Search results for "functional"

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

Structure–property relationship of isomeric diphenylethenyl-disubstituted dimethoxycarbazoles

2015

Isomeric 3,6-dimethoxy- and 2,7-dimethoxycarbazoles containing diphenylethenyl moieties were synthesized by condensation of the appropriate dimethoxycarbazoles with diphenylacetaldehyde. The solid-state structures and the molecular order of the compounds were proven by X-ray crystallography. Both compounds were found to be capable of glass formation with comparable glass transition temperatures (70–71 °C). They exhibited high thermal stabilities, with the 5% weight loss temperatures exceeding 375 °C. The isomer having diphenylethenyl groups at C-3 and C-6 positions and methoxy groups at C-2 and C-7 positions (3a) exhibited aggregation-induced emission (AIE), while its counterpart having dip…

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/.

First-principles study of the amorphous In3SbTe2phase change compound

2013

Ab initio molecular dynamics simulations based on density functional theory were performed to generate amorphous models of the phase change compound In${}_{3}$SbTe${}_{2}$ by quenching from the melt. In-Sb and In-Te are the most abundant bonds with only a minor fraction of Sb-Te bonds. The bonding geometry in the amorphous phase is, however, strongly dependent on the density in the range 6.448--5.75 g/cm${}^{3}$ that we investigated. While at high density the bonding geometry of In atoms is mostly octahedral-like as in the cubic crystalline phase of the ternary compound In${}_{3}$SbTe${}_{2}$, at low density we observed a sizable fraction of tetrahedral-like geometries similar to those pres…

Mindfulness, rumination, and coping skills in young women with Eating Disorders: A comparative study with healthy controls

2019

Eating Disorders (ED) have been associated with dysfunctional coping strategies, such as rumination. Promoting alternative ways of experiencing mental events, based on a mindfulness approach, might be the clue for learning more effective coping and regulatory strategies among young women with ED. This study examined the comparison between patients with ED diagnosis and healthy subjects in mindfulness, rumination and effective coping. In addition, we analyzed the independent association of those with the presence of ED. The study sample was formed by two groups of young women ranged 13-21 years: Twenty-five with an ED diagnosis and 25 healthy subjects. They were assessed by using the Freibur…

Supramolecular hierarchy among halogen and hydrogen bond donors in light-induced surface patterning

2015

Halogen bonding, a noncovalent interaction possessing several unique features compared to the more familiar hydrogen bonding, is emerging as a powerful tool in functional materials design. Herein, we unambiguously show that one of these characteristic features, namely high directionality, renders halogen bonding the interaction of choice when developing azobenzene-containing supramolecular polymers for light-induced surface patterning. The study is conducted by using an extensive library of azobenzene molecules that differ only in terms of the bond-donor unit. We introduce a new tetrafluorophenol-containing azobenzene photoswitch capable of forming strong hydrogen bonds, and show that an io…

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 $^{173}\mathrm{Yb}$.