• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.917-921
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• 2000

One of the major limitations of productivity and quality in machining is machining accuracy of the machine tools. The machining accuracy is affected by geometric, volumetric errors of the machine tools. This paper suggests the enhancement method of machining accuracy for precision machining of high quality metal reflection mirror or optics lens, etc. In this paper, we study 1) the compensation of linear pitch error with NC controller compensation function using laser interferometer measurement, 2) the method for enhancing the accuracy of NC milling machining by modeling and compensation of volumetric error, 3) the generation of the parabolic face profile. And the method is verified by the parabolic face machining experiment with a vertical three axes NC milling machine. After this study, we will inspect using On-machine measurement and study the repetitive machining by a compensated path

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.2
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• pp.66-75
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• 1989

Simple formulas for evaluating the radiation characteristics of an offset parabolic antennas are presented. The validity of the proposed equations was verified by comparing the results wit the numerical clculation. The offset parabolic antenna for the domestic broadcasting satellite has been designed by using of simple formulas. The radiation patterns of the desinged offset parabolic antenna show good agreement with experimental results.

• Journal of the Korean Society for Heat Treatment
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• v.14 no.5
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• pp.282-285
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• 2001

Based on the mass balance of anion and cation fluxes, the parabolic rate constant ($K_p$) of oxide grown during the high-temperature oxidation of metal is theoretically calculated. It is assumed that the diffusion of oxygen anion and metal cation through oxide scale obeys the Fick's 1st law, the growth of oxide is controlled by the diffusion of ions, electrical potential gradient as driving force for diffusion of ions is ignored, and oxidation occurs within an existing oxide layer. Then, the parabolic rate constant can be expressed by $K_p=[2{\rho}_{MmOn}{M^2}_{MmOn}(mD_oC_o{^e}+nD_MC_M{^e})/nm]$.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.473-484
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• 2015

Archimedes determined the center of gravity of a parabolic section as follows. For a parabolic section between a parabola and any chord AB on the parabola, let us denote by P the point on the parabola where the tangent is parallel to AB and by V the point where the line through P parallel to the axis of the parabola meets the chord AB. Then the center G of gravity of the section lies on PV called the axis of the parabolic section with $PG=\frac{3}{5}PV$. In this paper, we study strictly locally convex plane curves satisfying the above center of gravity properties. As a result, we prove that among strictly locally convex plane curves, those properties characterize parabolas.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.10 no.3
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• pp.412-418
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• 1999

The scattering characteristics of a prime-focus offset-parabolic antenna are analyzed using UTD. First, ray tracing method is used to locate the shadow boundaries, and then UTD is utilized to evalute the far-zone scattered magnetic field pattern. The field components included in the UTD analysis are the reflected, edge diffracted and creeping waves. The effects of circular caps attached to both edges of a prime-focus offset-parabolic antenna are investigated by comparing the scattered magnetic field patterns with those of a knife edge parabolic reflector.

• Steel and Composite Structures
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• v.27 no.6
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• pp.777-788
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• 2018

An investigation on the thermal buckling resistance of simply supported FGM beams having parabolic-concave thickness variation and temperature dependent material properties is presented in this paper. An analytical formulation based on the first order beam theory is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. a function of thickness variation is introduced which controls the parabolic variation intensity of the beam thickness without changing its original material volume. The results showed the high importance of taking into account the temperature-dependent material properties in the thermal buckling analysis of such critical beam sections. Different Influencing parametric on the thermal stability are studied which may help in design guidelines of such complex structures.

• International Journal of Railway
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• v.8 no.2
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• pp.46-49
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• 2015

In this paper, improved out-of-plane design of parabolic arches was proposed based on the current design code. The arches resist general loading by a combination of axial compression and bending actions, and the interaction formula between two extreme cases of axial and bending actions is generally used for the design. Firstly, the out-of-plane buckling strength of arches in a pure axial compression and a pure bending were studied. Then, out-of-plane design of parabolic aches under general transverse loading was investigated. From the results, it can be found that the proposed design equations provided good prediction of out-of-plane strength for parabolic arches which satisfy the thresholds for deep arches, while proposed design equations overestimated the buckling load of shallow arches.

• Steel and Composite Structures
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• v.29 no.5
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• pp.591-602
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• 2018

This research presents an investigation on the thermal buckling resistance of FGM plates having parabolic-concave thickness variation exposed to uniform and gradient temperature change. An analytical formulation is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. A specific function of thickness variation is introduced where it controls the parabolic variation intensity of the thickness without changing the original material volume. The results indicated that the loss ratio in buckling resistance is the same for any gradient temperature profile. Influencing geometrical and material parameters on the loss ratio in the thermal resistance buckling are investigated which may help in design guidelines of such complex structures.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.13-33
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• 2022

The quaternionic Calabi conjecture was introduced by Alesker-Verbitsky, analogous to the Kähler case which was raised by Calabi. On a compact connected hypercomplex manifold, when there exists a flat hyperKähler metric which is compatible with the underlying hypercomplex structure, we will consider the parabolic quaternionic Monge-Ampère equation. Our goal is to prove the long time existence and C^∞ convergence for normalized solutions as t → ∞. As a consequence, we show that the limit function is exactly the solution of quaternionic Monge-Ampère equation, this gives a parabolic proof for the quaternionic Calabi conjecture in this special setting.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.721-733
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• 2000

A paeabolic-elliptic system modelling chemotaxis is analysed. We study the behavior of solutions, especially the finite-time blowup of nonradial dolutions, to parabolic-elliptic system of n(n 2).