ISSN 0253-2778

CN 34-1054/N

2019 Vol. 49, No. 3

Display Method:
An analytical approach to degree profile of a random tree
FENG Qunqiang, ZHENG Boze
2019, 49(3): 173-181. doi: 10.3969/j.issn.0253-2778.2019.03.001
The degree profile in a random planted plane tree was considered. For any d≥1, it was proven that under suitable normalization, the number of vertices of degree d in a random planted plane tree with n edges has asymptotic normality, as n goes to infinity. The asymptotic formulae for the expectation and variance of this random variable were also given. An analytical method was employed in the proof.
Complexity of one-prey multi-predator system with impulsive effect and incomplete trophic transfer
CHENG Xian, YAN Ping, LIU Liping, ZHANG Changqin
2019, 49(3): 182-194. doi: 10.3969/j.issn.0253-2778.2019.03.002
A new one-prey multi-predator system with impulsive effect and incomplete trophic transfer was proposed. This system used a different rate of trophic absorption of predators from the rate of the conversion of consumed prey to predator in Ivlev-type functional responses. The extinction and permanence of the system with impulsive perturbation on the predators at fixed moments was investigated. And the conditions for asymptotically stable and permanence of the system was given by using Floquet theory and comparison theorem. Finally,numerical simulations demonstrated the obtained conclusions.
Maximum augmented Zagreb index of graphs with given vertex bipartiteness
GAO Fang, ZHA Shuping, WANG Zhen, ZHAO Duoduo, FANG Wei
2019, 49(3): 195-198. doi: 10.3969/j.issn.0253-2778.2019.03.003
Augmented Zagreb index (AZI) of a graph is widely used to study the heat information of heptanes and octanes in chemistry. Here graphs with given vertex bipartiteness were studied. The extremal graph having maximum AZI was given. The relationship between the extremal graph and complete bipartite graph was analyzed.
Spherically symmetric Finsler metrics with scalar flag curvature
LIU Min, SONG Weidong
2019, 49(3): 199-202. doi: 10.3969/j.issn.0253-2778.2019.03.004
Finsler geometry is Riemannian geometry without quadratic restriction,and the projectively flat Finsler metrics are very important in Finsler geometry.Here a new example of projectively flat spherically symmetric Finsler metric was given by investigating a PDE equivalent, and using Shen Zhongmin’s result, its flag curvature was obtained.
Anticipated time-dependent backward stochastic evolution equations
ZHANG Desheng, CHU Jing
2019, 49(3): 203-209. doi: 10.3969/j.issn.0253-2778.2019.03.005
A class of anticipated time-dependent backward stochastic evolution equation
The interaction solution to generalized (3+1)-dimensional shallow wave equation
2019, 49(3): 210-216. doi: 10.3969/j.issn.0253-2778.2019.03.006
By using the Hirota bilinear derivative method and the symbolic computation software Maple, the lump solution and the respiratory wave solution to the generalized (3+1)-dimensional shallow water wave equation were obtained. In combination with images, the dynamic properties (position, height, depth, velocity, and trajectory) of the lump-type soliton were studied. Finally, the interaction between different types of solutions were discussed, and it was found that lump-type solitons were phagocytosed by kink waves.
Three-dimensional numerical investigation into aerodynamic characteristics for a slender body of revolution under strong-source-field disturbance
XU Ming, WANG Zheng, LI Hua, ZHANG Shudao, HONG Tao, FU Zheng, DONG Zhiwei, AN Jianzhu, DONG Hang
2019, 49(3): 217-230. doi: 10.3969/j.issn.0253-2778.2019.03.007
A three-dimensional numerical investigation into aerodynamic characteristics for a slender body of revolution under strong-source-field disturbance was conducted for the sake of flight security.The problem was modelled as a three dimensional fluid dynamic model and then its governing equations were solved by the verified numerical methods.The solutions give not only the evolution of the flow field but also the aerodynamic characteristics of slender body of revolution,which indicates that the disturbance effects largely depend on both the incoming cruising speed of the slender body and the evolution of strong source field.
Nonlinear deformation topography of glassy nematic films under local illumination
CHENG Xingyu
2019, 49(3): 231-236. doi: 10.3969/j.issn.0253-2778.2019.03.008
Azobenzene-containing nematic glasses have an attractive application perspective in photo-driven deformation devices due to their unique photo-responsive properties. Based on the Fppl-von Kármán plate theory and a kinetics method, a numerical approach was developed to predict the nonlinear deformation topography of glassy nematic films under local illumination, and detailed results were given for two typical director fields of splay-bend and twist distributions when the spot of incident light is a circle. It is found that when the ratio of spot radius to film thickness is increased to a certain critical value, dramatic variation of the topography of the exposed part of the film occurs, accompanying the transition of Gauss curvature from positive to negative. This phenomenon is attributed to the spontaneous bending moments induced by attenuation of light intensity across film thickness, and may be applied to design new types of deformation devices with contactless control.
A multi-path optimization based video stabilization method
GAN Wenjie, ZHANG Juyong, DENG Jiansong
2019, 49(3): 237-243. doi: 10.3969/j.issn.0253-2778.2019.03.009
A multi-path optimization based video stabilization method was introduced, which is used to stabilize videos shot by hand-held devices in daily life. First, motions between two adjacent frames were estimated. Each frame of the input video was divided into a uniform mesh, and the motion of each mesh was estimated. Then the camera path was smoothed. The camera path was calculated by accumulating the motions estimated in the previous step, and a multi-path optimization based path smoothing model was designed to smooth the camera path. Finally, the stabilized video was calculated by warping each frame of the input video. The proposed method has been compared with some popular methods on running time and stabilization results. The comparison shows that the proposed method is efficient and can produce satisfactory results.
Tetrahedral mesh approximation to volume images based on variation
LI Hao, ZHANG Juyong
2019, 49(3): 244-258. doi: 10.3969/j.issn.0253-2778.2019.03.010
Tetrahedral meshes have been widely used in medicine and visualization. In general,to convert a volume image to a tetrahedral mesh,conventional methods first denoise the input volume image,then segment the image and finally construct a tetrahedral mesh.