Search results for "REPRESENTATION"

showing 10 items of 1710 documents

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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On the Directly and Subdirectly Irreducible Many-Sorted Algebras

2015

AbstractA theorem of single-sorted universal algebra asserts that every finite algebra can be represented as a product of a finite family of finite directly irreducible algebras. In this article, we show that the many-sorted counterpart of the above theorem is also true, but under the condition of requiring, in the definition of directly reducible many-sorted algebra, that the supports of the factors should be included in the support of the many-sorted algebra. Moreover, we show that the theorem of Birkhoff, according to which every single-sorted algebra is isomorphic to a subdirect product of subdirectly irreducible algebras, is also true in the field of many-sorted algebras.

Pure mathematicslcsh:MathematicsGeneral MathematicsSubalgebraUniversal enveloping algebralcsh:QA1-939directly irreducible many-sorted algebraSubdirect productsymbols.namesakemany-sorted algebraSubdirectly irreducible algebraAlgebra representationsymbolsDivision algebraMathematics::Metric GeometryCellular algebrasupport of a many-sorted algebrasubdirectly irreducible many-sorted algebraMathematicsFrobenius theorem (real division algebras)Demonstratio Mathematica
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On the representation of integers by indefinite binary Hermitian forms

2011

Given an integral indefinite binary Hermitian form f over an imaginary quadratic number field, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most s by f, as s tends to infinity.

Pure mathematicsrepresentation of integersGeneral MathematicsHyperbolic geometryAMS : 11E39 11N45 20H10 30F4001 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]symbols.namesake0103 physical sciencesEisenstein seriesCongruence (manifolds)group of automorphs0101 mathematicsQuaternionMathematicsBinary Hermitian formQuaternion algebraMathematics - Number TheorySesquilinear formta111010102 general mathematicsOrder (ring theory)Hermitian matrix[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]Bianchi group[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]symbolsMathematics::Differential Geometry010307 mathematical physics
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Normed Quasi *-Algebras: Bounded Elements and Spectrum

2020

Bounded elements of a Banach quasi *-algebra are intended to be those, whose images under every *-representation are bounded operators in a Hilbert space. This rough idea can be developed in several ways, as we shall see in the present chapter. These notions lead us to discuss a convenient concept of spectrum of an element in this context.

Pure mathematicssymbols.namesakeBounded functionSpectrum (functional analysis)Hilbert spacesymbolsContext (language use)Element (category theory)Representation (mathematics)Mathematics
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Determinant Bundles over Grassmannians

1989

Denoting by H the Hilbert space of square-integrable Dirac spinor fields on a manifold M, transforming according to a unitary representation p of a gauge group G, we have a linear representation of the group g of gauge transformations in the space H. If ρ is faithful we can consider g as a subgroup of the general linear group GL(H). By constructing representations of GL(H) we automatically obtain representations of g. It turns out that in the case when the dimension d of M is odd, g is contained in a smaller group GLp ⊂ GL(H) which has the property that it perturbs the subspace H+ ⊂ H consisting of eigenvectors of a Dirac operator belonging to positive eigenvalues, by an operator A for whic…

Pure mathematicssymbols.namesakeUnitary representationTrace (linear algebra)Dirac spinorGroup (mathematics)Gauge groupFredholm operatorsymbolsGeneral linear groupDirac operatorMathematics
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The Russian Economy: Prospects for Putin 4.0

2020

This project was implemented by the Centre for East European Policy Studies in cooperation with the Friedrich-Ebert-Stiftung in the Baltic States and European Commission Representation in Latvia

Putin’s reformsEconomic Relation Russia-ChinaRussia's regionsEconomic Relation Russia-Baltic StatesEconomic Relation Russia-European UnionRussia’s Dependency on the Energy SectorRepresentation (politics)EconomyEuropean policyState of Russian EconomyPolitical scienceRussian economy:SOCIAL SCIENCES::Social sciences::Political science [Research Subject Categories]Military Expenditure RussiaEuropean commissionEurasian Economic Union
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Instruction-based clinical eye-tracking study on the visual interpretation of divergence : how do students look at vector field plots?

2018

Relating mathematical concepts to graphical representations is a challenging task for students. In this paper, we introduce two visual strategies to qualitatively interpret the divergence of graphical vector field representations. One strategy is based on the graphical interpretation of partial derivatives, while the other is based on the flux concept. We test the effectiveness of both strategies in an instruction-based eye-tracking study with N = 41 physics majors. We found that students’ performance improved when both strategies were introduced (74% correct) instead of only one strategy (64% correct), and students performed best when they were free to choose between the two strategies (88…

QC1-999graafinen esitysUndergraduate StudentsPhysics Education ResearchGeneral Physics and AstronomyResearch MethodologyContext (language use)LernenAssessmentMachine learningcomputer.software_genre01 natural sciencesEducationVisual processingsilmänliikkeetddc:370Concept learning0103 physical sciencesvektorit (matematiikka)ddc:530ta516Wissensrepräsentation010306 general physicsDivergence (statistics)graphical representationsvisual processingeye-trackingLC8-6691studentsopiskelijatbusiness.industryPhysicsMultimethodology05 social sciencesConcepts & Principles050301 educationKognitives LernenSpecial aspects of educationSaccadic maskingPhysikdidaktikEye trackingPartial derivativeArtificial intelligencebusinessvector fields0503 educationcomputer
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Extended-order algebras as a generalization of posets

2011

Motivated by the recent study of several researchers on extended-order algebras, introduced by C. Guido and P. Toto as a possible common framework for the majority of algebraic structures used in many-valued mathematics, the paper focuses on the properties of homomorphisms of the new structures, considering extended-order algebras as a generalization of partially ordered sets. The manuscript also introduces the notion of extended-relation algebra providing a new framework for developing the theory of rough sets.

Quadratic algebraAlgebraInterior algebraJordan algebraGeneral MathematicsSubalgebraClifford algebraAlgebra representationDivision algebraAbstract algebraMathematicsDemonstratio Mathematica
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Banach Partial *-Algebras and Quantum Models

2007

C*-algebras are, as known, the basic mathematical ingredient of the Haag- Kastler (Haag and Kastler 1964) algebraic approach to quantum systems, with infinitely many degrees of freedom. The usual procedure starts, in fact, with associating to each bounded region V of the configuration space of the system the C*-algebra AV of local observables in V. The uniform completion A of the algebra generated by the AV ’s is then considered as the C*-algebra of observables of the system

Quadratic algebraDiscrete mathematicsPure mathematicsPartial traceOperator algebraMathematics::Operator AlgebrasQuantum groupSubalgebraAlgebra representationCCR and CAR algebrasC*-algebraMathematics
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tomocomd-camps and protein bilinear indices - novel bio-macromolecular descriptors for protein research: I. Predicting protein stability effects of a…

2010

Descriptors calculated from a specific representation scheme encode only one part of the chemical information. For this reason, there is a need to construct novel graphical representations of proteins and novel protein descriptors that can provide new information about the structure of proteins. Here, a new set of protein descriptors based on computation of bilinear maps is presented. This novel approach to biomacromolecular design is relevant for QSPR studies on proteins. Protein bilinear indices are calculated from the kth power of nonstochastic and stochastic graph–theoretic electronic-contact matrices, and , respectively. That is to say, the kth nonstochastic and stochastic protein bili…

Quantitative structure–activity relationshipProtein structureLinear regressionStability (learning theory)Bilinear interpolationCell BiologySegmented regressionRepresentation (mathematics)Linear discriminant analysisBiological systemMolecular BiologyBiochemistryMathematicsFEBS Journal
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