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Mathematics: Recent submissions

  • Measuring implications of the D-basis in biomedical applications 
    Adaricheva, Kira (2015-06-26)
  • Increasing the role of the D-basis in applications 
    Adaricheva, Kira (2015-06-06)
  • On complex algebras of subalgebras 
    Adaricheva, Kira; Pilitowska, Agata; Stanovsky, David (2006)
    Let V be a variety of algebras. We establish a condition (so called generalized entropic property), equivalent to the fact that for every algebra A 2 V, the set of all subalgebras of A is a subuniverse of the complex ...
  • Embedding finite lattices into finite biatomic lattices 
    Adaricheva, Kira; Wehrung, Freidrich (2005)
    For a class C of finite lattices, the question arises whether any lattice in C can be embedded into some atomistic, biatomic lattice in C. We provide answers to the question above for C being, respectively, — The class ...
  • Join-semidistributive lattices of relatively convex sets 
    Adaricheva, Kira (2004)
    We give two sufficient conditions for the lattice Co(Rn,X) of rel- atively convex sets of Rn to be join-semidistributive, where X is a finite union of segments. We also prove that every finite lower bounded lattice can ...
  • On scattered convex geometries 
    Adaricheva, Kira; Pouzet, Maurice (2015)
    A convex geometry is a closure space satisfying the anti-exchange axiom. For several types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the ...
  • Discovery of the D-basis in binary tables based on hypergraph dualization 
    Adaricheva, Kira; Nation, J.B. (2016)
    Discovery of (strong) association rules, or implications, is an important task in data management, and it nds application in arti cial intelligence, data mining and the semantic web. We introduce a novel approach for ...
  • A class of infinite convex geometries 
    Adaricheva, Kira; Nation, J.B. (2015)
    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 ...
  • Algebraic convex geometries revisited 
    Adaricheva, Kira (2014)
    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 ...
  • Notes on the description of join-distributive lattices by permutations 
    Adaricheva, Kira; Cz´edli, G´abor (2012)
    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 ...
  • Optimum basis of finite convex geometry 
    Adaricheva, Kira (2016)
    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 ...
  • On implicational bases of closure system with unique critical sets 
    Adaricheva, Kira; Nation, J.B. (2013)
    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 ...
  • Ordered direct implication basis of a finite closure system 
    Adaricheva, Kira; Nation, J.B.; Rand, R. (2012)
    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 ...
  • Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part II 
    Adaricheva, Kira; Nation, J.B. (2012)
    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 ...
  • Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part I 
    Adaricheva, Kira; Nation, J. B. (2012)
    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 ...
  • Representing finite convex geometries by relatively convex sets 
    Adaricheva, Kira (2011)
    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 ...
  • Stasheff polytope as a sublattice of permutohedron 
    Adaricheva, Kira (2011)
    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 ...
  • Realization of abstract convex geometries by point configurations. Part I 
    Adaricheva, Kira; Wild, Marcel (2007)
    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 Model for Nonlinear Waves in Graphene 
    Wei, Dongming; Hazim, Hamad; Elgindi, Mohamed; Soukiassian, Yeran (2015)
    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 ...
  • Characterization of Corneal Indentation Hysteresis 
    Wei, Dongming; Ko, Match W. L.; Leung, Christopher K.S (2015)
    The aim of this study is to design and develop a noninvasive corneal indentation method to measure the corneal hysteresis behavior under dynamic corneal indentation. Corneal indentation method is adapted for the design ...