Étant donnée une suite $A = (a_n)_{n\geqslant 0}$ d’entiers naturels tous au moins égaux à 2, on pose $q_0 = 1$ et, pour tout entier naturel n, $q_{n+1} = a_n q_n$. Tout nombre entier naturel $n\geqslant 1$ admet une unique représentation dans la base A, dite de Cantor, de la forme

$$ \begin{align*} m = \sum_{j\geqslant 0}\varepsilon_j(m)q_j\quad \text{avec} \quad 0\leqslant \varepsilon_j(m) < a_j = \frac{q_{j+1}}{q_j}. \end{align*} $$

$$ \begin{align*} S = \sum_{n \leqslant x}\Lambda(n) f(n) \end{align*} $$

$\Lambda $

$(a_n)_{n\geqslant 0}$

Nous étudions plusieurs exemples dans la base $A = (j+2)_{j\geqslant 0}$, dite factorielle. En particulier, si $s_A$ désigne la fonction somme de chiffres dans cette base et p parcourt la suite des nombres premiers, nous montrons que la suite $(s_A(p))_{p\in \mathcal {P}}$ est bien répartie dans les progressions arithmétiques, et que la suite $(\alpha s_A(p))_{p\in \mathcal {P}}$ est équirépartie modulo $1$ pour tout nombre irrationnel $\alpha $.

Cremation graves appear in different forms and shapes, from urns to simple pits and from single to plural graves. The challenging nature of highly fragmented cremated human remains renders the identification of multiple individuals within the same cremation grave rather complex. Osteological analyses alone are often insufficient to detect the presence of bone fragments from different individuals as they are small and diagnostic elements are often missing, although, detection of nonadult bone fragments within adult bone assemblages (or the other way around) points to the presence of at least two individuals—one adult and one nonadult—within the same grave. The combination of osteological analyses, radiocarbon dating, and strontium isotope ratios has proven to be particularly powerful. At different Belgian Metal Age sites, this novel multi-disciplinary approach enabled to identify the presence of bone fragments belonging to up to three different individuals within the same cremation grave who were cremated up to several centuries apart. Whether the presence of these two or three individuals in the same grave is intentional (e.g. curation) or not requires more in-depth analyses. This study shows the high level of complexity of cremation burial (intentionally or not) and shows the necessity to carry out all analytical measurements (i.e. radiocarbon dating, infrared, elemental and isotope analyses) on the same bone fragment to ensure the results are related to the same individual.

We evaluated the presence of bacterial pathogens in the milk of goats and their relationship with somatic cell count (SCC) and milk composition. The study was performed on a dairy farm in northern Slovakia. Half udder milk samples were collected from goats in June and July. The samples were divided on the basis of SCC into 4 bands (SCC1 lowest to SCC4 highest). Bacterial pathogens were only detected in 13% of samples. SCC3 and SCC4 had 15 and 25% positive samples respectively compared with SCC1 (2%) and SCC2 (14%). Coagulase-negative staphylococci (CNS) were the most common isolates (73%), of which Staphylococcus caprae was the most frequently isolated (65%). In samples with ≥ 1000 × 103 cells ml− 1 (SCC3, SCC4) there was higher somatic cell score (SCS) in the presence of a pathogen (7.48 ± 0.11) than without a pathogen (7.16 ± 0.05, P < 0.01). Statistically significant but weak negative correlations were observed between SCS and lactose, dry matter and non-fat dry matter. In conclusion, a higher percentage of bacteriologically positive milk samples was observed in both SCC3 and SCC4 groups but this does not explain the aetiology of high SCC in the milk of goats that are apparently free of bacteria. As a diagnostic tool, SCC is probably less useful in goats than in cows.

