On the regularity of a graph related to conjugacy classes of groups

AbstractGiven a finite group G, denote by Γ(G) the simple undirected graph whose vertices are the (distinct) non-central conjugacy class sizes of G, and for which two vertices of Γ(G) are adjacent if and only if they are not coprime numbers. In this note we prove that Γ(G) is a 2-regular graph if and only if it is a complete graph with three vertices, and Γ(G) is a 3-regular graph if and only if it is a complete graph with four vertices

Li1.4Al0.4Ge0.4Ti1.4(PO4)3 promising NASICON-structured glass-ceramic electrolyte for all-solid-state Li-based batteries: Unravelling the effect of diboron trioxide

Li-ion batteries (LIBs) are the ubiquitous technology to power portable electronics; however, for the next-generation of high-performing electrochemical energy storage systems for electric vehicles and smart grid facilities, breakthroughs are needed, particularly in the development of solid-state electrolytes, which may allow for enhanced energy density while enabling lithium metal anodes, combined with unrivalled safety and operative reliability. In this respect, here we present the successful synthesis of a glass-ceramic Li1.4Al0.4Ge0.4Ti1.4(PO4)3 NASICON-type solid-state electrolyte (SSE) through a melt-casting technique. Being grain boundaries crucial for the total ionic conductivity of SSEs, the effect of the addition of diboron trioxide (B2O3, 0.05 wt.%) to promote their liquefaction and restructuring is investigated, along with the effects on the resulting microstructures and ionic conductivities. By the thorough combination of structural-morphological and electrochemical techniques, we demonstrate that bulk materials show improved performance compared to their powder sintered counterpart, achieving remarkable ion mobility (> 0.1 mS cm–1 at –10 °C) and anodic oxidation stability (> 4.8 V vs Li+/Li). The addition of B2O3 positively affects the grain cohesion and growth, thus reducing the extension of the grain boundaries (and the related grain/grain interface resistance) and, therefore, increasing the overall ion mobility. In addition, B2O3 is seen to contrast the microcracks formation in the LAGTP system under study which, overall, shows very promising prospects as SSE for the next-generation of high-energy density, safe lithium-based batteries

EMOTIONAL FLUCTUATIONS OF BLOOD PRESSURE IN ADOLESCENTS: INFLUENCE OF THE REPETITION OF THE MEASUREMENT

Background. The optimal methodology to measure blood pressure (BP) in children remains controversial. Particularly relevant is the concern that anxiety may trigger a rising in BP during the first measurement, while the second and/or the third reading is lower because the child is more relaxed. However, experimental data concerning the pattern of repeated readings of BP are almost non existent. Therefore we accurately examined, by a repeated measures ANOVA design, the pressor response of a large group of healthy children, during the adolescent growth, to three consecutive BP measurements separated by one minute. Method. From a larger group of 719 well-being children aged 5-15 years examined in our hospital between July 2004 and March 2005, a cohort of 145 age-eligible children (11-14 years) was selected for this study. In each subject, BP readings were carried out in the supine position placing size-appropriate cuffies on the right arm and by making use of an oscillometric monitor, whose reliability is unaffected by the enviromental noise. Anthropometric parameters also were acquired. Data were analysed with a PC based statistic package (SPSS for Windows) testing the within-subjects differences. Results and conclusions. Data from the study are shown in the figure

New findings concerning cardiovascular manifestations emerging from long-term follow-up of 150 patients with the Williams-Beuren-Beuren syndrome.

AIMS: We investigated the prevalence, type, and course of congenital cardiac defects and systemic hypertension in our patients with Williams-Beuren-Beuren syndrome. METHODS AND RESULTS: We reviewed the clinical records of all patients with Williams-Beuren syndrome examined between 1981 and 2006. We identified 150 patients, aged from 7 months to 45 years, with a follow-up from 6 months to 25 years, the mean being 6.4 years. A cardiac anomaly was present in 113 of the 150 patients (75%). Defects were typical in over four-fifths of the group. We found supravalvar aortic stenosis in 73 of 113 patients (64.6%), isolated in 43. Pulmonary stenosis, isolated in 18 cases, was found in 51 of 113 (45.1%), while aortic coarctation and mitral valvar prolapse were each found in 7 (6.2%), 3 of the lesions is isolation. Atypical defects were found in 19 patients, tetralogy of Fallot in 2, atrial septal defects in 4, aortic and mitral valvar insufficiencies in 1 each, bicuspid aortic valves in 2, and ventricular septal defects in 9, 4 of the last being isolated. Systemic hypertension, observed in 33 patients (22%), was poorly controlled in 10. Diagnostic and/or interventional cardiac catheterization was undertaken in 24 patients, with 30 surgical procedures performed in 26 patients. Of the group, 3 patients died. CONCLUSION: Cardiac defects were present in three-quarters of our patients. Pulmonary arterial lesions generally improved, while supravalvar aortic stenosis often progressed. Atypical cardiac malformations, particularly ventricular septal defects, occurred frequently. Systemic hypertension was found in one-fifth, even in the absence of structural cardiac defects. The short-term mortality was low

The development of a Consensus Conference on Pediatric Procedural Sedation in the Emergency Department in Italy: From here where to?

Background: In Italy, as in many European countries, Pediatric Emergency Medicine is not formally recognized as a pediatric subspecialty, hindering nation-wide adoption of standards of care, especially in the field of procedural sedation and analgesia (PSA) in the Emergency Department (ED). For this reason PSA in Italy is mostly neglected or performed very heterogeneously and by different providers, with no reference standard. We aimed to describe the procedures and results of the first multidisciplinary and multi-professional Consensus Conference in Italy on safe and effective pediatric PSA in Italian EDs. Methods: The preparation, organization and conduct of the Consensus Conference, held in Florence in 2017, followed the recommended National methodological standards. Professionals from different specialties across the country were invited to participate. Results: Overall 86 recommendations covering 8 themes (pre-sedation evaluation, pharmacologic agents, monitoring, equipment and discharge checklists, training, non-pharmacologic techniques, the adult ED setting, impact on hospitalizations) were developed, taking into account the Italian training system and healthcare organization characteristics. Conclusion: The results of the first multidisciplinary and multi-professional Consensus Conference in Italy are meant to provide up-to-date national guidance to improve the standard of care of children undergoing painful and stressful procedures in the ED. The recommendations will be periodically updated as new relevant evidence is published