Rearrangement and Convergence in Spaces of Measurable Functions

We prove that the convergence of a sequence of functions in the space of measurable functions, with respect to the topology of convergence in measure, implies the convergence -almost everywhere ( denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space , and also on Orlicz spaces with respect to a finitely additive extended real-valued set function. In the space and in the space , of finite elements of an Orlicz space of a -additive set function, we introduce some parameters which estimate the Hausdorff measure of noncompactness. We obtain some relations involving these parameters when passing from a bounded set of , or , to the set of rearrangements

Compactness in Groups of Group-Valued Mappings

We introduce the concepts of extended equimeasurability and extended uniform quasiboundedness in groups of group-valued mappings endowed with a topology that generalizes the topology of convergence in measure. Quantitative characteristics modeled on these concepts allow us to estimate the Hausdorff measure of noncompactness in such a contest. Our results extend and encompass some generalizations of Frechet-Smulian and Ascoli-Arzela compactness criteria found in the literature

Regular measures of noncompactness and Ascoli-Arzela type compactness criteria in spaces of vector-valued functions

In this paper we estimate the Kuratowski and the Hausdorff measures of noncompactness of bounded subsets of spaces of vector-valued bounded functions and of vector-valued bounded differentiable functions. To this end, we use a quantitative characteristic modeled on a new equicontinuity-type concept and classical quantitative characteristics related to pointwise relative compactness. We obtain new regular measures of noncompactness in the spaces taken into consideration. The established inequalities reduce to precise formulas in some classes of subsets. We derive Ascoli-Arzela type compactness criteria

Macro-micro relationship in nanostructured functional composites

This paper examines the results of the characterization of two functional composites: Poly(methyl methacrylate) (PMMA)-Ce:YAG (yttrium aluminium garnet doped with cerium) and PMMA-cobalt hexacyanoferrate (CoHCF). The composites were prepared as possible emitters in the fields of lighting thermal sensors. The prepared composites were characterized using transmission electron microscopy (TEM), nuclear magnetic resonance (NMR) spectroscopy, thermogravimetric analysis (TGA), differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) analyses to study the correlation between micro and macro characteristics. We found that the molecular interactions of the two different fillers with the matrix were localized in different sites of the polymer chains. Moreover, the composites showed an increased thermal strength and stiffness, in particular the PMMA-Ce:YAG composite

Sicilian byzantine icons through the use of non-invasive imaging techniques and optical spectroscopy: The case of the madonna dell’elemosina

The iconographic heritage is one of the treasures of Byzantine art that have enriched the south of Italy, and Sicily in particular, since the early 16th century. In this work, the investigations of a Sicilian Icon of Greek-Byzantine origin, the Madonna dell’Elemosina, is reported for the first time. The study was carried out using mainly non-invasive imaging techniques (photography in reflectance and grazing visible light, UV fluorescence, infrared reflectography, radiography, and computed tomography) and spectroscopic techniques (X-ray fluorescence and infrared spectroscopy). The identification of the constituent materials provides a decisive contribution to the correct historical and artistic placement of the Icon, a treasure of the Eastern European historical community in Sicily. Some hidden details have also been highlighted. Most importantly, the information obtained enables us to define its conservation state, the presence of foreign materials, and to direct its protection and restoration

Clinical presentations leading to arrhythmogenic left ventricular cardiomyopathy

Objectives To describe a cohort of patients with arrhythmogenic left ventricular cardiomyopathy (ALVC), focusing on the spectrum of the clinical presentations. Methods Patients were retrospectively evaluated between January 2012 and June 2020. Diagnosis was based on (1) ≥3 contiguous segments with subepicardial/midwall late gadolinium enhancement in the left ventricle (LV) at cardiac magnetic resonance plus a likely pathogenic/pathogenic arrhythmogenic cardiomyopathy (AC) associated genetic mutation and/or familial history of AC and/or red flags for ALVC (ie, negative T waves in V4-6/aVL, low voltages in limb leads, right bundle branch block like ventricular tachycardia) or (2) pathology examination of explanted hearts or autoptic cases suffering sudden cardiac death (SCD). Significant right ventricular involvement was an exclusion criterion. Results Fifty-two patients (63% males, age 45 years (31-53)) composed the study cohort. Twenty-one (41%) had normal echocardiogram, 13 (25%) a hypokinetic non-dilated cardiomyopathy (HNDC) and 17 (33%) a dilated cardiomyopathy (DCM). Of 47 tested patients, 29 (62%) were carriers of a pathogenic/likely pathogenic DNA variant. Clinical contexts leading to diagnosis were SCD in 3 (6%), ventricular arrhythmias in 15 (29%), chest pain in 8 (15%), heart failure in 6 (12%) and familial screening in 20 (38%). Thirty patients (57%) had previously received a diagnosis other than ALVC with a diagnostic delay of 6 years (IQR 1-7). Conclusions ALVC is hidden in different clinical scenarios with a phenotypic spectrum ranging from normal LV to HNDC and DCM. Ventricular arrhythmias, chest pain, heart failure and SCD are the main clinical presentations, being familial screening essential for the affected relatives' identification

