• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1737-1751
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• 2015

For every doubling gauge g, we prove that there is a Cantor set of positive finite $H^g$-measure, $P^g$-measure, and $P^g_0$-premeasure. Also, we show that every compact metric space of infinite $P^g_0$-premeasure has a compact countable subset of infinite $P^g_0$-premeasure. In addition, we obtain a class of uniform Cantor sets and prove that, for every set E in this class, there exists a countable set F, with $\bar{F}=E{\cup}F$, and a doubling gauge g such that $E{\cup}F$ has different positive finite $P^g$-measure and $P^g_0$-premeasure.

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.19-24
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• 1994

Let P be a probability measure on the real line with Lebesque-density f. The usual estimator of the distribution function (≡df) of P for the sample $\chi$$_1$,…, $\chi$$\_$n/ is the empirical df: F$\_$n/(t)=(equation omitted). But this estimator does not take into account the smoothness of F, that is, the existence of a density f. Therefore, one should expect that an estimator which is better adapted to this situation beats the empirical df with respect to a reasonable measure of performance.(omitted)

• East Asian mathematical journal
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• v.38 no.5
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• pp.643-647
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• 2022

Let F² denote the space of entire functions f on ℂ that are square integrable with respect to the Gaussian measure $dG(z)={\frac{1}{\pi}}{e^{-{\mid}z{\mid}^2}}$, where dA(z) = dxdy is the ordinary area measure. The Fock-Dirichlet space $F^2_{\mathcal{D}}$ consists of all entire functions f with f' ∈ F². We estimate Taylor coefficients of functions in the Fock-Dirichlet space. The Fock-Nevanlinna space $F^2_{\mathcal{N}}$ consists of entire functions that possesses just a bit more integrability than square integrability. In this note we prove that $F^2_{\mathcal{D}}=F^2_{\mathcal{N}}$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.417-426
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• 2011

Let ${\mu}$ be a finite positive Borel measure on the unit ball $B{\subset}{\mathbb{C}}^n$ and ${\nu}$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, ${\sigma}$ is the rotation-invariant measure on S such that ${\sigma}(S) =1$. Let ${\mathcal{P}}[f]$ be the Poisson-$Szeg{\ddot{o}}$ integral of f and $\tilde{\mu}$ be the Berezin transform of ${\mu}$. In this paper, we show that if there is a constant M > 0 such that ${\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\mu}(z){\leq}M{\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\nu}(z)$ for all $f{\in}L^p(\sigma)$, then ${\parallel}{\tilde{\mu}}{\parallel}_{\infty}{\equiv}{\sup}_{z{\in}B}{\mid}{\tilde{\mu}}(z){\mid}<{\infty}$, and we show that if ${\parallel}{\tilde{\mu}{\parallel}_{\infty}<{\infty}$, then ${\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\mu}(z){\leq}C{\mid}{\mid}{\tilde{\mu}}{\mid}{\mid}_{\infty}{\int_S}{\mid}f(\zeta){\mid}^pd{\sigma}(\zeta)$ for some constant C.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.251-259
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• 2015

Let $\mathbb{F}^d_q$ be a d-dimensional vector space over a finite field $\mathbb{F}^d_q$ with q elements. We endow the space $\mathbb{F}^d_q$ with a normalized counting measure dx. Let ${\sigma}$ be a normalized surface measure on an algebraic variety V contained in the space ($\mathbb{F}^d_q$, dx). We define the restricted averaging operator AV by $A_Vf(X)=f*{\sigma}(x)$ for $x{\in}V$, where $f:(\mathbb{F}^d_q,dx){\rightarrow}\mathbb{C}$: In this paper, we initially investigate $L^p{\rightarrow}L^r$ estimates of the restricted averaging operator AV. As a main result, we obtain the optimal results on this problem in the case when the varieties V are any nondegenerate algebraic curves in two dimensional vector spaces over finite fields. The Fourier restriction estimates for curves on $\mathbb{F}^2_q$ play a crucial role in proving our results.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.147-156
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• 2020

