Search results for "Manipulation"

showing 10 items of 311 documents

Virtual and arrow Temperley–Lieb algebras, Markov traces, and virtual link invariants

2021

Let [Formula: see text] be the algebra of Laurent polynomials in the variable [Formula: see text] and let [Formula: see text] be the algebra of Laurent polynomials in the variable [Formula: see text] and standard polynomials in the variables [Formula: see text] For [Formula: see text] we denote by [Formula: see text] the virtual braid group on [Formula: see text] strands. We define two towers of algebras [Formula: see text] and [Formula: see text] in terms of diagrams. For each [Formula: see text] we determine presentations for both, [Formula: see text] and [Formula: see text]. We determine sequences of homomorphisms [Formula: see text] and [Formula: see text], we determine Markov traces […

Pure mathematicsAlgebra and Number TheoryMarkov chainComputer Science::Information Retrieval010102 general mathematicsAstrophysics::Instrumentation and Methods for AstrophysicsComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)0102 computer and information sciences01 natural sciencesTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES010201 computation theory & mathematicsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONComputingMethodologies_DOCUMENTANDTEXTPROCESSINGArrowComputer Science::General Literature0101 mathematicsAlgebra over a fieldVirtual linkComputingMilieux_MISCELLANEOUSMathematicsVariable (mathematics)Journal of Knot Theory and Its Ramifications
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Special arrangements of lines: Codimension 2 ACM varieties in P 1 × P 1 × P 1

2019

In this paper, we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimension 2 arithmetically Cohen–Macaulay (ACM) varieties in [Formula: see text], called varieties of lines. We also describe their ACM property from a combinatorial algebra point of view.

Pure mathematicsAlgebra and Number TheoryMathematics::Commutative AlgebraConfiguration of linesApplied Mathematics010102 general mathematicsarithmetically Cohen-Macaulay; Configuration of lines; multiprojective spaces0102 computer and information sciencesCodimension01 natural sciencesSettore MAT/02 - Algebraarithmetically Cohen-Macaulay010201 computation theory & mathematicsarithmetically Cohen–Macaulay Configuration of lines multiprojective spacesArithmetically Cohen-Macaulay Configuration of lines multiprojective spacesComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONSettore MAT/03 - Geometria0101 mathematicsarithmetically Cohen–Macaulaymultiprojective spacesMathematics
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Hypergestures in Complex Time: Creative Performance Between Symbolic and Physical Reality

2015

Musical performance and composition imply hypergestural transformation from symbolic to physical reality and vice versa. But most scores require movements at infinite physical speed that can only be performed approximately by trained musicians. To formally solve this divide between symbolic notation and physical realization, we introduce complex time (\(\mathbb {C}\)-time) in music. In this way, infinite physical speed is “absorbed” by a finite imaginary speed. Gestures thus comprise thought (in imaginary time) and physical realization (in real time) as a world-sheet motion in space-time, corresponding to ideas from physical string theory. Transformation from imaginary to real time gives us…

Pure mathematicsEuler-Lagrange equationSettore FIS/02 - Fisica Teorica Modelli E Metodi MatematiciSettore INF/01 - InformaticaInformationSystems_INFORMATIONINTERFACESANDPRESENTATION(e.g.HCI)Complex timeString theoryMeasure (mathematics)Imaginary timeTransformation (music)Motion (physics)AlgebraSettore MAT/02 - AlgebraComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONComplex time; Euler-lagrange equation; Hypergestures; Performance theory; String theory; World-sheets of space-timeString theoryWorld-sheets of space-timePerformance theoryHypergesturesRealization (systems)The ImaginaryGestureMathematics
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Rationality and Sylow 2-subgroups

2010

AbstractLet G be a finite group. If G has a cyclic Sylow 2-subgroup, then G has the same number of irreducible rational-valued characters as of rational conjugacy classes. These numbers need not be the same even if G has Klein Sylow 2-subgroups and a normal 2-complement.

