Related papers: BFKL, MM, Alpert-Rokhlin's transform, FFTW, ARPACK…
We investigate numerical solution of $Q^2$ evolution equations for structure functions in the nucleon and in nuclei. (Dokshitzer-Gribov-Lipatov-)Altarelli-Parisi and Mueller-Qiu evolution equations are solved in a brute-force method.…
We calculate $e^+e^- \to Q\bar{Q}(k) + anything in a certain momentum, k, region for heavy quark-antiquark (Q\bar{Q})production. In our chosen region we find that the number of heavy quark pairs produced is determined by BFKL dynamics and…
The coefficients of the nonlinear terms in a modified Altarelli-Parisi evolution equation with parton recombination are determined in the leading logarithmic ($Q^2$) approximation. The results are valid in the whole $x$ region and contain…
In this contribution we present the status of two numerical tools designed to study the small x limit of QCD. The first one is a Monte Carlo simulation of the BFKL evolution equation. In design of this approach emphasis has been placed on…
It has been recently found that the heavy quark-antiquark QQbar pair multiplicity, in certain phase space region (QQbar at short distance, soft and with small velocity), satisfies an evolution equation formally similar to the BFKL equation…
Within the framework of the Accardi-Fagnola-Quaegebeur (AFQ) representation free calculus of \cite{b}, we consider the problem of controlling the size of a quantum stochastic flow generated by a unitary stochastic evolution affected by…
We calculate production of quark-antiquark pairs in high energy proton-nucleus collisions both in the quasi-classical approximation of McLerran-Venugopalan model and including quantum small-$x$ evolution. The resulting production cross…
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…
The q-character is a strong tool to study finite-dimensional representations of quantum affine algebras. However, the explicit formula of the q-character of a given representation has not been known so far. Frenkel and Mukhin proposed the…
Q^2 evolution equations are important not only for describing hadron reactions in accelerator experiments but also for investigating ultrahigh-energy cosmic rays. The standard ones are called DGLAP evolution equations, which are…
In this paper we study a q-analogue of the convolution product on the line in detail. A convolution product on the braided line was defined algebraically by Kempf and Majid. We adapt their definition in order to give an analytic definition…
Using a general $q$-series expansion, we derive some nontrivial $q$-formulas involving many infinite products. A multitude of Hecke--type series identities are derived. Some general formulas for sums of any number of squares are given. A…
Motivated by recent proposals (Bialynicki-Birula, Mycielski; Haag, Bannier; Weinberg; Doebner, Goldin) for nonlinear quantum mechanical evolution equations for pure states some principal difficulties in the framework of usual quantum…
I give a physical discussion of the influence of particle number fluctuations on the high energy evolution in QCD. I emphasize the event-by-event description and the correspondence with the problem of `fluctuating pulled fronts' in…
This paper is mostly a survey, with a few new results. The first part deals with functional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and more generally under q-Heisenberg relations. The second part…
We postulate a master equation, written in the language of creation and annihilation operators, as a candidate for unambiguous quantum mechanical description of unstable particles. We have found Kraus representation for the evolution driven…
Carlitz has introduced q-analogues of the Bernoulli numbers around 1950. We obtain a representation of these q-Bernoulli numbers (and some shifted version) as moments of some orthogonal polynomials. This also gives factorisations of Hankel…
The functions on a lattice generated by the integer degrees of $q^2$ are considered, 0<q<1. The $q^2$-translation operator is defined. The multiplicators and the $q^2$-convolutors are defined in the functional spaces which are dual with…
I continue the investigation of a q-analogue of the convolution on the line started in a joint work with Koornwinder and based on a formal definition due to Kempf and Majid. Two different ways of approximating functions by means of the…
A simple solution to the BFKL equation is obtained as a series in the number of real gluons emitted with transverse momentum greater than some small cutoff $\mu$. This solution reveals physics inside the BFKL ladder which is hidden in the…