Search results for "15a"

showing 10 items of 26 documents

Singular quadratic Lie superalgebras

2012

In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and a classification of singular quadratic Lie superalgebras, i.e. those with a nonzero invariant. Finally, we study a class of quadratic Lie superalgebras obtained by the method of generalized double extensions.

Pure mathematics17B05Super Poisson bracketFOS: Physical sciencesLie superalgebraGraded Lie algebraRepresentation of a Lie groupMathematics::Quantum AlgebraMathematics::Representation TheoryMathematical PhysicsMathematicsQuadratic Lie superalgebrasDiscrete mathematicsAlgebra and Number TheoryInvariant[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]Simple Lie groupMathematics::Rings and AlgebrasMathematical Physics (math-ph)17B30Killing form[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT]Lie conformal algebraDouble extensionsGeneralized double extensionsAdjoint representation of a Lie algebra15A63 17B05 17B30 17B70Adjoint orbits 2000 MSC: 15A6317B70Fundamental representation
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Elementary symmetric functions of two solvents of a quadratic matrix equations

2008

Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n quadratic matrix equation X^2- L1X - L0 = 0, playing the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear second order difference equations with noncommutative coefficients. An application of our results to a simple physical problem is briefly discussed.

Pure mathematicsDifferential equationquadratic matrix equationFOS: Physical sciencesStatistical and Nonlinear Physicsdifference equationMathematical Physics (math-ph)Noncommutative geometrysolventquadratic matrix equation; solvent; difference equation; symmetric functions15A24Symmetric functionMatrix (mathematics)Quadratic equationSimple (abstract algebra)symmetric functionsVariety (universal algebra)Connection (algebraic framework)Mathematical PhysicsMathematics
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Special elements in a ring related to Drazin inverses

2013

In this paper, the existence of the Drazin (group) inverse of an element a in a ring is analyzed when amk = kan, for some unit k and m; n 2 N. The same problem is studied for the case when a* = kamk-1 and for the fk; s+1g-potent elements. In addition, relationships with other special elements of the ring are also obtained

Pure mathematicsDrazin inverse16E50Inverse010103 numerical & computational mathematicsInvolutory element01 natural sciencesSecondary: 16A300101 mathematicsMathematicsRingRing (mathematics)Science & TechnologyAlgebra and Number TheoryGroup (mathematics)Primary: 15A09010102 general mathematicsAnells (Algebra)15A09 [Primary]PowerDrazin inverseÀlgebra linealElement (category theory)16A30 [Secondary]Unit (ring theory)Linear and Multilinear Algebra
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Representation Theorems for Indefinite Quadratic Forms Revisited

2010

The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring the second representation theorem to hold is proved. A new simple and explicit example of a self-adjoint operator for which the second representation theorem does not hold is also provided.

Pure mathematicsGeneral MathematicsFOS: Physical sciencesMathematical proofDirac operator01 natural sciencesMathematics - Spectral Theorysymbols.namesakeOperator (computer programming)Simple (abstract algebra)0103 physical sciencesFOS: Mathematics0101 mathematicsSpectral Theory (math.SP)Mathematical PhysicsMathematicsRepresentation theorem010102 general mathematicsRepresentation (systemics)Mathematical Physics (math-ph)16. Peace & justice47A07 47A55 15A63 46C20Functional Analysis (math.FA)Mathematics - Functional AnalysisTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESsymbolsIndefinite quadratic forms ; representation theorems ; perturbation theory ; Krein spaces ; Dirac operator010307 mathematical physicsPerturbation theory (quantum mechanics)
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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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Unicity of biproportion

1994

International audience; The biproportion of S on margins of M is called the intern composition law, K: (S,M) -> X = K(S,M) / X = A S B. A and B are diagonal matrices, algorithmically computed, providing the respect of margins of M. Biproportion is an empirical concept. In this paper, the author shows that any algorithm used to compute a biproportion leads to the me result. Then the concept is unique and no longer empirical. Some special properties are also indicated.

Pure mathematicsupdating matrices[MATH] Mathematics [math]Composition (combinatorics)[SHS.ECO]Humanities and Social Sciences/Economics and Finance15A15 14N05 65Q05biproportionalbiproportionDiagonal matrixCalculus[ SHS.ECO ] Humanities and Social Sciences/Economies and finances[MATH]Mathematics [math][SHS.ECO] Humanities and Social Sciences/Economics and FinanceAnalysisMathematicsRAS
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The Rank of Trifocal Grassmann Tensors

2019

Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of the trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [6]. The rank of sequences of tensors converging to tensors associated with degenerat…

Rank (linear algebra)Tensor rankAlgebraMathematics - Algebraic GeometryDimension (vector space)Computer Science::Computer Vision and Pattern Recognitiongrassmann tensors computer vision tensor rankFOS: MathematicsProjective spaceSettore MAT/03 - GeometriaAlgebraic Geometry (math.AG)Analysis14N05 15A21 15A69Mathematics
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CCDC 2048904: Experimental Crystal Structure Determination

2021

Related Article: Mohamed El Haimer, Márta Palkó, Matti Haukka, Márió Gajdács, István Zupkó, Ferenc Fülöp|2021|RSC Advances|11|6952|doi:10.1039/D0RA10553H

Space GroupCrystallographyCrystal SystemCrystal StructureCell Parameters11a1213141515a1616a-octahydro-9H11H-quinazolino[32-d][123]triazolo[15-a][14]benzodiazepin-11-oneExperimental 3D Coordinates
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CCDC 2048905: Experimental Crystal Structure Determination

2021

Related Article: Mohamed El Haimer, Márta Palkó, Matti Haukka, Márió Gajdács, István Zupkó, Ferenc Fülöp|2021|RSC Advances|11|6952|doi:10.1039/D0RA10553H

Space GroupCrystallographyCrystal SystemCrystal StructureCell Parameters11a1213141515a1616a-octahydro-9H11H-quinazolino[32-d][123]triazolo[15-a][14]benzodiazepin-11-oneExperimental 3D Coordinates
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CCDC 1899383: Experimental Crystal Structure Determination

2019

Related Article: Fernando Rabasa-Alcañiz, Daniel Hammerl, Anabel Sánchez-Merino, Tomás Tejero, Pedro Merino, Santos Fustero, Carlos del Pozo|2019|Org.Chem.Front.|6|2916|doi:10.1039/C9QO00525K

Space GroupCrystallographyCrystal SystemCrystal StructureCell Parameters7-(trifluoromethyl)-6a77a1014b15a-hexahydro-6H8H9aH-[1]benzopyrano[3'4':45]pyrrolo[12-d]indeno[21-b][14]oxazin-8-oneExperimental 3D Coordinates
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