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

Sal: de salvador a inimigo público.

bitstream/item/28967/1/2010-296.pd

Determinação do equivalente de salinidade de sais substitutos do cloreto de sódio.

bitstream/item/74486/1/pub-194.pd

Coupled electronic and morphologic changes in graphene oxide upon electrochemical reduction

Peer reviewedPostprin

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

Método do índice de qualidade na determinação do frescor de peixes.

O Método do Índice de Qualidade é um sistema de controle de qualidade do frescor do pescado e baseia-se na avaliação objetiva dos principais atributos sensoriais de cada espécie de peixe, através de um sistema de pontos de demérito. O MIQ é baseado na avaliação visual e olfativa de certos atributos do peixe, principalmente a aparência dos olhos, pele e brânquias, juntamente com o odor e textura, através de um sistema de classificação por pontos de demérito, de 0 a 3. A pontuação de todos os atributos é somada para dar uma pontuação global sensorial, o chamado Índice de Qualidade (IQ). O método permite a avaliação da qualidade do pescado em questão, a previsão da validade comercial da espécie estudada, com a vantagem de ser barato, simples, requerer pouco treinamento em relação aos outros métodos e não destruir a amostra. Sua aplicação faz da análise sensorial, tão importante para avaliação do frescor do pescado, um método objetivo, permitindo de forma confiável e rápida, a avaliação da matéria-prima, seja a bordo das embarcações, no controle da matéria-prima nas indústrias, ou nos entrepostos e em postos de venda