Search results for "ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION"

showing 10 items of 140 documents

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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Sylow Normalizers with a Normal Sylow 2-Subgroup

2008

AbstractIf G is a finite solvable group and p is a prime, then the normalizer of a Sylow p-subgroup has a normal Sylow 2-subgroup if and only if all non-trivial irreducible real 2-Brauer characters of G have degree divisible by p.

Pure mathematicsSolvable groupGeneral MathematicsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONSylow theoremsMathematicsProceedings of the Edinburgh Mathematical Society
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Equilibrium real gas computations using Marquina's scheme

2003

Marquina's approximate Riemann solver for the compressible Euler equations for gas dynamics is generalized to an arbitrary equilibrium equation of state. Applications of this solver to some test problems in one and two space dimensions show the desired accuracy and robustness

Real gasApplied MathematicsMechanical EngineeringMathematical analysisMathematicsofComputing_NUMERICALANALYSISComputational MechanicsSolverSpace (mathematics)Compressible flowRiemann solverComputer Science ApplicationsEuler equationsRunge–Kutta methodssymbols.namesakeMechanics of MaterialsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONCompressibilitysymbolsMathematicsInternational Journal for Numerical Methods in Fluids
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The PCHIP subdivision scheme

2016

In this paper we propose and analyze a nonlinear subdivision scheme based on the monotononicity-preserving third order Hermite-type interpolatory technique implemented in the PCHIP package in Matlab. We prove the convergence and the stability of the PCHIP nonlinear subdivision process by employing a novel technique based on the study of the generalized Jacobian of the first difference scheme. MTM2011-22741

Scheme (programming language)Generalized JacobianStability (learning theory)MathematicsofComputing_NUMERICALANALYSIS010103 numerical & computational mathematics01 natural sciencesConvergence (routing)ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION0101 mathematicsMATLABMathematicscomputer.programming_languageSubdivisionNonlinear subdivision schemesbusiness.industryApplied MathematicsProcess (computing)Approximation order010101 applied mathematicsComputational MathematicsThird orderbusinessConvergencecomputerAlgorithmStability
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The set of conjugacy class sizes of a finite group does not determine its solvability

2014

Abstract We find a pair of groups, one solvable and the other non-solvable, with the same set of conjugacy class sizes.

Set (abstract data type)Discrete mathematicsMathematics::Group TheoryFinite groupTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESTheoryofComputation_COMPUTATIONBYABSTRACTDEVICESAlgebra and Number TheoryConjugacy classTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONMathematicsofComputing_DISCRETEMATHEMATICSMathematicsJournal of Algebra
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A New Embedded Coprocessor for Clifford Algebra based Software Intensive Systems

2011

Computer graphics applications require efficient tools to model geometric objects and their transformations. Clifford algebra (also known as geometric algebra) is receiving a growing attention in many research fields, such as computer graphics, machine vision and robotics, as a new, interesting computational paradigm that offers a natural and intuitive way to perform geometric calculations. At the same time, compute-intensive graphics algorithms require the execution of million Clifford operations. Clifford algebra based software intensive systems need therefore the support of specialized hardware architectures capable of accelerating Clifford operations execution. In this paper the archite…

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniCoprocessorSpeedupComputer sciencebusiness.industryembedded coprocessorsClifford algebraParallel computingcomputer graphicComputer graphicsGeometric algebracompute-intensive algorithmSoftwaresoftware intensive systemComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONcomputational geometryGraphicsClifford algebraField-programmable gate arraybusiness
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An Embedded, FPGA-based Computer Graphics Coprocessor with Native Geometric Algebra Support

2009

The representation of geometric objects and their transformation are the two key aspects in computer graphics applications. Traditionally, computer-intensive matrix calculations are involved in modeling and rendering three-dimensional (3D) scenery. Geometric algebra (aka Clifford algebra) is attracting attention as a natural way to model geometric facts and as a powerful analytical tool for symbolic calculations. In this paper, the architecture of Clifford coprocessor (CliffoSor) is introduced. CliffoSor is an embedded parallel coprocessing core that offers direct hardware support to Clifford algebra operators. A prototype implementation on a programmable gate array (FPGA) board is detailed…

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniSpeedupCoprocessorComputer scienceClifford algebraParallel computingRendering (computer graphics)Computer graphicsGeometric algebraHardware and ArchitectureComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONElectrical and Electronic EngineeringClifford algebra Computational geometry Embedded coprocessors Application-specific processor FPGA-based prototypingField-programmable gate arraySoftwareEuclidean vector
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