• Communications of Mathematical Education
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• v.10
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• pp.283-292
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• 2000

We shall introduce new concepts of near-rings, that is, strong reducibility and left semi ${\pi}$-regular near-rings. We will study every strong reducibility of near-ring implies reducibility of near-ring but this converse is not true, and also some characterizations of strong reducibility of near-rings. We shall investigate some relations between strongly reduced near-rings and left strongly regular near-rings, and apply strong reducibility of near-rings to the study of left semi ${\pi}$-regular near-rings, s-weekly regular near-rings and some other regularity of near-rings.

• East Asian mathematical journal
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• v.26 no.3
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• pp.397-401
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• 2010

We investigate some properties of strongly reduced near-rings and left regular near-rings, also show that a strongly reduced near-ring is reduced. Next, we will characterize that reducibility, strong reducibility and left regularity in near-rings.

• Korean Journal of Logic
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• v.20 no.1
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• pp.69-96
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• 2017

Wittgenstein criticizes explicitly Russell's theory of types and, in particular, his axiom of reducibility in the Tractatus Logico-Philosophicus. What, then, is the point of Wittgenstein's criticisms of Russell's theory of types? As a preliminary study to answer this question, I will examine how Wittgenstein criticized Russell's axiom of reducibility. Wittgenstein declares that Russell's axiom of reducibility is not a logical proposition, that if it is true it will be so mere by a happy chance and that "we can imagine a world in which the axiom of reducibility is not valid." What, then, is the ground for that? I will endeavor to show that by explicating the ideas of Wittgenstein's 1913 letter to Russell, those ideas decisively influenced on Ramsey's and Waismann's model which intended to show that the axiom of reducibility is not valid.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.587-591
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• 2009

The structure of a TL-subgroup can be understood from the representations of the TL-sub group as meets of TL-subgroups containing the TL-subgroup. Indeed, the structure of the meet of TL-subgroups can easily be obtained from the structures of the TL-subgroups and the structures of the TL-subgroups may be more simple than the structure of the meet. In this paper, we discuss meet-reducibility of TL-subgroups.

• Honam Mathematical Journal
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• v.31 no.2
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• pp.167-176
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• 2009

The aim of this paper is to obtain three interesting results for reducibility of Kamp$\'{e}$ de $\'{e}$riet function. The results are derived with the help of contiguous Gauss's second summation formulas obtained earlier by Lavoie et al. The results obtained by Bailey, Rathie and Nagar follow special cases of our main findings.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.187-189
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• 2008

We aim at presenting an interesting result for a reducibility of Exton's triple hypergeometric series $X_2$. The identity to be given here is obtained by combining Exton's Laplace integral representation for $X_2$ and Henrici's formula for the product of three hypergeometric series.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.53-56
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• 1985

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.69-76
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• 1996

We obtain some properties of reducible differential equations in the sense of Liapunov.

• Journal of the Korean Mathematical Society
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• v.25 no.2
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• pp.215-225
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• 1988

• East Asian mathematical journal
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• v.15 no.2
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• pp.247-253
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• 1999