• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권2호
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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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• 제27권3_4호
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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.

• 한국과학교육학회지
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• 제24권4호
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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.

• 충청수학회지
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• 제25권3호
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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.

• 대한수학회논문집
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• 제32권1호
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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.

• 대한수학회논문집
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• 제30권4호
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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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• 제59권2호
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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.

• 대한수학회논문집
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• 제15권4호
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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.

• 한국과학교육학회지
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• 제35권6호
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• pp.1063-1074
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• 2015

이 연구에서는 비유 생성 전략을 개발하여 이를 중학교 1학년 과학영재 수업에 적용하였다. 그리고 이 수업에서 5개 소집단의 과학영재들이 생성한 비유의 유형 및 과학영재들의 언어적 상호작용 양상과 비유 생성 패턴 및 비유 생성 전략에 대한 과학영재들의 인식을 조사하였다. 분석 결과, 비유 생성 전략을 활용한 수업에서 과학영재들이 개별적으로 생성한 비유는 일반적인 비유 생성 활동에서 보다 질이 좋은 유형의 비율이 높았으며, 소집단 활동을 거친 후에는 대부분 가장 좋은 유형의 비유를 생성하였다. 과학영재들의 언어적 상호작용은 각 단계의 영역별 하위 범주의 상호작용의 빈도 및 비율에서 약간 다른 경향이 나타났다. 그리고 소집단별 비유 생성 패턴은 심층적 소재 선택형, 포괄적 소재 선택형, 표면적 소재 선택형의 세 가지 유형이 나타났으며, 각 유형별로 대응 정교화 패턴이 다르게 나타났다. 과학영재들은 비유 생성 전략의 가치 및 태도 측면에서 긍정적으로 인식하고 있었으며, 비유 생성 전략이 더 정교한 비유를 생성하고, 창의적 사고를 하는데 도움이 되었다고 응답하였다. 따라서 비유 생성 전략은 과학영재들의 창의성 신장에 긍정적인 영향을 줄 것으로 기대된다.

• 호남수학학술지
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• 제34권3호
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• pp.327-340
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• 2012

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subsequently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. Very recently, Choi defined a $q$-extension of the generalized two variable Gottlieb polynomials ${\varphi}^2_n({\cdot})$ and presented their several generating functions. Also, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in m variables to give two generating functions of the generalized Gottlieb polynomials ${\varphi}^m_n({\cdot})$. Here, in the sequel of the above results for their possible general $q$-extensions in several variables, again, we aim at trying to define a $q$-extension of the generalized three variable Gottlieb polynomials ${\varphi}^3_n({\cdot})$ and present their several generating functions.