• The Mathematical Education
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• v.20 no.3
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• pp.23-26
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• 1982

Many interesting properties of a space curve C in E$^3$ may be investigated by means of the concept of spherical indicatrix of tangent, principal normal, or binormal, to C. The purpose of the present paper is to derive the representations of the Frenet frame field., curvature, and torsion of spherical indicatrix to C in terms of the quantities associated with C. Furthermore, several interesting properties of spherical indicatrix are found in the present paper.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.513-541
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• 2023

In this paper, we calculate Frenet frames, Frenet derivative formulas, curvatures, arc lengths, geodesic curvatures according to the Lorentzian 3-space ℝ³₁, Lorentzian sphere 𝕊²₁ and hyperbolic sphere ℍ²₀ of the spherical indicatrix curves of the spacelike Salkowski curve with the timelike principal normal in ℝ³₁ and draw the graphs of these indicatrix curves on the spheres.

• Journal of Mechanical Science and Technology
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• v.15 no.2
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• pp.239-247
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• 2001

Measured radiative heat fluxes on the furnace exit plane of a heavy duty power boiler of steam output 1650 T/h are discussed. A high-ash pulverized bituminous coal was used. Such measurements are necessary to improve heat fluxes inside a steam boiler furnace was manufactured. An extra small heat radiation sensor was placed in the water cooled head of the probe. The sensor had no direct contact with furnace gases and measured only the radiant energy. There was no exposure to convective heat transfer. With the radiometric probe, one can obtain a spherical indicatrix of radiation intensity as well as hemispherical radiative heat flux incident on any surface passing through a measuring point inside the furnace. Thus, the quantity of radiation energy, passing through the furnace exit plane, to the convective heating surfaces and the quantity of radiation energy going in the opposite direction were measured. A formula for relative radiative heat flux on the furnace exit plane has been proposed.

• Honam Mathematical Journal
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• v.19 no.1
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• pp.107-116
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• 1997

In this paper, we get some properties of curves of constant relative breadth in the Minkowski plane.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.263-285
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• 2023

In this paper, we investigate the spherical indicatrices of a new relationship between Bertrand pair curves in Euclidean 3-space. We obtain necessary and sufficient conditions for this type of Bertrand pair curves to be slant helix, and provide an example.

• Transactions of Materials Processing
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• v.22 no.1
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• pp.48-53
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• 2013

As the adoption of injection molding technology increases, injected-molded optical products require higher dimensional accuracy and optical stability than ever before. In the present study, four kinds of molding methods, i.e., conventional injection molding (CIM), injection/compression molding (ICM), rapid heat and cooling the mold(RHCM) and rapid injection/compression molding (RICM) were selected in order to investigate the optical anisotropy of a 7 inch Light Guide Plate(LGP) by examining the gap-wise distribution of birefringence and the extinction angle. The results indicate that the compression process can decrease flow-induced birefringence over the whole region and that rapid heating can decrease the birefringence level better than conventional molding. In addition, for the combination of compression and rapid heating a reversal flow was detected from the distribution of the extinction angle near the gate.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.873-892
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• 2020

Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere S^n-1 in ℝⁿ. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature.

• Transactions of Materials Processing
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• v.19 no.5
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• pp.296-304
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• 2010

It is still needed to study the effect of process conditions on the final properties of injection-molded parts for producing precision optical products. Especially, the optical anisotropy, i.e., birefringence, is a significant factor to affect the function of many optical components. In the present study we have focused on the effect of holding and compression processes on the birefringence remaining in the transparent disc by examining the gap-wise distribution of birefringence and extinction angle. As a result, two extra birefringence and extinction peaks near the center in thickness direction showed the effect of holding pressure, which came from the flow in packing stage. However, more uniform birefringence distribution than injection-only cases could be found in injection/compression cases. Depends on the process condition even the flow reversal could be found from the distribution of extinction angle. Finally, graphical representation of optical indicatrix was added for better understanding the final structure of injection-only and injection/compression cases.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.05b
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• pp.98-102
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• 2002

We investigated domains and conoscope under the polarizing microscope and the index of refraction on the c-plate GMO which has the ferroelectric and ferroelastic phase at room temperature. To observed the change of refractive index in connection with domain, we developed an apparatus to obtain the refractive index by measuring the Brewster's angle. The resolution of the minimum rotation angle of this apparatus is $0.001^{\circ}$. To obtain the refractive index map on the sample, the moving distance of XY stage loaded sample holder is 60 mm and the minimum moving distance is 0.002 mm. Also, To obtain the indicatrix for single crystal, vertical turntable with sample holder and XY stage was loading on horizontal turntable. The minimum resolution angle of this vertical turntable is $0.001^{\circ}$. We measured the refractive index of transparent materials such as ferroelectrics. In the case of $Gd_{2}(MoO_{4})_{3}$, the Brewster angle is $62.11^{\circ}$ and then, the refractive index is 1.8895 by using He-Ne Laser. Also the refractive distribution of c-plate GMO was obtained with $400{\mu}m{\times}120{\mu}m$.