A new numerical method based on LZB is proposed for nonsmooth dynamics on astronautics separation device in guided stage. Using Euler-Lagrange equations and the LZB method, the general calculating framework describing the whole dynamical motion including contact, collision with friction is established. Compared with FEM simulation time, numerical simulation implies that this method is valid.

The size effect of the raw B powder on the MgB₂ phase formation is studied by the technique of in-situ high temperature resistivity (HT-ρT) measurement. The onset temperature, T_onset, and the completion temperature, T_PF, of the phase formation are determined directly during the ongoing thermal process. These two temperatures, T_onset and T_PF of the sample synthesized using nanometer B and Mg powders (NanoB-MgB₂) are 440 and 490℃, respectively, the same as those of the sample using micrometer B and nanometer Mg powders (MicroB-MgB₂). This indicates that the phase formation temperature of MgB₂ do not depend on the B powder size. The upper limit of the sintering temperature, T_N, above which the sample loses superconductivity, is below 750℃ for NanoB-MgB₂, much lower than 980℃ for the MgB₂ prepared using micron-sized B powder and millimeter sized Mg powder (DM-MgB₂). In comparison with the sample directly sintered at 650℃<T_N, an interesting, irreversible transformation in the crystal structure of the MgB₂ phase is observed with the sample going through the stages of initial sintering at 750℃, then re-sintering at 650℃ in an Mg-rich environment after the processes of regrinding and pressing.

Superconducting MgB₂ thin films were fabricated on Mg substrate by using the hybrid physical-chemical vapor deposition (HPCVD) technique. The film has a T_c(onset)＝39.5K. The SEM images demonstrate that crystallite is compact. X-ray diffraction pattern indicates the film is polycrystalline with no preferring growing direction. The grain size is about 400nm-1.0μm. These results show that it is feasible to deposit MgB₂ thin films directly on Mg by HPCVD technique. It is advantaged to fabricate MgB₂ fibers directly on SiC carrier and MgB₂ superconductive wires.

In a recent paper, A. Reid, Shicheng Wang and Qing Zhou proved the following theorem: Let M₁ and M₂ be two closed aspherical Seifert 3-manifolds, whose fundamental groups have same rank. If the map f: M₁→M₂ is (π₁-surjective, i.e. f*π₁(M₁)=π₁(M₂), then f is of non-zero degree. Using this result, they also constructed a minimal Haken manifold and studied the epimorphism between the fundamental groups of 3-manifolds. In this paper, we prove that if we replace the condition "π₁-surjective" by "π₁-finite index", i.e. [π₁(M₂) : f*π₁(M₁)]<∞, the conclusion degf≠0 remans true.