Search results for "abstract"

showing 10 items of 1959 documents

A general metric regularity in asplund banach spaces

1998

This paper establishes a simple and easily-applied criterion for determining whether a multivalued mapping is metrically regular relatively to a subset in the range space.

Discrete mathematicsRange (mathematics)Control and OptimizationSimple (abstract algebra)Signal ProcessingMetric (mathematics)Banach spaceSpace (mathematics)AnalysisComputer Science ApplicationsMathematicsNumerical Functional Analysis and Optimization
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Thin Bases of Order Two

2001

AbstractA set A⊆N0 is called a basis of order two if A+A≔{a+a′∣a, a′∈A}=N0. If n∈N then A(n) denotes the number of a∈A with 1⩽a⩽n. In this paper bases A, B, C of order two are given such thatlimA(n)n=253,limB(n)n=72andlimC(n)n=101653.

Discrete mathematicsSet (abstract data type)Algebra and Number TheoryBasis (linear algebra)Order (group theory)ArithmeticMathematicsJournal of Number Theory
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On n–Fold Blocking Sets

1986

An n-fold blocking set is a set of n-disjoint blocking sets. We shall prove upper and lower bounds for the number of components in an n-fold blocking set in projective and affine spaces.

Discrete mathematicsSet (abstract data type)CombinatoricsQuantitative Biology::BiomoleculesSteiner systemBlocking setFold (higher-order function)Blocking (radio)Projective planeAffine transformationUpper and lower boundsMathematics
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M-valued Measure of Roughness for Approximation of L-fuzzy Sets and Its Topological Interpretation

2015

We develop a scheme allowing to measure the “quality” of rough approximation of fuzzy sets. This scheme is based on what we call “an approximation quadruple” \((L,M,\varphi ,\psi )\) where L and M are cl-monoids (in particular, \(L=M=[0,1]\)) and \(\psi : L \rightarrow M\) and \(\varphi : M \rightarrow L\) are satisfying certain conditions mappings (in particular, they can be the identity mappings). In the result of realization of this scheme we get measures of upper and lower rough approximation for L-fuzzy subsets of a set equipped with a reflexive transitive M-fuzzy relation R. In case the relation R is also symmetric, these measures coincide and we call their value by the measure of rou…

Discrete mathematicsSet (abstract data type)Identity (mathematics)Transitive relationScheme (mathematics)Fuzzy setTopologyMeasure (mathematics)Realization (systems)Interpretation (model theory)Mathematics
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On the longest common factor problem

2008

The Longest Common Factor (LCF) of a set of strings is a well studied problem having a wide range of applications in Bioinformatics: from microarrays to DNA sequences analysis. This problem has been solved by Hui (2000) who uses a famous constant-time solution to the Lowest Common Ancestor (LCA) problem in trees coupled with use of suffix trees. A data structure for the LCA problem, although linear in space and construction time, introduces a multiplicative constant in both space and time that reduces the range of applications in many biological applications. In this article we present a new method for solving the LCF problem using the suffix tree structure with an auxiliary array that take…

Discrete mathematicsSettore INF/01 - InformaticaSuffix tree[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]Generalized suffix treeDAWGsuffix tree[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]Data structureLongest common substring problemlaw.inventionCombinatoricsSet (abstract data type)Range (mathematics)lawLongest Common Factor ProblemSuffixLowest common ancestorMathematics
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Conjunction and Disjunction Among Conditional Events

2017

We generalize, in the setting of coherence, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. Given a prevision assessment on the conjunction of two conditional events, we study the set of coherent extensions for the probabilities of the two conditional events. Then, we introduce by a progressive procedure the notions of conjunction and disjunction for n conditional events. Moreover, by defining the negation of conjunction and of disjunction, we show that De Morgan’s Laws still hold. We also show that the associative and commutative properties are satisfied. Finally, we examine in detail the conjunction for a family \(\mathcal F\) of t…

