scholarly journals Approximating the Projective Model

1987 ◽  
pp. 273-282 ◽  
Author(s):  
Evangelos Kranakis
Keyword(s):  
Projective Model

scholarly journals FAMILIES OF AFFINE RULED SURFACES: EXISTENCE OF CYLINDERS

2016 ◽  
Vol 223 (1) ◽  
pp. 1-20 ◽  
Author(s):  
ADRIEN DUBOULOZ ◽  
TAKASHI KISHIMOTO
Keyword(s):  
Minimal Model ◽  
Finite Extension ◽  
Smooth Curve ◽  
Ruled Surfaces ◽  
Model Program ◽  
Minimal Model Program ◽  
Generic Fiber ◽  
Projective Model ◽  
The Family

We show that the generic fiber of a family $f:X\rightarrow S$ of smooth $\mathbb{A}^{1}$-ruled affine surfaces always carries an $\mathbb{A}^{1}$-fibration, possibly after a finite extension of the base $S$. In the particular case where the general fibers of the family are irrational surfaces, we establish that up to shrinking $S$, such a family actually factors through an $\mathbb{A}^{1}$-fibration $\unicode[STIX]{x1D70C}:X\rightarrow Y$ over a certain $S$-scheme $Y\rightarrow S$ induced by the MRC-fibration of a relative smooth projective model of $X$ over $S$. For affine threefolds $X$ equipped with a fibration $f:X\rightarrow B$ by irrational $\mathbb{A}^{1}$-ruled surfaces over a smooth curve $B$, the induced $\mathbb{A}^{1}$-fibration $\unicode[STIX]{x1D70C}:X\rightarrow Y$ can also be recovered from a relative minimal model program applied to a smooth projective model of $X$ over $B$.

Apollonius Surfaces, Circumscribed Spheres of Tetrahedra, Menelaus’s and Ceva’s Theorems in S2 × R and H2 × R Geometries

2021 ◽  
Author(s):  
Jenő Szirmai
Keyword(s):  
Geodesic Sphere ◽  
Geodesic Triangle ◽  
Projective Model ◽  
Geodesic Triangles

Abstract In the present paper we study $\mathbf{S}^2\!\times\!\mathbf{R}$ and $\mathbf{H}^2\!\times\!\mathbf{R}$ geometries, which are homogeneous Thurston 3-geometries. We define and determine the generalized Apollonius surfaces and with them define the ‘surface of a geodesic triangle’. Using the above Apollonius surfaces we develop a procedure to determine the centre and the radius of the circumscribed geodesic sphere of an arbitrary $\mathbf{S}^2\!\times\!\mathbf{R}$ and $\mathbf{H}^2\!\times\!\mathbf{R}$ tetrahedron. Moreover, we generalize the famous Menelaus’s and Ceva’s theorems for geodesic triangles in both spaces. In our work we will use the projective model of $\mathbf{S}^2\!\times\!\mathbf{R}$ and $\mathbf{H}^2\!\times\!\mathbf{R}$ geometries described by E. Molnár in [6].

Cotorsion pairs and model structures on Ch(R)

2011 ◽  
Vol 54 (3) ◽  
pp. 783-797 ◽  
Author(s):  
Gang Yang ◽  
Zhongkui Liu
Keyword(s):  
Model Structure ◽  
Cotorsion Pair ◽  
Projective Model ◽  
Cotorsion Pairs ◽  
Category Of Modules ◽  
The Given ◽  
Model Structures

AbstractWe show that if the given cotorsion pair $(\mathcal{A},\mathcal{B})$ in the category of modules is complete and hereditary, then both of the induced cotorsion pairs in the category of complexes are complete. We also give a cofibrantly generated model structure that can be regarded as a generalization of the projective model structure.

Hardware architecture for projective model calculation and false match refining using random sample consensus algorithm

2016 ◽  
Vol 25 (6) ◽  
pp. 063014
Author(s):  
Ehsan Azimi ◽  
Alireza Behrad ◽  
Mohammad Bagher Ghaznavi-Ghoushchi ◽  
Jamshid Shanbehzadeh
Keyword(s):  
Model Calculation ◽  
Random Sample ◽  
Hardware Architecture ◽  
Consensus Algorithm ◽  
Projective Model ◽  
False Match ◽  
Random Sample Consensus

scholarly journals Projective model for evaluation of scientific content impact

2019 ◽  
pp. 149-155
Author(s):  
Alina I. Petrushka ◽  
Andriy M. Peleshchyshyn
Keyword(s):  
Scientific Content ◽  
Projective Model

The number of contact primes of the canonical curve of genus p

1930 ◽  
Vol 26 (4) ◽  
pp. 453-457
Author(s):  
W. G. Welchman
Keyword(s):  
General Formula ◽  
Theta Functions ◽  
Cubic Surface ◽  
General Curve ◽  
Projective Model ◽  
Quartic Curve ◽  
Canonical Curve ◽  
Riemann Theta Functions ◽  
Sextic Curve ◽  
Special Case

1. It is known, from the theory of the Riemann theta-functions, that the canonical series of a general curve of genus p has 2P−1 (2P − 1) sets which consist of p − 1. points each counted twice. Taking as projective model of the curve the canonical curve of order 2p − 2 in space of p− 1 dimensions, whose canonical series is given by the intersection of primes, we have the number of contact primes of the curve. The 28 bitangents of a plane quartic curve, the canonical curve of genus 3, have been studied in detail since the days of Plücker. The number, 120, of tritangent planes of the sextic curve of intersection of a quadric and a cubic surface, the canonical curve of genus 4, has been obtained directly by correspondence arguments by Enriques. Enriques also remarks that the general formula 2P−1 (2p −1) is a special case of the formula of de Jonquières, which was proved, by correspondence methods, by Torelli§.

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