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61.
Matteo?BonforteEmail author Alessio?Figalli Juan?Luis?Vázquez 《Calculus of Variations and Partial Differential Equations》2018,57(2):57
We investigate quantitative properties of nonnegative solutions \(u(x)\ge 0\) to the semilinear diffusion equation \(\mathcal {L}u= f(u)\), posed in a bounded domain \(\Omega \subset \mathbb {R}^N\) with appropriate homogeneous Dirichlet or outer boundary conditions. The operator \(\mathcal {L}\) may belong to a quite general class of linear operators that include the standard Laplacian, the two most common definitions of the fractional Laplacian \((-\Delta )^s\) (\(0<s<1\)) in a bounded domain with zero Dirichlet conditions, and a number of other nonlocal versions. The nonlinearity f is increasing and looks like a power function \(f(u)\sim u^p\), with \(p\le 1\). The aim of this paper is to show sharp quantitative boundary estimates based on a new iteration process. We also prove that, in the interior, solutions are Hölder continuous and even classical (when the operator allows for it). In addition, we get Hölder continuity up to the boundary. Particularly interesting is the behaviour of solution when the number \(\frac{2s}{1-p}\) goes below the exponent \(\gamma \in (0,1]\) corresponding to the Hölder regularity of the first eigenfunction \(\mathcal {L}\Phi _1=\lambda _1 \Phi _1\). Indeed a change of boundary regularity happens in the different regimes \(\frac{2s}{1-p} \gtreqqless \gamma \), and in particular a logarithmic correction appears in the “critical” case \(\frac{2s}{1-p} = \gamma \). For instance, in the case of the spectral fractional Laplacian, this surprising boundary behaviour appears in the range \(0<s\le (1-p)/2\). 相似文献
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64.
Francesca Alessio Piero Montecchiari 《Calculus of Variations and Partial Differential Equations》2013,46(3-4):591-622
We consider a class of semilinear elliptic equations of the form $$ \label{eq:abs}-\Delta u(x,y,z)+a(x)W'(u(x,y,z))=0,\quad (x,y,z)\in\mathbb {R}^{3},$$ where ${a:\mathbb {R} \to \mathbb {R}}$ is a periodic, positive, even function and, in the simplest case, ${W : \mathbb {R} \to \mathbb {R}}$ is a double well even potential. Under non degeneracy conditions on the set of minimal solutions to the one dimensional heteroclinic problem $$-\ddot q(x)+a(x)W^{\prime}(q(x))=0,\ x\in\mathbb {R},\quad q(x)\to\pm1\,{\rm as}\, x\to \pm\infty,$$ we show, via variational methods the existence of infinitely many geometrically distinct solutions u of (0.1) verifying u(x, y, z) → ± 1 as x → ± ∞ uniformly with respect to ${(y, z) \in \mathbb {R}^{2}}$ and such that ${\partial_{y}u \not \equiv0, \partial_{z}u \not\equiv 0}$ in ${\mathbb {R}^{3}}$ . 相似文献
65.
Alessio Emanuele Biondo Alessandro Pluchino Andrea Rapisarda 《Journal of statistical physics》2013,151(3-4):607-622
In this paper we focus on the beneficial role of random strategies in social sciences by means of simple mathematical and computational models. We briefly review recent results obtained by two of us in previous contributions for the case of the Peter principle and the efficiency of a Parliament. Then, we develop a new application of random strategies to the case of financial trading and discuss in detail our findings about forecasts of markets dynamics. 相似文献
66.
