• 제목/요약/키워드: cardioid

검색결과 27건 처리시간 0.022초

SUFFICIENT CONDITIONS AND RADII PROBLEMS FOR A STARLIKE CLASS INVOLVING A DIFFERENTIAL INEQUALITY

  • Swaminathan, Anbhu;Wani, Lateef Ahmad
    • 대한수학회보
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    • 제57권6호
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    • pp.1409-1426
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    • 2020
  • Let 𝒜n be the class of analytic functions f(z) of the form f(z) = z + ∑k=n+1 αkzk, n ∈ ℕ defined on the open unit disk 𝔻, and let $${\Omega}_n:=\{f{\in}{\mathcal{A}}_n:\|zf^{\prime}(z)-f(z)\|<{\frac{1}{2}},\;z{\in}{\mathbb{D}}\}$$. In this paper, we make use of differential subordination technique to obtain sufficient conditions for the class Ωn. Writing Ω := Ω1, we obtain inclusion properties of Ω with respect to functions which map 𝔻 onto certain parabolic regions and as a consequence, establish a relation connecting the parabolic starlike class 𝒮P and the uniformly starlike UST. Various radius problems for the class Ω are considered and the sharpness of the radii estimates is obtained analytically besides graphical illustrations.

INCLUSION RELATIONS AND RADIUS PROBLEMS FOR A SUBCLASS OF STARLIKE FUNCTIONS

  • Gupta, Prachi;Nagpal, Sumit;Ravichandran, Vaithiyanathan
    • 대한수학회지
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    • 제58권5호
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    • pp.1147-1180
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    • 2021
  • By considering the polynomial function 𝜙car(z) = 1 + z + z2/2, we define the class 𝓢*car consisting of normalized analytic functions f such that zf'/f is subordinate to 𝜙car in the unit disk. The inclusion relations and various radii constants associated with the class 𝓢*car and its connection with several well-known subclasses of starlike functions is established. As an application, the obtained results are applied to derive the properties of the partial sums and convolution.

실험실 공기질 개선을 위한 라인디퓨져의 특성 평가 (Characteristic Evaluation of Line Diffusers for Air Quality Improvement of Laboratory)

  • 조수현;이철구
    • 한국공작기계학회논문집
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    • 제17권6호
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    • pp.14-22
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    • 2008
  • This study is aimed at suggesting a linear-type diffuser which is excellent in terms of range and elegance like existing diffusers in which amount and direction of wind can be freely controled, out of linear-type diffusers with the highest possibility to be adopted for living space of apartments whose height between floors is not so high and utilizing the linear-type diffuser in design. For the purpose, I examined necessary flow and noise properties of linear-type diffusers. Besides, I evaluated its ventilation capacity for persons in there by applying this in the actual living space. I evaluated features and air blast and found that in time of horizontal and vertical effusion, its T/L ratio is 1-1.5, similar to existing cardioid-type linear diffusers, while in time of slope effusion, it is similar to horizontal effusion in terms of range and it has medium figure in terms of pressure drop and effusion speed, indicating it can provide safe and pleasant indoor environment for persons in there in terms of ventilation.

다중 모드형 링 벡터 센서의 설계 (Design of a Multimode Type Ring Vector Sensor)

  • 임영섭;조치영;서희선;노용래
    • 한국음향학회지
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    • 제32권6호
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    • pp.484-493
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    • 2013
  • 통상의 수중 음향 센서는 단일 센서로는 음압의 크기만 측정할 뿐 외부 음원의 방향은 측정 할 수 없는 한계가 있다. 이에 본 논문에서는 링 센서를 사용하여 음원의 방향을 찾을 수 있는 구조를 제안하였다. 제안된 구조의 링 센서는 내부 압전 세라믹이 8등분되어 배열되어 있으며, 외부 음압에 대한 각 압전 세라믹 조각의 출력 전압을 적절히 조합하여 외부 음원의 방향을 파악할 수 있는 특성을 가진다. 나아가 링 센서의 반경, 압전 세라믹의 두께, 길이와 같은 구조 변수들의 영향을 분석하여, 벡터 센서의 감도를 향상 시킬 수 있는 방안을 제시하였다.

이동형 전자식 TACAN 안테나 설계 및 구현 (Design and Implementation of Mobile Electronically Scanned TACAN Antenna)

  • 박상진;구경헌
    • 한국전자파학회논문지
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    • 제26권1호
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    • pp.54-62
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    • 2015
  • 본 논문은 기생소자와 핀 다이오드 스위치를 이용한 전자식 전술 항법 장비(Tactical Air Navigation) 안테나에 대하여 설계 및 구현을 설명한다. 모터를 이용하여 기계적으로 안테나가 회전하는 대신 전자적으로 안테나를 회전시키기 위하여 기생소자를 원형 배열 형태로 배치하고, 핀 다이오드 스위치를 사용하였다. 방위정보를 포함하는 심장모양 패턴과 9개의 로브 패턴을 생성하기 위한 안테나의 구조적 특성과 설계 특징을 설명하고, 시뮬레이션을 수행하였다. 측정된 결과는 시뮬레이션과 일치하고, MIL-STD-291C 규격을 만족한다.

예인선배열 센서를 이용한 전방위 표적방위 탐지기 구현 (Implementation of the omnidirectional target bearing detector utilizing towed linear arrays)

  • 이성은;천승용;황수복;이형욱
    • 한국군사과학기술학회지
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    • 제5권1호
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    • pp.59-64
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    • 2002
  • Passive sonar system forms the various beams in any desired directions to obtain the improvement in Signal-to-Noise(S/N) ratio, bearing detection and localization of targets, and the attenuation of interferences from other directions. Detection of modern underwater targets is becoming increasingly difficult as noise reduction technology leads to considerably low-level acoustic emissions. Therefore, the improvement of beamforming is very important to detect modern underwater targets at the long range in the complex environmental sea. Also, to react to the fast attack mobiles such as torpedoes, port and starboard discrimination is required to be performed very quickly. In this paper, we proposed the implementation of omnidirectional target bearing detector without port and starboard ambiguity to detect effectively the low-level underwater targets. The port and starboard discrimination is performed by cardioid processing and the improvement of beamforming utilizes the cross correlation matrix of individual hydrophone pairs of linear array sensors. The sea test result shows that the system implemented is good for the detection of the low-level underwater targets.

RADIUS CONSTANTS FOR FUNCTIONS ASSOCIATED WITH A LIMACON DOMAIN

  • Cho, Nak Eun;Swaminathan, Anbhu;Wani, Lateef Ahmad
    • 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(ξ) maps 𝔻 univalently onto the region Ω bounded by the limacon curve (9u2 + 9v2 - 18u + 5)2 - 16(9u2 + 9v2 - 6u + 1) = 0. For 0 < r < 1, let 𝔻r := {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 𝓛f (𝔻r) ⊂ Ω for every 0 < r ≤ 𝜌, and $${\mathcal{L} _{f_0}}({\partial}{\mathbb{D}_{\rho})\;{\cap}\;{\partial}{\Omega}_{\ell}\;{\not=}\;{\emptyset}$$, where the function 𝓛f : 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.