In this work, we study some general property of a strongly correlated electron system deened on a lattice. Assuming that the system exhibits oo-diagonal-long-range-order, we show that this assumption implies the Meissner eeect. This extends to lattice systems previous results obtained for the continuous case.

A new \compressed straight" basis for the polynomial ring Z[ti;j ] is constructed. This basis is then employed to study the lattice of representations generated by the representations associated with row-convex shapes under the operations of intersection and linear span. Applications to ascertaining the Cohen-Macaulay property for rings associated to elements of this lattice are also given.

We introduce the notion of n-fold implicative filters and n-fold implicative lattice implication algebras. We give characterizations of n-fold implicative filters and nfold implicative lattice implication algebras. Finally, we construct an extension property for n-fold implicative filter. 2000 Mathematics Subject Classification. 03G10, 06B10.

Let H be a fixed finite graph and let → H be a hom-property, i.e. the set of all graphs admitting a homomorphism into H . We extend the definition of → H to include certain infinite graphs H and then describe the minimal reducible bounds for → H in the lattice of additive hereditary properties and in the lattice of hereditary properties.

The aim of this paper is to study the actions of the groups on lattices and to give some connections between the structure of a group and the structure of its subgroup lattice. Moreover, we shall introduce the concept of direct ∨-sum of G-sublattices and we shall present a generalization of a result about finite nilpotent groups. 1 Preliminaries Let (G, ·, e) be a monoid and L be a G–set (relat...

Given a non-negative integer k, we construct a lattice 3-simplex P with the following property: The affine semigroup QP associated to P is not normal, and every element q ∈ QP \ QP has lattice distance at least k above every facet of QP .

In this paper the dispersion property of index guided photonic crystal fibers (PCFs) of silica material has been investigated. The modal analysis is done to obtain the complex effective refractive index for: (i) Hexagonal lattice with circular air holes and first ring having elliptical cells (ii) Rectangular lattice with circular air holes and first ring having elliptical cells. The dispersion

We consider the families L of propositional superintuitionistic logics (s.i.l.) andNE(K) of normal modal logics (n.m.l.). It is well known that there is a duality between L and the lattice of varieties of pseudo-boolean algebras (or Heyting algebras), and also NE(K) is dually isomorphic to the lattice of varieties of modal algebras. Many important properties of logics, for instance, Craig’s int...

A complemented modular lattice L is coordinatizable, if it is isomorphic to the lattice L(R) of principal right ideals of some von Neumann regular ring R. All known sufficient conditions for coordinatizability, due first to J. von Neumann, then to B. Jónsson, are first-order. Nevertheless, we prove that coordinatizability of complemented modular lattices is not firstorder, even for countable 2-...

Let (M ;⊆) and (L ;⊆) be the lattices of additive induced-hereditary properties of graphs and additive hereditary properties of graphs, respectively. A property R∈Ma (∈ L) is called a minimal reducible bound for a property P∈Ma (∈ L) if in the interval (P;R) of the lattice M (L) there are only irreducible properties. The set of all minimal reducible bounds of a property P∈Ma in the lattice M we...