Finite Time Lag Research Articles

Sufficient conditions for stability and instability of autonomous functional-differential equations

Liapunov function determining sufficient conditions for stability of autonomous functional differential equations with finite time lag

A Mathematical Interpretation of the Kinetics of Elevated Temperature Stability Studies as Applied to Solid Formulations

When using kinetic principles and the Arrhenius equation to predict shelf life, it is convenient to use exaggerated storage temperatures. However, it is sometimes difficult to attain temperature equilibrium rapidly in these cases, and because accurate heating time estimates are essential for precise shelf life predictions, the time lags during sample heating and cooling may seriously affect the prediction accuracy. In this paper an equation is presented which relates the sample heating rate, storage time, temperature, and the heat of activation of the breakdown reaction. The solution of the equation is expressed as “Equilibrium Temperature Time Equivalent” or ETTE, and represents the effective time of storage at the oven temperature. The ETTE takes into account the finite time lag in attaining temperature equilibrium during the heating phase and during cooling after removal from the oven. A sample calculation is presented to indicate the magnitude of the error involved in using sample storage time which does not correct for the time necessary to attain temperature equilibrium. The ETTE permits the formulator to correct either storage times or his sampling times, thus making the error negligible.