Sentence examples for evolution operator are from inspiring English sources

In Section 2, the properties of the impulsive evolution operator are collected.

Next, four sufficient conditions that guarantee the exponential stability of impulsive evolution operator are given.

By means of spectral splitting methods we prove that the evolution operator is approximated by the Lie evolution operator, where the kernel of the Lie evolution operator is explicitly written.

In this paper a general scheme of the MPE is given, the evolution operator is derived for problems with smooth coefficients and the numerical algorithm is discussed.

The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (generalized minimum residual) technique.

In operation process, we firstly adopted the novel decimal coding to construct the chromosome, and then the differential evolution operator is adopted as the main optimizing scheme, while such techniques of the genetic algorithm, as the novel crossover-operator mutation-operator are designed to improve the result.

Hence the spectrum of the evolution operator is discrete, in other words the system has a finite relaxation time.

Defining the error propagator (tilde {U}(t)equiv U_{c} ^{dagger}(t)U (t)), the total evolution operator is written (U (t) = U_{c} (t tilde {U}(t)).

The evolution operator is obtained in the interaction picture where time evolution is given by the interaction Hamiltonian, which is the integral over space of the second term in the Lagrangian density given above: V=e\int d^3x\bar\psi\gamma^\mu\psi A_\mu and so, one has U=T\exp\left[-\frac{i}{\hbar}\int_{t_0}^tdt'V(t')\right] where T is the time ordering operator.

In order to improve the performance of the algorithm, a set of genetic operators and differential evolution operators are combined.

For doing so, we first investigate the nonuniform dichotomy spectrum of the linear evolution operators that admit a nonuniform exponential dichotomy, where the linear evolution operators are defined by nonautonomous differential equations x˙="A t)x in Rn.