The invariants of the non-degenerate representations of the group of the pseudo-orthogonal matrices SO (p, 1)

The invariants of the non-degenerate representations of the group of pseudo-orthogonal matrices SO(p, 1) are constructed.     

Generalised twists, , and the p-energy over a space of measure preserving maps

Let be a bounded Lipschitz domain and consider the energy functional

with p]1,∞[ over the space of measure preserving maps

In this paper we introduce a class of maps referred to as generalised twists and examine them in connection with the Euler–Lagrange equations associated with over . The main result is a surprising discrepancy between even and odd dimensions. Here we show that in even dimensions the latter system of equations admit infinitely many smooth solutions, modulo isometries, amongst such maps. In odd dimensions this number reduces to one. The result relies on a careful analysis of the full versus the restricted Euler–Lagrange equations where a key ingredient is a necessary and sufficient condition for an associated vector field to be a gradient.     

两种新型双极有机小分子发光材料的合成与发光

设计和合成了两种新的具有“双极(bipolar)”性质和发光性能的有机小分子化合物N-[4-(5-(2-苯基喹啉-4)-1,3,4-噁二唑-2)苯基]-N'-苯基-N,N'-二苯基-1,1'-联苯基-4,4'-二胺(TPDOPQ)和N,N'-双{4-[5-(2-苯基喹啉-4-基)-1,3,4-噁二唑-2]苯基}-N,N'-二苯基-1,1'-联苯基-4,4'-二胺[TPD(OPQ)₂]. 用¹H NMR, MS和元素分析进行了表征, 研究了化合物的热稳定性和光致发光性质, 并用循环伏安法测定了其电化学性能. 结果表明, 这两种合成的有机化合物同时具备空穴传导和电子输入双重功能, 光致发光性能优良, 热稳定性好, 能形成均衡薄膜, 因此可作为制作有机电致发光器件的候选材料.     

VORTEX-INDUCED VIBRATIONS OF TWO SIDE-BY-SIDE EULER-BERNOULLI BEAMS

Vortex-induced vibration of two side-by-side elastic beams in a cross flow is numerically studied. The two beams are identical and fixed at both ends. In the numerical approach, the Euler-Bernoulli beam theory is used to model the beam vibration, and the laminar Navier-Stokes equations are solved to give the flow field. The flow equations are resolved using a finite element method and the flow-induced forces are calculated at every time step in order to correctly reflect the fluid-beam interaction. The beam response is calculated using the modal analysis method. Free vibrations of the two beams with three pitch ratios, T/D=1·13, 1·7 and 3·0, where T is the gap between the centers of the two beams and D is the beam diameter, are simulated at Re=800. Results obtained are compared with experimental measurements and other numerical results obtained assuming a two-degree-of-freedom (2-d.o.f.) model. The agreement is good in general. Correlation analysis is carried out, showing that the phase relation is different for differentT /D. The short-time Fourier transform (STFT) method is used to carry out the spectral analysis, along with the conventional auto-regressive moving averaging (ARMA) method for comparison. The STFT analysis shows that the time evolution of fluid force and beam vibration for T/D=1·13 and 3·0 are stationary. For theseT /D ratios, the STFT results are consistent with the ARMA results, but give a clearer picture of the higher order harmonics. For T/D=1·7, the time evolution is non-stationary. The STFT analysis shows that there are three types of frequency spectrum for the fluid force, with one, two, and three dominant frequencies respectively. The spectra intermittently change in a random way during the evolution. The ARMA results, though consistent with previous experiments, can only reveal a particular feature of the three different types of spectrum. This suggests that the STFT method is more appropriate to analyze the spectra of non-stationary time series in the study of flow-induced vibrations.