The Final Neolithic and the Bronze Age (3000–800 BC) are periods of great transformations in the communities inhabiting the area of modern-day Belgium, as testified by archaeological evidence showing an increasing complexity in social structure, technological transformations, and large-scale contacts. By combining 599 available radiocarbon dates with 88 new 14C dates from 23 from funerary sites, this paper uses kernel density estimates to model the temporality in the use of inhumation vs. cremation burials, cremation deposits in barrows vs. flat graves, and cremation grave types. Additionally, by including 78 dates from settlements, changes in population dynamics were reconstructed. The results suggest a phase of demographic contraction around ca. 2200–1800 BC highlighted by a lack of dates from both settlements and funerary contexts, followed by an increase in the Middle Bronze Age, with the coexistence of cremation deposits in barrows and, in a lower number, in flat graves. At the end of the 14th–13th century BC, an episode of cultural change with the almost generalized use of flat graves over barrows is observed. Regional differentiations in the funerary practices and the simultaneous use of different grave types characterize the Late Bronze Age.

The current study explored dynamics of secure state attachment expectations in everyday life in middle childhood, specifically state attachment carry-over and reactivity to experiences of caregiver support in the context of stress. In two independent samples (one community sample, N = 123; one adoption sample, N = 69), children (8–12 years) daily reported on their state attachment for respectively 14 and 7 consecutive days. Additionally, they reported daily on their experiences of distress and subsequent experiences of caregiver support. Results in both samples indicated that secure state attachment on a day-to-day basis is characterized by a significant positive carry-over effect, suggesting that state attachment fluctuations are (partially) self-predictive. In Study 1, experiencing no support following distress significantly related to intraindividual decreases in secure state attachment; in Study 2, experiencing effective support during distress related to intra-individual increases in secure state attachment. Taken together, the current studies provide novel and important insights into how state attachment temporally evolves on a day-to-day basis in middle childhood.

Introduction. Exercise interventions may assist smoking cessation attempts. One such publicly available 10-week program, Walk or Run to Quit (WRTQ), demonstrated success in smoking cessation and physical activity (PA) outcomes. However, initial WRTQ participants (2016-2017) were fairly homogenous in their demographic profile. To increase diversity, subsidies for participation were offered in 2018. This study assessed how the subsidies affected participant demographics, running frequency, smoking cessation, intention to quit, and program attendance and completion. Methods. The $70 registration fee was subsidized for 41% of participants in 2018. A pre-postdesign was used, with participants completing surveys on their demographics and smoking and physical activity behaviours. Descriptive statistics compared the year subsidies were available (2018) and unsubsidized years (2016-2017) and subsidized and unsubsidized participants’ data from 2018. Results. The 2018 participants had lower average attendance and program completion rates compared to 2016-2017 and no statistically significant differences in demographics or smoking cessation and PA outcomes. There were no differences in smoking cessation, run frequency, or demographic variables between the subsidized and unsubsidized participants in 2018. Conclusions. Offering subsidies did not diversify the participant profile. Subsidies did not have a negative impact on attendance nor primary outcomes. Subsidies may not have addressed barriers that prevented a more diverse sample from participating in WRTQ, such as program location, timing, and design. Equitable access to smoking cessation programs remains essential. As subsidies may play a role in reducing financial barriers disproportionately faced by marginalized groups, the implementation of, and recruitment for, such subsidized programs requires further investigation.

Aeolianites and cemented foreshore deposits on South Africa's Cape south coast have the capacity to record and preserve events that transpired on them when they were composed of unconsolidated sand. Thirty-five Pleistocene elephant tracksites have been identified along this coastline. This abundance of sites along what was the margin of the vast Palaeo-Agulhas Plain allows for an appreciation of the forms that elephant tracks and traces can take in the context of the global proboscidean track record. They point to a significant regional elephant presence from Marine Isotope Stage (MIS) 11 (~400 ka) through MIS 5 (~130–80 ka) to MIS 3 (~35 ka) and also indicate repeated use of certain dune areas. They buttress Holocene and historical evidence that elephants made use of open areas in the region, and that the remaining “Knysna elephants” retreated into dense afrotemperate forest for protection in recent centuries. Analogies can be drawn between Pleistocene elephant tracks and Mesozoic dinosaur tracks, and some of the Cape south coast elephant tracks are among the largest Cenozoic (and hence, Quaternary) tracks ever to be described. A newly identified tracksite in this area may provide the first reported evidence of elephant trunk-drag impressions.

