Dually atomistic lattices

Chow Rings of Matroids and Atomistic Lattices

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. ...

Direct Decompositions of Atomistic Algebraic Lattices

Atomistic and multiscale analyses of brittle fracture in crystal lattices

Sulin Zhang,1,2,* Ting Zhu,3 and Ted Belytschko4 1Department of Mechanical Engineering, University of Arkansas, 204 Mechanical Building, Fayetteville, Arkansas 72701, USA 2Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA 3Woodruff School of Mechanical Engineering, Georgia Institute and Technology, Atlanta, Georgia 30332...

Dually Quasi

The variety DQD of semi-Heyting algebras with a weak negation, called dually quasi-De Morgan operation, and several of its subvarieties were investigated in the series [31], [32], [33], and [34]. In this paper we define and investigate a new subvariety JID of DQD, called “JI-distributive, dually quasi-De Morgan semi-Heyting algebras”, defined by the identity: x ∨ (y → z) ≈ (x ∨ y) → (x ∨ z), as...

Dually vertex-oblique graphs

A vertex with neighbours of degrees d1 ≥ · · · ≥ dr has vertex type (d1, . . . , dr). A graph is vertex-oblique if each vertex has a distinct vertex-type. While no graph can have distinct degrees, Schreyer, Walther and Mel’nikov [Vertex oblique graphs, same proceedings] have constructed infinite classes of super vertex-oblique graphs, where the degree-types of G are distinct even from the degre...