Search results for "model [interaction]"

showing 10 items of 1495 documents

An integral representation for decomposable measures of measurable functions

1994

We start with a measurem on a measurable space (Ω,A), decomposable with respect to an Archimedeant-conorm ⊥ on a real interval [0,M], which generalizes an additive measure. Using the integral introduced by the second author, a Radon-Nikodym type theorem, needed in what follows, is given.

Discrete mathematicsIntegral representationMarkov kernelMeasurable functionApplied MathematicsGeneral MathematicsDiscrete Mathematics and CombinatoricsInterval (graph theory)Type (model theory)Space (mathematics)Measure (mathematics)MathematicsAequationes Mathematicae
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Intersection subgroups of complex hyperplane arrangements

2000

Abstract Let A be a central arrangement of hyperplanes in C n , let M( A ) be the complement of A , and let L ( A ) be the intersection lattice of A . For X in L ( A ) we set A X ={H∈ A : H⫆X} , and A /X={H/X: H∈ A X } , and A X ={H∩X: H∈ A \ A X } . We exhibit natural embeddings of M( A X ) in M( A ) that give rise to monomorphisms from π 1 (M( A X )) to π 1 (M( A )) . We call the images of these monomorphisms intersection subgroups of type X and prove that they form a conjugacy class of subgroups of π 1 (M( A )) . Recall that X in L ( A ) is modular if X+Y is an element of L ( A ) for all Y in L ( A ) . We call X in L ( A ) supersolvable if there exists a chain 0⫅X 1 ⫅⋯⫅X d =X in L ( A ) …

Discrete mathematicsIntersection subgroupCommensuratorLattice (group)Center (category theory)Type (model theory)Characterization (mathematics)Centralizer and normalizerCombinatoricsConjugacy classModular elementArrangement of hyperplanesGeometry and TopologyMathematicsArrangement of hyperplanesTopology and its Applications
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Asymptotics for the Amitsur's Capelli - Type Polynomials and Verbally Prime PI-Algebras

2006

We consider associativePI-algebras over a field of characteristic zero. The main goal of the paper is to prove that the codimensions of a verbally prime algebra [11] are asymptotically equal to the codimensions of theT-ideal generated by some Amitsur's Capelli-type polynomialsEM,L* [1]. We recall that two sequencesan,bnare asymptotically equal, and we writean≃bn,if and only if limn→∞(an/bn)=1.In this paper we prove that\(c_n \left( {M_k \left( G \right)} \right) \simeq c_n \left( {E_{k^2 ,k^2 }^ * } \right) and c_n \left( {M_{k,l} \left( G \right)} \right) \simeq c_n \left( {E_{k^2 + l^2 ,2kl}^ * } \right) \)% MathType!End!2!1!, whereG is the Grassmann algebra. These results extend to all v…

Discrete mathematicsJacobson RadicalGeneral MathematicsPolynomial IdentityZero (complex analysis)Associative AlgebraField (mathematics)Type (model theory)Prime (order theory)Young TableauYoung DiagramPiAlgebra over a fieldExterior algebraMathematics
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Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation

2013

We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.

Discrete mathematicsLeast fixed point2-metric space common property (E.A) common limit range property weakly compatible mappings implicit relations fixed point.Metric spaceSchauder fixed point theoremArticle SubjectSettore MAT/05 - Analisi MatematicaFixed-point theoremType (model theory)Fixed-point propertyCoincidence pointFinite setMathematicsJournal of Operators
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The generalised type-theoretic interpretation of constructive set theory

2006

We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory. The generalisation involves replacing Martin-Löf type theory with a new type theory in which logic is treated as primitive instead of being formulated via the propositions-as-types representation. The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation. The generalisation involves replacing Martin-Löf type theory with a new type theory in which logic is treated as primitive. The primitive treatment of logic in type theories allows us to study reinterpretations of logic, such as the double-negation translation.

Discrete mathematicsLogicConstructive set theoryType (model theory)Translation (geometry)Constructive Set TheoryInterpretation (model theory)AlgebraPhilosophyType theoryDependent type theoryDependent Type TheoryComputer Science::Logic in Computer Science03F25Constructive set theory Dependent type theoryMathematics03F50
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Minimal Morse flows on compact manifolds

2006

Abstract In this paper we prove, using the Poincare–Hopf inequalities, that a minimal number of non-degenerate singularities can be computed in terms only of abstract homological boundary information. Furthermore, this minimal number can be realized on some manifold with non-empty boundary satisfying the abstract homological boundary information. In fact, we present all possible indices and types (connecting or disconnecting) of singularities realizing this minimal number. The Euler characteristics of all manifolds realizing this minimal number are obtained and the associated Lyapunov graphs of Morse type are described and shown to have the lowest topological complexity.

Discrete mathematicsLyapunov functionTopological complexityBoundary (topology)Type (model theory)Morse codeManifoldLyapunov graphslaw.inventionsymbols.namesakePoincaré–Hopf inequalitieslawEuler's formulasymbolsGravitational singularityGeometry and TopologyMathematics::Symplectic GeometryConley indexMathematicsTopology and its Applications
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On simple families of functions and their Legendrian mappings

2004

We study germs of $n$-parameter families of functions, that is, function-germs of the type $f : (\mathbb{R}^n \times \mathbb{R}, 0) \to (\mathbb{R}, 0)$ defined on the total space of the trivial bundle $ \mathbb{R}^n \times \mathbb{R} \to \mathbb{R}^n $. There is a natural notion of $V$-equivalence for such function-germs. We introduce the Young diagram of $n$-parameter families satisfying a non-degeneracy condition. We classify all such simple $n$-parameter families and give their versal deformations. This result has direct applications to contact and projective geometry.

Discrete mathematicsMathematics::Algebraic GeometryDiagram (category theory)Simple (abstract algebra)General MathematicsType (model theory)Space (mathematics)MathematicsProjective geometryProceedings of the London Mathematical Society
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A Mönch type fixed point theorem under the interior condition

2009

Abstract In this paper we show that the well-known Monch fixed point theorem for non-self mappings remains valid if we replace the Leray–Schauder boundary condition by the interior condition. As a consequence, we obtain a partial generalization of Petryshyn's result for nonexpansive mappings.

Discrete mathematicsMathematics::Functional AnalysisGeneralizationApplied MathematicsInterior conditionMathematics::Analysis of PDEsBanach spaceFixed-point theoremType (model theory)Mönch fixed point theoremBanach spacesStrictly star-shaped setLeray–Schauder conditionBoundary value problemAnalysisMathematicsJournal of Mathematical Analysis and Applications
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On the structure of the ultradistributions of Beurling type

2008

Let O be a nonempty open set of the k-dimensional euclidean space Rk. In this paper, we give a structure theorem on the ultradistributions of Beurling type in O. Also, other structure results on certain ultradistributions are obtained, in terms of complex Borel measures in O.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsAlgebra and Number TheoryEuclidean spaceRiesz–Markov–Kakutani representation theoremApplied MathematicsOpen setStructure (category theory)Banach spaceType (model theory)Computational MathematicsLocally convex topological vector spaceGeometry and TopologyAnalysisStructured program theoremMathematicsRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
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Meir-Keeler Type Contractions for Tripled Fixed Points

2012

Abstract In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.

Discrete mathematicsMetric spaceSettore MAT/05 - Analisi MatematicaGeneralizationGeneral MathematicsMathematics::General TopologyGeneral Physics and AstronomyFixed-point theoremTripled fixed point theorems Meir-Keeler type contractions partially ordered sets.Type (model theory)Fixed pointPartially ordered setMathematicsActa Mathematica Scientia
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