Bounced Model of Droplet on Moving Substrate

Firstly, we get the completely bouncing criteria Cr for droplet on moving substrate. The bouncing without splashing condition is $\mathrm{Cr}>1$. Then, we mainly research the effect of wind field for droplet, and get the completely bouncing criteria $\mathrm{Cr}_{\mathrm{wind}}$ for droplet with wind. Lastly, we get the contact angle of droplet on the moving substrate and calculate the Time Independent Reynolds Equation with $rho$ and $\mu$ are constant.Comment: 15 pages,3 figure

Dark Energy in Global Brane Universe

We discuss the exact solutions of brane universes and the results indicate the Friedmann equations on the branes are modified with a new density term. Then, we assume the new term as the density of dark energy. Using Wetterich's parametrization equation of state (EOS) of dark energy, we obtain the new term varies with the red-shift z. Finally, the evolutions of the mass density parameter $\Omega_2$, dark energy density parameter $\Omega_x$ and deceleration parameter q_2 are studied.Comment: 8 pages,4 figure

Genuine Dirac half-metal: A 2D d0-type ferromagnet Mg4N4

When the spin-orbit coupling (SOC) is absent, almost all the proposed half-metals with the twofold degenerate nodal points at the K (or K') in two-dimensional (2D) materials are misclassified as "Dirac half-metals" owing to the way graphene was utilized in the earliest studies. Actually, each band crossing point at K or K' is described by a 2D Weyl Hamiltonian with definite chirality; hence, it must be a Weyl point. To the best of our knowledge, there have been no reports of a genuine (i.e., fourfold degenerate) Dirac point half-metal in 2D yet. In this Letter, we proposed for the first time that the 2D d0-type ferromagnet Mg4N4 is a genuine Dirac half-metal with a fourfold degenerate Dirac point at the S high-symmetry point, intrinsic magnetism, high Curie temperature, 100% spin-polarization, robustness to the SOC and uniaxial and biaxial strains, and 100% spin-polarized edge states. The work can be seen as a starting point for future predictions of intrinsically magnetic materials with genuine Dirac points, which will aid the frontier of topo-spintronics researchers

Statefinder Parameters for Five-Dimensional Cosmology

We study the statefinder parameter in the five-dimensional big bounce model, and apply it to differentiate the attractor solutions of quintessence and phantom field. It is found that the evolving trajectories of these two attractor solutions in the statefinder parameters plane are quite different, and that are different from the statefinder trajectories of other dark energy models.Comment: 8 pages, 12 figures. accepted by MPL

Reconstruction of 5D Cosmological Model From Recent Observations

We use a parameterized equation of state (EOS) of dark energy to a 5D Ricci-flat cosmological solution and suppose the universe contains two major components: dark matter and dark energy. Using the recent observational datasets: the latest 182 type Ia Supernovae Gold data, the 3-year WMAP CMB shift parameter and the SDSS baryon acoustic peak, we obtain the best fit values of the EOS and two major components' evolution. We find that the best fit EOS crossing -1 in the near past $z\simeq 0.07$, the present best fit value of $w_x(0)<-1$ and for this model the universe experiences the acceleration at about $z\simeq 0.5$.Comment: 7 pages, 3 figs, Accept by IJMP

FIMO: A Challenge Formal Dataset for Automated Theorem Proving

We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO level, FIMO is currently tailored for the Lean formal language. It comprises 149 formal problem statements, accompanied by both informal problem descriptions and their corresponding LaTeX-based informal proofs. Through initial experiments involving GPT-4, our findings underscore the existing limitations in current methodologies, indicating a substantial journey ahead before achieving satisfactory IMO-level automated theorem proving outcomes