• 대한수학회논문집
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• 제34권2호
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• pp.543-555
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• 2019

In this paper, we give some results on ${\frac{zf^{\prime}(z)}{f(z)}}$ for the certain classes of holomorphic functions in the unit disc $E=\{z:{\mid}z{\mid}<1\}$ and on ${\partial}E=\{z:{\mid}z{\mid}=1\}$. For the function $f(z)=z^2+c_3z^3+c_4z^4+{\cdots}$ defined in the unit disc E such that $f(z){\in}{\mathcal{A}}_{\alpha}$, we estimate a modulus of the angular derivative of ${\frac{zf^{\prime}(z)}{f(z)}}$ function at the boundary point b with ${\frac{bf^{\prime}(b)}{f(b)}}=1+{\alpha}$. Moreover, Schwarz lemma for class ${\mathcal{A}}_{\alpha}$ is given. The sharpness of these inequalities is also proved.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.83-108
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• 1997

Chebysheff-Halley methods are probably the best known cubically convergent iterative procedures for solving nonlinear equa-tions. These methods however require an evaluation of the second Frechet-derivative at each step which means a number of function eval-uations proportional to the cube of the dimension of the space. To re-duce the computational cost we replace the second Frechet derivative with a fixed bounded bilinear operator. Using the majorant method and Newton-Kantorovich type hypotheses we provide sufficient condi-tions for the convergence of our method to a locally unique solution of a nonlinear equation in Banach space. Our method is shown to be faster than Newton's method under the same computational cost. Finally we apply our results to solve nonlinear integral equations appearing in radiative transfer in connection with the problem of determination of the angular distribution of the radiant-flux emerging from a plane radiation field.

• Interaction and multiscale mechanics
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• 제4권4호
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• pp.291-311
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• 2011

To simulate the self excited torsional vibrations of rotating drill strings (DSs) in vertical bore-holes, the nonlinear wave models of homogeneous and sectional torsional pendulums are formulated. The stated problem is shown to be of singularly perturbed type because the coefficient appearing before the second derivative of the constitutive nonlinear differential equation is small. The diapasons ${\omega}_b\leq{\omega}\leq{\omega}_l$ of angular velocity ${\omega}$ of the DS rotation are found, where the torsional auto-oscillations (of limit cycles) of the DS bit are generated. The variation of the limit cycle states, i.e. birth (${\omega}={\omega}_b$), evolution (${\omega}_b&lt;{\omega}&lt;{\omega}_l$) and loss (${\omega}={\omega}_l$), with the increase in angular velocity ${\omega}$ is analyzed. It is observed that firstly, at birth state of bifurcation of the limit cycle, the auto-oscillation generated proceeds in the regime of fast and slow motions (multiscale motion) with very small amplitude and it has a relaxation mode with nearly discontinuous angular velocities of elastic twisting. The vibration amplitude increases as ${\omega}$ increases, and then it decreases as ${\omega}$ approaches ${\omega}_l$. Sectional drill strings are also considered, and the conditions of the solution at the point of the upper and lower section joints are deduced. Besides, the peculiarities of the auto-oscillations of the sectional DSs are discussed.

• 대한수학회보
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• 제53권2호
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• pp.325-334
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• 2016

In this paper, a boundary version of the Schwarz lemma is investigated. We take into consideration a function $f(z)=z+c_{p+1}z^{p+1}+c_{p+2}z^{p+2}+{\cdots}$ holomorphic in the unit disc and $\|\frac{f(z)}{{\lambda}f(z)+(1-{\lambda})z}-{\alpha}\|$ < ${\alpha}$ for ${\mid}z{\mid}$ < 1, where $\frac{1}{2}$ < ${\alpha}$ ${\leq}{\frac{1}{1+{\lambda}}}$, $0{\leq}{\lambda}$ < 1. If we know the second and the third coefficient in the expansion of the function $f(z)=z+c_{p+1}z^{p+1}+c_{p+2}z^{p+2}+{\cdots}$, then we can obtain more general results on the angular derivatives of certain holomorphic function on the unit disc at boundary by taking into account $c_{p+1}$, $c_{p+2}$ and zeros of f(z) - z. We obtain a sharp lower bound of ${\mid}f^{\prime}(b){\mid}$ at the point b, where ${\mid}b{\mid}=1$.

• 대한수학회논문집
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• 제31권3호
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• pp.533-547
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• 2016

In this paper, a generalized boundary version of $Carath{\acute{e}}odory^{\prime}s$ inequality for holomorphic function satisfying $f(z)= f(0)+a_pz^p+{\cdots}$, and ${\Re}f(z){\leq}A$ for ${\mid}z{\mid}$<1 is investigated. Also, we obtain sharp lower bounds on the angular derivative $f^{\prime}(c)$ at the point c with ${\Re}f(c)=A$. The sharpness of these estimates is also proved.

