Smooth curve drawing using a Bessel function

2015 ◽  
Author(s):  
Y. Q. Du ◽  
M. J. Pan ◽  
Q. Li ◽  
L. Li
Keyword(s):  
Bessel Function ◽  
Smooth Curve

scholarly journals The Power Losses in Cable Lines Supplying Nonlinear Loads

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1374
Author(s):  
Bartosz Rozegnał ◽  
Paweł Albrechtowicz ◽  
Dominik Mamcarz ◽  
Monika Rerak ◽  
Maciej Skaza
Keyword(s):  
Bessel Function ◽  
Cross Section ◽  
Power Loss ◽  
Sine Wave ◽  
Active Power ◽  
New Method ◽  
Power Losses ◽  
Nonlinear Loads ◽  
Current Harmonics ◽  
Cable Lines

This paper presents the skin effect impact on the active power losses in the sheathless single-core cables/wires supplying nonlinear loads. There are significant conductor losses when the current has a distorted waveform (e.g., the current supplying diode rectifiers). The authors present a new method for active power loss calculation. The obtained results have been compared to the IEC-60287-1-1:2006 + A1:2014 standard method and the method based on the Bessel function. For all methods, the active power loss results were convergent for small-cable cross-section areas. The proposed method gives smaller power loss values for these cable sizes than the IEC and Bessel function methods. For cable cross-section areas greater than 185 mm2, the obtained results were better than those for the other methods. There were also analyses of extra power losses for distorted currents compared to an ideal 50 Hz sine wave for all methods. The new method is based on the current penetration depth factor calculated for every considered current harmonics, which allows us to calculate the precise equivalent resistance for any cable size. This research is part of our work on a cable thermal analysis method that has been developed.

scholarly journals Experimental Validation on Intersection Turning Trajectory Prediction Method for Advanced Driver Assistance System Based on Triclothoidal Curve

2021 ◽  
Vol 11 (13) ◽  
pp. 5900
Author(s):  
Yohei Fujinami ◽  
Pongsathorn Raksincharoensak ◽  
Shunsaku Arita ◽  
Rei Kato
Keyword(s):  
Traffic Accidents ◽  
Computational Cost ◽  
Prediction Method ◽  
Smooth Curve ◽  
Assistance System ◽  
Driver Assistance ◽  
Driver Assistance Systems ◽  
Trajectory Prediction ◽  
Left Turn ◽  
Left Hand

Advanced driver assistance systems (ADAS) for crash avoidance, when making a right-turn in left-hand traffic or left-turn in right-hand traffic, are expected to further reduce the number of traffic accidents caused by automobiles. Accurate future trajectory prediction of an ego vehicle for risk prediction is important to activate the assistance system correctly. Our objectives are to propose a trajectory prediction method for ADAS for safe intersection turnings and to evaluate the effectiveness of the proposed prediction method. Our proposed curve generation method is capable of generating a smooth curve without discontinuities in the curvature. By incorporating the curve generation method into the vehicle trajectory prediction, the proposed method could simulate the actual driving path of human drivers at a low computational cost. The curve would be required to define positions, angles, and curvatures at its initial and terminal points. Driving experiments conducted at real city traffic intersections proved that the proposed method could predict the trajectory with a high degree of accuracy for various shapes and sizes of the intersections. This paper also describes a method to determine the terminal conditions of the curve generation method from intersection features. We set a hypothesis where the conditions can be defined individually from intersection geometry. From the hypothesis, a formula to determine the parameter was derived empirically from the driving experiments. Public road driving experiments indicated that the parameters for the trajectory prediction could be appropriately estimated by the obtained empirical formula.

scholarly journals Higher rank Clifford indices of curves on a K3 surface

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Soheyla Feyzbakhsh ◽  
Chunyi Li
Keyword(s):  
Vector Bundles ◽  
Plane Curve ◽  
Smooth Curve ◽  
Line Bundles ◽  
K3 Surface ◽  
Clifford Index ◽  
Smooth Plane ◽  
Higher Rank ◽  
Rank Vector ◽  
Semistable Vector Bundle

