is determined by applying some mathematical relationship between geometrical trials in the initial billet shape and the final products. In forward projection a volume difference between the desired product shape and the final computed shape obtained by the rigid-plastic finite element method is used as a measure of incomplete filling of working material in the die. At first linear inter-/extrapolation is employed to find a proper trial shape for the initial billet and the method is successfully applied to some cases of different aspect ratios of the initial billet. However, when the initial guesses are not sufficiently near the optimal value linear inter-/extrapolation does not render complete die filling. For more general application, a fuzzy system is used in the forward projection technique in order to determine the initial billet shape for rib-web type forging. It has been thus shown that the fuzzy system is more reliable for the preform design in the rib-web type forging process.

• Journal of Educational Research in Mathematics
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• v.20 no.2
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• pp.163-183
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• 2010

It has long been of controversy what the meanings of probability is. And a century has past after the mathematical probability has been at the center of the school curriculum of it. Recently statistical meaning of probability becomes important for various reasons. However the simple modification of its definition is not enough. The computational reasoning of the probability and its practical application needs didactical changes and new instructional transformations along with the modification of it. Most of the current text books introduce probability as a limit of the relative frequencies, a statistical probability. But when the probability computation of the union of two events, or of the simultaneous events is faced on, they use mathematical probability for explanation and practices. Accordingly there is a gap for students in understanding those. Probability is an intuitive concept as far as it belongs to the domain of the experiential frequency. And frequency distribution must be the instructional bases for the (statistical) probability novices. This is what we mean by the probability in accordance with the distribution concepts. First of all, in order to explain the probability of the complementary event we should explain the empirical relative frequency of it first. These are the case for the union of two events and for the simultaneous events. Moreover we need to provide a logic of probabilistic guesses, inferences and decision, which we introduce with the name “the likelihood principle”, the most famous statistical principle. We emphasized this be done through the problems of practical decision making.