Evolution of spoon-shaped networks

We consider a regular embedded network composed by two curves, one of them closed, in a convex domain $\Omega$. The two curves meet only in one point, forming angle of $120$ degrees. The non-closed curve has a fixed end point on $\partial\Omega$. We study the evolution by curvature of this network. We show that the maximal existence time depends only on the area enclosed in the initial loop, if the length of the non-closed curve stays bounded from below during the evolution. Moreover, the closed curve shrinks to a point and the network is asymptotically approaching, after dilations and extraction of a subsequence, a Brakke spoon.Comment: arXiv admin note: substantial text overlap with arXiv:math/0302164 by other author

Some minimization problems for planar networks of elastic curve

In this note we announce some results that will appear in [6] (joint work with also Matteo Novaga) on the minimization of the functional $F(\Gamma)=\int_\Gamma k^2+1\,\mathrm{d}s$, where $\Gamma$ is a network of three curves with fixed equal angles at the two junctions. The informal description of the results is accompanied by a partial review of the theory of elasticae and a diffuse discussion about the onset of interesting variants of the original problem passing from curves to networks. The considered energy functional $F$ is given by the elastic energy and a term that penalize the total length of the network. We will show that penalizing the length is tantamount to fix it. The paper is concluded with the explicit computation of the penalized elastic energy of the 'Figure Eight', namely the unique closed elastica with self--intersections.Comment: 24 pages, 7 figure

Nontrivial solutions of quasilinear elliptic equations with natural growth term

We prove the existence of multiple solutions for a quasilinear elliptic equation containing a term with natural growth, under assumptions that are invariant by diffeomorphism. To this purpose we develop an adaptation of degree theory.Comment: 25 page

Calibrations for minimal networks in a covering space setting

In this paper we define a notion of calibration for an equivalent approach to the classical Steiner problem in a covering space setting and we give some explicit examples. Moreover we introduce the notion of calibration in families: the idea is to divide the set of competitors in a suitable way, defining an appropriate (and weaker) notion of calibration. Then, calibrating the candidate minimizers in each family and comparing their perimeter, it is possible to find the minimizers of the minimization problem. Thanks to this procedure we prove the minimality of the Steiner configurations spanning the vertices of a regular hexagon and of a regular pentagon

Synthesis and reactivity of new hydroxamates of pterostilbene for biomedical applications

In this thesis work I explored the feasibility of using the hydroxamic functionality for the reversible protection of the hydroxy group of natural polyphenols: -OH → -O-N(R1)COR2. Many phenolic compounds exhibit, in vitro, interesting bioactivities with potential applications in human health care. However their bioavailability after ingestion is limited by the modifications of the phenolic functionality introduced by the enzymes of phase II metabolism. The prodrug strategy has thus been adopted to protect the sensitive sites and to increase the absorption of the active molecule. As model compound for the project I have used pterostilbene, a natural phenol with a vast potential for pharmaceutical applications. The thesis work has been performed in part in the laboratory of Dr. Sabine Amslinger of the Institute of Organic Chemistry of the University of Regensburg within the Erasmus program. Eleven new derivatives of pterostilbene have been synthesised, purified and characterized by mass spectrometry and 1H and 13C NMR spectroscopy. A study has been carried out of the reactivity of these derivatives in aqueous solution at pH values close to those of the body compartments involved in the absorption of orally administered drugs (stomach and first intestinal tract). The rate of hydrolysis and what products are obtained strongly depend on the nature of the R1 and R2 substituents. Some reaction intermediates have been identified and reaction mechanisms proposed, regarding also E, Z isomerism equilibria. Some of the compounds obtain show considerable stability both in strongly acidic (stomach-like) and neutral (intestine-like) solutions, and are therefore interesting candidates for more elaborated assays. Stability tests in blood and pharmacokinetic studies in vivo (rat) are currently under way in the laboratory of Dr. M. Zoratti of the CNR Institute of Neuroscience.openTesi 3799Coperta da embargo sino al 12.12.201

End the Lockdown for Animals : Reflecting and Campaigning on Three Key Arenas of Human-Animal Interaction Linked to Zoonotic Diseases

Covid-19, SARS, MERS, Ebola, avian influenza: Wake-up calls for humanity to reassess our relationship with animals and the natural world. 73% of emerging infectious diseases in humans are zoonotic, originating in animals. Together, zoonoses account for billions of illnesses and millions of deaths across the globe. Their spread has direct connections to our use and misuse of animals, trapped, traded, bred, raised, confined, transported in ways that pose a serious risk for the development of zoonotic pathogens with the potential to infect human populations. In order to prevent future pandemics, three key animal protection issues must be tackled: the trade of live wild animals; the intensive confinement of animals farmed for food; fur farming and the fur trade.El Covid-19, el SARS, el MERS, el Ébola, la influenza aviar: llamadas de atención a la humanidad para reevaluar nuestra relación con los animales y el mundo natural. El 73% de las enfermedades infecciosas emergentes en humanos son zoonóticas y se originan en animales. Juntas, las zoonosis representan miles de millones de enfermedades y millones de muertes en todo el mundo. Su propagación tiene conexiones directas con nuestro uso y mal uso de los animales, atrapados, comercializados, criados, confinados, transportados de formas que representan un riesgo grave para el desarrollo de patógenos zoonóticos con el potencial de infectar poblaciones humanas. Para prevenir futuras pandemias, se deben abordar tres cuestiones clave de protección animal: el comercio de animales silvestres vivos; el confinamiento intensivo de animales criados para la alimentación; las granjas peleteras y el comercio de pieles