AbstractLet (X, H) be a polarized K3 surface with $$\mathrm {Pic}(X) = \mathbb {Z}H$$ Pic ( X ) = Z H , and let $$C\in |H|$$ C ∈ | H | be a smooth curve of genus g. We give an upper bound on the dimension of global sections of a semistable vector bundle on C. This allows us to compute the higher rank Clifford indices of C with high genus. In particular, when $$g\ge r^2\ge 4$$ g ≥ r 2 ≥ 4 , the rank r Clifford index of C can be computed by the restriction of Lazarsfeld–Mukai bundles on X corresponding to line bundles on the curve C. This is a generalization of the result by Green and Lazarsfeld for curves on K3 surfaces to higher rank vector bundles. We also apply the same method to the projective plane and show that the rank r Clifford index of a degree $$d(\ge 5)$$ d ( ≥ 5 ) smooth plane curve is $$d-4$$ d - 4 , which is the same as the Clifford index of the curve.

scholarly journals Eisenstein series and an asymptotic for the K-Bessel function

2021 ◽  
Author(s):  
Jimmy Tseng
Keyword(s):  
Asymptotic Expansion ◽  
Bessel Function ◽  
Eisenstein Series ◽  
Uniform Estimate ◽  
Positive Real ◽  
Dominant Term ◽  
Complex Order ◽  
Fixed Parameter ◽  
Real Argument ◽  
Real Analytic

AbstractWe produce an estimate for the K-Bessel function $$K_{r + i t}(y)$$ K r + i t ( y ) with positive, real argument y and of large complex order $$r+it$$ r + i t where r is bounded and $$t = y \sin \theta $$ t = y sin θ for a fixed parameter $$0\le \theta \le \pi /2$$ 0 ≤ θ ≤ π / 2 or $$t= y \cosh \mu $$ t = y cosh μ for a fixed parameter $$\mu >0$$ μ > 0 . In particular, we compute the dominant term of the asymptotic expansion of $$K_{r + i t}(y)$$ K r + i t ( y ) as $$y \rightarrow \infty $$ y → ∞ . When t and y are close (or equal), we also give a uniform estimate. As an application of these estimates, we give bounds on the weight-zero (real-analytic) Eisenstein series $$E_0^{(j)}(z, r+it)$$ E 0 ( j ) ( z , r + i t ) for each inequivalent cusp $$\kappa _j$$ κ j when $$1/2 \le r \le 3/2$$ 1 / 2 ≤ r ≤ 3 / 2 .

Cumulative yields of stable and long-lived isotopes of tin in neutron-induced fission

1983 ◽  
Vol 61 (11) ◽  
pp. 1490-1497 ◽  
Author(s):  
K. J. R. Rosman ◽  
J. R. De Laeter ◽  
J. W. Boldeman ◽  
H. G. Thode
Keyword(s):  
Stable Isotopes ◽  
Fine Structure ◽  
Fission Product ◽  
Mass Spectrometer ◽  
Smooth Curve ◽  
Mass Region ◽  
Neutron Fission ◽  
Source Mass ◽  
Induced Fission ◽  
Fission Yields

The relative cumulative fission yields of the six stable isotopes of tin (117Sn,118Sn, 119Sn, 120Sn, 122Sn, and 124Sn) and the long-lived isotope 126Sn have been measured in the thermal and epicadium neutron fission of 233U and 235U, and the epicadium neutron fission of 238U. Nanogram-sized fission product tin samples were extracted from irradiated uranium samples and analyzed in a solid source mass spectrometer. In each case a smooth curve can be drawn through the yield points of the seven isotopes of tin. There is, therefore, no evidence of "fine structure" in the 117 ≤ A ≤ 126 portion of the symmetric mass region.

