Characterization of chick pea <Emphasis Type="Italic">(Cicer arietum L)</Emphasis> pastes using squeezing flow viscometry

Domestic type and commercial chickpea pastes ('humus'), as well as a commercial soy substitute, were squeezed at a constant displacement rate between 150 mm parallel Teflon plates, mounted on an Instron Universal Testing Machine, before and after stirring. At 1 mm height the crosshead was stopped and the stress relaxation followed. The apparent stress at 1 mm height and that after 1 and 2 min relaxation were considered consistency measures of the pastes. They were reproducible parameters, and sensitive enough to monitor differences between the products, batches of the same product and stirred and unstirred samples. A stronger consistency was reflected not only by a high apparent compressive stress before and after relaxation but also in a higher yield stress, as determined in shear with a parallel plates sensor, suggesting that the paste's texture is determined by a solid like matrix. Stirring invariably reduced the pastes consistency presumably by an irreversible disruption of their microstructure. The presence of suspended solid particles had little or no effect on the pastes ability to retain their consistency after stirring.     

Composite quarks and leptons in supersymmetric grand unification

Chirality under SUSY-GUT is suggested as a sufficient condition for composites to be massless, in addition to the necessary anomaly matching á la 't Hooft. This results in a very stringent set of self-consistency requirements, which dictates also the number and structure of the generations. As an illustration I present an [SU(3)]³×[SUSY] model. It involves three generations (2 light + 1 heavy) and some other realistic features.     

Representations of simple games by social choice functions

We investigate possible constructions of choice procedures (social choice functions) for committees (simple games). The notion of a capacity of a committee is derived from our construction. We determine the capacity of strong, symmetric and weak simple games. We also provide an upper bound on the capacity of a simple game without veto players.     

Energy exchange in fast optical soliton collisions as a random cascade model

We study the dynamics of a probe soliton propagating in an optical fiber and exchanging energy in fast collisions with a random sequence of pump solitons. The energy exchange is induced by Raman scattering or by cubic nonlinear loss/gain. We show that the equation describing the dynamics of the probe soliton's amplitude has the same form as the equation for the local space average of energy dissipation in random cascade models in turbulence. We characterize the statistics of the probe soliton's amplitude by the τq exponents from multifractal theory and by the Cramér function S(x). We find that the nth moment of the two-time correlation function and the bit-error-rate contribution from amplitude decay exhibit power-law behavior as functions of propagation distance, where the exponents can be expressed in terms of τq or S(x).     

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.     

Closed incompressible surfaces in knot complements

In this paper we show that given a knot or link in a -plat projection with and , where is the length of the plat, if the twist coefficients all satisfy then has at least nonisotopic essential meridional planar surfaces. In particular if is a knot then contains closed incompressible surfaces. In this case the closed surfaces remain incompressible after all surgeries except perhaps along a ray of surgery coefficients in .

     

Bitangents of tropical plane quartic curves

Mathematische Zeitschrift - We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic...