Customers’ abandonment strategy in an <Emphasis Type="Italic">M</Emphasis> / <Emphasis Type="Italic">G</Emphasis> / 1 queue

We consider an M / G / 1 queue in which the customers, while waiting in line, may renege from it. We show the Nash equilibrium profile among customers and show that it is defined by two sequences of thresholds. For each customer, the decision is based on the observed past (which determines from what sequence the threshold is taken) and the observed queue length (which determines the appropriate element in the chosen sequence). We construct a set of equations that has the Nash equilibrium as its solution and discuss the relationships between the properties of the service time distribution and the properties of the Nash equilibrium, such as uniqueness and finiteness.     

Detection and Identification of Alkylating Agents by Using a Bioinspired “Chemical Nose”

Alkylating agents are simple and reactive molecules that are commonly used in many and diverse fields such as organic synthesis, medicine, and agriculture. Some highly reactive alkylating species are also being used as blister chemical‐warfare agents. The detection and identification of alkylating agents is not a trivial issue because of their high reactivity and simple structure. Herein, we report on a new multispot luminescence‐based approach to the detection and identification of alkylating agents. In order to demonstrate the potential of the approach, seven π‐conjugated oligomers and polymers bearing nucleophilic pyridine groups, 1 – 7 , were adsorbed onto a solid support and exposed to vapors of alkylators 8 – 15 . The alkylation‐induced color‐shift patterns of the seven‐spot array allow clear discrimination of the different alkylators. The spots are sensitive to minute concentrations of alkylators and, because the detection is based on the formation of new covalent bonds, these spots saturate at about 50 ppb.     

Wiener's tauberian theorem for spherical functions on the automorphism group of the unit disk

Our main result gives necessary and sufficient conditions, in terms of Fourier transforms, for an ideal in the convolution algebra of spherical integrable functions on the (conformal) automorphism group of the unit disk to be dense, or to have as closure the closed ideal of functions with integral zero. This is then used to prove a generalization of Furstenberg's theorem, which characterizes harmonic functions on the unit disk by a mean value property, and a “two circles” Morera type theorem (earlier announced by Agranovskii). The second author's work was partially supported by the fund for the promotion of research at the Technion-Israel Institute of Technology. The third author's work was partially supported by the Swedish Natural Science Research Council, and by the 1992 Wallenberg Prize from the Swedish Mathematical Society.     

Structural changes in block copolymers: coupling of electric field and mobile ions

We argue that the presence of dissociated ions in block copolymers under electric fields can induce strong morphological changes and even lead to phase transitions. We investigate, in particular, diblock copolymers in the body centered cubic (bcc) phase. In pure dielectric materials (no free charges), a dielectric breakdown is expected to occur for large enough electric fields, preempting any structural phase transition. On the other hand, dissociated ions are predicted to induce a phase transition to a hexagonal array of cylinders, at fields of about 10 V/microm or even lower. The strength of this mechanism can be tuned by controlling the amount of free ions present.