Search results for "complex"

showing 10 items of 5889 documents

Weakly uniformly continuous holomorphic functions and the approximation property

2001

Abstract We study the approximation property for spaces of Frechet and Gâteaux holomorphic functions which are weakly uniformly continuous on bounded sets. We show when U is a balanced open subset of a Baire or barrelled metrizable locally convex space, E , that the space of holomorphic functions which are weakly uniformly continuous on U -bounded sets has the approximation property if and only if the strong dual of E , E ′ b , has the approximation property. We also characterise the approximation property for these spaces of vector-valued holomorphic functions in terms of the tensor product of the corresponding space of scalar-valued holomorphic functions and the range space.

Discrete mathematicsPure mathematicsMathematics(all)Approximation propertyMathematics::Complex VariablesGeneral MathematicsHolomorphic functionSpace (mathematics)Identity theoremUniform continuityTensor productBergman spaceBounded functionMathematicsIndagationes Mathematicae
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Holomorphically ultrabornological spaces and holomorphic inductive limits

1987

Abstract The holomorphically ultrabornological spaces are introduced. Their relation with other holomorphically significant classes of locally convex spaces is established and separating examples are given. Some apparently new properties of holomorphically barrelled spaces are included and holomorphically ultrabornological spaces are utilized in a problem posed by Nachbin.

Discrete mathematicsPure mathematicsMathematics::Complex VariablesApplied MathematicsLocally convex topological vector spaceHolomorphic functionMathematics::Symplectic GeometryAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Identities of *-superalgebras and almost polynomial growth

2015

We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero.

Discrete mathematicsPure mathematicsPolynomialAlgebra and Number TheoryMathematics::Commutative Algebraalmost polynomial growthgraded involution010102 general mathematicsZero (complex analysis)Field (mathematics)010103 numerical & computational mathematics01 natural sciencesMatrix polynomialSquare-free polynomialSimple (abstract algebra)polynomial identity0101 mathematicsAlgebraically closed fieldCharacteristic polynomialMathematics
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Projective spaces on partially ordered sets and Desargues' postulate

1991

We introduce a generalized concept of projective and Desarguean space where points (and lines) may be of different size. Every unitary module yields an example when we take the 1-and 2-generated submodules as points and lines. In this paper we develop a method of constructing a wide range of projective and Desarguean spaces by means of lattices.

Discrete mathematicsPure mathematicsProjective harmonic conjugateCollineationComplex projective spaceProjective spaceGeometry and TopologyProjective planeQuaternionic projective spaceNon-Desarguesian planeProjective geometryMathematicsGeometriae Dedicata
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Embedding Locally Projective Planar Spaces Into Projective Spaces

1988

We shall show that a 3-dimensional locally projective planar space of finite order n can be embedded into a 3-dimensional projective space of order n, if it has at least n 3 points.

Discrete mathematicsPure mathematicsReal projective lineCollineationProjective unitary groupComplex projective spaceProjective spaceProjective planeQuaternionic projective spacePencil (mathematics)Mathematics
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Polynomial growth of the codimensions: a characterization

2009

Let A A be a not necessarily associative algebra over a field of characteristic zero. Here we characterize the T-ideal of identities of A A in case the corresponding sequence of codimensions is polynomially bounded.

Discrete mathematicsPure mathematicsSequencePolynomialApplied MathematicsGeneral MathematicsMathematicsofComputing_GENERALZero (complex analysis)Field (mathematics)Characterization (mathematics)codimensions polynomial identityBounded functionAssociative algebraGeneralLiterature_REFERENCE(e.g.dictionariesencyclopediasglossaries)Mathematics
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An almost nilpotent variety of exponent 2

2013

We construct a non-associative algebra A over a field of characteristic zero with the following properties: if V is the variety generated by A, then V has exponential growth but any proper subvariety of V is nilpotent. Moreover, by studying the asymptotics of the sequence of codimensions of A we deduce that exp(V) = 2.

Discrete mathematicsPure mathematicsSequenceSubvarietyGeneral MathematicsZero (complex analysis)Field (mathematics)Variety codimensions growth.NilpotentSettore MAT/02 - AlgebraExponential growthExponentVariety (universal algebra)Mathematics
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Generalized ``transition probability''

1975

An operationally meaningful symmetric function defined on pairs of states of an arbitrary physical system is constructed and is shown to coincide with the usual “transition probability” in the special case of systems admitting a quantum-mechanical description. It can be used to define a metric in the set of physical states. Conceivable applications to the analysis of certain aspects of Quantum Mechanics and to its possible modifications are mentioned.

Discrete mathematicsPure mathematicsTransition (fiction)Complex systemPhysical systemStatistical and Nonlinear PhysicsSymmetric functionSet (abstract data type)Probability amplitudeMetric (mathematics)Special case81.60Mathematical PhysicsMathematics
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An Exact Algorithm for the Quadratic Assignment Problem on a Tree

1989

The Tree QAP is a special case of the Quadratic Assignment Problem (QAP) where the nonzero flows form a tree. No condition is required for the distance matrix. This problem is NP-complete and is also a generalization of the Traveling Salesman Problem. In this paper, we present a branch-and-bound algorithm for the exact solution of the Tree QAP based on an integer programming formulation of the problem. The bounds are computed using a Lagrangian relaxation of this formulation. To solve the relaxed problem, we present a Dynamic Programming algorithm which is polynomially bounded. The obtained lower bound is very sharp and equals the optimum in many cases. This fact allows us to employ a redu…

Discrete mathematicsQuadratic assignment problemManagement Science and Operations ResearchTravelling salesman problemComputer Science ApplicationsReduction (complexity)Tree (data structure)symbols.namesakeExact algorithmLagrangian relaxationsymbolsInteger programmingGeneralized assignment problemMathematicsOperations Research
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Error-Free Affine, Unitary, and Probabilistic OBDDs

2018

We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results for the automata versions of these models.

Discrete mathematicsQuadratic growthLas vegas010102 general mathematicsProbabilistic logic02 engineering and technologyComputer Science::Computational ComplexityComputer Science::Artificial Intelligence01 natural sciencesUnitary stateAutomatonSuccinctnessComputer Science::Logic in Computer Science0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processingAffine transformation0101 mathematicsComputer Science::DatabasesZero errorMathematics
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