• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.983-1002
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• 2021

We investigate the non-existence of finite order transcendental entire solutions of Fermat-type differential-difference equations [f(z)f'(z)]ⁿ + P²(z)f^m(z + 𝜂) = Q(z) and [f(z)f'(z)]ⁿ + P(z)[∆_𝜂f(z)]^m = Q(z), where P(z) and Q(z) are non-zero polynomials, m and n are positive integers, and 𝜂 ∈ ℂ \ {0}. In addition, we discuss transcendental entire solutions of finite order of the following Fermat-type differential-difference equation P²(z) [f^(k)(z)]² + [αf(z + 𝜂) - 𝛽f(z)]² = e^r(z), where $P(z){\not\equiv}0$ is a polynomial, r(z) is a non-constant polynomial, α ≠ 0 and 𝛽 are constants, k is a positive integer, and 𝜂 ∈ ℂ \ {0}. Our results generalize some previous results.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1443-1455
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• 2017

Let $M_{z^N}(N{\in}{\mathbb{Z}}^d_+)$ be a bounded multiplication operator on a class of Hilbert spaces with orthogonal basis $\{z^n:n{\in}{\mathbb{Z}}^d_+\}$. In this paper, we prove that each reducing subspace of $M_{z^N}$ is the direct sum of some minimal reducing subspaces. For the case that d = 2, we find all the minimal reducing subspaces of $M_{z^N}$ ($N=(N_1,N_2)$, $N_1{\neq}N_2$) on weighted Bergman space $A^2_{\alpha}({\mathbb{B}}_2)$(${\alpha}$ > -1) and Hardy space $H^2({\mathbb{B}}_2)$, and characterize the structure of ${\mathcal{V}}^{\ast}(z^N)$, the commutant algebra of the von Neumann algebra generated by $M_{z^N}$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.991-1002
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• 2020

We show that when n > m, the following delay differential equation fⁿ(z)f'(z) + p(z)(f(z + c) - f(z))^m = r(z)e^q(z) of rational coefficients p, r doesn't admit any transcendental entire solutions f(z) of finite order. Furthermore, we study the conditions of α₁, α₂ that ensure existence of transcendental meromorphic solutions of the equation fⁿ(z) + f^n-2(z)f'(z) + P_d(z, f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z). These results have improved some known theorems obtained most recently by other authors.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.755-772
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• 2023

Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) and Fox-Wright function _rΨ_s(z).

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.179-188
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• 2006

For a given p-valent analytic function g with positive coefficients in the open unit disk $\Delta$, we study a class of functions $f(z) = z^p - \sum\limits{_{n=m}}{^\infty} a_nz^n(a_n{\geq}0)$ satisfying $$\frac 1 {p}{\Re}\;(\frac {z(f*g)'(z)} {(f*g)(z)})\;>\;\alpha\;(0{\leq}\;\alpha\;<\;1;z{\in}{\Delta})$$ Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special cases.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.687-696
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• 2013

In this note, we completely characterize the reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on $A^2_{\alpha}(D^2)$ where ${\alpha}$ > -1 and N, M are positive integers with $N{\neq}M$, and show that the minimal reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on the unweighted Bergman space and on the weighted Bergman space are different.

• Journal of Sensor Science and Technology
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• v.13 no.2
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• pp.101-109
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• 2004

This paper presents a novel z-axis accelerometer with perfectly aligned vertical combs fabricated using the extended sacrificial bulk micromachining (extended SBM) process. The z-axis accelerometer is fabricated using only one (111) SOI wafer and two photo masks without wafer bonding or CMP processes as used by other research efforts that involve vertical combs. In our process, there is no misalignment in lateral gap between the upper and lower comb electrodes, because all critical dimensions including lateral gaps are defined using only one mask. The fabricated accelerometer has the structure thickness of $30{\mu}m$, the vertical offset of $12{\mu}m$, and lateral gap between electrodes of $4{\mu}m$. Torsional springs and asymmetric proof mass produce a vertical displacement when an external z-axis acceleration is applied, and capacitance change due to the vertical displacement of the comb is detected by charge-to-voltage converter. The signal-to-noise ratio of the modulated and demodulated output signal is 80 dB and 76.5 dB, respectively. The noise equivalent input acceleration resolution of the modulated and demodulated output signal is calculated to be $500{\mu}g$ and $748{\mu}g$. The scale factor and linearity of the accelerometer are measured to be 1.1 mV/g and 1.18% FSO, respectively.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.453-468
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• 2022

In this article, we define a module M to be G^z-extending if and only if for each z-closed submodule X of M there exists a direct summand D of M such that X ∩ D is essential in both X and D. We investigate structural properties of G^z-extending modules and locate the implications between the other extending properties. We deal with decomposition theory as well as ring and module extensions for G^z-extending modules. We obtain that if a ring is right G^z-extending, then so is its essential overring. Also it is shown that the G^z-extending property is inherited by its rational hull. Furthermore it is provided some applications including matrix rings over a right G^z-extending ring.

• Proceedings of the Korean Magnestics Society Conference
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• 2007.05a
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• pp.235.2-235.2
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• 2007

• Clinical and Experimental Pediatrics
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• v.61 no.7
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• pp.226-230
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• 2018

Purpose: This pilot study assessed changes in the growth plate and growth rates in children during a 6-month period. Methods: The study included 31 healthy children (17 boys, 14 girls) under evaluation for growth retardation. Height, weight, bone age, insulin like growth factor-1 (IGF-1), and insulin like growth factor binding protein 3 (IGF-BP3) were measured at baseline and after 6 months. In addition, the diameter, thickness, and volume of the femoral and tibial growth plates were measured using magnetic resonance imaging. Results: The mean bone age in boys and girls was 11.7 and 10.7 years, respectively. In boys, height (z score) (-0.2 vs. 0.0), weight (z score) (0.8 vs. 1.1), body mass index (BMI) (z score) (1.27 vs. 1.5), IGF-1 (ng/mL) (343.6 vs. 501.8), and IGF-BP3 (ng/mL) (5,088.5 vs. 5,620.0) were significantly higher after 6 months. In girls, height (z score) (-1.0 vs. -0.7), weight (z score) (-0.5 vs. 0.1), BMI (z score) (-0.02 vs. 0.3), IGF-1 (ng/mL) (329.3 vs. 524.6), and IGF-BP3 (ng/mL) (4,644.4 vs. 5,593.6) were also significantly higher after 6 months. In both sexes, the mean diameter and volume of the femoral and tibial growth plates were significantly increased 6 months later. Conclusion: No significant correlation was found between changes in the growth plate and clinical parameters in children with growth retardation in this study, other than correlations of change in femoral diameter with weight and BMI. A larger, long-term study is needed to precisely evaluate the correlation between change in the growth plate and growth.