170,204 research outputs found
About the general chain rule for functions of bounded variation
No full textWe give an alternative proof of the general chain rule for functions of bounded variation (Ambrosio and Maso, 1990), which allows to compute the distributional differential of φ∘F, where φ∈LIP(Rm) and F∈BV(Rn,Rm). In our argument we build on top of recently established links between “closability of certain differentiation operators” and “differentiability of Lipschitz functions in related directions” (Alberti et al., 2023): we couple this with the observation that “the map that takes φ and returns the distributional differential of φ∘F is closable” to conclude. Unlike previous results in this direction, our proof can directly be adapted to the non-smooth setting of finite dimensional RCD spaces
Calculus and Fine Properties of Functions of Bounded Variation on RCD Spaces
Get PDFWe generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD spaces. In the infinite dimensional setting, we are able to define an analogue of the distributional differential and, on finite dimensional spaces, we prove fine properties and suitable calculus rules, such as the Vol’pert chain rule for vector valued functions
Local vector measures
Get PDFConsider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vector/matrix valued measures if the manifold is the Euclidean space. In more general curved contexts, the same objects can be perfectly understood via charts. However, charts are often unavailable in the less regular setting of metric geometry, where still the questions make sense. In this paper we propose a way to deal with this sort of problems and, more generally, to give a meaning to a concept of ‘measure acting in duality with sections of a given bundle’, loosely speaking. Despite the generality, several classical results in measure theory like Riesz's and Alexandrov's theorems have a natural counterpart in this setting. Moreover, as we are going to discuss, the notions introduced here provide a unified framework for several key concepts in nonsmooth analysis that have been introduced more than two decades ago, such as: Ambrosio-Kirchheim's metric currents, Cheeger's Sobolev functions and Miranda's BV functions. Not surprisingly, the understanding of the structure of these objects improves with the regularity of the underlying space. We are particularly interested in the case of RCD spaces where, as we will argue, the regularity of several key measures of the type we study nicely matches the known regularity theory for vector fields, resulting in a very effective theory. We expect that the notions developed here will help creating stronger links between differential calculus in Alexandrov spaces (based on Perelman's DC charts) and in RCD ones (based on intrinsic tensor calculus)
Intervención docente en la alfabetización inicial. Leer y escribir en proyectos para saber más sobre un tema
Get PDFFil: Molinari, María Claudia. Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educación; Argentina.Fil: Brena, Graciela. Escuela Graduada "Joaquín V. González", UNLP
The highly specialised gut of Fritillariidae (Appendicularia : Tunicata)
No full textThe morphology and some functions of the gut of Fritillaria pellucida and Fritillaria formica (Fritillaridae) were investigated by light and electron microscopy, and also by means of histochemical and immunohistochemical techniques. Fritillarids, very important for their abundance and ecological impact in marine ecosystems, have a very simplified gut: a straight oesophagus connects the pharynx to the digestive nucleus, composed of globular stomach and rectum, connected dorsally through a very short proximal intestine. The latter is characterised by a few (two to four) extremely specialised cells, completely filled with mitochondria associated tightly with membrane infoldings showing strong ATP-ase activity, and probably involved in the osmoregulation of internal body fluids. The gut is formed of an extremely low number of cells, which, although poorly diversified, are very large in the stomach and rectum. Food transfer along the gut depends on and is regulated by well-developed cardiac and pyloric valves, and signs of general digestive and absorptive activity are recognisable all along the brush border of the main tracts. The macroscopic organisation and cytological characters of the gut in fritillarids are completely different from those of the oikopleurids. In particular, fritillarids lack specialised cells for endocytosis and intracellular digestion, like those described in the genus Oikopleura. The general simplification and specialisation observed in Fritillaria gut may account for their elevated growth rate and abundant diffusion in all oceans
The exceptional "blind" gut of Appendicularia sicula (Appendicularia, Tunicata)
No full textIn this work, we studied for the first time the histology and ultrastructure of the gut of Appendicularia sicula and demonstrated the absence of any trace of anus. Appendicularians are small holoplanktonic tunicates,
characterised by very fast ingestion and quick food transfer along their gut. The high production of faecal pellets released in the aqueous environment, associated with a high filtration rate, highlights their important role in
marine ecosystems. Due to the absence of an anus, in contrast with other appendicularians, A. sicula, one of the
smallest species, accumulates undigested faecal material within its body, with consequent extreme enlargement of
its rectum. The gut, the epithelium of which is generally extremely reduced, is formed of an oesophagus, a globular
stomach, thin proximal and mid-intestine, and a huge rectum. The latter, when filled with faecal material, may
occupy most of the volume of the trunk in fully grown specimens. Although profoundly altered, the gut of these
