Crisp and L-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or L-fuzzy) ambiguous representations is a lattice and a compact Hausdorff Lawson upper semilattice. The categories of ambiguous and L-ambiguous representations are defined and investigated.

We study stochastic partly dissipative lattice systems with random coupled coefficients and multiplicative/additive white noise in a weighted space of infinite sequences. We first show that these stochastic partly dissipative lattice differential equations generate a random dynamical system. We then establish the existence of a tempered random bounded absorbing set and a global compact random a...

We consider the gauge potential A and argue that the minimum value of the volume integral of A (in Euclidean space) may have physical meaning, particularly in connection with the existence of topological structures. A lattice simulation comparing compact and non-compact “photodynamics” shows a jump in this quantity at the phase transition, supporting this idea.

A family of 2א0 Borel ideals on a compact lattice are constructed such that no two quotient lattices by ideals from this family are isomorphic.

We perform a high statistics calculation of the equation of state for non-compact QED on large lattices. The calculation extends to fermionic correlation lengths of 8, and it is combined with a nite size scaling analysis of the lattice data.

Singular and nonsingular flat bands in a Sierpinski fractal-like photonic lattice are reported. It is demonstrated that the lowest two bands, being isolated degenerate due to geometrical frustration, thus can be spanned by complete set of compact localized states. These states experimentally proven propagate diffractionless lattice. The results reveal interplay between single lattice, pave way ...

The question of characterizing the lattices of subvarieties of a variety of universal algebras seems to be very difficult. Some years ago a conjecture was that a lattice is isomorphic to the lattice of all extensions of an equational theory (or dually isomorphic to the lattice of subvarieties of a variety) iff it is algebraic and its greatest element is compact. In [2] and [3] W. Lampe proved t...

On Operators whose Compactness Properties are defined by Order by Safak Alpay Abstract. Let E be a Banach lattice. A subset B of E is called order bounded if there exist a, b in E such that a ≤ x ≤ b for each x ∈ B. Considering E in E′′, the bidual of E, a subset B of E is called b-order bounded in E if it is order bounded in the Banach lattice E′′. A bounded linear operator T : E → X is called...

In this paper, we prove that every lattice L has a congruencepreserving extension into a regular lattice L̃, moreover, every compact congruence of L̃ is principal. We construct L̃ by iterating a construction of the first author and F. Wehrung and taking direct limits. We also discuss the case of a finite lattice L, in which case L̃ can be chosen to be finite, and of a lattice L with zero, in which ...