No abstract uploaded!

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.

Surface parameterizations have been widely applied to digital geometry processing. In this paper, we propose an efficient conformal energy minimization (CEM) algorithm for computing conformal parameterizations of simply-connected open surfaces with a very small angular distortion and a highly improved computational efficiency. In addition, we generalize the proposed CEM algorithm to computing conformal parameterizations of multiply-connected surfaces. Furthermore, we prove the existence of a nontrivial accumulation point of the proposed CEM algorithm under some mild conditions. Several numerical results show the efficiency and robustness of the CEM algorithm comparing to the existing state-of-the-art algorithms. An application of the CEM on the surface morphing between simply-connected open surfaces is demonstrated thereafter. Thanks to the CEM algorithm, the whole computations for the surface morphing can be performed efficiently and robustly.

In [2], J. Arthur classifies the automorphic discrete spectrum of symplectic groups up to global Arthur packets. We continue with our investigation of Fourier coefficients and their implication to the structure of the cuspidal spectrum for symplectic groups ([16] and [20]). As result, we obtain certain characterization and construction of small cuspidal automorphic representations and gain a better understanding of global Arthur packets and of the structure of local unramified components of the cuspidal spectrum, which has impacts to the generalized Ramanujan problem as posted by P. Sarnak in [43].

In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in order to give a geometric interpretation of the dual Orlicz curvature measure. Based on the established variational formula, a solution to the dual Orlicz-Minkowski problem regarding the dual Orlicz curvature measure is provided.