• Journal of Astronomy and Space Sciences
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• v.34 no.1
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• pp.1-5
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• 2017

The F2-layer critical frequency (foF2) data from several ionosondes are employed to study the long-distance effect of the M8.8 Chile Earthquake of February 27, 2010, on the F2 layer. Significant perturbations of the peak F2-layer electron density have been observed following the earthquake at two South African stations, Hermanus and Madimbo, which are located at great circle distances of ~8,000 and ~10,000 km from the earthquake epicenter, respectively. Simplified estimates demonstrate that the observed ionospheric perturbations can be caused by a long-period acoustic gravity wave produced in the F-region by the earthquake.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.377-391
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• 2013

The main goal of this paper is to present the additional stability results of the following orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ for all $x,y,z$ with $x{\bot}y$, which has been introduced in the paper [11], in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.77-89
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• 2012

Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive functional equation (0.1) $f(2x+y)=2f(x)+f(y)$ and of the orthogonally quadratic functional equation (0.2) $2f(\frac{x}{2}+y)+2f(\frac{x}{2}-y)=f(x)+4f(y)$ for all $x$, $y$ with $x{\perp}y$ in orthogonality spaces.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.455-466
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• 2008

In, [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\left\|{\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i{\left\|^2+{\sum\limits_{i=1}^{n}}\right\|}{x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}x_j}}\right\|^2}={\sum\limits_{i=1}^{n}}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\cdots},x_{n}{\in}V$. Let V,W be real vector spaces. It is shown that if a mapping $f:V{\rightarrow}W$ satisfies $$(0.1){\hspace{10}}nf{\left({\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i \right)}+{\sum\limits_{i=1}^{n}}f{\left({x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}}x_i}\right)}\\{\hspace{140}}={\sum\limits_{i=1}^{n}}f(x_i)$$ for all $x_1$, ${\dots}$, $x_{n}{\in}V$ $$(0.2){\hspace{10}}2f\(\frac{x+y}{2}\)+f\(\frac{x-y}{2} \)+f\(\frac{y}{2}-x\)\\{\hspace{185}}=f(x)+f(y)$$ for all $x,y{\in}V$. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.2) in real Banach spaces.

• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.243-251
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• 2017

In this paper, we solve the additive ${\rho}-functional$ equations (0.1) $f(x+y)+f(x-y)-2f(x)={\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x))$, and (0.2) $2f(\frac{x+y}{2})+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$, where ${\rho}$ is a fixed (complex) number with ${\rho}{\neq}1$, Using the direct method, we prove the Hyers-Ulam stability of the additive ${\rho}-functional$ equations (0.1) and (0.2) in ${\beta}-homogeneous$ (complex) F-spaces.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.2
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• pp.46.1-46.1
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• 2021

태양으로부터 3Rs보다 높은 코로나 밝기의 대부분은 먼지에 의해 산란된 F코로나로부터 나온다. F코로나와 자유전자의 톰슨산란에 의한 K코로나를 분리하는 효과적인 방법은 편광을 이용하는 것으로 알려져 있고 현재 NASA와 천문연간 협력개발 중인 K코로나 관측 기기 COronal Diagnostic EXperiment(CODEX)도 편광을 이용한 분류를 기본으로 자유전자의 온도와 속도를 측정한다. 문제는 F코로나도 약간의 편광도를 가져서 K코로나와 구별이 불가능해지는데다 F코로나의 편광량은 먼지입자의 구성물질, 모양, 산란 위치 등에 따라 달라서 거의 예측이 불가능하고 지금까지 제대로 알려진 바도, 연구된 바도 없다. 우리는 CODEX에서 F코로나 편광량을 산출하기 위해 한 개의 협대역 필터(Narrow Bandpass Filter)를 추가장착하는 것을 제안하였고 그 중심파장과 밴드폭을 결정하였다. 몬테카를로 계산 결과 10장의 393.55nm 중심의 1.4nm폭 협대역필터와 393.5nm 중심의 10nm 협대역 필터비를 이용해 1Rs 화소의 해상도로 F코로나 편광량을 결정할 수 있을 것으로 예상된다. 2023년 CODEX 발사 후 본 관측이 성공적으로 수행된다면 F코로나의 편광량의 시간, 공간적 변화를 확인할 수 있으며 추가적으로 K코로나를 보다 정밀하게 분리해낼 수 있을 것으로 기대된다.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.319-328
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• 2016

In this paper, we solve the additive ρ-functional inequalities (0.1) ||f(2x-y)+f(y-x)-f(x)|| $\leq$ ||${\rho}(f(x+y)-f(x)-f(y))$||, where ρ is a fixed complex number with |ρ| < 1, and (0.2) ||f(x+y)-f(x)-f(y)|| $\leq$ ||${\rho}(f(2x-y)-f(y-x)-f(x))$||, where ρ is a fixed complex number with |ρ| < $\frac{1}{2}$. Using the direct method, we prove the Hyers-Ulam stability of the additive ρ-functional inequalities (0.1) and (0.2) in β-homogeneous F-spaces.

• The Pure and Applied Mathematics
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• v.26 no.1
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• pp.49-58
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• 2019

In this paper, I prove the stability problem for a quadratic-cubic functional equation $$f(x+ky)-k^2f(x+y)-k^2f(x-y)+f(x-ky)+f(kx)-{\frac{k^3-3k^2+4}{2}}f(x)+{\frac{k^3-k^2}{2}}f(-x)=0$$ in modular spaces by applying the direct method.

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.231-248
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• 2015

In this paper, we solve the following quadratic $\rho$-functional inequalities ${\parallel}f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-x(y)-f(z){\parallel}\;(0.1)\\{\leq}{\parallel}{\rho}(f(x+y+z+)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}<\frac{1}{8}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}\;(0.2)\\{\leq}{\parallel}{\rho}(f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}$ < 4. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic $\rho$-functional inequalities (0.1) and (0.2) in complex Banach spaces.