• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.325-334
• /
• 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 ${\mid}b{\mid}=1$.

• Structural Engineering and Mechanics
• /
• v.16 no.6
• /
• pp.655-674
• /
• 2003

Investigated in this study are the natural vibration characteristics of the coaxial cylindrical shells coupled with a fluid. Theoretical method is developed to find the natural frequencies of the shell using the finite Fourier series expansion, and their results are compared with those of finite element method to verify the validation of the method developed. The effect of the fluid-filled annulus and the boundary conditions on the modal characteristics of the coaxial shells is investigated using a finite element modeling.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2000.04a
• /
• pp.20-20
• /
• 2000

초음속 과소팽창 제트는 베럴충격파(Barrel shock), 팽창파(Expansion fan), 반사충격파(Reflected shocks), 마하디스크(Mach disc), 그리고 제트경계면(Exhaust-gas Jet boundary)로 이루어지는 여러 충격파 셀(Shock ceil)의 유동 형태를 나타난다. 이러한 초음속 과소팽창 제트가 수직 평판에 충돌하면 초음속 자유 제트와는 다른 변형된 유동장이 형성된다.

• Communications of the Korean Mathematical Society
• /
• v.15 no.1
• /
• pp.173-181
• /
• 2000

The objective of this paper is to study two dimensional steady gravitational waves on the interface between two immiscible, inviscid and incompressible fluids bounded above by a horizontal rigid boundary and below by a rigid step. A KdV equation for the first order perturbation in an asymptotic expansion can appear. However the coefficient of the KdV theory fails in that case. By a unified asymptotic method, we overcome this difficulty and derive a modified KdV equation with forcing. We find homogeneous steady solutions and present numerical solutions.

• Journal of applied mathematics & informatics
• /
• v.8 no.3
• /
• pp.683-691
• /
• 2001

A linearized finite-difference scheme is used to transform the initial/boundary-value problem associated with the nonlinear Schrodinger equation into a linear algebraic system. This method is developed by replacing the time and the nonlinear term by an appropriate parametric linearized scheme based on Taylor’s expansion. The resulting finite-difference method is analysed for stability and convergence. The results of a number of numerical experiments for the single-soliton wave are given.

• Proceedings of the Korean Ceranic Society Conference
• /
• 2002.10a
• /
• pp.178.1-178
• /
• 2002

• The Pure and Applied Mathematics
• /
• v.29 no.1
• /
• pp.113-124
• /
• 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 Ocean Engineering and Technology
• /
• v.10 no.3
• /
• pp.138-152
• /
• 1996

Many studies of heat transfer on the swirling flow or unswirled flow in a abrupt pipe expansion are widely carried out. The mechanism is not fully found evidently due to the instabilities of flow in a sudden change of the shape and appearance of turbulent shear layers in a recirculation region and secondary vortex near the corner. The purpose of this study is to obtain data through an experimental study of the swirling flow and heat transfer downstream of an abrupt expansion in a circular pipe with uniform heat flux. Experiments were carried out for the turbulent flow nd heat transfer downstream of an abrupt circular pipe expansion. The uniform heat flux condition was imposed to the downstream of the abrupt expansion by using an electrically heated pipe. Experimental data are presented for local heat transfer rates and local axial velocities in the tube downstream of an abrupt 3:1 & 2:1 expansion. Air was used as the working fluid in the upstream tube, the Reynolds number was varied from 60, 00 to 120, 000 and the swirl number range (based on the swirl chamber geometry, i.e. L/d ratio) in which the experiments were conducted were L/d=0, 8 and 16. Axial velocity increased rapidly at r/R=0.35 in the abrupt concentric expansion turbulent flow through the test tube in unswirled flow. It showed that with increasing axial distance the highest axial velocities move toward the tube wall in the case of the swirling flow abrupt expansion. A uniform wall heat flux boundary condition was employed, which resulted in wall-to-bulk temperatures ranging from 24.deg. C to 71.deg. C. In swirling flow, the wall temperature showed a greater increase at L/d=16 than any other L/d. The bulk temperature showed a minimum value at the pipe inlet, it also exhibited a linear increase with axial distance along the pipe. As swirl intensity increased, the location of peak Nu numbers was observed to shift from 4 to 1 step heights downstream of the expansion. This upstream movement of the maximum Nusselt number was accompanied by an increase in its magnitude from 2.2 to 8.8 times larger than fully developed tube flow values.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.1 no.4
• /
• pp.59-68
• /
• 1997

In analysis of underground structures, the effects of artificial boundary conditions are considered as one of the major reasons for differences from experimental results. These phenomena can be overcome by using the boundary elements which satisfy the multi-layered half space conditions. The fundamental solutions of multi-layered half-space for boundary element method is formulated satisfying the transmission and reflection of waves at each layer interface and radiation conditions at bottom layer. The governing equations can be obtained from the displacements at each layer which are expressed in terms of harmonic functions. All types of waves can be included using the complete response from semi-infinite integrals with respect to horizontal wavenumbers using expansion of Fourier series and Hankel transformation. Two dimensional Green's functions are derived from cylindrical Navier equations and potentials performing infinite integration in y-direction. In this case, it is effective to transform into two dimensional problem using semi-analytical integration and sinusoidal Bessel function. Some verifications are given to show the accuracy and efficiency of the developed method, and numerical examples to demonstrate the dynamic behavior of underground with various properties.

• The Journal of the Convergence on Culture Technology
• /
• v.4 no.4
• /
• pp.361-366
• /
• 2018

For each character constituting learning data, different fonts are added in pixel unit to create MASK, and then pixel values belonging to the MASK are divided into three groups. The experimental data are modified into skeletal forms, and then regional boundary operation is used to create a boundary that distinguishes the background region adjacent to the skeleton of the character from the background of the modified experimental data. Discordance values between the modified experimental data and the MASKs are calculated, and then the MASK with the minimum value is found. This MASK is selected as a finally recognized result for the given experiment data. The recognition algorithm using skeleton of the character and the regional boundary operation can easily extend the learning data set by adding new fonts to the given learning data, and also it is simple to implement, and high character recognition rate can be obtained.