Quasi-Exact Solvability and the direct approach to invariant subspaces

We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line which are not Lie-algebraic. It is also applied to generate potentials with multiple algebraic sectors. We discuss two illustrative examples of these two applications: an interesting generalization of the Lam\'e potential which posses four algebraic sectors, and a quasi-exactly solvable deformation of the Morse potential which is not Lie-algebraic.Comment: 17 pages, 3 figure

Suppression of Tc in the (Y0.9Ca0.1)Ba2Cu4-xFexO8 system

In this paper, the effects produced by the iron substitutions in the (Y0.9Ca0.1)Ba2Cu4-xFexO8 system on the superconducting and structural properties are studied. The Rietveld fit of the crystal structure and Mossbauer spectroscopy results of (Y0.9Ca0.1)Ba2Cu4-xFexO8 samples indicate that, the iron atoms occupy the Cu(1) sites of the (Cu-O)2 double chain in fivefold coordination at low iron concentrations. Besides at high iron concentrations the iron atoms occupy the Cu(1) sites of single Cu-O chainss and Cu(2) sites in the CuO2 planes of the (Y0.9Ca0.1)Ba2Cu4-xFexO8 phase with structural defects. Simultaneouly, as iron concentration increases, a faster decrease of Tc is observed in this material comapred with the YBa2Cu3-xFexO7-y system. According to the charge transfer model proposed for YBa2Cu4O8 under pressure, the decrease in the Cu(1)-O(4) bond length in parallel to the increase in the Cu(2)-O(4) bond length may affect the charge transfer mechanism leading to the suppression of Tc.Comment: submitted to Journal of Physics: Condensed Matter on 12 October 2001, 8 figures, 2 tables, 9 page

High and low Sérsic index bulges in Milky Way- and M31-like galaxies: origin and connection to the bar with TNG50

We study bulge formation in MW/M31-like galaxies in a A-cold dark matter scenario, focusing on the origin of high- and low-Sersic index bulges. For this purpose, we use TNG50, a simulation of the IllustrisTNG project that combines a resolution of similar to 8 x 10(4) M-circle dot in stellar particles with a cosmological volume 52 cMpc in extent. We parametrize bulge surface brightness profiles by the Sersic index and the bulge-to-total (BIT) ratio obtained from two-component photometric decompositions. In our sample of 287 MW/M31-like simulated galaxies, 17.1 per cent of photometric bulges exhibit high-Sersic indices and 82.9 per cent show low-Sersic indices. We study the impact that the environment, mergers and bars have in shaping the surface brightness profiles. We find no correlation between bulge properties and the environment where they reside. Simulated galaxies with higher Sersic indices show, on average, a higher fraction of ex situ stars in their kinematically selected bulges. For this bulge population, the last significant merger (total mass ratio m(sat)/m(host) > 0.1) occurs, on average, at later times. However, a substantial fraction of low-Sersic index bulges also experience a late significant merger. We find that bars play an important role in the development of the different types of photometric bulges. The fraction of simulated galaxies with bars is smaller for the high- than for the low-Sersic index population, reaching differences of 20 per cent at z > 1. Simulated galaxies with high fractions of ex situ stars in the bulge do not develop strong bars. Conversely, simulated galaxies with long-lived strong bars have bulges with ex situ fractions, f(ex situ )< 0.2

p21(Cip1) plays a critical role in the physiological adaptation to fasting through activation of PPARα.

Fasting is a physiological stress that elicits well-known metabolic adaptations, however, little is known about the role of stress-responsive tumor suppressors in fasting. Here, we have examined the expression of several tumor suppressors upon fasting in mice. Interestingly, p21 mRNA is uniquely induced in all the tissues tested, particularly in liver and muscle (>10 fold), and this upregulation is independent of p53. Remarkably, in contrast to wild-type mice, p21-null mice become severely morbid after prolonged fasting. The defective adaptation to fasting of p21-null mice is associated to elevated energy expenditure, accelerated depletion of fat stores, and premature activation of protein catabolism in the muscle. Analysis of the liver transcriptome and cell-based assays revealed that the absence of p21 partially impairs the transcriptional program of PPARα, a key regulator of fasting metabolism. Finally, treatment of p21-null mice with a PPARα agonist substantially protects them from their accelerated loss of fat upon fasting. We conclude that p21 plays a relevant role in fasting adaptation through the positive regulation of PPARα

Hexanucleotide Repeat Expansions in c9FTD/ALS and SCA36 Confer Selective Patterns of Neurodegeneration In Vivo

A G4C2 hexanucleotide repeat expansion in an intron of C9orf72 is the most common cause of frontal temporal dementia and amyotrophic lateral sclerosis (c9FTD/ALS). A remarkably similar intronic TG3C2 repeat expansion is associated with spinocerebellar ataxia 36 (SCA36). Both expansions are widely expressed, form RNA foci, and can undergo repeat-associated non-ATG (RAN) translation to form similar dipeptide repeat proteins (DPRs). Yet, these diseases result in the degeneration of distinct subsets of neurons. We show that the expression of these repeat expansions in mice is sufficient to recapitulate the unique features of each disease, including this selective neuronal vulnerability. Furthermore, only the G4C2 repeat induces the formation of aberrant stress granules and pTDP-43 inclusions. Overall, our results demonstrate that the pathomechanisms responsible for each disease are intrinsic to the individual repeat sequence, highlighting the importance of sequence-specific RNA-mediated toxicity in each disorder