• Communications of Mathematical Education
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• v.26 no.1
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• pp.51-69
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• 2012

The cognition of an intrinsic attribute play an important role in the process of theoretical generalization. It is the aim of this paper to study how the theoretical generalization is made. First of all, we suggest the What-if-only-strategy(WIOS) which is the strategy helping the cognition of an intrinsic attribute. And we propose the process of the theoretical generalization that go on the cognitive stage, WIOS stage, conjecture stage, justification stage and insight into an intrinsic attribute in order. We propose the process of generalization adding the concrete process cognizing an intrinsic attribute to the existing process of generalization. And we applied the proposed process of generalization to two mathematical theorem which is being managed in middle school. We got a conclusion that the what-if-only strategy is an useful method of generalization for the proposition. We hope that the what-if-only strategy is helpful for both teaching and learning the mathematical generalization.

• The Mathematical Education
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• v.51 no.4
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• pp.377-393
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• 2012

The understanding demands the different degree of the understanding according to student's learning situation. In this paper, we investigate what is the foundation for the complete understanding for the generalization in the generalization-process and justification of some concepts or some theories, through a case. We discovered that the completeness of the understanding in the generalization-process and justification requires 'the meaningful-mental object' which can give the meaning about the concept or theory to students. Students can do the generalization-process through the construction of 'the meaningful-mental object' and confirm the validity of generalization through 'the meaningful-mental object' which is constructed by them. And we can judge the whether students construct the completeness of the understanding or not, by 'the meaningful-mental object' of the student. Hence 'the meaningful-mental object' are vital condition for the generalization-process and justification.

• East Asian mathematical journal
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• v.16 no.2
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• pp.401-407
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• 2000

We give a generalization of the Bateman's polynomial $F_n(x)$ and also give two generating functions for the generalized polynomial.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.217-222
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• 1999

The aim of this research is to provide a generalization of the well-known, interesting and useful identity due to Preece by using classical Dixon`s theorem on a sum of \ulcornerF\ulcorner.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.429-437
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• 2014

Motivated by the recent investigations of several authors, in this paper we present a generalization of a result obtained recently by Choi et al. ([3]) involving hypergeometric identities. The result is obtained by suitably applying fractional calculus method to a generalization of the hypergeometric transformation formula due to Kummer.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.49-59
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• 2017

In this paper, a generalization of the exponential integral is given. As a consequence, several inequalities involving the generalized function are derived. Among other analytical techniques, the procedure utilizes the $H{\ddot{o}}lder^{\prime}s$ and Minkowskis inequalities for integrals.

• The KIPS Transactions:PartD
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• v.9D no.4
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• pp.543-554
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• 2002

GIS (Geographic Information Systems) need faster access and better visualization. For faster access and better visualization in GIS, map generalization and levels of detail are needed. Existing spatial indexing methods do not support map generalization. Also, a few existing spatial indexing methods supporting map generalization do not support ail map generalization operations. We propose a new index structure, i.e. the LR-tree, supporting ail map generalization operations. This paper presents algorithms for the searching and updating the LR-tree and the results of performance evaluation. Our index structure works better than other spatial indexing methods for map generalization.

• The Pure and Applied Mathematics
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• v.6 no.1
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• pp.33-37
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• 1999

We obtain a generalization of Behera and Panda's result on nonlinear scalar case to the vector version.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.563-572
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• 2008

In this paper, we discuss about a generalization of the Key Distribution Pattern which was proposed by C. Mitchell and F. Piper[6]. It is allowing secure communication between every n-pair of users($n\leq2$) in a large network for reducing storage requirements. We further suggest a generalization of K. Quinn's bounds in [9] for the number of subkeys in such general Key Distribution Patterns.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.83-85
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• 1985

Let K be a real function field over a real closed field F. Then there exists an F-place .phi.:K.rarw.F.cup.{.inf.}. This is Lang's Existence of Rational Place Theorem (6). There is an equivalent version of Lang's Theorem in (4). That is, if K is a function field over a field F, then, for any ordering P$_{0}$ on F which extends to K, there exists an F-place .phi.: K.rarw.F'.cup.{.inf.} where F' is a real closure of (F, P$_{0}$). In [2], Knebusch pointed out the converse of the version of Lang's Theorem is also true. By a valuation theoretic approach to Lang's Theorem, we have found out the following generalization of Lang and Knebusch's Theorem. Let K be an arbitrary extension field of a field F. then an ordering P$_{0}$ on F can be extended to an ordering P on K if there exists an F-place of K into some real closed field R containing F. Of course R$^{2}$.cap.F=P$_{0}$. The restriction K being a function field of F is vanished, though the codomain of the F-place is slightly varied. Therefore our theorem is a generalization of Lang and Knebusch's theorem.