• Kyungpook Mathematical Journal
• /
• v.47 no.1
• /
• pp.69-76
• /
• 2007

Let $f$ denote a mapping from an orthogonality space ($\mathcal{X}$, ${\bot}$) into a real Banach space $\mathcal{Y}$. In this paper, we prove the Hyers-Ulam-Rassias stability of the orthogonally cubic functional equations $f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)$ and $f(x+y+2z)+f(x+y-2z)+f(2x)+f(2y)=2f(x+y)+4f(x+z)+4f(x-z)+4f(y+z)+4f(y-z)$, where $x{\bot}y$, $y{\bot}z$, $x{\bot}z$.

• Communications of the Korean Mathematical Society
• /
• v.24 no.2
• /
• pp.277-280
• /
• 2009

In this paper, we prove the following two statements: (1) There exists a Hausdorff locally $Lindel{\ddot{o}}f$ centered-$Lindel{\ddot{o}}f$ space that is not star-$Lindel{\ddot{o}}f$. (2) There exists a $T_1$ locally compact centered-$Lindel{\ddot{o}}f$ space that is not star-$Lindel{\ddot{o}}f$. The two statements give a partial answer to Bonanzinga and Matveev [2, Question 1].

• The Pure and Applied Mathematics
• /
• v.25 no.3
• /
• pp.219-227
• /
• 2018

In this paper, we solve the additive ${\rho}$-functional equations $$(0.1)\;f(x+y)+f(x-y)-2f(x)={\rho}\left(2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)\right)$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < 1, and $$(0.2)\;2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ${\rho}$-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.

• MALSORI
• /
• no.58
• /
• pp.19-34
• /
• 2006

The present study investigates the vowels of Bahasa Malaysia and Bahasa Indonesia in terms of the first two formant frequencies and provides a three-dimensional formant chart of vowels by plotting F1, F2, and the frequency of datapoints on 4 different scales: Hz, mel, bark, and the number of ERB. For this study, we recruited 30 male native speakers of Bahasa Malaysia and Bahasa Indonesia (15 each) which include 6 vowels (i, e, a, o, u, e) in various contexts. The three-dimensional formant chart showed geophysics of vowel space, such that mountain peaks stand in particular locations with a higher frequency of occurrence of datapoints. The geophysics of vowel space may shed lights on the perceptual structure of vowel space. The results also showed that vowels in utterance-final positions have a significantly higher F1 and a significantly lower F2 than those in utterance-medial or utterance-initial positions, which means that vowels in utterance-final positions are more back and lower in vowel space than those in utterance-medial or utterance-initial positions.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.3
• /
• pp.397-408
• /
• 2015

In this paper, we solve the Hyers-Ulam stability problem for the following cubic type functional equation $$f(rx+sy)+f(rx-sy)=rs^2f(x+y)+rs^2f(x-y)+2r(r^2-s^2)f(x)$$in quasi-Banach space and non-Archimedean space, where $r={\neq}{\pm}1,0$ and s are real numbers.

• Korean Journal of Mathematics
• /
• v.21 no.1
• /
• pp.1-21
• /
• 2013

Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ (0.1) for all $x$, $y$, $z$ with $x{\bot}y$, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.13 no.1
• /
• pp.71-78
• /
• 2000

The main goal of this paper is to prove the following theorem ; Let (X, ${\rho}_1$) be a fuzzy normed linear space over K and (Y, ${\rho}_2$) be a fuzzy Banach space over K. If ${\chi}_{B_{{\parallel}{\cdot}{\parallel}}}{\supseteq}{\rho}*$, then (CF(X,Y), ${\rho}*$) is a fuzzy Banach space, where ${\rho}*(f)={\vee}{\lbrace}{\theta}{\wedge}\frac{1}{t({\theta},f)}\;{\mid}\;{\theta}{\in}(0,1){\rbrace}$, $f{\in}CF(X,Y)$, $B_{{\parallel}{\cdot}{\parallel}}$ is the closed unit ball on (CF(X, Y), ${\parallel}{\cdot}{\parallel}$ and ${\parallel}f{\parallel}={\vee}{\lbrace}P^2_{{\alpha}^-}(f(x))\;{\mid}\;P^1_{{\alpha}^-}(x)=1,\;x{\in}X{\rbrace}$, $f{\in}CF(X,Y)$, ${\alpha}{\in}(0,1)$.

