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We provide new conditions under which the alternating projection sequence converges in norm for the convex feasibility problem where a linear subspace with finite codimension $N\geq 2$ and a lattice cone in a Hilbert space are considered. The first result holds for any Hilbert lattice, assuming that the orthogonal of the linear subspace admits a basis made by disjoint vectors with respect to the lattice structure. The second result is specific for $\ell^2(\mathbb{N})$ and is proved when only one vector of the basis is not in the cone but the sign of its components is definitively constant and its support has finite intersection with the supports of the remaining vectors., Comment: 10 pages

For every $\alpha \in (0,+\infty)$ and $p,q \in (1,+\infty)$ let $T_\alpha$ be the operator $L^p[0,1]\to L^q[0,1]$ defined via the equality $(T_\alpha f)(x) := \int_0^{x^\alpha} f(y) d y$. We study the norms of $T_\alpha$ for every $p$, $q$. In the case $p=q$ we further study its spectrum, point spectrum, eigenfunctions, and the norms of its iterates. Moreover, for the case $p=q=2$ we determine the point spectrum and eigenfunctions for $T^*_\alpha T_\alpha$, where $T^*_\alpha$ is the adjoint operator., Comment: To appear in Rend. Circ. Mat. Palermo (2)

Let $d$ be any positive and non square integer. We prove an upper bound for the first two moments of the length $T(d)$ of the period of the continued fraction expansion for $\sqrt{d}$. This allows to improve the existing results for the large deviations of $T(d)$., Comment: Some misprints have been corrected. The new version of the paper is scheduled to appear in Mathematika

Current methods for the classification of number fields with small regulator depend mainly on an upper bound for the discriminant, which can be improved by looking for the best possible upper bound of a specific polynomial function over an hypercube. In this paper, we provide new and effective upper bounds for the case of fields with one complex embedding and degree between five and nine: this is done by adapting the strategy we have adopted to study the totally real case, but for this new setting several new computational issues had to be overcome. As a consequence, we detect the four number fields of signature (6,1) with smallest regulator; we also expand current lists of number fields with small regulator in signatures (3,1), (4,1) and (5,1)., Comment: 23 pages. Accepted for publication on Mathematics of Computation. The title has been changed under referee's suggestion. Several misprints have been corrected

Background: At the beginning of 2020, a high number of COVID-19 cases affected Italy in a short period, causing a difficult supply of medical equipment. To deal with the problem, many healthcare operators readapted different masks to medical devices, but no experiment was conducted to evaluate their performance. The aims of our study were: to assess the performances of three masks and a CPAP helmet in their original configuration and after modifications, in the maintenance of mean pressure and half-amplitude variations using different PEEP valves and to analyse the impact of antibacterial (AB) or antibacterial-viral (ABV) pre-valve PEEP filters on the effective PEEP delivered to the patients. Four pressure ports were installed on each mask (three on helmet), mean values and half amplitudes of pressure were recorded. Tests were performed with any, AB, ABV filter before the PEEP valve. CPAP helmet was the most efficient interface producing more stable mean pressure and less prominent half-amplitude variations but the non-medical masks, especially after the modifications, maintained a stable mean pressure value with only a moderate increase of half-amplitude. The use of AB and ABV filters, produced respectively an increase of 2,23% and 16.5% in mean pressure, compared to no filter condition. CPAP helmet is the most reliable interface in terms of detected performance, but readapted masks can assure almost a similar performance. The use of ABV filters before the PEEP valve significantly increases the detected mean pressure while the AB filters have almost a neutral effect., Comment: This paper, even if paginated folowing ACTA IMEKO standards, has still never been submitted to that journal

Let $Tr$ denote the trace $\mathbb{Z}$-module homomorphism defined on the ring $\mathcal{O}_{L} $ of the integers of a number field $L.$ We show that $Tr(\mathcal{O}_{L})\varsubsetneq \mathbb{Z}$ if and only if there is a prime factor $p$ of the degree of $L$ such that if $\wp _{1}^{e_{1}}...\wp _{s}^{e_{s}}$ is the prime factorization of the ideal $p\mathcal{O}_{L}$ in $\mathcal{O}_{L},$ then $p$ divides all powers $e_{1},...,e_{s}.$ Also, we prove that the equality $Tr(\mathcal{O}_{L})=\mathbb{Z}$ holds when $L$ is the compositum of certain number fields., Comment: 6 pages

We give upper bounds for the number of rational elliptic surfaces in some families having positive rank, obtaining in particular that these form a subset of density zero. This confirms Cowan's conjecture (arXiv:2009.08622v2) in the case $m,n\leq2$.

