In this paper, we study two Diophantine equations of the type p<sup>x</sup> + 9<sup>y</sup> = z<sup>2</sup> , where p is a prime number. We find that the equation 2<sup>x</...In this paper, we study two Diophantine equations of the type p<sup>x</sup> + 9<sup>y</sup> = z<sup>2</sup> , where p is a prime number. We find that the equation 2<sup>x</sup> + 9<sup>y</sup> = z<sup>2</sup> has exactly two solutions (x, y, z) in non-negative integer i.e., {(3, 0, 3),(4, 1, 5)} but 5<sup>x</sup> + 9<sup>y</sup> = z<sup>2</sup> has no non-negative integer solution.展开更多
In this paper, a mini max theorem was showed mega which the paper proves a new existent and unique result on solution of the boundary value problem for the nonlinear wave equation by using the mini max theorem.
Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|x...Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.展开更多
In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we ...In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.展开更多
For any positive integer n, the famous Smarandache power function SP（n） is defined as the smallest positive integer m such that n｜m^m, where m and n have the same prime divisors. The main purpose of this paper is u...For any positive integer n, the famous Smarandache power function SP（n） is defined as the smallest positive integer m such that n｜m^m, where m and n have the same prime divisors. The main purpose of this paper is using the elementary methods to study the positive integer solutions of an equation involving the Smarandache power function SP（n） and obtain some interesting results. At the same time, we give an open problem about the related equation.展开更多
车载自组织网络(vehicular ad hoc network,VANET)是构建智能交通系统的基础,其能够有效提高交通效率以及增加道路安全性.但由于其自身无线通信环境的开放性,车载自组织网络中的边缘节点易遭受到各种外部攻击.为了兼顾隐私保护和可追溯...车载自组织网络(vehicular ad hoc network,VANET)是构建智能交通系统的基础,其能够有效提高交通效率以及增加道路安全性.但由于其自身无线通信环境的开放性,车载自组织网络中的边缘节点易遭受到各种外部攻击.为了兼顾隐私保护和可追溯性并确保安全认证,一种有效的方法是采用车联网条件隐私保护认证方案.虽然目前已有各种车联网条件隐私保护认证方案被相继提出,但这些方案的安全性几乎都依赖于传统数论困难假设,难以具备后量子安全特性.因此,针对现有基于格的车联网条件隐私保护认证方案的安全和效率问题,同时为解决密钥托管问题,利用结构化格上的环上带误差学习决策困难假设以及环上小整数解困难假设,并结合拒绝抽样技术,设计了一种车联网中基于格的无抽样条件隐私保护聚合认证方案,并在随机预言机模型下证明了所提方案能够达到适应性安全.此外,通过性能评估展示了该方案在计算开销方面优于基于一般格的聚合认证方案.展开更多
文摘In this paper, we study two Diophantine equations of the type p<sup>x</sup> + 9<sup>y</sup> = z<sup>2</sup> , where p is a prime number. We find that the equation 2<sup>x</sup> + 9<sup>y</sup> = z<sup>2</sup> has exactly two solutions (x, y, z) in non-negative integer i.e., {(3, 0, 3),(4, 1, 5)} but 5<sup>x</sup> + 9<sup>y</sup> = z<sup>2</sup> has no non-negative integer solution.
基金the Natural Science Foundation of Southern Yangtze University China(0371)
文摘In this paper, a mini max theorem was showed mega which the paper proves a new existent and unique result on solution of the boundary value problem for the nonlinear wave equation by using the mini max theorem.
文摘Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.
文摘In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.
基金Supported by the Natural Science Foundation of China（10671155）
文摘For any positive integer n, the famous Smarandache power function SP（n） is defined as the smallest positive integer m such that n｜m^m, where m and n have the same prime divisors. The main purpose of this paper is using the elementary methods to study the positive integer solutions of an equation involving the Smarandache power function SP（n） and obtain some interesting results. At the same time, we give an open problem about the related equation.
文摘车载自组织网络(vehicular ad hoc network,VANET)是构建智能交通系统的基础,其能够有效提高交通效率以及增加道路安全性.但由于其自身无线通信环境的开放性,车载自组织网络中的边缘节点易遭受到各种外部攻击.为了兼顾隐私保护和可追溯性并确保安全认证,一种有效的方法是采用车联网条件隐私保护认证方案.虽然目前已有各种车联网条件隐私保护认证方案被相继提出,但这些方案的安全性几乎都依赖于传统数论困难假设,难以具备后量子安全特性.因此,针对现有基于格的车联网条件隐私保护认证方案的安全和效率问题,同时为解决密钥托管问题,利用结构化格上的环上带误差学习决策困难假设以及环上小整数解困难假设,并结合拒绝抽样技术,设计了一种车联网中基于格的无抽样条件隐私保护聚合认证方案,并在随机预言机模型下证明了所提方案能够达到适应性安全.此外,通过性能评估展示了该方案在计算开销方面优于基于一般格的聚合认证方案.