The functional equation related to a distance measure f(pr, qs) + f(ps, qr) = M(r, s)f(p, q) + M(p, q)f(r, s) can be generalized a sum form functional equation as follows $${\frac{1}{n}}{\sum\limits_{i=0}^{n-1}}f(P{\cdot}{\sigma}_i(Q))=M(Q)f(P)+M(P)f(Q)$$ where f, g is information measures, P and Q are the set of n-array discrete measure, and σ_i is a permutation for each i = 0, 1, ⋯, n-1. In this paper, we obtain the hyperstability of the above type functional equation.

• Phonetics and Speech Sciences
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• v.1 no.3
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• pp.73-85
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• 2009

This paper introduces the technique of synthesizing and evaluating human utterances with exaggerated or atypical prosody. Prosody exaggeration can be implemented by manipulating either the fundamental frequency (F0) contour, the segmental durations, or the intensity contour of an utterance. Of these three prosodic elements, two or more can be exaggerated at the same time. The algorithms of synthesis and evaluation were suggested. Learner utterances exaggerated in each of the three prosodic features were evaluated with respect to their original native versions in terms of the differences in their F0 contours, the segmental durations, and the intensity contours. The measure of differences was the Euclidean distance metric between the matching points in their F0 and intensity contours. The measure was calculated after the exaggerated learner utterances were aligned by the segments and rendered identical to their native version in terms of their segmental durations. For the evaluation of the segmental durations, no prior modifications were made in durations and the same measure was used. The results from the pilot experiment suggest the viability of this measure in the evaluation of learner utterances with atypical prosody with respect to their native versions.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.207-213
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• 1995

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measure on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$-algebras of F. If $r > 0$, let $J = [-r,0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert = sup_{s \in J}$\mid$\gamma(s)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E,F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$.

• Journal of Korean Society for Geospatial Information Science
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• v.21 no.3
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• pp.37-46
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• 2013

Similarity measure of catchments is essential for regionalization studies, which provide in depth analysis in hydrological response and flood estimations at ungauged catchments. However, this similarity measure is often biased to the selected catchments and is not clearly explained in hydrological sense. This study applied a type of hydrological similarity distance measure-Flood Estimation Handbook to 25 Geum River catchments, Korea. Three Catchment Characteristics, Area(A)-Annual precipitation(SAAR)-SCS Curve Number(CN), are used in Euclidian distance measures. Furthermore, six index of Flow Duration Curve are applied to clustering analysis of SPSS. The catchments' grouping of hydrological similarity measures suggests three groups (H1, H2 and H3) and the four catchments are not grouped in this study. The clustering analysis of FDC provides four Groups; F1, F2, F3 and F4. The six catchments (out of seven) of H1 are grouped in F1, while Sangyeogyo is grouped in F2. The four catchments (out of six) of H2 are also grouped in F2, while Cheongju and Guryong are grouped in F1. The catchments of H3 are categorized in F1. The authors examine the results (H1, H2 and H3) of similarity measure based on catchment physical descriptors with results (F1 and F2) of clustering based on catchment hydrological response. The results of hydrological similarity measures are supported by clustering analysis of FDC. This study shows a potential of hydrological catchment similarity measures in Korea.

• Journal of the Korean Institute of Intelligent Systems
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• v.25 no.4
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• pp.386-391
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• 2015

This paper proposed the optimal attributes for text classification based on Korean and Chinese linguistic features. The experiments committed to discover which is the best feature among n-grams which is known as language independent, morphemes that have language dependency and some other feature sets consisted with n-grams and morphemes showed best results. This paper used SVM classifier and Internet news for text classification. As a result, bi-gram was the best feature in Korean text categorization with the highest F1-Measure of 87.07%, and for Chinese document classification, 'uni-gram+noun+verb+adjective+idiom', which is the combined feature set, showed the best performance with the highest F1-Measure of 82.79%.