Search results for "Set theory"
showing 10 items of 751 documents
FROM DISCRETE KINETIC AND STOCHASTIC GAME THEORY TO MODELLING COMPLEX SYSTEMS IN APPLIED SCIENCES
2004
This paper deals with some methodological aspects related to the discretization of a class of integro-differential equations modelling the evolution of the probability distribution over the microscopic state of a large system of interacting individuals. The microscopic state includes both mechanical and socio-biological variables. The discretization of the microscopic state generates a class of dynamical systems defining the evolution of the densities of the discretized state. In general, this yields a system of partial differential equations replacing the continuous integro-differential equation. As an example, a specific application is discussed, which refers to modelling in the field of…
Homomorphs and wreath product extensions
1982
A homomorph is a class of (finite soluble) groups closed under the operation Q of taking epimorphic images. (All groups considered in this paper are finite and soluble.) Among those types of homomorphs that have found particular interest in the theory of finite soluble groups are formations and Schunck classes; the reader is referred to (2), § 2, for a definition of those classes. In the present paper we are interested in homomorphs satisfying the following additional closure property:(W0) if A is abelian with elementary Sylow subgroups, then each wreath product A G (with respect to an arbitrary permutation representation of G) with G ∊ is contained in .
Topological Insulators from a Chemist’s Perspective
2012
Topology and chemistry are deeply entangled subjects, whichmanifests in the way chemists like to think and approachproblems. Although not at first glance, topology allows thecategorizationoffundamentalinherentpropertiesofthehugenumber of different chemical compounds, carving out theunique features of a class of materials of different complexity,a topic which Turro worked out in his treatise on geometricaland topological thinking in chemistry.
Learning Molecular Classes from Small Numbers of Positive Examples Using Graph Grammars
2021
We consider the following problem: A researcher identified a small number of molecules with a certain property of interest and now wants to find further molecules sharing this property in a database. This can be described as learning molecular classes from small numbers of positive examples. In this work, we propose a method that is based on learning a graph grammar for the molecular class. We consider the type of graph grammars proposed by Althaus et al. [2], as it can be easily interpreted and allows relatively efficient queries. We identify rules that are frequently encountered in the positive examples and use these to construct a graph grammar. We then classify a molecule as being conta…
Separation conditions on controlled Moran constructions
2017
It is well known that the open set condition and the positivity of the $t$-dimensional Hausdorff measure are equivalent on self-similar sets, where $t$ is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions with this respect.
Are locally finite MV-algebras a variety?
2021
We answer Mundici's problem number 3 (D. Mundici. Advanced {\L}ukasiewicz calculus. Trends in Logic Vol. 35. Springer 2011, p. 235): Is the category of locally finite MV-algebras equivalent to an equational class? We prove: (i) The category of locally finite MV-algebras is not equivalent to any finitary variety. (ii) More is true: the category of locally finite MV-algebras is not equivalent to any finitely-sorted finitary quasi-variety. (iii) The category of locally finite MV-algebras is equivalent to an infinitary variety; with operations of at most countable arity. (iv) The category of locally finite MV-algebras is equivalent to a countably-sorted finitary variety. Our proofs rest upon th…
Correspondence between some metabelian varieties and left nilpotent varieties
2021
Abstract In the class of left nilpotent algebras of index two it was proved that there are no varieties of fractional polynomial growth ≈ n α with 1 α 2 and 2 α 3 instead it was established the existence of a variety of fractional polynomial growth with α = 7 2 . In this paper we investigate similar problems for varieties of commutative or anticommutative metabelian algebras. We construct a correspondence between left nilpotent algebras of index two and commutative metabelian algebras or anticommutative metabelian algebras and we prove that the codimensions sequences of the corresponding algebras coincide up to a constant. This allows us to transfer the above results concerning varieties of…
Character degrees, character codegrees and nilpotence class of p-groups
2021
Du and Lewis raised in 2016 the question of whether the nilpotence class of a p-group is bounded in terms of the number of character codegrees. In 2020, Croome and Lewis, gave a positive answer to ...
The ideal duplication
2021
AbstractIn this paper we present and study the ideal duplication, a new construction within the class of the relative ideals of a numerical semigroup S, that, under specific assumptions, produces a relative ideal of the numerical duplication $$S\bowtie ^b E$$ S ⋈ b E . We prove that every relative ideal of the numerical duplication can be uniquely written as the ideal duplication of two relative ideals of S; this allows us to better understand how the basic operations of the class of the relative ideals of $$S\bowtie ^b E$$ S ⋈ b E work. In particular, we characterize the ideals E such that $$S\bowtie ^b E$$ S ⋈ b E is nearly Gorenstein.
A Multiplicity result for a class of strongly indefinite asymptotically linear second order systems
2010
We prove a multiplicity result for a class of strongly indefinite nonlinear second order asymptotically linear systems with Dirichlet boundary conditions. The key idea for the proof is to bring together the classical shooting method and the Maslov index of the linear Hamiltonian systems associated to the asymptotic limits of the given nonlinearity.