• 대한수학회논문집
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• 제29권3호
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• pp.409-413
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• 2014

In this paper, we study some quantity equivalent to the norm of Bloch to $A^p_{\alpha}$ composition operator where Ap $A^p_{\alpha}$ is the weighted Bergman space on the unit ball of $\mathbb{C}^n$ (0 < p < ${\infty}$ and -1 < ${\alpha}$ < ${\infty}$).

• 대한수학회보
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• 제53권1호
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• pp.247-262
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• 2016

We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

• Current Optics and Photonics
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• 제5권4호
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• pp.431-443
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• 2021

Sparse unmixing has been proven to be an effective method for hyperspectral unmixing. Hyperspectral images contain rich spectral and spatial information. The means to make full use of spectral information, spatial information, and enhanced sparsity constraints are the main research directions to improve the accuracy of sparse unmixing. However, many algorithms only focus on one or two of these factors, because it is difficult to construct an unmixing model that considers all three factors. To address this issue, a novel algorithm called multiview-based spectral weighted and low-rank row-sparsity unmixing is proposed. A multiview data set is generated through spectral partitioning, and then spectral weighting is imposed on it to exploit the abundant spectral information. The row-sparsity approach, which controls the sparsity by the l_2,0 norm, outperforms the single-sparsity approach in many scenarios. Many algorithms use convex relaxation methods to solve the l_2,0 norm to avoid the NP-hard problem, but this will reduce sparsity and unmixing accuracy. In this paper, a row-hard-threshold function is introduced to solve the l_2,0 norm directly, which guarantees the sparsity of the results. The high spatial correlation of hyperspectral images is associated with low column rank; therefore, the low-rank constraint is adopted to utilize spatial information. Experiments with simulated and real data prove that the proposed algorithm can obtain better unmixing results.

• 지구물리와물리탐사
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• 제20권2호
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• pp.78-87
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• 2017

MWNI (Minimum Weighted Norm Interpolation)를 이용한 내삽 방법은 고차원으로 확장이 용이하고 상대적으로 계산 속도가 빠르다는 장점을 가지고 있으나 알리아스 효과가 존재하는 자료의 내삽에 취약하다. 이런 문제의 개선을 위해 제안된 방법이 모델제약(model-constrained) MWNI이다. 이 논문에서는 MWNI를 이용한 방법과 모델제약 MWNI 방법의 두가지 모듈을 개발한 후 알리아스 효과가 존재하는 자료의 내삽 결과를 비교하였다. 시공간 영역(t-x domain)과 주파수-파수 영역(f-k domain)의 결과 그림을 통해서 모델제약 MWNI를 적용했을 때의 결과가 더 효과적임을 확인할 수 있었다. 동해 울릉분지의 가스 하이드레이트 부존 지역의 현장 자료에 내삽을 적용한 결과, 가스침니 구간 전후로 진폭이 급격하게 변하는 자료에서도 내삽이 가능함을 확인할 수 있었다. 또한 매우 불규칙하고 넓은 구간에서 누락된 인공지진파 자료의 정규화를 통해 신호의 연결성 향상이 가능함을 보일 수 있었다. 결과적으로 이 논문에서 개발된 모듈은 현장의 다양한 여건에 의해 불규칙하거나 넓은 간격으로 얻어진 탄성파 자료의 정규화나 내삽에 효율적으로 활용될 수 있음을 확인하였다.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2002년도 봄 학술발표논문집 Vol.29 No.1 (A)
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• pp.727-729
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• 2002

본 논문에서 우리는 grey scale 영상을 weighted finite automata(WFA)로써 기술하는 두개의 알고리즘(2, 4)을 분석하였다. 또한 원영상과 WFA를 이용하여 압축된 영상간의 error를 분석하고 그 결과를 제시하였다. 구체적으로, 영상복원 tolerance $\delta$를 이용하여 찾아진 atomatone에 의해 복원된 영상과 원영상의 ι$^2$-norm의 차이가 $\delta$보다 작거나 같음을 증명하였다.

• Journal of Applied and Pure Mathematics
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• 제5권3_4호
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• pp.129-164
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• 2023

The aim of this work is to present some interesting results on weighted ergodic functions and prove the existence and uniqueness of Stepanov-like pseudo almost automorphic solutions using the spectral decomposition of the phase space developed by Adimy and co-authors. We also give the next challenge of this work.

• 말소리와 음성과학
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• 제7권3호
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• pp.131-138
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• 2015

In this paper, we propose L1-norm regularization for state vector adaptation of subspace Gaussian mixture model (SGMM). When you design a speaker adaptation system with GMM-HMM acoustic model, MAP is the most typical technique to be considered. However, in MAP adaptation procedure, large number of parameters should be updated simultaneously. We can adopt sparse adaptation such as L1-norm regularization or sparse MAP to cope with that, but the performance of sparse adaptation is not good as MAP adaptation. However, SGMM does not suffer a lot from sparse adaptation as GMM-HMM because each Gaussian mean vector in SGMM is defined as a weighted sum of basis vectors, which is much robust to the fluctuation of parameters. Since there are only a few adaptation techniques appropriate for SGMM, our proposed method could be powerful especially when the number of adaptation data is limited. Experimental results show that error reduction rate of the proposed method is better than the result of MAP adaptation of SGMM, even with small adaptation data.

• 대한수학회지
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• 제55권2호
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• pp.313-326
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• 2018

The paper studies some new ${\mathbb{C}}^n$-generalizations of Bergman type operators introduced by Shields and Williams depending on a normal pair of weight functions. We find the values of parameter ${\beta}$ for which these operators are bounded on mixed norm spaces L(p, q, ${\beta}$) over the unit ball in ${\mathbb{C}}^n$. Moreover, these operators are bounded projections as well, and the images of L(p, q, ${\beta}$) under the projections are found.

• 대한수학회논문집
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• 제18권2호
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• pp.263-280
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• 2003

We prove weighted L$^{p}$ estimates with respect to the non-isotropic norm for the (equation omitted)-equation on real ellipsoids, where weights are powers of the distance to the boundary. The non-isotropic norm is smaller than the usual norm, by a factor which is equal to the distance to the boundary in the complex tangential component and which is equal to the m-th root of the distance to the boundary in the complex normal component. Here n is the maximal order of contact of the boundary of the real ellipsoid with complex analytic curves.

• 대한수학회보
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• 제60권1호
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• pp.171-184
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• 2023

In this paper, we show that a complete translating soliton Σ^m in ℝⁿ for the mean curvature flow is stable with respect to weighted volume functional if Σ satisfies that the L^m norm of the second fundamental form is smaller than an explicit constant that depends only on the dimension of Σ and the Sobolev constant provided in Michael and Simon [12]. Under the same assumption, we also prove that under this upper bound, there is no non-trivial f-harmonic 1-form of L²_f on Σ. With the additional assumption that Σ is contained in an upper half-space with respect to the translating direction then it has only one end.