scholarly journals Analysis‐Suitable T‐Splines of arbitrary degree and dimension

PAMM ◽  
2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Philipp Morgenstern ◽  
Robin Görmer
Keyword(s):  
Arbitrary Degree

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.

scholarly journals A Multi-Frey Approach to Some Multi-Parameter Families of Diophantine Equations

2008 ◽  
Vol 60 (3) ◽  
pp. 491-519 ◽  
Author(s):  
Yann Bugeaud ◽  
Maurice Mignotte ◽  
Samir Siksek
Keyword(s):  
Lower Bounds ◽  
Diophantine Equations ◽  
Galois Representations ◽  
Arbitrary Degree ◽  
Famous Theorem ◽  
Linear Forms ◽  
Positive Integers ◽  
Level Lowering

AbstractWe solve several multi-parameter families of binomial Thue equations of arbitrary degree; for example, we solve the equation5uxn − 2r3s yn = ±1,in non-zero integers x, y and positive integers u, r, s and n ≥ 3. Our approach uses several Frey curves simultaneously, Galois representations and level-lowering, new lower bounds for linear forms in 3 logarithms due to Mignotte and a famous theorem of Bennett on binomial Thue equations.

scholarly journals Statistical Mechanics of Discrete Multicomponent Fragmentation

2020 ◽  
Vol 5 (4) ◽  
pp. 64
Author(s):  
Themis Matsoukas
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Closed Form ◽  
Fixed Number ◽  
Arbitrary Degree ◽  
Fragment Distribution ◽  
The Mean ◽  
Fragmentation Event

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity, and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation, and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.

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