Filters compatible with isomorphism testing

Like the lower central series of a nilpotent group, filters generalize the connection between nilpotent groups and graded Lie rings. However, unlike the case with the lower central series, the associated graded Lie ring may share few features with the original group: e.g. the associated Lie ring can be trivial or arbitrarily large. We determine properties of filters such that every isomorphism between groups is induced by an isomorphism between graded Lie rings.     

Self-dual Maxwell field on a null cone

As an introduction to the use of self-dual variables on a null cone, the Hamiltonian for the Maxwell field is set up on a null cone in Minkowski space. In this treatment, the vector potential (the connection) and the self-dual components of the Maxwell field are treated as independent configuration space variables. Because the initial surface is a null cone, additional primary and secondary constraints arise. These constraints can be grouped into first class and second class. The elimination of the second class constraints together with the reality conditions on the vector potential, reduce the independent phase space variables to two. In its final form the Hamiltonian can be expressed in terms of the product of the self-dual Maxwell field and its complex conjugate.     

Pervaporation of benzene/cyclohexane mixtures using ion-exchange membrane containing copper ions

The sorption, diffusion, and pervaporation (PV) properties of benzene/cyclohexane (Bz/Cx) mixtures on cation-exchange membranes containing copper ions (Cu(II)) were investigated. The equilibrium sorption isotherms of pure vapors in the membranes and the partial solubility of binary solutions in the membranes were described using the UNIQUAC model. The τ_iM and τ_Mi values were 0.978 and 0.591 for Bz, and 0.922 and 0.475 for Cx. The transient regimes of vapor sorption were employed to calculate the concentration-dependent diffusion coefficients. Long’s model sufficiently explained the diffusivity of Bz and Cx in the membranes. The pre-exponential factors were 3×10⁻¹³ m²/s and the plasticization factors were 3.0 and 3.6 for Bz and Cx, respectively. Excellent agreement was found with the experimental results applying the solubility and diffusivity data to simulate the pervaporation performance (flux and selectivity) using the modified Maxwell–Stefan equation. The membrane containing Cu(II) demonstrates better facilitating capability for Bz transport than that with Na(I), mainly due to its preferential sorption property toward Bz. Replacing Na(I) with Cu(II) into a Neosepta membrane resulted in better separation efficiency and higher Bz flux throughout the entire Bz concentration range.     

De Bruijn cycles for covering codes

A de Bruijn covering code is a q‐ary string S so that every q‐ary string is at most R symbol changes from some n‐word appearing consecutively in S. We introduce these codes and prove that they can have size close to the smallest possible covering code. The proof employs tools from field theory, probability, and linear algebra. Included is a table of the best known bounds on the lengths of small binary de Bruijn covering codes, up to R = 11 and n = 13, followed by several open questions in this area. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Asymptotic Regimes of Magnetic Bianchi Cosmologies

We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII₀, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII₀ cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magnetic Bianchi models, we rigorously establish that typical magnetic Bianchi VII₀ cosmologies exhibit the phenomena of asymptotic self-similarity breaking and Weyl curvature dominance in the late-time regime.     

Weak matching rules for quasicrystals

Weak matching rules for a quasicrystalline tiling are local rules that ensure that fluctuations in perp-space are uniformly bounded. It is shown here that weak matching rules exist forN-fold symmetric tilings, whereN is any integer not divisible by four. The result suggests that, contrary to previous indications, quasicrystalline ground states are not confined to those symmetries for which the incommensurate ratios of wavevectors are quadratic irrationals. An explicit method of constructing weak matching rules forN-fold symmetric tilings in two dimensions is presented. It is shown that the generalization of the construction yields weak matching rules in the case of icosahedral symmetry as well.