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Kowalczyk, Bogumila;Lecko, Adam;Lecko, Millenia;Sim, Young Jae
- Bulletin of the Korean Mathematical Society
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- v.55 no.6
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- pp.1859-1868
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- 2018
In the present paper, we have proved the sharp inequality ${\mid}H_{3,1}(f){\mid}{\leq}4$ and ${\mid}H_{3,1}(f){\mid}{\leq}1$ for analytic functions f with $a_n:=f^{(n)}(0)/n!$, $n{\in}{\mathbb{N}},$, such that $$Re\frac{f(z)}{z}>{\alpha},\;z{\in}{\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$$ for ${\alpha}=0$ and ${\alpha}=1/2$, respectively, where $$H_{3,1}(f):=\left|{\array{{\alpha}_1&{\alpha}_2&{\alpha}_3\\{\alpha}_2&{\alpha}_3&{\alpha}_4\\{\alpha}_3&{\alpha}_4&{\alpha}_5}}\right|$$ is the third Hankel determinant.
https://doi.org/10.4134/BKMS.b171122 인용 PDF KSCI

Ali, Rosihan M.;Lee, See Keong;Obradovic, Milutin
- Bulletin of the Korean Mathematical Society
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- v.57 no.4
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- pp.839-850
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- 2020
For functions f(z) = z + a₂z² + a₃z³ + ⋯ belonging to particular classes, this paper finds sharp bounds for the initial coefficients a₂, a₃, a₄, as well as the sharp estimate for the second order Hankel determinant H₂(2) = a₂a₄ - a₂³. Two classes are treated: first is the class consisting of f(z) = z + a₂z² + a₃z³ + ⋯ in the unit disk 𝔻 satisfying $$\|$\frac{z}{f(z)}$^{1+{\alpha}}\;f^{\prime}(z)-1\|<{\lambda},\;0<{\alpha}<1,\;0<{\lambda}{\leq}1.$$ The second class consists of Bazilevič functions f(z) = z+a₂z²+a₃z³+⋯ in 𝔻 satisfying $$Re\{$\frac{f(z)}{z}$^{{\alpha}-1}\;f^{\prime}(z)\}>0,\;{\alpha}>0.$$
https://doi.org/10.4134/BKMS.b190520 인용 PDF KSCI

박순홍;김양한;고병식
- Transactions of the Korean Society of Automotive Engineers
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- v.5 no.2
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- pp.162-172
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- 1997
We investigated passby noise measurement method in a small-sized semi-anechoic chamber satisfying the American based SAE J1470 Recommended Practice to facilitate the measurements. We have tired two passby noise prediction methods. One is line array microphone method in which the free space sound field is decomposed into its eigenfunctions in the spherical coordinates and rearranged according to the order of the spherical Hankel function. However, due to the characteristics of the spherical Hankel function, it is impossible to distinguish the function's characteristics according to the order in farfield. Consequently it can be applied in the transient region of the nearfield and the farfield. The other method is nearfield acoustic holography(NAH). Although measuring hologram for the several operational engine speeds by conventional scanning method is time-consuming work, we can greatly reduce the measuring time by selecting the appropriate engine speed through preexperimental knowledge. To verify this method we experimented with the outdoor passby noise measurements and the passby noise prediction in the small-sized semi-anechoic chamber for the identical passenger vehicle and obtained reasonable and acceptable results.
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Kim, Hee Joon
- Economic and Environmental Geology
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- v.18 no.1
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- pp.41-47
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- 1985
The filtering ability of $J_0$ and $J_1$ digital linear filters is compared by means of an adaptive linear filter. Any $J_0$ domain Hankel transform integral can be transformed mathematically into its corresponding $J_1$ domain integral. The apparent resistivities for any electrode configuration employed in resistivity soundings can be evaluated with a single $J_1$ filter. The $J_1$ filter usually has similar accuracy to, but shorter length than, the corresponding $J_0$ filter. The domain transformation from $J_0$ to $J_1$ enables us to use effective expressions of apparent resistivity, involving $J_1$ alone, not only for Schlumberger but also for dipole-dipole array.
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