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.     

Efficiency prices for optimal consumption plans. II

We consider an economy described by a setY of feasible consumption plans and a utility functionu.Y is assumed to be a convex and compact subset of s⁺, the non-negative cone of the spaces of all real sequences.u is assumed to be concave, increasing and continuous (in an appropriate sense) on the cone spanned byY. Our main result is that a point ofY is optimal iff it is competitive. Prepared under NSF Grant 2530 to Stanford University.     

Data storage in optical fibers and reconstruction by use of low-coherence spectral interferometry

We demonstrate optical data storage in optical fibers and reconstruction by use of low-coherence spectral interferometry. The information was stored by means of writing fiber Bragg gratings with different central wavelengths at different locations of the fiber. We need only a single short pulse is needed to read all the stored data. The maximum theoretical reconstruction rate that can be obtained with our technique is 10 Tbits/s. Our storage technique can be useful for identifying users in optical communication networks.     

The role of template in the synthesis of meso-hexamethyl-meso-hexaphenyl-calix[6]pyrrole: trihalogenated compounds as templates for the assembly of a host with a trigonal cavity

Trihalogenated compounds act as effective and selective templates in the template-assisted synthesis of meso-hexaphenyl-calix[6]pyrrole.     

Presentation of the creep curves of solid biological materials by a simplified mathematical version of the generalized Kelvin-Voigt model

Published creep equations, derived from the Kelvin-Voigt model with a discrete retardation time spectrum were used to generate data for linear presentation of the creep function. It is shown that 2–3 term creep functions, containing 4–6 constants, could be reduced to an algebraic expression having two constants only. Consequently, entire creep curves of a variety of biological and food materials could be described by a single type of equation in the form of:P (t) = k ₀ + k₁ t + t/(k₂ + k₃t) whereP (t) is the creep parameter (compliance, strain or deformation),k ₀ a constant representing the instantaneous compliance,k ₁ a constant representing the steady-state flow, andk ₂ andk ₃ the characteristic constants of the creep function (t) obtained by regression from the linear relationship oft/ (t) vst.