/ of an induced algebra. The general observations and the examples of correspondences presented in this paper are a first step towards development of a correspondence theory for lattices with operators. The classes of algebras considered in the paper have been introduced in [4]. They are a generalization of Boolean algebras with possibility operators introduced by [3] and Boolean algebras with ...

We produce a family of new, non-arithmetic lattices in PU(2, 1). All previously known examples were commensurable with lattices constructed by Picard, Mostow, and Deligne– Mostow, and fell into 9 commensurability classes. Our groups produce 5 new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for construc...

in this paper, we establish the theory of fuzzy ideal convergence on completely distributive lattices and give characterizations of some topological notions. we also study fuzzy limit structures and discuss the relationship between fuzzy co-topologies and fuzzy limit structures.

Part I of this paper is developed in the tradition of Stone-type dualities, where we present a new topological representation for general lattices (innuenced by and abstracting over both Goldblatt's 17] and Urquhart's 46]), identifying them as the lattices of stable compact-opens of their dual Stone spaces (stability refering to a closure operator on subsets). The representation is functorial a...

K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...

The search for large gap quantum spin Hall (QSH) and anomalous (QAH) insulators is important both fundamental practical interests. degenerate multi-orbitals $p_x,p_y$ in honeycomb lattice provides a paradigm QSH state with boosted topological of the first order atomic spin-orbit coupling. By using elementary band representation, we explore feasibility this mechanism general two-dimensional latt...

After Feichner and Yuzvinsky introduced the Chow ring associated to ranked atomistic lattices in 2003, little study of them was made before Adiprisito, Huh, and Katz used them to resolve the long-standing Heron-Rota-Walsh conjecture, proving along the way that the Chow rings of geometric lattices satisfy versions of Poincaré duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. ...

the paper deals with special types of $l$-ordered sets, $l$-fuzzy complete lattices, and fuzzy directed complete posets.first, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $l$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $l$-fuzzy complete lattice $(p;e)$, then the least fixpoint of $f$ is meet of ...

We present a generalization of the Luttinger-Tisza-Lyons-Kaplan (LTLK) theory classical ground states Bravais lattices with Heisenberg coupling to non-Bravais lattices. It consists adding certain Lagrange parameters diagonal Fourier transformed matrix analogous general state problem already published. This approach is illustrated by an application modified honeycomb lattice, which has exclusive...

All the posets/lattices considered here are finite with element 0. An element x of a poset satisfying certain properties is deletable if P − x is a poset satisfying the same properties. A class of posets is reducible if each poset of this class admits at least one deletable element. When restricted to lattices, a class of lattices is reducible if and only if one can go from any lattice in this ...