Green functions and nonlinear systems: Short time expansion

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with numerical results. The relevance of these results relies on the possibility of fully exploiting a gradient expansion in both classical and quantum field theory granting the existence of a strong coupling expansion. Having a Green function in this regime in quantum field theory amounts to obtain the corresponding spectrum of the theory.Comment: 7 pages, 3 figures. Version accepted for publication in International Journal of Modern Physics

De-marginalising and de-centring film studies in bodies, places and on screens

This paper presents a multimodal conversation that engages the personal teaching and learning experiences of the authors, Berenike Jung (in London when the conversation started) and Derilene Marco (in Johannesburg). Critically reflecting and engaging through an audio recording and letters, Jung and Marco ask each other about the processes of doing and performing the labour of decolonising film teaching in their respective courses and from different global locations. Keeping in mind the impositions and complexities of the pandemic, Jung and Marco also reflect upon the ways in which colonial posturing occurs in film studies spaces, such as highly visible international film conferences. In doing so, they reflect on how engagements such as these keep many scholars and their scholarship confined to traditional Eurocentric and North American strategies, methods and endorsements of approval and relevance. The piece is conversational and self-aware in its self-referential tone. It is intended that readers listen to parts of the audio if they please, but that they are not compelled to do so to find meaning

Extension of formal conjugations between diffeomorphisms

We study the formal conjugacy properties of germs of complex analytic diffeomorphisms defined in the neighborhood of the origin of ${\mathbb C}^{n}$. More precisely, we are interested on the nature of formal conjugations along the fixed points set. We prove that there are formally conjugated local diffeomorphisms $\phi, \eta$ such that every formal conjugation $\hat{\sigma}$ (i.e. $\eta \circ \hat{\sigma} = \hat{\sigma} \circ \phi$) does not extend to the fixed points set $Fix (\phi)$ of $\phi$, meaning that it is not transversally formal (or semi-convergent) along $Fix (\phi)$. We focus on unfoldings of 1-dimensional tangent to the identity diffeomorphisms. We identify the geometrical configurations preventing formal conjugations to extend to the fixed points set: roughly speaking, either the unperturbed fiber is singular or generic fibers contain multiple fixed points.Comment: 34 page

Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

Clifford algebras and new singular Riemannian foliations in spheres

Using representations of Clifford algebras we construct indecomposable singular Riemannian foliations on round spheres, most of which are non-homogeneous. This generalizes the construction of non-homogeneous isoparametric hypersurfaces due to by Ferus, Karcher and Munzner.Comment: 21 pages. Construction of foliations in the Cayley plane added. Proofs simplified and presentation improved, according to referee's suggestions. To appear in Geom. Funct. Ana

The first frost in the Pipe Nebula

Spectroscopic studies of ices in nearby star-forming regions indicate that ice mantles form on dust grains in two distinct steps, starting with polar ice formation (H2O rich) and switching to apolar ice (CO rich). We test how well the picture applies to more diffuse and quiescent clouds where the formation of the first layers of ice mantles can be witnessed. Medium-resolution near-infrared spectra are obtained toward background field stars behind the Pipe Nebula. The water ice absorption is positively detected at 3.0 micron in seven lines of sight out of 21 sources for which observed spectra are successfully reduced. The peak optical depth of the water ice is significantly lower than those in Taurus with the same visual extinction. The source with the highest water-ice optical depth shows CO ice absorption at 4.7 micron as well. The fractional abundance of CO ice with respect to water ice is 16+7-6 %, and about half as much as the values typically seen in low-mass star-forming regions. A small fractional abundance of CO ice is consistent with some of the existing simulations. Observations of CO2 ice in the early diffuse phase of a cloud play a decisive role in understanding the switching mechanism between polar and apolar ice formation.Comment: 17 pages, 8 figures, accepted by A&

Structure-Guided Recombination Creates an Artificial Family of Cytochromes P450

Creating artificial protein families affords new opportunities to explore the determinants of structure and biological function free from many of the constraints of natural selection. We have created an artificial family comprising ~3,000 P450 heme proteins that correctly fold and incorporate a heme cofactor by recombining three cytochromes P450 at seven crossover locations chosen to minimize structural disruption. Members of this protein family differ from any known sequence at an average of 72 and by as many as 109 amino acids. Most (>73%) of the properly folded chimeric P450 heme proteins are catalytically active peroxygenases; some are more thermostable than the parent proteins. A multiple sequence alignment of 955 chimeras, including both folded and not, is a valuable resource for sequence-structure-function studies. Logistic regression analysis of the multiple sequence alignment identifies key structural contributions to cytochrome P450 heme incorporation and peroxygenase activity and suggests possible structural differences between parents CYP102A1 and CYP102A2

HST emission-line images of nearby 3CR radio galaxies: two photoionization, accretion and feedback modes

We present HST/ACS narrow-band images of a low-z sample of 19 3C radio galaxies to study the H$\alpha$ and [OIII] emissions from the narrow-line region (NLR). Based on nuclear emission line ratios, we divide the sample into High and Low Excitation Galaxies (HEGs and LEGs). We observe different line morphologies, extended line emission on kpc scale, large [OIII]/H$\alpha$ scatter across the galaxies, and a radio-line alignment. In general, HEGs show more prominent emission line properties than LEGs: larger, more disturbed, more luminous, and more massive regions of ionized gas with slightly larger covering factors. We find evidence of correlations between line luminosities and (radio and X-ray) nuclear luminosities. All these results point to a main common origin, the active nucleus, which ionize the surrounding gas. However, the contribution of additional photoionization mechanism (jet shocks and star formation) are needed to account for the different line properties of the two classes. A relationship between the accretion, photoionization and feedback modes emerges from this study. For LEGs (hot-gas accretors), the synchrotron emission from the jet represents the main source of ionizing photons. The lack of cold gas and star formation in their hosts accounts for the moderate ionized-gas masses and sizes. For HEGs (cold-gas accretors), an ionizing continuum from a standard disk and shocks from the powerful jets are the main sources of photoionization, with the contribution from star formation. These components, combined with the large reservoir of cold/dust gas brought from a recent merger, account for the properties of their extended emission-line regions.Comment: accepted for publication on ApJ (22 pages, 12 figures