ESTIMATING SURFACE NORMALS IN NOISY POINT CLOUD DATA

2004 ◽  
Vol 14 (04n05) ◽  
pp. 261-276 ◽  
Author(s):  
NILOY J. MITRA ◽  
AN NGUYEN ◽  
LEONIDAS GUIBAS
Keyword(s):  
Point Cloud ◽  
Smooth Surface ◽  
Smooth Curve ◽  
Local Information ◽  
Least Square ◽  
Neighborhood Size ◽  
Point Cloud Data ◽  
Cloud Data ◽  
Normal Estimation ◽  
Least Square Fitting

In this paper we describe and analyze a method based on local least square fitting for estimating the normals at all sample points of a point cloud data (PCD) set, in the presence of noise. We study the effects of neighborhood size, curvature, sampling density, and noise on the normal estimation when the PCD is sampled from a smooth curve in ℝ2or a smooth surface in ℝ3, and noise is added. The analysis allows us to find the optimal neighborhood size using other local information from the PCD. Experimental results are also provided.

scholarly journals Connected Numbers and the Embedded Topology of Plane Curves

2018 ◽  
Vol 61 (3) ◽  
pp. 650-658 ◽  
Author(s):  
Taketo Shirane
Keyword(s):  
Plane Curve ◽  
Smooth Curve ◽  
Plane Curves ◽  
Irreducible Curve ◽  
Galois Cover ◽  
Splitting Number

AbstractThe splitting number of a plane irreducible curve for a Galois cover is effective in distinguishing the embedded topology of plane curves. In this paper, we define the connected number of a plane curve (possibly reducible) for a Galois cover, which is similar to the splitting number. By using the connected number, we distinguish the embedded topology of Artal arrangements of degree b ≥ 4, where an Artal arrangement of degree b is a plane curve consisting of one smooth curve of degree b and three of its total inflectional tangents.

scholarly journals Variability of the total ozone trend over Europe for the period 1950–2004 derived from reconstructed data

2008 ◽  
Vol 8 (11) ◽  
pp. 2847-2857 ◽  
Author(s):  
J. W. Krzyścin ◽  
J. L. Borkowski
Keyword(s):  
Total Ozone ◽  
A Priori ◽  
Smooth Curve ◽  
Ozone Level ◽  
Svalbard Archipelago ◽  
Small Areas ◽  
Ozone Data ◽  
Curve Fit ◽  
Long Term Changes

Abstract. The total ozone data over Europe are available for only few ground-based stations in the pre-satellite era disallowing examination of the spatial trend variability over the whole continent. A need of having gridded ozone data for a trend analysis and input to radiative transfer models stimulated a reconstruction of the daily ozone values since January 1950. Description of the reconstruction model and its validation were a subject of our previous paper. The data base used was built within the objectives of the COST action 726 "Long-term changes and climatology of UV radiation over Europe". Here we focus on trend analyses. The long-term variability of total ozone is discussed using results of a flexible trend model applied to the reconstructed total ozone data for the period 1950–2004. The trend pattern, which comprises both anthropogenic and "natural" component, is not a priori assumed but it comes from a smooth curve fit to the zonal monthly means and monthly grid values. The ozone long-term changes are calculated separately for cold (October–next year April) and warm (May–September) seasons. The confidence intervals for the estimated ozone changes are derived by the block bootstrapping. The statistically significant negative trends are found almost over the whole Europe only in the period 1985–1994. Negative trends up to −3% per decade appeared over small areas in earlier periods when the anthropogenic forcing on the ozone layer was weak . The statistically positive trends are found only during warm seasons 1995–2004 over Svalbard archipelago. The reduction of ozone level in 2004 relative to that before the satellite era is not dramatic, i.e., up to ~−5% and ~−3.5% in the cold and warm subperiod, respectively. Present ozone level is still depleted over many popular resorts in southern Europe and northern Africa. For high latitude regions the trend overturning could be inferred in last decade (1995–2004) as the ozone depleted areas are not found there in 2004 in spite of substantial ozone depletion in the period 1985–1994.

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