Bounds for the relative n-th nilpotency degree in compact groups

The line of investigation of the present paper goes back to a classical work of W. H. Gustafson of the 1973, in which it is described the probability that two randomly chosen group elements commute. In the same work, he gave some bounds for this kind of probability, providing information on the group structure. We have recently obtained some generalizations of his results for finite groups. Here we improve them in the context of the compact groups.Comment: 9 pages; to appear in Asian-European Journal of Mathematics with several improvement

Preoperative prostate biopsy and multiparametric magnetic resonance imaging: Reliability in detecting prostate cancer

Purpose The aim of the study was to analyse and compare the ability of multiparametric magnetic resonance imaging (mp–MRI) and prostate biopsy (PB) to correctly identify tumor foci in patients undergoing radical prostatectomy (RP) for prostate cancer (PCa). Materials and Methods 157 patients with clinically localised PCa with a PSA <10 ng/mL and a negative DRE diagnosed on the first (12 samples, Group A) or second (18 samples, Group B) PB were enrolled at our institution. All patients underwent mp-MRI with T2-weighted images, diffusion-weighted imaging, dynamic contrast enhanced-MRI prior to RP. A map of comparison describing each positive biopsy sample was created for each patient, with each tumor focus shown on the MRI and each lesion present on the definitive histological examination in order to compare tumor detection and location. The sensitivity of mp-MRI and PB for diagnosis was compared using Student’s t-test. The ability of the two exams to detect the prevalence of Gleason pattern 4 in the identified lesions was compared using a chi-square test. Results Overall sensitivity of PB and mp-MRI to identify tumor lesion was 59.4% and 78.9%, respectively (p<0.0001). PB missed 144/355 lesions, 59 of which (16.6%) were significant. mp-MRI missed 75/355 lesions, 12 of which (3.4%) were significant. No lesions with a GS≥8 were missed. Sensitivity of PB and mp-MRI to detect the prevalence of Gleason pattern 4 was 88.2% and 97.4%, respectively. Conclusions mp-MRI seems to identify more tumor lesions than PB and to provide more information concerning tumor characteristics

Early impairment of endothelial structure and function in young normal-weight women with polycystic ovary syndrome

The aim of this study was to evaluate the presence of early vascular damage in young normal-weight women with polycystic ovary syndrome (PCOS).Thirty young normal-weight women with PCOS, who had no additional metabolic or cardiovascular diseases, and 30 healthy women (controls) matched for age and body mass index were studied. A complete hormonal assay was performed in each subject. Serum insulin and glucose levels were measured at baseline and after the oral glucose tolerance test. Plasma endothelin-1 levels and serum lipid profile were also assessed. The endothelial function was studied by flow-mediated dilation on the brachial artery, and arterial structure was evaluated by intima-media thickness measurement using Doppler ultrasound of both common carotid arteries.A significant (P &lt; 0.05) difference in flow-mediated dilation (14.3 +/- 1.9% vs. 18.1 +/- 2.0% for PCOS patients and controls, respectively) and in intima-media thickness (0.53 +/- 0.09 mm vs. 0.39 +/- 0.08 mm for PCOS patients and controls, respectively) was found between PCOS and control subjects. Serum endothelin-1 levels were also significantly (P &lt; 0.05) higher in PCOS patients compared with controls (1.1 +/- 0.4 pmol/liter vs. 0.5 +/- 0.2 pmol/liter for PCOS patients and controls, respectively).In conclusion, our data show that young, normal-weight, nondyslipidemic, nonhypertensive women with PCOS have an early impairment of endothelial structure and function

Lattice Gas Analogue Of SK Model: A paradigm for the glass transition

We investigate the connection between the well known Sherrington-Kirkpatrick Ising Spin Glass and the corresponding Lattice Gas model by analyzing the relation between their thermodynamical functions. We present results of replica approach in the Replica Symmetric approximation and discuss its stability as a function of temperature and external source. Next we examine the effects of first order Replica Symmetry Breaking at zero temperature. We finally compare SK results with ours and suggest how the latter could be relevant to a description of the structural glass transition.Comment: 33 Pages, LaTeX file; 15 Figures added, some grammatical corrections. To appear in Journal of Physics

On the classification of OADP varieties

The main purpose of this paper is to show that OADP varieties stand at an important crossroad of various main streets in different disciplines like projective geometry, birational geometry and algebra. This is a good reason for studying and classifying them. Main specific results are: (a) the classification of all OADP surfaces (regardless to their smoothness); (b) the classification of a relevant class of normal OADP varieties of any dimension, which includes interesting examples like lagrangian grassmannians. Following [PR], the equivalence of the classification in (b) with the one of quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan algebras are explained.Comment: 13 pages. Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in a special issue of Science in China Series A: Mathematic

Reverse engineering of mandible and prosthetic framework: Effect of titanium implants in conjunction with titanium milled full arch bridge prostheses on the biomechanics of the mandible.

This study aimed at investigating the effects of titanium implants and different configurations of full-arch prostheses on the biomechanics of edentulous mandibles. Reverse engineered, composite, anisotropic, edentulous mandibles made of a poly(methylmethacrylate) core and a glass fibre reinforced outer shell were rapid prototyped and instrumented with strain gauges. Brånemark implants RP platforms in conjunction with titanium Procera one-piece or two-piece bridges were used to simulate oral rehabilitations. A lateral load through the gonion regions was used to test the biomechanical effects of the rehabilitations. In addition, strains due to misfit of the one-piece titanium bridge were compared to those produced by one-piece cast gold bridges. Milled titanium bridges had a better fit than cast gold bridges. The stress distribution in mandibular bone rehabilitated with a one-piece bridge was more perturbed than that observed with a two-piece bridge. In particular the former induced a stress concentration and stress shielding in the molar and symphysis regions, while for the latter design these stresses were strongly reduced. In conclusion, prosthetic frameworks changed the biomechanics of the mandible as a result of both their design and manufacturing technology

From 3D Hierarchical Scaffolds for Tissue Engineering to Advanced Hydrogel-Based and Complex Devices for in situ Cell or Drug Release☆

Abstract In the past few years, researchers have focused on the development of three-dimensional (3D) advanced scaffolds and multifunctional hydrogel-based materials. As reported in literature, 3D polymer-based composite scaffolds for tissue engineering have been manufactured through conventional and advanced manufacturing techniques, and different injectable materials and hydrogel-based systems have been proposed and studied. The aim of the current research was to define an approach in the development of multifunctional tools spanning from 3D hierarchical scaffolds for soft tissue engineering to advanced hydrogel-based devices for in situ cell or drug release. The mechanical/rheological behaviour as well as the structural/functional features of the designed devices were discussed and analyzed