Multifractal analysis of the Birkhoff sums of Saint-Petersburg potential

Let $((0,1], T)$ be the doubling map in the unit interval and $\varphi$ be the Saint-Petersburg potential, defined by $\varphi(x)=2^n$ if $x\in (2^{-n-1}, 2^{-n}]$ for all $n\geq 0$. We consider the asymptotic properties of the Birkhoff sum $S\_n(x)=\varphi(x)+\cdots+\varphi(T^{n-1}(x))$. With respect to the Lebesgue measure, the Saint-Petersburg potential is not integrable and it is known that $\frac{1}{n\log n}S\_n(x)$ converges to $\frac{1}{\log 2}$ in probability. We determine the Hausdorff dimension of the level set $\{x: \lim\_{n\to\infty}S\_n(x)/n=\alpha\} \ (\alpha>0)$, as well as that of the set $\{x: \lim\_{n\to\infty}S\_n(x)/\Psi(n)=\alpha\} \ (\alpha>0)$, when $\Psi(n)=n\log n, n^a$ or $2^{n^\gamma}$ for $a>1$, $\gamma>0$. The fast increasing Birkhoff sum of the potential function $x\mapsto 1/x$ is also studied.Comment: 17 page

Associations of Educational Attainment, Occupation, Social Class and Major Depressive Disorder among Han Chinese Women

Background The prevalence of major depressive disorder (MDD) is higher in those with low levels of educational attainment, the unemployed and those with low social status. However the extent to which these factors cause MDD is unclear. Most of the available data comes from studies in developed countries, and these findings may not extrapolate to developing countries. Examining the relationship between MDD and socio economic status in China is likely to add to the debate because of the radical economic and social changes occurring in China over the last 30 years. Principal findings We report results from 3,639 Chinese women with recurrent MDD and 3,800 controls. Highly significant odds ratios (ORs) were observed between MDD and full time employment (OR = 0.36, 95% CI = 0.25–0.46, logP = 78), social status (OR = 0.83, 95% CI = 0.77–0.87, logP = 13.3) and education attainment (OR = 0.90, 95% CI = 0.86–0.90, logP = 6.8). We found a monotonic relationship between increasing age and increasing levels of educational attainment. Those with only primary school education have significantly more episodes of MDD (mean 6.5, P-value = 0.009) and have a clinically more severe disorder, while those with higher educational attainment are likely to manifest more comorbid anxiety disorders. Conclusions In China lower socioeconomic position is associated with increased rates of MDD, as it is elsewhere in the world. Significantly more episodes of MDD occur among those with lower educational attainment (rather than longer episodes of disease), consistent with the hypothesis that the lower socioeconomic position increases the likelihood of developing MDD. The phenomenology of MDD varies according to the degree of educational attainment: higher educational attainment not only appears to protect against MDD but alters its presentation, to a more anxious phenotype

Spatiotemporal variability of soil nutrients and the responses of growth during growth stages of winter wheat in northern China.

Studying soil nutrient variability and its effect on the growth and development of crops under a traditional tillage mode is the foundation for comprehensively implementing precision agriculture policies at the field scale and ensuring excellent crop management. In this paper, a 28.5 hm2 winter wheat field under the traditional cultivation model in Tianzhuang town of Huantai County was selected as the research area. The mesh point method was utilized for sampling (60×60 m), and the characteristics of soil available nitrogen (AN), available phosphorus (AP) and available potassium (AK) variations in the before sowing, reviving, jointing, and filling stages of winter wheat were analyzed using geostatistical and GIS methods. Moreover, Pearson correlation analysis was used to study the response of wheat growth and development to soil nutrient variations. As the growth stages progressed, 1) each nutrient showed the characteristics of low-high-low and moderate variability. The highest AN and AK contents were found at the reviving stage, while AP reached a turning point at the jointing stage. The order of variability of each nutrient was AN>AP>AK. 2) The nutrient variations first increased and then decreased and showed medium to strong spatial correlation. The three nutrients were strongly spatially correlated in the before sowing stage and moderately spatially correlated during the reviving stage. During the jointing and filling stages, AN had moderate spatial correlation, and AP and AK had strong spatial correlation. The spatial correlation of each nutrient was the weakest in the reviving stage, and the spatial correlation of AN was strongest in the before sowing stage, while the spatial correlations of AP and AK were strongest in the jointing stage. The spatial correlation of each soil nutrient decreased from the before sowing stage to the reviving stage and from the jointing stage to the filling stage, and the spatial correlation increased from the reviving stage to the jointing stage. 3) The soil nutrient content first increased and then decreased, and the grades of the nutrients gradually decreased. 4) The correlation between soil nutrients and wheat growth gradually increased. AN had the highest correlation with wheat growth, followed by AK and AP. The effect of soil nutrients on the growth of wheat at the reviving stage was greater than the effect of nutrients in the current stage. The growth of wheat at the jointing stage was mainly influenced by nutrients in the current stage, while the growth of wheat at the filling stage was influenced by the nutrient contents of both the previous and current stages. Thus, the date of fertilizer supplementation should be postponed properly. In this study, the soil nutrient dynamics and their influence on the growth of wheat during the winter wheat growth period under the traditional field model were well described, and these results could provide a theoretical basis for the precision management of soil nutrients in the northern winter wheat area where the planting environment and cultivation management are relatively uniform

