• Journal for History of Mathematics
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• v.26 no.2_3
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• pp.131-148
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• 2013

Euler's formula provides the topological characteristics of geometrical objects including polyhedra, and so an important mathematical concept. Descriptions on Euler's formula had been in the textbooks according to the 3rd through 7th National Mathematics Curriculum. However, they are gone after that. In this study, we focus on Euler characteristic and Euler's formula as an educational material for educations for the gifted or after-school educations. We first look at the mathematical history and the applications of Euler's formula and national curriculums to search for its mathematical and educational meaning. We further make a suggestion for a learning environment which provides a better education relying on search activities, not just depending on memorization, illuminated from the education of Euler's formula.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.529-534
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• 2011

In this paper, we consider the q-analogues of Euler numbers and polynomials using the fermionic p-adic invariant integral on $\mathbb{Z}_p$. From these numbers and polynomials, we derive some interesting identities and properties on the q-analogues of Euler numbers and polynomials.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.623-630
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• 2013

In this paper, our aim is finding the term of generalized Eule polynomials. We also obtain some identities and relations involving the Bernoulli numbers, the Euler numbers and the Stirling numbers.

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.37-42
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• 2012

We give an elementary proof of Descartes' theorem for polyhedra. Since Descartes' theorem is equivalent to Euler's theorem for polyhedra, this also gives an elementary proof of Euler's theorem.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1007-1019
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• 2000

In this paper, we discuss a uniqueness problem for the Cauchy problem of the Euler equation. W give a sufficient condition on the vorticity to show the uniqueness of a class of generalized solution in terms of the generalized solution in terms o the generalized Besov space. The condition allows the iterated logarithmic singularity to the vorticity of the solution. We also discuss the break down (or blow up) condition for a smooth solution to the Euler equation under the related assumption.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.1081-1098
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• 2006

Mathematical analysis is made on a mesh free method for the compressible Euler equations. In particular, the Moving Least Square Reproducing Kernel (MLSRK) method is employed for space approximation. With the backward-Euler method used for time discretization, existence of discrete solution and it's $L^2-error$ estimate are obtained under a regularity assumption of the continuous solution. The result of numerical experiment made on the biconvex airfoil is presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.87-93
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• 2004

The E-Euler process has been proposed for autonomous dynamical systems in [7]. In this paper, the E-Euler process is extended to nonautonomous dynamical systems. When a discrete function is bounded or gradually decreases to ${\epsilon}\;<<\;1$ as $n\;{\rightarrow}\;{\infty}$, it is shown that the relative error converges to a constant or decreases.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.489-508
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• 2020

This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polylogarithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.

• Honam Mathematical Journal
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• v.29 no.1
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• pp.61-74
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• 2007

Th. M. Rassias obtained the Hyers-Ulam stability of the general Euler-Lagrange functional equation. In this paper we prove the stability of generlized Euler-Lagrange functional equations in the spirit of Hyers, Ulam, Rassias and G$\breve{a}$vruta.

• 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.