• Phonetics and Speech Sciences
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• v.10 no.2
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• pp.15-24
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• 2018

Earlier studies reported that the /o/ and /u/ phonemes of Seoul Korean were currently merging in the F1/F2 space. However, studies on perception tests have shown that rates of correctness were high, even in cases where the two vowels overlapped. This study explores whether there is another acoustic parameter that differentiates /o/ from /u/, besides the F1/F2 contrast. Seventy-five native speakers of Seoul Korean, born between 1953 and 1999, participated in a production test. The data collected were analyzed in terms of F1 and F2, H1-H2, and F0. The result shows that the /o/ and /u/ of female speakers almost overlap in the F1/F2 space for all ages, while H1-H2 values are significantly different between the two vowels regardless of age. On the other hand, the /o/ and /u/ of male speakers are largely well separated in the F1/F2 space, while the H1-H2 values between the two vowels are very close at all ages. F0 effect is relatively small for both male and female speakers, even though there is a statistically significant difference. The result of this study provides evidence that female speakers use phonation differences to distinguish /o/ from /u/, and that the F1/F2 contrast has been replaced by H1-H2 values.

• The Journal of the Acoustical Society of Korea
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• v.23 no.6
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• pp.454-461
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• 2004

This paper describes the acoustic characteristics of 8 Korean monophthongs. Two acoustic variables were newly manipulated the distance between Fl and F2 (Δ［F2-Fl］). which might be of help for the judgement of the vowel backness. and Euclidian distance between two vowels. ［에］ & ［애］ were observed to be merged in both male vowel space and the female's. respectively. The merger of ［우］ & ［오］, on the other hand, was only seen in the female space. In case of Fl, which concerns the vowel height. the scope of the females' was 1.36 times longer than that of the males' Regarding F2, which is related to the vowel backness. the females used a space 1.29 times longer than the males. The observation of Euclidian distance between the basic 3 vowels (이. 아. 우) showed that the females have longer distance than the males: ［이-아］ 1.25 times, ［아-우］ 1.45 times, and ［이-우］ 1.35 times. respectively.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.393-402
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• 2013

For 0 < $p$ < ${\infty}$, ${\alpha}$ > -1 and 0 < $r$ < 1, we show that if $f$ is in the space of Dirichlet type $\mathfrak{D}^p_{p-1}$, then ${\int}_{1}^{0}M_{p}^{p}(r,f^{\prime})(1-r)^{p-1}rdr$ < ${\infty}$ and ${\int}_{1}^{0}M_{(2+{\alpha})p}^{(2+{\alpha})p}(r,f^{\prime})(1-r)^{(2+{\alpha})p+{\alpha}}rdr$ < ${\infty}$ where $M_p(r,f)=\[\frac{1}{2{\pi}}{\int}_{0}^{2{\pi}}{\mid}f(re^{it}){\mid}^pdt\]^{1/p}$. For 1 < $p$ < $q$ < ${\infty}$ and ${\alpha}+1$ < $p$, we show that if there exists some positive constant $c$ such that ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathfrak{D}^p_{\alpha}}$ for all $f{\in}\mathfrak{D}^p_{\alpha}$, then ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathcal{B}_p(q)}$ where $\mathcal{B}_p(q)$ is the weighted Besov space. We also find the condition of measure ${\mu}$ such that ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.

• Phonetics and Speech Sciences
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• v.7 no.2
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• pp.157-162
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• 2015

This study reports on the effective way of displaying dynamic formant information on F1-F2 space. Conventional ways of F1-F2 space (different name of vowel triangle or vowel rectangle) have been used for investigating vowel characteristics of a speaker or a language based on statistics of the F1 and F2 values, which were computed by spectral envelope search method. Those methods were dealing mainly with the static information of the formants, not the changes of the formant values (i.e. dynamic information). So a better way of investigating dynamic informations from the formant values of speech signal is suggested so that more convenient and detailed investigation of the dynamic changes can be achieved on F1-F2 space. Suggested method used visualization of static and dynamic information in overlapped way to be able to observe the change of the formant information easily. Finally some examples of the implemented display on some cases of the continuous vowels are shown to prove the usefulness of suggested method.

• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.163-171
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• 1996

Observing that a locally weakly Lindel$\"{o}$f space is a quasi-F space if and only if it has an F-base, we show that every dense weakly Lindel$\"{o}$f subspace of an almost-p-space is C-embedded, every locally weakly Lindel$\"{o}$f space with a cocompact F-base is a locally compact and quasi-F space and that if Y is a dense weakly Lindel$\"{o}$f subspace of X which has a cocompact F-base, then $\beta$Y and X are homeomorphic. We also show that for any a separating nest generated intersection ring F on a space X, there is a separating nest generated intersection ring g on $\phi_{Y}^{-1}$(X) such that QF(w(X, F)) and ($\phi_{Y}^{-1}$(X),g) are homeomorphic and $\phi_{Y}_{x}$(g$^#$)=F$^#$.

• 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 Korean Mathematical Society
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• v.32 no.2
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• pp.279-287
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• 1995

Let $F$ be a set of distributions on R with the topology of weak convergence, and let $A$ be the $\sigma$-field generated by the open sets. We denote by $F_1^\infty$ the space consisting of all infinite sequence $(F_1, F_2, \cdots), F_n \in F and R_1^\infty$ the space consisting of all infinite sequences $(x_1, x_2, \cdots)$ of real numbers. Take the $\sigma$-field $F_1^\infty$ to be the smallest $\sigma$-field of subsets of $F_1^\infty$ containing all finite-dimensional rectangles and take $B_1^\infty$ to be the Borel $\sigma$-field $R_1^\infty$.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.339-348
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• 2000

We introduce the notion of the Finsler metrics compat-ible with a special Riemannian structure f of type (1,1) satisfying f6+f2=0 and investigate the properties of Finsler space with them.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1711-1726
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• 2014

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a generic lightlike submanifold M subject such that the structure vector field of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. The purpose of this paper is to prove a classification theorem of such an indefinite generalized Sasakian space form.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.1097-1104
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• 2015

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a lightlike hypersurface M subject such that the almost contact structure vector field ${\zeta}$ of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. We prove a classification theorem of such an indefinite generalized Sasakian space form.