animals does show several similarities to that of Fritillaria (a genus of the same family, Fritillariidae), with which it has in common many features such as specialised mitochondrial pump cells. In A. sicula, the structural simplifications of organs seem to reach their extreme condition in comparison to other appendicularians
IL TUBO DIGERENTE DI OIKOPLEURA DIOICA FOL 1872 (APPENDICULARIA): CARATTERIZZAZIONE ISTOCHIMICA E ISTOENZIMATICA
No full textLa struttura e la citologia del tubo digerente di Oikopleura dioica sono state in precedenza ricostruite su sezioni seriate studiate al MO e al ME. E' ora di interesse portare ulteriori contributi alla conoscenza delle funzoni dei vari tratti in considerazione che questi animali possiedono un particolare sistema di cattura del cibo e manifestano nemerose specializzazioni. Abbiamo studiato esemplari provenienti dall'allevamento della Stazione di Villefranche-sur-Mer fissati con varie miscele aldeidiche e trattati con tecniche istochimiche, istoenzimatiche e immunoistochimiche messe a punto sia per la MO che per la ME. I dati rivelano una distribuzione precisa delle attività enzimatiche e delle sostanze di accumulo, interpretabile alla luce di una compensazione fra alta efficienza di cattura dl cibo, rapido trasporto lungo il tubo digerente e il basso rendimento di assimilazione rivelato dall'emissione di pellet non completamente digeriti. Processi di assorbimento (fosfatasi alcalina), trasporto attivo (ATPasi) ed escrezione di cataboliti azotati (aminoacidoossidasi) avvengono in tutto il tubo digerente a carico delle cellule cigliate a microvilli e delle cellule a globi. Queste ultime, presenti nel lobo gastrico sinistro e nel retto, sono anche coinvolte in processi di endocitosi di proteine (perossidasi esogena) e di digestione extracellulare (amilasi, aminopeptidasi, fosfatasi acida, nucleotidasi, esterasi). La digestione extracellulare è a carico delle grandi cellule della banda gatrica che contengono granuli di secrezione positivi a vari enzimi idrolitici, la cui attività si ritrova nel pellet. La formazione del pellet fecale ha luogo nell'intestino verticale povero di attività enzimatiche. L'accumulo di lipidi avviene principalmente nel lobo gastrico destro e nell'intestino verticale, quello di materiale proteico nelle cellule a granuli del retto
Seminario sui servizi urbani e territoriali
No full textUniversità degli Studi di Genova, Facoltà di Architettura (In particolare G.Sergi ha redatto "La crisi degli strumenti urbanistici tradizionali" pp.1-4, "La riorganizzazione dei servizi su di una base comprensoriale e/o distrettuale" pp.5-14, "Criteri per la definizione di ambiti territoriali per la localizzazione dei servizi" pp.77-87
THE ALIMENTARY TRACT OF KOWALEVSKIIDAE (APPENDICULARIA, TUNICATA) AND EVOLUTIONARY IMPLICATIONS
No full textThe alimentary tract of Kowalevskia tenuis and K. oceanica, the only species of the appendicularian family Kowalevskiidae, was studied both at the light and electron microscope levels and compared with species belonging to the other two families of the class. Kowalevskids show interesting specializations: 1) the pharynx opens on both sides through two opposing spiracles, modified into long ciliated fissures, and possesses an original filtering system of ciliated combs arranged in two pairs of opposing longitudinal rows; 2) the endostyle is absent, its place being taken by a ciliated groove without any glandular cell; 3) posterior to the esophagus, the globular stomach and rectum form a digestive nucleus comprising a few, large cells including two well-developed, specialized valves, cardiac and pyloric; 4) special apical junctions bearing characteristics of both gap and adherens junctions are diffuse along the gut epithelium; 5) the heart is absent. Our data suggest that Kowalevskiidae underwent a high degree of specialization for food filtering and are more closely related to Fritillariidae, with which they share several characters, rather than Oikopleuridae, the latter probably representing the most primitive family of appendicularians
Multifarious activities of gut epithelium in an appendicularian (Oikopleura dioica : Tunicata)
No full textThe functions of the various gut regions of Oikopleura dioica (oesophagus, left and right gastric lobes, vertical intestine, mid-intestine and rectum) were investigated by means of histochemical, histoenzymatic and immunohistochemical techniques at light and electron microscopes. Ciliary food progression is evidenced by the presence of ATPases on cilia, along the entire gut, with the exception of the cardiac valve, a passive device controlling food direction. Absorptive processes (alkaline phosphatase), active transport (ATPases) and nitrogen excretion (D-amino acid oxidase) occur along the entire gut, in both ciliated microvillar and globular cells. The latter, typical of the left gastric lobe and rectum, are also involved in endocytotic processes (exogenous peroxidase as tracer) and intracellular digestion (alpha-amylase, aminopeptidase M, acid phosphatase, 5'-nucleotidase, non-specific esterase). The giant cells of the gastric band participate in extracellular digestion; they contain secretory granules positive to various hydrolytic enzymes, the activity of which is also recognisable in faecal pellets inside the intestinal lumen. Lipid storage occurs mainly in the right gastric lobe and vertical intestine, whereas protein storage takes place in the rectal granular cells. Epithelial transport and possible osmoregulation occur along the entire gut, especially at the level of diffuse baso-lateral interdigitations, which increase the plasmalemma surface enormously, are often associated with mitochondria and possess numerous ATPase pumps. Data extend previous histological observations and hypotheses on the physiological role of the various gut regions. The remarkable and specific location of enzymatic activities and nutrient storage are in agreement with the high capacity of O. dioica to process a great quantity of food very rapidly and efficiently
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