• The Journal of the Acoustical Society of Korea
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• v.15 no.2
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• pp.72-78
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• 1996

This thesis deals with a method to solve a two-and-one-half-dimensional ($2\frac12$ D) problem, which means that the ocean environment is two-dimensional whereas the source is fully three-dimensionally propagating, including three-dimensional refraction phenomena and three-dimensional back-scattering, using two-dimensional two-way parabolic equation method combined with Fourier synthesis. Two dimensional two-way parabolic equation method uses Galerkin's method for depth and Crank-Nicolson method and alternating direction for range and provides a solution available to range-dependent problem with wave-field back-scattered from discontinuous interface. Since wavenumber, k, is the function of depth and vertical or horizontal range, we can reduce a dimension of three-dimensional Helmholtz equation by Fourier transforming in the range direction. Thus transformed two-dimensional Helmholtz equation is solved through two-way parabolic equation method. Finally, we can have the $2\frac12$ D solution by inverse Fourier transformation of the spectral solution gained from in the last step. Numerical simulation has been carried out for a canonical ocean environment with stair-step bottom in order to test its accuracy using the present analysis. With this spectral parabolic equation method, we have examined three-dimensional acoustic propagation properties in a specified site in the Korean Straits.

• Journal of Advanced Navigation Technology
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• v.21 no.5
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• pp.466-471
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• 2017

SOTM is a device for the satellite communication on the move. Many studies are conducted on microstrip, waveguide and array antenna for the low profile of the SOTM's antenna. But those antennas have a problem that is difficult to adjust the polarization, and for that reason we have studied the parabolic antenna structure. The general form of parabolic reflector structure is circular, but we used cut-off shape reflector by cutting the upper and lower reflector for low profile antenna. Accordingly, this results in the decrease of reflector area which causes reduced gain and G/T ratio. In order to solve this problem, we have transformed and designed the sub reflector for improving the efficiency and gain of the cut- off shape parabolic antenna.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.3
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• pp.43-48
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• 2018

Offset parabolic antenna have been widely used for satellite communication system. To locate feedhorn on antenna system, it requires arbitrary structure which forces to fix on system. However, arbitrary scatterer increases sidelobe level of elevation axis. To solve this problem, we need to predict which angle level is increased by arbitrary scatterer simply. Because conventional simulation method takes a long time to simulate parabolic antenna system and needs exclusive software. In this paper we can calculate sidelobe angle simply by using raytracing method, check coincidence between calculated and simulated result and show how arbitrary scatterer affects sidelobe lavel of elevation axis of offset parabolic antenna depending on angle and location of arbitrary structure.

• Structural Engineering and Mechanics
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• v.77 no.1
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• pp.1-17
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• 2021

The influence of prestress force on the fundamental frequency and static deflection shape of uncracked Prestressed Concrete (PC) beams with a parabolic bonded tendon was examined in this paper. Due to the conflicts among existing theories, the analytical solutions for properly considering the dynamic and static behavior of these members is not straightforward. A series of experiments were conducted for a total period of approximately 2.5 months on a PC beam made with high strength concrete, subsequently and closely to the 28 days of age of concrete. Specifically, the simply supported PC member was short term subjected to free transverse vibration and three-point bending tests during its early-age. Subsequently, the experimental data were compared with a model that describes the dynamic behavior of PC girders as a combination of two substructures interconnected, i.e., a compressed Euler-Bernoulli beam and a tensioned parabolic cable. It was established that the fundamental frequency of uncracked PC beams with a parabolic bonded tendon is sensitive to the variation of the initial elastic modulus of concrete in the early-age curing. Furthermore, the small variation in experimental frequency with time makes doubtful its use in inverse problem identifications. Conversely, the relationship between prestress force and static deflection shape is well described by the magnification factor formula of the "compression-softening" theory by assuming the variation of the chord elastic modulus of concrete with time.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.17-30
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• 1997

In this work we approximate the solution of initialboun-dary value problem using a Galerkin-finite element method for the spatial discretization and Implicit Runge-Kutta method for the spatial discretization and implicit Runge-Kutta methods for the time stepping. To deal with the nonlinear term f(x, t, u), we introduce the well-known extrapolation sheme which was used widely to prove the convergence in $L_2$-norm. We present computational results showing that the optimal order of convergence arising under $L_2$-norm will be preserved in $L_{\infty}$-norm.

• Journal of The Korean Astronomical Society
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• v.39 no.4
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• pp.147-150
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• 2006

In this paper, initial value problem for dynamical astronomy will be established using parabolic cylindrical coordinates. Computation algorithm is developed for the initial value problem of gravity perturbed trajectories. Applications of the algorithm for the problem of final state predication are illustrated by numerical examples of seven test orbits of different eccentricities. The numerical results are extremely accurate and efficient in predicating final state for gravity perturbed trajectories which is of extreme importance for scientific researches as well as for military purposes. Moreover, an additional efficiency of the algorithm is that, for each of the test orbits, the step size used for solving the differential equations of motion is larger than 70% of the step size used for obtaining its reference final state solution.

• East Asian mathematical journal
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• v.4
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• pp.157-173
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• 1988

• Korean Journal of Mathematics
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• v.1
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• pp.21-26
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• 1993

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.793-803
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• 2000

An impulsive semilinear parabolic equation subject to Robin boundary condition is considered. We prove that for certain classes of impulsive sources and continuous initial data, the solutions of the problem under consideration blow up in the desired time interval.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.139-148
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• 2005

In this paper we extend the mixed finite element method and its $L_2$-error estimate for postprocessed solutions by using Crank-Nicolson time-discretization method. Global $O(h^2+({\Delta}t)^2)$-superconvergence for the lowest order Raviart-Thomas element ($Q_0-Q_{1,0}{\times}Q_{0,1}$) are obtained. Numerical examples are presented to confirm superconvergence phenomena.