Multi-objective optimization design for the multi-bubble pressure cabin in BWB underwater glider

In this paper, multi-objective optimization of a multi-bubble pressure cabin in the underwater glider with Blended-Wing-Body (BWB) is carried out using Kriging and the Non-dominated Sorting Genetic Algorithm (NSGA-II). Two objective functions are considered: buoyancy-weight ratio and internal volume. Multi-bubble pressure cabin has a strong compressive capacity, and makes full use of the fuselage space. Parametric modeling of the multi-bubble pressure cabin structure is automatic generated using UG secondary development. Finite Element Analysis (FEA) is employed to study the structural performance using the commercial software ANSYS. The weight of the primary structure is determined from the volume of the Finite Element Structure (FES). The stress limit is taken into account as the constraint condition. Finally, Technique for Ordering Preferences by Similarity to Ideal Solution (TOPSIS) method is used to find some trade-off optimum design points from all non-dominated optimum design points represented by the Pareto fronts. The best solution is compared with the initial design results to prove the efficiency and applicability of this optimization method. Keywords: Multi-objective optimization, Multi-bubble pressure cabin, Finite element analysis, Kriging, NSGA-II, TOPSI

Pediatric perforated appendicitis diagnosis based on the C-reactive protein/prealbumin ratio

Abstract Pediatric perforated appendicitis, prone to multiple complications, necessitates identifying potential serum biomarkers for early diagnosis and intervention. A cross-sectional study was conducted on patients under 16 with acute appendicitis, admitted to Hainan Women and Children’s Medical Center from January 2019 to July 2023. The patients were categorized into perforated and non-perforated groups. Among the 313 included patients, 106 (33.87%, 95% CI 28.59–39.14%) developed perforation. The C-reactive protein to prealbumin ratio (CPA) showed a significant difference between the perforated and non-perforated groups [6.63 (2.9–13.02) vs. 0.7 (0.11–2.18), p  3 predicting perforation was 76.2%, with a specificity of 81.6%, and an AUC of 0.816 (95% CI 0.747–0.886, p  2.2 predicting perforation was 85%, with a specificity of 85.7%, and an AUC of 0.919 (95% CI 0.859–0.979, p  3 and CPA > 2.2 can predict perforated appendicitis in patients aged 4–9 and 9–16, respectively

Assessments of Water-Soluble Inorganic Ions and Heavy Metals in Atmospheric Dustfall and Topsoil in Lanzhou, China

The chemical features of atmospheric dustfall and topsoil in the same region could reflect the processes of the migration, transport, and diffusion of pollutants in the atmospheric-soil system. Samples of atmospheric dustfall and topsoil were collected in Lanzhou City. The contents and correlation of water-soluble inorganic ions (WSIIs) and heavy metals in dustfall and topsoil were analyzed, the sources of heavy metals and WSIIs in dustfall were distinguished, and the potential ecological risks of heavy metals in dustfall and topsoil were evaluated. The highest contents of WSIIs are SO42− (18,594 mg·kg−1) and Ca2+ (10,070 mg·kg−1) in dustfall, and for SO42− (8271 mg·kg−1) and Na+ (1994 mg·kg−1) in topsoil. The concentrations of heavy metals (Pb, Cu, Zn, Cr, Cd, and Ni) in dustfall are considerably higher than those in topsoil. Combustion of biomass and coal, transportation and industrial activities are the major anthropogenic sources of WSIIs and heavy metals in Lanzhou. Pollution of heavy metals except Cr and Ni in dustfall, and Cu, Cr, and Ni in topsoil was up to different degrees, where the pollution of Cd was serious. The risk of Cd in dustfall is high while moderate in topsoil. This research could offer a reference for the atmospheric particle pollution prevention and control in Lanzhou

Splitting an Impacting Droplet by a Superhydrophobic Wire

Splitting a droplet into several segments is of great significance in many applications such as the detection of tiny liquid samples, whereas the surface tension tends to hold liquid to remain as one drop, causing difficulty in separating the droplet into pieces. In this work, a method is proposed to split an impacting droplet with a relatively high velocity or Weber number into two halves by a superhydrophobic wire. The effects of the wire wettability and the impact velocity of the droplet on the splitting phenomena and the efficacy to an anti-icing application are investigated. Compared to a hydrophilic wire, a superhydrophobic wire splits an impacting droplet at a relatively high speed of the Weber number greater than 3.1 and inhibits ice accretion at the temperature as low as −20 °C. The results suggest that a superhydrophobic wire can be utilized in the droplet manipulation and anti-icing applications such as power lines in high latitude areas