• 제목/요약/키워드: angular derivative

검색결과 51건 처리시간 0.021초

축대칭 열복사 해석을 위한 방향 미분항의 고찰 (Investigation of the Angular Derivative Term for the Analysis of Axisymmetric Thermal Radiation)

  • 김만영;백승욱;김기완
    • 대한기계학회논문집B
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    • 제27권5호
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    • pp.620-627
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    • 2003
  • Radiative heat transfer in an axisymmetric enclosure with absorbing, emitting, and scattering medium is studied here by using the different methods such as MDOM, FVM, and FVM2 with emphasis on the treatment of angular derivative term, which appears in a curvilinear coordinates due to angular redistribution. After final discretization equation for FVM2 is introduced by using the step scheme and directional weights, present approach is validated by applying it to three different benchmarking problems with absorbing, emitting, and scattering medium.

Calculating Dynamic Derivatives of Flight Vehicle with New Engineering Strategies

  • Mi, Baigang;Zhan, Hao;Chen, Baibing
    • International Journal of Aeronautical and Space Sciences
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    • 제18권2호
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    • pp.175-185
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    • 2017
  • This paper presents new differential methods for computing the combined and single dynamic stability derivatives of flight vehicle. Based on rigid dynamic mesh technique, the combined dynamic stability derivative can be achieved by imposing the aircraft pitching to the same angle of attack with two different pitching angular velocities and also translating it to the same additional angle of attack with two different rates of angle of attack. As a result, the acceleration derivative is identified. Moreover, the rotating reference frame is adopted to calculate the rotary derivatives when simulating the steady pull-up with different pitching angular velocities. Two configurations, the Hyper Ballistic Shape (HBS) and Finner missile model, are considered as evaluations and results of all the cases agree well with reference or experiment data. Compared to traditional ones, the new differential methods are of high efficiency and accuracy, and potential to be extended to the simulation of combined and single stability derivatives of directional and lateral.

AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARY

  • ORNEK, BULENT NAFI;AKYEL, TUGBA
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제23권1호
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    • pp.61-72
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    • 2016
  • In this paper, a boundary version of the Schwarz lemma for the holom- rophic function satisfying f(a) = b, |a| < 1, b ∈ ℂ and ℜf(z) > α, 0 ≤ α < |b| for |z| < 1 is invetigated. Also, we estimate a modulus of the angular derivative of f(z) function at the boundary point c with ℜf(c) = a. The sharpness of these inequalities is also proved.

RESULTS ASSOCIATED WITH THE SCHWARZ LEMMA ON THE BOUNDARY

  • Bulent Nafi Ornek
    • 대한수학회논문집
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    • 제38권2호
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    • pp.389-400
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    • 2023
  • In this paper, some estimations will be given for the analytic functions belonging to the class 𝓡(α). In these estimations, an upper bound and a lower bound will be determined for the first coefficient of the expansion of the analytic function h(z) and the modulus of the angular derivative of the function ${\frac{zh^{\prime}(z)}{h(z)}}$, respectively. Also, the relationship between the coefficients of the analytical function h(z) and the derivative mentioned above will be shown.

SOME RESULTS FOR THE CLASS OF ANALYTIC FUNCTIONS CONCERNED WITH SYMMETRIC POINTS

  • Ayse Nur Arabaci;Bulent Nafi Ornek
    • Korean Journal of Mathematics
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    • 제31권1호
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    • pp.25-33
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    • 2023
  • This paper's objectives are to present the $\mathcal{H}$ class of analytical functions and explore the many characteristics of the functions that belong to this class. Some inequalities regarding the angular derivative have been discovered for the functions in this class. In addition, the symmetry points on the unit disc are used for the obtained inequalities.

SOME RESULTS CONCERNED WITH HANKEL DETERMINANT FOR 𝓝 (𝜶) CLASS

  • Atli, Gizem;Ornek, Bulent Nafi
    • 대한수학회논문집
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    • 제36권4호
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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, …, zn 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.

BOUNDS OF HANKEL DETERMINANTS FOR ANALYTIC FUNCTION

  • Ornek, Bulent Nafi
    • Korean Journal of Mathematics
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    • 제28권4호
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    • pp.699-715
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    • 2020
  • In this paper, we give estimates of the Hankel determinant H2(1) in a novel class 𝓝 (𝜀) of analytical functions in the unit disc. In addition, the relation between the Fekete-Szegö function H2(1) and the module of the angular derivative of the analytical function p(z) at a boundary point b of the unit disk will be given. In this association, the coefficients in the Hankel determinant b2, b3 and b4 will be taken into consideration. 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.

ON BOUNDS FOR THE DERIVATIVE OF ANALYTIC FUNCTIONS AT THE BOUNDARY

  • Ornek, Bulent Nafi;Akyel, Tugba
    • Korean Journal of Mathematics
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    • 제29권4호
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    • pp.785-800
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    • 2021
  • In this paper, we obtain a new boundary version of the Schwarz lemma for analytic function. We give sharp upper bounds for |f'(0)| and sharp lower bounds for |f'(c)| with c ∈ ∂D = {z : |z| = 1}. Thus we present some new inequalities for analytic functions. Also, we estimate the modulus of the angular derivative of the function f(z) from below according to the second Taylor coefficients of f about z = 0 and z = z0 ≠ 0. Thanks to these inequalities, we see the relation between |f'(0)| and 𝕽f(0). Similarly, we see the relation between 𝕽f(0) and |f'(c)| for some c ∈ ∂D. The sharpness of these inequalities is also proved.

다차원 2계 중성자 수송방정식의 방향근사를 위한 영역상수법 (Piecewise-Constant Method for Angular Approximation for the Second-Order Multidimensional Neutron Transport Equations)

  • 노태완
    • 에너지공학
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    • 제16권1호
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    • pp.46-52
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    • 2007
  • 특정한 방향에 대해 방향중성자속(angular neutron flux)을 정의하는 방향차분 방정식(discrete-ordinates or $S_{N}$ equation)과 달리 방향변수를 구분된 방향영역에 대하여 적분한 값을 사용하고, 해당 방향영역 내에서 방향중성자속이 일정하다고 가정하는 영역상수법(piecewise-constant method)을 개발하였다. 기존 방향차분법과 본 연구에서 개발된 영역상수법을 1계 수송방정식(1'st-order Boltzmann transport equation)과 2계 우성 방정식(even-parity equation)에 적용하여 방향차분 방정식인 $S_{N}$ 방정식과 유사 방향차분방정식($S_{N}$-like equation)인 $PC_{N}$ 방정식을 유도하였다. 우성 방정식에 영역상수법을 적용한 경우 기존 방향차분법의 단점인 광첨두 현상(ray effect)이 현저히 감소함을 확인하였는데 이는 우성 방정식의 혼합 미분항의 기여도가 작아지기 때문인 것으로 판단된다. 이러한 이론은 우성 방정식에서 혼합 미분항이 제거된 단순우성 방정식(simplified even-parity equation)을 사용하는 경우 광첨두 현상이 완전 제거 또는 극단적으로 감소되었던 이전의 결과를 이론적으로 설명한다.

A SHARP SCHWARZ LEMMA AT THE BOUNDARY

  • AKYEL, TUGBA;ORNEK, NAFI
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제22권3호
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    • pp.263-273
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    • 2015
  • In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z) = a + cpzp + cp+1zp+1 + ... defined in the unit disc satisfying |f(z) − 1| < 1, where 0 < a < 2, we estimate a module of angular derivative at the boundary point b, f(b) = 2, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.