• 통합자연과학논문집
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• 제1권3호
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• pp.216-220
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• 2008

In general the Banach space $L^1(T^1)$ doesn't admit convergence in norm. Thus the convergence in norm of the partial sums can not be characterized in terms of Fourier coefficients without additional assumptions about the sequence$\{^{\^}f(\xi)\}$. The problem of $L^1(T^1)$-convergence consists of finding the properties of Fourier coefficients such that the necessary and sufficient condition for (1.2) and (1.3). This paper showed that let $\{{\alpha}_{\kappa}\}{\in}BV$ and ${\xi}{\Delta}a_{\xi}=o(1),\;{\xi}{\rightarrow}{\infty}$. Then (1.1) is a Fourier series if and only if $\{{\alpha}_{\kappa}\}{\in}{\Gamma}$.

• 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.

• 지구물리와물리탐사
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• 제19권4호
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• pp.220-227
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• 2016

해양 탄성파 탐사를 통해 취득한 자료에는 지하 매질에서 반사되어 오는 신호뿐만 아니라 해수면에서 되반사되어 발생하는 고스트가 존재한다. 고스트는 특정 주파수 성분을 약화시켜 탄성파 자료의 시간 해상도를 저하시킨다. 고스트를 효과적으로 제거하기 위해서는 정확한 고스트의 지연시간과 해수면의 반사계수가 요구된다. 고스트 지연시간은 해수면의 상하 움직임, 에어건과 스트리머의 움직임 및 벌림(offset) 거리 등에 의해 변하며, 해수면의 반사계수도 주파수, 평면파의 입사각 그리고 해상 상태에 따라 변한다. 이러한 영향을 고려한 고스트 지연시간을 추정하기 위하여 이 연구에서는 고스트 제거 트레이스 및 이의 자기상관 자료의 L-1 norm, L-2 norm 그리고 첨도(kurtosis)를 비교하였다. 자기상관자료의 L-1 norm을 계산하여 고스트 지연시간을 추정하는 것이 오차가 가장 적게 발생하였다. 현장자료의 파고를 고려하고 키르히호프 근사식을 이용하여 해수면의 반사계수를 계산하여 음원 및 수신기 고스트 제거에 적용하였다. 고스트를 제거함으로써 약화된 주파수 성분을 복원하였으며 시간 해상도가 향상된 구조보정 단면을 얻었다.

• Korean Journal of Mathematics
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• 제31권3호
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• pp.305-311
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• 2023

We exhibit some properties of the weighted Berezin transform T_αf on L^∞(B_n) and on L¹(B_n). As the main result, we prove that if f ∈ L^∞(B_n) with lim_k→∞ T^k_αf exists, then there exist unique M-harmonic function g and $h{\in}{\bar{(I-T_{\alpha})L^{\infty}(B_n)}}$ such that f = g + h. We also show that of the norm of weighted Berezin operator T_α on L¹(B_n, ν) converges to 1 as α tends to infinity, where ν is an ordinary Lebesgue measure.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 하계학술대회 논문집 B
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• pp.1131-1133
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• 1996

In this paper, we consider the mixed $L_1/H_{\infty}$ problems of finding internally stabilizing controllers which minimize the peak-to-peak gain of a certain closed loop transfer function with $H_{\infty}$-norm constraint on other closed loop transfer function(or vise versa). This problem is a useful framework for designing a controller with the norm constraints upon time and frequency domain. We formulate the mixed $L_1/H_{\infty}$ problem as LMI problems by using the reachable set. This paper offers the sufficient condition for the existence of suboptimal state feedback controller, and shows that suboptimal solution can be obtained by solving a finite-dimensional convex optimization and a line search.

• Communications for Statistical Applications and Methods
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• 제31권2호
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• pp.203-212
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• 2024

The area under the ROC curve (AUC) is one of the most common criteria used to measure the overall performance of binary classifiers for a wide range of machine learning problems. In this article, we propose a L₁-penalized AUC-optimization classifier that directly maximizes the AUC for high-dimensional data. Toward this, we employ the AUC-consistent surrogate loss function and combine the L₁-norm penalty which enables us to estimate coefficients and select informative variables simultaneously. In addition, we develop an efficient optimization algorithm by adopting k-means clustering and proximal gradient descent which enjoys computational advantages to obtain solutions for the proposed method. Numerical simulation studies demonstrate that the proposed method shows promising performance in terms of prediction accuracy, variable selectivity, and computational costs.

• 호남수학학술지
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• 제42권3호
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• pp.569-576
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• 2020

An element x ∈ E is called a norming point of P ∈ P(ⁿE) if ║x║ = 1 and |P(x)| = ║P║. For P ∈ P(ⁿE), we define Norm(P) = {x ∈ E : x is a norming point of P}. Norm(P) is called the norming set of P. We classify Norm(P) for P ∈ 𝒫(²𝑙²_∞).

• 한국IT서비스학회지
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• 제2권2호
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• pp.111-119
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• 2003

In this paper, an efficient block matching algorithm which is based on the Block Sum Pyramid Algorithm (BSPA) is presented. The cost of BSPA[1] was reduced in the proposed algorithm by using l2 norm and partial distortion elimination technique. Motion estimation accuracy of the proposed algorithm is equal to that of BSPA. The efficiency of the proposed algorithm was verified by experimental results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.25-37
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• 2001

We consider the finite element method applied to nonlinear Sobolev equation with smooth data and demonstrate for arbitrary order ($k{\geq}2$) finite element spaces the optimal rate of convergence in $L_{\infty}\;W^{1,{\infty}}({\Omega})$ and $L_{\infty}(L_{\infty}({\Omega}))$ (quasi-optimal for k = 1). In other words, the nonlinear Sobolev equation can be approximated equally well as its linear counterpart. Furthermore, we also obtain superconvergence results in $L_{\infty}(W^{1,{\infty}}({\Omega}))$ for the difference between the approximate solution and the generalized elliptic projection of the exact solution.

• 대한수학회보
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• 제58권1호
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• pp.205-215
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• 2021

In [1], Beznosova proved that the bound on the norm of the dyadic paraproduct with b ∈ BMO in the weighted Lebesgue space L2(w) depends linearly on the Ad2 characteristic of the weight w and extrapolated the result to the Lp(w) case. In this paper, we provide the weighted norm estimates of the dyadic paraproduct πb with b ∈ VMO and reduce the dependence of the Ad2 characteristic to 1/2 by using the property that for b ∈ VMO its mean oscillations are vanishing in certain cases. Using this result we also reduce the quadratic bound for the commutators of the Calderón-Zygmund operator [b, T] to 3/2.