• Journal of the Korean Mathematical Society
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• v.41 no.1
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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.

• Geophysics and Geophysical Exploration
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• v.10 no.2
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• pp.124-130
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• 2007

Least squares ($l^2$ norm) solutions of seismic inversion tend to be very sensitive to data points with large errors. The $l^1$ norm minimization gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) method gives efficient approximate solutions of these $l^1$ norm problems. I propose an efficient implementation of the IRLS method for a hybrid $l^1/l^2$ minimization problem that behaves as $l^2$ norm fit for small residual and $l^1$ norm fit for large residuals. The proposed algorithm shows more robust characteristics to the decision of the threshold value than the l1 norm IRLS inversion does with respect to the threshold value to avoid singularity.

• The Korean Journal of Applied Statistics
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• v.25 no.5
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.11C
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• pp.1073-1078
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• 2007

In this paper, we propose an iterative mixed norm image restoration algorithm using multi regularization parameters. A functional which combines the regularized $l_2$ norm functional and the regularized $l_4$ norm functional is proposed to efficiently remove arbitrary noise. The smoothness of each functional is determined by the regularization parameters. Also, a regularization parameter is used to determine the relative importance between the regularized $l_2$ norm functional and the regularized $l_4$ norm functional using kurtosis. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed. Experimental results demonstrate the capability of the proposed algorithm.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.21 no.4
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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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• v.27 no.3_4
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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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• v.3 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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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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• v.20 no.4
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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.

• The Korean Journal of Franchise Management
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• v.9 no.2
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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.