• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.467-476
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• 2017

In this paper, we obtain the stability of the additive-quadratic functional equation f(x+y, z+w)+f(x+y, z-w) = 2f(x, z)+2f(x, w)+2f(y, z)+2f(y, w) and the bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,\;w)+f(y,\;z)+f(y,\;w)$$ in 2-Banach spaces.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.163-179
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• 2016

Let $M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$ Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ and (0.2) $N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ in fuzzy Banach spaces, where ρ is a fixed real number with ρ ≠ 1.

• 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.

• Nuclear Medicine and Molecular Imaging
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• v.40 no.4
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• pp.228-232
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• 2006

Purpose: electrophilic $^{18}F(T_{1/2}=110\;min)$ radionuclide in the form of $[^{18}F]F_2$ gas is of great significance for labeling radiopharmaceuticals for positron omission tomography (PET). However, its production In high yield and with high specific radioactivity is still a challenge to overcome several problems on targetry. The aim of the present study was to develop a method suitable for the routine production of $[^{18}F]F_2$ for the electrophilic substitution reaction. Materials and Methods: The target was designed water-cooled aluminum target chamber system with a conical bore shape. Production of the elemental fluorine was carried out via the $^{18}O(p,n)^{18}F$ reaction using a two-step irradiation protocol. In the first irradiation, the target filled with highly enriched $^{18}O_2$ was irradiated with protons for $^{18}F$ production, which were adsorbed on the inner surface of target body. In the second irradiation, the mixed gas ($1%[^{19}F]F_2/Ar$) was leaded into the target chamber, fellowing a short irradiation of proton for isotopic exchange between the carrier-fluorine and the radiofluorine absorbed in the target chamber. Optimization of production was performed as the function of irradiation time, the beam current and $^{18}O_2$ loading pressure. Results: Production runs was performed under the following optimum conditions: The 1st irradiation for the nuclear reaction (15.0 bar of 97% enriched $^{18}O_2$, 13.2 MeV protons, 30 ${\mu}A$, 60-90 min irradiation), the recovery of enriched oxygen via cryogenic pumping; The 2nd irradiation for the recovery of absorbed radiofluorine (12.0 bar of 1% $[^{19}F]fluorine/argon$ gas, 13.2 MeV protons, 30 ${\mu}A$, 20-30 min irradiation) the recovery of $[^{18}F]fluorine$ for synthesis. The yield of $[^{18}F]fluorine$ at EOB (end of bombardment) was achieved around $34{\pm}6.0$ GBq (n>10). Conclusion: The production of $^{18}F$ electrophilic agent via $^{18}O(p,n)^{18}F$ reaction was much under investigation. Especially, an aluminum gas target was very advantageous for routine production of $[^{18}F]fluorine$. These results suggest the possibility to use $[^{18}F]F_2$ gas as a electrophilic substitution agent.

• Journal of the Korean Ceramic Society
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• v.24 no.2
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• pp.117-122
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• 1987

Glass forming ranges in the AlF3-(Mg＋Sr＋Ba)F2-P2O5 system are studied and ultraviolet transmission, infrared transmission, coefficient of refractive index, thermal expansion coefficient, density and chemical durability of the glasses are determined. Glass forming range is restricted MgF2 0-10wt%, SrF2 10-50wt%, BaF2 10-40wt% in this system. While BaF2 is substituted by SrF2, density and refractive index are decreased, micro hardness and thermal expansion coefficient are increased according to the increasing of SrF2 at fixed MgF2 contents. These samples represent high transmittance(93%) from 400nm to 3800nm and chemical durability of these samples show less than 0.3mg/$\textrm{cm}^2$$.$hy by weightloss.

• 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.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.315-330
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• 2009

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quadratic functional equation $$(0.1)\;\frac{1}{2}(f(2x+y)+f(2x-y)-f(-2x-y)-f(y- 2x))\\{\hspace{35}}=2f(x+y)+2f(x-y)+4f(x)-8f(-x)-2f(y)-2f(-y)$$ in fuzzy Banach spaces.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.69-76
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• 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 $x{\bot}y$, $y{\bot}z$, $x{\bot}z$.

• Journal of the Korean Magnetics Society
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• v.17 no.1
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• pp.1-5
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• 2007

The 1R(Infra-Red) spectrum and PL(Photoluminescence) of the antiferromagnetic pure $MnF_2$ and the single crystal $MnF_2(1.5%\;EuF_3)$ with the rutile structures were measured. The detailed analysis of the measured PL data showed the differences of the optical property between the single crystal $MnF_2(1.5%\;EuF_3)$ and the pure $MnF_2$. It was found that the additional PL peak by the doping of the $EuF_3$ in $MnF_2$ is originated from the f-d transition of $Eu^{3+}$ from the temperature dependent intensity measurement.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.449-460
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• 2020

In this paper, we investigate the stability of the additive-cubic functional equations f(x+ky)+f(x-ky)-k² f(x+y)-k² f(x-y)+(k²-1)f(x) - (k²-1)f(-x) = 0, f(x+ky)-f(ky-x)-k² f(x+y)+k² f(y-x)+2(k²-1)f(x)= 0, f(kx+y)+f(kx-y)-kf(x+y)-kf(x-y)-2f(kx)+2kf(x)= 0 by using the fixed point theory in the sense of L. Cădariu and V. Radu.