Universal Time Scale for Thermalization in Two-dimensional Systems

The Fermi-Pasta-Ulam-Tsingou problem, i.e., the problem of energy equipartition among normal modes in a weakly nonlinear lattice, is here studied in two types of two-dimensional (2D) lattices, more precisely in lattices with square cell and triangular cell. We apply the wave-turbulence approach to describe the dynamics and find multi-wave resonances play a major role in the transfer of energy among the normal modes. We show that, in general, the thermalization time in 2D systems is inversely proportional to the squared perturbation strength in the thermodynamic limit. Numerical simulations confirm that the results are consistent with the theoretical prediction no matter systems are translation-invariant or not. It leads to the conclusion that such systems can always be thermalized by arbitrarily weak many-body interactions. Moreover, the validity for disordered lattices implies that the localized states are unstable.Comment: 6 pages, 4 figure

Existence and Duality of Generalized ε-Vector Equilibrium Problems

We consider a generalized ε-vector equilibrium problem which contain vector equilibrium problems and vector variational inequalities as special cases. By using the KKM theorem, we obtain some existence theorems for the generalized ε-vector equilibrium problem. We also investigate the duality of this generalized ε-vector equilibrium problem and discuss the equivalence relation between solutions of primal and dual problems

Body Mass Index of Male Youths Aged 18-20 Years of the Han Nationality Living in Different Regions of China

The study was conducted to assess the nutritional status and levels of body mass index (BMI, kg/m2) and to evaluate the geographical distribution of male youths of the Han nationality in China. In total, 60,773 male youths, aged 18-20 years, of the Han nationality, were categorized into underweight, normal-weight, overweight, and obesity according to the international adult BMI cut-offs. Different levels of nutritional status and BMI of male youths of the Han nationality were compared among different areas. The mean BMI for the whole country was 20.6 in urban areas and 20.0 in rural areas. BMI increased from 20.1 among 18-year old youths to 20.5 among 20-year old youths. The prevalence of underweight among the male youths was 21.6%, while the prevalence of overweight and obesity were 4.6% and 0.6% respectively. For urban youths, the prevalence of underweight, overweight, and obesity were 21.0%, 6.8%, and 1.1% respectively, while these were, respectively, 21.9%, 3.3%, and 0.3% for rural youths. The nutritional status of the male youths in North-China was at the highest level (21.1) among the six areas, and the prevalence of underweight, overweight, and obesity were 14.3%, 9.1%, and 1.4% respectively. The highest prevalence of underweight was 29.8% in the North-West region, and the lowest prevalence of overweight was 2.2% in the South-Middle region, while the lowest prevalence of obesity was 0.2% in the South-West region. The nutritional status of the male youths was significantly different among different areas. Underweight was still prevalent in all male youth groups. Nonetheless, overweight was more prevalent among urban youths than among rural youths and was more prevalent in the North region than in the South region