Controlling chaos in nuclear spin generator system using backstepping design.
We design shifted transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of the banded Hessenberg form. The shifted transformation can be regarded as an extension of the extension employed in the well-known dqds algorithm for the symmetric tridiagonal eigenvalue problem. In this paper, we propose a new and effective shift strategy for the sequence of shifted transformations by considering the concept of the Newton shift....
It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...
It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...
We consider the second order initial value problem in a Hilbert space, which is a singular perturbation of a first order initial value problem. The difference of the solution and its singular limit is estimated in terms of the small parameter The coefficients are commuting self-adjoint operators and the estimates hold also for the semilinear problem.
Let (x,y,z) ∈ ℂ³. In this paper we shall study the solvability of singular first order partial differential equations of nilpotent type by the following typical example: , where . For this equation, our aim is to characterize the solvability on by using the Im P, Coker P and Ker P, and we give the exact forms of these sets.
The author considers the convergence of quasilinear nonstationary multistep methods for systems of ordinary differential with parameters. Sufficient conditions for their convergence are given. The new numerical method is tested for two examples and it turns out to be a little better than the Hamming method.
A general class of numerical methods for solving initial value problems for neutral functional-differential-algebraic systems is considered. Necessary and sufficient conditions under which these methods are consistent with the problem are established. The order of consistency is discussed. A convergence theorem for a general class of methods is proved.