Related papers: Fracture Functions and Jet Calculus
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…
Fractional calculus represents a natural tool for describing relativistic phenomena in pseudo-Euclidean space-time. In this study, Fractional modified special relativity is presented. We obtain fractional generalized relation for the time…
Within framework of the quantum calculus, we represent the partition function and the mass exponent of a multifractal, as well as the average of random variables distributed over self-similar set, on the basis of the deformed expansion in…
Vacuum and medium modified fragmentation functions are used to study the properties of hadrons produced in hard interactions, in $p$-$p$ and $A$-$A$ collisions, respectively. We study the modification of reconstructed jets and high…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
The perturbative quantum chromodynamics (pQCD) has been extremely successful in the prediction and description of main properties of quark and gluon jets. There are, however, some problems of the jet calculus with the higher order…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
In this paper we develop a functional calculus for a countable system of generators of contraction strongly continuous semigroups. As a symbol class of such calculus we use the algebra of polynomial tempered distributions. We prove a…
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…
A new calculus based on fractal subsets of the real line is formulated. In this calculus, an integral of order $\alpha, 0 < \alpha \leq 1$, called $F^\alpha$-integral, is defined, which is suitable to integrate functions with fractal…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
We present a new parton level Monte Carlo program for the calculation of jet cross sections in Deep Inelastic Scattering based on Born and next-to-leading order matrix elements. Using a class of invariant jet definition schemes, the program…
We present a combined QCD analysis of diffractive and leading proton deep inelastic scattering data using the framework of fracture functions. It is shown that this framework allows a precise and unified perturbative QCD description for the…
We introduce the concept of fractels for functions and discuss their analytic and algebraic properties. We also consider the representation of polynomials and analytic functions using fractels, and the consequences of these representations…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
Modified quark fragmentation functions in deeply inelastic $eA$ collisions and their QCD evolution equations are derived for the first time in the framework of multiple parton scattering. Induced radiation gives rise to additional terms in…
The paper develops a calculus for a class of real-valued functions having a quadratic variation. The main result is a solution of the representation problem for a class of evolutions having a quadratic variation. The result is applied to…
In this work we investigate the possibility of using the reflection algebra as a source of functional equations. More precisely, we obtain functional relations determining the partition function of the six-vertex model with domain-wall…
Jet calculus offers a unique mathematical technique to bridge the area of QCD resummation with Monte Carlo parton showers. With the ultimate goal of constructing next-to-next-to-leading logarithmic (NNLL) parton showers we study, using the…
A precise quantification of the medium-modification of the high transverse momenta jets in relativistic heavy ion collisions rely on consistent modelling of elastic and inelastic energy loss suffered by the jet and the concurrent underlying…