Pure mathematicsFinite groupConjugacy classGeneral MathematicsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONSylow theoremsRationalityMathematicsProceedings of the Edinburgh Mathematical Society
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A simple proof for the formula to get symmetrized powers of group representations

1993

A general formula to decompose the p-power of irreducible representations of an arbitrary space group into sum of sets of irreducible representations of such a group, having identical permutational symmetry, is presented. Its proof is based upon a straightforward application of the properties of the generalized projection (shift) operators. © 1993 John Wiley & Sons, Inc.

Pure mathematicsGroup (mathematics)Generalized projectionCondensed Matter PhysicsSpace (mathematics)Atomic and Molecular Physics and OpticsGroup representationSimple (abstract algebra)Representation theory of SUIrreducible representationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONPhysical and Theoretical ChemistrySymmetry (geometry)MathematicsInternational Journal of Quantum Chemistry
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An Algebraic Approach to Knowledge Representation

1999

This paper is an attempt to apply domain-theoretic ideas to a new area, viz. knowledge representation. We present an algebraic model of a belief system. The model consists of an information domain of special kind (belief algebra) and a binary relation on it (entailment). It is shown by examples that several natural belief algebras are, essentially, algebras of flat records. With an eye on this, we characterise those domains and belief algebras that are isomorphic to domains or algebras of records. For illustration, we suggest a system of axioms for revision in such a model and describe an explicit construction of what could be called a maxichoise revision.

Pure mathematicsKnowledge representation and reasoningComputer scienceBinary relationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONBelief systemNatural (music)IsomorphismAlgebraic numberBelief revisionLogical consequenceAxiom
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Unbounded C$^*$-seminorms and $*$-Representations of Partial *-Algebras

2009

The main purpose of this paper is to construct *-representations from unbounded C*-seminorms on partial *-algebras and to investigate their *-representations. © Heldermann Verlag.

Pure mathematicsMathematics::Functional AnalysisMathematics::Commutative AlgebraMathematics::Operator AlgebrasApplied MathematicsUnbounded C*-seminormFOS: Physical sciencesMathematical Physics (math-ph)Quasi *-algebraComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONMathematics::Metric GeometryPartial *-algebraConstruct (philosophy)Mathematics::Representation TheorySettore MAT/07 - Fisica Matematica(unbounded) *-representationAnalysisMathematical PhysicsMathematics
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On defects of characters and decomposition numbers

2017

We propose upper bounds for the number of modular constituents of the restriction modulo [math] of a complex irreducible character of a finite group, and for its decomposition numbers, in certain cases.

Pure mathematicsModulodefect of charactersGroup Theory (math.GR)01 natural sciences0103 physical sciencesComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONDecomposition (computer science)FOS: Mathematics0101 mathematicsRepresentation Theory (math.RT)Mathematics20C20Finite groupAlgebra and Number Theorybusiness.industry010102 general mathematicsModular design20C20 20C33Character (mathematics)heights of charactersdecomposition numbers20C33010307 mathematical physicsbusinessMathematics - Group TheoryMathematics - Representation Theory
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Skeleta of affine hypersurfaces

2014

A smooth affine hypersurface Z of complex dimension n is homotopy equivalent to an n-dimensional cell complex. Given a defining polynomial f for Z as well as a regular triangulation of its Newton polytope, we provide a purely combinatorial construction of a compact topological space S as a union of components of real dimension n, and prove that S embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S.

Pure mathematicsPolynomialMathematicsofComputing_GENERALAffinePolytopeComplex dimensionTopological spaceTriangulation14J70Mathematics - Algebraic GeometryComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsHomotopy equivalenceAlgebraic Topology (math.AT)Mathematics - Algebraic TopologyKato–Nakayama spaceAlgebraic Geometry (math.AG)SkeletonMathematicsToric degenerationTriangulation (topology)HomotopyLog geometry14J70 14R99 55P10 14M25 14T05RetractionHypersurfaceHypersurfaceNewton polytopeSettore MAT/03 - GeometriaGeometry and TopologyAffine transformationKato-Nakayama space14R99
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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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