Successioni di polinomi di tipo binomiale e operatori delta

In questa tesi riportiamo le definizioni ed i risultati principali relativi alla corrispondenza tra le successioni di polinomi di tipo binomiale (particolari basi dello spazio dei polinomi a coefficienti reali) e gli operatori delta, cioè operatori lineari sullo spazio dei polinomi che commutano con gli operatori di traslazione e il cui nucleo è costituito dai polinomi costanti. Nel capitolo 1 richiamiamo i concetti fondamentali sull'algebra delle serie formali e definiamo l'algebra degli operatori lineari invarianti per traslazione, dimostrando in particolare l'isomorfismo tra queste algebre. Nel capitolo 2, dopo aver dimostrato l'unicità della successione di base relativa ad un operatore delta, ricaviamo come esempio le successioni di base di tre operatori delta, che useremo durante tutto il capitolo: l'operatore derivata, l'operatore di differenza in avanti e l'operatore di differenza all'indietro. Arriviamo quindi a dimostrare un importante risultato, il Primo Teorema di Sviluppo, in cui facciamo vedere come le potenze di un operatore delta siano una base per l'algebra degli operatori invarianti per traslazione. Introducendo poi le successioni di Sheffer, possiamo dimostrare anche il Secondo Teorema di Sviluppo in cui esplicitiamo l'azione di un operatore invariante per traslazione su un polinomio, tramite un operatore delta fissato e una sua successione di Sheffer. Nell'ultima parte della tesi presentiamo i formalismi e alcune semplici operazioni del calcolo umbrale, che useremo per determinare le cosiddette costanti di connessione, ovvero le costanti che definiscono lo sviluppo di una successione binomiale in funzione di un'altra successione binomiale usata come base dello spazio dei polinomi

Introduzione al concetto di frazione: una proposta di didattica inclusiva con Mathematica

La scuola è costantemente in fase di aggiornamento; lo fa attraverso riforme e leggi, ma soprattutto attraverso la disponibilità degli insegnanti a rivedere e attualizzare i metodi di insegnamento. Negli ultimi anni, forse più velocemente che nel passato, la scuola ha sentito il bisogno di introdurre nuove tecnologie per avvicinarsi alla quotidianità degli studenti e per permettere a ognuno di accedere al sapere pur con modalità e tempistiche differenti. Nelle classi di oggi sono presenti alunni con disabilità e alunni con disturbi dell'apprendimento: all'insegnante è lasciato il compito di riuscire ad includere tutti, spiegando all'intera classe la lezione, anche attraverso l'ausilio di strumenti hardware e software. Questo lavoro di tesi si è concentrato sulla creazione di un pacchetto software, utilizzabile da insegnanti e studenti, per la didattica delle frazioni. Nel primo capitolo di questa tesi si esplorano le modalità dell'insegnamento in classe e si analizzano le difficoltà che gli studenti, con o senza bisogni educativi speciali, incontrano nel consolidare il concetto di frazione nella scuola secondaria di primo grado. Si cercano altresì motivazioni all'uso in classe di software didattici. Per completezza sull'argomento, nel secondo capitolo è riportata la teoria della costruzione degli insiemi dei numeri naturali, dei numeri interi e dei numeri razionali, dedicato agli insegnanti solamente. Nel terzo capitolo viene presentato il pacchetto software “Cake” realizzato nell'ambiente “Mathematica”: vuole essere un esempio di come le tecnologie possano aiutare la didattica scolastica, includendo tutti gli alunni senza ridimensionare gli obiettivi didattici. Nel quarto capitolo sono presentati i risultati di tre casi studio, come supporto alla scelta di introdurre tecnologie informatiche nella didattica. Il quinto e ultimo capitolo tira le conclusioni di questo lavoro di tesi e ne indica alcuni possibili sviluppi ed impieghi futuri

COVID-19 Incidence and Vaccine Effectiveness in University Staff, 1 March 2020–2 April 2022

