On Atkin-Swinnerton-Dyer congruence relations

In this paper we exhibit a noncongruence subgroup \G whose space of weight 3 cusp forms S_3(\G) admits a basis satisfying the Atkin-Swinnerton-Dyer congruence relations with two weight 3 newforms for certain congruence subgroups. This gives a modularity interpretation of the motive attached to S_3(\G) by A. Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.Comment: 25 page

The Effects of Minimal Length, Maximal Momentum and Minimal Momentum in Entropic Force

In this paper, the modified entropic force law is studied by using a new kind of generalized uncertainty principle which contains a minimal length, a minimal momentum and a maximal momentum. Firstly, the quantum corrections to the thermodynamics of a black hole is investigated. Then, according to Verlinde's theory, the generalized uncertainty principle (GUP) corrected entropic force is obtained. The result shows that the GUP corrected entropic force is related not only to the properties of the black holes, but also to the Planck length and the dimensionless constants $\alpha _{\rm{0}}$ and $\beta _{\rm{0}}$. Moreover, based on the GUP corrected entropic force, we also derive the modified Einstein's field equation (EFE) and the modified Friedmann equation.Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1604.0470

Ethyl 4-hy­droxy-6-(4-hy­droxy­phen­yl)-4-trifluoro­methyl-2-sulfanyl­idene-1,3-diazinane-5-carboxyl­ate ethanol monosolvate

The title compound, C14H15F3N2O4S·C2H5OH, was prepared by reaction of 4-hy­droxy­benzaldehyde, ethyl 4,4,4-trifluoro-3-oxobutano­ate and thio­urea. The hexa­hydro­pyrimidine ring adopts a half-chair conformation, the mean plane formed by the ring atoms excluding the C atom bonded to the eth­oxy­carbonyl group has an r.m.s. deviation of 0.0333 Å, and the dihedral angle between this plane and the benzene ring is 56.76 (5)°. The mol­ecular conformation is stabilized by an intra­molecular O—H⋯O hydrogen bond, generating an S(6) ring. The crystal structure is stabilized by inter­molecular O—H⋯O, O—H⋯S, N—H⋯O and N—H⋯S hydrogen bonds. The ethyl group of the ester unit is disordered over two positions, with an occupancy ratio of 0.757 (10):0.243 (10)

Berry's phase for coherent states of Landau levels

The Berry phases for coherent states and squeezed coherent states of Landau levels are calculated. Coherent states of Landau levels are interpreted as a result of a magnetic flux moved adiabatically from infinity to a finite place on the plane. The Abelian Berry phase for coherent states of Landau levels is an analog of the Aharonov- Bohm effect. Moreover, the non-Abelian Berry phase is calculated for the adiabatic evolution of the magnetic field B.Comment: 4 pages, 1 figur

Structural and Chemical Orders in Ni64.5Zr35.5 Metallic Glass by Molecular Dynamics Simulation

The atomic structure of Ni64.5Zr35.5 metallic glass has been investigated by molecular dynamics (MD) simulations. The calculated structure factors from the MD glassy sample at room temperature agree well with the X-ray diffraction (XRD) and neutron diffraction (ND) experimental data. Using the pairwise cluster alignment and clique analysis methods, we show that there are three types dominant short-range order (SRO) motifs around Ni atoms in the glass sample of Ni64.5Zr35.5, i.e., Mixed-Icosahedron(ICO)-Cube, Twined-Cube and icosahedron-like clusters. Furthermore, chemical order and medium-range order (MRO) analysis show that the Mixed-ICO-Cube and Twined-Cube clusters exhibit the characteristics of the crystalline B2 phase. Our simulation results suggest that the weak glass-forming ability (GFA) of Ni64.5Zr35.5 can be attributed to the competition between the glass forming ICO SRO and the crystalline Mixed-ICO-Cube and Twined-Cube motifs

A study on Fast Predicting the Washability Curve of Coal

AbstractA pure new MATLAB-based image recognition system was developed to compute the coal particle picture of same grain class through the digital image processing method, 13 image feature parameters was selected to be most representative image characteristic parameters. Take the above parameters as the input of RBF neural network, the density level of coal particles could be estimated, combined with the real ash content of each density level, the washability curve could be drawed. Experement show,the absolute error of the total ash is 2.375%,which is Slightly big in the China standards of coal preparation (GB/T477 -1998); the related coefficients of each indicator in both actual and predicted float-and-sink material are all close to 1, while the curves of λ, β, θ and δ are very similar and the deviation of ξ curve is relatively large