Search results for "Maple"

showing 10 items of 12 documents

Automatic calculation of massive two-loop self-energies with XLOOPS

1997

Abstract Within the program package XLOOPS it is possible to calculate self-energies up to the two-loop level for arbitrary massive particles. The program package — written in MAPLE (Char et al., Maple V Language Reference Manual (Springer, 1991); Char et al., Maple V Library Reference Manual (Springer, 1991)) — is designed to deal with the full tensor structure of the occurring integrals. This means that applications are not restricted to those cases where the reduction to scalars via equivalence theorem is allowed. The algorithms handle two-loop integrals analytically if this is possible. For those topologies where no analytic result for the general mass case is available, the diagrams ar…

AlgebraMaplePhysicsNuclear and High Energy PhysicsFull tensorQuantum mechanicsengineeringPreprintEquivalence (formal languages)engineering.materialInstrumentationNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
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RationalizeRoots: Software Package for the Rationalization of Square Roots

2019

The computation of Feynman integrals often involves square roots. One way to obtain a solution in terms of multiple polylogarithms is to rationalize these square roots by a suitable variable change. We present a program that can be used to find such transformations. After an introduction to the theoretical background, we explain in detail how to use the program in practice.

FOS: Computer and information sciencesComputer Science - Symbolic ComputationHigh Energy Physics - TheoryHigh energy particleFeynman integralComputationGeneral Physics and AstronomyFOS: Physical sciencesengineering.materialSymbolic Computation (cs.SC)Rationalization (economics)01 natural sciences010305 fluids & plasmasHigh Energy Physics - Phenomenology (hep-ph)Square root0103 physical sciencesComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONAlgebraic number010306 general physicsMathematical PhysicsVariable (mathematics)MapleMathematical Physics (math-ph)AlgebraHigh Energy Physics - PhenomenologyHigh Energy Physics - Theory (hep-th)Hardware and ArchitectureengineeringComputer Science - Mathematical SoftwareMathematical Software (cs.MS)
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Effect of sodium borohydride and hydrogen peroxide pretreatments on soda pulping of sugar maple (Acer saccharum)

2021

For recovering value-added wood-based organic material prior to delignification, sodium borohydride (NaBH4) and hydrogen peroxide (H2O2) pretreatments under alkaline conditions were performed before soda pulping of sugar maple (Acer saccharum) chips with sodium hydroxide (NaOH). In this investigation, it was determined whether the pulp yield could be increased by partly stabilizing the hemicelluloses by these pretreatments, and simultaneously obtains lower pulp kappa numbers. The results indicated that when aiming to the same kappa numbers (i.e., kappa numbers 14.3-20.5), roughly 3% higher pulp yield could be achieved if the chips were pretreated with alkaline 0.5% NaBH4 solutions, compared…

General Chemical EngineeringAcer saccharumengineering.material/dk/atira/pure/sustainabledevelopmentgoals/responsible_consumption_and_productionchemistry.chemical_compoundSodium borohydridestomatognathic systemGeneral Materials ScienceSugarHydrogen peroxide/dk/atira/pure/sustainabledevelopmentgoals/industry_innovation_and_infrastructureInnovationSodium borohydrideMapleChemistrySoda cookingGeneral ChemistryPulp and paper industryHydrogen peroxidestomatognathic diseasesSugar mapleSoda pulpingengineeringand InfrastructureSDG 9 - Industry Innovation and InfrastructureSDG 12 - Responsible Consumption and ProductionSDG 9 - IndustryPretreatmentJournal of Wood Chemistry and Technology
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Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators

2016

This paper is concerned with the $(p,q)$ -analog of Bernstein operators. It is proved that, when the function is convex, the $(p,q)$ -Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that verify these properties are considered. A global approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem are proved.

MapleDiscrete mathematicsModulus of smoothnesslcsh:MathematicsApplied Mathematics010102 general mathematicsApproximation theoremRegular polygonMonotonic functionFunction (mathematics)Type (model theory)engineering.materialVoronovskaja type theoremlcsh:QA1-93901 natural sciences010101 applied mathematics( p q ) $(pq)$ -Bernstein operatorsengineeringDiscrete Mathematics and Combinatorics0101 mathematics( p q ) $(pq)$ -calculusK-functionalAnalysisMathematicsDitzian-Totik first order modulus of smoothnessJournal of Inequalities and Applications
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A new method for computing one-loop integrals

1994

We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point functions both algebraically and numerically to all tensor cases. This program is written as a package for Maple. An additional Mathematica version is planned later.

