Integrals of groups. II

Funding: The first author was funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020, UIDP/00297/2020 (Center for Mathematics and Applications) and PTDC/MAT/PUR/31174/2017. The first, second and fourth authors gratefully acknowledge the support of the Fundação para a Ciência e a Tecnologia (CEMAT-Ciências FCT projects UIDB/04621/2020 and UIDP/04621/2020); and the fourth author gratefully acknowledge the support of the Universit‘a degli Studi di Milano–Bicocca (FA project ATE-2017-0035 “Strutture Algebriche”).An integral of a group G is a group H whose derived group (commutator subgroup) is isomorphic to G. This paper continues the investigation on integrals of groups started in the work [1]. We study: -- A sufficient condition for a bound on the order of an integral for a finite integrable group (Theorem 2.1) and a necessary condition for a group to be integrable (Theorem 3.2). -- The existence of integrals that are p-groups for abelian p-groups, and of nilpotent integrals for all abelian groups (Theorem 4.1). -- Integrals of (finite or infinite) abelian groups, including nilpotent integrals, groups with finite index in some integral, periodic groups, torsion-free groups and finitely generated groups (Section 5). -- The variety of integrals of groups from a given variety, varieties of integrable groups and classes of groups whose integrals (when they exist) still belong to such a class (Sections 6 and 7). -- Integrals of profinite groups and a characterization for integrability for finitely generated profinite centreless groups (Section 8.1). -- Integrals of Cartesian products, which are then used to construct examples of integrable profinite groups without a profinite integral (Section 8.2). We end the paper with a number of open problems.Peer reviewe

Density functional investigations of defect induced mid-gap states in graphane

We have carried out ab initio electronic structure calculations on graphane (hydrogenated graphene) with single and double vacancy defects. Our analysis of the density of states reveal that such vacancies induce the mid gap states and modify the band gap. The induced states are due to the unpaired electrons on carbon atoms. Interestingly the placement and the number of such states is found to be sensitive to the distance between the vacancies. Furthermore we also found that in most of the cases the vacancies induce a local magnetic moment.Comment: 15 page

Group-IV graphene- and graphane-like nanosheets

We performed a first principles investigation on the structural and electronic properties of group-IV (C, SiC, Si, Ge, and Sn) graphene-like sheets in flat and buckled configurations and the respective hydrogenated or fluorinated graphane-like ones. The analysis on the energetics, associated with the formation of those structures, showed that fluorinated graphane-like sheets are very stable, and should be easily synthesized in laboratory. We also studied the changes on the properties of the graphene-like sheets, as result of hydrogenation or fluorination. The interatomic distances in those graphane-like sheets are consistent with the respective crystalline ones, a property that may facilitate integration of those sheets within three-dimensional nanodevices

Ab initio simulations of the kinetic properties of the hydrogen monomer on graphene

The understanding of the kinetic properties of hydrogen (isotopes) adatoms on graphene is important in many fields. The kinetic properties of hydrogen-isotope (H, D and T) monomers were simulated using a composite method consisting of density functional theory, density functional perturbation theory and harmonic transition state theory. The kinetic changes of the magnetic property and the aromatic $\pi$ bond of the hydrogenated graphene during the desorption and diffusion of the hydrogen monomer was discussed. The vibrational zero-point energy corrections in the activation energies were found to be significant, ranging from 0.072 to 0.205 eV. The results obtained from quantum-mechanically modified harmonic transition state theory were compared with the ones obtained from classical-limit harmonic transition state theory over a wide temperature range. The phonon spectra of hydrogenated graphene were used to closely explain the (reversed) isotope effects in the prefactor, activation energy and jump frequency of the hydrogen monomer. The kinetic properties of the hydrogen-isotope monomers were simulated under conditions of annealing for 10 minutes and of heating at a constant rate (1.0 K/s). The isotope effect was observed; that is, a hydrogen monomer of lower mass is desorbed and diffuses more easily (with lower activation energies). The results presented herein are very similar to other reported experimental observations. This study of the kinetic properties of the hydrogen monomer and many other involved implicit mechanisms provides a better understanding of the interaction between hydrogen and graphene.Comment: Accepted by J. Phys. Chem.

