Search results for "FOS: Mathematics"

showing 10 items of 1448 documents

Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential

2015

This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations \[ -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\, x\in\mathbb{R}^{N}, \] where $1<p<N,0\leq\mu<\left((N-p)/p\right)^{p}$ and $Q\in L^{\infty}(\R^{N})$. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.

Work (thermodynamics)General Mathematicsmedia_common.quotation_subject010102 general mathematicsMathematical analysisGeneral Physics and AstronomyInfinity01 natural sciences010101 applied mathematicsSobolev spaceContinuationMathematics - Analysis of PDEs35J60 35B33FOS: Mathematics0101 mathematicsHardy's inequalityGradient estimateAnalysis of PDEs (math.AP)Mathematicsmedia_commonActa Mathematica Scientia
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Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry

2017

This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in $L^{1}$ spaces$.\ $We prove convergence to equilibrium at the rate $O\left( t^{-\frac{k}{2(k+1)+1}}\right) \ (t\rightarrow +\infty )$ for $L^{1}$ initial data $g$ in a suitable subspace of the domain of the generator $T$ where $k\in \mathbb{N}$ depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quantified version of Ingham's tauberian theorem by showing that $F_{g}(s):=\lim_{\varepsilon \rightarrow 0_{+}}\left( is+\varepsilon -T\right) ^{-1}g$ exists…

Work (thermodynamics)Generator (category theory)010102 general mathematicsBoundary (topology)Geometry[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]01 natural sciencesDomain (mathematical analysis)Functional Analysis (math.FA)010101 applied mathematicsMathematics - Functional AnalysisMathematics - Analysis of PDEsBounded functionConvergence (routing)SlabFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsAnalysisSubspace topologyMathematicsMathematical physicsAnalysis of PDEs (math.AP)
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The F-pure threshold of quasi-homogeneous polynomials

2018

Abstract Inspired by the work of Bhatt and Singh [3] we compute the F-pure threshold of quasi-homogeneous polynomials. We first consider the case of a curve given by a quasi-homogeneous polynomial f in three variables x , y , z of degree equal to the degree of xyz and then we proceed with the general case of a Calabi–Yau hypersurface, i.e. a hypersurface given by a quasi-homogeneous polynomial f in n + 1 variables x 0 , … , x n of degree equal to the degree of x 0 ⋯ x n .

Work (thermodynamics)PolynomialAlgebra and Number TheoryDegree (graph theory)010102 general mathematics01 natural sciencesCombinatoricsMathematics - Algebraic GeometryMathematics::Algebraic GeometryHypersurfaceHomogeneous0103 physical sciencesFOS: Mathematics010307 mathematical physics0101 mathematicsAlgebraic Geometry (math.AG)MathematicsJournal of Pure and Applied Algebra
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Irregular Time Dependent Obstacles

2010

Abstract We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and does not have regularity in the time variable. Two quite different procedures yield the same solution.

Yield (engineering)Parabolic obstacle problemVariational inequalities35K55 31B15 31B05Irregular obstacleLeast solutionComputer Science::RoboticsParabolic balayageLavrentiev phenomenonMathematics - Analysis of PDEsSupersolutionp-ParabolicObstacleVariational inequalityObstacle problemFOS: MathematicsApplied mathematicsTime variablePotentialAnalysisAnalysis of PDEs (math.AP)Mathematics
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Computational approach to compact Riemann surfaces

2017

International audience; A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on…

[ MATH ] Mathematics [math]Fundamental groupEquations[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]Holomorphic functionGeneral Physics and AstronomyFOS: Physical sciences010103 numerical & computational mathematics01 natural sciencessymbols.namesakeMathematics - Algebraic Geometrynumerical methodsFOS: MathematicsSpectral Methods0101 mathematics[MATH]Mathematics [math]Algebraic Geometry (math.AG)Mathematical PhysicsMathematicsCurvesKadomtsev-Petviashvili equationCollocationNonlinear Sciences - Exactly Solvable and Integrable SystemsPlane (geometry)Applied MathematicsRiemann surface010102 general mathematicsMathematical analysisStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Methods of contour integrationHyperelliptic Theta-FunctionsRiemann surfacessymbolsDispersion Limit[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph]Algebraic curveExactly Solvable and Integrable Systems (nlin.SI)Complex plane
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Building Anosov flows on $3$–manifolds

2014

We prove a result allowing to build (transitive or non-transitive) Anosov flows on 3-manifolds by gluing together filtrating neighborhoods of hyperbolic sets. We give several applications; for example: 1. we build a 3-manifold supporting both of a transitive Anosov vector field and a non-transitive Anosov vector field; 2. for any n, we build a 3-manifold M supporting at least n pairwise different Anosov vector fields; 3. we build transitive attractors with prescribed entrance foliation; in particular, we construct some incoherent transitive attractors; 4. we build a transitive Anosov vector field admitting infinitely many pairwise non-isotopic trans- verse tori.