MapleFeynman parametrizationFeynman integralNumerical analysisElectroweak interactionFOS: Physical sciencesGeneral Physics and Astronomyengineering.materialNumerical integrationRenormalizationAlgebraHigh Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)Hardware and ArchitectureComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONComputer Science::Mathematical SoftwareengineeringContraction (operator theory)Mathematics
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Stepwise Lateral Extension of Phenyl‐Substituted Linear Polyphenylenes

2019

Polyphenylenes (PPs) are unique polymers showing high mechanical strength and chemical stability, and having potential applications, for example, in proton transfer and gas‐separation membranes. Moreover, phenyl‐substituted linear PPs can serve as precursors for bottom‐up syntheses of graphene nanoribbons (GNRs), a new class of nanoscale carbon materials that appear promising for nanoelectronics. Notably, lateral extensions of linear PPs with appropriate “branched” phenyl substituents, that is, avoiding spatial overlap of benzene rings in their projections into a plane, can lead to wider GNRs with modulated electronic and optical properties. GNRs with widths up to ≈2 nm are obtained, but sy…

MapleMaterials sciencePolymers and Plastics010405 organic chemistryOrganic Chemistry02 engineering and technologyengineering.material021001 nanoscience & nanotechnology010402 general chemistryCondensed Matter Physics01 natural sciences0104 chemical scienceschemistry.chemical_compoundCyclopentadienonechemistryPolymer chemistryMaterials ChemistryLateral extensionengineeringPhysical and Theoretical Chemistry0210 nano-technologyGraphene nanoribbonsMacromolecular Chemistry and Physics
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oneloop 2.0 — A program package calculating one-loop integrals

1997

We present an improved version of our program package oneloop which -- written as a package for MAPLE -- solves one-loop Feynman integrals. The package is calculating one-, two- and three-point functions both algebraically and numerically to any tensor rank. In addition to the original version oneloop 2.0 also calculates infrared divergent integrals. Higher powers of propagator terms and the $O(\eps)$ parts relevant for two-loop calculations are now supported.

MaplePhysicsParticle physicsFeynman integralTensor rankFOS: Physical sciencesGeneral Physics and AstronomyPropagatorengineering.materialLoop (topology)High Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)Hardware and ArchitectureComputer Science::Mathematical SoftwareengineeringMathematical physicsComputer Physics Communications
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Convergence Properties of Genuine Bernstein–Durrmeyer Operators

2018

The genuine Bernstein–Durrmeyer operators have notable approximation properties, and many papers have been written on them. In this paper, we introduce a modified genuine Bernstein–Durrmeyer operators. Some approximation results, which include local approximation, error estimation in terms of the modulus of continuity and weighted approximation is obtained. Also, a quantitative Voronovskaya-type approximation will be studied. The convergence of these operators to certain functions is shown by illustrative graphics using MAPLE algorithms.

MapleRate of convergenceConvergence (routing)engineeringApplied mathematicsengineering.materialGraphicsModulus of continuityMathematics
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Dijet azimuthal correlations and conditional yields in pp and p+Pb collisions at sNN=5.02TeV with the ATLAS detector

2019

This paper presents a measurement of forward-forward and forward-central dijet azimuthal angular correlations and conditional yields in proton-proton (pp) and proton-lead (p + Pb) collisions as a p ...

PhysicsMapleLarge Hadron Collider010308 nuclear & particles physicsAtlas detectorNuclear Theoryengineering.material01 natural sciences7. Clean energyNuclear physicsAzimuthmedicine.anatomical_structureAtlas (anatomy)0103 physical sciencesmedicineengineeringPhysics::Accelerator PhysicsRapidityNuclear Experiment010306 general physicsNucleonSaturation (chemistry)Physical Review C
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Production of π0 and η mesons in Cu+Au collisions at sNN=200GeV

2018

Production of π0 and η mesons has been measured at midrapidity in Cu+Au collisions at sNN=200GeV. Measurements were performed in π0(η)→γγ decay channel in the 1(2)-20GeV/c transverse momentum range. A strong suppression is observed for π0 and η meson production at high transverse momentum in central Cu+Au collisions relative to the p+p results scaled by the number of nucleon-nucleon collisions. In central collisions the suppression is similar to Au+Au with comparable nuclear overlap. The η/π0 ratio measured as a function of transverse momentum is consistent with mT-scaling parametrization down to pT=2GeV/c, its asymptotic value is constant and consistent with Au+Au and p+p and does not show…

Quantum chromodynamicsPhysicsMapleMeson productionMeson010308 nuclear & particles physicsNuclear Theorychemistry.chemical_elementengineering.material16. Peace & justice01 natural sciencesCopperNuclear physicsFragmentation (mass spectrometry)chemistry0103 physical sciencesQuark–gluon plasmaengineeringHigh Energy Physics::ExperimentImpact parameterNuclear Experiment010306 general physicsPhysical Review C
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