• 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.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.473-486
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• 2021

We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions. From these polynomial relations, we deduce interesting identities with Fibonacci and Lucas numbers, and Euler numbers. The results must be regarded as companion results to some Fibonacci-Bernoulli identities, which we derived in our previous paper.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.71-84
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• 2007

J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.

• Structural Engineering and Mechanics
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• v.69 no.5
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• pp.479-486
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• 2019

Based on the displacement general solution of a pre-twisted Euler-Bernoulli beam, the shape function and stiffness matrix are deduced, and a new finite element model is proposed. Comparison analyses are made between the new proposed numerical model based on displacement general solution and the ANSYS solution by Beam188 element based on infinite approach. The results show that developed numerical model is available for the pre-twisted Euler-Bernoulli beam, and that also provide an accuracy finite element model for the numerical analysis. The effects of pre-twisted angle and flexural stiffness ratio on the mechanical property are also investigated.

• Advances in materials Research
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• v.7 no.3
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• pp.163-174
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• 2018

This article studies the free and forced vibrations of the carbon nanotubes CNTs embedded in an elastic medium including thermal and dynamic load effects based on nonlocal Euler-Bernoulli beam. A Winkler type elastic foundation is employed to model the interaction of carbon nanotube and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, high temperature change, Winkler modulus parameter, vibration mode and aspect ratio of short carbon nanotubes on the vibration frequency are analyzed and discussed. The non-local Euler-Bernoulli beam model predicts lower resonance frequencies. The research work reveals the significance of the small-scale coefficient, the vibrational mode number, the elastic medium and the temperature change on the non-dimensional natural frequency.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.17-34
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• 2006

Inverse coefficient identification problems associated with the fourth-order Sturm-Liouville operator in the steady state Euler-Bernoulli beam equation are investigated. Unlike previous studies in which spectral data are used as additional information, in this paper only boundary information is used, hence non-destructive tests can be employed in practical applications.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.277-283
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• 2008

The paper deals with the values at the negative integers of a certain Dirichlet series related to the Riemann zeta function and with the expression of these values in terms of Bernoulli numbers.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.301-309
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• 2020

Recently, M. Masjed-Jamai et al. in ([6]-[7]) and Srivastava et al. in ([15]-[16]) considered the parametric type of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. They proved some theorems and gave some identities and relations for these polynomials. In this work, we define the parametric poly-tangent numbers and polynomials. We give some relations and identities for the parametric poly-tangent polynomials.

• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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• pp.201-210
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• 2024

In this paper, we construcr the q-Bernoulli-Fibonacci numbers and polynomials. Finally, we investigate the distribution of the zeros of the q-Bernoulli-Fibonacci polynomials by using computer.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.399-412
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• 2001

In this paper, we consider that the q-analogue of w$\omega-Bernoulli numbers\; B_i(\omega, q)$. And we calculate the sums of products of two q-analogue of $\omega-Bernoulli numbers B_i(\omega, q)$ in complex cases. From this result, we obtain the Euler type formulas of the Carlitz´s q-Bernoulli numbers $\beta_i(q)$ and q-Bernoulli numbers $B_i(q)$. And we also calculate the p-adic Stirling type series by the definition of $B_i(\omega, q)$ in p-adic cases.