Combinatorial Hopf algebras, noncommutative Hall-Littlewood functions, and permutation tableaux

We introduce a new family of noncommutative analogues of the Hall-Littlewood symmetric functions. Our construction relies upon Tevlin's bases and simple q-deformations of the classical combinatorial Hopf algebras. We connect our new Hall-Littlewood functions to permutation tableaux, and also give an exact formula for the q-enumeration of permutation tableaux of a fixed shape. This gives an explicit formula for: the steady state probability of each state in the partially asymmetric exclusion process (PASEP); the polynomial enumerating permutations with a fixed set of weak excedances according to crossings; the polynomial enumerating permutations with a fixed set of descent bottoms according to occurrences of the generalized pattern 2-31.Comment: 37 pages, 4 figures, new references adde

Transport of positrons in the interstellar medium

This work investigates some aspects of the transport of low-energy positrons in the interstellar medium (ISM). We consider resonance interactions with magnetohydrodynamic waves above the resonance threshold. Below the threshold, collisions take over and deflect positrons in their motion parallel to magnetic-field lines. Using Monte-Carlo simulations, we model the propagation and energy losses of positrons in the different phases of the ISM until they annihilate. We suggest that positrons produced in the disk by an old population of stars, with initial kinetic energies below 1 MeV, and propagating in the spiral magnetic field of the disk, can probably not penetrate the Galactic bulge.Comment: 4 pages, 3 figures, accepted for publication in the proceeding of the 6th INTEGRAL worksho

Sigma and omega meson propagation in a dense nuclear medium

The propagation of the scalar ($\sigma$) and vector ($\omega$) mesons in nuclear matter is studied in detail using the Walecka model over a wide range of densities and including the effects of a finite $\sigma$ width through the inclusion of a two-pion loop. We calculate the dispersion relation and spectral functions of the $\sigma$ and (transverse and longitudinal) $\omega$ mesons, including the effect of $\sigma$-$\omega$ mixing in matter. It is shown that the mixing effect is quite important in the propagation of the (longitudinal) $\omega$ and $\sigma$ mesons above normal nuclear matter density. We find that there is a two-peak structure in the spectral function of the $\sigma$ channel, caused by $\sigma$-$\omega$ mixing.Comment: 17 pages including 6 ps files, submitted to Phys. Lett. B. Acknowledgement is revise

Tip-sample interactions in atomic force microscopy: I. Modulating adhesion between silicon nitride and glass

An adhesive interaction between a silicon nitride AFM tip and glass substrate in water is described. This adhesion is in the range 5-40 nN, of which a large component is likely to be due to hydrogen bonding between the silanol groups on both surfaces. The interaction can be modulated by a variety of buffers commonly used in biochemical and biological research, including sodium phosphate, tris(hydroxymethyl)aminomethane, glycine, and N-2-hydroxyethyl-piperazine N'-2-ethanesulfonic acid. Using these buffers it appears that there are effects of ion concentration, ion type and pH on the measured adhesion. Of the conditions examined, phosphate was most effective at reducing adhesion and could be used at concentrations as low as 10 mM at neutral pH. The results demonstrate that the chemical interactions between tip and sample can be modulated, and provide a basis for designing conditions for imaging and manipulating biological molecules and structures

Security Estimates for Quadratic Field Based Cryptosystems

We describe implementations for solving the discrete logarithm problem in the class group of an imaginary quadratic field and in the infrastructure of a real quadratic field. The algorithms used incorporate improvements over previously-used algorithms, and extensive numerical results are presented demonstrating their efficiency. This data is used as the basis for extrapolations, used to provide recommendations for parameter sizes providing approximately the same level of security as block ciphers with $80,$ $112,$ $128,$ $192,$ and $256$-bit symmetric keys

Supernova Constraints on MeV Dark Sectors from e+ e- Annihilations

Theories with dark forces and dark sectors are of interest for dark matter models. In this paper we find the region in parameter space that is constrained by supernova cooling constraints when the models include dark sector particles with masses around 100 MeV or less. We include only interactions with electrons and positrons. The constraint is important for small mixing parameters.Comment: 18 pages, 3 figure