• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.263-271
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• 2010

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, such as the Reidemeister set does in Nielsen fixed point theory. In this paper, using Heath and You's methods on Nielsen type numbers, we show that these numbers can be evaluated by the set of essential orbit classes under suitable hypotheses, and obtain some formulas in some special cases.

• East Asian mathematical journal
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• v.28 no.2
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• pp.135-158
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• 2012

The ideals of the rings of integers are used to induce rational number system as operators(=group homomorphisms). We modify this inducing method to be effective in teaching rational numbers in secondary school. Indeed, this modification provides a nice model for explaining the equality property to define addition and multiplication of rational numbers. Also this will give some explicit ideas for students to understand the concept of 'field' efficiently comparing with the integer number system.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.315-322
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• 2014

In this paper, we observe the behavior of complex roots of the tangent polynomials $T_n(x)$, using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the tangent polynomials $T_n(x)$. Finally, we give a table for the solutions of the tangent polynomials $T_n(x)$.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.14-17
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• 2003

By Mazur's theorem, the convex hull of a relatively compact subset a Banach space is also relatively compact. But this is not true any more in the space of fuzzy numbers endowed with the Hausdorff-Skorohod metric. In this paper, we establish a necessary and sufficient condition for which the convex hull of K is also relatively compact when K is a relatively compact subset of the space F(R$\^$k/) of fuzzy numbers of R$\^$k/ endowed with the Hausdorff-Skorohod metric.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.225-232
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• 2015

We consider Witt-type formula for the extension of Changchee and Daehee numbers and polynomials. We derive some identities and properties of those numbers and polynomials which are related to special polynomials.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.603-608
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• 2021

Fix k ≥ 3. If a multiplicative function f satisfies f(x₁ + x₂ + ⋯ + x_k) = f(x₁) + f(x₂) + ⋯ + f(x_k) for arbitrary positive triangular numbers x₁, x₂, …, x_k, then f is the identity function. This extends Chung and Phong's work for k = 2.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.695-704
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• 2023

Area problems for triangles and polygons whose vertices have Fibonacci numbers on a plane were presented by A. Shriki, O. Liba, and S. Edwards et al. In 2017, V. P. Johnson and C. K. Cook addressed problems of the areas of triangles and polygons whose vertices have various sequences. This paper examines the conditions of triangles and polygons whose vertices have Lucas sequences and presents a formula for their areas.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.305-315
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• 2015

Recently, Jianxin Liu, Hao Pan and Yong Zhang in [On the integral of the product of the Appell polynomials, Integral Transforms Spec. Funct. 25 (2014), no. 9, 680-685] established an explicit formula for the integral of the product of several Appell polynomials. Their work generalizes all the known results by previous authors on the integral of the product of Bernoulli and Euler polynomials. In this note, by using a special case of their formula for Euler polynomials, we shall provide several reciprocity relations between the special values of Tornheim's multiple series.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.1055-1075
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• 2010

In presented paper there were studied some properties of Benford's law. The existence of this law in not necessary large sets of numbers is a very interesting example that can show how the complex phenomena can appear in the positional number systems. Such systems seem to be very simple and intuitive and help us proceed with numbers. However, their simplicity in the case of usage in our lifetime is not necessary connected with the simplicity in the case of laws that govern them. Even if this laws indicate the existence of self-similar properties.

• The Korean Journal of Malacology
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• v.3 no.1
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• pp.24-34
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• 1987

The melaniid snails belonging to genus Semisulcospira were collected in the Kangwha and Yonchon areas of Korea in 1986 through 1987 in order to carry out a cytotaxonomic study, The snails were first narcotized with menthol and fixed with 70% ethyl alcohol for morphological identification. The gonads of adult snails were used for chromosome analyses by the technique of Imai et al. (1977) with minor modification. Slide preparations were observed under high power fields using a Leitz light miscroscope. The results obtained in the present stuedy are summarized as follows: 1)The sanils collected from Kangwha and Yonchon areas were identified as Semisulcospira forticosta(Martens, 1886)and S. gottschei (Martens, 1886) respectively.2)No specific differences were obwerved in details of the chromosome cycle between S. forticosta and S. gottschei.3) Diploid chromosome numbers observed at mitotic metaphase were 36. There was no difference in chromosome numbers between S. forticosta and S. gottschei.4) There were morphological differences in the karyotypes of the two species. The spermatogonial metaphase karyotype of S. forticosta consists of six pairs of metacentric, eleven pairs of submetacentric, and one pair of acrocentric chromosomes. The spermatogonial metaphase karyotype of S. gottschei consists of five pairs of metacentric, tselve pairs of submetacentric, and one pair of acrocentric chromosomes. Summarizing the aboxe results, the two species of Semisulcospira employed in this study have same chromosome numbers(2n=36)with different karyotypes.