Related papers: Join-continuity + Hypercontinuity = Prime continui…
Quasi-lattices are introduced in terms of 'join' and 'meet' operations. It is observed that quasi-lattices become lattices when these operations are associative and when these operations satisfy 'modularity' conditions. A fundamental…
We study uO convergence on infinitely distributive lattices, extending key properties known from Riesz spaces. We show that order continuity of uO convergence characterizes infinite distributivity. We examine O-adherence and uO adherence of…
Most comparisons of preferences are instances of single-crossing dominance. We examine the lattice structure of single-crossing dominance, proving characterisation, existence and uniqueness results for minimum upper bounds of arbitrary sets…
For a class of nonnegative, range-1 pair potentials in one dimensional continuous space we prove that any classical ground state of lower density >=1 is a tower-lattice, i.e., a lattice formed by towers of particles the heights of which can…
The boundary of every relatively compact Stein domain in a complex manifold of dimension at least two is connected. No assumptions on the boundary regularity are necessary. The same proofs hold also for $q$-complete domains, and in the…
We show that all balanced d-lattices must be complemented, answering a question of Chajda and Eigenthaler. (A bounded lattice is balanced if any two congruences agree on their 1-classes iff they agree on their 0-classes.) Our main tool is…
In an earlier paper, to describe how a congruence spreads from a prime interval to another in a finite lattice, I introduced the concept of prime-perspectivity and its transitive extension, prime-projectivity and proved the…
Let $L$ be a planar semimodular lattice. We call $L$ \emph{slim}, if it has no $\mthree$ sublattice. Let us define an \emph{SPS lattice} as a slim, planar, semimodular lattice $L$. In 2016, I proved a property of congruences of SPS lattices…
Given a poset $P$, the set, $\Gamma(P)$, of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory $\mathbf{C}$ of $\mathbf{Pos}_d$ (the category of posets and Scott-continuous maps) is said to be…
The peculiar phase-ordering properties of a lattice of coupled chaotic maps studied recently (A. Lema\^\i tre & H. Chat\'e, {\em Phys. Rev. Lett.} {\bf 82}, 1140 (1999)) are revisited with the help of detailed investigations of interface…
We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which…
We introduce the dimension monoid of a lattice L, denoted by Dim L. The monoid Dim L is commutative and conical, the latter meaning that the sum of any two nonzero elements is nonzero. Furthermore, Dim L is given along with the dimension…
We exhibit simple lattice systems, motivated by recently proposed cold atom experiments, whose continuum limits interpolate between real and $p$-adic smoothness as a spectral exponent is varied. A real spatial dimension emerges in the…
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…
The existence and stability of defect solitons supported by parity-time (PT) symmetric superlattices with nonlocal nonlinearity are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive or zero…
Continuing the study of the structure of semirings, we turn to the spectrum of prime congruences. Joo and Mincheva developed an elegant theory in the special case of idempotent semirings, which is generalized here to ``semiring pairs,''…
A poset is called upper homogeneous, or "upho," if all of its principal order filters are isomorphic to the whole poset. In previous work of the first author, it was shown that each (finite-type N-graded) upho lattice has associated to it a…
We define a quasimodule Q over a bounded lattice L in an analogous way as a module over a semiring is defined. The essential difference is that L need not be distributive. Also for quasimodules there can be introduced the concepts of inner…
We study near-alternating links whose diagrams satisfy conditions generalized from the notion of semi-adequate links. We extend many of the results known for adequate knots relating their colored Jones polynomials to the topology of…
We prove, e.g., that if lambda=chi^+=2^chi and S subseteq {delta<lambda:cf(delta) neq cf(chi)} is stationary then diamondsuit_lambda holds true.