• Journal of the Korean Society for Precision Engineering
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• v.14 no.1
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• pp.194-204
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• 1997

In this paper, we consider the rational approximation of multiple input delay systems. The method of computing Hankel singular values and vectors is firstly introduced, where explicitly shows the structure of the corresponding Hankel singular vectors. Secondly, rational approximants are obtained from output nor- mal relizations, which are constructed by Hankel singular values and vectors. As a result, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pad'e approximants.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.281-291
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• 2023

A normalized analytic function f is parabolic starlike if w(z) := zf' (z)/f(z) maps the unit disk into the parabolic region {w : Re w > |w - 1|}. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.92-108
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• 2023

We determine the upper bounds on fourth order Hankel determinants H⁽²⁾₄(f) and H⁽³⁾₄(f) for the class S^*_L of lemniscate starlike functions defined on the open unit disk which was introduced by Sokół and Stankiewicz in [17].

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.407-420
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• 2024

In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1139-1148
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• 2015

The estimate of third Hankel determinant $$H_{3,1}(f)=\left|a_1\;a_2\;a_3\\a_2\;a_3\;a_4\\a_3\;a_4\;a_5\right|$$ of the analytic function $f(z)=z+a2z^2+a3z^3+{\cdots}$, for which ${\Re}(1+zf^{{\prime}{\prime}}(z)/f^{\prime}(z))>-1/2$ are investigated. The corrected version of a known results [2, Theorem 3.1 and Theorem 3.3] are also obtained.

• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.5
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• pp.594-601
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• 2016

Mass estimation analysis of loose-parts in pressure vessel is necessary for the structural integrity assessment of pressure boundary in nuclear power plants. Mass of loose-parts can be generally estimated from the peak values and the center frequency of impact signals. Magnitude of impact signals is, however, inevitably attenuated according to the traveling distance of the signals and depending on the frequencies. Attenuation rate must be therefore carefully compensated for the precise estimation of loose-part mass. This paper proposes a new compensation method for the attenuation rate based on Bessel function instead of Hankel function in conventional method which has a limitation of usage in near the impact location. It was verified that the suggested compensating equation based on the Bessel function can be applied to the attenuation rate calculation without any limitation.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.231-242
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• 2018

We derive sharp upper bound on the initial coefficients and Hankel determinants for normalized analytic functions belonging to a class, introduced by Silverman, defined in terms of ratio of analytic representations of convex and starlike functions. A conjecture related to the coefficients for functions in this class is posed and verified for the first five coefficients.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.715-727
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• 2021

In this paper, we give some results an upper bound of Hankel determinant of H₂(1) for the classes of 𝓝 (𝜶). We get a sharp upper bound for H₂(1) = c₃ - c²₂ for 𝓝 (𝜶) by adding z₁, z₂, …, z_n zeros of f(z) which are different than zero. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained. Finally, the sharpness of the inequalities obtained in the presented theorems are proved.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.429-438
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• 2015

The objective of this paper is to obtain sharp upper bound for the second Hankel functional associated with the $k^{th}$ root transform $[f(z^k)]^{\frac{1}{k}}$ of normalized analytic function f(z) when it belongs to the class of starlike and convex functions with respect to symmetric points, defined on the open unit disc in the complex plane, using Toeplitz determinants.