The hardness of tensor decomposition problem has many achievements, but limited applications in cryptography, and the tensor decomposition problem has been considered to have the potential to resist quantum computing....The hardness of tensor decomposition problem has many achievements, but limited applications in cryptography, and the tensor decomposition problem has been considered to have the potential to resist quantum computing. In this paper, we firstly proposed a new variant of tensor decomposition problem, then two one-way functions are proposed based on the hard problem. Secondly we propose a key exchange protocol based on the one-way functions, then the security analysis, efficiency, recommended parameters and etc. are also given. The analyses show that our scheme has the following characteristics: easy to implement in software and hardware, security can be reduced to hard problems, and it has the potential to resist quantum computing.Besides the new key exchange can be as an alternative comparing with other classical key protocols.展开更多
The paper studies the existence of three nonnegative solutions to a type of three- point boundary value problem for second-order impulsive differential equations,and obtains the sufficient conditions for existence of ...The paper studies the existence of three nonnegative solutions to a type of three- point boundary value problem for second-order impulsive differential equations,and obtains the sufficient conditions for existence of three nonnegative solutions by means of the Leggett- Williams's fixed point theorem.展开更多
A class of singular nonlinear boundary value problems arising in the boundary layer behind expansion wave are studied.Sufficient conditions for the existence and uniqueness of positive solutions to the problems are es...A class of singular nonlinear boundary value problems arising in the boundary layer behind expansion wave are studied.Sufficient conditions for the existence and uniqueness of positive solutions to the problems are established by utilizing the monotonic approaching tech- nique.And a theoretical estimate formula for skin friction coefficient is presented.The numerical solution is presented by using the shoot method.The reliability and efficiency of the theoretical prediction are verified by numerical results.展开更多
Based on the combination of stochastic mathematics and conventional finite difference method,a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random phys...Based on the combination of stochastic mathematics and conventional finite difference method,a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random physical parameters,initial and boundary conditions is discussed.Begin with the analysis of steady-state heat conduction problems,difference discrete equations with random parameters are established,and then the computing formulas for the mean value and variance of temperature field are derived by the second-order stochastic parameter perturbation method.Subsequently,the proposed random model and method are extended to the field of transient heat conduction and the new analysis theory of stability applicable to stochastic difference schemes is developed.The layer-by-layer recursive equations for the first two probabilistic moments of the transient temperature field at different time points are quickly obtained and easily solved by programming.Finally,by comparing the results with traditional Monte Carlo simulation,two numerical examples are given to demonstrate the feasibility and effectiveness of the presented method for solving both steady-state and transient heat conduction problems.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.61303212,61170080,61202386)the State Key Program of National Natural Science of China(Grant Nos.61332019,U1135004)+2 种基金the Major Research Plan of the National Natural Science Foundation of China(Grant No.91018008)Major State Basic Research Development Program of China(973 Program)(No.2014CB340600)the Hubei Natural Science Foundation of China(Grant No.2011CDB453,2014CFB440)
文摘The hardness of tensor decomposition problem has many achievements, but limited applications in cryptography, and the tensor decomposition problem has been considered to have the potential to resist quantum computing. In this paper, we firstly proposed a new variant of tensor decomposition problem, then two one-way functions are proposed based on the hard problem. Secondly we propose a key exchange protocol based on the one-way functions, then the security analysis, efficiency, recommended parameters and etc. are also given. The analyses show that our scheme has the following characteristics: easy to implement in software and hardware, security can be reduced to hard problems, and it has the potential to resist quantum computing.Besides the new key exchange can be as an alternative comparing with other classical key protocols.
基金the Foundation of Educational Department of Shanghai City(No.05EZ52)
文摘The paper studies the existence of three nonnegative solutions to a type of three- point boundary value problem for second-order impulsive differential equations,and obtains the sufficient conditions for existence of three nonnegative solutions by means of the Leggett- Williams's fixed point theorem.
基金the National Natural Science Foundation of China （No. 50476083）.
文摘A class of singular nonlinear boundary value problems arising in the boundary layer behind expansion wave are studied.Sufficient conditions for the existence and uniqueness of positive solutions to the problems are established by utilizing the monotonic approaching tech- nique.And a theoretical estimate formula for skin friction coefficient is presented.The numerical solution is presented by using the shoot method.The reliability and efficiency of the theoretical prediction are verified by numerical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.90816024,10872017 and 10876100)the Defense Industrial Technology Development Program(Grant Nos.A2120110001 and B2120110011)the 111 Project(Grant No.B07009)
文摘Based on the combination of stochastic mathematics and conventional finite difference method,a new numerical computing technique named stochastic finite difference for solving heat conduction problems with random physical parameters,initial and boundary conditions is discussed.Begin with the analysis of steady-state heat conduction problems,difference discrete equations with random parameters are established,and then the computing formulas for the mean value and variance of temperature field are derived by the second-order stochastic parameter perturbation method.Subsequently,the proposed random model and method are extended to the field of transient heat conduction and the new analysis theory of stability applicable to stochastic difference schemes is developed.The layer-by-layer recursive equations for the first two probabilistic moments of the transient temperature field at different time points are quickly obtained and easily solved by programming.Finally,by comparing the results with traditional Monte Carlo simulation,two numerical examples are given to demonstrate the feasibility and effectiveness of the presented method for solving both steady-state and transient heat conduction problems.
