Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models

We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians showing eigenvalues and resonances at the threshold of the continuous spectrum and we analyze the effect of various type of perturbations on the spectral singularities. We provide algorithms to obtain convergent series expansions for the coordinates of the singularities.Comment: 20 page

Spin dependent point potentials in one and three dimensions

We consider a system realized with one spinless quantum particle and an array of $N$ spins 1/2 in dimension one and three. We characterize all the Hamiltonians obtained as point perturbations of an assigned free dynamics in terms of some ``generalized boundary conditions''. For every boundary condition we give the explicit formula for the resolvent of the corresponding Hamiltonian. We discuss the problem of locality and give two examples of spin dependent point potentials that could be of interest as multi-component solvable models.Comment: 15 pages, some misprints corrected, one example added, some references modified or adde

Idiopathic Pulmonary Fibrosis (IPF) incidence and prevalence in Italy

Background: Studies of Idiopathic Pulmonary Fibrosis (IPF) epidemiology show regional variations of incidence and prevalence; no epidemiological studies have been carried out in Italy. Objective: To determine incidence and prevalence rates of IPF in the population of a large Italian region.Methods: in this cross-sectional study study data were collected on all patients of 18 years of age and older admitted as primary or secondary idiopathic fibrosing alveolitis (ICD9-CM 516.3) to Lazio hospitals, from 1/1/2005 to 31/12/2009, using regional hospital discharge, population and cause of death databases. Reporting accuracy was assessed on a random sample of hospital charts carrying the ICD9-CM 516.3, 516.8, 516.9 and 515 codes, by reviewing radiology and pathology findings to define cases as IPF “confident”, “possible” or “inconsistent”. Results: Annual prevalence and incidence of IPF were estimated at 25.6 per 100,000 and 7.5 per 100,000 using the ICD9-CM code 516.3 without chart audit while they were estimated at 31.6 per 100,000 and at 9,3 per 100,000 for the IPF “confident” definition after hospital chart audit. Conclusion: The data provide a first estimate of IPF incidence in Italy and indicate that incidence and prevalence in southern European regions may be similar to those observed in northern Europe and North America. (Sarcoidosis Vasc Diffuse Lung Dis 2014; 31: 191-197

A Quantum Model of Feshbach Resonances

We consider a quantum model of two-channel scattering to describe the mechanism of a Feshbach resonance. We perform a rigorous analysis in order to count and localize the energy resonances in the perturbative regime, i.e., for small inter-channel coupling, and in the non-perturbative one. We provide an expansion of the effective scattering length near the resonances, via a detailed study of an effective Lippmann-Schwinger equation with energy-dependent potential.Comment: 29 pages, pdfLaTe

Organocatalysis and beyond: Activating reactions with two catalytic species

Since the beginning of the millennium, organocatalysis has been gaining a predominant role in asymmetric synthesis and it is, nowadays, a foundation of catalysis. Synergistic catalysis, combining two or more different catalytic cycles acting in concert, exploits the vast knowledge acquired in organocatalysis and other fields to perform reactions that would be otherwise impossible. Merging organocatalysis with photo-, metallo- and organocatalysis itself, researchers have ingeniously devised a range of activations. This feature review, focusing on selected synergistic catalytic approaches, aims to provide a flavor of the creativity and innovation in the area, showing ground-breaking examples of organocatalysts, such as proline derivatives, hydrogen bond-mediated, Cinchona alkaloids or phosphoric acids catalysts, which work cooperatively with different catalytic partners

Turning renewable feedstocks into a valuable and efficient chiral phosphate salt catalyst

Solketal, the chiral acetonide of glycerol, has been employed as the starting material in the design of a novel punctually chiral phosphate sodium salt for catalytic applications in organic and asymmetric synthesis. The racemate and the two enantiomers of the substrate are economic and commercially available, straightforwardly prepared in high yields from naturally occurring feedstocks. Therefore, remarkably, both enantiomers of the final catalyst can be synthesized by simple procedures in high yield and in compliance with several principles of green chemistry. To further demonstrate the usefulness of the novel catalyst, its application in a solventless protocol for cyanohydrin synthesis from a series of aldehydes has been presented

Asymmetric Organocatalysis-A Powerful Technology Platform for Academia and Industry: Pregabalin as a Case Study

Enantioselective organocatalysis has quickly established itself as the third pillar of asymmetric catalysis. It is a powerful technology platform, and it has a tremendous impact in both academic and industrial settings. By focusing on pregabalin, as a case study, this Perspective aims to show how a process amenable to industry of a simple chiral molecule can be tackled in several different ways using organocatalysis

Is Cooled Radiofrequency Genicular Nerve Block and Ablation a Viable Option for the Treatment of Knee Osteoarthritis?

Background The purpose of this study was to determine demographic and psychosocial factors that influence the effectiveness of cooled radiofrequency genicular nerve ablation (C-RFA) and block in patients with chronic knee pain secondary to osteoarthritis (OA). Methods A retrospective review was completed including patients with knee OA who underwent genicular nerve ablation or block or both. Patient information collected included opioid use, psychological comorbidities, smoking history, body mass index, and medical comorbidities. Success was defined using the Osteoarthritis Research Society International criterion of greater than or equal to 50% reported pain relief from the procedure. Patients without a diagnosis of knee OA and patients with ipsilateral total knee arthroplasty were excluded. Patient factors were compared between (1) those that did or did not respond to the initial block and (2) those that did or did not respond to C-RFA. Results Of the 176 subjects that underwent genicular nerve block, 31.8% failed to respond to the procedure. Subjects that failed the initial block were significantly more likely to have psychological comorbidities, smoking history, and diabetes. Of the subjects that proceeded to genicular nerve ablation, 53.7% reported less than 50% pain relief, and 46.3% reported pain relief greater than or equal to 50% at the first follow-up visit. While the presence of psychological comorbidities, smoking, and diabetes were associated with first-stage block failures, these patient factors were not associated with second-stage ablation failures. Conclusions C-RFA may be an effective adjunct therapy as part of a multimodal pain regimen; however, individual patient characteristics must be considered