• Journal of Astronomy and Space Sciences
• /
• v.22 no.2
• /
• pp.139-146
• /
• 2005

A model of advection-dominated accretion flows has been highlighted in the last decade. Most of calculations are based on self-similar solutions of equations governing the accreting flows. We revisit self-similar solutions of the simplest form of advection-dominated accretion flows. We explore the parameter space thoroughly and seek another category of self-similar solutions. In this study we allow the parameter f less than zero, which denotes the fraction of energy transported through advection. We have found followings: 1. For f > 0, in real ADAF solutions the ratio of specific heats ${\gamma}$ satisfies 1 < ${\gamma}$ < 5/3 for O ${\leq}$ f ${\leq}$ 1. On the other hands, in wind solutions a rotating disk does not exist. 2. For f < 0, in real ADAF solutions with ${\epsilon}$ greater than zero ${\gamma}$ requires rather exotic range, that is, ${\gamma}$ < 1 or ${\gamma}$ > 5/3. When -5/2 < ${\epsilon}$' < 0, however, allowable ${\gamma}$ can be found in ${\gamma}$ < 5/3, in which case 4{\Omega}_0$,_ is imaginary. 3. For a negative $u_0$,+ with f > 0, solutions are only allowed with exotic ${\gamma}$, that is, 1 < ${\gamma}$ or ${\gamma}$ > (5f/2-5/3)/(5f/2-1)when O < f < 2/5, (5f/2-5/3)/(5f/2-1) < ${\gamma}$ < 1 when f > 2/5. Since ${\epsilon}$' is negative, 4{\Omega}_0$,+ is again an imaginary quantity. For a negative $u_0$,+ with f < 0, ${\gamma}$ is allowed in 1 < 7 < (5|f|/2 + 5/3)/(5|f|/2 + 1). We briefly discuss physical implications of what we have found.

• Communications of the Korean Mathematical Society
• /
• v.18 no.4
• /
• pp.653-659
• /
• 2003

Let $1{\;}\leq{\;}p{\;}\infty{\;}and{\;}{\alpha}{\;}>{\;}-1$. If f is a holomorphic self-map of the open unit disc U of C with f(0) = 0, then the quantity $\int_U\;\{\frac{$\mid$f'(z)$\mid$}{1\;-\;$\mid$f(z)$\mid$^2}\}^p\;(1\;-\;$\mid$z$\mid$)^{\alpha+p}dxdy$ is equivalent to the operator norm of the composition operator $C_f{\;}:{\;}B{\;}\rightarrow{\;}A^{p,{\alpha}$ defined by $C_fh{\;}={\;}h{\;}\circ{\;}f{\;}-{\;}h(0)$, where B and $A^{p,{\alpha}$ are the Bloch space and the weighted Bergman space on U respectively.

• Speech Sciences
• /
• v.1
• /
• pp.201-211
• /
• 1997

Acoustically a naturally-spoken vowel is composed of five formants. However, the acoustic quality of a vowel is known to be mostly determined by $F_1\;and\;F_2$. The main purpose of this study was to examine how synthesized vowels with $F_1\;and\;F_2$ are perceived by Korean native speakers. In addion, we are interested in finding whether the synthesized vowels are perceived differently by standard Korean speakers and Kyungnam regional dialect speakers. In the experiment 9 Seoul standard Korean speakers and 9 Kyungnam dialect speakers heard 536 vowels synthesized in vowel space with $F_1\;by\;F_2$ and categorized them into one of 10 Korean vowels. The resultant vowel map showed that each Korean vowel occupies an unique area in the two-dimensional vowel space of $F_1\;by\;F_2$, and confirmed that $F_1\;and\;F_2$ play important roles in the perception of vowels. The results also showed that the Seoul speakers and the Kyungnam speakers perceive the synthesized vowels differently. For example, /e/ versus /$\varepsilon$/ contrast, /y/, and /$\phi$/ are perceived differently by the Seoul speakers, whereas they were perceptually confused by the Kyungnam speakers. These results might be due to the different vowel systems of the standard Korean and the Kyungnam regional dialect. While the latter uses a six-vowel system which has no /e/ vs /$/ contrast, /v/ vs /i/ contrast, /y/, and /$\phi$/, the former recognizes these as different vowels. This result suggests that the vowel system of differing dialect restricts the perception of the Korean vowels. Unexpectedly /i/ does not occupy any area in the vowel apace. This result suggests that /i/ cannot be synthesized without $F_3$.