Search results for "GRADE"

showing 10 items of 695 documents

The associated graded module of the test module filtration

2017

We show that each direct summand of the associated graded module of the test module filtration $\tau(M, f^\lambda)_{\lambda \geq 0}$ admits a natural Cartier structure. If $\lambda$ is an $F$-jumping number, then this Cartier structure is nilpotent on $\tau(M, f^{\lambda -\varepsilon})/\tau(M, f^\lambda)$ if and only if the denominator of $\lambda$ is divisible by $p$. We also show that these Cartier structures coincide with certain Cartier structures that are obtained by considering certain $\mathcal{D}$-modules associated to $M$ that were used to construct Bernstein-Sato polynomials. Moreover, we point out that the zeros of the Bernstein-Sato polynomial $b_{M,f}$ attached to an \emph{$F$-…

Pure mathematicsAlgebra and Number TheoryMathematics::Commutative Algebra010102 general mathematicsGraded ring010103 numerical & computational mathematicsMathematics - Commutative AlgebraCommutative Algebra (math.AC)01 natural sciencesMathematics - Algebraic GeometryMathematics::Algebraic GeometryFiltration (mathematics)FOS: Mathematics0101 mathematicsAlgebraic Geometry (math.AG)Mathematics
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Star calculus on Jacobi manifolds

2002

Abstract We study the Gerstenhaber bracket on differential forms induced by the two main examples of Jacobi manifolds: contact manifolds and l.c.s. manifolds. Moreover, we obtain explicit expressions of the generating operators and the derivations on the algebra of multivector fields. We define star operators for contact manifolds and l.c.s. manifolds and we study some of its properties.

Pure mathematicsDifferential formStar operatorMathematical analysisContact manifoldMathematics::Geometric TopologyGerstenhaber algebraConnected sumManifoldComputational Theory and MathematicsRicci-flat manifoldDifferential topologyGraded Poisson bracketsMathematics::Differential GeometryGeometry and TopologyLocally conformal symplectic manifoldLie algebroidMathematics::Symplectic GeometryHyperkähler manifoldAnalysisMathematicsSymplectic geometryPoisson algebraDifferential Geometry and its Applications
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Polynomial identities for the Jordan algebra of upper triangular matrices of order 2

2012

Abstract The associative algebras U T n ( K ) of the upper triangular matrices of order n play an important role in PI theory. Recently it was suggested that the Jordan algebra U J 2 ( K ) obtained by U T 2 ( K ) has an extremal behaviour with respect to its codimension growth. In this paper we study the polynomial identities of U J 2 ( K ) . We describe a basis of the identities of U J 2 ( K ) when the field K is infinite and of characteristic different from 2 and from 3. Moreover we give a description of all possible gradings on U J 2 ( K ) by the cyclic group Z 2 of order 2, and in each of the three gradings we find bases of the corresponding graded identities. Note that in the graded ca…

Pure mathematicsPolynomialAlgebra and Number TheoryJordan algebraTriangular matrixJordan polynomial identities graded upper triangularCyclic groupField (mathematics)CodimensionBasis (universal algebra)CombinatoricsSettore MAT/02 - AlgebraOrder (group theory)Mathematics
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Graded polynomial identities and exponential growth

2009

Let $A$ be a finite dimensional algebra over a field of characteristic zero graded by a finite abelian group $G$. Here we study a growth function related to the graded polynomial identities satisfied by $A$ by computing the exponential rate of growth of the sequence of graded codimensions of $A$. We prove that the $G$-exponent of $A$ exists and is an integer related in an explicit way to the dimension of a suitable semisimple subalgebra of $A$.

Pure mathematicsPolynomialMathematics::Commutative AlgebraApplied MathematicsGeneral MathematicsMathematics::Rings and AlgebrasMathematics - Rings and AlgebrasSettore MAT/02 - Algebra16R10 16W50 16P90Exponential growthRings and Algebras (math.RA)FOS: Mathematicsgraded algebra polynomial identity growth codimensionsMathematics
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Truncated modules and linear presentations of vector bundles

2018

We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles as well as on the existence of graded Artinian modules with pure resolutions. Our method allows one to produce several new examples, and provides an alternative point of view on the existing ones.

Pure mathematicsRank (linear algebra)General Mathematics[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]Vector bundle010103 numerical & computational mathematicsLinear presentationCommutative Algebra (math.AC)01 natural sciences[ MATH.MATH-AC ] Mathematics [math]/Commutative Algebra [math.AC]Mathematics - Algebraic GeometryComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsPoint (geometry)MSC: 13D02 16W50 15A30 14J600101 mathematicsVector bundleAlgebraic Geometry (math.AG)MathematicsMathematics::Commutative Algebra010102 general mathematicsConstruct (python library)Graded truncated moduleMathematics - Commutative AlgebraInstanton bundleCohomology[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Matrix of co nstant rank[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Constant (mathematics)
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THE STATE OF FRACTIONAL HEREDITARY MATERIALS (FHM)

