THE ESTABLISHMENT OF MATHEMATICAL MODEL OF THE TAKE-OFF SPEED OF AERIALS OF FREESTYLE SKIING

The take-off speed of freestyle skiing aerials is one of the key factors which can decide the success. However, the take-off speed depends on snow quality, circumstance condition, in-run slope angle, in-run distance, air resistance and skiers’ action. By using sports biomechanics, mathematical model and numerical simulation method and combining theory with experiment, this study sets up a mathematical model of outside circumstance and skiers’ self-adjustment, simulates the changes of inside and outside stress in each stage of sliding, calculates the parameters intuitively and then forms into speed values. The setup of this model can provide scientific guidance for ensuring necessary take-off speed for specific actions

STUDY ON THE INFLUENCE OF CHANGES OF AIR RESISTANCE ATHLETES’ TAKING-OFF SPEED IN FREESTYLE SKIING AERIALS

Freestyle skiing is a competitive sport in the open-air environment. The air resistance that athlete meets in the process of slipping, transition and entering stage determines the athletes’ taking-off speed, thus affecting the performance in competition. This paper set up a function model of frontal area and time about L, T, F, DF, F and other single action in the process completed, and establishes the function between windward area and time in specific action. It studies and analyses the influence of air resistance on athlete’s taking-off speed, combining with the results of the taking-off speed calculation software. The main findings are shown as follows: When the wind speed each increases 0.8 m/s in the leaving platform phase, athlete's taking-off speed will decrease 0.4m/s. When the wind speed is low, the change of wind direction exerts little impact on athletes’ taking-off speed

Study of the B−→K−ηηcB^-\to K^-\eta\eta_c decay due to the DDˉD\bar{D} bound state

We study the $B^-\to K^-\eta \eta_c$ decay by taking into account the $S$-wave contributions from the pseudoscalar meson--pseudoscalar meson interactions within the unitary coupled-channel approach, where the $D\bar{D}$ bound state is dynamically generated. In addition, the contribution from the intermediate resonance $K_0^*(1430)$, with $K_0^*(1430)\to K^-\eta$, is also considered. Our results show that there is a clear peak around $3730$~MeV in the $\eta \eta_c$ invariant mass distribution, which could be associated with the $D \bar{D}$ bound state. The future precise measurements of the $B^-\to K^-\eta \eta_c$ process at the Belle II and LHCb experiments could be, therefore, used to check the existence of the $D \bar{D}$ bound state, and to deepen our understanding of the hadron-hadron interactions.Comment: 8 pages, 8 figure

Study on evolution of a predator–prey model in a polluted environment

In this paper, we investigate the effects of pollution on the body size of prey about a predator–prey evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment. Firstly, an eco-evolutionary predator–prey model incorporating the rapid evolution is formulated to investigate the effects of rapid evolution on the population density and the body size of prey by applying the quantitative trait evolutionary theory. The results show that rapid evolution can increase the density of prey and avoid population extinction, and with the worsening of pollution, the evolutionary traits becomes smaller gradually. Next, by employing the adaptive dynamic theory, a long-term evolutionary model is formulated to evaluate the effects of long-term evolution on the population dynamics and the effects of pollution on the body size of prey. The invasion fitness function is given, which reflects whether the mutant can invade successfully or not. Considering the trade-off between the intrinsic growth rate and the evolutionary trait, the critical function analysis method is used to investigate the dynamics of such slow evolutionary system. The results of theoretical analysis and numerical simulations conclude that pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution leads to a smaller body size of prey due to natural selection, while the opposite is more likely to generate evolutionary branching