We construct lattices with quadratic structure over the integers in quadratic number fields having the property that the rank of the quadratic structure is constant and equal to the rank of the lattice in all reductions modulo maximal ideals. We characterize the case in which such lattices are free. The construction gives a representative of the genus of such lattices as an orthogonal sum of “s...

Upper and lower bounds are derived for the decoding complexity of a general lattice L. The bounds are in terms of the dimension n and the coding gain of L, and are obtained based on a decoding algorithm which is an improved version of Kannan’s method. The latter is currently the fastest known method for the decoding of a general lattice. For the decoding of a point x, the proposed algorithm rec...

Let L = (Li | i ∈ I) be a family of lattices in a nontrivial lattice variety V, and let φi : Li → M , for i ∈ I, be isotone maps (not assumed to be lattice homomorphisms) to a common lattice M (not assumed to lie in V). We show that the maps φi can be extended to an isotone map φ : L → M , where L = FreeV L is the free product of the Li in V. This was known for L = V, the variety of all lattice...

The ordering of quantum dots in three-dimensional quantum dot lattices is investigated by grazing-incidence small-angle X-ray scattering (GISAXS). Theoretical models describing GISAXS intensity distributions for three general classes of lattices of quantum dots are proposed. The classes differ in the type of disorder of the positions of the quantum dots. The models enable full structure determi...

Twisted vertex operators based on rational lattices have had many applications in vertex operator algebra theory and conformal field theory. In this paper, “relativized” twisted vertex operators are constructed in a general context based on isometries of rational lattices, and a generalized twisted Jacobi identity is established for them. This result generalizes many previous results. Relatived...

The theory of vector lattices appeared in early thirties of this century and is connected with the names of L. V. Kantorovich, F. Riesz, and H. Freudenthal. The study of vector spaces equipped with an order relation compatible with a given norm structure was evidently motivated by the general circumstances that brought to life functional analysis in those years. Here the general inclination to ...

The paper is devoted to complete proofs of theorems on consistency on cubic lattices for 3 × 3 determinants. The discrete nonlinear equations on Z defined by the condition that the determinants of all 3×3 matrices of values of the scalar field at the points of the lattice Z that form elementary 3 × 3 squares vanish are considered; some explicit concrete conditions of general position on initial...

A general parametrization for all three-dimensional crystal lattices is presented in this paper which guarantees that the three primitive vectors constructed by the parametrization are the three shortest possible, linearly independent lattice vectors existing in the whole lattice. The parameter space of this so-called minimum distance parametrization (MDP) can easily be confined to contain only...

ABSTRACT Standard OFDM systems are associated with a rectangular grid in the time-frequency plane. However such a setup is in general not optimal for pulse shaping OFDM systems for doubly dispersive channels. We introduce lattice-OFDM systems (LOFDM), which are OFDM systems constructed with respect to general lattices in the time-frequency plane. We show how to design optimal pulse shapes for L...

One of the most important elements in a lattice are the irreducible elements. For example, when the lattice is finite, which is usual in the computational case, it forms a base from which the complete lattice is obtained. These elements are also important in Formal Concept Analysis, since they are the basic information of a relational system. In the general fuzzy framework of multi-adjoint conc...