We report on the investigation of symmetrical properties of lithium niobate (LiNbO3) domain walls utilizing the nonlinear Cherenkov radiation. Compared with LiNbO3 bulk crystals, new nonzero elements of the χ(2) tensor at domain walls are found by the Cherenkov second harmonic generation (CSHG) and Cherenkov sum frequency generation (CSFG) measurement. Experimen...

Defining Lattice Computing as the class of algorithms that either construct the computations using the lattice operators inf and sup, or use lattice theory to produce generalizations or fusions of previous approaches, we find that a host of algorithms for data processing, classification and signal filtering have been produced over the last decades. We give a fast and brief review, that by no me...

A variational fit to the lattice energy of two heavy-light mesons Abstract Recent lattice calculations on the interaction energy of two heavy-light mesons (Q 2 ¯ q 2) are interpreted in terms of the potential of the corresponding single heavy-light meson (Q¯ q). This model leads to a large overestimate of the binding compared with the lattice data – unless the basic Q¯ q potential is modified t...

Grothendieck toposes are studied via the process of taking the associated Sl-enriched category of relations. It is shown that this process is adjoint to that of taking the topos of sheaves of an abstract category of relations. As a result, pullback and comma toposes are calculated in a new way. The calculations are used to give a new characterization of localic morphisms and to derive interpola...

A 2-form between two sup-lattices L and R is defined to be a suplattice bimorphism L×R → 2. Such 2-forms are equivalent to Galois connections, and we study them and their relation to quantales, involutive quantales and quantale modules. As examples we describe applications to C*-algebras.

The Galois number Gn(q) is defined to be the number of subspaces of the n-dimensional vector space over the finite field GF (q). When q is prime, we prove that Gn(q) is equal to the number Ln(q) of n-dimensional mod q lattices, which are defined to be lattices (that is, discrete additive subgroups of n-space) contained in the integer lattice Z and having the property that given any point P in t...

For a small quantaloid Q, a Q-closure space is a small category enriched in Q equipped with a closure operator on its presheaf category. We investigate Q-closure spaces systematically with specific attention paid to their morphisms and, as preordered fuzzy sets are a special kind of quantaloid-enriched categories, in particular fuzzy closure spaces on fuzzy sets are introduced as an example. By...

We present and analyse low-temperature series and complex-temperature partition function zeros for the q-state Potts model with q = 4 on the honeycomb lattice and q = 3, 4 on the triangular lattice. A discussion is given on how the locations of the singularities obtained from the series analysis correlate with the complex-temperature phase boundary. Extending our earlier work, we include a simi...