A new voting protocol was proposed to solve the problem that most of the existing voting protocols require a trusted management authority. This protocol comprehensively makes use of homomorphic encryption, threshold cryptography, blind signature, ring signature, zero knowledge proof, and so on, to resolves the coexistence problem between robustness and the absence of trusted third party under the assumption that no one abstains from voting or the authority does not cheat conspiracy with other voters when one voter abstains from voting, at the same time, anonymity, eligibility, robustness, verifiability and no trusted third party are also satisfied.

To resolve the problem that the existing adaptive slicing algorithm in 3D printing cannot retain effectively model characteristics, a new adaptive slicing method for recognizing and retaining model characteristics was proposed. Firstly, the definition of model characteristic was extended, and the concept of loss and offset of model characteristic was introduced. Secondly, a characteristic recognition method was proposed, the key point of which is to make use of the fact that the surface complexity and number of contours must change around the model characteristics. Finally, based on existing adaptive slicing algorithms, this algorithm retained model characteristics by slicing the model with minimum layer thickness near the model characteristics. On the self-developed software Slicer3DP, the following algorithms were implemented: the uniform slicing algorithm, the adaptive slicing algorithm and the proposed slicing algorithm. By comparing these algorithms, it is found that the proposed slicing algorithm resolves effectively the loss and offset of model characteristics while maintaining both slicing precision and efficiency. The result shows that the proposed method can be used for 3D printing with high precision requirement.

To resolve the peculiar problem of the Jacobian matrix for a special class of nonlinear equations, an improved Newton mtheod was proposed based on the dual space. This paper proposed an explicit formula to compute the dual space of an ideal in a point through polynomial multiplication, and constructed augmented equations using the dual space. Meanwhile, the Jacobian matrix of augmented equations at initial point was full rank, and then the algorithm recovered quadratical convergence of Newton's iteration. The experimental results show that after three iterations, the accuracy of computation can achieve 10^(-15). The proposed method further enriches the theories of the dual space of ideal in algebra geometry and provides a new method for the numerical calculation in engineering applications.