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

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

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

Tailoring the gradient ultrafine-grained structure in low-carbon steel during drawing with shear

Conventional drawing and drawing with shear were conducted on the rods of low-carbon steel. Deformation by simple drawing forms basically a homogenous structure and leads to a uniform change in microhardness along the billet volume. A comparative analysis of the models of these processes showed that shear drawing of steel at room temperature reduces energy characteristics in half, normal forces on the die – by 1,8, and enhances the strain intensity from 0,5 to 1,6. During drawing with shear, strain-induced cementite dissolution occurs and a gradient structure is formed, which increases the microhardness of the surface layer up to values close to 7 000 MPa

Promising methods of SPD to obtain nanostructured metallic materials

© 2016, Institute of Problems of Mechanical Engineering.The manuscript provides the results of investigations and the analysis of advanced schemes of severe plastic deformation (SPD) creating conditions of non-monotonic exposure at drawing and rolling of long-length metallic materials. The manuscript shows the efficiency of schemes in terms of nanostructured states processing and the advance of further studies for possible commercial implementation

Analysis of shear deformation scheme efficiency in plastic structure formation processes

The paper is devoted to the analysis of such an important factor as deformation behavior in the simple shear conditions.It is shown that non-monotonous character of material plastic flow exerts significant influence on the intensity of initial structure refinement. Induced non-monotonous character that ensures formation of equiaxed structural states plays an important role in the process

3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering

A survey is given on the status of 3-loop heavy flavor corrections to deep-inelastic structure functions at large enough virtualities $Q^2$.Comment: 13 pages Latex, 8 Figures, Contribution to the Proceedings of EPS 2015 Wie

Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations

Various of the single scale quantities in massless and massive QCD up to 3-loop order can be expressed by iterative integrals over certain classes of alphabets, from the harmonic polylogarithms to root-valued alphabets. Examples are the anomalous dimensions to 3-loop order, the massless Wilson coefficients and also different massive operator matrix elements. Starting at 3-loop order, however, also other letters appear in the case of massive operator matrix elements, the so called iterative non-iterative integrals, which are related to solutions based on complete elliptic integrals or any other special function with an integral representation that is definite but not a Volterra-type integral. After outlining the formalism leading to iterative non-iterative integrals,we present examples for both of these cases with the 3-loop anomalous dimension $\gamma_{qg}^{(2)}$ and the structure of the principle solution in the iterative non-interative case of the 3-loop QCD corrections to the $\rho$-parameter.Comment: 13 pages LATEX, 2 Figure

Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-$N$ space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as $_2F_1$ Gau\ss{} hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using $q$-product and series representations implied by Jacobi's $\vartheta_i$ functions and Dedekind's $\eta$-function. The corresponding representations can be traced back to polynomials out of Lambert--Eisenstein series, having representations also as elliptic polylogarithms, a $q$-factorial $1/\eta^k(\tau)$, logarithms and polylogarithms of $q$ and their $q$-integrals. Due to the specific form of the physical variable $x(q)$ for different processes, different representations do usually appear. Numerical results are also presented.Comment: 68 pages LATEX, 10 Figure