Electrocardiogram analysis in Anderson-Fabry disease: a valuable tool for progressive phenotypic expression tracking

BackgroundElectrocardiogram (ECG) has proven to be useful for early detection of cardiac involvement in Anderson-Fabry disease (AFD); however, little evidence is available on the association between ECG alterations and the progression of the disease.Aim and MethodsTo perform a cross sectional comparison of ECG abnormalities throughout different left ventricular hypertrophy (LVH) severity subgroups, providing ECG patterns specific of the progressive AFD stages. 189 AFD patients from a multicenter cohort underwent comprehensive ECG analysis, echocardiography, and clinical evaluation.ResultsThe study cohort (39% males, median age 47 years, 68% classical AFD) was divided into 4 groups according to different degree of left ventricular (LV) thickness: group A & LE; 9 mm (n = 52, 28%); group B 10-14 mm (n = 76, 40%); group C 15-19 mm (n = 46, 24%); group D & GE; 20 mm (n = 15, 8%). The most frequent conduction delay was right bundle branch block (RBBB), incomplete in groups B and C (20%,22%) and complete RBBB in group D (54%, p < 0.001); none of the patients had left bundle branch block (LBBB). Left anterior fascicular block, LVH criteria, negative T waves, ST depression were more common in the advanced stages of the disease (p < 0.001). Summarizing our results, we suggested ECG patterns representative of the different AFD stages as assessed by the increases in LV thickness over time (Central Figure). Patients from group A showed mostly a normal ECG (77%) or minor anomalies like LVH criteria (8%) and delta wave/slurred QR onset + borderline PR (8%). Differently, patients from groups B and C exhibited more heterogeneous ECG patterns: LVH (17%; 7% respectively); LVH + LV strain (9%; 17%); incomplete RBBB + repolarization abnormalities (8%; 9%), more frequently associated with LVH criteria in group C than B (8%; 15%). Finally, patients from group D showed very peculiar ECG patterns, represented by complete RBBB + LVH and repolarization abnormalities (40%), sometimes associated with QRS fragmentation (13%).ConclusionsECG is a sensitive tool for early identification and long-term monitoring of cardiac involvement in patients with AFD, providing "instantaneous pictures" along the natural history of AFD. Whether ECG changes may be associated with clinical events remains to be determined

Tc-99m labelled bone scintigraphy in suspected cardiac amyloidosis

Aims: To perform evaluation of widely embraced bone scintigraphy-based non-biopsy diagnostic criteria (NBDC) for ATTR amyloid cardiomyopathy (ATTR-CM) in clinical practice, and to refine serum free light chain (sFLC) ratio cut-offs that reliably exclude monoclonal gammopathy (MG) in chronic kidney disease. Methods and results: A multi-national retrospective study of 3354 patients with suspected or histologically proven cardiac amyloidosis (CA) referred to specialist centres from 2015 to 2021; evaluations included radionuclide bone scintigraphy, serum and urine immunofixation, sFLC assay, eGFR measurement and echocardiography. Seventy-nine percent (1636/2080) of patients with Perugini grade 2 or 3 radionuclide scans fulfilled NBDC for ATTR-CM through absence of a serum or urine monoclonal protein on immunofixation together with a sFLC ratio falling within revised cut-offs incorporating eGFR; 403 of these patients had amyloid on biopsy, all of which were ATTR type, and their survival was comparable to non-biopsied ATTR-CM patients (p = 0.10). Grade 0 radionuclide scans were present in 1091 patients, of whom 284 (26%) had CA, confirmed as AL type (AL-CA) in 276 (97%) and as ATTR-CM in only one case with an extremely rare TTR variant. Among 183 patients with grade 1 radionuclide scans, 122 had MG of whom 106 (87%) had AL-CA; 60/61 (98%) without MG had ATTR-CM. Conclusion: The NBDC for ATTR-CM are highly specific [97% (95% CI 0.91-0.99)] in clinical setting, and diagnostic performance was further refined here using new cut-offs for sFLC ratio in patients with CKD. A grade 0 radionuclide scan all but excludes ATTR-CM but occurs in most patients with AL-CA. Grade 1 scans in patients with CA and no MG are strongly suggestive of early ATTR-type, but require urgent histologic corroboration