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

Is there a caustic crossing in the lensed quasar Q2237+0305 observational data record?

We re-investigate the gravitationally lensed system Q2237+0305 data record to quantify the probability of having a caustic crossing in the A component. Several works assume that this is the case, but no quantitative analysis is available in the literature. We combine the datasets from the OGLE and GLITP collaborations to accurately trace the prominent event in the lightcurve for the A component of the system. Then the observed event is compared with synthetic light curves derived from trajectories in magnification maps. These maps are generated using a ray-tracing technique. We take more than 10^9 trajectories and test a wide range of different physical properties of the lensing galaxy and the source quasar (lens transverse velocity, microlens mass, source intensity profile and source size). We found that around 75% of our good trajectories (i.e. that are consistent with the observations) are caustic crossings. In addition, a high transverse velocity exceeding 300 km/s, a microlens mass of about 0.1 M_sun and a small standard accretion disk is the best parameter combination. The results justify the interpretation of the OGLE-GLITP event in Q2237+0305A as a caustic crossing. Moreover, the physical properties of the lens and source are in very good agreement with previous works. We also remark that a standard accretion disk is prefered to those simpler approaches, and that the former should be used in subsequent simulations.Comment: 5 pages, 3 figures, 3 tables, to appear in MNRA

Quantum Mechanics on the cylinder

A new approach to deformation quantization on the cylinder considered as phase space is presented. The method is based on the standard Moyal formalism for R^2 adapted to (S^1 x R) by the Weil--Brezin--Zak transformation. The results are compared with other solutions of this problem presented by Kasperkovitz and Peev (Ann. Phys. vol. 230, 21 (1994)0 and by Plebanski and collaborators (Acta Phys. Pol. vol. B 31}, 561 (2000)). The equivalence of these three methods is proved.Comment: 21 pages, LaTe

Total IgA and IgA reactivity to antigen I/II epitopes in HLA-DRB1*04 positive subjects

Bacterial adherence to the acquired dental pellicle, important in dental caries (caries), is mediated by receptor-adhesins such as salivary agglutinin binding to Streptococcus mutans antigen I/II (I/II). Ten selected I/II epitopes were chosen to determine their reactivity to human salivary IgA. Previous studies suggested that a specific HLA biomarker group (HLA-DRB1*04) may have differential influence of immune responses to I/II. However, it was not known whether secretory IgA (SIgA) responses to the selected epitopes from HLA-DRB1*04 positive subjects were different compared to controls, or across other caries-related factors such as total IgA (TIgA). Thirty-two total subjects were matched according to HLA type, gender, ethnicity and age. HLA genotyping, oral bacterial, immunoglobulin and antibody analyses were performed. A large observed difference emerged with regard to the natural immune reservoir of TIgA in HLA-DRB1*04 positive subjects, specifically, a 27.6% reduction compared to controls. In contrast to all other epitopes studied, HLA-DRB1*04 positive subjects also exhibited reduced reactivity to I/II epitope 834–853. HLA-DRB1*04 positive subjects exhibited lower specific SIgA activity/TIgA to 834–853 and also a lower specific reactivity to 834–853/whole cell S. mutans UA159. Furthermore, HLA-DRB1*04 positive subjects exhibited lower responses to I/II in its entirety. The large observed difference in TIgA and the 834–853 reactivity pattern across multiple measures suggest potentially important connections pertaining to the link between HLA-DRB1*04 and caries

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Effects of alirocumab on types of myocardial infarction: insights from the ODYSSEY OUTCOMES trial

AIMS: The third Universal Definition of Myocardial Infarction (MI) Task Force classified MIs into five types: Type 1, spontaneous; Type 2, related to oxygen supply/demand imbalance; Type 3, fatal without ascertainment of cardiac biomarkers; Type 4, related to percutaneous coronary intervention; and Type 5, related to coronary artery bypass surgery. Low-density lipoprotein cholesterol (LDL-C) reduction with statins and proprotein convertase subtilisin-kexin Type 9 (PCSK9) inhibitors reduces risk of MI, but less is known about effects on types of MI. ODYSSEY OUTCOMES compared the PCSK9 inhibitor alirocumab with placebo in 18 924 patients with recent acute coronary syndrome (ACS) and elevated LDL-C (>/=1.8 mmol/L) despite intensive statin therapy. In a pre-specified analysis, we assessed the effects of alirocumab on types of MI. METHODS AND RESULTS: Median follow-up was 2.8 years. Myocardial infarction types were prospectively adjudicated and classified. Of 1860 total MIs, 1223 (65.8%) were adjudicated as Type 1, 386 (20.8%) as Type 2, and 244 (13.1%) as Type 4. Few events were Type 3 (n = 2) or Type 5 (n = 5). Alirocumab reduced first MIs [hazard ratio (HR) 0.85, 95% confidence interval (CI) 0.77-0.95; P = 0.003], with reductions in both Type 1 (HR 0.87, 95% CI 0.77-0.99; P = 0.032) and Type 2 (0.77, 0.61-0.97; P = 0.025), but not Type 4 MI. CONCLUSION: After ACS, alirocumab added to intensive statin therapy favourably impacted on Type 1 and 2 MIs. The data indicate for the first time that a lipid-lowering therapy can attenuate the risk of Type 2 MI. Low-density lipoprotein cholesterol reduction below levels achievable with statins is an effective preventive strategy for both MI types

Distributionally chaotic families of operators on Fréchet spaces

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure and Applied Analysis (CPAA) following peer review. The definitive publisher-authenticated version Conejero, J. A., Kostić, M., Miana, P. J., & Murillo-Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces.Communications on Pure and Applied Analysis, 2016, vol. 15, no 5, p. 1915-1939, is available online at: http://dx.doi.org/10.3934/cpaa.2016022The existence of distributional chaos and distributional irregular vectors has been recently considered in the study of linear dynamics of operators and C-0-semigroups. In this paper we extend some previous results on both notions to sequences of operators, C-0-semigroups, C-regularized semigroups, and alpha-timesintegrated semigroups on Frechet spaces. We also add a study of rescaled distributionally chaotic C-0-semigroups. Some examples are provided to illustrate all these results.The first and fourth authors are supported in part by MEC Project MTM2010-14909, MTM2013-47093-P, and Programa de Investigacion y Desarrollo de la UPV, Ref. SP20120700. The second author is partially supported by grant 174024 of Ministry of Science and Technological Development, Republic of Serbia. The third author has been partially supported by Project MTM2013-42105-P, DGI-FEDER, of the MCYTS; Project E-64, D.G. Aragon, and Project UZCUD2014-CIE-09, Universidad de Zaragoza. The fourth author is supported by a grant of the FPU Program of Ministry of education of Spain.Conejero, JA.; Kostic, M.; Miana Sanz, PJ.; Murillo Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces. Communications on Pure and Applied Analysis. 15(5):1915-1939. https://doi.org/10.3934/cpaa.2016022S1915193915