We study here the poset DP (X) of density preserving continuous maps defined on a Hausdorff sapce X and show that it is a complete lattice for a compact Hausdorff space without isolated points. We further show that for countably compact T3 spaces X and Y without isolated points, DP (X) and DP (Y ) are order isomorphic if and only if X and Y are homeomorphic. Finally, Magill’s result on the rema...

We show that for each aspherical compact complex surface X whose fundamental group π fits into a short exact sequence 1 → K → π → π1(S) → 1 where S is a compact hyperbolic Riemann surface and the group K is finitelypresentable, there is a complex structure on S and a nonsingular holomorphic fibration f : X → S which induces the above short exact sequence. In particular, the fundamental groups o...

A basic question in geometry is to understand compact locally homogeneous manifolds, i.e., those compact manifolds that can be locally modelled on a homogeneous space J\H of a finite-dimensional Lie group H. This means that there is an atlas on a manifold M consisting of local diffeomorphisms with open sets in J\H where the transition functions between these open sets are given by translations ...

We construct, in discrete two-component systems with cubic nonlinearity, stable states emulating Skyrmions of the classical field theory. In the two-dimensional case, an analog of the baby Skyrmion is built on the square lattice as a discrete vortex soliton of a complex field [whose vorticity plays the role of the Skyrmion's winding number (WN)], coupled to a radial "bubble" in a real lattice f...

J/Ψ and ηc above the QCD critical temperature Tc are studied in anisotropic quenched lattice QCD, considering whether the cc̄ systems above Tc are compact quasi-bound states or scattering states. We adopt the standard Wilson gauge action and O(a)-improved Wilson quark action with renormalized anisotropy as/at = 4 at β = 6.10 on 163 × (14−26) lattices, which correspond to the spatial lattice volu...

Anisotropic lattice QCD studies of penta-quarks(5Q) with JP = 1/2± and 3/2± are presented at the quenched level together with tetra-quarks(4Q). The standard gauge action at β = 5.75 and O(a) improved quark (clover) action with κ = 0.1410(0.010)0.1440 are employed on the anisotropic lattice with the renormalized anisotropy as/at = 4. The “hybrid boundary condition(HBC)” is adopted to discriminat...

In this article we consider a graphene sheet that is folded in various compact geometries with arbitrary topology described by a certain genus, g. While the Hamiltonian of these systems is defined on a lattice one can take the continuous limit. The obtained Dirac-like Hamiltonian describes well the low energy modes of the initial system. Starting from first principles we derive an index theorem...

In this paper, we revisit the lattice representation of continuous piecewise affine (PWA) function and give a formal proof of its representation ability. Based on this, we derive the irredundant lattice PWA representation through removal of redundant terms and literals. Necessary and sufficient conditions for irredundancy are proposed. Besides, we explain how to remove terms and literals in ord...

Staggered fermions are constructed for the transverse lattice regularization scheme. The weak perturbation theory of transverse lattice non-compact QED is developed in lightcone gauge, and we argue that for fixed lattice spacing this theory is ultraviolet finite, order by order in perturbation theory. However, by calculating the anomalous scaling dimension of the link fields, we find that the i...