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…
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.
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…
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.
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.
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…
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.
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.
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 ...
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…