Background: University workers undergo intense social interactions due to the frequent contact with students and colleagues and lectures in crowdy conditions. The aim of our study was to assess the incidence of COVID-19 infection and vaccine effectiveness in a cohort of workers of the University of Trieste from 1 March 2020 (start of the pandemic) through 2 April 2022. Methods: The University of Trieste implemented a number of public health policies to contain the spread of SARS-CoV-2 on the campus, including prompt contact tracing, the enhanced ventilation of all premises, fomites disinfection and the mandatory use of face masks indoors. In compliance with the surveillance protocol of the local public health department, university personnel were tested for SARS-CoV-2 by polymerase chain reaction (PCR) on a nasopharyngeal swab on demand, in the event of symptoms consistent with COVID-19 or for contact tracing, following close contact with a confirmed COVID-19 case. The incidence rates of SARS-CoV-2 infections were estimated as the number of cases by the number of person-days (p-d) at risk. The multivariable Cox proportional hazard regression model was employed to investigate the risk of primary COVID-19 infection, adjusting for a number of potential confounders and expressing the risk as the adjusted hazard ratio (aHR) with a 95% confidence interval (95% CI). Results: The incidence of SARS-CoV-2 infection among the university staff was lower than that of healthcare workers (HCWs) of the same area. Compared to unvaccinated colleagues (6.55 × 10,000 p-d), the raw incidence of SARS-CoV-2 infection was higher among university workers immunized with one (7.22 × 10,000 p-d) or two (7.48 × 10,000 p-d) doses of the COVID-19 vaccine, decreasing in those receiving the booster (1.98 × 1000 p-d). The risk of infection increased only in postgraduate medical trainees (aHR = 2.16; 95% CI: 1.04; 4.48), though this was limited to the Omicron transmission period. After the implementation of the national vaccination campaign against COVID-19, workers immunized with the booster were less likely than unvaccinated workers to be infected by SARS-CoV-2 both before (aHR = 0.10; 95% CI: 0.06; 0.16) and after (aHR = 0.37; 95% CI: 0.27; 0.52) the Omicron transmission period. The vaccine effectiveness of the booster was 90% (=(1−0.10) × 100) before versus 63% (=(1−0.37) × 100) during the Omicron wave, without a significant difference between homologous (three doses of m-RNA vaccines) and heterologous (first two doses of Vaxzevria followed by a third dose of m-RNA vaccine) immunization. Conclusions: The incidence of SARS-CoV-2 infection in the university staff was lower than that of HCWs of ASUGI, likely because the testing-on-demand schedule inevitably missed asymptomatic infections. Therefore, the observed significantly protective effect of the booster dose in university personnel referred to symptomatic SARS-CoV-2 infections. The infection prevention and control policies implemented by the University of Trieste managed to equalize the biological risk between the administrative and teaching staff

Molnupiravir, Nirmatrelvir/Ritonavir, or Sotrovimab for High-Risk COVID-19 Patients Infected by the Omicron Variant: Hospitalization, Mortality, and Time until Negative Swab Test in Real Life

Background. Several drugs which are easy to administer in outpatient settings have been authorized and endorsed for high-risk COVID-19 patients with mild–moderate disease to prevent hospital admission and death, complementing COVID-19 vaccines. However, the evidence on the efficacy of COVID-19 antivirals during the Omicron wave is scanty or conflicting. Methods. This retrospective controlled study investigated the efficacy of Molnupiravir or Nirmatrelvir/Ritonavir (Paxlovid®) or Sotrovimab against standard of care (controls) on three different endpoints among 386 high-risk COVID-19 outpatients: hospital admission at 30 days; death at 30 days; and time between COVID-19 diagnosis and first negative swab test result. Multinomial logistic regression was employed to investigate the determinants of hospitalization due to COVID-19-associated pneumonia, whereas time to first negative swab test result was investigated by means of multinomial logistic analysis as well as Cox regression analysis. Results. Only 11 patients (overall rate of 2.8%) developed severe COVID-19-associated pneumonia requiring admission to hospital: 8 controls (7.2%); 2 patients on Nirmatrelvir/Ritonavir (2.0%); and 1 on Sotrovimab (1.8%). No patient on Molnupiravir was institutionalized. Compared to controls, hospitalization was less likely for patients on Nirmatrelvir/Ritonavir (aOR = 0.16; 95% CI: 0.03; 0.89) or Molnupiravir (omitted estimate); drug efficacy was 84% for Nirmatrelvir/Ritonavir against 100% for Molnupiravir. Only two patients died of COVID-19 (rate of 0.5%), both were controls, one (aged 96 years) was unvaccinated and the other (aged 72 years) had adequate vaccination status. At Cox regression analysis, the negativization rate was significantly higher in patients treated with both antivirals—Nirmatrelvir/Ritonavir (aHR = 1.68; 95% CI: 1.25; 2.26) and Molnupiravir (aHR = 1.45; 95% CI: 1.08; 1.94). However, COVID-19 vaccination with three (aHR = 2.03; 95% CI: 1.51; 2.73) or four (aHR = 2.48; 95% CI: 1.32; 4.68) doses had a stronger effect size on viral clearance. In contrast, the negativization rate reduced significantly in patients who were immune-depressed (aHR = 0.70; 95% CI: 0.52; 0.93) or those with a Charlson index ≥ 3 (aHR = 0.63; 0.41; 0.95) or those who had started the respective treatment course 3+ days after COVID-19 diagnosis (aOR = 0.56; 95% CI: 0.38; 0.82). Likewise, at internal analysis (excluding patients on standard of care), patients on Molnupiravir (aHR = 1.74; 95% CI: 1.21; 2.50) or Nirmatrelvir/Ritonavir (aHR = 1.96; 95% CI: 1.32; 2.93) were more likely to turn negative earlier than those on Sotrovimab (reference category). Nonetheless, three (aHR = 1.91; 95% CI: 1.33; 2.74) or four (aHR = 2.20; 95% CI: 1.06; 4.59) doses of COVID-19 vaccine were again associated with a faster negativization rate. Only 64.7% of patients were immunized with 3+ doses of COVID-19 vaccines in the present study. Again, the negativization rate was significantly lower if treatment started 3+ days after COVID-19 diagnosis (aHR = 0.54; 95% CI: 0.32; 0.92). Conclusions. Molnupiravir, Nirmatrelvir/Ritonavir, and Sotrovimab were all effective in preventing hospital admission and/or mortality attributable to COVID-19. However, hospitalizations also decreased with higher number of doses of COVID-19 vaccines. Although they are effective against severe disease and mortality, the prescription of antivirals should be carefully scrutinized by double opinion, not only to contain health care costs but also to reduce the risk of generating resistant SARS-CoV-2 strains. Only 64.7% of patients were in fact immunized with 3+ doses of COVID-19 vaccines in the present study. High-risk patients should prioritize COVID-19 vaccination, which is a more cost-effective approach than antivirals against severe SARS-CoV-2 pneumonia. Likewise, although both antivirals, especially Nirmatrelvir/Ritonavir, were more likely than standard of care and Sotrovimab to reduce viral shedding time (VST) in high-risk SARS-CoV-2 patients, vaccination had an independent and stronger effect on viral clearance. However, the effect of antivirals or COVID-19 vaccination on VST should be considered a secondary benefit. Indeed, recommending Nirmatrelvir/Ritonavir in order to control VST in high-risk COVID-19 patients is rather questionable since other cheap, large spectrum and harmless nasal disinfectants such as hypertonic saline solutions are available on the market with proven efficacy in containing VST

