Search results for "combinatoric"

showing 10 items of 1776 documents

Lattices of Jordan algebras

2010

AbstractCommutative Jordan algebras play a central part in orthogonal models. The generations of these algebras is studied and applied in deriving lattices of such algebras. These lattices constitute the natural framework for deriving new orthogonal models through factor aggregation and disaggregation.

Kronecker productNumerical AnalysisPure mathematicsProjectorsAlgebra and Number TheoryJordan algebraNon-associative algebraBinary operationsLatticeAlgebrasymbols.namesakeBinary operationCommutative Jordan algebraLattice (order)Kronecker matrix productsymbolsDiscrete Mathematics and CombinatoricsGeometry and TopologyNest algebraCommutative algebraCommutative propertyMathematicsLinear Algebra and its Applications
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Quantitative uniqueness estimates for pp-Laplace type equations in the plane

2016

Abstract In this article our main concern is to prove the quantitative unique estimates for the p -Laplace equation, 1 p ∞ , with a locally Lipschitz drift in the plane. To be more precise, let u ∈ W l o c 1 , p ( R 2 ) be a nontrivial weak solution to div ( | ∇ u | p − 2 ∇ u ) + W ⋅ ( | ∇ u | p − 2 ∇ u ) = 0  in  R 2 , where W is a locally Lipschitz real vector satisfying ‖ W ‖ L q ( R 2 ) ≤ M for q ≥ max { p , 2 } . Assume that u satisfies certain a priori assumption at 0. For q > max { p , 2 } or q = p > 2 , if ‖ u ‖ L ∞ ( R 2 ) ≤ C 0 , then u satisfies the following asymptotic estimates at R ≫ 1 inf | z 0 | = R sup | z − z 0 | 1 | u ( z ) | ≥ e − C R 1 − 2 q log R , where C > 0 depends …

Laplace's equationLaplace transformPlane (geometry)Applied MathematicsWeak solution010102 general mathematicsta111Type (model theory)Lipschitz continuity01 natural sciencesBeltrami equation010101 applied mathematicsCombinatoricspp-Laplace equationBeltrami equationstrong unique continuation principleUniqueness0101 mathematicsAnalysisMathematicsNonlinear Analysis: Theory, Methods and Applications
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The doodle of a finitely determined map germ from R2 to R3

2009

Let f:U⊂R2→R3 be a representative of a finitely determined map germ f:(R2,0)→(R3,0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere Sϵ2 centered at the origin in R3, call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles.

Large classCombinatoricsIntersectionGeneral MathematicsTransversal (combinatorics)Image (category theory)Topological classificationGermMathematicsAdvances in Mathematics
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Problemas históricos y dificultades de los estudiantes en la conceptualización de sustancia compuesto químico

2008

Este trabajo ofrece un análisis histórico sobre los problemas que tuvo que resolver la ciencia hasta llegar a la construcción de los conceptos macroscópicos de sustancia y compuesto químico en el contexto de la teoría daltoniana. Por otra parte, en él se muestran algunas de las dificultades de comprensión que estos conceptos ofrecen a los estudiantes. Para determinarlas, se realiza un estudio transversal con alumnos de 15 a 18 años, lo que permite evaluar el significado que otorgan a la idea de sustancia, al tiempo que se constata la necesidad de su comprensión para poder entender los cambios químicos. Por último, se plantea la existencia de ciertas semejanzas entre las ideas sobre la compo…

Learning difficultiesProblemes històricsDificultades de aprendizajeContext (language use)Dificultats d'aprenentatgeEducationEpistemologyComprehensionCompost químicSustanciaTransversal (combinatorics)SubstancePsychologyRelation (history of concept)Problemas históricosCompuesto químicoHistorical problemsSubstànciaMeaning (linguistics)Chemical compoundEnseñanza de las ciencias: revista de investigación y experiencias didácticas
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Fixed point theorems in generalized partially orderedG-metric spaces

2010

In this paper, we consider the concept of a $\Omega$-distance on a complete partially ordered G-metric space and prove some fixed point theorems.

Least fixed pointCombinatoricsPure mathematicsMetric spaceSettore MAT/05 - Analisi MatematicaModeling and SimulationFixed point theorem G-metric spaces $\Omega$-distanceFixed-point theoremSpace (mathematics)Fixed-point propertyComputer Science ApplicationsMathematicsMathematical and Computer Modelling
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Vertical representation of C∞-words

2015

We present a new framework for dealing with C ∞ -words, based on their left and right frontiers. This allows us to give a compact representation of them, and to describe the set of C ∞ -words through an infinite directed acyclic graph G. This graph is defined by a map acting on the frontiers of C ∞ -words. We show that this map can be defined recursively and with no explicit reference to C ∞ -words. We then show that some important conjectures on C ∞ -words follow from analogous statements on the structure of the graph G.

