Various characterizations of finite convex geometries
are well known. This note provides similar characterizations for
possibly infinite convex geometries whose lattice of closed sets is
strongly coatomic and lower ...
Representation of convex geometry as an appropriate join of compatible
orderings of the base set can be achieved, when closure operator of
convex geometry is algebraic, or finitary. This bears to the finite case proved
by ...
Let L be a join-distributive lattice with length n and width (Ji L) k.
There are two ways to describe L by k − 1 permutations acting on an n-element set:
a combinatorial way given by P.H. Edelman and R. E. Jamison in ...
Convex geometries form a subclass of closure systems with unique
criticals, or UC-systems. We show that the F-basis introduced in [6] for UC-
systems, becomes optimum in convex geometries, in two essential parts of ...
We show that every optimum basis of a nite closure system,
in D. Maier's sense, is also right-side optimum, which is a parameter of a
minimum CNF representation of a Horn Boolean function. New parameters
for the size ...
Closure system on a nite set is a unifying concept in logic programming,
relational data bases and knowledge systems. It can also be presented
in the terms of nite lattices, and the tools of economic description of a
...
Part I proved that for every quasivariety K of structures
(which may have both operations and relations) there is a semilattice
S with operators such that the lattice of quasi-equational theories of
K (the dual of the ...
We show that for every quasivariety K of structures (where
both functions and relations are allowed) there is a semilattice S with
operators such that the lattice of quasi-equational theories of K (the dual
of the lattice ...
A closure system with the anti-exchange axiom is called a convex
geometry. One geometry is called a sub-geometry of the other if its closed sets
form a sublattice in the lattice of closed sets of the other. We prove that ...
An assosiahedron Kn, known also as Stasheff polytope, is a multifaceted
combinatorial object, which, in particular, can be realized as a convex
hull of certain points in Rn, forming (n − 1)-dimensional polytope1.
A ...
The Edelman-Jamison problem is to characterize those abstract
convex geometries that are representable by a set of points in the plane. We
show that some natural modification of the Edelman-Jamison problem is equivalent
to ...
A lumped-parameter nonlinear spring-mass model which takes into
account the third-order elastic sti ness constant is considered for mod-
eling the free and forced axial vibrations of a graphene sheet with one
xed end ...
We study the relation between measure theoretic entropy and escape of mass for the case of a singular diagonal flow on the moduli space of three-dimensional unimodular lattices
It is known that hyperbolic dynamical systems admit a unique invariant probability measure with maximal entropy. We prove an effective version of this statement and use it to estimate an upper bound for Hausdorff dimension ...
Let G be a connected semisimple Lie group of real rank 1 with finite center, let be a non-uniform lattice in G and a any diagonalizable element in G. We investigate the relation between the metric entropy of a acting ...
Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal
ows on homogeneous spaces nG, where G is any connected ...
In this paper we study the dimension of a family of sets arising in open dynamics. We use exponential mixing results for diagonalizable ows in compact homogeneous spaces X to show that the Hausdorff dimension of set of ...
Let x = (x1; : : : ; xd) 2 [1; 1]d be linearly independent over Z, set K = f(ez; ex1z; ex2z : : : ; exdz) : jzj 1g:We prove sharp estimates for the growth of a polynomial of degree n, in terms of En(x) := supfkPk d+1 ...
Let a be a Kleene's ordinal notation of a nonzero computable ordinal. We give a su cient condition on a, so that for every 1 a {computable family of two embedded sets, i.e. two sets A;B, with A properly contined in B, ...
We give a su cient condition for an in nite computable family of 1
a sets, to have computable positive but undecidable numberings, where a
is a notation for a nonzero computable ordinal. This extends a theorem
proved ...