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

The role of GRK2 in hypertension and regulation of GPR30

In the hypertensive state, the expression of G protein-coupled receptor kinase 2 (GRK2) level is elevated. On the other hand, the expression of GPR30, a recently discovered GPCR is greatly impaired. The current study focuses on investigating the roles of these two proteins in regulating G protein signaling under the normal and hypertensive states. Angiotensin II and vasopressin were used to examine the effects of GRK2 on Gq coupled GPCR signaling. ERK phosphorylation was proportionally enhanced with GRK2 over-expression. On the other hand, using arborization and wrinkle assays, I have shown that GRK2 acts as a negative regulator of Gs signaling in VSMCs. Aortic ring segments were used to examine the vascular reactivity mediated by GPR30. In WKY rats, the GPR30 agonists aldostrone and G1 attenuated phenylephrine mediated vasoconstriction, while the GPR30 antagonist G15 was able to block the effects of aldosterone but not G1. A wound assay was utilized to estimate the effects of GPR30 activation on endothelial cell migration and proliferation. The G1 effect on wound healing was also seen to be GPR30 independent and EC specific. Overall, these investigations suggest that altering GRK2 expression is able to regulate both Gq and Gs signaling in VSMCs. GPR30 plays a crucial role in vascular reactivity and growth regulatory mechanisms. However, GRK2 and GPR30 do not seem to co-localized or interact in the cell