## 2017年 第3期

2017, (3): 1-19. doi: 10.3969/j.issn.1000-5641.2017.03.001

In this paper, we studied representations of finite-dimensional Lie superalgebras over an algebraically closed field \begin{document} $\mathbb{F}$ \end{document} of characteristic p > 2. It was shown that simple modules of a finite-dimensional Lie superalgebra over \begin{document} $\mathbb{F}$ \end{document} are finite-dimensional, and there exists an upper bound on the dimensions of simple modules. Moreover, a finite-dimensional Lie superalgebra can be embedded into a finite-dimensional restricted Lie superalgebra. We gave a criterion on simplicity of modules over a finite-dimensional restricted Lie superalgebra \begin{document} ${\mathfrak{g}}$ \end{document}, and defined a restricted Lie super subalgebra, then obtained a bijection between the isomorphism classes of simple modules of \begin{document} ${\mathfrak{g}}$ \end{document} and those of this restricted subalgebra. These results are generalization of the corresponding ones in Lie algebras of prime characteristic.

2017, (3): 20-28. doi: 10.3969/j.issn.1000-5641.2017.03.002

2017, (3): 29-38. doi: 10.3969/j.issn.1000-5641.2017.03.003

2017, (3): 39-47. doi: 10.3969/j.issn.1000-5641.2017.03.004

2017, (3): 48-53. doi: 10.3969/j.issn.1000-5641.2017.03.005

2017, (3): 54-63. doi: 10.3969/j.issn.1000-5641.2017.03.006

2017, (3): 64-77, 86. doi: 10.3969/j.issn.1000-5641.2017.03.007

2017, (3): 78-86. doi: 10.3969/j.issn.1000-5641.2017.03.008

2017, (3): 87-93, 132. doi: 10.3969/j.issn.1000-5641.2017.03.009

Based on our former theoretical analysis [Yaling Yin, et al, Opt. Commun. 281(22), 5511 (2008)], we experimentally design a simple optical device to generate a neat semi-Gaussian laser beam (SGB) without diffraction fringes by using a coherence attenuator and a thin sharp blade. The coherence attenuator is composed of two organic glasses and a piece of plastic film rotated by a motor, which can efficiently decrease the coherence of the laser field. In the experiment, we use He-Ne laser as light source and obtain a 632.8 nm neat SGB without diffraction fringes with a quality factor QSGB=1:16.42 at the propagating position z=0.5 cm. The experimental results show that the generated SGB's quality factor decreases with the increasing of the propagating distance. The ascent border width of the generated SGB is independent on the waist radius and wavelength of the incident Gaussian beam, which corresponds well with the theoretical analysis. Our generated SGB can be widely used in modern optics for its asymmetric intensity profile and good propagating properties.
2017, (3): 94-98. doi: 10.3969/j.issn.1000-5641.2017.03.010

In order to study the integration and the stability of autonomous Birkhoffian systems, we propose four kinds of gradient systems to represent the autonomous Birkhoffian systems. By analysing the relationship between the gradient systems and the Birkhoffian systems, we obtain the conditions that the Birkhoffian systems can be transformed into a kind of four gradient systems. Then, we use the properties of gradient system to investigate the problems of integration and stability of the Birkhoffian systems. Finally, we give some examples to illustrate the application of the theory.
2017, (3): 99-106. doi: 10.3969/j.issn.1000-5641.2017.03.011

2017, (3): 107-113. doi: 10.3969/j.issn.1000-5641.2017.03.012

2017, (3): 114-119. doi: 10.3969/j.issn.1000-5641.2017.03.013

2017, (3): 120-132. doi: 10.3969/j.issn.1000-5641.2017.03.014

2017, (3): 133-144. doi: 10.3969/j.issn.1000-5641.2017.03.015

2017, (3): 145-152. doi: 10.3969/j.issn.1000-5641.2017.03.016