• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1171-1187
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• 2011

Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly regular pair. In this paper, we provide the same improvement for a jointly regular family: let h : ${\mathbb{P}}_{\mathbb{Q}}^n{\rightarrow}{{\mathbb{R}}$ be the logarithmic absolute height on the projective space, let r(f) be the D-ratio of a rational map f which is de ned in [10] and let {$f_1,{\ldots},f_k|f_l:\mathbb{A}^n{\rightarrow}\mathbb{A}^n$} bbe finite set of polynomial maps which is defined over a number field K. If the intersection of the indeterminacy loci of $f_1,{\ldots},f_k$ is empty, then there is a constant C such that $ \sum\limits_{l=1}^k\frac{1}{def\;f_\iota}h(f_\iota(P))>(1+\frac{1}{r})f(P)-C$ for all $P{\in}\mathbb{A}^n$ where r= $max_{\iota=1},{\ldots},k(r(f_l))$.

• The Korean Journal of Mycology
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• v.25 no.3 s.82
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• pp.202-208
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• 1997

In this study, we evaluated the use of RAPD method to discriminate among strains of Fusarium species including F. oxysporum and f. sp. of F. oxysporum. As a result of the amplication, fifteen primers showed total 180 bands ranging from 0.2 to 3 Kb. Among those 180 bands, 126 polymorphic bands were used for bionominal matrix code (0, 1), and UPGMA dendrogram analysis. Fusarium oxysporum isolate 355 showed high similarity with F. oxysporum isolate 358 at 0.9603. Fusarium roseum isolate 87 and F. oxysporum isolate 358, F. o. f. sp. lycopersici isolate 69 and F. o. f. sp. melongena 68 showed low similarity of 0.3809. Fusarium oxysporum isolate 361 and F. o. f. sp. raphani isolate 218 showed similarity of 0.8730, F. oxysoprum isolate 354 and unidentified Fusarium sp. isolate 228 showed similarity matrix of 0.7936, and F. roseum isolate 87 and F. o. f. sp. raphani isolate 57 showed similarity matrix of 0.5873.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.91-101
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• 2015

In this paper, we investigate the stability of the functional equation f(-x + y + z + w) + f(x - y + z + w) + f(x + y - z + w) + f(x + y + z - w) = 3f(x) + f(-x) + 3f(y) + f(-y) + 3f(z) + f(-z) + 3f(w) + f(-w) by using the direct method in the sense of Hyers.

• The Journal of the Acoustical Society of Korea
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• v.34 no.4
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• pp.288-294
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• 2015

The fiber optic Sagnac interferometer is well established as a sensor for detection of physical perturbations such as acoustic and vibration. In this paper acoustic signals generated in the cylindrical cavity submerged in transformer oil were measured by the fiber optic sensor array in one Sagnac loop. Two different external sound frequencies, $f_1$ and $f_2$, were applied to the sensor array simultaneously by using piezoelectric with frequency range from 5 kHz to 90 kHz. Based on the experimental results, fiber optic sensor detected harmonic series of applied sound frequency such as $f_1$, $f_2$, $2f_1$, $2f_2$, ${\mid}f_1-f_2{\mid}$, ${\mid}f_1+f_2{\mid}$. Suggested fiber optic sensor array can be applied to monitor physical quantities such as internal sound pressure and vibration due to partial discharge in the real electric transformer system.

• Journal of the Korean Magnetics Society
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• v.16 no.5
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• pp.261-263
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• 2006

In order to investigate the magnetic properties of Eu ions in the single crystal $MnF_2$, the temperature dependent magnetic susceptibilities of the antiferromagnetic $MnF_2$ and the single crystal $MnF_2$(1.5% $EuF_3$) with the rutile structures were measured in the temperature range from 4K to 300K. The detailed analysis of the measured susceptibilities showed that the magnetic susceptibility by the doping of the small amount $EuF_3$ in the antiferromagnetic single crystal $MnF_2$ follows the antiferromagnetic Curie-Weiss law with the negative paramagnetic Curie temperature similarly as in $MnF_2$. It was also found that Eu ion has +3 valence. This solves the long standing discrepancy on this problem.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.757-770
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• 2009

In this paper, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation (0.1) f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f(-2y) - 4f(y) - 4f(-y) in Banach spaces.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.193-204
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• 2007

In this paper, we investigate some results concerning the stability of the following quadratic type functional equation: f(x + y) + f(x - y) + f(y + z) + f(y - z) + f(z + x) + f(z - x) = 4f(x) + 4f(y) + 4f(z).

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.387-397
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• 1996

Let G be a finite group and F be a field of characteristic $p \geq 0$. Let $\Gamma = F^f G$ be a twisted group algebra corresponding to a 2-cocycle $f \in Z^2(G,F^*), where F^* = F - {0}$ is the multiplicative subgroup of F.

• 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.

• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.39-47
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• 2012

Let $\mathcal{F}$ be a family of meromorphic functions in a domain D, and let $k$, $n({\geq}2)$ be two positive integers, and let $S=\{a_1,a_2,{\ldots},a_n\}$, where $a_1$, $a_2$, ${\ldots}$, $a_n$ are distinct finite complex numbers. If for each $f{\in}\mathcal{F}$, all zeros of $f$ have multiplicity at least $k+1$, $f$ and $G(f)$ share the set $S$ in $D$, where $G(f)=P(f^{(k)})+H(f)$ is a differential polynomial of $f$, then$\mathcal{F}$ is normal in $D$.