We investigate the distribution of rational points on singular cubic surfaces,whose coordinates have few prime factors.The key tools used are universal torors,the circle method and results on linear equations in primes.
This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of P3 Qgiven by the following equation x0（x12+ x22）-x33= ...This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of P3 Qgiven by the following equation x0（x12+ x22）-x33= 0 in agreement with the Manin-Peyre conjectures.展开更多
There have been some mathematics methods to model farm vehicle engine universal characteristic mapping(EUCM).Nevertheless,any of different mathematics methods used would possess its own strengths and weaknesses.As a r...There have been some mathematics methods to model farm vehicle engine universal characteristic mapping(EUCM).Nevertheless,any of different mathematics methods used would possess its own strengths and weaknesses.As a result,these modeling methods about EUCM are not the same among the most vehicle manufacturers.In order to obtain a better robustness EUCM,an improved ant colony optimization was introduced into a traditional cubic surface regression method for modeling EUCM.Based on this method,the test data were regressed into a three-dimensional cubic surface,after that it was cut by some equal specific fuel consumption(ESFC)planes,more than twenty two-dimensional ESFC equations were obtained.Furthermore,the engine speed in every ESFC equation was discretized to obtain a set of ESFC points,and this set of ESFC points was linked into a closed curve by a given sequence via the improved ant colony algorithm.In order to improve the modeling speed,dimensionality reduction and discretization methods were adopted.In addition,a corresponding simulation platform was also developed to obtain an optimal system configuration.There were 48000 simulation search tests carried out on the platform,and the major parameters of the algorithm were determined.In this way the EUCM was established successfully.In contrast with other methods,as a result of the application of the novel bionic intelligent algorithm,it has better robustness,less distortion and higher calculating speed,and it is available for both gasoline engines and diesel engines.展开更多
文摘We investigate the distribution of rational points on singular cubic surfaces,whose coordinates have few prime factors.The key tools used are universal torors,the circle method and results on linear equations in primes.
基金supported by the program PRC 1457-Au For Di P(CNRS-NSFC)supported by National Natural Science Foundation of China(Grant No.11531008)+1 种基金the Ministry of Education of China(Grant No.IRT16R43)the Taishan Scholar Project of Shandong Province
文摘This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of P3 Qgiven by the following equation x0（x12+ x22）-x33= 0 in agreement with the Manin-Peyre conjectures.
基金The authors thank the financial and experimental support from FAW(First Auto Works),especially thank the contribution of Cheng Xuejun,Nie Xixian,Ye Wenhui and Chen Yuchun.
文摘There have been some mathematics methods to model farm vehicle engine universal characteristic mapping(EUCM).Nevertheless,any of different mathematics methods used would possess its own strengths and weaknesses.As a result,these modeling methods about EUCM are not the same among the most vehicle manufacturers.In order to obtain a better robustness EUCM,an improved ant colony optimization was introduced into a traditional cubic surface regression method for modeling EUCM.Based on this method,the test data were regressed into a three-dimensional cubic surface,after that it was cut by some equal specific fuel consumption(ESFC)planes,more than twenty two-dimensional ESFC equations were obtained.Furthermore,the engine speed in every ESFC equation was discretized to obtain a set of ESFC points,and this set of ESFC points was linked into a closed curve by a given sequence via the improved ant colony algorithm.In order to improve the modeling speed,dimensionality reduction and discretization methods were adopted.In addition,a corresponding simulation platform was also developed to obtain an optimal system configuration.There were 48000 simulation search tests carried out on the platform,and the major parameters of the algorithm were determined.In this way the EUCM was established successfully.In contrast with other methods,as a result of the application of the novel bionic intelligent algorithm,it has better robustness,less distortion and higher calculating speed,and it is available for both gasoline engines and diesel engines.
