We prove that every distributive algebraic lattice with at most א1 compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module. The א1 bound is optimal, as we find a distributive algebraic lattice D with א2 compact elements that is not isomorphic to the congruence lattice of any algebra with almost permutable congruences (hence n...

We examine the strong coupling limit of both compact and non-compact quantum electrodynamics (QED) on a lattice with staggered Fermions. We show that every SU(NL) quantum antiferromagnet with spins in a particular fundamental representation of the SU(NL) Lie algebra and with nearest neighbor couplings on a bipartite lattice is exactly equivalent to the infinite coupling limit of lattice QED wit...

We have simulated the pure gauge compact QED with fixed boundary conditions, on lattices from 6 4 to 16 4. We argue that a lattice with this fixed boundary imposition corresponds actually to a lattice with spherical topology. We have found the presence of a phase transition without any trace of discontinuity. Moreover, the specific heat and the Binder cumulant are qualitatively consistent with ...

Let X be a locally finite tree, and let G = Aut(X). Then G is a locally compact group. We show that if X has more than one end, and if G contains a discrete subgroup Γ such that the quotient graph of groups Γ\\X is infinite but has finite covolume, then G contains a non-uniform lattice, that is, a discrete subgroup Λ such that Λ\G is not compact, yet has a finite G-invariant measure. 0. Notatio...

We study glueball and meson scattering in compact QED2+1 gauge theory in a Hamiltonian formulation and on a momentum lattice. We compute ground state energy and mass, and introduce a compact lattice momentum operator for the computation of dispersion relations. Using a non-perturbative time-dependent method we compute scattering cross sections for glueballs and mesons. We compare our results wi...

Compact polymers are self-avoiding random walks that visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform numerical calculations is generating a sufficiently large number of randomly sampled configurations. We present a Monte Carlo algorithm that uniformly samples com...

In this paper, we illustrate a method to enumerate two-dimensional directed animals, with compact sources, on both the square and the triangular lattice. We give a recursive description of these structures from which we deduce their generating function, according to various parameters: the area, the right half-width and the number of compact sources. We determine the average number of compact s...

Let ? be a lattice in a simple higher rank Lie group G. We describe all locally compact (not necessarily Lie) groups H in which ? can be embedded as a lattice. For lattices ? in rank one groups G (with the only exception of non-uniform lattices in G ' SL 2 (R), which are virtually free groups) we give a similar description of all possible locally compact groups H, in which ? can be embedded as ...

We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. W...