• 대한수학회지
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• 제55권3호
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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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• 제30권1호
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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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• 제55권2호
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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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• 제35권1호
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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.

• 인지과학
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• 제10권3호
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• pp.17-28
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• 1999

양안 부등 정보에 근거하여 모사 된 타원형 및 포물선형 반원주체가 관찰거리가 변화함에 딸 체계적으로 왜곡되어 지각되었다. 실험1과 실험3의 두 가지 관찰조건 모두에서, 타원형 반원주체는 45 cm의 관찰거리에서는 실제 모양과 근사하게 지각되었으나 135 cm의 관찰거리에서는 실제 곡면성의 75%로 과소 평가되어 지각되었다. 실험2에서는, 관찰거리에 대한 정보가 풍부할 때, 포물선형 반원주체가 45 cm의 관찰거리에서 실제 곡면성에 비해 118%의 곡면 성을 갖는 것으로 과장되어 지각되었으며, 90 cm의 관찰거리에서는 실제에 근접하여 지각되었고, 135 cm의 관찰거리에서는 실제 곡면성에 비해 85%로 과소 평가되어 지각되었다. 관찰거리에 대한 정보가 감소된 관찰조건에서는 모든 관찰거리에서 실제의 곡면 성 보다 다소 과소 평가되어 지각되었다. 예를 들어, 45 cm의 관찰거리에서는 실제 곡면성에 근접하여 지각되었고, 135 cm의 관찰거리에서는 실제 곡면성에 비해 68%로 과소 평가되어 지각되었다. 이러한 실험 결과들은 시각기제가 양안 부등을 추정한 관찰거리로 척도와(scale) 하여 3차원 모양을 표상 하게 된다는 설명을 지지하고, 이에 대립되는 가정, 즉 거리에 따라 변하지 않는 부등 곡률(disparity curvature)을 탐지해 냄으로써 3차원 모양을 직접 지각할 수 있다는 가정이 타당하지 않음을 시사한다.

• 전자공학회논문지A
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• 제31A권2호
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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.

• 대한토목학회논문집
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• 제29권2A호
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• pp.145-153
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• 2009

본 연구에서는 포물선 아치의 횡-비틂 좌굴 강도에 관한 연구를 수행하였다. 포물선 아치는 아치의 중립축을 따라 곡률이 변하므로 일정한 곡률을 갖는 원형 아치의 경우보다 횡-비틂 좌굴 강도식을 유도하는 것이 복잡하며, 이에 대한 연구가 미흡한 실정이다. 본 연구에서는 ?의 효과를 고려하여 변곡률을 갖는 아치의 횡-비틂 좌굴식을 유도하고 포물선 아치의 좌굴강도를 계산하기 위하여 유한차분법을 이용한 수치해법을 제안하였다. 이러한 수치해법은 기존 연구자 및 유한요소해석 결과와 비교하였으며, 그 타당성을 검증하였다. 마지막으로, 변수해석을 수행하여 라이즈비의 영향에 따른 원형과 포물선 아치의 횡-비틂 좌굴 강도를 비교 분석하였다.

• 소음진동
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• 제10권2호
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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.

• 한국전산유체공학회지
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• 제13권1호
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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.

• 반도체디스플레이기술학회지
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• 제15권4호
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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.