• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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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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• 제61권1호
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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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• 제21권2E호
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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.

• 한국군사과학기술학회지
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• 제5권2호
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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.

• 한국음향학회지
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• 제22권6호
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• pp.482-488
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• 2003

선 배열을 이용한 빔 형성시 특정 지향 방향을 기준으로 반대 방향에 동일한 이득을 갖게 되어 수신단에서는 좌/우측 방위구분에 있어 모호성을 갖는다 이에 본 논문에서는 선 배열에 카디오이드 빔을 적용하여 좌/우측 방위 구분의 모호성을 해결하고, 아울러 어레이 합성 처리 기법을 사용하여 음원에 대한 공간적 데이터 수를 증가시키고 음원으로부터 얻은 정보를 코히어런트 합성 처리함으로써 배열 센서가 갖는 공간적인 분해능의 한계를 극복하였다. 시뮬레이션 결과에서는 좌/우측 방위 구분에 대한 성능을 어레이 합성 횟수에 따라 나타내었다.

• 호남수학학술지
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• 제43권4호
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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.

• 대한수학회지
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• 제59권2호
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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.