On non-equilibria threshold strategies in ticket queues

In many real-life queueing systems, a customer may balk upon arrival at a queueing system, but other customers become aware of it only at the time the balking customer was to start service. Naturally, the balking is an outcome of the queue length, and the decision is based on a threshold. Yet the inspected queue length contains customers who balked. In this work, we consider a Markovian queue with infinite capacity and with customers that are homogeneous with respect to their cost reward functions. We show that that no threshold strategy can be a Nash equilibrium strategy. Furthermore, we show that for any threshold strategy adopted by all, the individual’s best response is a double threshold strategy. That is, join if and only if one of the following is true: (i) the inspected queue length is smaller than one threshold, or (ii) the inspected queue length is larger than a second threshold. Our model is under the assumption that the response time of the server when he finds out that a customer balked is negligible. We also discuss the validity of the result when the response time is not negligible.     

Asymptotic centers and best compact approximation of operators intoC(K)

The existence of best compact approximations for all bounded linear operators fromX intoC(K) is related to the behavior of asymptotic centers inX ^*. IfK is just one convergent sequence, the condition is that everyω ^*-convergent sequence inX ^* will have an asymptotic center. We first study this property, solving some open problems in the theory of asymptotic centers. IfK is more “complex,” the asymptotic centers should behave “continuously.” We use this observation to construct operators fromC[0,1] intoC(ω ²) and from ?₁ intoL ₁ without best compact approximation. We also construct spacesX ₁,X ₂, isomorphic to a Hilbert space, and operatorsT ₁,∶X ₁→C(ω ²),T ₂∶?₁→X ₂ without best compact approximations.     

Simply connected coset complexes for rank 1 groups of Lie type

This work was partially supported by BSF 92-00320     

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.     

Baryon-antibaryon annihilations,unitarity and the pomeron

We show that baryon-antibaryon annihilations into mesons contribute, via unitarity, mainly to the pomeron term in the total $\text{B}$B cross section. The meson-exchange term is mainly built by non-annihilation processes. These results are contrary to previous ideas according to which $\text{B}$B annihilations are responsible for the difference between $\text{σ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(}\text{B}\text{B}\text{)}$ and σ_tot(BB) and contribute to the meson exchange term. Our conclusions are based on an explicit duality diagram model which we discuss in some detail. However, a much wider class of models give similar results. Experimental tests of our ideas are proposed.