• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.263-267
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• 2014

We study the growth rate of $H^1$ Sobolev norm of the solutions to Gross-Neveu and Thirring equations. A well-known result is the double exponential rate. We show that the $H^1$ Sobolev norm grows at most an exponential rate exp($ct^2$).

• Journal of architectural history
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• v.2 no.1 s.3
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• pp.25-41
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• 1993

This study was made to analyze the housing adjustment phenomenon in the first half of Chosun Dynasty by applying Microsociological approach. By reviewing the housing adjustment theory of Morris and Winter, research model for the period was developed in terms of socioeconomic characteristics, normative housing deficit (=cultural norm-housing condition+family norm), constraints, behavioral propensities, and housing adjustment mechanism with the following results : 1. In the first half of Chosun Dynasty the size of the house, the house site and decorating items were specified by law (cultural norm) according to the social status. Although the law was constraints for the housing phenomenon, it was not applied universally. Frequantly the law was violated by the upper class. By the middle of the Dynasty the family norm became more important for the housing phenomenon than the cultural norm. 2. Efforts were made to practice the Confucianism as a cultural norm in the first half of Chosun Dynasty At that time Husband-Living-in-Wife's-House was more popular than Wife-Living-in-Husband's-House. Because the customs were against the Confucianism, the latter was encouraged by law. But it did not change. Instead a compromised system became popular in the middle of the Dynasty. The house shrine was practiced to increase the symbolism of the family, which, in turn, exerted influences in deciding the housing site (cultural norm). These cultural norm was not accepted as the family norm untill the second half of the Dynasty. These trends forced the man and woman use separate areas of the house, and formulated a hierarchic positions within a house. 3. It was shown that the settlement of Confucianism as a family norm was closely related to the popularization of the Ondol system in the house, which functioned as one of the behavioral propensities to encourage diversity of space for many purposes. Though the Ondol system was accepted as a useful heating system earlier, this became more popular in the middle of the Dynasty because the housing pattern with Ondol fitted very well with a large family system with patriarchism. Ondol system for one or two rooms substituted Ondol for all rooms in the second half of the Dynasty. 4. From the beginning of the Dynasty housing adjustment of the family was determined by the social status and by law (cultural norm). Within this cultural norm each family decided its adjustment mechanism according to its economic ability (family norm). Family norm was more important factor than the cultural norm to determine the micro-space pattern in the house. But this period witnessed the formations of new conditions by the ruling class's efforts to implement new ethics for hierarchy and sexual discrimination. According to these conditions the Confucianism overruled the family norm in the later period.

• The Journal of the Korea Contents Association
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• v.13 no.5
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• pp.443-450
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• 2013

This study is about that how accessibility or norm influence to use diversity or usage of internet contents. Two hypotheses tested by statistic analysis. The major finding of this study are as follows. First, the greater the physical accessibility or intellectual accessibility, the greater the use diversity of internet contents. Second, the greater the physical accessibility or intellectual accessibility, the greater the usage of internet contents. Third, the greater the subject norm, the smaller the usage of internet contents. This study provides some implications that subject norm can influence to reduce usage of internet contents. The limitations, and future direction are discussed.

• Honam Mathematical Journal
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• v.42 no.3
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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_∞).

• Journal of the Korean Institute of Landscape Architecture
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• v.30 no.6
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• pp.38-46
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• 2003

Perceived crowding is known as a necessary method to evaluate social carrying capacity in recreational settings. But according to the results of previous research, perceived crowding, use density, and satisfaction have shown weak and indirect correlations. The theory of visitors’ adjustment is one of several possible explanations for this poor relation. But the validity of the visitors’ adjustment theory has not been not inspected clearly. Therefore, the purposes of this study are to understand visitors’ adjustment theory and to examine visitors’ adjustment to the overuse of recreational settings. Study hypotheses were formulated through literature review and related to visitors’ adjustment in recreation density. Pour hypotheses were established and inspected with the case study, i.e., Rationalization : Visitors’ satisfaction isn't related to use density in recreation setting, 2) Product-shift : Preference norm is related to current use density, 3) Self-selection : Visitors’ satisfaction for the use level is generally high, and 4) Displacement : Norm interference is related to willingness to revisit. The case study was conducted during May and June,2001. According to the results of this survey, visitors adjust to overuse of recreation setting through rationalization and product shift (hypotheses l/2 acceptance). Current use density isn't related to visitors’ satisfaction and willingness to revisit (see table 3). And visitors’ preference norm is modified by situation (see table 4). Visitors’ satisfaction and willingness to revisit don't show a high correlation but moderately high (see table 5, hypothesis 3 acceptance). Differences between visitors’ preference norm and current use density is norm interference. Norm interference isn't related to willingness to revisit (see table 7). Therefore, the norm interference concept is not a useful method to explain visitors’ adjustment to the degree of overuse in a recreational setting (hypothesis 4 rejection). As for future directions, the following are proposed: 1) correctly understanding and reestablishing the visitor norm and norm interference concept, 2) introducing a composite research method to monitor visitors’ behavior and survey visitors’ attitudes and coping responses. These efforts would be helpful in the Planning and management of recreational settings to improve the quality of visitors’ experiences.

