Related papers: An x-Space Analysis of Evolution Equations: Soffer…
We propose a new evolution equation for the gluon density relevant for the region of small $x_B$. It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists…
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.…
In this paper, we present {\tt SMKA18} analysis which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through…
We formulate the momentum-space Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for structure functions measurable in deeply inelastic scattering. We construct a six-dimensional basis of structure functions that…
We study the effect of absorptive corrections due to parton recombination on the parton distributions of the proton. A more precise version of the GLRMQ equations, which account for non-linear corrections to DGLAP evolution, is derived. An…
In this paper, we study a second-order, nonlinear evolution equation with damping arising in elastodynamics. The nonlinear term is monotone and possesses a convex potential but exhibits anisotropic and nonpolynomial growth. The appropriate…
We prove the well-posedness of non-autonomous linear evolution equations for generators $A(t): D(A(t)) \subset X \to X$ whose pairwise commutators are complex scalars and, in addition, we establish an explicit representation formula for the…
We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact…
We discuss the structure of the ``forward visible'' (FW) parts of double and skewed distributions related to usual distributions through reduction relations. We use factorized models for double distributions (DDs) f(x, alpha) in which one…
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…
We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the…
We present a solution of the DGLAP evolution equations, written in terms of Sudakov form factors to describe the branching and no-branching probabilities, using a parton branching Monte Carlo method. We demonstrate numerically that this…
We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic…
Despite the strong focus of regularization on ill-posed problems, the general construction of such methods has not been fully explored. Moreover, many previous studies cannot be clearly adapted to handle more complex scenarios, albeit the…
We investigate an alternative to the DGLAP evolution of structure functions through the use of Fixed Order Perturbation Theory. Remarkable agreement between the two methods are found in the polarized sector for a wide $x$, $Q^2$ region.…
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…
We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on…
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…
The solution of DGLAP evolution equation for the twist-3 gluon operators is obtained in the Double Logarithmic Approximation of QCD perturbation theory. The method used for the solution is similar to the reggeon field theory. The…
Double hard scattering in proton-proton collisions is described in terms of double parton distributions. We derive bounds on these distributions that follow from their interpretation as probability densities, taking into account all…