In this paper a class of parallel Rosenbrock Formulas in real-time simulation is constructed for the multiprocessor system. A-stable formulas of two-stage thirdorder and A(α)-stable formulas with α≈87° of thre...In this paper a class of parallel Rosenbrock Formulas in real-time simulation is constructed for the multiprocessor system. A-stable formulas of two-stage thirdorder and A(α)-stable formulas with α≈87° of three-stage forth-order are constructed. The numerical examples demonstrate that these formulas can solve the initial problems for the stiff ordinary differential equations with high efficiency.展开更多
Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Suf...Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained.展开更多
The existence and uniqueness of the global smooth solution to the initial-boundary valueproblem of a system of multi-dimensions SRWE are proved. The sufficient conditions of 'blowingup' of the solution are given.
Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference...Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form {j=1∑nαj（z）f1（λj1）（z＋cj）=R2（z,f2（z））,j=1∑nβj（z）f2（λj2）（z＋cj）=R1（z,f1（z））. where λij （j = 1, 2,…, n; i = 1, 2） are finite non-negative integers, and cj （j = 1, 2,… , n） are distinct, nonzero complex numbers, αj（z）, βj（z） （j = 1,2,… ,n） are small functions relative to fi（z） （i =1, 2） respectively, Ri（z, f（z）） （i = 1, 2） are rational in fi（z） （i =1, 2） with coefficients which are small functions of fi（z） （i = 1, 2） respectively.展开更多
Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 < α < n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) < p1q < ∞1,Q(...Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 < α < n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) < p1q < ∞1,Q(x) and K(x) satisfy some suitable conditions.It is shown that every positive regular solution(u(x)1,v(x)) is symmetric about some plane by developing the moving plane method in an integral form.Moreover,regularity of the solution is studied.Finally,the nonexistence of positive solutions to the system in the case 0 < p1q <(n+α)/(n-α) is also discussed.展开更多
In this paper, sane sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
文摘In this paper a class of parallel Rosenbrock Formulas in real-time simulation is constructed for the multiprocessor system. A-stable formulas of two-stage thirdorder and A(α)-stable formulas with α≈87° of three-stage forth-order are constructed. The numerical examples demonstrate that these formulas can solve the initial problems for the stiff ordinary differential equations with high efficiency.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10672143 and 10572021
文摘Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev＇s type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained.
文摘The existence and uniqueness of the global smooth solution to the initial-boundary valueproblem of a system of multi-dimensions SRWE are proved. The sufficient conditions of 'blowingup' of the solution are given.
基金supported by the National Natural Science Foundation of China(10471067)NSF of Guangdong Province(04010474)
文摘Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form {j=1∑nαj（z）f1（λj1）（z＋cj）=R2（z,f2（z））,j=1∑nβj（z）f2（λj2）（z＋cj）=R1（z,f1（z））. where λij （j = 1, 2,…, n; i = 1, 2） are finite non-negative integers, and cj （j = 1, 2,… , n） are distinct, nonzero complex numbers, αj（z）, βj（z） （j = 1,2,… ,n） are small functions relative to fi（z） （i =1, 2） respectively, Ri（z, f（z）） （i = 1, 2） are rational in fi（z） （i =1, 2） with coefficients which are small functions of fi（z） （i = 1, 2） respectively.
基金supported by Chinese National Science Fund for Distinguished Young Scholars (Grant No.10925104)National Natural Science Foundation of China (Grant No.11001221)+1 种基金the Foundation of Shaanxi Province Education Department (Grant No. 2010JK549)the Foundation of Xi’an Statistical Research Institute (Grant No.10JD04)
文摘Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 < α < n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) < p1q < ∞1,Q(x) and K(x) satisfy some suitable conditions.It is shown that every positive regular solution(u(x)1,v(x)) is symmetric about some plane by developing the moving plane method in an integral form.Moreover,regularity of the solution is studied.Finally,the nonexistence of positive solutions to the system in the case 0 < p1q <(n+α)/(n-α) is also discussed.
文摘In this paper, sane sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.
