1,721,226 research outputs found
Rationalizability of square roots
No full textFeynman integral computations in theoretical high energy particle physics frequently involve square roots in the kinematic variables. Physicists often want to solve Feynman integrals in terms of multiple polylogarithms. One way to obtain a solution in terms of these functions is to rationalize all occurring square roots by a suitable variable change. In this paper, we give a rigorous definition of rationalizability for square roots of ratios of polynomials. We show that the problem of deciding whether a single square root is rationalizable can be reformulated in geometrical terms. Using this approach, we give easy criteria to decide rationalizability in most cases of square roots in one and two variables. We also give partial results and strategies to prove or disprove rationalizability of sets of square roots. We apply the results to many examples from actual computations in high energy particle physics. (C) 2020 Elsevier Ltd. All rights reserved
Bhabha scattering and a special pencil of K3 surfaces
No full textWe study a pencil of K3 surfaces that appeared in the 2-loop diagrams in Bhabha scattering. By analysing in detail the Picard lattice of the general and special members of the pencil, we identify the pencil with the celebrated Apéry-Fermi pencil, that was related to Apéry's proof of the irrationality of ζ(3) through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts
K3 surfaces with two involutions and low Picard number
No full textLet X be a complex algebraic K3 surface of degree 2d and with Picard number rho. Assume that X admits two commuting involutions: one holomorphic and one anti-holomorphic. In that case, rho >= 1 when d = 1 and rho >= 2 when d >= 2. For d = 1, the first example defined over Q with rho = 1 was produced already in 2008 by Elsenhans and Jahnel. A K3 surface provided by Kondo, also defined over Q, can be used to realise the minimum rho = 2 for all d >= 2. In these notes we construct new explicit examples of K3 surfaces over the rational numbers realising the minimum rho = 2 for d = 2, 3, 4. We also show that a nodal quartic surface can be used to realise the minimum rho = 2 for infinitely many different values of d. Finally, we strengthen a result of Morrison by showing that for any even lattice N of rank 1 <= r <= 10 and signature (1, r - 1) there exists a K3 surface Y defined over R such that Pic Y-C = Pic Y congruent to N
Diritto e letteratura
No full textIl contributo traccia la storia della nascita del filone "diritto e letteratura" e delinea il contributo che esso può apportare negli studi giuridici
Silybin and the liver: From basic research to clinical practice
No full textHerbal products are increasingly used, mainly in chronic liver disease. Extracts of milk thistle, Silymarin and silybin, are the most prescribed natural compounds, with different indications, but with no definitive results in terms of clinical efficacy. This review analyzes the available studies on the effects of the purified product silybin, both as a free and a conjugated molecule, on liver cells or on experimentally induced liver damage, and in patients with liver disease. We searched PUBMED for articles pertaining to the in vitro and in vivo effects of silybin, its antifibrotic, anti-inflammatory, and antioxidant properties, as well as its metabolic effects, combined with the authors' own knowledge of the literature. Results indicate that the bioavailability of silybin phytosome is higher than that of silymarin and is less influenced by liver damage; silybin does not show significant interactions with other drugs and at doses < 10 g/d has no significant side effects. Experimental studies have clearly demonstrated the antifibrotic, antioxidant and metabolic effects of silybin; previous human studies were insufficient for confirming the clinical efficacy in chronic liver disease, while ongoing clinical trials are promising. On the basis of literature data, silybin seems a promising drug for chronic liver disease
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