Related papers: Evolution equations in QCD and QED
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
The results of a two-loop calculation in the Feynman gauge of both the DGLAP and the ERBL evolution kernels for transversely polarized distributions are presented. The structure of these evolution kernels is discussed in detail. In…
The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the…
We explain particular, unique, approximate solutions of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations and also solutions of DGLAP evolution equations by using regge behaviour of structure functions and method of…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
Closed expressions are presented for the contributions to QCD non-singlet forward evolution kernels $P(z)$ for the DGLAP equation and to $V(x,y)$ for non-forward (ER-BL) evolution equation for a certain class of diagrams which include…
This article reviews and discusses 1) the discovery and early work on the evolution of quasars and AGNs, 2) the different techniques used to find quasars and their suitability for evolutionary studies, 3) the current status of our knowledge…
An evolution-type differential equation encodes the intersection theory of tautological classes on the Hilbert scheme of a family of nodal curves.
In the paper we review some recent results of the theory of hierarchies of quantum evolution equations.
We investigate the symmetry of the linear q-difference equations which are associated with some q-Painlev\'e equations. We apply it for adjustment of the expression of the time evolution on the q-Painlev\'e equations in terms of the Weyl…
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…
Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
In this paper we present a new and efficient analytical solutions for evolving the QED$\otimes$QCD DGLAP evolution equations in mellin space and obtain the parton distribution functions (PDFs) in perturbative QCD including the QED…
We analize the use of algorithms based in x-space for the solution of renormalization group equations of DGLAP-type and test their consistency by studying bounds among partons distributions - in our specific case Soffer's inequality and the…
New methods of solutions of the DGLAP equation and their implementation through NNLO in QCD are briefly reviewed. We organize the perturbative expansion that describes in $x$-space the evolved parton distributions in terms of scale…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
We consider stochastic equations for the class of formal mappings. Existence and uniqueness of solution, as well as evolution property are proved.
We analytically solved the QED $\otimes$ QCD coupled DGLAP evolution equations at leading order (LO) quantum electrodynamics (QED) and next to leading order (NLO) quantum chromodynamics (QCD) approximations, using the Laplace transform…
The properties and behaviour of the solutions of the recently obtained $k_t$-dependent evolution equations are investigated. When used to reproduce transverse momentum spectra of hadrons in Semi-Inclusive DIS, an encouraging agreement with…