Abstract:
In the title compound, C21H25NO4, the dihydropyridine ring adopts a flattened boat conformation. The N atom and the sp3 C atom deviate in the same direction from the mean plane of the other four C atoms, by 0.269 (6) and 0.111 (6) , respectively. This mean plane is inclined to the 4-methoxyphenyl ring by 87.3 (5)°. The cyclohexenone ring has a sofa conformation with the C atom bearing the methyl groups deviating from the mean plane through the other five C atoms by 0.628 (6) . There is a short C—H...O hydrogen bond in the molecule. In the crystal, molecules are linked by an N—H...O hydrogen bond to form chains propagating along the c-axis direction.

Abstract:
We investigate the spectrum and eigenstates of ultracold fermionic atoms in the bilayer honeycomb optical lattice. In the low energy approximation, the dispersion relation has parabolic form and the quasiparticles are chiral. In the presence of the effective magnetic field, which is created for the system with optical means, the energy spectrum shows an unconventional Landau level structure. Furthermore, the experimental detection of the spectrum is proposed with the Bragg scattering techniques.

Abstract:
We study quantum phases of ultracold bosonic atoms in a two-dimensional optical superlattice. The extended Bose-Hubbard model derived from the system of ultracold bosonic atoms in an optical superlattice is solved numerically with Gutzwiller approach. We find that the modulated superfluid(MS), Mott-insulator (MI) and density-wave(DW) phases appear in some regimes of parameters. The experimental detection of the first order correlations and the second order correlations of different quantum phases with time-of-flight and noise-correlation techniques is proposed.

Abstract:
We study a two-dimensional fermionic square lattice, which supports the existence of two-dimensional Weyl semimetal, quantum anomalous Hall effect, and $2\pi$-flux topological semimetal in different parameter ranges. We show that the band degenerate points of the two-dimensional Weyl semimetal and $2\pi$-flux topological semimetal are protected by two distinct novel hidden symmetries, which both corresponds to antiunitary composite operations. When these hidden symmetries are broken, a gap opens between the conduction and valence bands, turning the system into a insulator. With appropriate parameters, a quantum anomalous Hall effect emerges. The degenerate point at the boundary between the quantum anomalous Hall insulator and trivial band insulator is also protected by the hidden symmetry.

Abstract:
First, we study a square fermionic lattice that supports the existence of massless Dirac fermions, where the Dirac points are protected by a hidden symmetry. We also consider two modified models with a staggered potential and the diagonal hopping terms, respectively. In the modified model with a staggered potential, the Dirac points exist in some range of magnitude of the staggered potential, and move with the variation of the staggered potential. When the magnitude of the staggered potential reaches a critical value, the two Dirac points merge. In the modified model with the diagonal hopping terms, the Dirac points always exist and just move with the variation of amplitude of the diagonal hopping. We develop a mapping method to find hidden symmetries evolving with the parameters. In the two modified models, the Dirac points are protected by this kind of hidden symmetry, and their moving and merging process can be explained by the evolution of the hidden symmetry along with the variation of the corresponding parameter.

Abstract:
We present a new general and much simpler scheme to construct various quantum phase transitions (QPTs) in spin chain systems with matrix product ground states. By use of the scheme we take into account one kind of matrix product state (MPS) QPT and provide a concrete model. We also study the properties of the concrete example and show that a kind of QPT appears, accompanied by the appearance of the discontinuity of the parity absent block physical observable, diverging correlation length only for the parity absent block operator, and other properties which are that the fixed point of the transition point is an isolated intermediate-coupling fixed point of renormalization flow and the entanglement entropy of a half-infinite chain is discontinuous.

Abstract:
A new type of multi-point multi-wavelength pyrometer for solid propellant rocket engine flame distribution measurement was developed successfully. The instrument can record the radiation fluxes of 8 wavelengths for uniformly distributed 6 points on the target surface, which are well defined by the holes on the field stop lens. The fast-response pyrometer with the specially designed synchronous data acquisition system can assure that the recorded thermal radiation fluxes of different spectrum region are of the same time and the same true temperature even with dramatically changed targets.

Abstract:
The honeycomb lattice possesses a novel energy band structure, which is characterized by two distinct Dirac points in the Brillouin zone, dominating most of the physical properties of the honeycomb structure materials. However, up till now, the origin of the Dirac points is unclear yet. Here, we discover a hidden symmetry on the honeycomb lattice and prove that the existence of Dirac points is exactly protected by such hidden symmetry. Furthermore, the moving and merging of the Dirac points and a quantum phase transition, which have been theoretically predicted and experimentally observed on the honeycomb lattice, can also be perfectly explained by the parameter dependent evolution of the hidden symmetry.

Abstract:
In quantum mechanics, accidental degeneracy refers to the energy degeneracy which occurs coincidently, without any protection of symmetry. Here, we prove a theorem that any two-fold degeneracy (accidental or not) in a quantum system is protected by a novel hidden symmetry, which can be expressed by an antiunitary operator with its square being $-1$. In this sense, the so-called accidental degeneracy is not really accidental, which acctually implies a hidden antiunitary symmetry (HAS). The above theorem has important application in the accidental degeneracy problem in the energy bands of crystals. As a typical example, a Weyl semimetal phase in a cubic lattice is introduced, where the degenerate Weyl nodes are exactly protected by the HAS.