Let Fqbe the finite field,q=p^(k),with p being a prime and k being a positive integer.Let F_(q)^(*)be the multiplicative group of Fq,that is F_(q)^(*)=F_(q){0}.In this paper,by using the Jacobi sums and an analog of H...Let Fqbe the finite field,q=p^(k),with p being a prime and k being a positive integer.Let F_(q)^(*)be the multiplicative group of Fq,that is F_(q)^(*)=F_(q){0}.In this paper,by using the Jacobi sums and an analog of Hasse-Davenport theorem,an explicit formula for the number of solutions of cubic diagonal equation x_(1)^(3)+x_(2)^(3)+…+x_(n)^(3)=c over Fqis given,where c∈F_(q)^(*)and p≡1(mod 3).This extends earlier results.展开更多
The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impul- sive diff...The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impul- sive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach.展开更多
Let Fq stand for the finite field of odd characteristic p with q elements（q=pn,n∈N）and Fq＊ denote the set of all the nonzero elements of Fq.In this paper,by using the augmented degree matrix and the result given b...Let Fq stand for the finite field of odd characteristic p with q elements（q=pn,n∈N）and Fq＊ denote the set of all the nonzero elements of Fq.In this paper,by using the augmented degree matrix and the result given by Cao,we obtain a formula for the number of rational points of the following equation over Fq：f（x 1,x 2,...,x n）=（a1 x1 x2d＋a2 x2 x3d...＋a（n-1）x（n-1）xnd＋an xn x1d）λ-bx1（d1）x2d2...xn（dn）,with ai,b∈Fq＊,n≥2,λ〉0 being positive integers,and d,di being nonnegative integers for 1≤i n.This technique can be applied to the polynomials of the form h1λ=h2 with λ being positive integer and h1,h2∈Fq[x 1,x 2,...,x n].It extends the results of the Markoff-Hurwitz-type equations.展开更多
基金Supported by the Natural Science Foundation of Henan Province(232300420123)the National Natural Science Foundation of China(12026224)the Research Center of Mathematics and Applied Mathematics,Nanyang Institute of Technology。
文摘Let Fqbe the finite field,q=p^(k),with p being a prime and k being a positive integer.Let F_(q)^(*)be the multiplicative group of Fq,that is F_(q)^(*)=F_(q){0}.In this paper,by using the Jacobi sums and an analog of Hasse-Davenport theorem,an explicit formula for the number of solutions of cubic diagonal equation x_(1)^(3)+x_(2)^(3)+…+x_(n)^(3)=c over Fqis given,where c∈F_(q)^(*)and p≡1(mod 3).This extends earlier results.
基金Supported by the National Natural Science Foundation of China (Grant No. 10772046)
文摘The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impul- sive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach.
基金Supported partially by the Key Program of Universities of Henan Province(17A110010)Science and Technology Department of Henan Province(152300410180,142300410107,182102210379)+1 种基金China Postdoctoral Science Foundation Funded Project(2016M602251)the National Natural Science Foundation of China(11501387,U1504105)
文摘Let Fq stand for the finite field of odd characteristic p with q elements（q=pn,n∈N）and Fq＊ denote the set of all the nonzero elements of Fq.In this paper,by using the augmented degree matrix and the result given by Cao,we obtain a formula for the number of rational points of the following equation over Fq：f（x 1,x 2,...,x n）=（a1 x1 x2d＋a2 x2 x3d...＋a（n-1）x（n-1）xnd＋an xn x1d）λ-bx1（d1）x2d2...xn（dn）,with ai,b∈Fq＊,n≥2,λ〉0 being positive integers,and d,di being nonnegative integers for 1≤i n.This technique can be applied to the polynomials of the form h1λ=h2 with λ being positive integer and h1,h2∈Fq[x 1,x 2,...,x n].It extends the results of the Markoff-Hurwitz-type equations.
