• 대한수학회지
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• 제41권1호
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• pp.21-38
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• 2004

We prove that a Banach space that is convex-transitive and such that for some element u in the unit sphere, and for every subspace Μ containing u, it happens that the subset of norm attaining functionals on Μ is second Baire category in $M^{*}$ is, in fact, almost-transitive and superreflexive. We also obtain a characterization of finite-dimensional spaces in terms of functions that attain their supremum: a Banach space is finite-dimensional if, for every equivalent norm, every rank-one operator attains its numerical radius. Finally, we describe the subset of norm attaining functionals on a space isomorphic to $\ell$$_1$, where the norm is the restriction of a Luxembourg norm on $L_1$. In fact, the subset of norm attaining functionals for this norm coincides with the subset of norm attaining functionals for the usual norm.m.

• 지구물리와물리탐사
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• 제10권2호
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• pp.124-130
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• 2007

탄성파 역산에 있어서 가장 널리 사용되는 최소자승($l^2$ norm)해는 이상치(outlier)에 매우 민감하게 반응하는 경향이 있다. 이에 반해서 $l^1$ norm을 최소화하는 해는 이상치에 강인한 면을 보이나 일반적으로 좀 더 많은 계산이 필요하다. 반복적가중의 최소자승법(Iteratively reweighted least squares [IRLS] method)을 이용하면 이러한 $l^1$ norm 문제의 근사해(approximate solution)를 효율적으로 구할 수 있다. 본 논문에서는 작은 크기의 잔여분은 $l^2$ norm으로 처리하며, 큰 크기의 잔여분은 $l^1$ norm으로 처리하는 하이브리드 $l^1/l^2$ norm 최소화를 IRLS 방법에 쉽게 적용하는 구현 기법을 소개한다. 소개된 알고리즘은 특이치(singularity)처리를 위한 임계값의 결정에 민감하게 반응하는 기존의 $l^1$ norm IRLS 방법과는 달리 임계값 결정에 상관없이 늘 강인한 역산의 특성을 보여준다.

• 응용통계연구
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• 제25권5호
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• pp.829-835
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• 2012

When the input features are generated by factors in a classification problem, it is more meaningful to identify important factors, rather than individual features. The $F_{\infty}$-norm support vector machine(SVM) has been developed to perform automatic factor selection in classification. However, the $F_{\infty}$-norm SVM may suffer from estimation inefficiency and model selection inconsistency because it applies the same amount of shrinkage to each factor without assessing its relative importance. To overcome such a limitation, we propose the adaptive $F_{\infty}$-norm ($AF_{\infty}$-norm) SVM, which penalizes the empirical hinge loss by the sum of the adaptively weighted factor-wise $L_{\infty}$-norm penalty. The $AF_{\infty}$-norm SVM computes the weights by the 2-norm SVM estimator and can be formulated as a linear programming(LP) problem which is similar to the one of the $F_{\infty}$-norm SVM. The simulation studies show that the proposed $AF_{\infty}$-norm SVM improves upon the $F_{\infty}$-norm SVM in terms of classification accuracy and factor selection performance.

• 한국통신학회논문지
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• 제32권11C호
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• pp.1073-1078
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• 2007

본 논문에서는 다중 정규화 매개 변수를 이용한 혼합 norm 영상 복원 방식을 제안한다. 임의의 분포를 갖는 첨가 노이즈를 효율적으로 제거하기 위해 정규화 완화 $l_2$ 함수와 정규화 완화 $l_4$ 함수를 결합한 새로운 혼합 norm 정규화 완화 함수가 유도된다. 각 완화 함수의 완화도를 제어하기 위해 개별적인 정규화 매개 변수가 정의되고, 정규화 완화 $l_2$ 함수와 정규화 완화 $l_4$ 함수의 상대적 기여도를 제어하기 위한 혼합 norm 정규화 매개 변수가 kurtosis를 이용해 정의된다. 안정적인 해를 얻기 위해 반복기법이 사용되었으며, 이들의 수렴 여부가 분석되었다. 다양한 분포를 갖는 첨가 노이즈가 실험에 사용되었으며, 이를 통해서 제안된 방식의 성능을 평가할 수 있었다.

