• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.307-319
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• 2022

The present paper deals with the upper bound of third order Hankel determinant for a certain subclass of analytic functions associated with Cardioid domain in the open unit disc E = {z ∈ ℂ : |z| < 1}. The results proved here generalize the results of several earlier works.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.75-98
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• 2021

In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p, q)-Fekete-Szegö inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.

• The Journal of the Acoustical Society of Korea
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• v.21 no.2E
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• pp.71-80
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• 2002

This paper suggests the Cardioid beamforming algorithm of the doublet sensors employing DIFAR (directional frequency analysis and recording) sensor signals in the frequency domain. The algorithm enables target bearing estimation using the signals from directional sensors. The algorithm verifies its applicability by successfully estimating bearings of a target projecting ten narrow-band signals in shallow water. The estimated bearings agree very well with those from GPS (global positioning system) data. Assuming the bearings from GPS data to be real values, the estimation errors are analyzed statistically. The histogram of estimation errors in each frequency have Gaussian shape, the mean and standard deviation dropping in the ranges -1.1°∼ 6.7°and 13.3∼43.6°, respectively. Estimation errors are caused by SNR (signal to noise ratio) degradation due to propagation loss between the source and receiver, daily fluctuating geo-magnetic fields, and non-stationary background noises. If multiple DIFAR systems are employed, in addition to bearing, range information could be estimated and finally localization or tracking of a target is possible.

• Journal of the Korea Institute of Military Science and Technology
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• v.5 no.2
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• pp.169-184
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• 2002

In order to extract bearing information from the directional sensors of DIFAR(directional frequency analysis and recording) that is a kind of passive sonobuoy, the cardioid beamforming algorithm applicable to DIFAR system was studied in the frequency domain. the algorithm uses narrow-band signals propagated though the media from the acoustic sources such as ship machineries. The proposed algorithm is expected to give signal to noise ratio of 6dB when it uses the maximum response axis(MRA) among the Cardioid beams. The estimated bearings agree very well with those from GPS data. Assuming the bearings from GPS data to be real values, the estimation errors are analyzed statistically. The histogram of estimation errors in each frequency have Gaussian shape, the mean and standard deviation dropping in the ranges -1.1~$6.7^{\circ}$ and 13.3~$43.6^{\circ}$, respectively. Estimation errors are caused by SMR degradation due to propagation loss between the source and receiver, daily fluctuating geo-magnetic fields, and non-stationary background noises. If multiple DIFAR systems are employed, in addition to bearing, range information could be estimated and finally localization or tracking of a target is possible.

• The Journal of the Acoustical Society of Korea
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• v.22 no.6
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• pp.482-488
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• 2003

Line may receiver contains an ambiguity on conjugate bearings, because of lacking aperture in transverse direction. To solve the left/right bearing ambiguity of line-array receiver we used line-array with cardioid beam. In addition, the synthetic aperture method adopts coherent processing of sub-aperture signals at successive time intervals in the beam domain. We presented performances about division of left/right bearing ambiguity according to array synthetic number of times in this paper.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.627-639
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• 2021

Numerical techniques are used to determine the radius of convexity of the starlike functions related to cardioid shaped bounded domain. In addition, radius constants of certain starlikeness associated with right half plane of various starlike functions are computed.

• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.353-365
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• 2022

Let 𝓐 be the collection of analytic functions f defined in 𝔻 := {ξ ∈ ℂ : |ξ| < 1} such that f(0) = f'(0) - 1 = 0. Using the concept of subordination (≺), we define $$S^*_{\ell}\;:=\;\{f{\in}A:\;\frac{{\xi}f^{\prime}({\xi})}{f({\xi})}{\prec}{\Phi}_{\ell}(\xi)=1+{\sqrt{2}{\xi}}+{\frac{{\xi}^2}{2}},\;{\xi}{\in}{\mathbb{D}}\}$$, where the function 𝚽_ℓ(ξ) maps 𝔻 univalently onto the region Ω_ℓ bounded by the limacon curve (9u² + 9v² - 18u + 5)² - 16(9u² + 9v² - 6u + 1) = 0. For 0 < r < 1, let 𝔻_r := {ξ ∈ ℂ : |ξ| < r} and 𝒢 be some geometrically defined subfamily of 𝓐. In this paper, we find the largest number 𝜌 ∈ (0, 1) and some function f₀ ∈ 𝒢 such that for each f ∈ 𝒢 𝓛_f (𝔻_r) ⊂ Ω_ℓ for every 0 < r ≤ 𝜌, and $${\mathcal{L} _{f_0}}({\partial}{\mathbb{D}_{\rho})\;{\cap}\;{\partial}{\Omega}_{\ell}\;{\not=}\;{\emptyset}$$, where the function 𝓛_f : 𝔻 → ℂ is given by $${\mathcal{L}}_f({\xi})\;:=\;{\frac{{\xi}f^{\prime}(\xi)}{f(\xi)}},\;f{\in}{\mathcal{A}}$$. Moreover, certain graphical illustrations are provided in support of the results discussed in this paper.