• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.927-944
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• 2022

Let $\vec{p}{\in}(0,\;1]^n$ be an n-dimensional vector and A a dilation. Let $H^{\vec{p}}_A(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of $H^{\vec{p}}_A(\mathbb{R}^n)$ and establishing a uniform estimate for corresponding atoms, the authors prove that the Fourier transform of $f{\in}H^{\vec{p}}_A(\mathbb{R}^n)$ coincides with a continuous function F on ℝⁿ in the sense of tempered distributions. Moreover, the function F can be controlled pointwisely by the product of the Hardy space norm of f and a step function with respect to the transpose matrix of A. As applications, the authors obtain a higher order of convergence for the function F at the origin, and an analogue of Hardy-Littlewood inequalities in the present setting of $H^{\vec{p}}_A(\mathbb{R}^n)$.

• Journal of Astronomy and Space Sciences
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• v.26 no.4
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• pp.467-478
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• 2009

The super-geomagnetic storms called 2003 Halloween event globally occurred during the period of 29 through 31 which are the following days when the solar flares of X18 class exploded on 28 October 2003. The S4 index from GPS signal strength and the peak electron density ($NmF_2$) from GPS tomography method are analyzed according to the date. The occurrences of the cycle slip and scintillation in the GPS signals are 1,094 and 1,387 on 28 and 29 October, respectively and these values are higher than 604 and 897 on 30 and 31 October. These mean the ionospheric disturbances are not always generated by the period of geomagnetic storm. Therefore, GPS S4 index is useful to monitor the ionospheric disturbances. Behaviors of ionospheric electron density estimated from GPS tomography method are analyzed with the date. At UT = 18 hr, the maximum $NmF_2$ is shown on 28 October. It agrees with $NmF_2$ variation measured from Anyang ionosonde, and the GPS signal are better condition on 30 and 31 October than 28 October. In conclusion, GPS signal condition is relation with geomagnetic activities, and depend upon the variation of the electron density. We will study the long-term data to examine the relationship between the GPS signal quality and the electron density as the further works.

• Phonetics and Speech Sciences
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• v.2 no.4
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• pp.185-192
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• 2010

The acoustic vowel space has been used as an acoustic parameter in dysarthric speech. The aim of this work was to examine mathematical formulae for acoustic vowel space and to apply these to Korean speakers with idiopathic Parkinson's disease(IPD). Five acoustic parameters were chosen from earlier works and one new parameter was proposed, the pentagonal vowel space. The six parameters included triangular vowel space (3 area), irregular quadrilateral vowel space (4 area), irregular pentagonal vowel space (5 area), vowel articulatory index (VAI), formant centralization ratio (FCR) and F2i/F1u ratio (F2 ratio). An experimental group of 32 IPD patients(male:female=16:16) and a control group of twenty healthy people (male:female=8:12) participated in the study and repeated vowels (/a-i-u-e-o/) three times. A correlation analysis was performed among the six parameters, 2-way ANOVA was done with gender and groups as independent factors, and an independent sample t-test was conducted between the male and the female group as post hoc comparison. All parameters were highly correlated with each other and only the FCR showed a high negative correlation with the others. The results of ANOVA showed a significant difference in F2 ratio, 3 area, 4 area and 5 area between gender and in 4 area and 5 area between groups. For the male members of the two groups, significant statistical differences were found in all parameters whereas no such differences were found for the female members. These findings indicated that the vowel space of the female group was wider than the vowel space of the male group. These differences may have been caused by gender-specific speech styles rather than by patho-physiological mechanisms. We also claim that the pentagonal vowel space is better than the other vowel spaces at representing the disordered speech in natural speech situations.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.183-198
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• 1999

Let $\mathcal{F}(B)$ be the Fresnel class on an abstract Wiener space (B, H, ${\omega}$) which consists of functionals F of the form : $$F(x)={\int}_H\;{\exp}\{i(h,x)^{\sim}\}df(h),\;x{\in}B$$ where $({\cdot}{\cdot})^{\sim}$ is a stochastic inner product between H and B, and $f$ is in $\mathcal{M}(H)$, the space of all complex-valued countably additive Borel measures on H. We introduce the concepts of an $L_p$ analytic Fourier-Feynman transform ($1{\leq}p{\leq}2$) and a convolution product on $\mathcal{F}(B)$ and verify the existence of the $L_p$ analytic Fourier-Feynman transforms for functionls in $\mathcal{F}(B)$. Moreover, we verify that the Fresnel class $\mathcal{F}(B)$ is closed under the $L_p$ analytic Fourier-Feynman transform and the convolution product, respectively. And we investigate some interesting properties for the $n$-repeated $L_p$ analytic Fourier-Feynman transform on $\mathcal{F}(B)$. Finally, we show that several results in [9] come from our results in Section 3.