• 방사성폐기물학회지
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• 제21권4호
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• pp.481-487
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• 2023

Concerning the apprehensions about naturally occurring radioactive materials (NORM) residues, the International Atomic Energy Agency (IAEA) and its member nations have acknowledged the imperative to ensure the radiation safety of NORM industries. Residues with elevated radioactivity concentrations are predominantly produced during NORM processing, in the form of scale and sludge, referred to as technically enhanced NORM (TENORM). Substantial quantities of TENORM residues have been released externally due to the dismantling of NORM processing factories. These residues become concentrated and fixed in scale inside scrap pipes. To assess the radioactivity of scales in pipes of various shapes, a Monte Carlo simulation was employed to determine dose rates corresponding to the action level in TENORM regulations for different pipe diameters and thicknesses. Onsite gamma spectrometry was conducted on a scrap iron pipe from the titanium dioxide manufacturing factory. The measured dose rate on the pipe enabled the estimation of NORM concentration in the pipe scale onsite. The derived action level in dose rate can be applied in the NORM regulation procedure for on-site judgments.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.541-555
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• 2009

The primary purpose of this paper is to prove the fuzzy version of Riesz theorem in n-normed linear space as a generalization of linear n-normed space. Also we study some properties of fuzzy n-norm and introduce a concept of fuzzy anti n-norm.

• Journal of applied mathematics & informatics
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• 제3권2호
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• pp.245-252
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• 1996

We described a relationship of the $L_2$ norm of the $L_2$norm of a Bzier curve and l2 norm of its confrol points. The use of Bezier curves finds much application in the general description of curves and surfaces and provided the mathematical basis for many computer graphics system. We define the $L_2$ norm for Bezier curves and find a upper and lower bound for many computer graphics system. We define the $L_2$ norm for Bezier curves and find a upper and lower bound for the $L_2$ norm with respect to the $L_2$ norm for its control points for easy computation.

• 대한수학회지
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• 제45권6호
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• pp.1769-1784
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• 2008

The group Hameo (M, $\omega$) of Hamiltonian homeomorphisms of a connected symplectic manifold (M, $\omega$) was defined and studied in [7] and further in [6]. In these papers, the authors consistently used the $L^{(1,{\infty})}$-Hofer norm (and not the $L^{\infty}$-Hofer norm) on the space of Hamiltonian paths (see below for the definitions). A justification for this choice was given in [7]. In this article we study the $L^{\infty}$-case. In view of the fact that the Hofer norm on the group Ham (M, $\omega$) of Hamiltonian diffeomorphisms does not depend on the choice of the $L^{(1,{\infty})}$-norm vs. the $L^{\infty}$-norm [9], Y.-G. Oh and D. McDuff (private communications) asked whether the two notions of Hamiltonian homeomorphisms arising from the different norms coincide. We will give an affirmative answer to this question in this paper.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.485-491
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• 2012

In this paper, we show the norm attaining paranormal operators have a nontrivial invariant subspace. Also, we show the norm attaining quadratically hyponormal weighted shift is subnormal.

• 한국프랜차이즈경영연구
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• 제9권2호
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• pp.31-38
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• 2018

Purpose - In recent years, many companies include franchises have acquire customers by making an online stores and they are carrying out permission marketing activities with e-mail and SMS. Permission marketing requires voluntary customer approval for receiving commercial messages such as cross-selling and upselling. Therefore, it is necessary for the business to induce the customer's acceptance. The purpose of this study is to examine which type of different messages can affect higher in consumer persuasion. Thus, we investigated the impact of descriptive norm message on intention of reception in an online store context, and its interaction with chronic regulatory focus. Research design, data, and methodology - This study hypothesized that the descriptive norm message would affect positive influences to consumers' intension of reception. Specially, this study inquired into whether the interaction effect between descriptive norm and regulatory focus. To verify the hypothesis, we conducted 2 × 2 between-subject factorial design with message type (general message and descriptive norm message) and regulatory focus(promotion focus and prevention focus) as independent variables. Participants of the experiment were assigned to one of 2 kind experimental situations randomly according to characteristics of message type. A total of 131 participants (descriptive norm message: 65, general message: 66) responded for this study. The data were analyzed using frequency analysis, exploratory factor analysis, and two-way ANOVA. Result - The results of the study are as follows. First, we found main effects of the descriptive norm message. The intention of reception were significantly higher in the descriptive norm message rather than general message as in previous researches. Second, interaction effect between the descriptive norm message and regulatory focus was significant. The prevention focus (vs. promotion focus) were hight in a positive behavior intention when the descriptive norm message was given. Conclusions - This study verifies the main effect and interaction effect of descriptive norm message and regulatory focus on the consumers' intention of reception in permission marketing, and persuasive message in the online store context. The results of this study will provide various advantages to companies that want to establish long lasting relationship with customers by carrying out permission marketing in the future.