Related papers: Fracture Functions and Jet Calculus
A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…
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…
Machine learning has become an essential tool in jet physics. Due to their complex, high-dimensional nature, jets can be explored holistically by neural networks in ways that are not possible manually. However, innovations in all areas of…
We develop the notion of shower partons and determine their distributions in jets in the framework of the recombination model. The shower parton distributions obtained render a good fit of the fragmentation functions. We then illustrate the…
The purpose of this paper is to study a generalization of strongly $\eta$-convex functions using the fractal calculus developed by Yang \cite{Yang}, namely generalized strongly $\eta$-convex function. Among other results, we obtain some…
Multifractal analysis has been used to diagnoze cracked and healthy rotors. Is has been shown that the complexity and regularity criteria of the dynamical systems defined by the multiple scaling of the time series can indicate the damages…
The problem of determining the underlying dynamics of a system when only given data of its state over time has challenged scientists for decades. In this paper, the approach of using machine learning to model the updates of the phase space…
We investigate some basic applications of Fractional Calculus (FC) to Newtonian mechanics. After a brief review of FC, we consider a possible generalization of Newton's second law of motion and apply it to the case of a body subject to a…
In this short review paper, we discuss some of the recent advances in the field of parton fragmentation processes into hadrons as well as their possible modifications in QCD media. Hadron production data in e+e-, deep inelastic scattering…
We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the Output Function Evaluation…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
A new framework is sketched for the treatment of the hadronisation of a highly-virtual quark and anti-quark jet pair created in electron-positron annihilations. As in such a case, factorization theorem does not work, a new scale-evolution…
A continuum model of crack propagation is presented and discussed. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic and viscoelastic effects are…
Starting with the interpretation of parton evolution with rapidity as a branching-diffusion process, we describe the different kinds of fluctuations of the density of partons which affect the properties of QCD scattering amplitudes at…
Fractal concepts have been introduced in the accretion disc as a new feature. Due to the fractal nature of the flow, its continuity condition undergoes modifications. The conserved stationary fractal flow admits only saddle points and…
We outline an extension of the classical Langevin equation to a quantum formulation of the treatment of dissipation and fluctuations of all collective degrees of freedom with unitary evolution of a many-fermion system within an extension of…
Parton evolution with the rapidity essentially is a branching diffusion process. We describe the fluctuations of the density of partons which affect the properties of QCD scattering amplitudes at moderately high energies. We arrive at…
We briefly summarize theoretical methods for carrying out QCD calculations to next-to-leading order in perturbation theory. In particular, we describe a new general algorithm that can be used for computing arbitrary jet cross sections in…
The calculus correspondence has been known to exist between generic pedal evolutions and generic wave front evolutions. In this paper, we first extend the known results on the calculus correspondence to evolutions with multi-parameters, and…
We review the recent researches of numerical simulations on faulting, which are interpreted in this paper as the evolution of the state of the fault plane and the evolution of fault structure. The theme includes the fault constitutive…