A Minimum problem for finite sets of real numbers with non-negative sum

Let $n$ and $r$ be two integers such that $0 < r \le n$; we denote by $\gamma(n,r)$ [$\eta(n,r)$] the minimum [maximum] number of the non-negative partial sums of a sum $\sum_{1=1}^n a_i \ge 0$, where $a_1, \cdots, a_n$ are $n$ real numbers arbitrarily chosen in such a way that $r$ of them are non-negative and the remaining $n-r$ are negative. Inspired by some interesting extremal combinatorial sum problems raised by Manickam, Mikl\"os and Singhi in 1987 \cite{ManMik87} and 1988 \cite{ManSin88} we study the following two problems: \noindent$(P1)$ {\it which are the values of $\gamma(n,r)$ and $\eta(n,r)$ for each $n$ and $r$, $0 < r \le n$?} \noindent$(P2)$ {\it if $q$ is an integer such that $\gamma(n,r) \le q \le \eta(n,r)$, can we find $n$ real numbers $a_1, \cdots, a_n$, such that $r$ of them are non-negative and the remaining $n-r$ are negative with $\sum_{1=1}^n a_i \ge 0$, such that the number of the non-negative sums formed from these numbers is exactly $q$?} \noindent We prove that the solution of the problem $(P1)$ is given by $\gamma(n,r) = 2^{n-1}$ and $\eta(n,r) = 2^n - 2^{n-r}$. We provide a partial result of the latter problem showing that the answer is affirmative for the weighted boolean maps. With respect to the problem $(P2)$ such maps (that we will introduce in the present paper) can be considered a generalization of the multisets $a_1, \cdots, a_n$ with $\sum_{1=1}^n a_i \ge 0$. More precisely we prove that for each $q$ such that $\gamma(n,r) \le q \le \eta(n,r)$ there exists a weighted boolean map having exactly $q$ positive boolean values.Comment: 15 page

Land use affects the soil C sequestration in alpine environment, NE Italy

Soil carbon sequestration is strongly affected by soil properties, climate, and anthropogenic activities. Assessing these drivers is key to understanding the effect of land use on soil organic matter stabilization. We evaluated land use and soil depth influencing patterns of soil organic matter stabilization in three types of soil profiles located under the same pedogenetic matrix and alpine conditions but with different vegetation cover. The stock in soil organic carbon in the mean 0–20 cm layer increased from prairie (31.9 t ha−1) to prairie in natural reforestation (42 t ha−1) to forest (120 t ha−1), corresponding to increments of 1.3-fold prairie, for prairie in natural reforestation, and of 3.8-fold prairie for forest. The forest showed the highest humic carbon (21.7 g kg−1), which was 2.8 times greater than the prairie in natural reforestation and 4 times higher than the prairie. 13C-NMR spectroscopic measurements suggested a different C pattern. The prairie in natural reforestation and the prairie were characterized by a higher content in O,N-alkyl C with respect to the forest. Alkyl C and aromatic C in the prairie in natural reforestation and prairie did not show relevant differences while they decreased with respect to the forest. Carboxyl and phenolic C groups were markedly higher in forest and prairie than prairie in natural reforestation. Alkyl C, carboxyl C, and phenolic C prevailed in the Ah horizons whereas aromatic C and O,N-alkyl C were dominant in the B horizons. Overall, the marked distribution of O,N-alkyl C and alkyl C in humic substances (HS) indicates a low degree of humification. Nevertheless, in forest, the relatively high presence of aromatic C designated HS endowed with a relatively high humification degree. Thus, our results might suggest that in the alpine environment of NE Italy differences in soil organic matter (SOM) stocks and characteristics are affected by land use and anthropic activities

Vaccine hesitancy among Ukrainian refugees

Background On February 2022, Russia invaded Ukraine so several refugees went to Poland, Romania, Russia, but also to Italy. Several factors contributed to low vaccination coverage in Ukraine and the occurrence of epidemic outbreaks. The purpose of our study was to analyze the main characteristics of refugees who accessed the Rozzano Vaccination Center (Italy), and the attitude towards proposed vaccinations. Methods In March-July 2022, we conducted a cross sectional study on Ukrainian refugees under the age of 18. On the basis of their vaccination certificates or antibody dosages, the doctor proposed to the parents (or legal guardians) any vaccinations to be carried out on the basis of the Italian Vaccinal Calendar. Refused or accepted vaccinations were registered and the data exported for statistical analysis. COVID-19 vaccination was excluded from our analysis. Results 27 refugees missed the appointment, so 79 Ukrainian refugees have been included in the study. Females represented the 51.90% of patients; the average age was 7.11 (sd 4.92) years. The most refused vaccinations were: HPV, MMR and men C. Significant differences due to age were found for Men C and Chickenpox. Conclusions The efforts made to ensure complete care and promote vaccination among refugees, offering them a complete evaluation of the vaccination status and the possibility of being vaccinated for free, seem to be insufficient to convince most refugees to get vaccinated

Electrocardiography for Assessment of Hypertensive Heart Disease: A New Role for an Old Tool