2014

The widespread interest on the hereditary behavior of biological and bioinspired materials motivates deeper studies on their macroscopic ``minimal" state. The resulting integral equations for the detected relaxation and creep power-laws, of exponent $\beta$, are characterized by fractional operators. Here strains in $SBV_{loc}$ are considered to account for time-like jumps. Consistently, starting from stresses in $L_{loc}^{r}$, $r\in [1,\beta^{-1}], \, \, \beta\in(0,1)$ we reconstruct the corresponding strain by extending a result in [42]. The ``minimal" state is explored by showing that different histories delivering the same response are such that the fractional derivative of their differ…

Pure mathematicsState variableApplied MathematicsZero (complex analysis)State (functional analysis)Integral equationAction (physics)Fractional calculusFractional hereditary materials power-law functionally graded microstructureExponentDiscrete Mathematics and CombinatoricsRelaxation (physics)Settore ICAR/08 - Scienza Delle CostruzioniMathematics
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The graded Lie algebra structure of Lie superalgebra deformation theory

1989

We show how Lie superalgebra deformation theory can be treated by graded Lie algebras formalism. Rigidity and integrability theorems are obtained.

Pure mathematics[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]Simple Lie groupMathematics::Rings and Algebras010102 general mathematicsStatistical and Nonlinear PhysicsLie superalgebraKilling form01 natural sciencesAffine Lie algebra[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]Lie conformal algebraGraded Lie algebraAlgebraAdjoint representation of a Lie algebraRepresentation of a Lie group0103 physical sciences010307 mathematical physics0101 mathematicsComputingMilieux_MISCELLANEOUSComputer Science::DatabasesMathematical PhysicsMathematicsLetters in Mathematical Physics
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Development of extracellular vesicle-based medicinal products: A position paper of the group “Extracellular Vesicle translatiOn to clinicaL perspecti…

2021

International audience; Extracellular vesicles (EV) are emergent therapeutic effectors that have reached clinical trial investigation. To translate EV-based therapeutic to clinic, the challenge is to demonstrate quality, safety, and efficacy, as required for any medicinal product. EV research translation into medicinal products is an exciting and challenging perspective. Recent papers, provide important guidance on regulatory aspects of pharmaceutical development, defining EVs for therapeutic applications and critical considerations for the development of potency tests. In addition, the ISEV Task Force on Regulatory Affairs and Clinical Use of EV-based Therapeutics as well as the Exosomes C…

Quality ControlKnowledge management[SDV.BIO]Life Sciences [q-bio]/BiotechnologyBiological medicinal productsmedia_common.quotation_subjectDrug Compounding[SDV]Life Sciences [q-bio]Regulatory requirementsPharmaceutical ScienceMarketing authorizationExosomesChemistry Techniques Analytical03 medical and health sciencesExtracellular Vesicles0302 clinical medicineDrug DevelopmentDrug Stability[CHIM]Chemical SciencesHumansQuality (business)ComputingMilieux_MISCELLANEOUS030304 developmental biologymedia_commonCell-free therapySecretome0303 health sciencesClinical Trials as TopicClinical-grade EVScientific progressbusiness.industryDrug Administration RoutesExtracellular vesicleDrugs InvestigationalRegulatory affairs3. Good health[SDV.BIO] Life Sciences [q-bio]/BiotechnologyClinical trialEuropeAnalytics030220 oncology & carcinogenesisPosition paperMedicinal productsBusinessMicrovesicles
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Small-x physics at the LHeC

2018

The Large Hadron-electron Collider LHeC is a proposed upgrade of the LHC. It would add an electron beam to the LHC, and make it possible to study electron-proton and electron-nucleus collisions at very high energies. We present some of the highlights of the LHeC physics program related to the studies of partonic structure of protons and nuclei, and to the non-linear QCD phenomena visible at small $x$.

Quantum chromodynamicsPhysicsLarge Hadron ColliderNuclear TheoryNuclear TheoryHigh Energy Physics::PhenomenologyFOS: Physical scienceshiukkasfysiikkalaw.inventionNuclear physicsNuclear Theory (nucl-th)High Energy Physics - PhenomenologyUpgradeHigh Energy Physics - Phenomenology (hep-ph)lawPhysics::Accelerator PhysicsHigh Energy Physics::ExperimentNuclear Experiment (nucl-ex)ColliderNuclear ExperimentydinfysiikkaNuclear theoryNuclear Experiment
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Highlights and perspectives of the Mainz microtron MAMI

2003

Abstract An overview of the idea behind the physics of the MAMI laboratory and its realization is given. The introduction attempts to show the importance of the physics of hadrons in the general realm and emphasizes the low energy domain as the key to study Quantum Chromo Dynamics (QCD). Next some highlights of results at MAMI are presented illustrating this idea. New significant experiments to proceed with this approach to QCD are discussed. This is followed by a description of the upgrade of the existing MAMI B with 0.885 GeV to MAMI C with 1.5 GeV and of the new experimental equipment making the new experiments possible.

Quantum chromodynamicsPhysicsNuclear physicsNuclear and High Energy PhysicsParticle physicsLow energyUpgradeHigh Energy Physics::ExperimentNuclear ExperimentMicrotronProgress in Particle and Nuclear Physics
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