Combined coronary and late-enhanced multidetector-computed tomography for delineation of the etiology of left ventricular dysfunction: comparison with coronary angiography and contrast-enhanced cardiac magnetic resonance imaging

AIMS: To evaluate whether comprehensive evaluation of coronary anatomy and delayed enhancement (DE) by multidetector-computed tomography (MDCT) would allow determination of etiology of left ventricular dysfunction (LVD) as compared with coronary angiography (CA) and DE-magnetic resonance (CMR). METHODS AND RESULTS: Seventy-one consecutive patients (50 males, 59 +/- 16 years) with LVD (ejection fraction: 26 +/- 11%) of unknown etiology underwent MDCT, LGE (late Gd-DTPA-enhanced)-CMR and CA. Patients were classified into four groups according to coronary artery disease (CAD) by CA and LGE-CMR patterns. Patients (n = 24) with CAD and transmural or sub-endocardial DE by CMR were considered having definite ischaemic LVD (group 1). Patients (n = 36) without CAD by CA and with no/atypical LGE-CMR were considered non-ischaemic LVD (group 2). Further we identified four patients with transmural DE but no CAD (group 3) and seven patients with CAD but no DE (group 4). On per-patient basis, combined coronary and DE-MDCT had excellent agreement (kappa = 0.89; P < 0.001) with CA/LGE-CMR to classify patients into the same four groups. Sensitivity, specificity and accuracy of MDCT were 97, 92 and 94%, respectively for detecting patients with definite (group 1) or likely (groups 3 and 4) ischaemic LVD. CONCLUSION: Combined coronary and DE-MDCT can accurately differentiate ischaemic vs. non-ischaemic etiology of LVD

Image resampling and discretization effect on the estimate of myocardial radiomic features from T1 and T2 mapping in hypertrophic cardiomyopathy

Radiomics is emerging as a promising and useful tool in cardiac magnetic resonance (CMR) imaging applications. Accordingly, the purpose of this study was to investigate, for the first time, the effect of image resampling/discretization and filtering on radiomic features estimation from quantitative CMR T1 and T2 mapping. Specifically, T1 and T2 maps of 26 patients with hypertrophic cardiomyopathy (HCM) were used to estimate 98 radiomic features for 7 different resampling voxel sizes (at fixed bin width), 9 different bin widths (at fixed resampling voxel size), and 7 different spatial filters (at fixed resampling voxel size/bin width). While we found a remarkable dependence of myocardial radiomic features from T1 and T2 mapping on image filters, many radiomic features showed a limited sensitivity to resampling voxel size/bin width, in terms of intraclass correlation coefficient (&gt; 0.75) and coefficient of variation (&lt; 30%). The estimate of most textural radiomic features showed a linear significant (p &lt; 0.05) correlation with resampling voxel size/bin width. Overall, radiomic features from T2 maps have proven to be less sensitive to image preprocessing than those from T1 maps, especially when varying bin width. Our results might corroborate the potential of radiomics from T1/T2 mapping in HCM and hopefully in other myocardial diseases

A new device to seal large coronary aneurysms: a case report

<p>Abstract</p> <p>Introduction</p> <p>Coronary artery aneurysm is an uncommon disease. It is defined as a coronary artery dilatation, exceeding the diameter of the normal adjacent segment or the diameter of the patient's largest coronary vessel by 1.5 to 2 times. Coronary artery aneurysms are typically diagnosed by coronary angiography. The prognosis of coronary artery aneurysm is not well known and the management is challenging.</p> <p>Case presentation</p> <p>A 68-year-old Italian-Caucasian man presented to our hospital with angina. Coronary angiography revealed a large coronary aneurysm of the right coronary artery, which was successfully treated by the percutaneous implantation of an MGuard™stent.</p> <p>Conclusion</p> <p>This case report provides evidence that coronary artery aneurysms, even if very large, can be safely treated by MGuard™stent implantation. We strongly emphasize the high flexibility and good deliverability of this device, which leads to the complete exclusion of the aneurysm mediated by the process of endothelization of its thin mesh sleeves.</p