Search results for " Conformal"

showing 10 items of 51 documents

Lie properties of symmetric elements in group rings

2009

Abstract Let ∗ be an involution of a group G extended linearly to the group algebra KG . We prove that if G contains no 2-elements and K is a field of characteristic p ≠ 2 , then the ∗-symmetric elements of KG are Lie nilpotent (Lie n -Engel) if and only if KG is Lie nilpotent (Lie n -Engel).

Pure mathematicsAdjoint representation010103 numerical & computational mathematicsCentral series01 natural sciencesGraded Lie algebraMathematics::Group TheoryRepresentation of a Lie groupGroup ring LieLie nilpotentGroup algebra0101 mathematicsMathematics::Representation TheoryMathematicsDiscrete mathematicsAlgebra and Number TheorySimple Lie groupTEORIA DOS GRUPOSMathematics::Rings and Algebras010102 general mathematicsLie conformal algebraAdjoint representation of a Lie algebraLie n-EngelNilpotent groupSymmetric element
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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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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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Next-to-next-to-leading order prediction for the photon-to-pion transition form factor

2003

We evaluate the next-to-next-to-leading order corrections to the hard-scattering amplitude of the photon-to-pion transition form factor. Our approach is based on the predictive power of the conformal operator product expansion, which is valid for a vanishing $\beta$-function in the so-called conformal scheme. The Wilson--coefficients appearing in the non-forward kinematics are then entirely determined from those of the polarized deep-inelastic scattering known to next-to-next-to-leading accuracy. We propose different schemes to include explicitly also the conformal symmetry breaking term proportional to the $\beta$-function, and discuss numerical predictions calculated in different kinemati…

Quantum chromodynamicsPhysicsNuclear and High Energy PhysicsParticle physicsPhysicsForm factor (quantum field theory)Order (ring theory)FOS: Physical sciencesConformal mapAstronomy and AstrophysicsDeep inelastic scatteringHigh Energy Physics - PhenomenologyPionHigh Energy Physics - Phenomenology (hep-ph)transition form factor ; conformal operator ; product expansionConformal symmetryOperator product expansionMathematical physics
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Incidence of mandibular osteoradionecrosis (MORN) after intensity modulated radiotherapy (IMRT) versus 3D conformal radiotherapy (3D-CRT): A systemat…

2022

Background: Analyze the incidence of MORN after head and neck radiotherapy by two novel irradiation techniques. 3DCRT and IMRT and compare the success rates of distinct authors. Material and Methods: An electronic search in Pubmed (MEDLINE), Ovid. Google Scholar and Cochrane Library (Wiley). databases was conducted with the key words Radiotherapy, Conformal[Mesh] OR Radiotherapy. Intensity-Modulated[Mesh]) AND Osteoradionecrosis[Mesh] for all databases. The inclusion criteria randomized controlled trials (RCT), as well as prospective and retrospective cohort studies published in English; MORN patients treated with 3D-CRT y IMRT. Results: 27 articles were selected from 194 initially found. 1…

RadiotherapyIncidencequality assessment toolCollRadioteràpiaclinical trialMandibleNecrosiCapNecrosisOsteoradionecrosisOtorhinolaryngologyHumansmandibular third molarSurgeryRadiotherapy Intensity-ModulatedRadiotherapy ConformalHeadGeneral DentistryNeckconsortUNESCO:CIENCIAS MÉDICASoral surgeryMedicina Oral Patología Oral y Cirugia Bucal
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Mass-flux-based outlet boundary conditions for the lattice Boltzmann method

2009

We present outlet boundary conditions for the lattice Boltzmann method. These boundary conditions are constructed with a mass-flux-based approach. Conceptually, the mass-flux-based approach provides a mathematical framework from which specific boundary conditions can be derived by enforcing given physical conditions. The object here is, in particular, to explain the mass-flux-based approach. Furthermore, we illustrate, transparently, how boundary conditions can be derived from the emerging mathematical framework. For this purpose, we derive and present explicitly three outlet boundary conditions. By construction, these boundary conditions have an apparent physical interpretation which is fu…

Statistics and ProbabilityMathematical analysisMason–Weaver equationBoundary conformal field theoryStatistical and Nonlinear PhysicsDifferent types of boundary conditions in fluid dynamicsSingular boundary methodBoundary knot methodBoundary conditions in CFDFree boundary problemBoundary value problemStatistical physicsStatistics Probability and UncertaintyMathematicsJournal of Statistical Mechanics: Theory and Experiment
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Annihilators of tensor density modules

