Graphic matroids and the multicommodity transportation problem

A necessary and sufficient condition for unimodularity in the multicommodity transportation problem is established, and the constructive proof yields an equivalent, single commodity network flow problem for the class of problems satisfying the condition. The concept of a graphic matroid is used to establish the transformation.     

Irreducible quantum dynamical semigroups

We study some irreducible and ergodic properties of quantum dynamical semigroups, and apply our methods to semigroups of Lindblad type.     

Dedekind sums and class numbers

Formulas for the class number of an imaginary quadratic number field are proved. Some of these formulas were previously established byBerndt and byGoldstein andRazar with the use of analytic methods. The proofs given here use Dirichlet's classical class number formula, but otherwise the proofs are completely elementary. A key ingredient in the proofs is the reciprocity theorem for Dedekind-Rademacher sums.     

Oxygen dissociation relaxation behind oblique shocks

Nearly frozen oxygen dissociation relaxation has been investigated behind oblique shocks. Photographs of the shock have been taken and density profiles of the relaxation zones have been measured by means of a multibeam-laser-differential interferometer. Calculations of the relaxation zones with different published dissociation rate coefficients have been done for evaluating the experiments.     

The essential nonlinearity ofN-level quantum thermodynamics

This paper explores the possibility that linear dynamical maps might be used to describe the energy-conserving, entropy-increasing motions which occur in closed thermodynamic systems as they approach canonical thermal equilibrium. ForN-level quantum systems withN>2, we prove that no such maps exist which are independent of the initial state.     

Hadronization of excited nucleons in nuclear collisions at ISR energies

Calorimeters downstream of the intersection of pα and αα beams in the ISR have been used to study the hadronization of excited nucleons. These data extend and support the conclusions from previous studies of the A-dependence of particle multiplicities in ultrarelativistic p-nucleus collisions, which provided evidence that the proton hadronizes outside the nuclear volume.     

Characterizations of taut semi-local rings

Summary It is proved that the following statements are equivalent for semi-local domain R:1) R is taut (i.e., for each non-maximal prime ideal P in R, height P+depth P=altitude R).2) Every integral domain which contains and is integral over R is taut.3) R[1/b]. satisfies the second chain condition for prime ideals (s.c.c.), for each non-zero b in the Jacobson radical J of R.4) R[1/b] satisfies the first chain condition for prime ideals (f.c.c.), for some non-zero b in J.5) For each depth one prime ideal P in R, R_P satisfies the s.c.c. and height P=altitude R−1.6) R(X) is taut, where X is an indeterminate.7) For each pair of analytically independent elements b, c in R, R(c/b) is taut and altitude R(c/b)=altitude R−1.8) Each maximal set of analytically independent elements in R contains either one element or altitude R elements. Much of the theorem is then generalized (with suitable modifications) to rings which contain and are integral over a taut semi-local ring. Entrata in Redazione il 5 dicembre 1975. Research on this paper was supported in part by the National Science Foundation grant NSF GP-28939-1.