On the local solvability of a class of degenerate second order operators with complex coefficients

We study the local solvability of a class of operators with multiple characteristics. The class considered here complements and extends the one previously studied in Federico and Parmeggiani (CPDEs 2016, Vol. 41), in that in this paper we consider some cases of operators with complex coefficients that were not present in Federico and Parmeggiani. The class of operators considered here ideally encompasses classes of degenerate parabolic and Schrodinger type operators. We will give local solvability theorems. In general, one has L-2 local solvability, but also cases of local solvability with better Sobolev regularity will be presented

Finite lifetime eigenfunctions of coupled systems of harmonic oscillators

We find a Hermite-type basis for which the eigenvalue problem associated to the operator $H_{A,B}:=B(-\partial_x^2)+Ax^2$ acting on $L^2({\bf R};{\bf C}^2)$ becomes a three-terms recurrence. Here $A$ and $B$ are two constant positive definite matrices with no other restriction. Our main result provides an explicit characterization of the eigenvectors of $H_{A,B}$ that lie in the span of the first four elements of this basis when $AB\not= BA$.Comment: 11 pages, 1 figure. Some typos where corrected in this new versio

Modelling cytoskeletal traffic: an interplay between passive diffusion and active transport

We introduce the totally asymmetric exclusion process with Langmuir kinetics (TASEP-LK) on a network as a microscopic model for active motor protein transport on the cytoskeleton, immersed in the diffusive cytoplasm. We discuss how the interplay between active transport along a network and infinite diffusion in a bulk reservoir leads to a heterogeneous matter distribution on various scales. We find three regimes for steady state transport, corresponding to the scale of the network, of individual segments or local to sites. At low exchange rates strong density heterogeneities develop between different segments in the network. In this regime one has to consider the topological complexity of the whole network to describe transport. In contrast, at moderate exchange rates the transport through the network decouples, and the physics is determined by single segments and the local topology. At last, for very high exchange rates the homogeneous Langmuir process dominates the stationary state. We introduce effective rate diagrams for the network to identify these different regimes. Based on this method we develop an intuitive but generic picture of how the stationary state of excluded volume processes on complex networks can be understood in terms of the single-segment phase diagram.Comment: 5 pages, 7 figure

Global Gevrey hypoellipticity for the twisted Laplacian on forms

We study in this paper the global hypoellipticity property in the Gevrey category for the generalized twisted Laplacian on forms. Different from the 0-form case, where the twisted Laplacian is a scalar operator, this is a system of differential operators when acting on forms, each component operator being elliptic locally and degenerate globally. We obtain here the global hypoellipticity in anisotropic Gevrey space

Kieślowski Re-read: On Reality, Realism and Cinema

By referencing Italian auteurs Ermanno Olmi and Federico Fellini, this paper offers a re-reading of Krzysztof Kieślowski’s reflections on cinema that places the practice of describing reality and uttering “a statement of fact” about people’s lives and the world as a long-lasting, structuring foundation of his episteme and workshop

Between the point of view and the point of being: the space of the stereoscopic tours

One of the most interesting features of the travel stereoviews series is not the three-dimensional effect but rather the intertwined outcome of realism and \u201cbeing-thereness\u201d for the early-20th-century armchair traveler\u2019s experience. On the set of Italy through the Stereoscope, the viewer\u2019s \u201cpath of the gaze\u201d was a novelty compared to with 2D photographs and stereoviews. The Underwood & Underwood publishing company created a stereoscopic multimodal tour to improve the impression of realism with a proprioceptive perception of the scene. The procedure of textual d\ue9brayage, the description of the experience as it is happening here and now, the direction of the viewer\u2019s gaze with a narrative itinerary, the changing of the visual convergence along with the variation of the points of attention: All of these elements fostered a synesthesia for the spectator. The result is immersion in an explorable space between the \u201cpoint of view\u201d (2D images) and the \u201cpoint of being\u201d (virtual reality)

Guardare Venezia: la citt\ue0 come dispositivo visuale

This essay develops a previous paper (Parmeggiani, 2010) with the issues of Venice as a visual apparatus (Foucault, 1980), of the tourists as fl\ue2neurs (Benjamin, 1991), of their sightseeing and dynamic gazing at the urban landscape, and of their searching for the backstage (Goffman, 1959) and looking for icons to achieve cultural capital (Bourdieu, 2011). It analyzes how tourists relate to icons of a globalized visual culture where Venice has produced many other simulacra (Baudrillard, 1994), and it focuses on how social activists have tried to remediate (Bolter & Grusin, 1999) some icons of Venice to protest against the mass tourism and the loss of local identity . The identity of the city, as represented by tourist images, is the result of a long cultural process that has taken place since the Renaissance and continues to exert its effects even today. The author uses visual sociology to analyze both a corpus of mass media images (photographs on websites, postcards, brochures, stock photography) and a visual documentation of the practices of tourists visiting Venice. Following this methodology, the article describes how pictures of the city have become one of the key drivers of mass tourism there, which is considered unsustainable by a portion of the resident community. The first part of this approach (analysis of the images) concerns the urban icons, those that become standard generative models for other visual representations. Some pictures are used to describe the genesis of the icons as well as their reproduction, distribution, and remediation throughout time. The second part of the methodology (analysis with the images) concerns some documentation (photographs and videos) observing the performances of tourists in Venice. Mass tourism is described by its social practices of looking, gazing, photographing, and acquiring images. The focus is on the cycle of the production and consumption of cultural capital and icons through visual practices. The article uses a selection of photographs as an integral part of research. Photographs, postcards, and artwork that have influenced the process of creating Venetian icons help in the investigation of the tourists\u2019 relationships with the urban space and its residents, and they also help to explain the visual identity of the Serenissima in our collective imagination

Subunit Balls for Symbols of Pseudodifferential Operators

AbstractIn this work we shall study a definition of subunit ball for non-negative symbols of sub-elliptic pseudodifferential operators, extending in phase-space the one given by Stein, Nagel, and Wainger in the differential-operator case. Using microlocal methods introduced by Fefferman and Phong, we prove that these balls can be straightened, by means of a canonical transformation, to contain and be contained in boxes of certain sizes, which we give in terms of the size of the symbol. After microlocalizing the symbol, in Section 3 we define classes of subunit symbols and study some of their basic properties. Then we define the subunit ball. In the last section the main structure theorems, in the (n+n)-dimensional elliptic case and in the (1+1)- and (2+2)-dimensional nonelliptic–nondegenerate cases are stated and proved

On Kohn’s sums of squares of complex vector fields

This is a survey of some recent alternative way of proving a subelliptic estimate, first proven by J. J. Kohn, for certain sums of squares of complex vector fields. My approach here makes it possible to extend the result also to more general families of complex vector fields, to perturbations of sums of squares operators by a first-order complex term and furthermore to a pseudodifferential setting