We compute the three-loop corrections to helicity amplitudes for $q\bar{q}\to Q\bar{Q}$ scattering in massless QCD. In Lorentz decomposition of amplitude we avoid evanescent structures and map corresponding form factors directly physical amplitudes. reduce master integrals express them terms harmonic polylogarithms. The renormalised exhibit infrared divergences dipole quadrupole type, as predic...

The classical Weyl Law says that if NM(?) denotes the number of eigenvalues Laplace operator on a d-dimensional compact manifold M without boundary are less than or equal to ?, then $${N_M}(\lambda ) = c{\lambda ^d} + O({\lambda ^{d - 1}}).$$ This paper explores prospects improvements remainders products manifolds. In particular we obtain polynomial improvement remainder for spheres, demonstrat...

A bstract We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD. For the first time, we include corrections due to massive fermion loops which give rise integrals over elliptic curves. results missing master needed compute amplitude and obtain an form finite remainders terms iterated using rationalised kinematics field sampl...

A bstract We present all two-loop five-parton leading-colour finite remainders in the spinor-helicity formalism by analysing numerical evaluations of their known expressions terms Mandelstam invariants. Recasting them variables allows us to obtain which are more compact, faster evaluate, numerically stable and manifestly free from poles higher order than necessary. At same time, due better scal...

This essay proposes that current-day notions of fugitivity, understood in the terms Fred Moten as a category irregular escapes easy representations and predications, can undiscipline music histories productive ways. Among these: it inflect musicological thinking through attention to sonic remainders haunted pasts; decenter understandings aesthetic; lead more nuanced about imbrication an “underc...

Teaching subresultant prs’s is an unpleasant experience because there is a misunderstanding about the role of Sylvester’s two matrices and how they affect the signs of the sequences. Almost all articles and texts on the subject perform operations in Z[x] and use a form of pseudo-division that distorts the signs of the polynomial remainders; hence, sentences like “forget about the signs” appear ...