Supporting the Aspecific Physiological Defenses of Upper Airways Against Emerging SARS-CoV-2 Variants

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Primary SARS-CoV-2 Infections, Re-infections and Vaccine Effectiveness during the Omicron Transmission Period in Healthcare Workers of Trieste and Gorizia (Northeast Italy), 1 December 2021-31 May 2022

Objective: To evaluate the incidence of primary and recurrent COVID-19 infections in healthcare workers (HCWs) routinely screened for SARS-CoV-2 by nasopharyngeal swabs during the Omicron wave. Design: Dynamic Cohort study of HCWs (N = 7723) of the University Health Agency Giuliano Isontina (ASUGI), covering health services of the provinces of Trieste and Gorizia (Northeast Italy). Cox proportional hazard model was employed to estimate the risk of primary as well as recurrent SARS-CoV-2 infection from 1 December 2021 through 31 May 2022, adjusting for a number of confounding factors. Results: By 1 December 2021, 46.8% HCWs of ASUGI had received the booster, 37.2% were immunized only with two doses of COVID-19 vaccines, 6.0% only with one dose and 10.0% were unvaccinated. During 1 March 2020-31 May 2022, 3571 primary against 406 SARS-CoV-2 recurrent infections were counted among HCWs of ASUGI, 59.7% (=2130/3571) versus 95.1% (=386/406) of which occurring from 1 December 2021 through 31 May 2022, respectively. All HCWs infected by SARS-CoV-2 during 1 December 2021 through 31 May 2022 presented mild flu-like disease. Compared to staff working in administrative services, the risk of primary as well as recurrent SARS-CoV-2 infection increased in HCWs with patient-facing clinical tasks (especially nurses and other categories of HCWs) and in all clinical wards but COVID-19 units and community health services. Regardless of the number of swab tests performed during the study period, primary infections were less likely in HCWs immunized with one dose of COVID-19 vaccine. By contrast, the risk of SARS-CoV-2 re-infection was significantly lower in HCWs immunized with three doses (aHR = 0.58; 95%CI: 0.41; 0.80). During the study period, vaccine effectiveness (VE = 1-aHR) of the booster dose declined to 42% against re-infections, vanishing against primary SARS-CoV-2 infections. Conclusions: Though generally mild, SARS-CoV-2 infections and re-infections surged during the Omicron transmission period. Compared to unvaccinated colleagues, the risk of primary SARS-CoV-2 infection was significantly lower in HCWs immunized just with one dose of COVID-19 vaccines. By Italian law, HCWs immunized only with one dose were either suspended or re-assigned to job tasks not entailing patient facing contact; hence, while sharing the same biological risk of unvaccinated colleagues, they arguably had a higher level of protection against COVID-19 infection. By contrast, SARS-CoV-2 re-infections were less likely in HCWs vaccinated with three doses, suggesting that hybrid humoral immunity by vaccination combined with natural infection provided a higher level of protection than vaccination only. In this stage of the pandemic, where SARS-CoV-2 is more infectious yet much less pathogenic, health protection measures in healthcare premises at higher biological risk seem the rational approach to control the transmission of the virus