The adoption of a new funerary ritual with all its social and cognitive meanings is of great importance to understanding social transformations of past societies. The first known occurrence of cremation in the territory corresponding to modern Belgium dates back to the Mesolithic period. From the end of the Neolithic onward, the practice of cremation was characterized by periods in which this rite was predominant and periods of contractions, defined by a decrease in the use of this funerary ritual. This paper aims to quantify such phenomenon for the first time by modeling discontinuities in burial practices through kernel density analysis of 1428 radiocarbon (14C) dates from 311 archaeological sites located in Belgium from the Mesolithic to the Middle Ages. Despite possible taphonomic and sampling biases, the results highlight the existence of periods with a large uptake of cremation rite followed by periods of contractions; such discontinuities took place in correlation with changes in the socio-economical structure of local communities, as, for example, during the later Middle Bronze Age and at the end of the Roman Period.

Cascading effects of high trophic levels onto lower trophic levels have been documented in many ecosystems. Some studies also show evidence of extended trophic cascades, in which guilds dependent on lower trophic levels, but uninvolved in the trophic cascade themselves, are affected by the trophic cascade due to their dependence on lower trophic levels. Top-down effects of large mammals on plants could lead to a variety of extended trophic cascades on the many guilds dependent on plants, such as pollinators. In this study, floral-visitor and floral abundances and assemblages were quantified within a series of 1-ha manipulations of large-mammalian herbivore density in an African savanna. Top-down effects of large mammals on the composition of flowers available for floral visitors are first shown, using regressions of herbivore activity on metrics of floral and floral-visitor assemblages. An extended trophic cascade is also shown: the floral assemblage further altered the assemblage of floral visitors, according to a variety of approaches, including a structural equation modelling approach (model with an extended trophic cascade was supported over a model without, AICc weight = 0.984). Our study provides support for extended trophic cascades affecting floral visitors, suggesting that trophic cascades can have impacts throughout entire communities.

We performed a molecular and epidemiologic study of a healthcare-associated rhinovirus outbreak to better understand transmission in neonatal intensive care settings. Sequencing of the 7 outbreak strains revealed 4 distinct clades, indicating multiple sources. A single clade infected 3 patients in adjacent rooms, suggesting horizontal transmission. We observed 1 rhinovirus-associated death.

In this contribution, the impact of extreme environmental conditions in terms of energy-level radiation of protons on silicon–germanium (SiGe)-integrated circuits is experimentally studied. Canonical representative structures including linear (passive interconnects/antennas) and non-linear (low-noise amplifiers) are used as carriers for assessing the impact of aggressive stress conditions on their performances. Perspectives for holistic modeling and characterization approaches accounting for various interaction mechanisms (substrate resistivity variations, couplings/interferences, drift in DC and radio frequency (RF) characteristics) for active samples are down to allow for optimal solutions in pushing SiGe technologies toward applications with harsh and radiation-intense environments (e.g. space, nuclear, military). Specific design prototypes are built for assessing mission-critical profiles for emerging RF and mm-wave applications.

Sea surface reservoir ages (R) are reported from radiocarbon (14C) measurements of the annual growth bands of coral Siderastrea siderea collected on the Atlantic coast off Martinique Island, in the Lesser Antilles volcanic arc. Mean values of R are similar between 1835 and 1845 during pre-anthropogenic times at 385±30 yr and between 1895 and 1905 at 382±20 yr when there was a huge eruption from the Montagne Pelée volcano in 1902–1903. Limited 14C aging of sea surface (~40 yr) may be due to enhanced volcanic activity. Variability of R is slightly greater during 1835–1845 than during 1895–1905. It is linked to a moderate increase of ∆14C of 5‰, strengthened by a clear increase of δ18O of 0.4‰. This is attributed to a decrease of the northward advection of the South Atlantic Waters into the western tropical North Atlantic and Caribbean Sea and relative enhanced westward flux of the tropical North Atlantic surface waters, the southern waters having lower values of 14C and δ18O than the North Atlantic ones. From 1835 to 1845, the fraction of the South Atlantic Waters transported up to Martinique Island was reduced from 25% to 15%.

