On Nichols algebras associated to simple racks

This is a report on the present state of the problem of determining the dimension of the Nichols algebra associated to a rack and a cocycle. This is relevant for the classification of finite-dimensional complex pointed Hopf algebras whose group of group-likes is non-abelian. We deal mainly with simple racks. We recall the notion of rack of type D, collect the known lists of simple racks of type D and include preliminary results for the open cases. This notion is important because the Nichols algebra associated to a rack of type D and any cocycle has infinite dimension. For those racks not of type D, the computation of the cohomology groups is needed. We discuss some techniques for this problem and compute explicitly the cohomology groups corresponding to some conjugacy classes in symmetric or alternating groups of low order.Comment: 26 pages, minor change

In Situ Thermal Generation of Silver Nanoparticles in 3D Printed Polymeric Structures

Polymer nanocomposites have always attracted the interest of researchers and industry because of their potential combination of properties from both the nanofillers and the hosting matrix. Gathering nanomaterials and 3D printing could offer clear advantages and numerous new opportunities in several application fields. Embedding nanofillers in a polymeric matrix could improve the final material properties but usually the printing process gets more difficult. Considering this drawback, in this paper we propose a method to obtain polymer nanocomposites by in situ generation of nanoparticles after the printing process. 3D structures were fabricated through a Digital Light Processing (DLP) system by disolving metal salts in the starting liquid formulation. The 3D fabrication is followed by a thermal treatment in order to induce in situ generation of metal nanoparticles (NPs) in the polymer matrix. Comprehensive studies were systematically performed on the thermo-mechanical characteristics, morphology and electrical properties of the 3D printed nanocomposites

On Nichols algebras over PGL(2,q) and PSL(2,q)

We compute necessary conditions on Yetter-Drinfeld modules over the groups \mathbf{PGL}(2,q)=\mathbf{PGL}(2,\FF_q) and \mathbf{PSL}(2,q)=\mathbf{PSL}(2,\FF_q) to generate finite dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with group of group-likes isomorphic to one of these groups. As a by-product of the techniques developed in this work, we prove that there is no non-trivial finite-dimensional pointed Hopf algebra over the Mathieu groups $M_{20}$ and $M_{21}=\mathbf{PSL}(3,4)$.Comment: Minor change

Screening for elderly patients admitted to the emergency department requiring specialized geriatric care

BACKGROUND: There is a need for a brief geriatric assessment (BGA) tool to screen elderly patients admitted to the Emergency Department (ED) for their risk of a long hospital stay. OBJECTIVE: To examine whether a BGA administered to elderly patients admitted to the ED may predict the risk of a long hospital stay in the geriatric acute care unit. METHODS: This study had a prospective cohort study design, enrolling 424 elderly patients (mean age 84.0 +/- 6.5 years, 31.6% male) who were evaluated in the ED using a BGA composed of the following items: age, gender, number of medications taken daily, history of falls during the past 6 months, Mini-Mental State Examination (MMSE) score, and non-use of home-help services (i.e., living alone without using any formal or informal home services or social help). The length of stay (LOS) was calculated in days. Patients were separated into three groups based on LOS: low (<8 days), intermediate (8-13 days), and high (>13 days). RESULTS: The prevalence of male gender was higher among patients with the longest LOS compared to those with intermediate LOS (p = 0.002). There were more patients with a history of falls in the high LOS group compared to the intermediate LOS group (p = 0.001) and the low LOS group (p < 0.001). The classification tree showed that male patients with an MMSE score <20 who fell with age under 85 years formed the end node with the greatest relative risk (RR) of a long hospital stay (RR = 14.3 with p < 0.001). CONCLUSIONS: The combination of a history of falls, male gender, cognitive impairment, and age under 85 years identified elderly ED patients at high risk of a long hospital stay

Association between vitamin D deficiency and long hospital stay in geriatric acute care unit: results from a pilot cohort study

Finding a biomarker of long length-of-stay (LOS) would provide a simple solution to target frail older inpatients at such risk. The aim of this study was to determine whether serum 25-hydroxyvitamin D (25OHD) deficiency, defined as serum concentration <25 nmol/L, was associated with long LOS among inpatients admitted to a geriatric acute care unit. Three hundred and six older inpatients (mean age 84.6 +/- 6.4 years, 61.8 % women) were consecutively included in this longitudinal prospective cohort study. Patients were separated into two groups according to LOS tertiles: highest tertile (>= 14 days; n = 120) versus the other two tertiles combined (<14 days; n = 186). Serum 25OHD deficiency (58.3 vs. 38.7 %, P = 0.001) and the prevalence of male gender (58.3 vs. 28.5 %, P < 0.001) were higher among inpatients with the highest LOS compared with those with lower LOS. Serum 25OHD deficiency [odds ratio (OR) = 2.22, P = 0.001 for unadjusted model; OR = 1.87, P = 0.012 for fully adjusted model) and male gender (OR = 2.87, P < 0.001 for unadjusted model; OR = 2.64, P = 0.001 for full model) were associated with a high LOS. Vitamin D deficiency and male gender were risk factors for a long LOS in this pilot study. Using these risk factors to identify inpatients at risk of long LOS may be helpful in adapting early care plans, and thus improving inpatients\u27 health and shortening LOS

Pointed Hopf algebras over some sporadic simple groups

Any finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group, with the possible exception of the Fischer groups Fi22, the Baby Monster B and the Monster M, is a group algebra.Comment: 4 pages, v4: Minor changes, more groups include