• Journal of the Korean Institute of Telematics and Electronics
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• v.10 no.6
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• pp.25-44
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• 1973

The please relation between motive force and result is reviewed in view point of the correlation function as well as the redundancy in a continuous signal which permits the sampled treatment. A new correlation function (to be named Time Dependent Correlation Function) which is a functon of time, is defined in order to indicate the variation of the correlation between two signals. As application a phase looked loop is analysed which shows the increase of correlation between input signal and output signal of the loop after the application of the input signal. Finally again the T.D.Correlation Function method is used to show how the polyphase envelope detection-method is justifiable by this method.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.1
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• pp.13-17
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• 2003

A continuous solution of the Dirichlet boundary value problem for the heat equation $u_t$＝$a2u_{xx}$ using a fuzzy system is described. We first apply the Crank-Nicolson method to obtain a discrete solution at the grid points for the heat equation. Then we find a continuous function to represent approximately the discrete values at the grid points in the form of a bicubic spline function (equation omitted) that can in turn be represented exactly by a fuzzy system. We show that the computed values at non-grid points using the bicubic spline function is much smaller than the ones obtained by linear interpolations of the values at the grid points. We also show that the fuzzy rule table in the fuzzy system representation of the bicubic spline function can be viewed as a gray scale image. Hence, the fuzzy rules provide a visual representation of the functions of two variables where the contours of different levels for the function are shown in different gray scale levels

• Journal of Korean Society of Industrial and Systems Engineering
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• v.39 no.1
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• pp.123-129
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• 2016

In the manufacturing industry fields, thousands of quality characteristics are measured in a day because the systems of process have been automated through the development of computer and improvement of techniques. Also, the process has been monitored in database in real time. Particularly, the data in the design step of the process have contributed to the product that customers have required through getting useful information from the data and reflecting them to the design of product. In this study, first, characteristics and variables affecting to them in the data of the design step of the process were analyzed by decision tree to find out the relation between explanatory and target variables. Second, the tolerance of continuous variables influencing on the target variable primarily was shown by the application of algorithm of decision tree, C4.5. Finally, the target variable, loss, was calculated by a loss function of Taguchi and analyzed. In this paper, the general method that the value of continuous explanatory variables has been used intactly not to be transformed to the discrete value and new method that the value of continuous explanatory variables was divided into 3 categories were compared. As a result, first, the tolerance obtained from the new method was more effective in decreasing the target variable, loss, than general method. In addition, the tolerance levels for the continuous explanatory variables to be chosen of the major variables were calculated. In further research, a systematic method using decision tree of data mining needs to be developed in order to categorize continuous variables under various scenarios of loss function.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.47-56
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• 2003

This note is concerned with some properties of fixed points and periodic points. First, we have constructed a generalized continuous function to give a proof for the fact that, as the reverse of the Sharkovsky theorem[16], for a given positive integer n, there exists a continuous function with a period-n point but no period-m points wherem is a predecessor of n in the Sharkovsky ordering. Also we show that the composition of two transcendental meromorphic functions, one of which has at least three poles, has infinitely many fixed points.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.773-778
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• 2009

Recently, Xue et al. [Computers and Mathematics with Applications 55 (2008) 1215-1224] proposed a formula for the expected value of a function of a fuzzy variable based on the assumption that the fuzzy variable has a continuous membership function. In conclusion, they remained the case where the membership function of the fuzzy variable is discontinuous for the future research, and then expected to get similar results. Thus this note is to propose a new formula for the expected value of a function of a general fuzzy variable which is not restricted on having a continuous membership function. Furthermore, we give an example which cannot be applied to the formula that Xue et al. proposed. We also use the same example given by Xue et al. to show how to apply the new formula.

