1. "This paper

~~talk~~ talks about

the normal form of

a/the **D**uffing-van der Pol oscillator under nonautonomous parametric perturbations. The author

~~gave~~ gives a new generalization of

__Poincaré__**'**s normal form theory to nonautonomous differential equations applied to the Duffing-van der Pol oscillator under a nonautonomous bounded parametric perturbation. The nonautonomous normal form is calculated for parameter values corresponding to the pitchfork scenario. In this paper, the author

~~used~~ uses the computer

__algebra__ (?) program Maple to

~~effort accomplish the enormous computational~~ [how about *"to handle the enormous computational requirements."*] Finally, the author also

~~indicate~~ [shows the...; demonstrates the...(?)] application of the normal form, which can be used to

~~the~~ study nonautonomous bifurcation phenomena."

2. "This paper

~~introduced~~ introduces ~~about~~ the dichotomy spectrum for linear

~~dunamic~~ dynamic equations

in

on a time scale T (

~~e. g.~~ e.g. [no space] T=Z or

). This new spectrum consists of at most N closed intervals of the real line. In the autonomous cases with

these intervals reduce to the real parts of the eigenvalues of A. In

~~any cases~~ [In any case? In many cases?] the spectral intervals are associated with invariant vector

~~boundles~~ [bundles(?)] comprising solutions with a common exponential growth rate. A spectral theorem, which

~~desribes~~ describes all possible forms of the dichotomy spectrum, is the main result of this paper."