• Phonetics and Speech Sciences
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• v.2 no.4
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• pp.229-238
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• 2010

This study investigates the differences in acoustic parameters in vowel space across hearing loss, gender and vowels. The parameters include F1, F2, Euclidean Distance between vowels, and vowel triangular area comprised of /i/, /a/ and /u/. For this study, 20 hearing-impaired and normal hearing adults as a control group were asked to read 7 Korean vowels (/a, $\wedge$, o, u, w, i, $\varepsilon$/). Subjects' readings were recorded by NasalView and analyzed by Praat. Results showed that F1 were significantly higher in the hearing impaired group than in the normal hearing group, higher in the female group than in male group, and higher in low vowels than in high vowels. And the means of F2 was significantly higher in the hearing impaired group than in normal hearing group, higher in high vowels than in low vowels, and there was no difference between male and female group. Secondly, Euclidean distance between vowels was significantly shorter in the hearing-impaired group than in the normal group. Finally, acoustic vowel space area was significantly smaller in the hearing-impaired group than in the normal hearing group. The hearing-impaired group showed that front vowels tended to be backed and back vowels to be fronted.

• Smart Media Journal
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• v.12 no.9
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• pp.134-141
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• 2023

In this paper, we propose a ToF-Stereo fusion sensor system for 3D space scanning that increases the recognition rate of 3D objects, guarantees object detection quality, and is robust to the environment. The ToF-Stereo sensor fusion system uses a method of fusing the sensing values of the ToF sensor and the Stereo RGB sensor, and even if one sensor does not operate, the other sensor can be used to continuously detect an object. Since the quality of the ToF sensor and the Stereo RGB sensor varies depending on the sensing distance, sensing resolution, light reflectivity, and illuminance, a module that can adjust the function of the sensor based on reliability estimation is placed. The ToF-Stereo sensor fusion system combines the sensing values of the ToF sensor and the Stereo RGB sensor, estimates the reliability, and adjusts the function of the sensor according to the reliability to fuse the two sensing values, thereby improving the quality of the 3D space scan.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1085-1100
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• 2023

For any given function f, we focus on the so-called prescribed mean curvature problem for the measure e^-f(|x|2)dx provided thate^-f(|x|2) ∈ L¹(ℝⁿ⁺¹). More precisely, we prove that there exists a smooth hypersurface M whose metric is ds² = dρ² + ρ²d𝜉² and whose mean curvature function is ${\frac{1}{n}}(\frac{u^p}{{\rho}^{\beta}})e^{f({\rho}^2)}{\psi}(\xi)$ for any given real constants p, β and functions f and ψ where u and ρ are the support function and radial function of M, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere 𝕊ⁿ, $${\sum_{i,j}}({{\delta}_{ij}-{\frac{{\rho}_i{\rho}_j}{{\rho}^2+|{\nabla}{\rho}|^2}})(-{\rho}ji+{\frac{2}{{\rho}}}{\rho}j{\rho}i+{\rho}{\delta}_{ji})={\psi}{\frac{{\rho}^{2p+2-n-{\beta}}e^{f({\rho}^2)}}{({\rho}^2+|{\nabla}{\rho}|^2)^{\frac{p}{2}}}}$$ under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)={\frac{t}{2}}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.

• Bulletin of the Korean Space Science Society
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• 2009.10a
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• pp.38.1-38.1
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• 2009

In this paper we present the first results of summer-time F region irregularities during low solar condition observed using the Gadanki MST radar. Echoes were observed on all 20 nights of radar observations and were mostly confined to the post-midnight hours. Echo morphology is very different from the equinoxial post-sunset plume-like features reported earlier from Gadanki. Echo SNRs are lower by 25 dB than their equinoxial post-sunset counterpart, and are quite comparable to the equinoxial irregularities in the post-midnight hours, which are essentially the decaying post-sunset irregularities. The Doppler velocities, which lie in the range of $\pm$ 100 m s-1, show upward/northward motion of the irregularities during the initial phase in contrast to the observed predominant downward/southward velocities associated with the decaying equinoxial post-midnight F region irregularities. Spectral widths of the summer echoes, which are well below 50 m s-1 and are very similar to those of the decaying equinoxial irregularities, represent the presence of weak plasma turbulence. Simultaneous observations made using a collocated ionosonde show no ionogram trace during 2200-0530 LT except for a few occasions. Weak frequency type spread F observed during midnight hours occurred without prior occurrence of range spread F. Concurrent ionosonde observations made from magnetic equatorial location Trivandrum also show very similar result and thus no height rise of the F layer during the midnight hours could be monitored. The preliminary analysis suggests that the post-midnight irregularities reported here are mostly freshly generated ones. The observations are discussed in the light of other observational results reported earlier and the current under standing on the post-midnight occurrence F region irregularities in summer.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.377-383
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• 1996

For a given separable space X which contains no copy of $C_0$ and a weakly compact T, we show that a Dunford integrable function $f : [a,b] \to X$ is intrinsically-separable valued if and only if f is McShane integrable. Also, for a given separable space X which contains no copy of $C_0$, a weakly compact T and a Dunford integrable function f we show that if there exists a sequence $(f_n)$ of McShane integrable functions from [a,b] to X such that for each $x^* \in X^*, x^*f_n \to x^*f$ a.e., then f is McShane integrable. Finally, let X contain no copy of $C_0$. If $f : [a,b] \to X$ is McShane integrable, then F is a countably additive on $\sum$.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.311-324
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• 1997

We show that if $f \in L^{\infty}(D^n)$ satisfies Sf = rf for some r in the unit circle, where S is any convex combination of the iterations of Berezin operator, then f is n-harmonic. And we give some remarks and a conjecture on the space $M_2={f \in L^2(D^2, m \times m)\midBf = f$.