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Abstract: Leonard and Pellikaan developed the qth power algorithm to compute module bases for the integral closure of the polynomial ring in a class of function fields. In this paper, their algorithm is adapted to efficiently obtain an -basis for a class of Riemann–Roch spaces without having to compute the entire integral closure. This reformulation allows one to determine the complexity of the algorithm. Further, we obtain a simple characterization of the integral closure. [Copyright &y& Elsevier]

In order to improve the accuracy and performance of traditional image threshold segmentation algorithm, this paper proposes a multithreshold segmentation method named improved Harris hawk optimization (IMHHO). Firstly, IMHHO adopts Tent map and elite opposition-based learning to initialize population and enhance the diversity. Secondly, IMHHO uses quadratic interpolation to generate new individuals and enhance the local search ability. Finally, IMHHO adopts improved Gaussian disturbance method to disturb optimal solution, which coordinates the local and global search ability. Then, the performance of IMHHO is tested based on 14 benchmark functions. In image segmentation, different algorithms are tested to compare the comprehensive performance based on Otsu and Renyi entropy. Experiments show that IMHHO performs better in the three kinds of benchmark functions; the segmentation effect is directly proportional to the number of thresholds; compared with other algorithms, IMHHO has better comprehensive performance. [ABSTRACT FROM AUTHOR]