Left ventricular (LV) hypertrophy (LVH), detected either by electrocardiography (ECG) or echocardiography (ECHO), has long been recognized as a powerful predictor of serious cardiovascular (CV) sequelae.A very large and highly consistent body of evidence indicates that LVH is not only an adaptation to increased hemodynamic load in hypertension, but is also independently associated with an enhanced risk for myocardial infarction, cardiac sudden death, congestive heart failure, and stroke in the general population, as well as in patients with systemic hypertension, coronary heart disease, chronic kidney disease, and atrial fibrillation. Intriguingly, the cumulative incidence of cardiovascular events increases progressively with increasing LV mass (LVM), without evidence of any threshold separating the postulated “compensatory” from “pathological” LVH. In other words, patients with LVM in the upper-normal range already have increased risk for CV events

INVERSE RELATIONSHIP BETWEEN AORTIC ROOT DIAMETER AND RENAL FUNCTION IN HYPERTENSIVE SUBJECTS

Recent studies suggest that enlarged aortic root diameter (ARD) may predict cardiovascular events in absence of aneurysmatic alterations. Little is known about the influence of renal function on ARD. Our study was aimed to assess the relationships between glomerular filtration rate (GFR) and ARD in hypertensive subjects

Effects of fuel composition on charge preparation, combustion and knock tendency in a high performance GDI engine. Part I: RANS analysis

The paper analyses the effects of fuel composition modelling in a turbocharged GDI engine for sport car applications. Particularly, a traditional single-component gasoline-surrogate fuel is compared to a seven-component fuel model available in the open literature. The multi-component fuel is represented using the Discrete-Continuous-Multi-Component modelling approach, and it is specifically designed in order to match the volatility of an actual RON95 European gasoline. The comparison is carried out following a detailed calibration with available experimental measurements for a full load maximum power engine speed operation of the engine, and differences are analyzed and critically discussed for each of the spray evolution, mixture stratification and combustion. In the present paper (Part I), a RANS approach is used to preliminarily investigate the behaviour of the fuel model on the average engine cycle. In the subsequent Part II of the same paper, the numerical framework is evolved into a more refined LES approach, in order to take into account cycle-to-cycle variations in mixture formation and knock tendency

Effects of fuel composition on charge preparation, combustion and knock tendency in a high performance GDI engine. Part II: Les analysis

As discussed in the Part I of this paper, a numerical activity is carried out in order to analyse the effects of fuel composition modelling in a turbocharged GDI engine for sport car applications. While Part I analyses the "ensemble averaged" macroscopic effects on spray evolution, mixture stratification, combustion and knock tendency, in Part II of this paper cycle-to-cycle variations are analysed and discussed using a multi-cycle LES numerical framework, again comparing results from a more traditional single-component fuel surrogate model to those of a multi-component one. A purposely developed numerical approach is applied to properly account for the effects of the Discrete-Continuous-Multi-Component fuel formulation on the charge preparation: just before the spark timing, each vaporized fuel fraction is lumped back into a single-component surrogate fuel to allow the combustion model (ECFM-3Z, in its LES formulation) to take place. At the beginning of a new injection process, the numerical framework for the injected spray is switched back to Multi-Component, thus allowing each fuel fraction to independently spread, vaporize and diffuse in the combustion chamber according to the cycle-specific characteristics. A detailed comparison between the two fuel formulations is carried out on both average and rms values of the most influencing fields just before the spark discharge

Land use affects the soil C sequestration in alpine environment, NE Italy

Soil carbon sequestration is strongly affected by soil properties, climate, and anthropogenic activities. Assessing these drivers is key to understanding the effect of land use on soil organic matter stabilization. We evaluated land use and soil depth influencing patterns of soil organic matter stabilization in three types of soil profiles located under the same pedogenetic matrix and alpine conditions but with different vegetation cover. The stock in soil organic carbon in the mean 0\u201320 cm layer increased from prairie (31.9 t ha1) to prairie in natural reforestation (42 t ha1) to forest (120 t ha1), corresponding to increments of 1.3-fold prairie, for prairie in natural reforestation, and of 3.8-fold prairie for forest. The forest showed the highest humic carbon (21.7 g kg1), which was 2.8 times greater than the prairie in natural reforestation and 4 times higher than the prairie. 13C-NMR spectroscopic measurements suggested a different C pattern. The prairie in natural reforestation and the prairie were characterized by a higher content in O,N-alkyl C with respect to the forest. Alkyl C and aromatic C in the prairie in natural reforestation and prairie did not show relevant differences while they decreased with respect to the forest. Carboxyl and phenolic C groups were markedly higher in forest and prairie than prairie in natural reforestation. Alkyl C, carboxyl C, and phenolic C prevailed in the Ah horizons whereas aromatic C and O,N-alkyl C were dominant in the B horizons. Overall, the marked distribution of O,N-alkyl C and alkyl C in humic substances (HS) indicates a low degree of humification. Nevertheless, in forest, the relatively high presence of aromatic C designated HS endowed with a relatively high humification degree. Thus, our results might suggest that in the alpine environment of NE Italy differences in soil organic matter (SOM) stocks and characteristics are affected by land use and anthropic activities

Retraction Note: Impact of Different Treatment of Whole-Body Cryotherapy on Circulatory Parameters

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