• Title/Summary/Keyword: angular derivative

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

  • Kim, Man-Young;Baek, Seung-Wook;Kim, Ki-Wan
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.27 no.5
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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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    • v.18 no.2
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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
    • The Pure and Applied Mathematics
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    • v.23 no.1
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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
    • Communications of the Korean Mathematical Society
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    • v.38 no.2
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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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    • v.31 no.1
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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
    • 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, …, 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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    • v.28 no.4
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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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    • v.29 no.4
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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.

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

  • Noh, Tae-Wan
    • Journal of Energy Engineering
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    • v.16 no.1 s.49
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    • pp.46-52
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    • 2007
  • The piecewise constant angular approximation is developed to replace the conventional angular quadrature sets in the solution of the second-order, multi-dimensional $S_{N}$ neutron transport equations. The newly generated quadrature sets by this method substantially mitigate ray effects and can be used in the same manner as the conventional quadrature sets are used. The discrete-ordinates and the piecewise-constant approximations are applied to both the first-order Boltzmann and the second-order form of neutron transport equations in treating angular variables. The result is that the mitigation of ray effects is only achieved by the piecewise-constant method, in which new angular quadratures are generated by integrating angle variables over the specified region. In other sense, the newly generated angular quadratures turn out to decrease the contribution of mixed-derivative terms in the even-parity equation that is one of the second-order neutron transport equation. This result can be interpreted as the entire elimination or substantial mitigation of ray effect are possible in the simplified even-parity equation which has no mixed-derivative terms.

A SHARP SCHWARZ LEMMA AT THE BOUNDARY

  • AKYEL, TUGBA;ORNEK, NAFI
    • The Pure and Applied Mathematics
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    • v.22 no.3
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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.