Search results for "102"

Bing meets Sobolev

2019

We show that, for each $1\le p < 2$, there exists a wild involution $\mathbb S^3\to \mathbb S^3$ in the Sobolev class $W^{1,p}(\mathbb S^3,\mathbb S^3)$.

Devroye Inequality for a Class of Non-Uniformly Hyperbolic Dynamical Systems

2005

In this paper, we prove an inequality, which we call "Devroye inequality", for a large class of non-uniformly hyperbolic dynamical systems (M,f). This class, introduced by L.-S. Young, includes families of piece-wise hyperbolic maps (Lozi-like maps), scattering billiards (e.g., planar Lorentz gas), unimodal and H{\'e}non-like maps. Devroye inequality provides an upper bound for the variance of observables of the form K(x,f(x),...,f^{n-1}(x)), where K is any separately Holder continuous function of n variables. In particular, we can deal with observables which are not Birkhoff averages. We will show in \cite{CCS} some applications of Devroye inequality to statistical properties of this class…

On a generalisation of Krein's example

2017

We generalise a classical example given by Krein in 1953. We compute the difference of the resolvents and the difference of the spectral projections explicitly. We further give a full description of the unitary invariants, i.e., of the spectrum and the multiplicity. Moreover, we observe a link between the difference of the spectral projections and Hankel operators.

Compactness and $s$-numbers for polynomials

2018

Boundary Regularity for the Porous Medium Equation

2018

We study the boundary regularity of solutions to the porous medium equation $u_t = \Delta u^m$ in the degenerate range $m>1$. In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the parabolic boundary has a solution which attains the boundary values, provided that the spatial domain satisfies the elliptic Wiener criterion. This condition is known to be optimal, and it is a consequence of our main theorem which establishes a barrier characterization of regular boundary points for general -- not necessarily cylindrical -- domains in ${\bf R}^{n+1}$. One of our fundamental tools is a new strict comparison principle between sub- and superpara…

All congruences below stability-preserving fair testing or CFFD

2020

AbstractIn process algebras, a congruence is an equivalence that remains valid when any subsystem is replaced by an equivalent one. Whether or not an equivalence is a congruence depends on the set of operators used in building systems from subsystems. Numerous congruences have been found, differing from each other in fine details, major ideas, or both, and none of them is good for all situations. The world of congruences seems thus chaotic, which is unpleasant, because the notion of congruence is at the heart of process algebras. This study continues attempts to clarify the big picture by proving that in certain sub-areas, there are no other congruences than those that are already known or …

Positive linear maps on normal matrices

2018

For a positive linear map [Formula: see text] and a normal matrix [Formula: see text], we show that [Formula: see text] is bounded by some simple linear combinations in the unitary orbit of [Formula: see text]. Several elegant sharp inequalities are derived, for instance for the Schur product of two normal matrices [Formula: see text], [Formula: see text] for some unitary [Formula: see text], where the constant [Formula: see text] is optimal.

𝔸1-contractibility of affine modifications

2019

We introduce Koras–Russell fiber bundles over algebraically closed fields of characteristic zero. After a single suspension, this exhibits an infinite family of smooth affine [Formula: see text]-contractible [Formula: see text]-folds. Moreover, we give examples of stably [Formula: see text]-contractible smooth affine [Formula: see text]-folds containing a Brieskorn–Pham surface, and a family of smooth affine [Formula: see text]-folds with a higher-dimensional [Formula: see text]-contractible total space.

Abelian Gradings on Upper Block Triangular Matrices

2012

AbstractLet G be an arbitrary finite abelian group. We describe all possible G-gradings on upper block triangular matrix algebras over an algebraically closed field of characteristic zero.

On the slope of hyperelliptic fibrations with positive relative irregularity

2016

Let $f:\, S \to B$ be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus $g\geq 2$ with relative irregularity $q_f$. We show a sharp lower bound on the slope $\lambda_f$ of $f$. As a consequence, we prove a conjecture of Barja and Stoppino on the lower bound of $\lambda_f$ as an increasing function of $q_f$ in this case, and we also prove a conjecture of Xiao on the ampleness of the direct image of the relative canonical sheaf if $\lambda_f<4$.