[ MATH ] Mathematics [math]Pure mathematicsAnosov flowMathematics::Dynamical Systems3–manifolds[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)$3$–manifolds01 natural sciencesFoliationsSet (abstract data type)MSC: Primary: 37D20 Secondary: 57M9957M99Diffeomorphisms0103 physical sciencesAttractorFOS: Mathematics0101 mathematics[MATH]Mathematics [math]Mathematics - Dynamical SystemsManifoldsMathematics::Symplectic Geometry3-manifold37D20 57MMathematicsTransitive relation37D20010308 nuclear & particles physics010102 general mathematicsTorusMathematics::Geometric TopologyFlow (mathematics)Anosov flowsFoliation (geology)Vector fieldhyperbolic plugsGeometry and Topologyhyperbolic basic set3-manifold
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Bifurcations in the elementary Desboves family

2017

International audience; We give an example of a family of endomorphisms of $\mathbb{P}^2(\mathbb{C})$ whose Julia set depends continuously on the parameter and whose bifurcation locus has non-empty interior.

[ MATH ] Mathematics [math]Pure mathematicsEndomorphismMathematics - Complex VariablesApplied MathematicsGeneral Mathematics010102 general mathematicsDynamical Systems (math.DS)MSC: 32H50 37F4516. Peace & justice01 natural sciencesJulia setDynamicsRational mapsBifurcation locus0103 physical sciencesFOS: Mathematics32H50 37F45 37F50010307 mathematical physics0101 mathematics[MATH]Mathematics [math]Complex Variables (math.CV)Mathematics - Dynamical SystemsMathematics
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Surfaces of minimal degree of tame representation type and mutations of Cohen–Macaulay modules

2017

We provide two examples of smooth projective surfaces of tame CM type, by showing that any parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in projective 5-space is either a single point or a projective line. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a complete classification of rigid ACM bundles is given in terms of the action of the braid group in three strands.

[ MATH ] Mathematics [math]Pure mathematicsFibonacci numberGeneral MathematicsType (model theory)Rank (differential topology)Commutative Algebra (math.AC)01 natural sciencesMathematics - Algebraic GeometryACM bundlesVarieties of minimal degreeMathematics::Algebraic Geometry0103 physical sciencesFOS: MathematicsMathematics (all)Rings0101 mathematics[MATH]Mathematics [math]Algebraic Geometry (math.AG)MathematicsDiscrete mathematics14F05 13C14 14J60 16G60010102 general mathematicsVarietiesMCM modulesACM bundles; MCM modules; Tame CM type; Ulrich bundles; Varieties of minimal degree; Mathematics (all)Ulrich bundlesMathematics - Commutative AlgebraQuintic functionElliptic curveTame CM typeProjective lineBundles010307 mathematical physicsIsomorphismIndecomposable moduleMSC: 14F05; 13C14; 14J60; 16G60
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The dual and the double of a Hopf algebroid are Hopf algebroids

2017

Let $H$ be a $\times$-bialgebra in the sense of Takeuchi. We show that if $H$ is $\times$-Hopf, and if $H$ fulfills the finiteness condition necessary to define its skew dual $H^\vee$, then the coopposite of the latter is $\times$-Hopf as well. If in addition the coopposite $\times$-bialgebra of $H$ is $\times$-Hopf, then the coopposite of the Drinfeld double of $H$ is $\times$-Hopf, as is the Drinfeld double itself, under an additional finiteness condition.

[ MATH ] Mathematics [math]Pure mathematicsGeneral Computer ScienceDuality (optimization)01 natural sciencesTheoretical Computer ScienceMathematics::Category TheoryMathematics::Quantum AlgebraMathematics - Quantum Algebra0103 physical sciencesFOS: Mathematics[MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA]Quantum Algebra (math.QA)[ MATH.MATH-CT ] Mathematics [math]/Category Theory [math.CT]0101 mathematics[MATH]Mathematics [math]Hopf algebroid[MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT]Mathematics[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA]Algebra and Number TheoryMSC: 16T99 18D10[ MATH.MATH-QA ] Mathematics [math]/Quantum Algebra [math.QA]010308 nuclear & particles physicsbialgebroid[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]010102 general mathematicsMathematics::Rings and AlgebrasSkewMathematics - Rings and Algebras[MATH.MATH-CT] Mathematics [math]/Category Theory [math.CT][ MATH.MATH-RA ] Mathematics [math]/Rings and Algebras [math.RA]Dual (category theory)Rings and Algebras (math.RA)Theory of computation[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA]duality
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Categorical action of the extended braid group of affine type $A$

2017

Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group.

[ MATH ] Mathematics [math]Pure mathematicsGeneral MathematicsCategorificationBraid groupGeometric intersection01 natural sciencesMathematics - Geometric TopologyMorphismMathematics::Category TheoryQuiverMathematics - Quantum Algebra0103 physical sciencesFOS: MathematicsQuantum Algebra (math.QA)Representation Theory (math.RT)0101 mathematics[MATH]Mathematics [math]MathematicsHomotopy categoryGroup (mathematics)Applied Mathematics010102 general mathematicsQuiverBraid groupsGeometric Topology (math.GT)16. Peace & justiceCategorificationCategorical actionBounded functionMSC: 20F36 18E30 57M99 13D99010307 mathematical physicsAffine transformationMathematics - Representation Theory
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