Particular Integrability and (Quasi)-exact-solvability

A notion of a particular integrability is introduced when two operators commute on a subspace of the space where they act. Particular integrals for one-dimensional (quasi)-exactly-solvable Schroedinger operators and Calogero-Sutherland Hamiltonians for all roots are found. In the classical case some special trajectories for which the corresponding particular constants of motion appear are indicated.Comment: 13 pages, typos correcte

Experimental phase functions of mm-sized cosmic dust grains

We present experimental phase functions of three types of millimeter-sized dust grains consisting of enstatite, quartz and volcanic material from Mount Etna, respectively. The three grains present similar sizes but different absorbing properties. The measurements are performed at 527 nm covering the scattering angle range from 3 to 170 degrees. The measured phase functions show two well defined regions i) soft forward peaks and ii) a continuous increase with the scattering angle at side- and back-scattering regions. This behavior at side- and back-scattering regions are in agreement with the observed phase functions for the Fomalhaut and HR 4796A dust rings. Further computations and measurements (including polarization) for millimeter sized-grains are needed to draw some conclusions about the fluffy or compact structure of the dust grains

A compactness theorem for scalar-flat metrics on manifolds with boundary

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential Equation

Runaway evaporation for optically dressed atoms

Forced evaporative cooling in a far-off-resonance optical dipole trap is proved to be an efficient method to produce fermionic- or bosonic-degenerated gases. However in most of the experiences, the reduction of the potential height occurs with a diminution of the collision elastic rate. Taking advantage of a long-living excited state, like in two-electron atoms, I propose a new scheme, based on an optical knife, where the forced evaporation can be driven independently of the trap confinement. In this context, the runaway regime might be achieved leading to a substantial improvement of the cooling efficiency. The comparison with the different methods for forced evaporation is discussed in the presence or not of three-body recombination losses

On maximum entropy priors and a most likely likelihood in auditing

There are two basic questions auditors and accountants must consider when developing test and estimation applications using Bayes' Theorem: What prior probability function should be used and what likelihood function should be used. In this paper we propose to use a maximum entropy prior probability function MEP with the most likely likelihood function MLL in the Quasi-Bayesian QB model introduced by McCray (1984). It is defined on an adequate parameter. Thus procedure only needs an expected value of θ0 known (in this paper the expected tainting) to obtain a MEP all an auditor or accountant need to supply are the range, as with any other prior, and the expected tainting, θ0. We will see some practical applications of the methodology proposed about internal control evaluation in auditing

On the existence of initial data containing isolated black holes

We present a general construction of initial data for Einstein's equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays the role of the inner boundary of the Cauchy surface. The black hole is taken to be instantaneously isolated if its outgoing null rays are shear-free. Starting from the choice of a conformal metric and the freely specifiable part of the extrinsic curvature in the bulk, we give a prescription for choosing the shape of the inner boundaries and the boundary conditions that must be imposed there. We show rigorously that with these choices, the resulting non-linear elliptic system always admits solutions.Comment: 11 pages, 2 figures, RevTeX

Real-World Attainment of Low-Density Lipoprotein Cholesterol Goals in Patients at High Risk of Cardiovascular Disease Treated with High-Intensity Statins: The TERESA Study

Despite steady improvements in cardiovascular disease (CVD) prevention, a scarce proportion of patients achieve the recommended LDL-C goals, even under high-intensity lipid-lowering therapy (LLT). Our study aimed to evaluate the attainment rate of LDL-C targets recommended by the 2019 European guidelines, and to characterize potential factors associated with LDL-C goal achievement and change patterns in LLT. We conducted a retrospective, observational study on patients treated with high-intensity atorvastatin or rosuvastatin +/- ezetimibe at cardiology and internal medicine clinics across Spain. It included 1570 evaluable patients (median age: 62 years; established CVD: 77.5% [myocardial infarction: 34.3%]; and 85.8% at very high cardiovascular risk). Rosuvastatin +/- ezetimibe was the LLT in 52.2% of patients, and atorvastatin +/- ezetimibe in 47.8%. LLT had been modified in 36.8% of patients (side effects: 10%), being the most common switch from atorvastatin- to rosuvastatin-based treatment (77.2%). The risk-based LDL-C goal attainment rate was 31.1%, with 78.2% high-risk and 71.7% very high-risk patients not achieving the recommended LDL-C targets. Established CVD and familial hypercholesterolemia were significantly associated with the non-achievement of LDL-C goals. Although having limitations, this study shows that the guideline-recommended LDL-C goal attainment rate is still suboptimal despite using high-intensity statin therapy in a real-world setting in Spain