The Polarized Two-Loop Massive Pure Singlet Wilson Coefficient for Deep-Inelastic Scattering

We calculate the polarized massive two--loop pure singlet Wilson coefficient contributing to the structure functions $g_1(x,Q^2)$ analytically in the whole kinematic region. The Wilson coefficient contains Kummer--elliptic integrals. We derive the representation in the asymptotic region $Q^2 \gg m^2$, retaining power corrections, and in the threshold region. The massless Wilson coefficient is recalculated. The corresponding twist--2 corrections to the structure function $g_2(x,Q^2)$ are obtained by the Wandzura--Wilczek relation. Numerical results are presented.Comment: 22 pages Latex, 8 Figure

Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams

Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.Comment: 13 pages LATEX, one style file, Proceedings of Loops and Legs in Quantum Field Theory -- LL2014,27 April 2014 -- 02 May 2014 Weimar, German

Extent of regretted sexual intercourse among young teenagers in Scotland: a cross sectional survey

No abstract available

Review of the Supply of and Demand for Further Education in Scotland

These documents provide are an Executive Summary and Full Report of the background to, methodology for, and overall conclusions and recommendations of a review of the supply of and demand for Further Education (FE) provision in Scottish Further Education colleges in 2000. The review was commissioned by the Scottish Further Education Funding Council (SFEFC), and carried out between November 1999 and June 2000 by a team of researchers drawn from the Scottish Further Education Unit (SFEU), the Centre for Research in Lifelong Learning, Glasgow Caledonian University/University of Stirling, and the Applied Statistics Group, Napier University

The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering

We calculate the massive two--loop pure singlet Wilson coefficients for heavy quark production in the unpolarized case analytically in the whole kinematic region and derive the threshold and asymptotic expansions. We also recalculate the corresponding massless two--loop Wilson coefficients. The complete expressions contain iterated integrals with elliptic letters. The contributing alphabets enlarge the Kummer-Poincar\'e letters by a series of square-root valued letters. A new class of iterated integrals, the Kummer-elliptic integrals, are introduced. For the structure functions $F_2$ and $F_L$ we also derive improved asymptotic representations adding power corrections. Numerical results are presented.Comment: 42, pages Latex, 8 Figure

Nested Integrals and Rationalizing Transformations

A brief overview of some computer algebra methods for computations with nested integrals is given. The focus is on nested integrals over integrands involving square roots. Rewrite rules for conversion to and from associated nested sums are discussed. We also include a short discussion comparing the holonomic systems approach and the differential field approach. For simplification to rational integrands, we give a comprehensive list of univariate rationalizing transformations, including transformations tuned to map the interval $[0,1]$ bijectively to itself.Comment: manuscript of 25 February 2021, in "Anti-Differentiation and the Calculation of Feynman Amplitudes", Springe

The O(α2)O(\alpha^2) Initial State QED Corrections to e+e−e^+e^- Annihilation to a Neutral Vector Boson Revisited

We calculate the non-singlet, the pure singlet contribution, and their interference term, at $O(\alpha^2)$ due to electron-pair initial state radiation to $e^+ e^-$ annihilation into a neutral vector boson in a direct analytic computation without any approximation. The correction is represented in terms of iterated incomplete elliptic integrals. Performing the limit $s \gg m_e^2$ we find discrepancies with the earlier results of Ref.~\cite{Berends:1987ab} and confirm results obtained in Ref.~\cite{Blumlein:2011mi} where the effective method of massive operator matrix elements has been used, which works for all but the power corrections in $m^2/s$. In this way, we also confirm the validity of the factorization of massive partons in the Drell-Yan process. We also add non-logarithmic terms at $O(\alpha^2)$ which have not been considered in \cite{Berends:1987ab}. The corrections are of central importance for precision analyzes in $e^+e^-$ annihilation into $\gamma^*/Z^*$ at high luminosity.Comment: 4 pages Latex, 2 Figures, several style file

Impact of a theoretically based sex education programme (SHARE) delivered by teachers on NHS registered conceptions and terminations: final results of cluster randomised trial

<b>Objective</b>: To assess the impact of a theoretically based sex education programme (SHARE) delivered by teachers compared with conventional education in terms of conceptions and terminations registered by the NHS. Design Follow-up of cluster randomised trial 4.5 years after intervention. <b>Setting</b>: NHS records of women who had attended 25 secondary schools in east Scotland. <b>Participants</b>: 4196 women (99.5% of those eligible). <b>Intervention</b>: SHARE programme (intervention group) v existing sex education (control group). <b>Main outcome measure</b>: NHS recorded conceptions and terminations for the achieved sample linked at age 20. <b>Results</b>: In an "intention to treat" analysis there were no significant differences between the groups in registered conceptions per 1000 pupils (300 SHARE v 274 control; difference 26, 95% confidence interval –33 to 86) and terminations per 1000 pupils (127 v 112; difference 15, –13 to 42) between ages 16 and 20. <b>Conclusions</b>: This specially designed sex education programme did not reduce conceptions or terminations by age 20 compared with conventional provision. The lack of effect was not due to quality of delivery. Enhancing teacher led school sex education beyond conventional provision in eastern Scotland is unlikely to reduce terminations in teenagers

Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums

The construction of Mellin-Barnes (MB) representations for non-planar Feynman diagrams and the summation of multiple series derived from general MB representations are discussed. A basic version of a new package AMBREv.3.0 is supplemented. The ultimate goal of this project is the automatic evaluation of MB representations for multiloop scalar and tensor Feynman integrals through infinite sums, preferably with analytic solutions. We shortly describe a strategy of further algebraic summation.Comment: Contribution to the proceedings of the Loops and Legs 2014 conferenc

Comparison of regional blood flow values measured by radioactive and fluorescent microspheres

Fluorescent microspheres (FM) have become an attractive alternative to radioactive microspheres (RM) for the measurement of regional blood flow (RBF). The aim of the present study was to investigate the comparability of both methods by measuring RBF with FM and RM. Eight anaesthetised pigs received simultaneous, left atrial injections of FM and RM with a diameter of 15 mum at six different time points. Blood reference samples were collected from the descending aorta. RBF was determined in tissue samples of the myocardium, spleen and kidneys of all 8 animals. After radioactivity of the tissue samples was determined, the samples were processed automatically for measuring fluorescence using a recently developed filter device (SPU). RBF was calculated with both the isotope and spectrometric data of both methods for each sample resulting in a total of 10,512 blood flow values. The comparison of the RBF values yielded high linear correlation (mean r(2) = 0.95 +/- 0.03 to 0.97 +/- 0.02) and excellent agreement (bias 5.4-6.7%, precision 9.9-16.5%) of both methods. Our results indicate the validity of MS and of the automated tissue processing technique by means of the SPU. Copyright (C) 2002 S. Karger AG, Basel