Search results for "obol"

Complex Analysis and Dynamical Systems VII

2017

Vertical versus horizontal Sobolev spaces

2020

Let $\alpha \geq 0$, $1 < p < \infty$, and let $\mathbb{H}^{n}$ be the Heisenberg group. Folland in 1975 showed that if $f \colon \mathbb{H}^{n} \to \mathbb{R}$ is a function in the horizontal Sobolev space $S^{p}_{2\alpha}(\mathbb{H}^{n})$, then $\varphi f$ belongs to the Euclidean Sobolev space $S^{p}_{\alpha}(\mathbb{R}^{2n + 1})$ for any test function $\varphi$. In short, $S^{p}_{2\alpha}(\mathbb{H}^{n}) \subset S^{p}_{\alpha,\mathrm{loc}}(\mathbb{R}^{2n + 1})$. We show that the localisation can be omitted if one only cares for Sobolev regularity in the vertical direction: the horizontal Sobolev space $S_{2\alpha}^{p}(\mathbb{H}^{n})$ is continuously contained in the vertical Sobolev sp…

A Global Sensitivity Analysis Toolbox to Quantify Drivers of Vegetation Radiative Transfer Models

2017

Abstract Global sensitivity analysis (GSA) enables to gain insight into the functioning of radiative transfer models (RTMs) by identifying the driving input variables of RTM spectral outputs such as reflectance, fluorescence, or radiance. This contribution introduces automated radiative transfer models operator's (ARTMO’s) new GSA toolbox. With the GSA toolbox the majority of ARTMO’s available RTMs can be decomposed into its driving variables. For a selected RTM output, a GSA identifies the most influential and noninfluential input variables according to Sobol' first-order and total-order indices. The toolbox can process RTM spectral outputs for any kind of optical sensor setting within the…

Buchwaldoboletus lignicola (Boletaceae), a rare basidiomycete from Europe

2017

AbstractBuchwaldoboletus lignicola is a rare basidiomycete with fragmented distribution in Europe. The taxonomy, ecology and distribution of this species is reported. The new locality from central Sicily widens the area of distribution of B. lignicola in Europe.

Notulae to the Italian alien vascular flora: 2

2016

In this contribution, new data concerning the Italian distribution of alien vascular flora are presented. It includes new records, exclusions and confirmations for Italy or for Italian administrative regions for taxa in the genera Ageratum, Aster, Buddleja, Cedrus, Centranthus, Cephalotaxus, Clerodendrum, Cotoneaster, Cyperus, Honorius, Lantana, Ligustrum, Morus, Muscari, Oenothera, Opuntia, Platycladus, Plumbago, Pseudotsuga, Sedum, Sporobolus, Stachys, Ulmus and Yucca. A nomen novum, Stachys talbotii, is proposed as a replacement name for Sideritis purpurea.

On the continuous and discontinuous maximal operators

2018

Abstract In the first part of this paper we study the regularity properties of a wide class of maximal operators. These results are used to show that the spherical maximal operator is continuous W 1 , p ( R n ) ↦ W 1 , p ( R n ) , when p > n n − 1 . Other given applications include fractional maximal operators and maximal singular integrals. On the other hand, we show that the restricted Hardy–Littlewood maximal operator M λ , where the supremum is taken over the cubes with radii greater than λ > 0 , is bounded from L p ( R n ) to W 1 , p ( R n ) but discontinuous.

Pharmacogenomic Characterization and Isobologram Analysis of the Combination of Ascorbic Acid and Curcumin—Two Main Metabolites of Curcuma longa—in C…

2017

ABSTRACT Curcuma longa has long been used in China and India as anti-inflammatory agent to treat a wide variety of conditions. Here we investigated chemoprofiles of three Curcuma species and observed a great variety of phytochemicals with curcumin being among the few present in all three species. On the other hand ascorbic acid (AA) was a compound that was solely found in Curcuma longa. In the present study we explored the cytotoxic effect of a curcumin/AA combination toward human cancer cell lines. The curcumin/AA combination was assessed by isobologram analysis using the Loewe additivity drug interaction model. The drug combination showed additive cytotoxicity towards CCRF-CEM and CEM/ADR…

Sharp capacity estimates for annuli in weighted R^n and in metric spaces

2017

We obtain estimates for the nonlinear variational capacity of annuli in weighted R^n and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted R^n. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted R^n, which …

Strong BV-extension and W1,1-extension domains

2021

We show that a bounded domain in a Euclidean space is a $W^{1,1}$-extension domain if and only if it is a strong $BV$-extension domain. In the planar case, bounded and strong $BV$-extension domains are shown to be exactly those $BV$-extension domains for which the set $\partial\Omega \setminus \bigcup_{i} \overline{\Omega}_i$ is purely $1$-unrectifiable, where $\Omega_i$ are the open connected components of $\mathbb{R}^2\setminus\overline{\Omega}$.

Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation

2021

We look for solutions to the Schr\"{o}dinger-Poisson-Slater equation $$- \Delta u + \lambda u - \gamma (|x|^{-1} * |u|^2) u - a |u|^{p-2}u = 0 \quad \text{in} \quad \mathbb{R}^3, $$ which satisfy \begin{equation*} \int_{\mathbb{R}^3}|u|^2 \, dx = c \end{equation*} for some prescribed $c>0$. Here $ u \in H^1(\mathbb{R}^3)$, $\gamma \in \mathbb{R},$ $ a \in \mathbb{R}$ and $p \in (\frac{10}{3}, 6]$. When $\gamma >0$ and $a > 0$, both in the Sobolev subcritical case $p \in (\frac{10}{3}, 6)$ and in the Sobolev critical case $p=6$, we show that there exists a $c_1>0$ such that, for any $c \in (0,c_1)$, the equation admits two solutions $u_c^+$ and $u_c^-$ which can be characterized respectively…