ON STABILITY OF THE EQUAIONS Bu0(t) = Au(t)

Abstract

The stability of solutions of the equation Bu 0 (t) = Au(t) is considered, where A and B are closed linear operators on a Banach space. Under the well-posedness condition it is proved that if the imaginary part of the spectrum of the pencil (¸B ¡ A) is countable, then a bounded uniformly continuous solution u(t) of the equation is asymptotically almost periodic if and only if the functions e ¸tu (t), (¸2 iR), have uniformly convergent means. A condition of exponential stability also is given when the generalized eigenvectors and associated root vectors of the linear pencil (¸B ¡ A) form a Riesz basis.

Forensic Science

“…The pyrolysis products of dimethylamphetamine have been studied by GC/MS, headspace GC/MS, and LC/ESI/MS (348). Methamphetamine and other related stimulant samples were profiled using headspace SPME/ GC/MS (349,350), capillary GC (351), and GC/MS, GC/PIMS, and GC/MS/MS (352). The combined use of δ 2 H, δ 13 C, and δ 15 N isotopic data along with 2 H NMR was used to study the synthetic pathways used in the preparation of MDA and N-substituted homologues (353).…”

Detection of methamphetamine in indoor air using dynamic solid phase microextraction: a supplementary method to surface wipe sampling

“…It allows rapid sample collection, does not use organic solvents, is easy to use, and is selective. 29 SPME has been used with GC-MS for qualitative analysis of headspace vapors of surface wipes 30,31 hair, 32 and street methamphetamine 33,34 but has not been evaluated for determination of methamphetamine in indoor air. Our preliminary studies showed that SPME met the criteria of sensitivity and rapidity, but in its passive mode SPME bres could be exposed to varying volumes of air depending on air currents within the premises.…”