Semilinear equations in bounded cylinders: Morse index and bifurcation from one-dimensional solutions

In this paper, we study positive one-dimensional solutions (i.e., solutions that depend only on one variable) for a class of semilinear elliptic problems in bounded cylinders in $\mathbb R^N$, $N \geq 2$. We compute the Morse index of such solutions and deduce from it the existence of least-energy solutions which are not one-dimensional, under suitable hypotheses on the nonlinearity and on the base of the cylinder. Furthermore, we analyze the appearance of more positive solutions, bifurcating from the one-dimensional ones, when we scale the base.Comment: 13 pages. Comments are welcom

Normalized solutions to a Schr\"odinger-Bopp-Podolsky system under Neumann boundary conditions

In this paper we study a Schr\"odinger-Bopp-Podolsky system of partial differential equations in a bounded and smooth domain of $\mathbb R^3$ with a non constant coupling factor. Under a compatibility condition on the boundary data we deduce existence and multiplicity of solutions by means of the Ljusternik-Schnirelmann theory.Comment: Comments and suggestions are welcom

Comparative morphology of tongue surface in Neotropical aerial insectivore bats (Mammalia: Chiroptera)

Comparative morphological characters in Neotropical bats are mostly restricted to external and cranio-dentary complexes, and few studies focusing on other morphological complexes have been carried out. In the case of tongue morphology, comparative analyses of the structure have been restricted to the superfamily Noctilionoidea with a wide range of diets, and Molossidae, a strictly aerial insectivore family. In this paper, we studied the morphology of tongue papillae in 10 aerial insectivore Neotropical bat species, representing six families (Emballonuridae, Furipteridae, Thyropteridae, Mormoopidae, Natalidae, and Vespertilionidae), and data from the previous study of Molossidae were compared. We studied tongues in light and scanning electron microscopes following material preparation protocols. We observed two types of sensitive papillae, circumvallate and fungiform, the latter at times presenting a groove surrounding the papillae. Nine mechanic types were observed, one of them, which we called flaky-like, not hitherto described. All Vespertilionoidea families (Vespertilionidae, Natalidae, and Molossidae) presented, as diagnosing characters, fungiform papillae distributed throughout the tongue, as well as anteriorly at the dorsum, and scale-like papillae on the medial lobe directed laterally and anteriorly. Emballonuridae showed the simplest tongue morphology regarding the presence and abundance of some papillae. Families composing the clade Furipteridae + Thyropteridae + Mormoopidae presented small and non-grooved fungiform papillae, and mechanical bifid papillae were absent. In summary, this study has provided additional traits (putative synapomorphies) of the bat tongue to support the clades on the current bat phylogeny

Energy stability for a class of semilinear elliptic problems

In this paper, we consider semilinear elliptic problems in a bounded domain $\Omega$ contained in a given unbounded Lipschitz domain $\mathcal C \subset \mathbb R^N$. Our aim is to study how the energy of a solution behaves with respect to volume-preserving variations of the domain $\Omega$ inside $\mathcal C$. Once a rigorous variational approach to this question is set, we focus on the cases when $\mathcal C$ is a cone or a cylinder and we consider spherical sectors and radial solutions or bounded cylinders and special one-dimensional solutions, respectively. In these cases, we show both stability and instability results, which have connections with related overdetermined problems.Comment: 33 page

Energy stability for a class of semilinear elliptic problems

In this paper, we consider semilinear elliptic problems in a bounded domain $\Omega$ contained in a given unbounded Lipschitz domain $\mathcal C \subset \mathbb R^N$. Our aim is to study how the energy of a solution behaves with respect to volume-preserving variations of the domain $\Omega$ inside $\mathcal C$. Once a rigorous variational approach to this question is set, we focus on the cases when $\mathcal C$ is a cone or a cylinder and we consider spherical sectors and radial solutions or bounded cylinders and special one-dimensional solutions, respectively. In these cases, we show both stability and instability results, which have connections with related overdetermined problems

Behavioural responses of the colonial sea squirt botrylloides violaceus oka to suspended food micro‐ particles in laboratory cultures

Violet sea squirts are noteworthy model organisms, because they provide insights into various physiologic processes, including cell senescence, ageing, apoptosis and allorecognition. Consequently, their culture is critical to permit experimental studies. Most papers refer to short periods of rearing using various feeds, both living and conserved, missing a formal justification for their use or indications of their actual nutritional value. Here, we use two behavioural responses— the percentage of open siphons and the frequency of zooid contractions—as compared to the abundance of suspended microparticles during feeding tests, to identify feeds able to promote filter-feeding. The results will enable to formulate compound diets that maximise positive physiological responses. Our tests demonstrated that plant items, such as dry microalgae and cyanobacteria (Arthrospira platensis, commercially known as Spirulina), along with living planktonic Haptophyta (Isochrysis galbana), trigger clear positive reactions, represented by a higher frequency of zooid contractions and larger proportions of open siphons. These responses correspond to decreases in the concentrations of suspended microparticles during the experiment and indicate higher filter-feeding activity. In contrast, feeds commonly administered to colonies, such as milk powder, dried eggs and artificial plankton, triggered negative behavioural responses, and their intake was lower during the feeding trials

Razjede in njihovo celjenje pri pacientih po amputaciji

Uvod: Najpogostejši vzroki, ki vplivajo na celjenje razjed pri pacientih po amputaciji, so periferna arterijska bolezen, sladkorna bolezen in kronična venska insuficienca. Namen raziskave je bil prepoznati dejavnike, ki lahko vplivajo na celjenje razjede na amputacijskem krnu. Metode: Uporabljena je bila kvantitativna neeksperimentalna raziskovalna metodologija. Izvedena je bila retrospektivna raziskava s pregledom negovalne dokumentacije o spremljanju razjede. V raziskavo je bilo vključenih 134 pacientov po amputaciji spodnjega uda z razjedo, hospitaliziranih v letu 2017. Uporabljeni sta bili opisna statistika in logistična regresija. Rezultati: Razjedo, nastalo zaradi različnih vzrokov, je imelo 134 pacientov. Ženske imajo v primerjavi v moškimi več možnosti za prisotnost razjede ob odpustu (RO = 4,8, 95 % IZ: 1–22), prav tako pacienti, ki so imeli razjedo že ob sprejemu (RO = 7,7, 95 % IZ: 3–19,2), in tisti z več kot eno razjedo (RO = 4,7, 95 % IZ: 1–22,3). Pri pacientih, ki imajo razjedo na amputacijskem krnu, imajo večjo možnost, da se bo ta do konca rehabilitacije zacelila (RO = 0,2, 95 % IZ: 0,1–0,6 p = 0,004). Diskusija in zaključek: Ugotovitve nakazujejo, da je pri ženskah večja verjetnost, da razjeda ob odpustu ne bo zaceljena, kot pri pacientih, pri katerih je bila razjeda prisotna že ob sprejemu, in pri tistih, ki imajo več razjed. Treba bi bilo izvesti raziskavo, ki bi zajela večje število pacientov. Prav tako bi bilo treba natančneje določiti parametre spremljanja