Search results for "Applied Mathematics"

showing 10 items of 4379 documents

Combinatorial isomorphism between Fibonacci classes

2008

Abstract In 1985 Simion and Schmidt showed that the set S n (T 3) of length n permutations avoiding the set of patterns T 3={123, 132, 213} is counted by (the second order) Fibonacci numbers. They also presented a constructive bijection between the set F n–1 of length (n–1) binary strings with no two consecutive 1s and S n (T 3). In 2005, Egge and Mansour generalized the first Simion-Simion’s result and showed that S n (T p ), the set of permutations avoiding the patterns T p ={12…p, 132, 213}, is counted by the (p–1)th order Fibonacci numbers. In this paper we extend the second Simion-Schmidt’s result by giving a bijection between the set of length (n–1) binary strings with no (p–1) consec…

Discrete mathematicsAlgebra and Number TheoryFibonacci numberApplied MathematicsHamiltonian pathCombinatoricsSet (abstract data type)Gray codesymbols.namesakeBijectionsymbolsOrder (group theory)IsomorphismBinary stringsAnalysisMathematicsJournal of Discrete Mathematical Sciences and Cryptography
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The variance of the $\ell _p^n$-norm of the Gaussian vector, and Dvoretzky’s theorem

2019

Discrete mathematicsAlgebra and Number TheoryGaussian vectorDvoretzky's theoremApplied MathematicsNorm (mathematics)Order statisticAnalysisMathematicsSt. Petersburg Mathematical Journal
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On the weight distribution of perfect binary codes

2021

In this paper, we give a new proof of the closed-form formula for the weight distribution of a perfect binary single-error-correcting code.

Discrete mathematicsAlgebra and Number TheoryPerfect codes Binary codes Hamming codes Weight distribution.Hamming boundApplied MathematicsBinary numberTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESSettore MAT/05 - Analisi MatematicaWeight distributionCode (cryptography)Binary codeSettore MAT/03 - GeometriaHamming codeAnalysisMathematics
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Some integral type fixed point theorems in Non-Archimedean Menger PM-Spaces with common property (E.A) and application of functional equations in dyn…

2013

In this paper, we prove some integral type common fixed point theorems for weakly compatible mappings in Non-Archimedean Menger PM-spaces employing common property (E.A). Some examples are furnished which demonstrate the validity of our results. We extend our main result to four finite families of self-mappings employing the notion of pairwise commuting. Moreover, we give an application which supports the usability of our main theorem.

Discrete mathematicsAlgebra and Number TheoryWeakly compatible mappingApplied MathematicsFixed-point theoremNon-Archimedean Menger PM-spaceT-normt-normFixed pointType (model theory)Fixed pointCommon property (E.A)Dynamic programmingComputational MathematicsMenger's theoremSettore MAT/05 - Analisi MatematicaCommon propertyPairwise comparisonGeometry and TopologyProperty (E.A)AnalysisMathematics
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On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions

1983

Discrete mathematicsAlgebraApplied MathematicsVector-valued functionAnalysisMathematicsNonlinear Analysis: Theory, Methods & Applications
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Absolutely continuous functions with values in a Banach space

2017

Abstract Let Ω be an open subset of R n , n > 1 , and let X be a Banach space. We prove that α-absolutely continuous functions f : Ω → X are continuous and differentiable (in some sense) almost everywhere in Ω.

Discrete mathematicsApplied Mathematics010102 general mathematicsBanach space0102 computer and information sciencesAbsolute continuity01 natural sciencesw⁎-DifferentiabilitySobolev spaceMetric differentiability010201 computation theory & mathematicsSettore MAT/05 - Analisi MatematicaPointwise Lipschitz functionAlmost everywhereDifferentiable function0101 mathematicsAnalysisMathematics
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A note on the admissibility of modular function spaces

2017

Abstract In this paper we prove the admissibility of modular function spaces E ρ considered and defined by Kozlowski in [17] . As an application we get that any compact and continuous mapping T : E ρ → E ρ has a fixed point. Moreover, we prove that the same holds true for any retract of E ρ .

Discrete mathematicsApplied Mathematics010102 general mathematicsModular formModular function spaceFixed pointFixed point01 natural sciences010101 applied mathematicsRetractAdmissible space0101 mathematicsAnalysisMathematics
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On 2-(n^2,2n,2n-1) designs with three intersection numbers

2007

The simple incidence structure $${\mathcal{D}(\mathcal{A},2)}$$ , formed by the points and the unordered pairs of distinct parallel lines of a finite affine plane $${\mathcal{A}=(\mathcal{P}, \mathcal{L})}$$ of order n > 4, is a 2 --- (n 2,2n,2n---1) design with intersection numbers 0,4,n. In this paper, we show that the converse is true, when n ? 5 is an odd integer.

Discrete mathematicsApplied Mathematics2-designsOrder (ring theory)ParallelComputer Science ApplicationsCombinatoricsIntegerIntersectionIncidence structureSimple (abstract algebra)Affine plane (incidence geometry)Settore MAT/03 - GeometriaMathematics
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On Sturmian Graphs

2007

AbstractIn this paper we define Sturmian graphs and we prove that all of them have a certain “counting” property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of compact directed acyclic word graphs of central Sturmian words. In order to prove this result, we give a characterization of the maximal repeats of central Sturmian words. We show also that, in analogy with the case of Sturmian words, these graphs converge to infinite ones.

Discrete mathematicsApplied MathematicsCDAWGsContinued fractionsSturmian wordSturmian wordsCharacterization (mathematics)RepeatsDirected acyclic graphCombinatoricsIndifference graphSturmian words CDAWGs Continued fractions RepeatsChordal graphComputer Science::Discrete MathematicsDiscrete Mathematics and CombinatoricsContinued fractionWord (group theory)Computer Science::Formal Languages and Automata TheoryReal numberMathematics
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Potential approach in marginalizing Gibbs models

1999

Abstract Given an undirected graph G or hypergraph potential H model for a given set of variables V , we introduce two marginalization operators for obtaining the undirected graph G A or hypergraph H A associated with a given subset A ⊂ V such that the marginal distribution of A factorizes according to G A or H A , respectively. Finally, we illustrate the method by its application to some practical examples. With them we show that potential approach allow defining a finer factorization or performing a more precise conditional independence analysis than undirected graph models. Finally, we explain connections with related works.

Discrete mathematicsApplied MathematicsComparability graphStrength of a graphClique graphlaw.inventionTheoretical Computer ScienceCombinatoricslawGraph powerArtificial IntelligenceGibbs modelLine graphGraph (abstract data type)FactorizationNull graphMarginalizationRandom geometric graphHypergraph modelsSoftwareMathematicsInternational Journal of Approximate Reasoning
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