We study elliptic surfaces over $\mathbb{Q}(T)$ with coefficients of a Weierstrass model being polynomials in $\mathbb{Q}[T]$ with degree at most 2. We derive an explicit expression for their rank over $\mathbb{Q}(T)$ depending on the factorization and other simple properties of certain polynomials. Finally, we give sharp estimates for the ranks of the considered families and we present several applications, among which there are lists of rational points, generic families with maximal rank and generalizations of former results.

In this paper we study couples of finite separable extensions of the function field $\mathbb{F}_q(T)$ which are arithmetically equivalent, i.e. such that prime ideals of $\mathbb{F}_q[T]$ decompose with the same inertia degrees in the two fields, up to finitely many exceptions. In the first part of this work, we extend previous results by Cornelissen, Kontogeorgis and Van der Zalm to the case of non-geometric extensions of $\mathbb{F}_q(T)$, which are fields such that their field of constants may be bigger than $\mathbb{F}_q$. In the second part, we explicitly produce examples of non-geometric extensions of $\mathbb{F}_2(T)$ which are equivalent and non-isomorphic over $\mathbb{F}_2(T)$ and non-equivalent over $\mathbb{F}_4(T)$, solving a particular Inverse Galois Problem., Comment: 18 pages. Comments are welcome

This study explores the determinants of popularity within friendship and advice networks. We involved almost 200 college students in an experiment to predict how personality traits, self-monitoring, creativity, intelligence, energy, and beauty influence the development of friendship and advice networks. Our results indicate that physical attractiveness is a key to develop both friendship and task-related interactions, whereas perceived intelligence and creativity play an important role in the advice network. Our findings seem to support the idea that there might be a kernel of truth in the stereotype that attractiveness correlates with positive social traits and successful outcomes.

We propose a text classification tool based on support vector machines for the assessment of organizational leadership styles, as appearing to Twitter users. We collected Twitter data over 51 days, related to the first 30 Italian organizations in the 2015 ranking of Forbes Global 2000-out of which we selected the five with the most relevant volumes of tweets. We analyzed the communication of the company leaders, together with the dialogue among the stakeholders of each company, to understand the association with perceived leadership styles and dimensions. To assess leadership profiles, we referred to the 10-factor model developed by Barchiesi and La Bella in 2007. We maintain the distinctiveness of the approach we propose, as it allows a rapid assessment of the perceived leadership capabilities of an enterprise, as they emerge from its social media interactions. It can also be used to show how companies respond and manage their communication when specific events take place, and to assess their stakeholder's reactions.

This study looks for signals of economic awareness on online social media and tests their significance in economic predictions. The study analyses, over a period of two years, the relationship between the West Texas Intermediate daily crude oil price and multiple predictors extracted from Twitter, Google Trends, Wikipedia, and the Global Data on Events, Language, and Tone database (GDELT). Semantic analysis is applied to study the sentiment, emotionality and complexity of the language used. Autoregressive Integrated Moving Average with Explanatory Variable (ARIMAX) models are used to make predictions and to confirm the value of the study variables. Results show that the combined analysis of the four media platforms carries valuable information in making financial forecasting. Twitter language complexity, GDELT number of articles and Wikipedia page reads have the highest predictive power. This study also allows a comparison of the different fore-sighting abilities of each platform, in terms of how many days ahead a platform can predict a price movement before it happens. In comparison with previous work, more media sources and more dimensions of the interaction and of the language used are combined in a joint analysis.

Prior research has emphasised the importance of informal advice networks for knowledge sharing and peer learning. We use Social Network Analysis to detect individuals who play a strategic role in advice networks. Even if roles have been extensively described, how to identify people within them is still an open issue. Furthermore, we investigate whether an association between key players and the big five personality traits exists, by means of nonparametric statistics. To achieve this, we present a case study which involves roughly 180 university students. We found 21 of them playing a key role. Results give evidence of significant associations between key positions and Conscientiousness, Neuroticism and Agreeableness; whereas no evidence is found for a relationship with Extraversion or Openness to Experience. Consistently, personality emerges as a relevant indicator for predicting people who are more likely to play a strategic role, even when connection patterns are unknown.

Let $P_n(y_1,\ldots,y_n):= \prod_{1\leq i