相关论文: Less Singular Terms and Small x Evolution in a Sol…
We derive an approximation approach to evolution of the longitudinal structure function, by using a Laplace-transform method. We solve the master equation and derive the longitudinal structure function as a function of the initial condition…
We show that the all order summation of small x logarithms cannot be included in the Q^2 evolution of structure functions because the NLLx corrections overwhelm the LLx contribution.
The resummation of $O(\alpha_s^{l+1} \ln^{2l} x)$ terms in the evolution kernels of non--singlet combinations of unpolarized and polarized structure functions is investigated. The agreement with complete calculations up to order…
We discuss the phenomenological extraction of the leading $ j$-plane singularity from singlet structure functions $ F_s $ measured at small $ x. $ Using a saddle-point method we show that $ {\rm d ln} F_s /{\rm d ln}{1 \over x} $ is a…
While combining large language models (LLMs) with evolutionary algorithms (EAs) shows promise for solving complex optimization problems, current approaches typically evolve individual solutions, often incurring high LLM call costs. We…
Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly…
This talks examines the effect of angular ordering on the small-x evolution of the unintegrated gluon distribution, and discusses the characteristic function for the CCFM equation.
A brief overview is presented of recent developments concerning resummed small-x evolution, based upon the renormalization group equation. The non-singlet and singlet structure functions are discussed for both polarized and unpolarized…
In this article we study an elliptic problem with degenerate coercivity. We will show that the presence of some lower order terms has a regularizing effect on the solutions.
The scalar and vector Laplacians are basic operators in physics and engineering. In applications, they show up frequently perturbed by lower-order terms. The effect of such perturbations on mixed finite element methods in the scalar case is…
The limitations of three-dimensional semi-classical gravity are explored in the context of a conformally invariant theory for a self-interacting scalar field. The analysis of the theory's scaling behaviour reveals that scalar-loop effects…
The possibility of a strong $a$-theorem in six dimensions is examined in multi-flavor $\phi^3$ theory. Contrary to the case in two and four dimensions, we find that in perturbation theory the relevant quantity $\tilde{a}$ increases…
We obtain a lower bound for the period of periodic solutions of semilinear evolution equations for the full range of nonlinear terms for which standard local existence theory applies. This lower bound depends on the Lipschitz constant of…
High-energy factorization in QCD is investigated beyond leading order and its relationship to the factorization theorem of mass singularities is established to any collinear accuracy. Flavour non-singlet observables are shown to be regular…
We consider a two-point correlator in massless $\phi^3$ model within the ladder approximation . The spectral density of the correlator is known explicitly and does not contain any resonances. Meanwhile making use of the standard sum rules…
Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by…
Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes.…
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
We summarize our recent result for a splitting function for small x evolution which includes resummed small x logarithms deduced from the leading order BFKL equation with the inclusion of running coupling effects. We compare this improved…
A modification of the collinear evolution equations as an appropriate approach to improve the behavior of parton distribution functions in the region of small longitudinal momentum fractions, and to find more theoretical arguments to…