Stable multi-sets

In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are equivalent to stable sets.  For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable multi-sets and conditions for them to be facet defining are determined.  The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets emerge as an important substructure in the design of optical networks. Received: February 14, 2001/Revised version: September 7, 2001     

The Downs-Thomson Paradox: Existence, Uniqueness and Stability of User Equilibria

Consider a network where two routes are available for users wishing to travel from a source to a destination. On one route (which could be viewed as private transport) service slows as traffic increases. On the other (which could be viewed as public transport) the service frequency increases with demand. The Downs-Thomson paradox occurs when improvements in service produce an overall decline in performance as user equilibria adjust. Using the model proposed by Calvert [10], with a ⋅|M|1 queue corresponding to the private transport route, and a bulk-service infinite server queue modelling the public transport route, we give a complete analysis of this system in the setting of probabilistic routing. We obtain the user equilibria (which are not always unique), and determine their stability.AMS subject classification: 60K30, 90B15, 90B20, 91A10, 91A13This revised version was published online in June 2005 with corrected coverdate     

Model-dependent nature of blowtorch effect on the escape and equilibration rates

We analyze the relaxation behavior of a bistable system when the background temperature profile is inhomogeneous due to the presence of a localized hot region (blowtorch) on one side of the potential barrier. Since the diffusion equation for inhomogeneous medium is model-dependent, we consider two physical models to study the kinetics of such system. Using a conventional stochastic method, we obtain the escape and equilibration rates of the system for the two physical models. For both models, we find that the hot region enhances the escape rate from the well where it is placed while it retards the escape rate from the other well. However, the value of the escape rate from the well where the hot region is placed differs for the two models while that of the escape rate from the other well is identical for both. This work, for the first time, gives a detailed report of the similarities and differences of the escape rates and, hence, exposes the common and distinct features of the two known physical models in determining the way the bistable system relaxes. Received 25 September 2001     

A Scanning Electron Microscopy study of water in soil

Cold stage Scanning Electron Microscopy (SEM) with a rapid cooling technique makes it possible to investigate the water phase within unsaturated porous media. It is thought that this technique preserves the main features of the micromorphology of the water menisci as it exists in the liquid phase in soils. Saddle-shaped elements, as well as pendular rings of water, were observed with concave and convex curvatures of the water-air interface. The hydraulic conductivity of an unsaturated soil may be inferred from SEM photographs. Observations of isolated water menisci indicate the existence of an immobile water domain. The surface geometry of the water menisci was analyzed quantitatively and surface tension and capillary pressure were determined.     

Cyclopolymerisation. 3. Mitt. ESR-Untersuchungen von Diallylaminen mit Redox-Systemen

Ohne Zusammenfassung     

Stereo- and regioselectivity in asymmetric synthesis of α-amino substituted benzocyclic compounds

The enantiomerically pure chiral benzocyclic amines 6–8 were obtained by asymmetric transamination of the corresponding prochiral ketones 9a–c. The method involves: (a) formation of chiral imines 10a–c from the prochiral ketones 9a–c and the inexpensive chiral auxiliary (R)- or (S)-phenylethylamine (PEA); (b) asymmetrically induced reduction of these imines to the diastereomeric amines 11a–c and 12a–c; (c) catalytic hydrogenation to remove the benzylic fragment of the chiral PEA auxiliary. The stereoselectivity of the imine reduction, as well as the regioselectivity of the catalytic hydrogenation, are strongly dependent on the size of the saturated ring condensed with the benzene ring. This approach was used to develop a convenient, high yielding, and stereoselective route to several practically important optically active α-amino substituted benzocyclic compounds.