We give algorithms for computing the densest k-dimensional sublattice of an arbitrary lattice, and related problems. This is an important problem in the algorithmic geometry of numbers that includes as special cases Rankin’s problem (which corresponds to the densest sublattice problem with respect to the Euclidean norm, and has applications to the design of lattice reduction algorithms), and th...

A general class of hopping models on a finite bipartite lattice is considered, including the Hubbard model and the Falicov-Kimball model. For the half-filled band, the single-particle density matrix ρ(x, y) in the ground state and in the canonical and grand canonical ensembles is shown to be constant on the diagonal x = y, and to vanish if x 6= y and if x and y are on the same sublattice. For f...

A discrete multidimensional system is the set of solutions to a linear partial difference equations defined on lattice $$\mathbb {Z}^n$$ . This paper shows that it determined by unique coarsest sublattice, in sense this sublattice determine ; therefore correct domain definition system. In turn, defining Galois group symmetries leave invariant These results find application understanding propert...

This is a simple but realistic microscopic theory of spontaneous spin reorientation in rare-earth perovskites, orthoferrites RFeO3 and orthochromites RCrO3, induced by the 4f-3d interaction, namely, interaction well-isolated ground-state Kramers doublet or non-Kramers quasi-doublet 4f ion with an effective magnetic field 3d sublattice. Both temperature nature spin-reorientation transition are r...

the aim of this paper is to introduce and study set- valued homomorphism on lattices and t-rough lattice with respect to a sublattice. this paper deals with t-rough set approach on the lattice theory. the result of this study contributes to, t-rough fuzzy set and approximation theory and proved in several papers. keywords: approximation space; lattice; prime ideal; rough ideal; t-rough set; set...

Let σ be a permutation of the set {1,2, — -, n} and let Π(N) denote the lattice of partitions of {1,2, •••,%}. There is an obvious induced action of σ on Π(N); let Π(N)σ — L denote the lattice of partitions fixed by σ. The structure of L is analyzed with particular attention paid to ^f, the meet sublattice of L consisting of 1 together with all elements of L which are meets of coatoms of L. It ...

D. Lau raised the problem of determining the cardinality of the set of all partial clones of Boolean functions whose total part is a given Boolean clone. The key step in the solution of this problem, which was obtained recently by the authors, was to show that the sublattice of strong partial clones on {0, 1} that contain all total functions preserving the relation ρ0,2 = {(0, 0), (0, 1), (1, 0...

The spin dynamics of the semiclassical Heisenberg model with uniaxial anisotropy, on the layered triangular lattice with antiferromagnetic coupling for both intralayer nearest neighbor interaction and interlayer interaction is studied both in the ordered phase and in the paramagnetic phase, using the Monte Carlo-molecular dynamics technique. The important quantities calculated are the full dyna...

We have used positron annihilation spectroscopy and infrared absorption measurements to study the Ga sublattice defects in epitaxial Ga(1-x)MnxAs with Mn content varying from 0% to 5%. We show that the Ga vacancy concentration decreases and As antisite concentration increases with increasing Mn content. This is in agreement with thermodynamical considerations for the electronic part of the form...