Discrete mathematicsSettore MAT/06 - Probabilita' E Statistica MatematicaComputer scienceConditional events · Conditional random quantities · Con- junction · Disjunction · Negation · Quasi conjunction · Coherent previ- sion assessments · Coherent extensions · De Morgan’s Laws02 engineering and technologyCoherence (philosophical gambling strategy)Settore MAT/01 - Logica Matematica01 natural sciencesDe Morgan's lawsConjunction (grammar)Set (abstract data type)010104 statistics & probabilitysymbols.namesakeNegation0202 electrical engineering electronic engineering information engineeringsymbols020201 artificial intelligence & image processing0101 mathematicsAlgorithmCommutative propertyAssociative propertyEvent (probability theory)
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High Order in Space and Time Schemes Through an Approximate Lax-Wendroff Procedure

2017

This paper deals with the scheme proposed by the authors in Zorio, Baeza and Mulet (J Sci Comput 71(1):246–273, 2017). This scheme is an alternative to the techniques proposed in Qiu and Shu (SIAM J Sci Comput 24(6):2185–2198, 2003) to obtain high-order accurate schemes using Weighted Essentially Non Oscillatory finite differences and approximating the flux derivatives required by the Cauchy-Kovalevskaya procedure by simple centered finite differences. We analyse how errors in first-order terms near discontinuities propagate through both versions of the Cauchy-Kovalevskaya procedure. We propose a fluctuation control, for which the approximation of the first-order derivative to be used in th…

Discrete mathematicsSpacetimeLax–Wendroff methodSimple (abstract algebra)Scheme (mathematics)Finite differenceApplied mathematicsFluxClassification of discontinuitiesInterpolationMathematics
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Estimating the length of minimal spanning trees in compression of files

1984

Compression of a formatted file by a minimal spanning tree (MST) is studied. Here the records of the file are considered as the nodes of a weighted undirected graph. Each record pair is connected in the graph and the corresponding arc is weighted by the sum of field lengths of those fields which differ in the two records. The actual compression is made by constructing an MST of the graph and by storing it in an economic way to preserve the information of the file. The length of the MST is a useful measure in the estimation of the power of the compression. In the paper we study upper bounds of this length, especially in the case where the field lengths of the different fields may vary. The u…

Discrete mathematicsSpanning treeComputer Networks and CommunicationsApplied MathematicsShortest-path treeMinimum spanning treeConnected dominating setCombinatoricsComputational MathematicsGraph (abstract data type)Undirected graphSoftwareMathematicsofComputing_DISCRETEMATHEMATICSMathematicsMinimum degree spanning treeBIT
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Minimum node weight spanning trees searching algorithm for broadcast transmission in sensor networks

2017

A minimum node weight spanning tree in a weighted, directed graph is a tree whose node with maximum out-weight is minimal among all spanning trees. This type of trees are important because they appear in the solutions of the maximum lifetime broadcasting problem in wireless sensor networks. In a complete graph build of N nodes there are NN-2 spanning trees and to find such trees it is necessary to perform more than O(NN-2) operations. In this paper we propose an algorithm for searching the minimum node weight spanning trees in the graph. In the proposed algorithm, instead of calculating the symbolic determinant of the generalized Laplacian matrix, numerical operations on its exponents are p…

Discrete mathematicsSpanning treeComputer sciencegraph theory010401 analytical chemistryDecision treeComplete graph020206 networking & telecommunications02 engineering and technologyDirected graphspanning trees01 natural sciences0104 chemical sciencessensor networksSearch algorithm0202 electrical engineering electronic engineering information engineeringGraph (abstract data type)Algorithm designLaplacian matrixdata broadcasting2017 Twelfth International Conference on Digital Information Management (ICDIM)
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Graph languages defined by systems of forbidden structures: A survey

1988

This paper deals with different ways of defining graph languages. These are the so-called forbidden structures. Some results on decision problems, their complexity, and set theoretic closure properties are scetched. A normal form, the minimal systems, are given. Finally the influence of the different kinds of forbidden structures on the descriptive power of the systems is shown.

Discrete mathematicsTheoretical computer scienceA-normal formVoltage graphGraph (abstract data type)Decision problemNull graphForbidden graph characterizationMathematics
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