Zinc phthalocyanine (ZnPc) thin films were prepared by pulsed laser deposition (PLD) using KrF laser (λ = 248 nm, τ = 5 ns). The effect of laser fluence (in the region from 10 to 100 mJ/cm2) and repetition rate of 50 and 200 Hz to the film growth and its properties was investigated. The growth of ZnPc thin film was in situ monitored using transmission measurement in ultraviolet-visible spectral range. The optical properties in conjunction with density functional theory/time-dependent density functional theory calculations suggested the growth of the film in β-phase. X-ray diffraction also revealed crystalline character of the film. The electrical properties analyzed by van der Pauw method exhibited resistivity ρ ≈ 108–1010 Ω cm. Fourier transform infrared spectroscopy analyses revealed low deterioration of PLD deposited ZnPc films. We demonstrate that, by finely tuning the deposition conditions, PLD is a successful technique for fabrication of ZnPc thin films.

Egg consumption is a major source of dietary cholesterol, a nutrient that may disrupt glucose metabolism. We prospectively evaluated the relation between egg consumption and cholesterol-intake and diabetes in 65 364 French disease-free women who responded to a validated diet history questionnaire in 1993. Egg consumption included hardboiled eggs and eggs consumed in an omelette or a mixed dish, and dietary cholesterol was estimated using a French nutrient database. Over 14 years of follow-up, 1803 incident diabetes cases were identified through self-reports, supplementary questionnaires and drug reimbursement information. Multivariable Cox regression models were adjusted for age, education, menopause, menopausal hormone therapy, hypertension and hypercholesterolaemia, BMI, physical activity, smoking, alcohol, fruit, vegetables, processed red meat, coffee and sugar and artificially sweetened beverages. No association was observed between egg consumption and risk of type 2 diabetes. When comparing women who consumed at least five eggs per week with non-consumers, the multivariable hazard ratio (HR) was found to be 1·00 (95 % CI 0·78, 1·29; across categories, Ptrend=0·11). Women in the highest quintile of dietary cholesterol had a 40 % higher rate of diabetes compared with those in the lowest quintile (HR 1·40; 95 % CI 1·19, 1·63; across quintiles, Ptrend<0·0001). A 100 mg increase of dietary cholesterol per 4184 kJ (or 1000 kcal) was associated with a 14 % increase in the risk of diabetes (HR 1·14; 95 % CI 1·02, 1·26). In this large prospective cohort, we observed an association between dietary cholesterol and type 2 diabetes, but no association with egg consumption. In the absence of a clear underlying mechanism and potential residual confounding, these results should be interpreted with caution.

Postprandial inflammation is an important factor for human health since chronic low-grade inflammation is associated with chronic diseases. Dairy products have a weak but significant anti-inflammatory effect on postprandial inflammation. The objective of the present study was to compare the effect of a high-fat dairy meal (HFD meal), a high-fat non-dairy meal supplemented with milk (HFM meal) and a high-fat non-dairy control meal (HFC meal) on postprandial inflammatory and metabolic responses in healthy men. A cross-over study was conducted in nineteen male subjects. Blood samples were collected before and 1, 2, 4 and 6 h after consumption of the test meals. Plasma concentrations of insulin, glucose, total cholesterol, LDL-cholesterol, HDL-cholesterol, TAG and C-reactive protein (CRP) were measured at each time point. IL-6, TNF-α and endotoxin concentrations were assessed at baseline and endpoint (6 h). Time-dependent curves of these metabolic parameters were plotted, and the net incremental AUC were found to be significantly higher for TAG and lower for CRP after consumption of the HFM meal compared with the HFD meal; however, the HFM and HFD meals were not different from the HFC meal. Alterations in IL-6, TNF-α and endotoxin concentrations were not significantly different between the test meals. The results suggest that full-fat milk and dairy products (cheese and butter) have no significant impact on the inflammatory response to a high-fat meal.