scholarly journals Anti‐symplectic involutions for Lagrangian spheres in a symplectic quadric surface

2021 ◽  
Author(s):  
Joontae Kim ◽  
Jiyeon Moon
Keyword(s):  
Quadric Surface

Mathematical Modelling the Process of Cup Wheel Precision Grinding of Rotating Concave Paraboloid

2016 ◽  
Vol 693 ◽  
pp. 837-842
Author(s):  
Fu Yi Xia ◽  
Li Ming Xu ◽  
De Jin Hu
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Abrasive Particle ◽  
Influence Factors ◽  
Machining Process ◽  
Quadric Surface ◽  
Precision Grinding ◽  
Cup Wheel ◽  
The Mathematical Model ◽  
Trajectory Equation

A novel principle of cup wheel grinding of rotating concave quadric surface was proposed. The mathematical model of machining process was established to prove the feasibility of precision grinding of rotating concave paraboloid based on the introduced principle. The conditions of non-interference grinding of concave paraboloid were mathematically derived. The processing range and its influence factors were discussed. The trajectory equation of abrasive particle was concluded. Finally, the math expressions of numerical controlled parameters was put forward in the process of grinding of the concave paraboloid.

INTERSECTING A RAY WITH A QUADRIC SURFACE

1992 ◽  
pp. 275-283 ◽  
Author(s):  
Joseph M. Cychosz ◽  
Warren N. Waggenspack
Keyword(s):  
Quadric Surface

Hand Tracking Using a Quadric Surface Model and Bayesian Filtering

2003 ◽  
pp. 129-141 ◽  
Author(s):  
Roberto Cipolla ◽  
Bjorn Stenger ◽  
Arasanathan Thayananthan ◽  
Philip H. S. Torr
Keyword(s):  
Hand Tracking ◽  
Surface Model ◽  
Bayesian Filtering ◽  
Quadric Surface

scholarly journals K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES

2021 ◽  
pp. 1-41
Author(s):  
KENNETH ASCHER ◽  
KRISTIN DEVLEMING ◽  
YUCHEN LIU
Keyword(s):  
Complete Intersection ◽  
Moduli Space ◽  
Moduli Spaces ◽  
K3 Surfaces ◽  
Moduli Of Curves ◽  
Quadric Surface ◽  
Intersection Curves

Abstract We show that the K-moduli spaces of log Fano pairs $\left(\mathbb {P}^1\times \mathbb {P}^1, cC\right)$ , where C is a $(4,4)$ curve and their wall crossings coincide with the VGIT quotients of $(2,4)$ , complete intersection curves in $\mathbb {P}^3$ . This, together with recent results by Laza and O’Grady, implies that these K-moduli spaces form a natural interpolation between the GIT moduli space of $(4,4)$ curves on $\mathbb {P}^1\times \mathbb {P}^1$ and the Baily–Borel compactification of moduli of quartic hyperelliptic K3 surfaces.

Incidence scrolls

1933 ◽  
Vol 29 (2) ◽  
pp. 235-244
Author(s):  
W. G. Welchman
Keyword(s):  
General Type ◽  
Ruled Surfaces ◽  
Quadric Surface ◽  
General Elliptic

1. The work of this paper was undertaken with a view to finding out what ruled surfaces can be determined by incidences, i.e. generated by the lines which meet a certain set of spaces which I shall call a base. Such ruled surfaces I shall call incidence scrolls. In [3] the lines which meet three lines generate a quadric surface. In [4] it is easy to show that a base consisting of a line and three planes gives the general rational quartic scroll, while the lines which meet five planes in [4] give the general elliptic quintic scroll. One might be tempted to think that at least all the rational normal scrolls could be obtained as incidence scrolls by taking for base a suitable number of spaces containing directrix curves, but unfortunately there is a residual surface except in the case of the rational scrolls of general type and of those with a directrix line.

On the tritangent planes of a quadri-cubic space curve

1935 ◽  
Vol 4 (3) ◽  
pp. 159-169
Author(s):  
H. W. Richmond
Keyword(s):  
Plane Curve ◽  
Space Curve ◽  
Quadric Surface ◽  
Geometrical Aspect ◽  
Quartic Curve ◽  
Abelian Functions

With any twisted curve of order six is associated a system of planes, usually finite in number, which touch the curve at three distinct points. The curve with its system of tritangent planes possesses properties which recall the properties of a plane quartic curve and its system of bitangent lines; and this is specially true of the sextic which is the intersection of a cubic and a quadric surface. But whereas the properties of the plane curve were discovered by geometrical methods, such methods have only recently been applied with success to the space-curve; the earliest properties were obtained by Clebsch from his Theory of Abelian Functions. In the absence of any one place to which reference can conveniently be made, an account of these properties in their geometrical aspect will be useful.

II.—The Irreducible System of Concomitants of Two Double Binary (2, 1) Forms

1926 ◽  
Vol 45 (1) ◽  
pp. 3-13
Author(s):  
W. Saddler
Keyword(s):  
Quadric Surface ◽  
Binary Forms ◽  
Irreducible System ◽  
Simultaneous System ◽  
Twisted Cubics

Little is known of the details of systems of concomitants belonging to double binary forms. The cases of the single ground form of orders (1, 1), (2, 1), (2, 2) respectively, together with the simultaneous system of any number of (1, 1) forms, are the only four cases, which have been published. The following pages establish the simultaneous system of two (2, 1) forms.This system is fundamental for the geometrical treatment of two twisted cubics lying upon a quadric surface and having four common points.

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