We investigate hypercyclic and chaotic behavior of linear strongly continuous semigroups. We give necessary and sufficient conditions on the semigroup to be hypercyclic, and sufficient conditions on the spectrum of an operator to generate a hypercyclic semigroup. A variety of examples is provided.

In this paper, we investigate L p -estimates for the solution of the Stokes equation in a half space H where 1 ≤ p ≤ ∞. It is shown that the solution of the Stokes equation is governed by an analytic semigroup on BU C σ (H ), C 0,σ (H ) or L ∞ σ (H ). From the operatortheoretical point of view it is a surprising fact that the corresponding result for L 1 σ (H ) does not hold true. In fact, there exists an L 1 -function f satisfying divf = 0 such that the solution of the corresponding resolvent equation with right hand side f does not belong to L 1 . Taking into account however a recent result of Kozono on the nonlinear Navier-Stokes equation, the L 1 -result is not surprising and even natural. We also show that the Stokes operator admits a R-bounded H ∞ -calculus on L p for 1 < p < ∞ and obtain as a consequence maximal L p -L q -regularity for the solution of the Stokes equation.

The NO concentrations released from donor compounds are difficult to predict as they are determined by formation and inactivation reactions. To calculate the concentrations of NO over time, we have developed a mathematical model which is based on a system of two differential equations describing the first order decomposition of the NO donor in association with the third order reaction of NO with oxygen. Although there is no closed formula for the solution, it can be easily computed by any standard numerical differential solver or simulation software with the following input parameters: initial concentration and decomposition rate constant of the NO donor, O2 concentration, and rate constant for NO autoxidation. The model was validated by monitoring NO release from 2,2-diethyl-1-nitroso-oxyhydrazine (DEA/NO) with a Clark-type NO-sensitive electrode at two different temperatures (25 and 37 degrees C) and DEA/NO concentrations ranging from 1 to 10 microM. Under all conditions, there was an excellent agreement between experimental and calculated data. In addition to the computer modeling, we present graphical plots which allow a rough but very easy estimation of the actual NO concentrations if appropriate computer software should not be available.

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