The main purpose of this paper is to use the Fourier expansion for character sums and the mean value theorem of Dirichlet L-functions to study the asymptotic property of the difference between a D. H. Lehmer number an...The main purpose of this paper is to use the Fourier expansion for character sums and the mean value theorem of Dirichlet L-functions to study the asymptotic property of the difference between a D. H. Lehmer number and its inverse modulo p （an odd prime）, A interesting mean square value formula is also given.展开更多
Energy consumption is an important quality index in the production of seamless tubes. The complex factors affecting energy consumption make it difficult to build its mechanism model, and optimization is also very diff...Energy consumption is an important quality index in the production of seamless tubes. The complex factors affecting energy consumption make it difficult to build its mechanism model, and optimization is also very difficult, if not impossible. The piercing process was divided into three parts based on the production process, and an energy consumption prediction model was proposed based on the step mean value staged multiway partial least square meth- od. On the basis of the batch process prediction model, a genetic algorithm was adopted to calculate the optimum mean value of each process parameter and the minimum piercing energy consumption. Simulation proves that the op- timization method based on the energy consumption prediction model can obtain the optimum process parameters effectively and also provide reliable evidences for practical production.展开更多
文摘The main purpose of this paper is to use the Fourier expansion for character sums and the mean value theorem of Dirichlet L-functions to study the asymptotic property of the difference between a D. H. Lehmer number and its inverse modulo p （an odd prime）, A interesting mean square value formula is also given.
基金Item Sponsored by National Natural Science Foundation of China (60674063)
文摘Energy consumption is an important quality index in the production of seamless tubes. The complex factors affecting energy consumption make it difficult to build its mechanism model, and optimization is also very difficult, if not impossible. The piercing process was divided into three parts based on the production process, and an energy consumption prediction model was proposed based on the step mean value staged multiway partial least square meth- od. On the basis of the batch process prediction model, a genetic algorithm was adopted to calculate the optimum mean value of each process parameter and the minimum piercing energy consumption. Simulation proves that the op- timization method based on the energy consumption prediction model can obtain the optimum process parameters effectively and also provide reliable evidences for practical production.