COVID-19 susceptibility and vaccination coverage for measles, rubella and mumps in students and healthcare workers in Trieste hospitals (NE Italy)

Background: Measles, mumps, and rubella (MMR) vaccines have been suggested as preventive measures to protect subjects from the worst sequelae of COVID-19 infection because neutralizing antibodies can cross-react with other viruses. Aim: To verify COVID-19 infection in MMR vaccinated and non-vaccinated healthcare workers and medical students in Trieste Hospitals. Results: Nurse aids resulted in significantly more infections than structured physicians (OR 1.80; 95% CI 1.14-2.80) while students resulted in less infections (OR, 0.66; 95% CI 0.43-1.01). The presence of an MMR vaccination was inversely associated with COVID-19 (OR, 0.77; 95% CI 0.61-0.96) but only in univariate analysis. In the multivariable logistic regression analysis, MMR vaccination lost statistical significance (OR, 0.86; 95%CI 0.62-1.20). On 13 HCWs hospitalized for COVID-19, 11 resulted not vaccinated for MMR. Discussion: Our study found a mild, non-significant reduction in SARS-CoV-2 infections in workers vaccinated with MMR

Assessment of dermal absorption of beryllium and copper contained in temple tips of eyeglasses

Dermal exposure to hazardous substances such as chemicals, toxics, metallic items and other contaminants may present substantial danger for health. Beryllium (Be) is a hazardous metal, especially when inhaled and/or in direct contact with the skin, associated with chronic beryllium disease (CBD) and Be sensitization (BeS). The objective of this study was to investigate the percutaneous penetration of beryllium and copper contained in metallic items as eyeglass temple tips (specifically BrushCAST (R) Copper Beryllium Casting Alloys containing Be 0.35 < 2.85%; Cu 95.3-98.7%), using Franz diffusion cells. This work demonstrated that the total skin absorption of Cu was higher (8.86%) compared to Be (4.89%), which was expected based on the high percentage of Cu contained in the eyeglass temple tips. However, Be accumulated significantly in the epidermis and dermis (up to 0.461 mu g/cm(2)) and, to a lesser extent, in the stratum corneum (up to 0.130 mu g/cm2) with a flux of permeation of 3.52 +/- 4.5 mu g/cm(2)/hour and lag time of 2.3 +/- 1.3 h, after cutaneous exposure of temple tip into 1.0 mL artificial sweat for 24 h. Our study highlights the importance of avoiding the use of Be alloys in items following long-term skin contact

In vitro dermal penetration of nickel nanoparticles.

Nickel nanoparticles (NiNPs) represent a new type of occupational exposure because, due to the small size/high surface, they can release more Ni ions compared to bulk material. It has been reported a case of a worker who developed sensitization while handling nickel nanopowder without precautions. Therefore there is the need to assess whether the skin absorption of NiNPs is higher compared to bulk nickel. Two independent in vitro experiments were performed using Franz diffusion cells. Eight cells for each experiment were fitted using intact and needle-abraded human skin. The donor phase was a suspension of NiNPs with mean size of 77.7 \ub1 24.1 nm in synthetic sweat. Ni permeated both types of skin, reaching higher levels up to two orders of magnitude in the damaged skin compared to intact skin (5.2 \ub1 2.0 vs 0.032 \ub1 0.010 \u3bcg cm(-2), p = 0.006) at 24 h. Total Ni amount into the skin was 29.2 \ub1 11.2 \u3bcg cm(-2) in damaged skin and 9.67 \ub1 2.70 \u3bcg cm(-2) in intact skin (mean and SD, p = 0.006). Skin abrasions lead to doubling the Ni amount in the epidermis and to an increase of ten times in the dermis. This study demonstrated that NiNPs applied on skin surface cause an increase of nickel content into the skin and a significant permeation flux through the skin, higher when a damaged skin protocol was used. Preventive measures are needed when NiNPs are produced and used due to their higher potential to enter in our body compared to bulk nickel