Search results for "Functional analysis"

Quasi-Continuous Vector Fields on RCD Spaces

2021

In the existing language for tensor calculus on RCD spaces, tensor fields are only defined $\mathfrak {m}$ -a.e.. In this paper we introduce the concept of tensor field defined ‘2-capacity-a.e.’ and discuss in which sense Sobolev vector fields have a 2-capacity-a.e. uniquely defined quasi-continuous representative.

A quasiconformal composition problem for the Q-spaces

2017

Given a quasiconformal mapping $f:\mathbb R^n\to\mathbb R^n$ with $n\ge2$, we show that (un-)boundedness of the composition operator ${\bf C}_f$ on the spaces $Q_{\alpha}(\mathbb R^n)$ depends on the index $\alpha$ and the degeneracy set of the Jacobian $J_f$. We establish sharp results in terms of the index $\alpha$ and the local/global self-similar Minkowski dimension of the degeneracy set of $J_f$. This gives a solution to [Problem 8.4, 3] and also reveals a completely new phenomenon, which is totally different from the known results for Sobolev, BMO, Triebel-Lizorkin and Besov spaces. Consequently, Tukia-V\"ais\"al\"a's quasiconformal extension $f:\mathbb R^n\to\mathbb R^n$ of an arbitr…

Quasiconformal mappings and global integrability of the derivative

1991

Quasiextremal distance domains and extension of quasiconformal mappings

1985

Formation of Ordered Structures in Quenching Experiments: Scaling Theory and Simulations

1987

In this note we want to address the particular problem of the formation of ordered structures resulting from “quenching experiments”. The generic experimental situation is depicted in Figure 1. Initially the system is in an unordered random state in the one-phase region. Then the temperature is lowered (for some systems like polymers the coexistence curve is inverted so that the temperature must be raised) until the system is in the two phase region. The system is now in a non-equilibrium situation and evolves toward equilibrium. It is during the evolution toward equilibrium that the system develops ordered structures /1,2/.

Magnetic octupole moment of Yb-173 using collinear laser spectroscopy

2021

The hyperfine constants of the $4{f}^{14}6s6p^{3}P_{2}^{o}$ state in neutral Yb have been measured using three different dipole transitions. This state was recently shown to have a comparatively large hyperfine magnetic octupole splitting, and thus a puzzlingly large magnetic octupole moment. The measurement is performed using collinear laser spectroscopy on a fast atomic beam, which provides a straightforward route to probing long-lived metastable atomic states with high resolution. From the combined analysis of all three lines we find no significant evidence for a nonzero octupole moment in $^{173}\mathrm{Yb}$.

Evolutionary Spectrum for Random Field and Missing Observations

2012

There are innumerable situations where the data observed from a non-stationary random field are collected with missing values. In this work a consistent estimate of the evolutionary spectral density is given where some observations are randomly missing.

Resolvent Estimates Near the Boundary of the Range of the Symbol

2019

The purpose of this chapter is to give quite explicit bounds on the resolvent near the boundary of Σ(p) (or more generally, near certain “generic boundary-like” points.) The result is due (up to a small generalization) to Montrieux (Estimation de resolvante et construction de quasimode pres du bord du pseudospectre, 2013) and improves earlier results by Martinet (Sur les proprietes spectrales d’operateurs nonautoadjoints provenant de la mecanique des fluides, 2009) about upper and lower bounds for the norm of the resolvent of the complex Airy operator, which has empty spectrum (Almog, SIAM J Math Anal 40:824–850, 2008). There are more results about upper bounds, and some of them will be rec…

Magnetic order in UCu4+xAl8−x

1992

Abstract A neutron diffraction study has been performed on UCu4+xAl8−x. The compound was chosen as an example of a uranium-based system, which goes from a magnetically ordered state to a pure heavy-fermion state. In the range x = 0.25–1, UCu4+xAl8−x orders in a simple collinear antiferromagnetic structure. With increasing concentration of Cu, the ordering temperature decreases and moment compensation develops due to the increasing hybridization of the 5f electrons.

Classification criteria for regular trees

2021

Esitämme säännöllisten puiden parabolisuudelle yhtäpitäviä ehtoja. We give characterizations for the parabolicity of regular trees. peerReviewed