Related papers: Fracture functions from cut vertices
The concept of derivative coordinate functions proved useful in the formulation of analytic fractal functions to represent smooth symmetric binary fractal trees [1]. In this paper we introduce a new geometry that defines the fractal space…
I present a calculation of the one particle deep inelastic cross section in the target fragmentation region in (\phi^3)_6. The renormalized cross section gets a large logarithmic correction whose coefficient is precisely the scalar DGLAP…
Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…
This talk discusses the effective field theory view of deep inelastic scattering. In such an approach, the standard factorization formula of a hard coefficient multiplied by a parton distribution function arises from matching of QCD onto an…
A theoretical foundation is developed for active seismic reconstruction of fractures endowed with spatially-varying interfacial condition (e.g.~partially-closed fractures, hydraulic fractures). The proposed indicator functional carries a…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.
Within a perturbative approach to Quantum Chromodynamics (QCD), we show how to extend ordinary DGLAP longitudinal evolution equations to include the radiative transverse momentum generated in the collinear branching regime. Considering…
Semi-inclusive hadron-production processes are becoming important in high-energy hadron reactions. They are used for investigating properties of quark-hadron matters in heavy-ion collisions, for finding the origin of nucleon spin in…
We consider electroweak radiative corrections to hard inclusive processes at the TeV scale, and we investigate how collinear logarithms factorize in a spontaneously broken gauge theory, similarly to the DGLAP analysis in QCD. Due to the…
In this paper, we give a review of fractal calculus which is an expansion of standard calculus. Fractal calculus is applied for functions which are not differentiable or integrable on totally disconnected fractal sets such as middle-$\mu$…
The one-particle inclusive cross section in deeply inelastic lepton--nucleon scattering, expressed in terms of parton densities and fragmentation functions being differential in the invariant mass of the observed hadron and of the incoming…
This note briefly presents a new method for enlarging the functional space of a "spectral-gap-like" estimate of exponential decay on a semigroup. A particular case of the method was first devised in hal-00076709 for the spatially…
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…
Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this…
Polarized inclusive deep-inelastic diffractive scattering is dealt with in a quantum field theoretic approach. The process can be described in the general framework of non-forward scattering processes using the light-cone expansion in the…
We present and discuss the release of novel sets of collinear, variable-flavor-number-scheme fragmentation functions for axial-vector, fully heavy $T_{4c}(1^{+-})$ and $T_{4b}(1^{+-})$ tetraquarks. Working within the single-parton…
Semi-inner-products in the sense of Lumer are extended to convex functionals. This yields a Hilbert-space like structure to convex functionals in Banach spaces. In particular, a general expression for semi-inner-products with respect to one…