• East Asian mathematical journal
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• v.36 no.3
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• pp.331-335
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• 2020

We consider HNN extensions 〈B, t : t^―1Ht = K〉, where H, K are in the center of B. We show that conjugating automorphisms of those HNN extensions are inner if B satisfies certain conditions.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.45-50
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• 1997

The purpose of this paper is to give a characterization of automorphisms of the weighted Lotka-Volterra algebra $(A,\omega)$ at idempotent elements and to offer a condition that $(A,\omege)$ becomes a Jordan algebra.

• East Asian mathematical journal
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• v.37 no.3
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• pp.307-317
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• 2021

In this paper, we deal with a problem to determine the type of automorphisms of the unit disc in ℂ in terms of intrinsic geometry. We will characterize the hyperbolicity and parabolicity of automorphism by the distance function of the Poincaré metric.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.6
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• pp.1492-1511
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• 2013

A novel, chaotic map that is based on concatenated torus automorphisms is proposed in this paper. As we know, cat map, which is based on torus automorphism, is highly chaotic and is often used to encrypt information. But cat map is periodic, which decreases the security of the cryptosystem. In this paper, we propose a novel chaotic map that concatenates several torus automorphisms. The concatenated mechanism provides stronger chaos and larger key space for the cryptosystem. It is proven that the period of the concatenated torus automorphisms is the total sum of each one's period. By this means, the period of the novel automorphism is increased extremely. Based on the novel, concatenated torus automorphisms, two application schemes in image encryption are proposed, i.e., 2D and 3D concatenated chaotic maps. In these schemes, both the scrambling matrices and the iteration numbers act as secret keys. Security analysis shows that the proposed, concatenated, chaotic maps have strong chaos and they are very sensitive to the secret keys. By means of concatenating several torus automorphisms, the key space of the proposed cryptosystem can be expanded to $2^{135}$. The diffusion function in the proposed scheme changes the gray values of the transferred pixels, which makes the periodicity of the concatenated torus automorphisms disappeared. Therefore, the proposed cryptosystem has high security and they can resist the brute-force attacks and the differential attacks efficiently. The diffusing speed of the proposed scheme is higher, and the computational complexity is lower, compared with the existing methods.

• Kyungpook Mathematical Journal
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• v.12 no.2
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• pp.263-266
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• 1972

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.603-611
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• 2020

In this manuscript, we discuss the relationship between prime rings and automorphisms satisfying differential identities involving commutators and anti-commutators on Lie ideals. In addition, we provide an example which shows that we cannot expect the same conclusion in case of semiprime rings.

• East Asian mathematical journal
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• v.30 no.3
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• pp.293-302
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• 2014

In this paper we provide a rigorous proof for the fact that there are exactly 8 connected Alexander quandles of order $2^5$ by combining properties of fixed point free automorphisms of finite abelian 2-groups and the classification of conjugacy classes of GL(5, 2). Furthermore we verify that six of the eight associated Alexander modules are simple, whereas the other two are semisimple.

• East Asian mathematical journal
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• v.39 no.1
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• pp.11-21
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• 2023

Non-trivial automorphisms of the unit disc in the complex plane can be classified by three classes; elliptic, parabolic and hyperbolic automorphisms. This classification is due to a representation in the projective special linear group of the real field, or in terms of fixed points on the closure of the unit disc. In this paper, we will characterize this classification by the distance function of the Poincaré metric on the interior of the unit disc.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.709-718
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• 2023

The inner automorphism groups of quandles are related to the classification problem of quandles. The inner automorphism group of a quandle is generated by inner automorphisms which are presented by columns in the operation table of the quandle. In this paper, we describe inner automorphisms of an abelian extension of a quandle by expressing columns of the operation table of the extended quandle as columns of the operation table of the original quandle. Such a description will be helpful in studying inner automorphism groups of abelian extensions of quandles.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.411-415
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• 2012

In 1995 it was proved by Gonz$\acute{a}$lez-Diez that the cyclic group generated by a p-gonal automorphism of a closed Riemann surface of genus at least two is unique up to conjugation in the full group of conformal automorphisms. Later, in 2008, Gromadzki provided a different and shorter proof of the same fact using the Castelnuovo-Severi theorem. In this paper we provide another proof which is shorter and is just a simple use of Sylow's theorem together with the Castelnuovo-Severi theorem. This method permits to obtain that the cyclic group generated by a conformal automorphism of order p of a handlebody with a Kleinian structure and quotient the three-ball is unique up to conjugation in the full group of conformal automorphisms.