Search results for "Ambient space"

showing 3 items of 3 documents

Champs de vecteurs analytiques et champs de gradients

2002

A theorem of Łojasiewicz asserts that any relatively compact solution of a real analytic gradient vector field has finite length. We show here a generalization of this result for relatively compact solutions of an analytic vector field X with a smooth invariant hypersurface, transversally hyperbolic for X, where the restriction of the field is a gradient. This solves some instances of R. Thom's Gradient Conjecture. Furthermore, if the dimension of the ambient space is three, these solutions do not oscillate (in the sense that they cut an analytic set only finitely many times); this can also be applied to some gradient vector fields.

HypersurfaceRelatively compact subspaceApplied MathematicsGeneral MathematicsMathematical analysisGradient conjectureVector fieldAnalytic setInvariant (mathematics)MathematicsAmbient spaceErgodic Theory and Dynamical Systems
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Multiprojective spaces and the arithmetically Cohen-Macaulay property

2019

AbstractIn this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for ℙ1× ℙ1and, more recently, in (ℙ1)r. In ℙ1× ℙ1the so called inclusion property characterises the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in ℙm× ℙn. In such an ambient space it is equivalent to the so-called (⋆)-property. Moreover, we start an investigation of the ACM property in ℙ1× ℙn. We give a new construction that highlights how different the behavior of the ACM property is in this setting.

Pure mathematicsArithmetically Cohen-Macaulay multiprojective spacesProperty (philosophy)points in multiprojective spaces arithmetically Cohen-Macaulay linkageGeneral MathematicsStar (graph theory)Space (mathematics)Commutative Algebra (math.AC)01 natural sciencesMathematics - Algebraic Geometryarithmetically Cohen-MacaulayTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY0103 physical sciencesFOS: Mathematics0101 mathematicsAlgebraic Geometry (math.AG)Mathematics010102 general mathematics14M05 13C14 13C40 13H10 13A15Mathematics - Commutative Algebrapoints in multiprojective spacesAmbient spaceSettore MAT/02 - Algebra010307 mathematical physicsSettore MAT/03 - Geometrialinkage
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Estimates for Sums of Eigenvalues of the Free Plate via the Fourier Transform

2017

Using the Fourier transform, we obtain upper bounds for sums of eigenvalues of the free plate.

Tension (physics)Applied MathematicsSums of eigenvaluesMathematical analysisFree plate35P15 35J40 74K20General MedicineMathematics::Spectral TheoryDomain (mathematical analysis)Ambient spaceMathematics - Spectral TheoryPhysics::Fluid Dynamicssymbols.namesakeFourier transformVolume (thermodynamics)Dimension (vector space)Bilaplace operatorSettore MAT/05 - Analisi MatematicasymbolsFOS: MathematicsSpectral Theory (math.SP)AnalysisEigenvalues and eigenvectorsMathematics
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