Abstract kinetic equations with positive collision operators

We consider "forward-backward" parabolic equations in the abstract form $Jd \psi / d x + L \psi = 0$, $0< x < \tau \leq \infty$, where $J$ and $L$ are operators in a Hilbert space $H$ such that $J=J^*=J^{-1}$, $L=L^* \geq 0$, and $\ker L = 0$. The following theorem is proved: if the operator $B=JL$ is similar to a self-adjoint operator, then associated half-range boundary problems have unique solutions. We apply this theorem to corresponding nonhomogeneous equations, to the time-independent Fokker-Plank equation $\mu \frac {\partial \psi}{\partial x} (x,\mu) = b(\mu) \frac {\partial^2 \psi}{\partial \mu^2} (x, \mu)$, $0<x<\tau$, $\mu \in \R$, as well as to other parabolic equations of the "forward-backward" type. The abstract kinetic equation $T d \psi/dx = - A \psi (x) + f(x)$, where $T=T^*$ is injective and $A$ satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in the introductio

Nuovi approcci per la riabilitazione dell&#8217;arto superiore paretico dopo ictus cerebri

Il deficit funzionale dell\u2019arto superiore \ue8 una tra le pi\uf9 invalidanti sequele dello stroke. Esso gioca, infatti, un ruolo fondamentale nelle attivit\ue0 della vita quotidiana (ADL) e nella vita sociale e lavorativa. Per fronteggiare questa problematica, negli ultimi anni sono state introdotte nuove metodiche riabilitative. Questa revisione si propone di fornire una sintesi dei nuovi approcci riabilitativi, sulla base di un\u2019analisi della letteratura, con riferimento alle evidenze e alle prove di efficacia, distinguendo i risultati nelle diverse fasi del percorso riabilitativo (acuta, subacuta, cronica). \uc8 stata condotta una ricerca bibliografica, estesa al periodo gennaio 2013-luglio 2018. Sono stati selezionati 124 studi relativi a Trial Clinici, che avessero come oggetto pazienti adulti (&gt; 18 anni) affetti da ictus cerebri, riabilitati con le seguenti metodiche: Action Observation Training (AOT), Bilateral Transfer (BT), Bio-feedback (BF), Constraint Induced Motor Therapy (CIMT), Mirror Therapy (MT), Realt\ue0 Virtuale (VR), Robot Assistance (RA), Stimolazione Elettrica Funzionale e Neuromuscolare (FES e NMES) e Stimolazione Transcranica con Correnti Dirette (tDCS). La revisione ha evidenziato che la letteratura non \ue8 esaustiva, n\ue9 omogenea circa le metodiche analizzate. I dati pi\uf9 rilevanti sono quelli relativi alla CIMT in fase cronica e alla MT in fase subacuta. Altri dati interessanti sono stati evidenziati per la MT in fase cronica e per la FES e NMES in fase cronica. I risultati meno significativi invece sono stati riscontrati con l\u2019utilizzo della VR in fase subacuta, della RA in fase cronica e della tDCS in fase subacuta

Distonia flessoria dell&#8217;arto superiore post-stroke evoluta in distonia estensoria, dopo inoculo di tossina botulinica

