A sublattice in a lattice is called supermodular if, for every two elements, one of which belongs to the sublattice, at least one of their meet and join also belongs to the sublattice. In this note, we describe supermodular sublattices in products of relatively complemented lattices.

We introduce the concept of Mσ-approachability for a semicontinuous function (i.e. a nonadditive measure) on a σ-complete sublattice of a locally complete σ-continuous lattice L and using it we extend a nonadditive measure from a sublattice of L to a σ-complete sublattice of L. AMS Mathematics Subject Classification (2000): 28A12, 28C15, 28B10

There are characteristic classes that are the obstructions to the vanishing of the differentials in the Lyndon-Hochischild-Serre spectral sequence of an extension of an integral lattice L by a group G. These characteristic classes exist in the r-th page of the spectral sequence provided differentials di = 0 for all i < r. If L further decomposes into a sum of G-sublattice L = L ⊕ L, we show tha...

We study when the existence of an increasing selection can be derived from the monotonicity of a multifunction w.r.t. an extension of the basic order from points to subsets. The most interesting results emerge when the target is a lattice and monotonicity is interpreted in one of the ways suggested by A.F. Veinott, Jr. An increasing selection exists if (1) the multifunction is weakly ascending ...

In this paper we present an extendible, block gluing Z shift of finite type W el in which the topological entropy equals the L-projectional entropy for a two-dimensional sublattice L ( Z, even so W el is not a full Z extension of W el L . In particular this example shows that Theorem 4.1 of [3] does not generalize to r-dimensional sublattices L for r > 1. Nevertheless we are able to reprove and...

The main result of this paper is the following theorem: If a projective Boolean algebra B is generated by its sublattice L, then there is a projective distributive lattice D which is a sublattice of L and generates B.

Superionic ice is a special group of ice phases at high temperature and pressure, which may exist in ice-rich planets and exoplanets. In superionic ice liquid hydrogen coexists with a crystalline oxygen sublattice. At high pressures, the properties of superionic ice are largely unknown. Here we report evidence that from 280 GPa to 1.3 TPa, there are several competing phases within the close-pac...

J 1 − J 2 quantum Heisenberg antiferromagnet on the triangular lattice: a group symmetry analysis of order by disorder. Abstract On the triangular lattice, for J 2 /J 1 between 1/8 and 1, the classical Heisen-berg model with first and second neighbor interactions presents four-sublattice ordered ground-states. Spin-wave calculations of Chubukov and Jolicoeur [9] and Korshunov [10] suggest that ...

For two- and three-dimensional topological insulators whose unit cells consist of multiple sublattices, the boundary terminating at which type sublattice can affect time-reversal invariant momentum Dirac points helical states are located. By incorporating a generic theory representative model, we reveal that this interesting property allows realization Majorana modes domain walls forming on whe...

A bimonotone linear inequality is a linear inequality with at most two nonzero coefficients that are of opposite signs (if both different from zero). A linear inequality defines a halfspace that is a sublattice of Rn (a subset closed with respect to componentwise maximum and minimum) if and only if it is bimonotone. Veinott has shown that a polyhedron is a sublattice if and only if it can be de...