• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.27 no.5
• /
• pp.620-627
• /
• 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.

• International Journal of Aeronautical and Space Sciences
• /
• v.18 no.2
• /
• pp.175-185
• /
• 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.

• The Pure and Applied Mathematics
• /
• v.23 no.1
• /
• pp.61-72
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.389-400
• /
• 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.

• Korean Journal of Mathematics
• /
• v.31 no.1
• /
• pp.25-33
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.715-727
• /
• 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, …, z_n 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.

• Korean Journal of Mathematics
• /
• v.28 no.4
• /
• pp.699-715
• /
• 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.

• Korean Journal of Mathematics
• /
• v.29 no.4
• /
• pp.785-800
• /
• 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.

• Journal of Energy Engineering
• /
• v.16 no.1 s.49
• /
• pp.46-52
• /
• 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.

• The Pure and Applied Mathematics
• /
• v.22 no.3
• /
• pp.263-273
• /
• 2015

In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z) = a + c_pz^p + c_p+₁z^p+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.