• The Mathematical Education
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• v.60 no.4
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• pp.543-554
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• 2021

The dynamic geometric environment plays a positive role in solving students' geometric problems. Students can infer invariance in change through dragging, and help solve geometric problems through the analysis method. In this study, the continuous spectrum of the dynamic geometric environment can be used to solve problems of students. The continuous spectrum can be used in the 'Understand the problem' of Polya(1957)'s problem solving stage. Visually representation using continuous spectrum allows students to immediately understand the problem. The continuous spectrum can be used in the 'Devise a plan' stage. Students can define a function and explore changes visually in function values in a continuous range through continuous spectrum. Students can guess the solution of the optimization problem based on the results of their visual exploration, guess common properties through exploration activities on solutions optimized in dynamic geometries, and establish problem solving strategies based on this hypothesis. The continuous spectrum can be used in the 'Review/Extend' stage. Students can check whether their solution is equal to the solution in question through a continuous spectrum. Through this, students can look back on their thinking process. In addition, the continuous spectrum can help students guess and justify the generalized nature of a given problem. Continuous spectrum are likely to help students problem solving, so it is necessary to apply and analysis of educational effects using continuous spectrum in students' geometric learning.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.375-389
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• 2017

The purpose of this study is to analyze the difference and inter-connectivity between the definition of continuity in school mathematics and the definition of academic mathematics in four perspectives. These difference and inter-connectivity have not analyzed in previous papers. According to this study, the definition of 'continuity and discontinuity at one point' in school mathematics depends on the limit processing but in academic mathematics it depends on the topology of the domain. The target function of the continuous function in school mathematics is a function whose domain is limited to an interval or a union of intervals, but the target function of the continuous function in academic mathematics is all functions. Based on these results, the following two opinions are given in relation to the concept of continuity in school mathematics. First, since the notion of local continuity in school mathematics is based on limit processing, the contents of 2009-revised textbooks that deal with discontinuity at special point not belonging to the domain is appropriate. Here the discontinuity appears as types of infinite discontinuity, removable discontinuity, and step discontinuity. Second, the definition of a general continuous function is proposed to "if there is no discontinuity point in the domain of a function y = f(x), we call the function f a continuous function." This definition allows the discontinuity at special point in non-domain, but is consistent with the definition in academic mathematics.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.226-231
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• 1991

A graphic control language using function block diagram approach is designed and implemented, applicable to real-time control for continuous process automation system. The procedure implementing the control language is composed of three parts, editor, compiler, and executer. The editor generates the control algorithm file, which contains function block information in the text form, by menu-driven method on the color graphic screen. The compiler translates the contents of the control algorithm file to machine codes and their related data. Then, the executer generates a task that makes the machine codes executed at every sampling period in the target processor. The validity of the concept in its design and implementaion is assured by on-line simulation in the multi-function controller designed for continuous process automation.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.789-830
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• 2003

By forming completions of families of noncommutative polynomials, we define a notion of noncommutative continuous function and locally bounded Borel function that give a noncommutative analogue of the functional calculus for elements of commutative $C^{*}$-algebras and von Neumann algebras. These notions give a precise meaning to $C^{*}$-algebras defined by generator and relations and we show how they relate to many parts of operator and operator algebra theory.

• Journal of the Korean Institute of Intelligent Systems
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• v.1 no.2
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• pp.16-34
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• 1991

It has been widely accepted that expert systems must reason from multiple sources of information that is to some degree evidential - uncertain, imprecise, and occasionally inaccurate - called evidential information. Evidence theory (Dempster/Shafet theory) provides one of the most general framework for representing evidential information compared to its alternatives such as Bayesian theory or fuzzy set theory. Many expert system applications require evidence to be specified in the continuous domain - such as time, distance, or sensor measurements. However, the existing evidence theory does not provide an effective approach for dealing with evidence about continuous variables. As an extension to Strat's pioneeiring work, this paper provides a new combination rule, a new method for mass function transffrmation, and a new method for rendering joint mass fuctions which are of great utility in evidence theory in the continuous domain.