Introduzione - Descrizione di un caso clinico riguardante la comparsa di un atteggiamento posturale distonico estensorio di mano e polso dell\u2019arto superiore in una paziente emiplegica trattata con tossina botulinica per il controllo dell\u2019ipertono spastico flessorio dell\u2019arto. Presentazione del caso - Una donna caucasica di 59 anni affetta da emiplegia spastica sinistra \ue8 stata ricoverata presso l\u2019U.O. di Riabilitazione Specialistica dell\u2019Ospedale San Carlo di Milano. Il disturbo motorio era insorto xxx giorni prima in seguito a una vasta emorragia cerebrale intraparenchimale fronto-parietale destra. La paziente era stata sottoposta a craniotomia decompressiva e successiva cranioplastica. All\u2019ingresso la paziente si presentava con ridotta vigilanza, neglect ed emiplegia spastica sinistra. Successivamente il quadro neuromotorio migliorava progressivamente con la comparsa di iniziale motilit\ue0 artuale sinistra e miglioramento del quadro cognitivo e del neglect. L\u2019arto superiore sinistro presentava un marcato ipertono spastico associato a dolore e impotenza funzionale (atteggiamento in schema flessorio con mano chiusa a pugno, gomito flesso e spalla addotta). Circa tre mesi dopo era effettuato un trattamento ecoguidato della spasticit\ue0 focale con tossina botulinica A (muscolo pronatore rotondo, flessore superficiale e profondo delle dita, flessori radiale e ulnare del carpo, bicipite brachiale), ottenendo un miglioramento clinico e funzionale. Rivalutata dopo cinque mesi, la paziente presentava un buon controllo dell\u2019ipertono flessorio con presenza di motilit\ue0 attiva antigravitaria ai vari fulcri dell\u2019arto superiore. Si evidenziava, per\uf2, la comparsa di una distonia focale a livello della muscolatura estensoria del polso e della mano sinistri che rimanevano atteggiati in supinazione ed estensione con conseguente compromissione delle attivit\ue0 funzionali potenzialmente possibili. Era pertanto effettuato un altro trattamento ecoguidato focale con tossina botulinica A (Dysport, fl 500 UI) nei muscoli estensore radiale lungo carpo (150 UI), estensore radiale breve del carpo (150 UI), estensore comune delle dita (100 UI) ed estensore ulnare del carpo (100 UI). Era poi effettuato un trattamento fisioterapico mirato con stretching muscolare e rieducazione neuromotoria e propriocettiva, associato a ciclo di terapia occupazionale per il recupero delle attivit\ue0 funzionali. La paziente era valutata clinicamente e con test funzionali, prima e dopo il trattamento. Conclusioni - Il caso descrive una paziente che, in seguito a un\u2019emorragia cerebrale, ha sviluppato un\u2019emiplegia con spasticit\ue0 flessoria dell\u2019arto superiore sinistro. Dopo il trattamento con tossina botulina dei muscoli flessori, si era evidenziata una riduzione della spasticit\ue0 flessoria, contestualmente associata alla comparsa di una spasticit\ue0 estensoria, in un contesto di lento e progressivo recupero della motilit\ue0 attiva. Il trattamento con tossina botulinica ha permesso il controllo degli aspetti posturali distonici e un recupero funzionale significativo dell\u2019arto superiore plegico nella paziente esaminata, dimostrandosi efficace nel migliorare la funzionalit\ue0 dell\u2019arto superiore in caso di distonia focale posturale post-emorragia cerebrale. Attualmente sono in corso controlli clinici seriati al fine di valutare la persistenza dell\u2019efficacia del trattamento. Bibliografia - 1. Muhammad Umar, Tahir Masood, Mazhar Badshah. Post-Stroke Focal Hand Dystonia; Botulinum Toxin And Task Specific Training. The Professional Medical Journal (www.theprofesional.com) - 2. Nakamura Y. Botulinum toxin for treatment of the focal dystonia. 2017 Jul 29;57(7):367-72. doi: 10.5692/clinicalneurol.cn-001018. Epub 2017 Jul 24

Multi-wavelength observations of blazar AO 0235+164 in the 2008-2009 flaring state

The blazar AO 0235+164 (z = 0.94) has been one of the most active objects observed by Fermi Large Area Telescope (LAT) since its launch in Summer 2008. In addition to the continuous coverage by Fermi, contemporaneous observations were carried out from the radio to γ-ray bands between 2008 September and 2009 February. In this paper, we summarize the rich multi-wavelength data collected during the campaign (including F-GAMMA, GASP-WEBT, Kanata, OVRO, RXTE, SMARTS, Swift, and other instruments), examine the cross-correlation between the light curves measured in the different energy bands, and interpret the resulting spectral energy distributions in the context of well-known blazar emission models. We find that the γ-ray activity is well correlated with a series of near-IR/optical flares, accompanied by an increase in the optical polarization degree. On the other hand, the X-ray light curve shows a distinct 20 day high state of unusually soft spectrum, which does not match the extrapolation of the optical/UV synchrotron spectrum. We tentatively interpret this feature as the bulk Compton emission by cold electrons contained in the jet, which requires an accretion disk corona with an effective covering factor of 19% at a distance of 100 R g. We model the broadband spectra with a leptonic model with external radiation dominated by the infrared emission from the dusty torus. © 2012. The American Astronomical Society. All rights reserved

