The factorization approximation for the Master Equation

We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω₀, where ω₀ is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small.     

The entropies of renewal systems

Renewal systems are symbolic dynamical systems originally introduced by Adler. IfW is a finite set of words over a finite alphabetA, then the renewal system generated byW is the subshiftX _W ⊂A ^Z formed by bi-infinite concatenations of words fromW. Motivated by Adler’s question of whether every irreducible shift of finite type is conjugate to a renewal system, we prove that for every shift of finite type there is a renewal system having the same entropy. We also show that every shift of finite type can be approximated from above by renewal systems, and that by placing finite-type constraints on possible concatenations, we obtain all sofic systems. The authors were supported in part by NFS grants DMS-8706284, DMS-8814159 and DMS-8820716.     

On centroid branches of trees from certain families

We obtain various results involving the centroid branches of randomly chosen trees from simply generated families.     

Some asymptotic results useful in enumeration problems

Suppose one is given two related generating functionsa(x) = a _n x ⁿ andb(x) = b _n x ⁿ , often it is of interest to determine the limiting behaviour of the quantitiesa _n /b _n We survey some earlier results of this nature and give some new ones     

Gas chromatographic assay with pharmacokinetic applications for monitoring T-2 and HT-2 toxins in plasma

A gas-liquid chromatographic (GLC) method for monitoring T-2 and HT-2 toxins in plasma was developed. The procedure involved extraction of the toxins with ethyl acetate, chromatography on a C18 reversed-phase column and derivatization with heptafluorobutyric anhydride (HFBA). The T-2 and HT-2 HFBA derivatives were chromatographed on OV-17 at various temperatures and measured with an electron-capture detector. Iso-T-2 toxin and iso-HT-2 toxin were used as internal standards. Recoveries averaged 95.1 +/- 8.6% for T-2 toxin and 102.1 +/- 5.2% for HT-2 toxin at levels ranging from 40 to 120 ng/ml. The limits of detection were 30 and 5 ng/ml of T-2 and HT-2 toxin, respectively. The range of the assay covers plasma concentrations at which toxicity becomes manifest. The pharmacokinetic application of this GLC method is illustrated by simultaneous monitoring of T-2 and HT-2 toxins levels in plasma obtained after intravenous administration of T-2 toxin to a dog.     

The outer-distance of nodes in random trees

The outer-distance of a nodeu in a rooted treeT _n is the height of the subtree determined byu and all nodesv such thatu is on the path joiningv and the root ofT. We show that the expected outer-distance of nodes of treesT _n in certain families is asymptotic toB logn where the constantB depends on .