Sharp Stability of Log-Sobolev and Moser-Onofri inequalities on the Sphere

In this paper, we are concerned with the stability problem for endpoint conformally invariant cases of the Sobolev inequality on the sphere $\mathbb{S}^n$. Namely, we will establish the stability for Beckner's log-Sobolev inequality and Beckner's Moser-Onofri inequality on the sphere. We also prove that the sharp constant of global stability for the log-Sobolev inequality on the sphere $\mathbb{S}^n$ must be strictly smaller than the sharp constant of local stability for the same inequality. Furthermore, we also derive the non-existence of the global stability for Moser-Onofri inequality on the sphere $\mathbb{S}^n$.Comment: 22 page

On the equivalence of the Nernst theorem and its consequence

One general consequence of the Nernst theorem is derived, i.e., the various heat capacities of a thermodynamic system under different constraints approach zero as the temperature approaches absolute zero. The temperature dependence of the heat capacity of any thermodynamic system at ultra-low temperatures is revealed through this consequence. Moreover, the general form and the simplest expression of the heat capacities of thermodynamic systems at ultra-low temperatures are deduced. Some significant discussion and results are given. One new research method is provided by using this consequence. Finally, the equivalence between the Nernst theorem and its consequence is rigorously proved, so that this consequence may be referred to another description of the third law of thermodynamics

Relationship of Family Environment, Psychological Resilience, Campus Bullying with Tobacco Use among Preadolescents

Objective. To explore the relationship between family environment, psychological resilience, campus bullying and tobacco use in early adolescence. Methods. According to the principle of cluster sampling, 4,792 students from grade 4 to grade 6 in five primary schools in Baise City and county were selected from February to November 2018, including 2,522 males (52.63%), 2,236 females (46.66%)and 34 missing genders (0.71%); the average age was (11.8 ± 0.5) years; 2,721 students in urban areas (56.78%) and 2,071 students in county towns (43.22%); 4,313 Zhuang (90.00%), 365 Han (7.62%), 98 other ethnic groups (Yao, Miao, Yi, etc.) (2.05%). The General Family Environment Questionnaire, Adolescent Mental Resilience Scale, School Bullying Questionnaire, and Tobacco Use Questionnaire were used for evaluation, and logistic regression was used to analyze the effect relationship between the study variables. Results. 467 people tried to smoke, and the total detection rate was 9.75%. The number of smokers was 334, and the total detection rate was 6.97%. Boys’ tobacco attempt and smoking behavior were higher than girls (χ2 were 57.230 and 56.013, P < 0. 001). Multivariate logistic regression analysis showed that the risk of tobacco attempt of boys was 2.37 times thanthat of girls (OR = 0.468, 95% CI 0.377 ~ 0.582), the risk of smoking in boys is 2.5 times that in girls 32 times (OR = 0.422, 95% CI 0.324 ~ 0.551); older adolescents had more tobacco attempts (OR = 1.609, 95% CI 1.446 ~ 1.791)and smoking behavior (OR = 2.026, 95% CI 1.776 ~ 2.310); campus bullying increased the risk of smoking behavior among adolescents (OR = 1.106, 95% CI 1.073 ~ 1.140). Psychological resilience (personal strength), family intimacy and family rules can effectively reduce the risk of adolescent tobacco attempts (personal strength, OR = 0.964, 95% CI = 0.951 ~ 0.976; family intimacy, OR = 0.946, 95% CI 0.892 ~ 0.984; family rules, OR = 0.949, 95% CI 0.930 ~ 0.965) and smoking behavior (personal strength, OR = 0.962, 95% CI 0.947 ~ 0.977; family intimacy, OR = 0.937, 95% CI 0.885 ~ 0.992; family rules, OR = 0.952, 95% CI 0.932 ~ 0.973). Conclusion. Campus bullying increases the risk of smoking behavior among adolescents. Psychological resilience (personal strength), family intimacy and family rules can effectively reduce teenagers’ tobacco attempts and smoking behavior

Solar-driven sodium thermal electrochemical converter coupled to a Brayton heat engine: Parametric optimization

[EN]A novel high-efficiency device comprised of three subsystems, a solar collector, a sodium thermal electrochemical converter, and a non-recuperative Brayton heat engine, is modeled by taking into account the main internal and external irreversibility sources. The model extends previous works in which the heat waste of the electrochemical converter is used as heat input in a Brayton gas turbine to study its performance and feasibility when a solar energy input is added. The operative working temperatures of three subsystems are determined by energy balance equations. The dependence of the efficiency and power output of the overall system on the solar concentration ratio, the current density, the thickness of the electrolyte, and the adiabatic pressure ratio (or temperature ratio) of the Brayton cycle is discussed in detail. The maximum efficiencies and power output densities are calculated and the states of the maximum efficiency-power density are determined under different given solar concentration ratios. The parametric optimum selection criteria of a number of critical parameters of the overall system are provided and the matching problems of the three subsystems are properly addressed. It is found that under a solar concentration around 1350, the maximum efficiency and power output density of the proposed hybrid system can reach, respectively, 29.6% and 1:23 105 W/m2. These values amount approximately 32.7% and 156% compared to those of the solar-driven sodium thermal electrochemical converter system without the bottoming Brayton cycle. The Pareto front obtained from numerical multiobjective and multi-parametric methods endorses previous findings.China Scholarship Council under the State Scholarship Fund (No. 201806310020), People’s Republic of China