Related papers: QCD Evolution Equations: Numerical Algorithms from…
Numerical solution of DGLAP $Q^2$ evolution equations is studied for polarized parton distributions by using a ``brute-force" method. NLO contributions to splitting functions are recently calculated,and they are included in our analysis.…
We analyze general convergence properties of the Taylor expansion of observables to finite chemical potential in the framework of an effective 2+1 flavor Polyakov-quark-meson model. To compute the required higher order coefficients a novel…
We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. The method is based on integral transforms realized…
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…
The first passage time problem is considered for stochastic logistic growth model with constant harvesting and multiplicative environmental noise. Explicit expressions for the moments and cumulants of both upcrossing and downcrossing FPTs…
Second-order sufficient conditions for local optimality have been playing an important role in local convergence analysis of optimization algorithms. In this paper, we demonstrate that this condition alone suffices to justify the linear…
In this article, we present the mathematical analysis of the convergence of the linearized Crank-Nicolson Galerkin method for a nonlinear Schrodinger problem related to a domain with a moving boundary. The convergence analysis of the…
An analytical method is presented to solve generalized QCD evolution equations for the time development of parton cascades in a nuclear environment. Closed solutions for the spectra of produced partons with respect to the variables time,…
When using Laguerre and Hermite spectral methods to numerically solve PDEs in unbounded domains, the number of collocation points assigned inside the region of interest is often insufficient, particularly when the region is expanded or…
The classical orthogonal polynomials (Hermite, Laguerre and Jacobi) are involved in a vast number of applications in physics and engineering. When large degrees $n$ are needed, the use of recursion to compute the polynomials is not a good…
Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients…
QCD evolution equations in minimal subtraction schemes have a hidden symmetry: One can construct three operators that commute with the evolution kernel and form an $SL(2)$ algebra, i.e. they satisfy (exactly) the $SL(2)$ commutation…
The next-to-next-to-leading order perturbative QCD corrections to R_tau and the higher moments of the invariant mass distribution in the hadronic tau decays are considered. The renormalization scheme dependence of these corrections is…
An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically…
The parton distributions in the proton are evaluated dynamically using a nonlinear QCD evolution equation - the DGLAP equation with twist-4 (the GLR-MQ-ZSR) corrections - starting from a low scale $\mu^2$, where the nucleon consists of…
A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked…
We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-$Q$ fields at the Wilson-Fisher fixed point in the $O(2)$…
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…
In this paper we study the numerical method for approximating the random periodic solution of semiliear stochastic evolution equations. The main challenge lies in proving a convergence over an infinite time horizon while simulating…
We present the singular Euler--Maclaurin expansion, a new method for the efficient computation of large singular sums that appear in long-range interacting systems in condensed matter and quantum physics. In contrast to the traditional…