Left and rightDiscrete mathematicsGeneral Computer ScienceComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)16. Peace & justiceDirected acyclic graphTheoretical Computer ScienceCombinatoricsDirected setRecursive functionsGraph (abstract data type)Null graphComputer Science::Formal Languages and Automata TheoryMathematicsofComputing_DISCRETEMATHEMATICSMathematicsTheoretical Computer Science
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Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n)

2003

We prove an Amitsur-Levitzki type theorem for the Lie superalgebras osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras gl(p,q) cannot satisfy an Amitsur-Levitzki type super identity if p, q are non zero and conjecture that neither can any other classical simple Lie superalgebra with the exception of osp(1,2n).

Lie superalgebraType (model theory)17B2001 natural sciencesInterpretation (model theory)CombinatoricsIdentity (mathematics)Simple (abstract algebra)Mathematics::Quantum Algebra0103 physical sciencesFOS: Mathematics0101 mathematicsRepresentation Theory (math.RT)Classical theoremMathematics::Representation TheoryMathematical PhysicsPhysicsConjecture[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]010308 nuclear & particles physics010102 general mathematicsMathematics::Rings and AlgebrasStatistical and Nonlinear Physics16. Peace & justice17B56[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]17B20; 17B56Mathematics - Representation Theory
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Steiner systems and configurations of points

2020

AbstractThe aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner SystemS(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configur…

Linear codes; Monomial ideals; Stanley Reisner rings; Steiner systems; Symbolic powersSteiner systemsBetti numberPolynomial ring0102 computer and information sciencesAlgebraic geometrySymbolic powers01 natural sciencessymbols.namesakeMathematics - Algebraic GeometryLinear codesTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYMonomial idealsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsMathematics - CombinatoricsIdeal (ring theory)0101 mathematicsCommutative algebraAlgebraic Geometry (math.AG)Complement (set theory)MathematicsDiscrete mathematicsHilbert series and Hilbert polynomialApplied Mathematics010102 general mathematicsStanley Reisner ringsLinear codes Monomial ideals Stanley Reisner rings Steiner systems Symbolic powersComputer Science Applications51E10 13F55 13F20 14G50 94B27Settore MAT/02 - AlgebraSteiner systemSteiner systems Monomial ideals Symbolic powers Stanley Reisner rings Linear codes010201 computation theory & mathematicssymbolsCombinatorics (math.CO)Settore MAT/03 - GeometriaMathematicsofComputing_DISCRETEMATHEMATICS
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On semi-fredholm properties of a boundary value problem inR + n

1988

The paper considers a boundary value problem with the help of the smallest closed extensionL ∼ :H k →H k 0×B h 1×...×B h N of a linear operatorL :C (0) ∞ (R + n ) →L(R + n )×L(R n−1)×...×L(R n−1). Here the spacesH k (the spaces ℬ h ) are appropriate subspaces ofD′(R + n ) (ofD′(R n−1), resp.),L(R + n ) andC (0) ∞ (R + n )) denotes the linear space of smooth functionsR n →C, which are restrictions onR + n of a function from the Schwartz classL (fromC 0 ∞ , resp.),L(R n−1) is the Schwartz class of functionsR n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L ∼) and for the uniqueness of solutionsL ∼ U=F are expressed. In addition, ana prio…

Linear mapCombinatoricsGeneral MathematicsLinear spaceMathematical analysisFunction (mathematics)Boundary value problemUniquenessAlgebra over a fieldLinear subspaceMathematicsIsrael Journal of Mathematics
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Trunk Packing Revisited

2007

For trunk packing problems only few approximation schemes are known, mostly designed for the European standard DIN 70020 [6] with equally sized boxes [8, 9, 11, 12]. In this paper two discretized approaches for the US standard SAE J1100 [10] are presented, which make use of different box sizes. An exact branch-and-bound algorithm for weighted independent sets on graphs is given, using the special structure of the SAE standard. Another branch-and-bound packing algorithm using linear programs is presented. With these algorithms axis-oriented packings of different box sizes in an arbitrary trunk geometry can be computed efficiently.

Linear programming relaxationCombinatoricsDiscrete mathematicsPacking problemsDiscretizationLinear programmingBranch and priceStructure (category theory)Approximation algorithmBranch and cutMathematics
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