Related papers: An analytic solution to LO coupled DGLAP evolution…
This paper introduces a new accurate model for periodic fractional optimal control problems (PFOCPs) using Riemann-Liouville (RL) and Caputo fractional derivatives (FDs) with sliding fixed memory lengths. The paper also provides a novel…
The explicit expressions for the non-singlet DIS structure function g_1 at small $x$ are obtained by resumming the leading logarithmic contributions. The role played by the fits for the initial parton densities currently used in the DGLAP…
We study experimentally observable signals for nonlinear QCD dynamics in deep inelastic scattering (DIS) at small Bjorken variable $x$ and moderate virtuality $Q^2$, by quantifying differences between the linear…
We present a framework for constructing Generalized Parton Distributions (GPDs) using holographic QCD in the large $N_c$ limit, with a focus on low-x and finite skewness. Our approach utilizes holographic amplitudes for exclusive…
We show that combining forward and backward evolution allows to extract the residues of the triple-pole pomeron and of the other singularities for 10 GeV$^2 \le Q^2 \le 1000$ GeV$^2$. In this approach, the essential singularity generated by…
Explicit expressions for the singlet g_1 at small x and small Q^2 are obtained with the total resummation of the leading logarithmic contributions. It is shown that g_1 practically does not depend on Q^2 in this kinematic region. In…
We propose the novel p-branch-and-bound method for solving two-stage stochastic programming problems whose deterministic equivalents are represented by non-convex mixed-integer quadratically constrained quadratic programming (MIQCQP)…
We examine the latest HERA experimental measurements of the $Q^2$ logarithmic derivative of the proton structure function. We analyze the characteristics of DGLAP with and without screening, as well as a Regge type model, and compare their…
We propose a systematic approximation scheme for solving GLAP evolution equations at small Bjorken-$x$. The approximate solutions interpolate smoothly between hard (singular as $x^{-(1+\lambda)}$, $\lambda> 0$) and soft (singular at most as…
QCD evolution equations that naturally include longitudinal (non-propagating) fields and heavy quarks are derived. We start with the integral equations of quantum field kinetics and obtain the master equations, similar to DGLAP evolution…
Within the framework of generalized factorization of higher-twist contributions, including modification to splitting functions of both quark and gluon, we get and numerically resolve the medium-modified DGLAP (mDGLAP) evolution equations.…
We investigate the use of half-precision floating-point numbers (FP16) in mixed-precision linear solvers for lattice QCD simulations. Since the emergence of GPUs for general-purpose, mixed-precision algorithms that combine single-precision…
In this paper, a mathematical model is developed to describe the evolution of the concentration of compounds through a gas chromatography column. The model couples mass balances and kinetic equations for all components. Both single and…
The explicit expressions for the non-singlet DIS structure functions obtained at small x by resumming the most singular logarithmic contributions are discussed and compared in detail with the DGLAP evolution for different values of x and…
We present a first study of gluonic twist-four corrections to the deep inelastic structure function F_2 at small x and small Q^2. The calculations are based upon the double logarithmic approximation of the coupled twist-four evolution…
We present a simple discretization scheme for the hypersingular integral representation of the fractional Laplace operator and solver for the corresponding fractional Laplacian problem. Through singularity subtraction, we obtain a…
Renormalization group evolution equations describing the scale dependence of quantities in quantum chromodynamics (QCD) play a central role in the interpretation of experimental data. Arguably the most important evolution equations for…
A method of obtaining parton distributions directly from data is revealed in this series. In the process, the first step would be developing appropriate matrix solutions of the evolution equations in $x$ space. A division into commuting and…
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…
A matrix-based approach to numerical integration of the DGLAP evolution equations is presented. The method arises naturally on discretisation of the Bjorken x variable, a necessary procedure for numerical integration. Owing to peculiar…