2007

Abstract We describe the two-sided ideals in the universal enveloping algebras of the Lie algebras of vector fields on the line and the circle which annihilate the tensor density modules. Both of these Lie algebras contain the projective subalgebra, a copy of sl 2 . The restrictions of the tensor density modules to this subalgebra are duals of Verma modules (of sl 2 ) for Vec ( R ) and principal series modules (of sl 2 ) for Vec ( S 1 ) . Thus our results are related to the well-known theorem of Duflo describing the annihilating ideals of Verma modules of reductive Lie algebras. We find that, in general, the annihilator of a tensor density module of Vec ( R ) or Vec ( S 1 ) is generated by …

Tensor density modulesPure mathematicsVerma moduleAlgebra and Number TheorySubalgebraMathematics::Rings and AlgebrasUniversal enveloping algebraGeneralized Verma moduleAffine Lie algebraLie conformal algebraAnnihilating idealsMathematics::Quantum AlgebraTensor product of modulesTensor densityMathematics::Representation TheoryMathematicsJournal of Algebra
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Hom-Lie quadratic and Pinczon Algebras

2017

ABSTRACTPresenting the structure equation of a hom-Lie algebra 𝔤, as the vanishing of the self commutator of a coderivation of some associative comultiplication, we define up to homotopy hom-Lie algebras, which yields the general hom-Lie algebra cohomology with value in a module. If the hom-Lie algebra is quadratic, using the Pinczon bracket on skew symmetric multilinear forms on 𝔤, we express this theory in the space of forms. If the hom-Lie algebra is symmetric, it is possible to associate to each module a quadratic hom-Lie algebra and describe the cohomology with value in the module.

[ MATH ] Mathematics [math]Universal enveloping algebra01 natural sciencesCohomologyFiltered algebraQuadratic algebraMathematics::Category Theory0103 physical sciences[MATH]Mathematics [math]0101 mathematicsMSC: 17A45 17B56 17D99 55N20ComputingMilieux_MISCELLANEOUSMathematicsSymmetric algebraAlgebra and Number TheoryQuadratic algebrasMathematics::Rings and Algebras010102 general mathematicsUp to homotopy algebras16. Peace & justiceLie conformal algebraHom-Lie algebrasAlgebraDivision algebraAlgebra representationPhysics::Accelerator PhysicsCellular algebra010307 mathematical physics
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An Optimized Architecture for CGA Operations and Its Application to a Simulated Robotic Arm

2022

Conformal geometric algebra (CGA) is a new geometric computation tool that is attracting growing attention in many research fields, such as computer graphics, robotics, and computer vision. Regarding the robotic applications, new approaches based on CGA have been proposed to efficiently solve problems as the inverse kinematics and grasping of a robotic arm. The hardware acceleration of CGA operations is required to meet real-time performance requirements in embedded robotic platforms. In this paper, we present a novel embedded coprocessor for accelerating CGA operations in robotic tasks. Two robotic algorithms, namely, inverse kinematics and grasping of a human-arm-like kinematics chain, ar…

conformal geometric algebraSettore ING-INF/05 - Sistemi Di Elaborazione Delle Informazioniapplication-specific processorsComputer Networks and CommunicationsHardware and ArchitectureControl and Systems EngineeringSignal Processingcomputational geometryFPGA-based prototypingElectrical and Electronic Engineeringapplication-specific processors; Clifford Algebra; computational geometry; conformal geometric algebra; FPGA-based prototyping; grasping; human-like robotic arms; inverse kinematics
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Analysis of cardiac and pulmonary complication probabilities after radiation therapy for patients with early-stage breast cancer

2009

Objective. The purpose of this study was to evaluate the radiobiological implications of clinical use of respiratory-gated techniques for postoperative radiation therapy of early-stage left-sided breast cancer after breast-conserving surgery. Material and methods. Radiation therapy treatment plans of 80 patients with early-stage breast cancer (stage I–II), receiving whole breast irradiation after breast-conserving therapy, were analyzed. The control group consisting of 47 patients received standard radiation therapy, and the respiratory-gated group consisting of 33 patients received deep inspiration-gated radiation therapy. Normal tissue complication probabilities (NTCP) for cardiac mortali…

medicine.medical_specialtyRespiratory-Gated Imaging TechniquesHeart Diseasesearly-stage breast cancermedicine.medical_treatmentBreast NeoplasmsMastectomy SegmentalStatistics NonparametricCohort StudiesBreast cancerWhole Breast Irradiationnormal tissue complication probabilitymedicineHumansBreastStage (cooking)Radiation Injuriesrespiratory-gated radiotherapyPneumonitisNeoplasm StagingProbabilitybusiness.industryrespiratory-gated radiotherapy; early-stage breast cancer; breast-conserving therapy; normal tissue complication probabilityPatient SelectionRespirationPulmonary ComplicationRadiotherapy DosageGeneral Medicinemedicine.diseaseLatviaSurgeryRadiation therapyRadiation Pneumonitisbreast-conserving therapyFemaleRadiotherapy AdjuvantRadiotherapy ConformalComplicationbusinessTomography X-Ray ComputedMastectomyMedicina
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