Olaya Domarco Claudia Kieler Christine Pirker Carina Dinhof Bernhard Englinger Johannes M. Reisecker Gerald Timelthaler Marcos D. García Carlos Peinador Bernhard K. Keppler Walter Berger Alessio Terenzi 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2019,131(24):8091-8096
Metal‐driven self‐assembly afforded a multitude of fascinating supramolecular coordination complexes (SCCs) with applications as catalysts, host–guest, and stimuli‐responsive systems. However, the interest in the biological applications of SCCs is only starting to emerge and thorough characterization of their behavior in biological milieus is still lacking. Herein, we report on the synthesis and detailed in‐cell tracking of a Pt2L2 metallacycle. We show that our hexagonal supramolecule accumulates in cancer cell nuclei, exerting a distinctive blue fluorescence staining of chromatin resistant to UV photobleaching selectively in nucleolar G4‐rich regions. SCC co‐localizes with epitopes of the quadruplex‐specific antibody BG4 and replaces other well‐known G4 stabilizers. Moreover, the photophysical changes accompanying the metallacycle binding to G4s in solution (fluorescence quenching, absorption enhancement) also take place intracellularly, allowing its subcellular interaction tracking. 相似文献
67.
Batyr Garlyyev Kathrin Kratzl Marlon Rück Jan Michali
ka Johannes Fichtner Jan M. Macak Tim Kratky Sebastian Günther Mirza Cokoja Aliaksandr S. Bandarenka Alessio Gagliardi Roland A. Fischer 《Angewandte Chemie (International ed. in English)》2019,58(28):9596-9600
High oxygen reduction (ORR) activity has been for many years considered as the key to many energy applications. Herein, by combining theory and experiment we prepare Pt nanoparticles with optimal size for the efficient ORR in proton‐exchange‐membrane fuel cells. Optimal nanoparticle sizes are predicted near 1, 2, and 3 nm by computational screening. To corroborate our computational results, we have addressed the challenge of approximately 1 nm sized Pt nanoparticle synthesis with a metal–organic framework (MOF) template approach. The electrocatalyst was characterized by HR‐TEM, XPS, and its ORR activity was measured using a rotating disk electrode setup. The observed mass activities (0.87±0.14 A mgPt?1) are close to the computational prediction (0.99 A mgPt?1). We report the highest to date mass activity among pure Pt catalysts for the ORR within similar size range. The specific and mass activities are twice as high as the Tanaka commercial Pt/C catalysis. 相似文献
68.
Edoardo Milotti Alessio Del Fabbro Chiara Dalla Pellegrina Roberto Chignola 《Physica A》2008,387(16-17):4204-4214
Experimental measurements on semi-synchronous tumor cell populations show that after a few cell cycles they desynchronize completely, and this desynchronization reflects the intercell variability of cell-cycle duration. It is important to identify the sources of randomness that desynchronize a population of cells living in a homogeneous environment: for example, being able to reduce randomness and induce synchronization would aid in targeting tumor cells with chemotherapy or radiotherapy. Here we describe a statistical approach to the analysis of the desynchronization measurements that is based on minimal modeling hypotheses, and can be derived from simple heuristics. We use the method to analyze existing desynchronization data and to draw conclusions on the randomness of cell growth and proliferation. 相似文献
69.
Experimental Evidence of Chemical Components in the Bonding of Helium and Neon with Neutral Molecules 下载免费PDF全文
70.
Marco Masi Maria Chiara Zonno Alessio Cimmino Pierluigi Reveglia Alexander Berestetskiy Angela Boari 《Natural product research》2018,32(13):1537-1547
Ambrosia artemisiifolia L. is responsible for serious allergies induced on humans. Different approaches for its control were proposed during the COST Action FA1203 “Sustainable management of Ambrosia artemisiifolia in Europe” (SMARTER). Fungal secondary metabolites often show potential herbicidal activity. Three phytotoxins were purified from the fungal culture filtrates of Colletotrichum gloeosporioides, isolated from infected leaves of A. artemisiifolia. They were identified by spectroscopic and chemical methods as colletochlorin A, orcinol and tyrosol (1, 2 and 3). The absolute configuration 6’R to colletochlorin A was assigned for the first time applying the advanced Mosher’s method. When assayed by leaf-puncture on A. artemisiifolia only 1 caused the appearance of large necrosis. The same symptoms were also induced by 1 on ambrosia plantlets associated with plant wilting. On Lemna minor, colletochlorin A caused a clear fronds browning, with a total reduction in chlorophyll content. 相似文献