Search results for " Classical"
showing 10 items of 301 documents
Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups
2020
This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group $\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every intrinsic $L$-Lipschitz graph over a subset of a $k$-dimensional horizontal subgroup $\mathbb{V}$ of $\mathbb{H}^n$ can be extended to an intrinsic $L'$-Lipschitz graph over the entire subgroup $\mathbb{V}$, where $L'$ depends only on $L$, $k$, and $n$. We further prove that $1$-dimensional intrinsic $1$-Lipschitz graphs in $\mathbb{H}^n$, $n\in \mathbb{N}$, admit corona decompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants. This complements results that…
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…
Topological two-dimensional Su–Schrieffer–Heeger analog acoustic networks: Total reflection at corners and corner induced modes
2021
In this work, we investigate some aspects of an acoustic analogue of the two-dimensional Su-Schrieffer-Heeger model. The system is composed of alternating cross-section tubes connected in a square network, which in the limit of narrow tubes is described by a discrete model coinciding with the two-dimensional Su-Schrieffer-Heeger model. This model is known to host topological edge waves, and we develop a scattering theory to analyze how these waves scatter on edge structure changes. We show that these edge waves undergo a perfect reflection when scattering on a corner, incidentally leading to a new way of constructing corner modes. It is shown that reflection is high for a broad class of edg…
Biological control of invasive stink bugs: review of global state and future prospects
2020
International audience; Invasive stink bugs (Hemiptera: Pentatomidae) are responsible for high economic losses to agricul-ture on a global scale. The most important species, dating from recent to old invasions, includeBagrada hilaris (Burmeister), Halyomorpha halys (Stal), Piezodorus guildinii (Westwood), Nezara vir-idula (L.), and Murgantia histrionica (Hahn). Bagrada hilaris, H. halys,andN. viridula are nowalmost globally distributed. Biological control of these pests faces a complex set of challenges thatmust be addressed to maintain pest populations below the economic injury level. Several case studiesof classical and conservation biological control of invasive stink bugs are reported …
Role of nitric oxide pathway in the conditioned rewarding effects of MDMA in mice.
2017
It is estimated that 2.1 million young adults used MDMA/Ecstasy in the last year in Europe. Vulnerable subjects can develop dependence after MDMA abuse but currently there does not exist an effective treatment for this disorder. The nitric oxide (NO) pathway seems to have an important role on the rewarding effects of different drugs and has been proposed as a new pharmacological treatment for psychostimulant addiction. In the present study, we intend to evaluate whether the blockade of the NO synthesis (NOS) interferes with the rewarding effects of MDMA in the conditioned preference place (CPP) paradigm in young adult male mice. Our results indicated that mice treated with 7-nitroindazole (…
Effects of bingeing on fat during adolescence on the reinforcing effects of cocaine in adult male mice
2016
Binge eating is a specific form of overeating characterized by intermittent excessive eating. In addition to altering the neurobiological reward system, several studies have highlighted that consumption of palatable food increases vulnerability to drug use. The aim of the present study was to evaluate the effects of a high-fat diet consumed in a binge pattern during adolescence on the reinforcing effects of cocaine. After 40 days of binge-eating for 2 h, three days a week (PND 29–69), the reinforcing effects of cocaine on conditioning place preference and intravenous self-administration paradigm were evaluated in adolescent male mice. Circulating leptin and ghrelin levels and the effects of…
Sustained oscillations in the MAP kinase cascade.
2016
Abstract The MAP kinase cascade is a network of enzymatic reactions arranged in layers. In each layer occurs a multiple futile cycle of phosphorylations. The fully phosphorylated substrate then serves as an enzyme for the layer below. This paper focuses on the existence of parameters for which Hopf bifurcations occur and generate periodic orbits. Furthermore it is explained how geometric singular perturbation theory allows to generalize results from simple models to more complex ones.
Neurons in the pigeon caudolateral nidopallium differentiate Pavlovian conditioned stimuli but not their associated reward value in a sign-tracking p…
2016
AbstractAnimals exploit visual information to identify objects, form stimulus-reward associations, and prepare appropriate behavioral responses. The nidopallium caudolaterale (NCL), an associative region of the avian endbrain, contains neurons exhibiting prominent response modulation during presentation of reward-predicting visual stimuli, but it is unclear whether neural activity represents valuation signals, stimulus properties, or sensorimotor contingencies. To test the hypothesis that NCL neurons represent stimulus value, we subjected pigeons to a Pavlovian sign-tracking paradigm in which visual cues predicted rewards differing in magnitude (large vs. small) and delay to presentation (s…
Space-filling vs. Luzin's condition (N)
2013
Let us assume that we are given two metric spaces, where the Hausdorff dimension of the first space is strictly smaller than the one of the second space. Suppose further that the first space has sigma-finite measure with respect to the Hausdorff measure of the corresponding dimension. We show for quite general metric spaces that for any measurable surjection from the first onto the second space, there is a set of measure zero that is mapped to a set of positive measure (both measures are the Hausdorff measures corresponding to the Hausdorff dimension of the first space). We also study more general situations where the measures on the two metric spaces are not necessarily the same and not ne…
$\Omega$-symmetric measures and related singular integrals
2019
Let $\mathbb{S} \subset \mathbb{C}$ be the circle in the plane, and let $\Omega: \mathbb{S} \to \mathbb{S}$ be an odd bi-Lipschitz map with constant $1+\delta_\Omega$, where $\delta_\Omega>0$ is small. Assume also that $\Omega$ is twice continuously differentiable. Motivated by a question raised by Mattila and Preiss in [MP95], we prove the following: if a Radon measure $\mu$ has positive lower density and finte upper density almost everywhere, and the limit $$ \lim_{\epsilon \downarrow 0} \int_{\mathbb{C} \setminus B(x,\epsilon)} \frac{\Omega\left((x-y)/|x-y|\right)}{|x-y|} \, d\mu(y) $$ exists $\mu$-almost everywhere, then $\mu$ is $1$-rectifiable. To achieve this, we prove first that if …