Exact loop-variables formulation of pure gauge lattice QCD3 is derived from the Wilson version of the model. The observation is made that the resulting model is two-dimensional. This significant feature is shown to be a unique property of the gauge field. The model is defined on the infinite genus surface which covers regularly the original three-dimensional lattice. Similar transformation appl...

On the Riemann property of angular lattice sums and the one-dimensional limit of two-dimensional lattice sums BY ROSS C. MCPHEDRAN*, I. J. ZUCKER, LINDSAY C. BOTTEN AND NICOLAE-ALEXANDRU P. NICOROVICI CUDOS, School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia Department of Physics, King’s College London, The Strand, London WC2R 2LS, UK School of Mathematical Science...

Let {gt} be a nonquasiunipotent one-parameter subgroup of a connected semisimple Lie group G without compact factors; we prove that the set of points in a homogeneous spaceG/Γ (Γ an irreducible lattice inG) with bounded {gt}-trajectories has full Hausdorff dimension. Using this we give necessary and sufficient conditions for this property to hold for any Lie group G and any lattice Γ in G.

Magnetic property of antiferromagnets with two-dimensional distorted triangular lattice structures, β′-Me4P[Pd(dmit)2]2 and β′-Et2Me2P[Pd(dmit)2]2, was investigated by the muon spin relaxation method. Enhancement of the muon spin depolarization associated with the critical slow-down effect suggests that the spin dynamics due to the twoand three-dimensional magnetic correlations reflects the dev...

In abstract algebra courses, teachers are often confronted with the task of drawing subgroup lattices. For purposes of instruction, it is usually desirable that these lattices be planar graphs (with no crossings). We present a characterization of abelian groups with this property. We also resolve the following problem in the abelian case: if the subgroup lattice is required to be drawn hierarch...

In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems LLL (Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this arti...

We prove that whenever a Kac-Moody group over a finite field is a lattice of its buildings, it has a fundamental domain with respect to which the induction cocycle is L for any p∈ [1; +∞). The proof uses elementary counting arguments for root group actions on buildings. The applications are the possibility to apply some lattice superrigidity, and the normal subgroup property for Kac-Moody latti...

We deene new selection criteria for lattice rules for quasi-Monte Carlo integration. The criteria examine the projections of the lattice over subspaces of small or successive dimensions. Their computation exploits the dimension-stationarity of certain lattice rules, and of other low-discrepancy point sets sharing this property. Numerical results illustrate the usefulness of these new gures of m...

The collection of convex subsets of a multipartite tournament T forms a lattice C(T ). Given a lattice structure for C(T ), we deduce properties of T . In particular, we find conditions under which we can detect clones in T . We also determine conditions on the lattice which will imply that T is bipartite, except for a few cases. We classify the ambiguous cases. Finally, we study a property of ...