Search results for " Regular"
showing 10 items of 197 documents
Laurent series expansion of a class of massive scalar one-loop integrals toO(ε2)
2005
We use dimensional regularization to calculate the O({epsilon}{sup 2}) expansion of all scalar one-loop one-, two-, three-, and four-point integrals that are needed in the calculation of hadronic heavy quark production. The Laurent series up to O({epsilon}{sup 2}) is needed as input to that part of the next-to-next-to-leading order corrections to heavy flavor production at hadron colliders where the one-loop integrals appear in the loop-by-loop contributions. The four-point integrals are the most complicated. The O({epsilon}{sup 2}) expansion of the three- and four-point integrals contains in general polylogarithms up to Li{sub 4} and functions related to multiple polylogarithms of maximal …
One-loop corrections to four-point functions with two external massive fermions and two external massless partons
2002
We present a complete set of one-loop matrix elements relevant for the hadroproduction of heavy quarks in next-to-leading order employing dimensional regularization to isolate ultraviolet and soft divergences. All results of the perturbative calculation are given in detail. These one-loop matrix elements can also be used as input in the determination of the corresponding next-to-leading order cross sections for heavy flavor photoproduction and in photon-photon reactions, as well as for any of the relevant crossed processes. Our results are tested against the results of other related studies in which unpolarized and longitudinally polarized processes were considered.
Dimensional reduction methods in QCD
1994
We apply the technique of dimensional reduction to massless quantum chromodynamics. It is shown that compared to conventional dimensional regularization methods calculations of radiative corrections at the one-loop level are less involved. We discuss the use of helicity methods within this framework and as an application we evaluate the one-loop corrections to the parity-violating cross sections and to the quark forwardbackward asymmetric polarization in\(e^ + e^ - \to V \to q\bar q(g)\). Finally, we demonstrate that further simplifications occur in the computation of structure functions including the parity-violating structure function in quark- and gluoninitiated electroproduction process…
Creating “mathematically” sustainable world: from the spirograph, a reverse path
2014
The approach to the subject of mathematic learning, represents, in the pedagogical-educational field, a problematic situation. Nowadays we attend to an heated discussion on the character of the basic mathematical concepts, on the analytical-critical succession between processes and objects. The purpose of these notes is to recover and to value the contribution of the autopoiesis theory in the characterization of the mathematical domain going beyond the mere reiteration, inspecting and testing new and generative paths of ideas. In this mechanism we would insert the use of the spirograph as a disturbing, uncertain element able to nourish the “mind-system”.
Perturbative quantum field theory
2000
pQFT In this chapter we repeat the main steps towards a derivation of the Feynman rules, following the well-known path of canonical quantization. This is standard material, and readers who are not acquainted with such topics are referred to [Bjorken and Drell 1965, Bogoliubov and Shirkov 1980, Itzykson and Zuber 1980, Kaku 1993, Weinberg 1995, Peskin and Schroeder 1995, Teller 1997]. We hope that the short summary given here, similar to that in [Kreimer 1997a], is helpful for readers who want to refresh their memory. Having introduced Feynman rules, we next introduce Schwinger–Dyson equations as a motivation for the introduction of Z -factors. We remark on dimensional regularization and giv…
Mboat7 down-regulation by hyper-insulinemia induces fat accumulation in hepatocytes.
2020
Background: Naturally occurring variation in Membrane-bound O-acyltransferase domain-containing 7 (MBOAT7), encoding for an enzyme involved in phosphatidylinositol acyl-chain remodelling, has been associated with fatty liver and hepatic disorders. Here, we examined the relationship between hepatic Mboat7 down-regulation and fat accumulation. Methods: Hepatic MBOAT7 expression was surveyed in 119 obese individuals and in experimental models. MBOAT7 was acutely silenced by antisense oligonucleotides in C57Bl/6 mice, and by CRISPR/Cas9 in HepG2 hepatocytes. Findings: In obese individuals, hepatic MBOAT7 mRNA decreased from normal liver to steatohepatitis, independently of diabetes, inflammatio…
Sul cd. Fragmentum Dositheanum
2021
Through a special examination of some features of the text commonly referred to as Fragmentum Dositheanum, the author argues that, despite the reference in a paragraph to the knowledge of ‘regulae’, the classical jurisprudential work from which the fragment is taken was not a book of regulae, but an elementary work of a close scholastic nature; moreover, according to the author, this scholastic work might be Gaius’ Res cottidianae.
Multiple solutions with sign information for a (p,2)-equation with combined nonlinearities
2020
We consider a parametric nonlinear Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p,2)-equation) and with a reaction which has the competing effects of two distinct nonlinearities. A parametric term which is (p−1)-superlinear (convex term) and a perturbation which is (p−1)-sublinear (concave term). First we show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, all with sign information. Then by strengthening the regularity of the two nonlinearities we produce two more nodal solutions, for a total of seven nontrivial smooth solutions all with sign informations. Our proofs use critical point theory, critical gro…
Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems
2020
We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter λ > 0. We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution.
A Lebesgue-type decomposition on one side for sesquilinear forms
2021
Sesquilinear forms which are not necessarily positive may have a dierent behavior, with respect to a positive form, on each side. For this reason a Lebesgue-type decomposition on one side is provided for generic forms satisfying a boundedness condition.