Search results for " set"

showing 10 items of 2095 documents

Enumerable classes of total recursive functions: Complexity of inductive inference

1994

This paper includes some results on complexity of inductive inference for enumerable classes of total recursive functions, where enumeration is considered in more general meaning than usual recursive enumeration. The complexity is measured as the worst-case mindchange (error) number for the first n functions of the given class. Three generalizations are considered.

Discrete mathematicsClass (set theory)Mathematics::CombinatoricsTheoretical computer scienceRecursively enumerable setRecursive functionsEnumerationInductive reasoningMathematics
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Periodic Groups Covered by Transitive Subgroups of Finitary Permutations or by Irreducible Subgroups of Finitary Transformations

1999

Let X be either the class of all transitive groups of finitary permutations, or the class of all periodic irreducible finitary linear groups. We show that almost primitive X-groups are countably recognizable, while totally imprimitive X-groups are in general not countably recognizable. In addition we derive a structure theorem for groups all of whose countable subsets are contained in totally imprimitive X-subgroups. It turns out that totally imprimitive p-groups in the class X are countably recognizable.

Discrete mathematicsClass (set theory)Transitive relationMathematics::Operator AlgebrasApplied MathematicsGeneral MathematicsMathematics::General TopologyUltraproductCombinatoricsMathematics::LogicCountable setFinitaryStructured program theoremMathematicsTransactions of the American Mathematical Society
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Mappings of finite distortion: The zero set of the Jacobian

2003

This paper is part of our program to establish the fundamentals of the theory of mappings of finite distortion [6], [1], [8], [13], [14], [7] which form a natural generalization of the class of mappings of bounded distortion, also called quasiregular mappings. Let us begin with the definition. We assume that Ω ⊂ Rn is a connected open set. We say that a mapping f : Ω → Rn has finite distortion if:

Discrete mathematicsClass (set theory)Zero setGeneralizationApplied MathematicsGeneral MathematicsOpen setDistortion (mathematics)symbols.namesakeBounded functionJacobian matrix and determinantsymbolsCoincidence pointMathematicsJournal of the European Mathematical Society
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ℓp-solutions of countable infinite systems of equations and applications to electrical circuits

1991

In the preceding chapter we have studied a lumped parameter model of a class of circuits containing a finite number of elements. Here we are interested in qualitative properties of the network in Figure 3.1.

Discrete mathematicsClass (set theory)lawTruncation error (numerical integration)Electrical networkCountable setInfinite systemsFinite setMathematicslaw.inventionNormed vector spaceElectronic circuit
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Some properties of vertex-oblique graphs

2016

The type t G ( v ) of a vertex v ? V ( G ) is the ordered degree-sequence ( d 1 , ? , d d G ( v ) ) of the vertices adjacent with v , where d 1 ? ? ? d d G ( v ) . A graph G is called vertex-oblique if it contains no two vertices of the same type. In this paper we show that for reals a , b the class of vertex-oblique graphs G for which | E ( G ) | ? a | V ( G ) | + b holds is finite when a ? 1 and infinite when a ? 2 . Apart from one missing interval, it solves the following problem posed by Schreyer et?al. (2007): How many graphs of bounded average degree are vertex-oblique? Furthermore we obtain the tight upper bound on the independence and clique numbers of vertex-oblique graphs as a fun…

Discrete mathematicsClique-sumNeighbourhood (graph theory)020206 networking & telecommunications0102 computer and information sciences02 engineering and technology01 natural sciencesTheoretical Computer ScienceMetric dimensionCombinatoricsIndifference graphNew digraph reconstruction conjecture010201 computation theory & mathematicsChordal graphIndependent set0202 electrical engineering electronic engineering information engineeringDiscrete Mathematics and CombinatoricsBound graphirregular graphsindependence numbervertex-oblique graphslexicographic productMathematicsDiscrete Mathematics
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On a generalization of Goguen's category Set(L)

2007

The paper considers a category which generalizes Goguen's category Set(L) of L-fuzzy sets with a fixed basis L. We show the necessary and sufficient conditions for the generalized category to be a quasitopos and consider additional inner structure supplied by the latter property.

Discrete mathematicsClosed categoryArtificial IntelligenceLogicDiagram (category theory)Complete categoryMathematics::Category TheoryCategoryConcrete categoryCategory of setsEnriched categoryMathematicsTopological categoryFuzzy Sets and Systems
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Precise bounds for the sequential order of products of some Fréchet topologies

1998

Abstract The sequential order of a topological space is the least ordinal for which the corresponding iteration of the sequential closure is idempotent. Lower estimates for the sequential order of the product of two regular Frechet topologies and upper estimates for the sequential order of the product of two subtransverse topologies are given in terms of their fascicularity and sagittality. It is shown that for every countable ordinal α, there exists a Lasnev topology such that the sequential order of its square is equal to α.

Discrete mathematicsClosure (topology)Topological spaceSequential spaceSquare (algebra)CombinatoricsProduct (mathematics)IdempotenceOrder (group theory)Countable setGeometry and TopologySequential orderFréchet (Fréchet-Urysohn) topologyProductMathematicsTopology and its Applications
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Dimensions of random affine code tree fractals

2014

We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.

Discrete mathematicsCode (set theory)v-variable fractalsApplied MathematicsGeneral MathematicsProbability (math.PR)ta111Dynamical Systems (math.DS)self-similar setsTree (descriptive set theory)Box countingFractalIterated function systemMathematics - Classical Analysis and ODEsHausdorff dimensionClassical Analysis and ODEs (math.CA)FOS: MathematicsAffine transformationMathematics - Dynamical Systems28A80 60D05 37H99RandomnessMathematics - ProbabilityMathematics
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Archimedean actions on median pretrees

2001

In this paper we consider group actions on generalized treelike structures (termed ‘pretrees’) defined simply in terms of betweenness relations. Using a result of Levitt, we show that if a countable group admits an archimedean action on a median pretree, then it admits an action by isometries on an [open face R]-tree. Thus the theory of isometric actions on [open face R]-trees may be extended to a more general setting where it merges naturally with the theory of right-orderable groups. This approach has application also to the study of convergence group actions on continua.

Discrete mathematicsCombinatoricsGroup actionBetweenness centralityGroup (mathematics)General MathematicsFace (geometry)Convergence (routing)Countable setAction (physics)MathematicsMathematical Proceedings of the Cambridge Philosophical Society
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On the Distribution ofB3-Sequences

1996

Abstract An infinite set of natural numbers is called aB3-sequence if all sumsa1+a2+a3withaj∈Aanda1⩽a2⩽a3are distinct. LetA(n) be the number of positive elements ⩽ninA. P. Erdos conjectures that everyB3-sequenceAsatisfies lim infn→∞ A(n) n−1/3=0. In this paper we prove that no sequence satisfyingA(n)∼αn1/3can be aB3-sequence. We also give other necessary conditions for aB3-sequence.

Discrete mathematicsCombinatoricsSequenceInfinite setAlgebra and Number TheoryDistribution (number theory)Natural numberMathematicsJournal of Number Theory
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