• 대한수학회보
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• 제50권4호
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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 ${\alpha}{\in}(0,1)$.

• 대한수학회보
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• 제60권4호
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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.

• 충청수학회지
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• 제21권2호
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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 $L^{\infty}({\partial}D)$.

• 전자공학회논문지
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• 제50권12호
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• pp.197-204
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• 2013

본 논문에서는 주파수 영역에서 협대역 신호를 광대역으로 확장하는 새로운 인공 대역 확장 기술을 제안한다. 제안한 기술은 협대역 신호를 여기 신호와 스펙트럼 포락선 성분으로 분리하고, 주파수 영역에서 각각 독립적인 방법으로 확장한다. 여기 신호는 저대역의 하모닉 구조가 고대역에서 유지되도록 확장하고, 스펙트럼 포락선은 부대역별 에너지를 기반으로 NMF방법으로 확장한다. 마지막으로 시간 축에서 프레임 사이의 상관관계를 기반으로 스펙트럼 위상을 결정하여 최종 광대역 신호를 생성한다. 주관적 청취 평가를 통하여 제안한 방법으로 대역 확장된 신호가 원 협대역 신호보다 음질이 향상된 것을 확인하였다.

• 대한수학회지
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• 제53권3호
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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 $Vit{\acute{o}}rio$.

• 대한수학회논문집
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• 제10권2호
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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.

• 대한음성학회지:말소리
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• 제49호
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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.

• 전력전자학회:학술대회논문집
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• 전력전자학회 1999년도 전력전자학술대회 논문집
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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).

• 대한수학회논문집
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• 제5권1호
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• pp.119-122
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• 1990

• Korean Journal of Mathematics
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• 제1권
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• pp.55-64
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• 1993