• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.587-597
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• 2017

In this paper we define the (p, q)-analogue of Bernoulli numbers and polynomials by generalizing the Bernoulli numbers and polynomials, Carlitz's type q-Bernoulli numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Bernoulli numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Bernoulli polynomials by using computer.

• 대한수학회논문집
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• 제35권3호
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• pp.759-771
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• 2020

In this article, a hybrid class of the q-Hermite based Apostol type Frobenius-Genocchi polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating function methods. Furthermore, we consider some relationships for q-Hermite based Apostol type Frobenius-Genocchi polynomials of order α associated with q-Apostol Bernoulli polynomials, q-Apostol Euler polynomials and q-Apostol Genocchi polynomials.

• 대한수학회지
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• 제38권1호
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• pp.101-123
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• 2001

For a linear operator Q from R(sup)d into R(sup)d and 0$\alpha$ and parameter b on the other. characterization of strictly (Q,b)-semi-stable distributions among (Q,b)-semi-stable distributions is made. Existence of (Q,b)-semi-stable distributions which are not translation of strictly (Q,b)-semi-stable distribution is discussed.

• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.397-404
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• 2012

In this article, the reverse q-H$\ddot{o}$lder type inequality and two dimensional q-H$\ddot{o}$lder's inequality are established. We also obtain some q-integral inequalities by using q-H$\ddot{o}$lder's inequality which give q-Hardy's inequalities as spacial cases.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.805-811
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• 2010

It is the aim of this paper to observe an interesting phenomenon of 'scattering' of the zeros of the q-Bernoulli polynomials $B_{n,q}(x)$ for -1 < q < 0 in complex plane. Observe that the structure of the zeros of the Genocchi polynomials $G_n(x)$ resembles the structure of the zeros of the q-Bernoulli polynomials $B_{n,q}(x)$ as q $\rightarrow$ -1.

• East Asian mathematical journal
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• 제19권1호
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• pp.133-150
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• 2003

This paper will show that the relation (1.1) $$L^1({\Omega}){\subset}C_0(\bar{\Omega}){\subset}H_{p,q}$$ if 1/p'-1/n(1-2/q')<0 where p'=p/(p-1) and q'=q/(q-1) where $H_{p.q}=(W^{1,p}_0,W^{-1,p})_{1/q,q}$. We also intend to investigate the control problems for the retarded systems with $L^1(\Omega)$-valued controller in $H_{p,q}$.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1277-1284
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• 2010

One purpose of this paper is to consider the reflection symmetries of the q-Genocchi polynomials $G^*_{n,q}(x)$. We also observe the structure of the roots of q-Genocchi polynomials, $G^*_{n,q}(x)$, using numerical investigation. By numerical experiments, we demonstrate a remarkably regular structure of the real roots of $G^*_{n,q}(x)$.

• 대한수학회지
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• 제44권4호
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• pp.915-929
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• 2007

The main result of this paper is to construct the derivative twisted p-adic (h, q)-L-functions at s = 0. We obtain twisted version of Theorem 4 in [17]. We also obtain twisted (h, q)-extension of Proposition 1 in [3].

• 대한수학회논문집
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• 제33권1호
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• pp.207-236
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• 2018

We obtain recursion formulas for q-hypergeometric and q-Appell series. We also find recursion formulas for the general double q-hypergeometric series. It is shown that these recursion relations can be expressed in terms of q-derivatives of the respective q-hypergeometric series.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2003년도 춘계 학술발표회논문집
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• pp.77-84
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• 2003

For stochastic strong ground motion simulation, frequency-dependent Q model (= $Q_{o}$ $f^{η}$) were evaluated for major geographical blocks according to the epicentral distance ranges by using a lateral Q tomography technique. The inversed Q results were used to qualitatively identify seismic albedos of each Q blocks and were compared with the previous Q studies. In addition, a functional Q model calibrated to the low frequency spectra of local earthquakes were suggested especially for use in analysing large and distant regional earthquake events.s.