• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.353-359
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• 2017

Starting from a t-norm T, it is possible to construct a class of new t-norms, so-called T-generalized t-norm. The purpose of this paper is to describe some properties of this class of generalized t-norms. An algebraic structure as well as a binary relation among t-norms are also investigated. Some open problems are discussed as well.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.30-35
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• 2009

We investigate the properties of fuzzy relations, metrics and $\bigodot$-equivalence relation on a stsc quantale lattice L and a commutative cqm-lattice. In particular, pseudo-(quasi-) metrics induce $\bigodot$-(quasi)-equivalence relations.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1371-1385
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• 2022

For setting a general weight function on n dimensional complex space ℂⁿ, we expand the classical Fock space. We define Fock type space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ of entire functions with a mixed norm, where 0 < p, q < ∞ and t ∈ ℝ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$. As a result of this application, the space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ is especially characterized by a Lipschitz type condition.

• Journal of Korean Neurosurgical Society
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• v.65 no.2
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• pp.315-324
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• 2022

Objective : The aim of this study was to verify the equivalence and effectiveness of the tablet-administered Korean Repeatable Battery for the Assessment of Neuropsychological Status (K-RBANS) for the prevention and early detection of dementia. Methods : Data from 88 psychiatry and neurology patient samples were examined to evaluate the equivalence between tablet and paper administrations of the K-RBANS using a non-randomly equivalent group design. We calculated the prediction scores of the tablet-administered K-RBANS based on demographics and covariate-test scores for focal tests using norm samples and tested format effects. In addition, we compared the receiver operating characteristic curves to confirm the effectiveness of the K-RBANS for preventing and detecting dementia. Results : In the analysis of raw scores, line orientation showed a significant difference (t=-2.94, p<0.001), and subtests showed small to large effect sizes (0.04-0.86) between paper- and tablet-administered K-RBANS. To investigate the format effect, we compared the predicted scaled scores of the tablet sample to the scaled scores of the norm sample. Consequently, a small effect size (d≤0.20) was observed in most of the subtests, except word list and story recall, which showed a medium effect size (d=0.21), while picture naming and subtests of delayed memory showed significant differences in the one-sample t-test. In addition, the area under the curve of the total scale index (TSI) (0.827; 95% confidence interval, 0.738-0.916) was higher than that of the five indices, ranging from 0.688 to 0.820. The sensitivity and specificity of TSI were 80% and 76%, respectively. Conclusion : The overall results of this study suggest that the tablet-administered K-RBANS showed significant equivalence to the norm sample, although some subtests showed format effects, and it may be used as a valid tool for the brief screening of patients with neuropsychological disorders in Korea.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.533-541
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• 2006

let E be a Finsler modules over $C^*$-algebras. A with norm-map $\rho$ and L(E) set of all A-linear bonded operators on E. We show that the canonical homomorphism ${\phi}:L(E){\rightarrow}L(E_I)$ sending each operator T to its restriction $T|E_I$ is injective if and only if I is an essential ideal in the underlying $C^*$-algebra A. We also show that $T{\in}L(E)$ is a bounded below if and only if ${\mid}{\mid}x{\mid}{\mid}={\mid}{\mid}{\rho}{\prime}(x){\mid}{\mid}$ is complete, where ${\rho}{\prime}(x)={\rho}(Tx)$ for all $x{\in}E$. Also, we give a necessary and sufficient condition for the equivalence of the norms generated by the norm map.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1387-1401
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• 2019

Consider a finite measure space (${\Omega}$, ${\Sigma}$, ${\mu}$) and a Banach space $X({\mu})$ consisting of (equivalence classes of) real measurable functions defined on ${\Omega}$ such that $f{\chi}_A{\in}X({\mu})$ and ${\parallel}f{\chi}_A{\parallel}{\leq}{\parallel}f{\parallel}$, ${\forall}f{\in}({\mu})$, $A{\in}{\Sigma}$. We prove that if it satisfies the subsequence property, then it is an ideal of measurable functions and has an equivalent norm under which it is a Banach function space. As an application we characterize norms that are equivalent to a Banach function space norm.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.99-106
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• 2005

We present a relation between the orthogonality of the constrained Legendre polynomials over the triangular domain and the BB ($B{\acute{e}zier}\;-Bernstein$) coefficients of the polynomials using the equivalence of orthogonal complements. Using it we also show that the best constrained degree reduction of polynomials in BB form equals the best approximation of weighted Euclidean norm of coefficients of given polynomial in BB form from the coefficients of polynomials of lower degree in BB form.

• Asian Journal for Public Opinion Research
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• v.9 no.2
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• pp.188-211
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• 2021

Decreasing response rates to traditional survey methods, like face-to-face and telephone interviews, have led survey practitioners around the world to seek new ways of conducting surveys in recent years." The COVID-19 pandemic exacerbated this problem because it made conducting face-to-face interviews even more difficult than before. For example, it made conducting face-to-face surveys infeasible in 2020 in South Korea, and so the Korean Academic Multimode Open Survey (KAMOS) was unable to conduct a planned face-to-face survey to recruit new panel members. The entire 8,514-member panel, established via two-stage probability-based sampling from 2016 to 2019, was invited to take three online/telephone surveys in 2020. Of these panel members, 1,352 responded to at least one survey in 2020. To test to what extent the panel remained representative of the adult South Korean population, we compared the two groups of panel members: those who responded to at least one survey in 2020 and those who did not. After weighting both groups on the basis of age, sex, and geographical area, we analyzed their responses to some of the questions that were asked during multiple rounds of the face-to-face panel-recruiting interviews. Using Cohen's d for survey items that could be analyzed numerically and Cramér's V for categorical items, we were able to conclude that the respondents to the 2020 surveys were equivalent to the non-respondents in terms of both demographics and in the answers they originally gave to substantive questions on a variety of topics related to social science or public opinion research, including questions about quality of life, societal issue, and politics (Cohen's d items <0.2, 95% CI; Cramér's V items <0.1, 95% CI). This analysis may provide a model for others who wish to test the continued representativeness of their panel or who would like to use a different survey mode or change some other aspect of their methodology and test whether it is equivalent to their former methodology. Our success in building a panel that retained its representativeness may be useful to those in other countries where face-to-face surveys had previously been the norm but are becoming increasingly difficult to conduct.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.6
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• pp.1318-1324
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• 2003

There are two problems in the conventional ART1 algorithm. One is in similarity testing method of the conventional ART1 between input patterns and stored patterns. The other is that vigilance threshold of conventional ART1 influences the number of clusters and the rate of recognition. In this paper, new similarity testing method and dynamical vigilance threshold method are proposed to solve these problems. The former is similarity test method using the rate of norm of exclusive-NOR between input patterns and stored patterns and the rate of nodes have equivalence value, and the latter method dynamically controls vigilance threshold to similarity using fuzzy operations and the sum operation of Yager. To check the performance of new methods, we used 26 alphabet characters and nosed characters. In experiment results, the proposed methods are better than the conventional methods in ART1, because the proposed methods are less sensitive than the conventional methods for initial vigilance and the recognition rate of the proposed methods is higher than that of the conventional methods.