• 대한수학회논문집
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• 제33권4호
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• pp.1205-1215
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• 2018

In this paper, a boundary version of the $Carath{\acute{e}}odory^{\prime}s$ inequality is investigated. We shall give an estimate below ${\mid}f^{\prime}(b){\mid}$ according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_1{\neq}0$. The sharpness of these estimates is also proved.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권1호
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• pp.113-124
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• 2022

In this paper, we plan to introduce the class of the analytic functions called 𝒫 (b) and to investigate the various properties of the functions belonging this class. The modulus of the second coefficient c₂ in the expansion of f(z) = z+c₂z²+… belonging to the given class will be estimated from above. Also, we estimate a modulus of the second angular derivative of f(z) function at the boundary point 𝛼 with f'(𝛼) = 1 - b, b ∈ ℂ, by taking into account their first nonzero two Maclaurin coefficients.

• Journal of Pharmaceutical Investigation
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• 제41권3호
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• pp.161-171
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• 2011

The objective of the present study is to systematically characterize a linear viscoelastic behavior of petroleum jelly in small amplitude oscillatory shear flow fields correspondent to the rheological ground state. With this aim, using a strain-controlled rheometer, the dynamic viscoelastic properties of commercially available petroleum jelly have been measured at $37^{\circ}C$ (body temperature) over a wide range of angular frequencies at an extremely small strain amplitude of 0.1 %. In this article, the linear viscoelastic behavior was reported in detail and then explained from a structural view-point of petroleum jelly and discussed in depth with respect to the consumer's requirements. Main findings obtained from this study can be summarized as follows : (1) The storage modulus is always greater than the loss modulus over an entire range of angular frequencies studied, meaning that the linear viscoelastic behavior of petroleum jelly is dominated by an elastic nature rather than a viscous nature. (2) Petroleum jelly shows a desirable linear viscoelastic behavior with respect to the consumer's requirements because it is undesirable for the product to flow down from the skin at an initial stage upon contact with the human skin. (3) A fractional derivative model shows an excellent applicability to describe a linear viscoelastic behavior of petroleum jelly. However, this model should be used with a special caution because there exists no physical meaning for the model parameters. (4) A modified form of the Cox-Merz rule gives a good ability to predict the relationship between steady shear flow properties (nonlinear behavior) and dynamic viscoelastic properties (linear behavior) for petroleum jelly.

• 한국지능시스템학회논문지
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• 제19권2호
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• pp.168-173
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• 2009

본 논문은 수중 차의 차속도와 프로펠러 각속도를 추정하는 문제를 다룬다. 계단식 관측기는 측정된 위치 값으로부터 속도값 추정을 위해 사용한다. 고이득 관측기(high-gain observer)에 전형적으로 생기는 전형적인 문제를 없애기 위하여 계단식 구조의 관측기가 설계되었다. 고이득 관측기처럼 시스템 다이나믹스와 파라미터로부터 무관하게 설계할 수 있으며 단순한 구조를 가진다 관측기의 첫 단계에서 출력 값이 추정되고 측정된 출력의 1계 미분 값이 관측기의 두 번째 단계를 통해 추정된다. 또한 출력의 n 번째 미분 값은 관측기의 n+1 번째 단계에서 추정된다. 제안된 관측기가 전체 점근적 안정도를 보장함을 보여준다. 시뮬레이션 결과는 기존의 고이득 관측기에 비해 제안된 관측기가 수중 차의 차속도와 프로펠러 각속도를 더 우수하게 추정함을 보여준다.

• International Journal of Aeronautical and Space Sciences
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• 제11권3호
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• pp.167-174
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• 2010

The design, dynamics, and control allocation of tri-rotor unmanned aerial vehicles (UAVs) are introduced in this paper. A trirotor UAV has three rotor axes that are equidistant from its center of gravity. Two designs of tri-rotor UAV are introduced in this paper. The single tri-rotor UAV has a servo-motor that is installed on one of the three rotors, which enables rapid control of its motion and its various attitude changes-unlike a quad-rotor UAV that depends only on the angular velocities of four rotors for control. The other design is called 'coaxial tri-rotor UAV,' which has two rotors installed on each rotor axis. Since the tri-rotor type of UAV has the yawing problem induced from an unpaired rotor's reaction torque, it is necessary to derive accurate dynamic and design control logic for both single and coaxial tri-rotors. For that reason, a control strategy is proposed for each type of tri-rotor, and nonlinear simulations of the altitude, Euler angle, and angular velocity responses are conducted by using a classical proportional-integral-derivative controller. Simulation results show that the proposed control strategies are appropriate for the control of single and coaxial tri-rotor UAVs.