多复变数的二阶微分从属

在文[1－2]的基础上讨论了多复变数中的二阶微分从属,取得了一些结果。这些结果是文[1-5]中的一些结果的推广。     

Splitting methods for second‐order initial value problems

We consider implicit integration methods for the solution of stiff initial value problems for second-order differential equations of the special form y' = f(y). In implicit methods, we are faced with the problem of solving systems of implicit relations. This paper focuses on the construction and analysis of iterative solution methods which are effective in cases where the Jacobian of the right‐hand side of the differential equation can be split into a sum of matrices with a simple structure. These iterative methods consist of the modified Newton method and an iterative linear solver to deal with the linear Newton systems. The linear solver is based on the approximate factorization of the system matrix associated with the linear Newton systems. A number of convergence results are derived for the linear solver in the case where the Jacobian matrix can be split into commuting matrices. Such problems often arise in the spatial discretization of time‐dependent partial differential equations. Furthermore, the stability matrix and the order of accuracy of the integration process are derived in the case of a finite number of iterations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Verifiable Partial Escrow of Integer Factors

We construct an efficient interactive protocol for realizing verifiable partial escrow of the factors of an integer n with time-delayed and threshold key recovery features. The computational cost of the new scheme amounts to 10k P multiplications of numbers of size of P, where P is a protocol parameter which permits n of size up to ( P) - 4 to be dealt with and k is a security parameter which controls the error probability for correct key escrow under 1/2^k. The new scheme realizes a practical method for fine tuning the time complexity for factoring an integer, where the complexity tuning has no respect to the size of the integer.     

On a class of second order Fuchsian hyperbolic equations

Summary We study a class of second order Fuchsian hyperbolic operators. The well-posedness of the Cauchy problem in a space of regular distributions is proved, together with results on the propagation of singularities of the solution. Moreover we give a representation formula for the distribution solutions of the homogeneous equation.     

Hilbert boundary-value problem for a class of singular matrix-functions

We present a statement and a solution of a Hilbert boundary-value problem for n×n matrix-functions, the singularity of which is characterized by a given integral n×n matrix. For the homogeneous problem we find solvability conditions and the number of linearly independent solutions; for the nonhomogeneous problem we find conditions of solvability and the number of these solutions. We make essential use of the standard left factorization of the coefficient of the problem.Translated from Matematicheskie Zametki, Vol. 15, No. 4, pp. 587–594, April, 1974.In conclusion, the author thanks A. V. Batyrev for valuable discussions and remarks.     

A class of second order differential equations

We study the differential equationf″=N(f)f′ ² +M(f)f′+L(f), whereL, M, N are rational functions, and prove that if the differential equation has a transcendental meromorphic solutionf with order,p(f)>2, then the differential equation must be one of nine forms; and, moreover, we construct examples showing the existence of these nine forms with a transcendental meromorphic solution.     

Periodic solutions for a class of non-autonomous second order systems

The purpose of this paper is to study the existence of periodic solutions of non-autonomous second-order systems

     

On a class of second order variational problems with constraints

We study the structure of optimal solutions for a class of constrained, second order variational problems on bounded intervals. We show that, for intervals of length greater than some positive constant, the optimal solutions are bounded inC ¹ by a bound independent of the length of the interval. Furthermore, for sufficiently large intervals, the ‘mass’ and ‘energy’ of optimal solutions are almost uniformly distributed.     

Periodic solutions of a class of superquadratic second order Hamiltonian systems

§1　IntroductionInthispaperwediscusstheexistenceofthesolutionforthefollowingsecondorderHamiltoniansystemx¨ Ax ΔF(x)=0,(1.1)whereAisann×nrealsymmetricmatrixandisnon-definite,F∈C1(Rn,R),andΔF(x)denotesthegradientofF.WhileworksforsecondorderHamiltonsystemshavemostlybeendoneundertheconditionA=0,westudythecasewhereA≠0andisnon-definiteinthepapers[1,2].DefineH=H1,2T([0,T],Rn)={x:R→Rn|xisabsolutelycontinuous,x∈L2([0,T],Rn),x(0)=x(T),x(0)=x(T)}and〈x,y〉=∫T0[(x(t),y(t)) (x…     

Periodic solutions of a class of second order non-autonomous Hamiltonian systems

Some existence theorems are obtained for periodic solutions of non-autonomous second order systems by using the least action principle and minimax methods in critical point theory. Our results extend and improve many previously known results.     

On the optimization of a class of second order iterative schemes

This paper analyzes and studies the second order scheme of de Pillis' type, which is used for the solution of a linear system. This study leads to a monoparametric family of second order schemes of the aforementioned type and a method of selecting the optimal one is presented. In addition a number of concluding remarks is made and various applications and examples are given, which effectively show in some cases the superiority of our optimal second order scheme over the fastest first order ones like the SOR and AOR schemes. Many points are also made for the possibility of improving on the convergence rates of the optimal scheme of this paper, which suggest further research in this area.     

Subharmonic solutions for a class of non-quadratic second order Hamiltonian systems

In this paper, some existence theorems are obtained for infinitely subharmonic solutions of second order Hamiltonian systems under non-quadratic conditions. The approach is the minimax principle. Our results greatly extend and improve some known results.     

一类偏积分微分方程二阶差分全离散格式

本给出了数值求解一类偏积分微分方程的二阶全离散差分格式．采用了Crank-Nicolson格式；积分项的离散利用了Lubieh的二阶卷积积分公式；给出了稳定性的证明，误差估计及收敛性的结果．