Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time, we find that when Nash equilibrium exists the pay off function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example where quantum game and classical game may differ. When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.Comment: 5 pages and 3 figure

Discrete mechanics Based on Finite Element Methods

Discrete Mechanics based on finite element methods is presented in this paper. We also explore the relationship between this discrete mechanics and Veselov discrete mechanics. High order discretizations are constructed in terms of high order interpolations.Comment: 14 pages, 0 figure

THE ACUTE EFFECTS OF KNEE ON DYNAMIC HAMSTRING STRETCH DURING SIDE-CUTTING IN FEMALE ATHLETES

The purpose of this study was to investigate the effects of dynamic hamstring stretch on knee joint biomechanical parameters during side-step cutting in female athletes. Methods: Ten participants performed 45-degree side-step cutting for the pre-test and post-test and then dynamic hamstring stretch included single-leg standing with straight leg raise and straight leg hip flexion intervened after pre-test, respectively. Data were collected synchronously by 8 VICON cameras (250 Hz), 1 Kistler force plate (1000 Hz), and 5 Delsys wireless EMG sensors (2000 Hz) during side-step cutting. Results: Participants showed significantly greater hamstrings activation and muscle co-contraction (H/Q ratio) on post-test during deceleration phase at the peak valgus moment. Vertical ground reaction force and knee varus moment decreased significantly on post-test during deceleration phase at the peak varus moment.. Conclusion: Dynamic stretch could increase the activation of the hamstring, and improved buffering impact of the knee joint

Proton mass decomposition

We report the results on the proton mass decomposition and also on the related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of $N_f = 2+1$ DWF configurations with three lattice spacings and volumes, and several pion masses including the physical pion mass. With 1-loop perturbative calculation and proper normalization of the glue operator, we find that the $u, d,$ and $s$ quark masses contribute 9(2)\% to the proton mass. The quark energy and glue field energy contribute 31(5)\% and 37(5)\% respectively in the $\overline{MS}$ scheme at $\mu = 2$ GeV. The trace anomaly gives the remaining 23(1)\% contribution. The $u,d,s$ and glue momentum fractions in the $\overline{MS}$ scheme are consistent with the global analysis at $\mu = 2$ GeV.Comment: 6 pages. Proceedings of the 35th International Symposium on Lattice Field Theory (Lattice2017), Granada, Spai