Painlev\'e V and a Pollaczek-Jacobi type orthogonal polynomials

We study a sequence of polynomials orthogonal with respect to a one parameter family of weights w(x):=w(x,t)=\rex^{-t/x}\:x^{\al}(1-x)^{\bt},\quad t\geq 0, defined for $x\in[0,1].$ If $t=0,$ this reduces to a shifted Jacobi weight. Our ladder operator formalism and the associated compatibility conditions give an easy determination of the recurrence coefficients. For $t>0,$ the factor \rex^{-t/x} induces an infinitely strong zero at $x=0.$ With the aid of the compatibility conditions, the recurrence coefficients are expressed in terms of a set of auxiliary quantities that satisfy a system of difference equations. These, when suitably combined with a pair of Toda-like equations derived from the orthogonality principle, show that the auxiliary quantities are a particular Painlev\'e V and/or allied functions. It is also shown that the logarithmic derivative of the Hankel determinant, D_n(t):=\det(\int_{0}^{1} x^{i+j} \:\rex^{-t/x}\:x^{\al}(1-x)^{\bt}dx)_{i,j=0}^{n-1}, satisfies the Jimbo-Miwa-Okamoto $\sigma-$form of the Painlev\'e V and that the same quantity satisfies a second order non-linear difference equation which we believe to be new.Comment: 23 pages, typos corrected, references adde

From northern Italian to Asian wh-in situ : A theory of low focus movement

The mainstream literature on the Romance dialects of northern Italy has explained the morphosyntax of clause-internal wh-elements in answer-seeking interrogatives as either the result of interrogative movement into the lower portion of the high left periphery (Munaro et al. 2001, Poletto & Pollock 2015, a.o.), or as a canonical instance of scope construal (Manzini & Savoia 2005;2011). New empirical evidence from Romance suggests that there is more at stake in the computation of wh-interrogatives than we used to think, and that neither of the existing approaches to northern Italian 'wh-in situ' can be maintained. Here, I argue that northern Italian dialects and Asian languages are, at least in this respect, more similar than we originally thought, and then I offer a new, derivationally economic and cross-linguistically supported understanding of the morphosyntax of northern Italian wh-in situ: the theory of wh-to-foc. Accordingly, all cross-linguistic core properties of this phenomenon can be attributed to different combinations of the setting of universal micro-parameters related to the interrogative movement of wh-elements

RGB interface emulation with Infineon Aurix MCU

openQuesta ricerca studia l’emulazione dell’interfaccia RGB digitale parallela utilizzando il microcontrollore AurixTM TC3xx di Infineon, in particolare la variante TC375. Nonostante le caratteristiche avanzate del microcontrollore, manca un supporto nativo per questa interfaccia. Questo studio cerca di risolvere questa limitazione utilizzando il General Timer Module (GTM) della famiglia Aurixtexttrademark, con particolare attenzione alle applicazioni automotive. Una panoramica di Infineon e del suo dipartimento MC di Padova fornisce le basi e spiega le motivazioni alla base della ricerca. Viene approfondita la conoscenza delle basi tecnologiche, evidenziando l’architettura System on Chip AurixTM TC37x, il GTM e l’interfaccia RGB digitale parallela. Hardware e strumenti chiave come la scheda di sviluppo TC375 Lite Kit di Aurix, l’analizzatore logico Saleae 16 Pro e l’oscilloscopio Tektronix serie 6 sono messi in evidenza per illustrare il loro ruolo centrale nel processo di ricerca. La metodologia di ricerca è dettagliata e comprende considerazioni sulla progettazione del sistema e tecniche di implementazione del firmware. L’obiettivo primario è emulare l’interfaccia RGB a una frequenza di aggiornamento di 100 Hz per immagini in scala di grigi a 8 bit. I risultati confermano la fattibilità dello sforzo di emulazione. I test funzionali verificano la corretta temporizzazione del sistema e l’integrità del segnale. Tuttavia, sono emersi alcuni vincoli, in particolare le limitazioni hardware, come le difficoltà di trasferimento dei dati al GTM a causa del System Peripheral Bus e la mancanza di flessibilità nella selezione del clock dell’interfaccia RGB. Nonostante queste difficoltà, i risultati confermanoil potenziale dell’emulazione con il microcontrollore AurixTM TC375. Lo studio si conclude evidenziando le implicazioni e proponendo strade per la ricerca futura, suggerendo il passaggio alla serie TC39x e l’esplorazione del supporto di immagini RGB a colori. La sintesi di questa ricerca evidenzia la sua rilevanza per l’emulazione avanzata di interfacce basate su microcontrollori, in particolare nel settore automobilistico.This research investigates the emulation of the Digital Parallel RGB Interface using the InfineonAurixTMTC3xx microcontroller, specifically the TC375 variant. Despite the advanced features of the microcontroller, there is an inherent lack of native support for this interface. This study attempts to address this limitation by using the General Timer Module (GTM) inherent to the AurixTMfamily, with a primary focus on automotive applications. An overview of Infineon and its MC department in Padua provides the basis and explains the motivation behind the research. A deeper understanding of the technological basis is established, highlighting the AurixTM TC37x System on Chip Architecture, the GTM and the Digital Parallel RGB Interface. Key hardware and tools such as the AurixTM TC375 Lite Kit Development Board, the Saleae 16 Pro Logic Analyzer, and the Tektronix 6 Series Oscilloscope are highlighted to illustrate their central role in the research process. The research methodology is detailed and includes system design considerations and firmware implementation techniques. The primary objective is to emulate the RGB interface at a refresh rate of 100 Hz for 8-bit grayscale images. The results confirmthe feasibility of the emulation effort. Functional tests verify correct system timing and signal integrity. However, certain constraints are revealed, particularly hardware limitations such as the challenges of transferring data to the GTM due to the System Peripheral Bus and the lack of flexibility in selecting the RGB interface clock. Despite these challenges, the results confirmthe potential of emulation using the AurixTM TC375 microcontroller. The study concludes by highlighting the implications and offering avenues for future research, suggesting transitions to the TC39x series and the exploration of full-color RGB image support. The summary of this research highlights its relevance to advanced microcontrollerbased interface emulation, particularly in the automotive domain