In [1, 2], we get an explicit description of cubic cyclic fields by proving the following Theorem A. Let U={η∈（?）（p）|N<sub>2（p）</sub>η=1}, where p is a primitive cubic root of unity. Write G=U/U&l...In [1, 2], we get an explicit description of cubic cyclic fields by proving the following Theorem A. Let U={η∈（?）（p）|N<sub>2（p）</sub>η=1}, where p is a primitive cubic root of unity. Write G=U/U<sup>3</sup>. Suppose η∈（?）（p） such that 1, η, （?） are representative elements in a subgroup of order 3 of G. Let s=T<sub>（?）（P）</sub>.（?）η be the trace of η, and then the roots of x<sup>3</sup>-3x-s=0 define a展开更多
We study a class of non-densely defined impulsive neutral stochastic functional differential equations driven by an independent cylindrical fractional Brownian motion （fBm） with Hurst parameter H ∈ （1/2, 1） in th...We study a class of non-densely defined impulsive neutral stochastic functional differential equations driven by an independent cylindrical fractional Brownian motion （fBm） with Hurst parameter H ∈ （1/2, 1） in the Hilbert space. We prove the existence and uniqueness of the integral solution for this kind of equations with the coefficients satisfying some non-Lipschitz conditions. The results are obtained by using the method of successive approximation.展开更多
Let F<sub>q</sub> be a finite field of q elements, where q=p<sup>1</sup>, l≥1, p is an odd prime. Let c<sub>i</sub>（i=1,...,n） be nonzero elements of F<sub>q</sub>. S...Let F<sub>q</sub> be a finite field of q elements, where q=p<sup>1</sup>, l≥1, p is an odd prime. Let c<sub>i</sub>（i=1,...,n） be nonzero elements of F<sub>q</sub>. Suppose that d<sub>1</sub>...,d<sub>n</sub> are fixed positive integers andd<sub>i</sub> divides q--1 for all i. Let N be the number of solutions （x<sub>1</sub>,...,x<sub>n</sub>） ∈F<sub>q</sub><sup>n</sup> to the展开更多
基金Project supported by the National Natural Science Foundation of China
文摘In [1, 2], we get an explicit description of cubic cyclic fields by proving the following Theorem A. Let U={η∈（?）（p）|N<sub>2（p）</sub>η=1}, where p is a primitive cubic root of unity. Write G=U/U<sup>3</sup>. Suppose η∈（?）（p） such that 1, η, （?） are representative elements in a subgroup of order 3 of G. Let s=T<sub>（?）（P）</sub>.（?）η be the trace of η, and then the roots of x<sup>3</sup>-3x-s=0 define a
基金Acknowledgements The authors were deeply grateful to the anonymous referees for the careful reading, valuable comments, and correcting some errors, which have greatly improved the quality of the paper. This work was supported by the National Natural Science Foundation of China （Grant No. 11371029）.
文摘We study a class of non-densely defined impulsive neutral stochastic functional differential equations driven by an independent cylindrical fractional Brownian motion （fBm） with Hurst parameter H ∈ （1/2, 1） in the Hilbert space. We prove the existence and uniqueness of the integral solution for this kind of equations with the coefficients satisfying some non-Lipschitz conditions. The results are obtained by using the method of successive approximation.
基金Project supported by the National Natural Science Foundation of China.
文摘Let F<sub>q</sub> be a finite field of q elements, where q=p<sup>1</sup>, l≥1, p is an odd prime. Let c<sub>i</sub>（i=1,...,n） be nonzero elements of F<sub>q</sub>. Suppose that d<sub>1</sub>...,d<sub>n</sub> are fixed positive integers andd<sub>i</sub> divides q--1 for all i. Let N be the number of solutions （x<sub>1</sub>,...,x<sub>n</sub>） ∈F<sub>q</sub><sup>n</sup> to the
