• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.677-688
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• 2018

In this paper, we introduce and investigate a new subclass of bi-univalent functions defined by $S{\breve{a}}l{\breve{a}}gean$ q-calculus operator in the open disk ${\mathbb{U}}$. For functions belonging to the subclass, we obtain estimates on the first two Taylor-Maclaurin coefficients ${\mid}a_2{\mid}$ and ${\mid}a_3{\mid}$. Some consequences of the main results are also observed.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.319-330
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• 2020

We introduce a new subclass of q-bi-univalent functions of complex order related to shell-like curves connected with the Fibonacci numbers. We obtain the coefficient estimates and Fekete-Szegö inequalities for the functions belonging to this class. Relevant connections with various other known classes have been illustrated.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.689-700
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• 2023

In this note, we establish a new subfamily of spirallike functions by making use of a generalized q-integral operator. We examine characterization rule for functions which are member of this subclass. We further obtain coefficient estimate, subordination results and integral mean inequalities for functions in this class. The Fekete-Szegö inequalities are also derived.

• Korean Journal of Mathematics
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• v.19 no.1
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• pp.65-75
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• 2011

We obtain multiplicity results for the nonlinear biharmonic problem with variable coefficient. We prove by the Leray-Schauder degree theory that the nonlinear biharmonic problem has multiple solutions for the biharmonic problem with the variable coefficient semilinear term under some conditions.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.125-135
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• 2012

We obtain the multiple solutions for the fourth order elliptic problem with a variable coefficient and a jumping semilinear term. We have a result that there exist at least two solutions if the variable coefficient of the semilinear term crosses some number of the eigenvalues of the biharmonic eigenvalue problem. We obtain this multiplicity result by applying the Leray-Schauder degree theory.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.455-462
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• 2012

The cyclic group $Cn={\langle}(12{\cdots}n){\rangle}$ acts on the set ($^{[n]}_k$) of all $k$-subsets of [$n$]. In this action of $C_n$ the number of orbits of size $d$, for $d|n$, is $$O^{n,k}_d=\frac{1}{d}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})(^{n/s}_{k/s})$$. Stanton and White[7] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)=\frac{1}{[d]_{q^{n/d}}}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})[^{n/s}_{k/s}]{_q}^s$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a combinatorial proof for the positivity of coefficients of the orbit polynomial $O^{n,3}_d(q)$.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.349-358
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• 2017

The cyclic group $C_n={\langle}(12{\cdots}n){\rangle}$ acts on the set $(^{[n]}_k)$ of all k-subsets of [n]. In this action of $C_n$ the number of orbits of size d, for d | n, is $$O^{n,k}_d={\frac{1}{d}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})(^{n/s}_{k/s})$$. Stanton and White [6] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)={\frac{1}{[d]_{q^{n/d}}}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})[^{n/s}_{k/s}]_{q^s}$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a constructive proof for the positivity of coefficients of the orbit polynomial $O^{n,2}_d(q)$.

• Journal of Korea Water Resources Association
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• v.43 no.5
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• pp.445-453
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• 2010

Energy loss at manholes, often exceeding friction loss of pipes under surcharged flow, is considered as one of the major causes of inundation in urban area. Therefore, it is necessary to analyze head losses at manholes, especially in case of surcharged flow. Hydraulic experimental apparatus which can change the manhole shape (square, circular) were installed for this study. In the experiments, two inflows ($Q_1,\;Q_2$) were varied from 0 to $4{\ell}$/sec and 15 combinations were tested in total. The flow ratios $Q_2/Q_3$ were varied from 0 to 1 for a total flow $Q_3$ ($Q_3=Q_1+Q_3$) of 2, 3, and $4{\ell}$/sec, respectively. The variation of head losses were strongly influenced by the lateral inflow because the head loss coefficient increases as the flow ratio $Q_2/Q_3$ increases. There was no significant difference of head loss between square manhole and circular one, and also no large variation of head loss as discharges change. The relation equations between K and $Q_2/Q_3$ were suggested in this paper.

• Korean Journal of Optics and Photonics
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• v.10 no.1
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• pp.53-57
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• 1999

We established the laser oscillator using Nd:YAG crystal grown at Ssang Yong company in Korea and investigated the characteristics of oscillation, Q-switching and wave front of output beam. We measured the single pass gain by controlling the threshold input energy with two output couplers of different output reflectances. Moreover, we compared the gain measured by different output couplers with the gain directly measured by the laser amplifier. The peak power of Q-switching, the pulse width, and the single pass gain coefficient at the threshold energy were 1.5 MW, 30ns, and 0.0958 cm-$^1$ respectively and they were compared with those of the commercial Nd:YAG crystal. Our crystal was proved to be as good as the commercial crystal.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.25 no.1
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• pp.108-113
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• 2014

This paper presents the influence on the transmission characteristics of swelling in rectangular waveguides for Q-band. We derived the Green's functions of the waveguide with eigenfunction expansion method. The reflection coefficient of the waveguide with a swelling is calculated by using internal impedance in order to investigate the influence of swelling in the waveguide. In order to check the validity of the theoretical analysis, the calculated reflection coefficients are compared with the measured results.