• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.45-56
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• 2015

In this paper, we study the relation between two dynamical systems (V, f) and (V, g) with $f{\circ}g=g{\circ}f$. As an application, we show that an endomorphism (respectively a polynomial map with Zariski dense, of bounded Preper(f)) has only finitely many endomorphisms (respectively polynomial maps) of bounded degree which are commutable with f.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.955-964
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• 2015

Let K be a number field and let S be a finite set of primes of K containing all the infinite ones. Let ${\alpha}_0{\in}{\mathbb{A}}^1(K){\subset}{\mathbb{P}}^1(K)$ and let ${\Gamma}_0$ be the set of the images of ${\alpha}_0$ under especially all Chebyshev morphisms. Then for any ${\alpha}{\in}{\mathbb{A}}^1(K)$, we show that there are only a finite number of elements in ${\Gamma}_0$ which are S-integral on ${\mathbb{P}}^1$ relative to (${\alpha}$). In the light of a theorem of Silverman we also propose a conjecture on the finiteness of integral points on an arbitrary dynamical system on ${\mathbb{P}}^1$, which generalizes the above finiteness result for Chebyshev morphisms.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2016.05a
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• pp.627-629
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• 2016

Open source software when promoting development in R&D has many advantages and is becoming an open software - based R&D projects continuously created in a number of countries. However, there are still limits to the creation of effective performance in R&D projects, as well as difficulty of the project implementation because it not yet established an appropriate management plan for the open source R&D projects in the public sector. Therefore, through investigating a number of previous studies and practices, we intend to enhance the effectiveness of the system by suggesting concrete measures for promoting and managing open source nature in a preperiodic point of view on the public sector open source software R&D projects.