• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.140-144
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• 2005

We investigate the P-generating functions, L-generating functions, and A-generating function, respectively induced by product t-norms, Lukasiewicz t-norms and additive semi-groups. Furthermore, we investigate the relations among them.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.591-601
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• 2009

In the present paper, one new generalized 'useful' information generating function and two new relative 'useful' information generating functions have been defined with their particular and limiting cases. It is interesting to note that differentiations of these information generating functions at t=0 or t=1 give some known and unknown generalized measures of useful information and 'useful' relative information. The information generating functions facilitates to compute various measures and that has been illustrated by applying these information generating functions for Uniform, Geometric and Exponential probability distributions.

• The Mathematical Education
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• v.63 no.3
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• pp.451-466
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• 2024

This study investigated elementary preservice teachers' conceptions of a generating line, an ambiguous concept in school mathematics. The preservice teachers' conceptions of a generating line can be classified into four types: (a) only cones have generating lines, (b) only cones and cylinders have generating lines, (c) solids of revolution have generating lines, (d) straight lines on the lateral surface are generating lines. 22.1% of all preservice teachers believed that only cones have generating lines, and most of them followed the definition of a generating line presented in elementary mathematics textbooks. The conception that only cones and cylinders have generating lines was the least investigated. However, since there were instances where generating lines were defined with the use of a director curve, it became important to explore topics more thoroughly, such as generating lines of a truncated cone. 27.9% of all preservice teachers believed that solids of revolution have generating lines. This conception was marked by differing opinions on whether spheres also have generating lines. The conception that straight lines on the lateral surface are generating lines was the most frequently investigated. This conception differs from the traditional view in school mathematics because it suggests using a director curve to define generating lines. Based on these analysis results, the researcher developed specific teaching methods that considered both subject matter knowledge and pedagogical content knowledge for preservice teachers. In addition, the researcher proposed a consensus definition of a generating line in mathematics education.

• Journal of The Korean Association For Science Education
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• v.24 no.4
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• pp.722-730
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• 2004

The purpose of this study was to test the notion that the inter-individual difference in hypothesis-generating is presumably detected by differentiating subjects' EEG correlation patterns of the prefrontal lobes. To test the notion of the inter-individual difference by EEG analysis, eight healthy undergraduate volunteers' EEG signals on the prefrontal lobes were recorded during hypothesis-generating and resting with eyes-closed condition. Their EEG signals were analyzed by time durations and transformed into correlation patterns. The results showed that subjects' EEG correlation patterns during hypothesis-generating were significantly different among individuals. In addition, the EEG correlation patterns were decreased during hypothesis-generating thinking. Furthermore, subject's EEG correlation showed a fluctuationpattern through-out hypothesis-generating, which is presumably caused by the difference of subjects' thinking activities in hypothesis-generating. This study also suggests a possibility that student's scientific thinking ability and the difficulty of scientific knowledge generating may be measured by the analysis of subject's EEG correlation pattern of the prefrontal lobes.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.475-489
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• 2012

A plateau in a Motzkin path is a sequence of three steps: an up step, a horizontal step, then a down step. We find three different forms for the bivariate generating function for plateaus in Motzkin paths, then generalize to longer plateaus. We conclude by describing a further generalization: a continued fraction form from which one can easily derive new multivariate generating functions for various kinds of path statistics. Several examples of generating functions are given using this technique.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.75-84
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• 2017

In recent years, several interesting families of generating functions for various classes of hypergeometric functions were investigated systematically. In the present paper, we introduce a new family of extended Wright type hypergeometric function and obtain several classes of generating relations for this extended Wright type hypergeometric function.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.429-438
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• 2015

In this paper, we discuss how the operational calculus can be exploited to the theory of mixed generating functions. We use operational methods associated with multi-variable Hermite polynomials, Laguerre polynomials and Bessels functions to drive identities useful in electromagnetism, fluid mechanics etc. Certain special cases giving bilateral generating relations related to these special functions are also discussed.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.325-333
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• 2019

Motivated by the results on generating functions investigated by H. Exton and many other authors, we derive certain (presumably) new generating functions for generalized Mittag-Leffler-type functions. Specifically, we introduce a new class of generating relations (which are partly bilateral and partly unilateral) involving the generalized Mittag-Leffler function. Also we present some special cases of our main result.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.691-696
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• 2000

Very recently Professor Exton derived an interesting hypergeometric generating relation. The authors aim at deriving another hypergeometric generating relation by using the same technique developed by Exton. Some interesting special cases have also been given.

• Journal of The Korean Association For Science Education
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• v.35 no.6
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• pp.1063-1074
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• 2015

In this study, we developed an analogy-generating strategy and applied this to a 7th grade science-gifted class. The types of analogies they generated, verbal interactions and analogy-generating patterns, and perceptions of five groups on the analogy-generating strategy were examined. The analyses of the results revealed that there was a higher proportion of the elaborated analogies in terms of quality generated by science-gifted students individually in the analogy-generating strategy than in general analogy-generating activity. After having small group activities, most small groups generated the elaborated analogies. The frequencies and percentages of verbal interactions of each sub-stage were found to be slightly different. Analogy-generating patterns in small groups were categorized into three types; selecting in-depth source, selecting inclusive source, and selecting surficial source. The elaborating patterns of mapping between a target concept and analogies were different among the types. Science-gifted students positively perceived in terms of its values and attitudes toward the analogy-generating strategy, and they responded that the analogy-generating strategy was helpful in generating more elaborated analogies and fostering creative thinking. Therefore the analogy-generating strategy is expected to generate positive impact on the creativity of science-gifted students.