Bounds for Arcs of Arbitrary Degree in Finite Desarguesian Planes

2015 ◽  
Vol 24 (4) ◽  
pp. 184-196 ◽  
Author(s):  
J. W. P. Hirschfeld ◽  
E. V. D. Pichanick
Keyword(s):  
Arbitrary Degree ◽  
Desarguesian Planes

Non-uniform subdivision for B-splines of arbitrary degree

2009 ◽  
Vol 26 (1) ◽  
pp. 75-81 ◽  
Author(s):  
S. Schaefer ◽  
R. Goldman
Keyword(s):  
Arbitrary Degree ◽  
B Splines

scholarly journals Codimension One Holomorphic Distributions on the Projective Three-space

2018 ◽  
Vol 2020 (23) ◽  
pp. 9011-9074 ◽  
Author(s):  
Omegar Calvo-Andrade ◽  
Maurício Corrêa ◽  
Marcos Jardim
Keyword(s):  
Projective Space ◽  
Moduli Space ◽  
Tangent Bundle ◽  
Projective Variety ◽  
Arbitrary Degree ◽  
Codimension One ◽  
Quot Scheme ◽  
Space Of Distributions ◽  
Three Space

Abstract We study codimension one holomorphic distributions on the projective three-space, analyzing the properties of their singular schemes and tangent sheaves. In particular, we provide a classification of codimension one distributions of degree at most 2 with locally free tangent sheaves and show that codimension one distributions of arbitrary degree with only isolated singularities have stable tangent sheaves. Furthermore, we describe the moduli space of distributions in terms of Grothendieck’s Quot-scheme for the tangent bundle. In certain cases, we show that the moduli space of codimension one distributions on the projective space is an irreducible, nonsingular quasi-projective variety. Finally, we prove that every rational foliation and certain logarithmic foliations have stable tangent sheaves.

Origin shifts in divergent Feynman integrals

1969 ◽  
Vol 47 (12) ◽  
pp. 1263-1269 ◽  
Author(s):  
Robert E. Pugh
Keyword(s):  
Sum Rules ◽  
Tensor Rank ◽  
Linear Quadratic ◽  
Arbitrary Degree ◽  
Recursion Relations ◽  
Feynman Integrals ◽  
Shift Of Origin

The surface terms arising from a shift of origin in divergent Feynman integrals are considered. Sum rules and recursion relations between these terms are derived for an arbitrary degree of divergence and tensor rank. These relations are explicitly solved for linear, quadratic, cubic, and quartic divergences.

scholarly journals On the Dielectric Function of Partially Amorphous Olivine Dust

1996 ◽  
Vol 150 ◽  
pp. 447-450
Author(s):  
David K. Lynch ◽  
S. Mazuk
Keyword(s):  
Solar System ◽  
Dielectric Function ◽  
Optical Constants ◽  
Continuous Distribution ◽  
New Technique ◽  
Arbitrary Degree ◽  
Atomic Disorder ◽  
Disordered Solids ◽  
A New Technique

AbstractWe present a new technique for computing the optical constants for partially disordered solids based on their crystalline optical constants. The technique assumes that the material is composed of a continuous distribution of oscillators (CDO) and that the degree of atomic disorder can be described by one, or at most two, scalar parameters. We apply the technique to an oft-mentioned solar system material, olivine, and show that its dielectric functions can be predicted for an arbitrary degree of disorder.

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