Heavy Snow will turn to a natural disaster, and will bring big economic losses. The authors hope to establish a mathematic model and a plan to illustrate how to sweep off the snow on main roads in a city so as to ensure the smooth flow of traffic. The research will become a basis on which the government can workout some plans against the snow disasters. Firstly we made some assumptions, then studied the working process of snow-sweepers and derived a snow sweeping model. Based on this model, the relationship between working speed of snow-sweeper and snow thickness, a working model of snow-sweeper, and minimum sets of snow-sweeper needed were established. A deep-searching model and a model of snow-sweeping tree, and a computer program in PASCAL to determine the minimum number of snow-sweeper and the snow sweeping plans on main roads were obtained. We tried several solutions to deal with this problem, such as using piecewise curve fitting to transform a formula h~ vc relating to a cubic equation operation to formula vc~ h ,using trial and error method to determine the minimum number of snow sweepers, using deep searching and tree structure in one-stroke processing in a complicated two-way road system, and also a matrix to deal with the deep searching.

In the research of computer vision and machine perception, 3D objects are usually represented by 2-manifold triangular meshes M. In this paper, we present practical and efficient algorithms to construct iso-contours, bisectors, and Voronoi diagrams of point sites onM, based on an exact geodesic metric. Compared to euclidean metric spaces, the Voronoi diagrams onMexhibit many special properties that fail all of the existing euclidean Voronoi algorithms. To provide practical algorithms for constructing geodesicmetric- based Voronoi diagrams onM, this paper studies the analytic structure of iso-contours, bisectors, and Voronoi diagrams onM. After a necessary preprocessing of model M, practical algorithms are proposed for quickly obtaining full information about iso-contours, bisectors, and Voronoi diagrams on M. The complexity of the construction algorithms is also analyzed. Finally, three interesting applications—surface sampling and reconstruction, 3D skeleton extraction, and point pattern analysis—are presented that show the potential power of the proposed algorithms in pattern analysis.

We study the modularity of the genus zero open Gromov-Witten potentials and its generating matrix factorizations for elliptic orbifolds. These objects constructed by Lagrangian Floer theory are a priori well-defined only around the large volume limit. It follows from modularity that they can be analytically continued over the global Kähler moduli space.

The standard Yee's scheme for the Maxwell eigenvalue problems places the discrete electric field variable at the midpoints of the edges of the grid cells. It performs well when the permittivity is a scalar field. However, when the permittivity is a Hermitian full tensor filed it would generate un-physical complex eigenvalues or frequencies. In this paper, we propose a finite element method which can be interpreted as a modified Yee's scheme to overcome this difficulty. This interpretation enables us to create a fast FFT eigensolver that can compute very effectively the band structure of the anisotropic photonic crystal with SC and FCC lattices. Furthermore, we overcome the usual large null space associated with the Maxwell eigenvalue problem by deriving a null-space free discrete eigenvalue problem which involves a crucial Hermitian positive definite linear system to be solved in each of the iteration steps. It is demonstrated that the CG method without preconditioning converges in 37 iterations even when the dimension of the matrix is as large as $5,184,000$.

Surface-related-multiple wavefields constitute redundant information in conventional migration and can often be difficult to attenuate. However, when used for migration, multiple wavefields can improve subsurface illumination. Unfortunately, the process of imaging using multiples involves the management of crosstalk, which largely restricts its application. Crosstalk causes phantom images formed by spurious correlation of unrelated events in a migration process. These events can be unrelated orders of multiples in the source and receiver wavefields; they can also be one event associated with a reflector in the source wavefield and another event generated by a different reflector in the receiver wavefield. We have first examined crosstalk by explicitly investigating its generation mechanisms in a migration process and classifying it into different categories based on causality. Following this analysis, crosstalk can be predicted in a migration process and subtracted in the image domain; however, this method is usually difficult to apply due to the complexity of wavefield separation and adaptive subtraction. Furthermore, we develop different algorithms to attenuate the crosstalk, including a deconvolution imaging condition, a least-squares migration (LSM) method, and an advanced algorithm combining LSM with a deconvolution imaging condition. We evaluate these different strategies with synthetic examples. A deconvolution imaging condition can attenuate some crosstalk, but it is less effective at suppressing strong coherent crosstalk events. However, the LSM method can fundamentally address the crosstalk issue, and this approach is further optimized when combined with a deconvolution imaging condition.