Search results for "combinatoric"

showing 10 items of 1776 documents

Weak chord-arc curves and double-dome quasisymmetric spheres

2014

Let $\Omega$ be a planar Jordan domain and $\alpha>0$. We consider double-dome-like surfaces $\Sigma(\Omega,t^{\alpha})$ over $\overline{\Omega}$ where the height of the surface over any point $x\in\overline{\Omega}$ equals $\text{dist}(x,\partial\Omega)^{\alpha}$. We identify the necessary and sufficient conditions in terms of $\Omega$ and $\alpha$ so that these surfaces are quasisymmetric to $\mathbb{S}^2$ and we show that $\Sigma(\Omega,t^{\alpha})$ is quasisymmetric to the unit sphere $\mathbb{S}^2$ if and only if it is linearly locally connected and Ahlfors $2$-regular.

Unit sphereChord (geometry)QA299.6-43330C65 30C62Mathematics::Complex VariablesApplied Mathematics010102 general mathematicsdouble-dome-like surfacesMetric Geometry (math.MG)16. Peace & justice01 natural sciencesOmegachord-arc propertyCombinatoricsMathematics - Metric GeometryFOS: Mathematicsquasisymmetric spheresAhlfors 2-regularityMathematics::Metric GeometrySPHERESGeometry and Topology0101 mathematicsahlfors 2-regularityAnalysisMathematics
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Relatively weakly open convex combinations of slices

2018

We show that c 0 c_0 and, in fact, C ( K ) C(K) for any scattered compact Hausdorff space K K have the property that finite convex combinations of slices of the unit ball are relatively weakly open.

Unit sphereCombinatoricsDiscrete mathematicsProperty (philosophy)Applied MathematicsGeneral Mathematics010102 general mathematicsHausdorff spaceRegular polygon0101 mathematics01 natural sciencesMathematics
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A Short Proof that Some Mappings of the Unit Ball of ℓ2 Are Never Nonexpansive

2020

It is known that some particular self-mappings of the closed unit ball Bl2 of l2 with no fixed points cannot be nonexpansive with respect to any renorming of l2. We give here a short proof of this ...

Unit sphereCombinatoricsGeneral Mathematics010102 general mathematics0101 mathematicsFixed point01 natural sciencesMathematicsThe American Mathematical Monthly
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Almost square Banach spaces

2014

We single out and study a natural class of Banach spaces -- almost square Banach spaces. In an almost square space we can find, given a finite set $x_1,x_2,\ldots,x_N$ in the unit sphere, a unit vector $y$ such that $\|x_i-y\|$ is almost one. These spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2. We provide several examples and characterizations of almost square spaces. We prove that non-reflexive spaces which are M-ideals in their biduals are almost square. We show that every separable space containing a copy of $c_0$ can be renormed to be almost square. A local and a weak version of almost square spa…

Unit sphereMathematics::Functional AnalysisApplied Mathematics010102 general mathematicsBanach spaceSpace (mathematics)01 natural sciencesSquare (algebra)Functional Analysis (math.FA)Separable spaceMathematics - Functional Analysis010101 applied mathematicsCombinatoricsUnit vectorFOS: MathematicsDual polyhedron0101 mathematics46B20 46B04 46B07Finite setAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Analytic structure in fibers of H∞(Bc0)

2020

Abstract Let H ∞ ( B c 0 ) be the algebra of all bounded holomorphic functions on the open unit ball of c 0 and M ( H ∞ ( B c 0 ) ) the spectrum of H ∞ ( B c 0 ) . We prove that for any point z in the closed unit ball of l ∞ there exists an analytic injection of the open ball B l ∞ into the fiber of z in M ( H ∞ ( B c 0 ) ) , which is an isometry from the Gleason metric of B l ∞ to the Gleason metric of M ( H ∞ ( B c 0 ) ) . We also show that, for some Banach spaces X, B l ∞ can be analytically injected into the fiber M z ( H ∞ ( B X ) ) for every point z ∈ B X .

Unit sphereOpen unitApplied Mathematics010102 general mathematicsBanach spaceHolomorphic function01 natural sciences010101 applied mathematicsCombinatoricsBounded functionBall (mathematics)0101 mathematicsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Diameter 2 properties and convexity

2015

We present an equivalent midpoint locally uniformly rotund (MLUR) renorming $X$ of $C[0,1]$ on which every weakly compact projection $P$ satisfies the equation $\|I-P\| = 1+\|P\|$ ($I$ is the identity operator on $X$). As a consequence we obtain an MLUR space $X$ with the properties D2P, that every non-empty relatively weakly open subset of its unit ball $B_X$ has diameter 2, and the LD2P+, that for every slice of $B_X$ and every norm 1 element $x$ inside the slice there is another element $y$ inside the slice of distance as close to 2 from $x$ as desired. An example of an MLUR space with the D2P, the LD2P+, and with convex combinations of slices of arbitrary small diameter is also given.

Unit sphereSmall diameter46B04 46B20General Mathematics010102 general mathematicsRegular polygon01 natural sciencesMidpointConvexityFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsCombinatoricsNorm (mathematics)FOS: Mathematics0101 mathematicsMathematicsStudia Mathematica
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Separation of unitary representations of connected Lie groups by their moment sets

2005

AbstractWe show that every unitary representation π of a connected Lie group G is characterized up to quasi-equivalence by its complete moment set.Moreover, irreducible unitary representations π of G are characterized by their moment sets.

Unitary representationSimple Lie group(gK)-moduleLie groupCombinatoricsUnitary representationRepresentation of a Lie groupRepresentation theory of SUUnitary groupFundamental representationMoment setMaximal torusAnalysisMathematicsJournal of Functional Analysis
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"Table 208" of "Measurement of the correlation between flow harmonics of different order in lead-lead collisions at $\sqrt{s_{NN}}$=2.76 TeV with the…

2015

RMS eccentricity scaled v_n.

V2InclusiveMathematics::CombinatoricsMathematics::Probability2760.0Physics::Accelerator PhysicsComputer Science::Symbolic ComputationAstrophysics::Earth and Planetary AstrophysicsPB PB --> CHARGED X
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"Table 207" of "Measurement of the correlation between flow harmonics of different order in lead-lead collisions at $\sqrt{s_{NN}}$=2.76 TeV with the…

2015

RMS eccentricity scaled v_n.

V2InclusiveMathematics::CombinatoricsMathematics::Probability2760.0Physics::Accelerator PhysicsComputer Science::Symbolic ComputationAstrophysics::Earth and Planetary AstrophysicsPB PB --> CHARGED X
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"Figure 2.6" of "Measurements of Higher-Order Flow Harmonics in Au+Au Collisions at sqrt(s_NN) = 200 GeV"

2020

Charged hadron mean $$ in each $p_T$ bins used for the $v_n$ measurements in Au+Au collisions at 200 GeV.

V2Mathematics::CombinatoricsV4V3High Energy Physics::PhenomenologypTNUCLEUS NUCLEUS --> CHARGED XQuadrangular Flow200.0Triangular FlowInclusiveElliptic FlowTransverse MomentumAU AU --> CHARGED XComputer Science::Symbolic ComputationHigh Energy Physics::ExperimentNuclear Experiment
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