• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.749-761
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• 2018

Here, we calculate the evolution equation of the reduced hh-curvature and the Ricci scalar along the Finslerian Ricci flow. We prove that Finsler Ricci flow preserves positivity of the reduced hh-curvature on finite time. Next, it is shown that evolution of Ricci scalar is a parabolic-type equation and moreover if the initial Finsler metric is of positive flag curvature, then the flag curvature, as well as the Ricci scalar, remain positive as long as the solution exists. Finally, we present a lower bound for Ricci scalar along Ricci flow.

• East Asian mathematical journal
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• v.30 no.1
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• pp.79-91
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• 2014

We consider the parabolic evolution differential equation such as heat equation and porus-medium equation on a Riemannian manifold M whose Ricci curvature is bounded below by $-(n-1)k^2$ and bounded below by 0 on some amount of M. We derive some bounds of differential quantities for a positive solution and some inequalities which resemble Harnack inequalities.

• 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.

• Steel and Composite Structures
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• v.35 no.1
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• pp.43-59
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• 2020

In this study, free vibration analysis of laminated composite parabolic thick plate frames by using finite element method is introduced. Governing equations of an eigenvalue problem are obtained from First Order Shear Deformation Theory (FSDT). Finite element method is employed to obtain natural frequency values from the governing differential equations. The frames consist of two flat square plates and one singly curved plate. Parameters like radii of curvature, aspect ratio, ply orientation and boundary conditions are investigated to understand their effect on dynamic behavior of such a structure. In addition, multi-bay structures of such geometry with different stacking order are also taken into account. The composite frame structures are also modeled and simulated via ANSYS to verify the accuracy of the present study.

• Korean Journal of Cognitive Science
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• v.10 no.3
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• pp.17-28
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• 1999

Systematic distortions in perceived 3-D shape were obtained for elliptical and parabolic stereoscopic surfaces viewed at different distances under full and reduced cue conditions. In both conditions of Experiments 1 and 3, elliptical hemi-cylinders a appeared near veridical at the 45 cm viewing distances and flattened up to 74% of veridical at 135 cm. In Experiment 2, under full cue conditions, parabolic hemi-cylinders a appeared stretched to 118% of veridical at 45 cm, near veridical at 90 cm, and flattened to 85% of veridical at 135 cm. Under reduced cue conditions parabolas appeared flatter overall: veridical curvature was obtained at 45 cm viewing distance with flatness increasing to 68% of veridical at 135 cm. Results support a scaling explanation of perceived 3-D shape from disparity and rule out the alternative hypothesis that disparity curvature, an optical invariant, provides information for the direct perception of 3-D s shape.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.2
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• pp.45-52
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• 1994

A curvature variable taper is proposed for a waveguide-microstrip transition. It is applied to a ridge waveguide. The curvature depends on the taper length and difference of waveguide's height and microstrip substrate's height. The taper is manufactured easier than the other tapers. It's reflection coefficient is smaller than the parabolic taper's below one wavelengrh. The results of experiment show that S$_{11}$ is below -20dB and SS$_{21}$ is about -0.5dB in the band of 10~15 GHz. These results are good agreement with the theoritical values.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2A
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• pp.145-153
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• 2009

The lateral-torsional buckling strengths of the parabolic arches are investigated in this study. The curvatures of a parabolic arch vary along the center line of the arch. Thus, the problem is much more complicated comparing that of arches with constant curvature such as circular arches. Moreover, most of previous studies are limited to the circular arches. In this study, lateral-torsional buckling equations are derived for the arches with varying curvatures considering the warping effects. To obtain the buckling strength of parabolic arches, numerical solutions based on the finite difference technique are provided. The numerical solutions are compared with the those of previous researchers and finite element analyses. Then, the lateral-torsional strengths of parabolic arches are successfully verified. Finally, comparison study of critical buckling loads of parabolic arches with those of circular arches for the various rise to span ratios are discussed.

• Journal of KSNVE
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• v.10 no.2
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• pp.353-360
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• 2000

Numerical methods are developed for calculating the natural frequencies and mode shapes of the tapered cantilever arches with variable curvature. The differential equations governing the free vibrations of such arches are derived and solved numerically, in which the effect of rotatory inertia is included. The parabolic shape is chosen as the arch with variable curvature while both the prime and quadratic arched members are considered as the tapered arch with variable curvature while both the prime and quadratic arched members are considered as the tapered arch. Comparisons the natural jfrequencies between this study and finite element method SAP 90 seve to validate the numerical method developed herein. The lowest four natural frequencies are reported as a function of four non-dimensional system parameters. The effects of both the rotatory inertia and cross-sectional shape are reported. Also, the typical mode shapes of stress resultants as well as the displacements are reported.

• Journal of computational fluids engineering
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• v.13 no.1
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• pp.21-27
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• 2008

A numerical study for laminar flow in the entrance region of helical tubes for uniform inlet velocity conditions is carried out by means of the finite volume method to investigate the effects of Reynolds number, pitch and curvature ratio on the flow development. This results cover a curvature ratio range of 1/10$\sim$1/320, a pitch range of 0.0$\sim$3.2, and a Reynolds number range of 125$\sim$2000. It has been found that the curvature ratio does significantly effect on the angle of flow development, but the pitch and Reynolds number do not. The characteristic angle $\phi_c(=\phi/\sqrt{\delta})$, or the non-dimensional length $\overline{l}(=l\sqrt{\delta}cos(atan\lambda)/d)$ can be used to represent the flow development for uniform inlet velocity conditions. In uniform inlet velocity conditions, the growth of boundary layer delays the flow development attributed to centrifugal force, and in which conditions the amplitude of flow oscillations is smaller than that in parabolic inlet velocity conditions. If the pitch increases or if the curvature ratio or Reynolds number decreases, the minimum friction factor and the fully developed average friction factor normalized with the friction factor of a straight tube and the flow oscillations decrease.

• Journal of the Semiconductor & Display Technology
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• v.15 no.4
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• pp.1-9
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• 2016

The warpage on mobile phone camera packages occurs due to the CTE(Coefficient of Thermal Expansion) mismatch between a thin silicon die and a substrate. The warpage in the optical instruments such as camera module has an effect on the field curvature, which is one of the factors degrading the optical performance and the product yield. In this paper, we studied the effect of die bonding epoxy on the package and optical performance of mobile phone camera packages. We calculated the warpages of camera module packages by using a finite element analysis, and their shapes were in good agreement showing parabolic curvature. We also measured the warpages and through-focus MTF of camera module specimens with experiments. The warpage was improved on an epoxy with low elastic modulus at both finite element analysis and experiment results, and the MTF performance increased accordingly. The results show that die bonding epoxy affects the warpage generated on the image sensor during the packaging process, and this warpage eventually affects the optical performance associated with the field curvature.