scholarly journals Weber’s formula for the bitangents of a smooth plane quartic

2019 ◽  
pp. 5-17
Author(s):  
Alessio Fiorentino
Keyword(s):  
Smooth Plane

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 Diffraction of plane elastic waves by a crack, with application to a problem of brittle fracture

1963 ◽  
Vol 3 (3) ◽  
pp. 325-339 ◽  
Author(s):  
M. Papadopoulos
Keyword(s):  
Elastic Waves ◽  
Scattered Field ◽  
Velocity Potential ◽  
Elastic Solid ◽  
Step Function ◽  
Free Surface Waves ◽  
Dependent Variables ◽  
Smooth Plane ◽  
New Feature ◽  
Set Up

AbstractA crack is assumed to be the union of two smooth plane surfaces of which various parts may be in contact, while the remainder will not. Such a crack in an isotropic elastic solid is an obstacle to the propagation of plane pulses of the scalar and vector velocity potential so that both reflected and diffracted fields will be set up. In spite of the non-linearity which is present because the state of the crack, and hence the conditions to be applied at the surfaces, is a function of the dependent variables, it is possible to separate incident step-function pulses into either those of a tensile or a compressive nature and the associated scattered field may then be calculated. One new feature which arises is that following the arrival of a tensile field which tends to open up the crack there is necessarily a scattered field which causes the crack to close itself with the velocity of free surface waves.

scholarly journals A Novel Adaptive Non-Local Means-Based Nonlinear Fitting for Visibility Improving

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 741
Author(s):  
Hongtao Wu ◽  
Lei Jia ◽  
Ying Meng ◽  
Xiao Liu ◽  
Jinhui Lan
Keyword(s):  
Filter Design ◽  
Trade Off ◽  
Nonlinear Fitting ◽  
Local Means ◽  
Fitting Method ◽  
Central Pixel ◽  
Smooth Plane ◽  
Non Local ◽  
Geometric Surface ◽  
Weight Coefficients

The spatial-based method has become the most widely used method in improving the visibility of images. The visibility improving is mainly to remove the noise in the image, in order to trade off denoising and detail maintaining. A novel adaptive non-local means-based nonlinear fitting method is proposed in this paper. Firstly, according to the smoothness of the intensity around the central pixel, eight kinds of templates with different precision are exploited to approximate the central pixel through a novel adaptive non-local means filter design; the approximate weight coefficients of templates are derived from the approximation credibility. Subsequently, the fractal correction is used to smooth the denoising results. Eventually, the Rockafellar multiplier method is employed to generalize the smooth plane fitting to any geometric surface, thus yielding the optimal fitting of the center pixel approximation. Through a large number of experiments, it is clearly elucidated that compared with the classical spatial iteration-based methods and the recent denoising algorithms, the proposed algorithm is more robust and has better effect on denoising, while keeping more original details during denoising.

Motions of a top on a smooth plane without separation

2013 ◽  
Vol 48 (2) ◽  
pp. 128-133
Author(s):  
G. M. Rozenblat
Keyword(s):  
Smooth Plane

Situations of Fluid Polishing Processes for Ultra-Smooth Surface

2011 ◽  
Vol 215 ◽  
pp. 83-88 ◽  
Author(s):  
G.Q. Pan ◽  
Z.W. Wang ◽  
Dong Hui Wen
Keyword(s):  
Smooth Surface ◽  
Curved Surface ◽  
Technical Parameters ◽  
Inner Surface ◽  
Smooth Plane

This paper give some literatures for the technology of fluid polishing. Methods of fluid polishing using for optics curved surface, ultra-smooth plane and inner surface of non-circular curved surface. Each method is explained by above classifications, and some domestic cases which can produce ultra-smooth surface in different conditions, parts and technical parameters is listed and evaluated.

scholarly journals Components of the Hilbert scheme of space curves on low-degree smooth surfaces

2015 ◽  
Vol 26 (02) ◽  
pp. 1550017 ◽  
Author(s):  
Jan O. Kleppe ◽  
John C. Ottem
Keyword(s):  
Hilbert Scheme ◽  
Smooth Surface ◽  
Plane Curve ◽  
Picard Number ◽  
Connected Space ◽  
Space Curves ◽  
Cubic Surfaces ◽  
Smooth Component ◽  
Low Degree ◽  
Smooth Plane

We study maximal families W of the Hilbert scheme, H(d, g)sc, of smooth connected space curves whose general curve C lies on a smooth surface S of degree s. We give conditions on C under which W is a generically smooth component of H(d, g)sc and we determine dim W. If s = 4 and W is an irreducible component of H(d, g)sc, then the Picard number of S is at most 2 and we explicitly describe, also for s ≥ 5, non-reduced and generically smooth components in the case Pic (S) is generated by the classes of a line and a smooth plane curve of degree s - 1. For curves on smooth cubic surfaces the first author finds new classes of non-reduced components of H(d, g)sc, thus making progress in proving a conjecture for such families.

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