Related papers: An Analytical Expression for the Non-Singlet Struc…
Properties of the mappings \begin{align*} C&\mapsto\frac1{(2\pi i)^2}\int_{\Gamma_1}\int_{\Gamma_2}f(\lambda,\mu)\,R_{1,\,\lambda}\,C\, R_{2,\,\mu}\,d\mu\,d\lambda, C&\mapsto\frac1{2\pi i}\int_{\Gamma}g(\lambda)R_{1,\,\lambda}\,C\,…
We consider the problem of learning multi-ridge functions of the form f(x) = g(Ax) from point evaluations of f. We assume that the function f is defined on an l_2-ball in R^d, g is twice continuously differentiable almost everywhere, and A…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We define a general scheme for the evolution of fragmentation functions which resums soft gluon logarithms in a manner consistent with fixed order evolution. We present an explicit example of our approach in which double logarithms are…
We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\^o calculus, such…
We calculate DIS-scheme splitting and coefficient functions for electromagnetic deep inelastic scattering with small x resummations, as given by the NLL BFKL equation with running coupling and approximate NLL resummed impact factors. The…
Study of parton distribution function (PDF) is a topic of significant interest in QCD. To overcome the shortcomings of conventional PDFs, several alternative methods have been suggested in recent years. The present work reports the x…
We present a method to calculate the $x$--space expressions of massless or massive operator matrix elements in QCD and QED containing local composite operator insertions, depending on the discrete Mellin index $N$, directly, without…
A non--singlet QCD analysis of the structure function $F_2(x,q^2)$ in LO, NLO, NNLO and N$^3$LO is performed based on the world data for charged lepton scattering. We determine the valence quark parton densities and present their…
An outstanding problem in QCD and jet physics is the factorization and resummation of logarithms that arise due to phase space constraints, so-called non-global logarithms (NGLs). In this paper, we show that NGLs can be factorized and…
The contribution of quarks with masses m >> Lambda_QCD is the only part of the structure functions in deep-inelastic scattering (DIS) which is not yet known at the next-to-next-to-leading order (NNLO) of perturbative QCD. We present…
This paper presents a quadratic formula-based nonlinear representation for a given single-variable function f(x), $-1 \leq x \leq 1$. First, we construct the explicit polynomial coefficient functions a(x), b(x), and c(x) using a…
We obtain analytic results for integrated triple-collinear splitting functions that emerge as collinear counter-terms in the context of the nested soft-collinear subtraction scheme arXiv:1702.01352 . With these results, all integrated…
In this paper we discuss the definition, the construction and the implementation of \textit{generalised antenna functions} for final-state radiation up to Next-to-Next-to-Leading Order (NNLO) in QCD. Generalised antenna functions…
The Fueter-Sce mapping theorem stands as one of the most profound outcomes in complex and hypercomplex analysis, producing hypercomplex generalizations of holomorphic functions. In recent years, delving into the factorization of the second…
The eigenfunctions and eigenvalues of the Fokker-Planck operator with linear drift and constant diffusion are required for expanding time-dependent solutions and for evaluating our recent perturbation expansion for probability densities…
The logarithmic slope of diffractive structure function is a potential observable to separate the hard and soft contributions in diffraction, allowing to disentangle the QCD dynamics. In this paper we extend our previous analyzes and…
In the present contribution, we study the Landau-Lifshitz-Gilbert equation with two versions of structural derivatives recently proposed: the scale $q-$derivative in the non-extensive statistical mechanics and the axiomatic metric…
We compute the next-to-next-to-leading order (NNLO) contributions to the three splitting functions governing the evolution of unpolarized non-singlet combinations of quark densities in perturbative QCD. Our results agree with all partial…
Near-degenerate electronic structures remain a major challenge for conventional single-reference density functional theory (DFT). To address this problem, we propose time-dependent $\Delta$SCF (TD$\Delta$SCF), a novel linear-response scheme…