• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.523-531
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• 2013

In this paper we construct a new type of $q$-Bernstein polynomials related to $q$-Euler numbers and polynomials with weak weight ${\alpha}$ ; $E^{(\alpha)}_{n,q}$, $E^{(\alpha)}_{n,q}(x)$ respectively. Some interesting results and relationships are obtained.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.599-609
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• 2017

We construct degenerated Euler polynomials of the second kind and find some basic properties of this polynomials. From this paper, we can see degenerated alternative power sum is defined and is related to degenerated Euler polynomials of the second kind. Using this power sum, we have a number of symmetric properties of degenerated Euler polynomials of the second kind.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.205-215
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• 2017

In this paper, we consider a modified Euler polynomials ${\tilde{E}}_{n,q}(x)$ with variable $[x]_q$ and investigate some interesting properties of the Euler polynomials. We also give some relationships between the modified Euler polynomials and their Hurwitz zeta function. Finally, we derive some identities associated with Bernstein polynomials.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.867-879
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• 2014

It is known that the orbifold Euler characteristic $e_{orb}(S)$ of a log del Pezzo surface S of rank one satisfies the inequality $0{\leq}e_{orb}(S){\leq}3$. In this note, we show that the orbifold Euler characteristic of S is strictly positive, i.e., 0 < $e_{orb}(S)$. Moreover, we also show, by construction, the existence of log del Pezzo surfaces of rank one with arbitrarily small orbifold Euler characteristic.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.463-469
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• 2014

In this paper, we construct new q-extension of Euler polynomials with weight 0. These modified q-Euler polynomials are useful to study various identities of Carlitz's q-Bernoulli numbers.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.67-77
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• 1999

For a orientation-shift model supported on the unit sphere, Euler angles are the conventional measure to parametrize orientation-shifts. The essential role which is played by rotationally symmetry of an underlying distribution is reviewed. In this paper we propose the inference procedure based on Euler angles for the rotationally symmetric spherical distribution. The likelihood ratio test(LRT) based on the Euler angles is worked out. The asymptotic distribution of the test under the null hypotheses and certain contiguous alternatives is obtained.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.491-499
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• 2005

Recently, Kim[2,6] has introduced an interesting Euler­Barnes' numbers and polynomials. In this paper, we construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their properties.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.397-406
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• 1997

In this paper we introduce GESS method and show that dynamics of the system ｙ＇=A(s,t,y) ｙ is more faithfully approxi-mated by GESS method that by Euler method. Numerical experiments are given for the comparison of GESS method with Euler method.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.449-457
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• 2017

In this paper, we shall provide several properties of Dedekind sums with quasi-periodicity Euler functions. In particular, we present a representation of these Dedekind sums in terms of the Eulerian functions and the tangent functions.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.107-114
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• 2018

In this paper, we give some identities for the higher-order Euler functions arising from the Fourier series of them. In addition, we investigate some formulae related to Bernoulli functions which are derived from our identities.