• Geophysics and Geophysical Exploration
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• v.9 no.1
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• pp.44-49
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• 2006

In this study, the resolution capabilities of electrical resistivity tomography (ERT) in the monitoring of $CO_2$ injection are investigated. The pole-pole and bipole-bipole electrode configuration types are used between two uncased boreholes straddling the $CO_2$ plume. Forward responses for an initial pre-injection model and three models for subsequent stages of $CO_2$ injection are calculated for the two different electrode configuration types, noise is added and the theoretical data are inverted with both L1- and L2-norm optimisation. The results show that $CO_2$ volumes over a certain threshold can be detected with confidence. The L1-norm proved superior to the L2-norm in most instances. Normalisation of the inverted models with the pre-injection inverse model gives good images of the regions of changing resistivity, and an integrated measure of the total change in resistivity proves to be a valid measure of the total injected volume.

• Economic and Environmental Geology
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• v.28 no.4
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• pp.433-438
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• 1995

The most popular minimization method is based on the least-squares criterion, which uses the $L_2$ norm to quantify the misfit between observed and synthetic data. The solution of the least-squares problem is the maximum likelihood point of a probability density containing data with Gaussian uncertainties. The distribution of errors in the geophysical data is, however, seldom Gaussian. Using the $L_2$ norm, large and sparsely distributed errors adversely affect the solution, and the estimated model parameters may even be completely unphysical. On the other hand, the least-absolute-deviation optimization, which is based on the $L_1$ norm, has much more robust statistical properties in the presence of noise. The solution of the $L_1$ problem is the maximum likelihood point of a probability density containing data with longer-tailed errors than the Gaussian distribution. Thus, the $L_1$ norm gives more reliable estimates when a small number of large errors contaminate the data. The effect of outliers is further reduced by M-fitting method with Cauchy error criterion, which can be performed by iteratively reweighted least-squares method.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.63-78
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• 2008

We generalize several integral inequalities for analytic functions on the open unit polydisc $U^n={\{}z{\in}C^n||zj|<1,\;j=1,...,n{\}}$. It is shown that if a holomorphic function on $U^n$ belongs to the mixed norm space $A_{\vec{\omega}}^{p,q}(U^n)$, where ${\omega}_j(\cdot)$,j=1,...,n, are admissible weights, then all weighted derivations of order $|k|$ (with positive orders of derivations) belong to a related mixed norm space. The converse of the result is proved when, p, q ${\in}\;[1,\;{\infty})$ and when the order is equal to one. The equivalence of these conditions is given for all p, q ${\in}\;(0,\;{\infty})$ if ${\omega}_j(z_j)=(1-|z_j|^2)^{{\alpha}j},\;{\alpha}_j>-1$, j=1,...,n (the classical weights.) The main results here improve our results in Z. Anal. Anwendungen 23 (3) (2004), no. 3, 577-587 and Z. Anal. Anwendungen 23 (2004), no. 4, 775-782.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.81-90
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• 2002

The least informative (favorable) distributions, minimizing Fisher information for a multivariate location parameter, are derived in the parametric class of the exponential-power spherically symmetric distributions under the following characterizing restrictions; (i) a bounded variance, (ii) a bounded value of a density at the center of symmetry, and (iii) the intersection of these restrictions. In the first two cases, (i) and (ii) respectively, the least informative distributions are the Gaussian and Laplace, respectively. In the latter case (iii) the optimal solution has three branches, with relatively small variances it is the Gaussian, them with intermediate variances. The corresponding robust minimax M-estimators of location are given by the $L_2$-norm, the $L_1$-norm and the $L_{p}$ -norm methods. The properties of the proposed estimators and their adaptive versions ar studied in asymptotics and on finite samples by Monte Carlo.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.109-127
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• 2007

We classify complete, locally homogeneous metrics with finite volume on four-dimensional manifolds which are critical points for the squared $L^2-norm$ functionals of either the full Riemannian curvature tensor or the Weyl curvature tensor defined on the space of Riemannian metrics.