Related papers: Method of Analytic Evolution of Flat Distribution …
Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive meson electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in…
In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the…
Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order $n$ that are uniformly valid for unbounded complex values of the argument $z$, including the real interval $0 \leq z \leq 1$ in which the zeros in…
We describe the N=1 supersymmetric evolution of the parton distributions with coupled gluinos and scalar quarks (Exact Supersymmetric Altarelli Parisi or ESAP). Superymmetric distributions are generated radiatively and studied as a function…
The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…
We examine the large-order behaviour of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from…
Linear and Quadratic Discriminant Analysis (LDA and QDA) are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not…
We study the application of generalized symmetry for reducing nonlinear partial differential equations. We construct the ansatzes for dependent variable $u$ which reduce the scalar partial differential equation with two independent…
We use the BLM procedure to eliminate the renormalization scale ambiguity in the evolution equation for the non-singlet deep-inelastic structure function $F_2^{\text NS}(x,Q).$ The scale of the QCD coupling in the $\overline{\text{MS}}$…
A method of evaluation of spacelike QCD observables ${\cal D}(Q^2)$ is developed, motivated by the renormalon structure of these quantities. A related auxiliary quantity ${\widetilde {\cal D}}(Q^2)$ is introduced, which is renomalization…
We construct off-diagonal parton distributions defined on the interval 0 < X < 1 starting from the off-forward distributions defined by Ji. We emphasize the particular role played by the symmetry relations in the "ERBL-like" region. We find…
We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate…
Discriminant analysis, including linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA), is a popular approach to classification problems. It is well known that LDA is suboptimal to analyze heteroscedastic data, for…
We investigate numerical solution of the Dokshitzer-Gribov-Lipatov-Altarelli- Parisi (DGLAP) Q^2 evolution equation for the transversity distribution Delta_T q or the structure function h_1. The leading-order (LO) and next-to- leading-order…
I present a highly efficient method for evolving parton distributions in perturbative QCD. The method allows evolving the parton distribution functions according to any of the commonly-used truncations of the evolution equations (which…
The analytic and formal solutions of certain family of $q$-difference-differential equations under the action of a complex perturbation parameter is considered. The previous study of the last two authors provides information in the case…
We give a refined description of the dominant spectrum of a non-local operator that models growth and equal mitosis of cells. More precisely we look at the spectrum in half planes at the right hand side of the first accumulation point of…
Analytic solutions and their formal asymptotic expansions for a family of the singularly perturbed $q-$difference-differential equations in the complex domain are constructed. They stand for a $q-$analog of the singularly perturbed partial…
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusion processes with killing on $[0,\infty)$. We obtain criteria for the exponential convergence to a unique quasi-stationary distribution in total…
We formulate a consistent 1/N_c^2 expansion of the QCD evolution equations for the twist-three quark distributions g_2(x,Q^2), h_L(x,Q^2) and e(x,Q^2) based on the interpretation of the evolution as a three-particle quantum-mechanical…