• Publications of The Korean Astronomical Society
• /
• v.30 no.2
• /
• pp.309-313
• /
• 2015

If the present universe is slightly open then pre-inflation curvature would appear as a cosmic dark-flow component of the CMB dipole moment. We summarize current cosmological constraints on this cosmic dark flow and analyze the possible constraints on parameters characterizing the pre-inflating universe in an inflation model with a present-day very slightly open ${\Lambda}CDM$ cosmology. We employ an analytic model to show that for a broad class of inflation-generating effective potentials, the simple requirement that the observed dipole moment represents the pre-inflation curvature as it enters the horizon allows one to set upper and lower limits on the magnitude and wavelength scale of pre-inflation fluctuations in the inflaton field and the curvature parameter of the pre-inflation universe, as a function of the fraction of the total initial energy density in the inflaton field. We estimate that if the current CMB dipole is a universal dark flow (or if it is near the upper limit set by the Planck Collaboration) then the present constraints on ${\Lambda}CDM$ cosmological parameters imply rather small curvature ${\Omega}_k{\sim}0.1$ for the pre-inflating universe for a broad range of the fraction of the total energy in the inflaton field at the onset of inflation. Such small pre-inflation curvature might be indicative of open-inflation models in which there are two epochs of inflation.

• The Bulletin of The Korean Astronomical Society
• /
• v.44 no.2
• /
• pp.58.4-58.4
• /
• 2019

In a homogeneous and isotropic universe, the solution to the Einstein Field equation is the Friedmann-Robertson-Lemaître-Walker metric, which describes an expanding Universe with spatial curvature. The curvature has profound implications, in particular regarding the early universe. In this talk, I will review the state-of-the-arts constraints on the spatial curvature of the Universe using different cosmological observations. In particular, I will focus on model-independent tests using baryon acoustic oscillations and supernovae.

• International Journal of CAD/CAM
• /
• v.6 no.1
• /
• pp.65-71
• /
• 2006

Based on the smoothness criterion of minimum curvature variation of the curve, tangent angle constraints guaranteeing an optimized geometric Hermite (OGH) curve both mathematically and geometrically smooth is given, and new methods for constructing composite optimized geometric Hermite (COH) curves are presented in this paper. The comparison of the new methods with Yong and Cheng's methods based on strain energy minimization is included.

• Journal of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.183-205
• /
• 2024

In this paper, for an m-dimensional (m ≥ 5) complete non-compact submanifold M immersed in an n-dimensional (n ≥ 6) simply connected Riemannian manifold N with negative sectional curvature, under suitable constraints on the squared norm of the second fundamental form of M, the norm of its weighted mean curvature vector |H_f| and the weighted real-valued function f, we can obtain: • several one-end theorems for M; • two Liouville theorems for harmonic maps from M to complete Riemannian manifolds with nonpositive sectional curvature.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1053-1068
• /
• 2021

We investigate the spacelike hypersurface Mⁿ with constant mean curvature (CMC) in a Lorentz Einstein manifold Lⁿ⁺¹₁, which is supposed to obey some appropriate curvature constraints. Applying a suitable Simons type formula jointly with the well known generalized maximum principle of Omori-Yau, we obtain some rigidity classification theorems and pinching theorems of hypersurfaces.

• The Journal of Korea Robotics Society
• /
• v.16 no.3
• /
• pp.250-259
• /
• 2021

Path planning is one of the important technologies for automated parking. It requires to plan a collision-free path considering the vehicle's kinematic constraints such as minimum turning radius or steering velocity. In a complex parking lot, Rapidly-exploring Random Tree^* (RRT^*) can be used for planning a parking path, and Reeds-Shepp or Hybrid Curvature can be applied as a tree-extension method to consider the vehicle's constraints. In this case, each of these methods may affect the computation time of planning the parking path, path-tracking error, and parking success rate. Therefore, in this study, we conduct comparative analysis of two tree-extension functions: Reeds-Shepp (RS) and Hybrid Curvature (HC), and show that HC is a more appropriate tree-extension function for parking path planning. The differences between the two functions are introduced, and their performances are compared by applying them with RRT^*. They are tested at various parking scenarios in simulation, and their advantages and disadvantages are discussed by computation time, cross-track error while tracking the path, parking success rate, and alignment error at the target parking spot. These results show that HC generates the parking path that an autonomous vehicle can track without collisions and HC allows the vehicle to park with lower alignment error than those of RS.

• Proceedings of the Polymer Society of Korea Conference
• /
• 2006.10a
• /
• pp.294-294
• /
• 2006

Diblock copolymers whose morphology in the bulk is dictated by the volume fraction of the components and segmental interactions were confined within nanoscopic cylindrical pores. Since the confining geometry is nonplanar and nanoscopic, the extreme imposed curvature, comparable to molecular dimensions, places significant packing frustration on the chains. When incommensurability between the repeating period of diblock copolymers and the diameter of nanopore is coupled with the curvature, it causes the marked departures from bulk or even thin film behavior. The entropy penalty from the constraints and the curvature of the physical confinement determines unique nanostructures available only with this curved confinement.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.10 no.3
• /
• pp.392-398
• /
• 1986

It is often occurred that exhaust pipe of an internal combustion engine should be bent due to some geometrical constraints. Especially for automobiles most of exhaust pipes of engines have curvature to avoid rear axles. In this paper effects of pipe curvature on the exhaust noise of a diesel engine have been studied experimentally. Experiments were carried out on a 4-cycle, 2164cc diesel engine. Two types of curvature, circular arc and retangle, were tested. Sound pressure level (SPL) and power spectrum of the exhaust noise were measured by inserting bent pipes of different curvature dimensions into the exhaust pipe at various engine operating conditions. The following results were obtained from this study. Among the engine operating conditions the exhaust noise was affected mainly by engine revolution speed. The noise was reduced by the circular arc bent pipe. The effectiveness of an arc bent pipe on the noise reduction was dominated by its arc angle and the maximum noise reduction was obtained by the angle of 180.deg.. But the noise reduction could not be obtained by the rectangular bent pipe, and at high engine speed the noise was rather increased due to turbulence of exhaust gas.

• Journal of Korean Society of Steel Construction
• /
• v.9 no.4 s.33
• /
• pp.673-682
• /
• 1997

The main purpose of this paper is to investigate the effects of rotatory inertia and shear deformation on the natural frequencies of arches with variable curvature. The differential equations are derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. The governing equations are solved numerically for parabolic, circular and elliptic geometries with hinged-hinged, hinged-clamped and clamped-clamped end constraints. For each cases, the four lowest frequency parameters are presented as functions of the two dimensionless system parameters; the arch rise to span length ratio, and the slenderness ratio.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10b
• /
• pp.54-59
• /
• 1993

This paper presents a method of estimating 3-D surface geometrical features that are necessary for 3-D object recognition and image interpretation. The features, such as surface needle maps and curvatures, are computed from range or intensity images. In general, the range and intensity images are prone to noises, and hence the features computed by differentiation calculi on such a noisy image are hardly applicable to industrial recognition tasks. In our approach, we try to obtain a more accurate estimate of the features by using a least-squares minimization procedure subject to local curvature consistency constraints. The algorithm is robust with respect to noises and is completely independent of the viewpoint at which the image is taken. The performance of the ajgoritlim is evaluated using both synthetic data and real intensity images.