The spectral energy distribution of fermi bright blazars

We have conducted a detailed investigation of the broadband spectral properties of the γ-ray selected blazars of the Fermi LAT Bright AGN Sample (LBAS). By combining our accurately estimated Fermi γ-ray spectra with Swift, radio, infra-red, optical, and other hard X-ray/γ-ray data, collected within 3 months of the LBAS data taking period, we were able to assemble high-quality and quasi-simultaneous spectral energy distributions (SED) for 48 LBAS blazars. The SED of these γ-ray sources is similar to that of blazars discovered at other wavelengths, clearly showing, in the usual log ν-log ν Fν representation, the typical broadband spectral signatures normally attributed to a combination of low-energy synchrotron radiation followed by inverse Compton emission of one or more components. We have used these SED to characterize the peak intensity of both the low- and the high-energy components. The results have been used to derive empirical relationships that estimate the position of the two peaks from the broadband colors (i.e., the radio to optical, αro, and optical to X-ray, αox, spectral slopes) and from the γ-ray spectral index. Our data show that the synchrotron peak frequency (νSpeak) is positioned between 1012.5 and 1014.5 Hz in broad-lined flat spectrum radio quasars (FSRQs) and between 10 13 and 1017 Hz in featureless BL Lacertae objects. We find that the γ-ray spectral slope is strongly correlated with the synchrotron peak energy and with the X-ray spectral index, as expected at first order in synchrotron-inverse Compton scenarios. However, simple homogeneous, one-zone, synchrotron self-Compton (SSC) models cannot explain most of our SED, especially in the case of FSRQs and low energy peaked (LBL) BL Lacs. More complex models involving external Compton radiation or multiple SSC components are required to reproduce the overall SED and the observed spectral variability. While more than 50% of known radio bright high energy peaked (HBL) BL Lacs are detected in the LBAS sample, only less than 13% of known bright FSRQs and LBL BL Lacs are included. This suggests that the latter sources, as a class, may be much fainter γ-ray emitters than LBAS blazars, and could in fact radiate close to the expectations of simple SSC models. We categorized all our sources according to a new physical classification scheme based on the generally accepted paradigm for Active Galactic Nuclei and on the results of this SED study. Since the LAT detector is more sensitive to flat spectrum γ-ray sources, the correlation between νSpeak and γ-ray spectral index strongly favors the detection of high energy peaked blazars, thus explaining the Fermi overabundance of this type of sources compared to radio and EGRET samples. This selection effect is similar to that experienced in the soft X-ray band where HBL BL Lacs are the dominant type of blazars. © 2010 The American Astronomical Society

Insights into the high-energy γ-ray emission of Markarian 501 from extensive multifrequency observations in the Fermi era

We report on the γ-ray activity of the blazar Mrk 501 during the first 480 days of Fermi operation. We find that the average Large Area Telescope (LAT) γ-ray spectrum of Mrk 501 can be well described by a single power-law function with a photon index of 1.78 ± 0.03. While we observe relatively mild flux variations with the Fermi-LAT (within less than a factor of two), we detect remarkable spectral variability where the hardest observed spectral index within the LAT energy range is 1.52 ± 0.14, and the softest one is 2.51 ± 0.20. These unexpected spectral changes do not correlate with the measured flux variations above 0.3 GeV. In this paper, we also present the first results from the 4.5 month long multifrequency campaign (2009 March 15-August 1) on Mrk 501, which included the Very Long Baseline Array (VLBA), Swift, RXTE, MAGIC, and VERITAS, the F-GAMMA, GASP-WEBT, and other collaborations and instruments which provided excellent temporal and energy coverage of the source throughout the entire campaign. The extensive radio to TeV data set from this campaign provides us with the most detailed spectral energy distribution yet collected for this source during its relatively low activity. The average spectral energy distribution of Mrk 501 is well described by the standard one-zone synchrotron self-Compton (SSC) model. In the framework of this model, we find that the dominant emission region is characterized by a size ≲0.1 pc (comparable within a factor of few to the size of the partially resolved VLBA core at 15-43 GHz), and that the total jet power (≃1044 erg s-1) constitutes only a small fraction (∼10-3) of the Eddington luminosity. The energy distribution of the freshly accelerated radiating electrons required to fit the time-averaged data has a broken power-law form in the energy range 0.3 GeV-10 TeV, with spectral indices 2.2 and 2.7 below and above the break energy of 20 GeV. We argue that such a form is consistent with a scenario in which the bulk of the energy dissipation within the dominant emission zone of Mrk 501 is due to relativistic, proton-mediated shocks. We find that the ultrarelativistic electrons and mildly relativistic protons within the blazar zone, if comparable in number, are in approximate energy equipartition, with their energy dominating the jet magnetic field energy by about two orders of magnitude. © 2011. The American Astronomical Society

Variational linear problems in wave- obstacle interaction.

We discuss the problem of the steady two-dimensional flow past fixed disturbances in an open channel of finite depth. We consider different types of obstacles: submerged or surface-piercing bodies and localized perturbations of a horizontal bottom. By a special variational approach, we prove the unique solvability of the linearized problem for supercritical velocities of the unperturbed flow. We also discuss extensions of the variational method to the limit case of a submerged beam and to subcritical velocities

On the Neumann-Kelvin Problem in Bounded Domains

AbstractA theorem on unique solvability for an elliptic problem in a polygonal domain with a second-order boundary condition on part of the boundary is proved. The relation with a well-posed formulation of the plane Neumann-Kelvin problem is discussed