Search results for "PSC"
showing 10 items of 183 documents
Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces
2015
We show that the Heisenberg group is not minimal in looking down. This answers Problem 11.15 in `Fractured fractals and broken dreams' by David and Semmes, or equivalently, Question 22 and hence also Question 24 in `Thirty-three yes or no questions about mappings, measures, and metrics' by Heinonen and Semmes. The non-minimality of the Heisenberg group is shown by giving an example of an Ahlfors $4$-regular metric space $X$ having big pieces of itself such that no Lipschitz map from a subset of $X$ to the Heisenberg group has image with positive measure, and by providing a Lipschitz map from the Heisenberg group to the space $X$ having as image the whole $X$. As part of proving the above re…
POINTS OF $\varepsilon$ -DIFFERENTIABILITY OF LIPSCHITZ FUNCTIONS FROM ${\bb R}^n$ TO ${\bb R}^{n-1}$
2002
This paper proves that for every Lipschitz function $f:{\bb R}^n\longrightarrow {\bb R}^m,\;m < n$ , there exists at least one point of $\varepsilon$ -differentiability of $f$ which is in the union of all $m$ -dimensional affine subspaces of the form $q_0+{\rm span}\{q_1,q_2,\ldots,q_m\},\;{\rm where}\;q_j(j=0,1,\ldots,m)$ are points in ${\bb R}^n$ with rational coordinates.
Proper 1-ball contractive retractions in Banach spaces of measurable functions
2005
In this paper we consider the Wosko problem of evaluating, in an infinite-dimensional Banach space X, the infimum of all k > 1 for which there exists a k-ball contractive retraction of the unit ball onto its boundary. We prove that in some classical Banach spaces the best possible value 1 is attained. Moreover we give estimates of the lower H-measure of noncompactness of the retractions we construct. 1. Introduction Let X be an infinite-dimensional Banach space with unit closed ball B(X) and unit sphere S(X). It is well known that, in this setting, there is a retraction of B(X) onto S(X), that is, a continuous mapping R : B(X) ! S(X) with Rx = x for all x 2 S(X). In (4) Benyamini and Sternf…
Singular integrals on regular curves in the Heisenberg group
2019
Let $\mathbb{H}$ be the first Heisenberg group, and let $k \in C^{\infty}(\mathbb{H} \, \setminus \, \{0\})$ be a kernel which is either odd or horizontally odd, and satisfies $$|\nabla_{\mathbb{H}}^{n}k(p)| \leq C_{n}\|p\|^{-1 - n}, \qquad p \in \mathbb{H} \, \setminus \, \{0\}, \, n \geq 0.$$ The simplest examples include certain Riesz-type kernels first considered by Chousionis and Mattila, and the horizontally odd kernel $k(p) = \nabla_{\mathbb{H}} \log \|p\|$. We prove that convolution with $k$, as above, yields an $L^{2}$-bounded operator on regular curves in $\mathbb{H}$. This extends a theorem of G. David to the Heisenberg group. As a corollary of our main result, we infer that all …
ICT for external use in Croatian four- and five-star hotels
2016
The Purpose – The objective of the paper is to examine the implementation of advanced technology and promotional supports in hotel companies and to compare their performance in four- and five-star hotels. More specifically, ICT for external use are analysed, i.e. customer relationship management (CRM), communication with customers, promotional supports, and online order receptions. Design/Methodology/Approach – The empirical research took place in 38 upscale (26 four and 12 five-star) hotels located in Croatia, in the regions of Dalmatia, Istria, and Kvarner, and in the city of Zagreb. The data were collected through a structured questionnaire administered mainly during personal interviews …
Ospedale psichiatrico di Sassari
2015
Il testo è relativo all'Ospedale psichiatrico di Sassari, sorto alla fine dell'Ottocento e rimasto in funzione sino al 1998, è stata redatta nell'ambito della ricerca (PRIN 2008), "I complessi manicomiali in Italia tra Otto e Novecento. Atlante del patrimonio storico-architettonico ai fini della conoscenza e della valorizzazione", sviluppata da ricercatori della Seconda Università di Napoli (coordinamento nazionale), dei Politecnici di Milano e Torino, delle Università di Camerino, Palermo, Pisa e Reggio Calabria. La scheda illustra, attraverso i diversi testi e un vasto repertorio iconografico, costituito da disegni, immagini d’epoca e fotografie – sia l’origine sia le trasformazioni dei c…
Riesz transform and vertical oscillation in the Heisenberg group
2023
We study the $L^{2}$-boundedness of the $3$-dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. Inspired by the notion of vertical perimeter, recently defined and studied by Lafforgue, Naor, and Young, we first introduce new scale and translation invariant coefficients $\operatorname{osc}_{\Omega}(B(q,r))$. These coefficients quantify the vertical oscillation of a domain $\Omega \subset \mathbb{H}$ around a point $q \in \partial \Omega$, at scale $r > 0$. We then proceed to show that if $\Omega$ is a domain bounded by an intrinsic Lipschitz graph $\Gamma$, and $$\int_{0}^{\infty} \operatorname{osc}_{\Omega}(B(q,r)) \, \frac{dr}{…
Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities
2018
We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\Omega\subset \mathbb R^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in $\Omega\times \Omega$ via couplings.
Alteration-Induced Volcano Instability at La Soufrière de Guadeloupe (Eastern Caribbean)
2021
International audience; Volcanoes are unstable structures that deform laterally and frequently experience mass wasting events. Hydrothermal alteration is often invoked as a mechanism that contributes significantly to volcano instability. We present a study that combines laboratory experiments, geophysical data, and large-scale numerical modeling to better understand the influence of alteration on volcano stability, using La Soufrière de Guadeloupe (Eastern Caribbean) as a case study. Laboratory experiments on variably altered (advanced argillic alteration) blocks show that uniaxial compressive strength, Young's modulus, and cohesion decrease as a function of increasing alteration, but that …
On Limiting Fréchet ε-Subdifferentials
1998
This paper presents an e-sub differential calculus for nonconvex and nonsmooth functions. We extend the previous work by Jofre et all to the case where the functions are lower semicontinuous instead of locally Lipschitz.