• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1377-1387
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• 2013

Let $f$ be a harmonic mapping on the unit disc ${\Delta}$ in $\mathbb{C}$. We give some condition for $f$ to be a quasiconformal homeomorphism on ${\Delta}$ and to have a quasiconformal extension to the whole plane $\bar{\mathbb{C}}$. We also obtain quasiconformal extension results for starlike harmonic mappings of order ${\alpha}{\in}(0,1)$.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.933-955
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• 2023

For any prime number p, let J(p) be the set of positive integers n such that the numerator of the n^th harmonic number in the lowest terms is divisible by this prime number p. We consider an extension of this set to the generalized harmonic numbers, which are a natural extension of the harmonic numbers. Then, we present an upper bound for the number of elements in this set. Moreover, we state an explicit condition to show the finiteness of our set, together with relations to Bernoulli and Euler numbers.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.269-278
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• 2008

Let ${\partial}D$ be the boundary of the open unit disk D in the complex plane and $L^p({\partial}D)$ the class of all complex, Lebesgue measurable function f for which $\{\frac{1}{2\pi}{\int}_{-\pi}^{\pi}{\mid}f(\theta){\mid}^pd\theta\}^{1/p}<{\infty}$. Let P be the orthogonal projection from $L^p({\partial}D)$ onto ${\cap}_{n<0}$ ker $a_n$. For $f{\in}L^1({\partial}D)$, ${\hat{f}}(z)=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}P_r(t-\theta)f(\theta)d{\theta}$ is the harmonic extension of f. Let ${\hat{P}}$ be the composition of P with the harmonic extension. In this paper, we will show that if $1, then ${\hat{P}}:L^p({\partial}D){\rightarrow}H^p(D)$ is bounded. In particular, we will show that ${\hat{P}}$ is unbounded on $L^{\infty}({\partial}D)$.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.12
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• pp.197-204
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• 2013

In this paper, we propose a new method for artificial bandwidth extension of narrow-band signal in frequency domain. In the proposed method, a narrow-band signal is decomposed into excitation signal and spectral envelope, which are extended independently in frequency domain. The excitation signal is extended such that low-band harmonic structure is maintained in high band, and the spectral envelope is extended based on sub-band energy using NMF. Finally, the spectral phase is determined based on signal correlation between frames in time domain, resulting in the final wide-band signal. The subjective evaluation verified that the wide-band signal generated by the proposed method has a higher quality than the original narrow-band signal.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.583-595
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• 2016

In the present note, we deal with $L^2$ harmonic 1-forms on complete submanifolds with weighted $Poincar{\acute{e}}$ inequality. By supposing submanifold is stable or has sufficiently small total curvature, we establish two vanishing theorems for $L^2$ harmonic 1-forms, which are some extension of the results of Kim and Yun, Sang and Thanh, Cavalcante Mirandola and $Vit{\acute{o}}rio$.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.357-363
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• 1995

We study non-existence of $L^2$-harmonic p-forms on a complete, non-compact Riemannian manifold without boundary as extension of results of K. Yano in the case of compact.

• MALSORI
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• no.49
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• pp.63-75
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• 2004

Most existing telephone speech transmitted in current public networks is band-limited to 0.3-3.4 kHz. Compared with wideband speech(0-8 kHz), the narrowband speech lacks low-band (0-0.3 kHz) and high-band(3.4-8 kHz) components of sound. As a result, the speech is characterized by the reduced intelligibility and a muffled quality, and degraded speaker identification. Bandwidth extension is a technique to provide wideband speech quality, which means reconstruction of low-band and high-band components without any additional transmitted information. Our new approach considers to exploit harmonic synthesis method for reconstruction of low-band speech over the CELP coded speech. A spectral distortion measurement and listening test are introduced to assess the proposed method, and the improvement of synthesized speech quality was verified.

• Proceedings of the KIPE Conference
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• 1999.07a
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• pp.667-670
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• 1999

An active power filter is used to eliminate harmonic currents. This paper applied the extension pq theory to harmonic currents compensation. An active power filter based on extension pq theory is more effective than pq theory in 3-phase unsymmetrical voltage system. When extension pq theory is used, the result of simulation present source current is not distorted. Pulse-width modulation method is CRPWM(Current-Regulated PWM).

• Communications of the Korean Mathematical Society
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• v.5 no.1
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• pp.119-122
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• 1990

• Korean Journal of Mathematics
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• v.1
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• pp.55-64
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• 1993