scholarly journals The Toeplitz algebra has nuclear dimension one

2019 ◽  
Vol 51 (3) ◽  
pp. 554-562
Author(s):  
Laura Brake ◽  
Wilhelm Winter
Keyword(s):  
Toeplitz Algebra ◽  
Dimension One

scholarly journals Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Total Variation ◽  
Piecewise Constant ◽  
Geometrical Properties ◽  
Total Variation Denoising ◽  
Fidelity Term ◽  
Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

scholarly journals Nonlinear Conditions for Ultradifferentiability

2021 ◽  
Author(s):  
David Nicolas Nenning ◽  
Armin Rainer ◽  
Gerhard Schindl
Keyword(s):  
General Validity ◽  
Dimension One ◽  
Analogous Theorem

AbstractA remarkable theorem of Joris states that a function f is $$C^\infty $$ C ∞ if two relatively prime powers of f are $$C^\infty $$ C ∞ . Recently, Thilliez showed that an analogous theorem holds in Denjoy–Carleman classes of Roumieu type. We prove that a division property, equivalent to Joris’s result, is valid in a wide variety of ultradifferentiable classes. Generally speaking, it holds in all dimensions for non-quasianalytic classes. In the quasianalytic case we have general validity in dimension one, but we also get validity in all dimensions for certain quasianalytic classes.

scholarly journals From non-local Eringen’s model to fractional elasticity

2018 ◽  
Vol 24 (6) ◽  
pp. 1935-1953 ◽  
Author(s):  
Anton Evgrafov ◽  
José C. Bellido
Keyword(s):  
Riesz Potential ◽  
Heterogeneous Material ◽  
Research Literature ◽  
Stress Concentrations ◽  
Uniqueness Of Solutions ◽  
Numerical Studies ◽  
Smooth Kernels ◽  
Ill Posed ◽  
Non Local ◽  
Dimension One

Eringen’s model is one of the most popular theories in non-local elasticity. It has been applied to many practical situations with the objective of removing anomalous stress concentrations around geometric shape singularities, which appear when local modelling is used. Despite the great popularity of Eringen’s model within the mechanical engineering community, even the most basic questions such as the existence and uniqueness of solutions have been rarely considered in research literature for this model. In this work we focus on precisely these questions, proving that the model is in general ill-posed in the case of smooth kernels, the case which appears rather often in numerical studies. We also consider the case of singular, non-smooth kernels and for the paradigmatic case of Riesz potential we establish the well-posedness of the model in fractional Sobolev spaces. For such a kernel, in dimension one the model reduces to the well-known fractional Laplacian. Finally, we discuss possible extensions of Eringen’s model to spatially heterogeneous material distributions.

scholarly journals Boundary quotients of the right Toeplitz algebra of the affine semigroup over the natural numbers

10.53733/90 ◽  
2021 ◽  
Vol 52 ◽  
pp. 109-143
Author(s):  
Astrid An Huef ◽  
Marcelo Laca ◽  
Iain Raeburn
Keyword(s):  
Regular Representation ◽  
Crossed Product ◽  
Ideal Structure ◽  
Toeplitz Algebra ◽  
Natural Numbers ◽  
Kms States ◽  
C Algebra ◽  
Affine Semigroup ◽  
Natural Dynamics ◽  
The Right

We study the Toeplitz $C^*$-algebra generated by the right-regular representation of the semigroup ${\mathbb N \rtimes \mathbb N^\times}$, which we call the right Toeplitz algebra. We analyse its structure by studying three distinguished quotients. We show that the multiplicative boundary quotient is isomorphic to a crossed product of the Toeplitz algebra of the additive rationals by an action of the multiplicative rationals, and study its ideal structure. The Crisp--Laca boundary quotient is isomorphic to the $C^*$-algebra of the group ${\mathbb Q_+^\times}\!\! \ltimes \mathbb Q$. There is a natural dynamics on the right Toeplitz algebra and all its KMS states factor through the additive boundary quotient. We describe the KMS simplex for inverse temperatures greater than one.

scholarly journals A Note on One-dimensional Varieties Over the Complex p-adic Field

2018 ◽  
Vol 11 (4) ◽  
pp. 1046-1057
Author(s):  
Amran Dalloul
Keyword(s):  
One Dimensional ◽  
Dimension One

In this paper, we study the varieties V ⊆ C 4 p of dimension one that contain points of the form (x1, x2, exp(x1), exp(x2)) by using tools from Non-Archimedian Analysis.

scholarly journals Extended gradient systems: Dimension one

2000 ◽  
Vol 6 (3) ◽  
pp. 503-518 ◽  
Author(s):  
Siniša Slijepčević
Keyword(s):  
Gradient Systems ◽  
Dimension One
Sign in / Sign up

Export Citation Format

Share Document