Related papers: Evolution of the longitudinal structure function a…
The planar elliptic extension of the Laplacian growth is, after a proper parametrization, given in a form of a solution to the equation for area-preserving diffeomorphisms. The infinite set of conservation laws associated with such elliptic…
The deep-inelastic deuteron structure function (SF) $F_2^D(x_D,Q^2)$ in the covariant approach in light-cone variables is considered. The $x_D$ and $Q^2$-dependences of SF are calculated. The QCD analysis of generated data both for…
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…
In this work, using the Laplace transformation technique we present our results for non-singlet quark distributions as well as nucleon structure function $F_2(x,Q^2)$ in unpolarized case at next-to-next-to-leading order (NNLO) QCD accuracy.…
A time dependent variational approach is used to derive the equations of motion for the \lambda \phi^4 model. The simultaneous evolution of the quantum fluctuations and of the classical part of the field is considered in a lattice of 1+1…
We comment on the uniqueness of t-evolution$(t=log(Q^2/\Lambda^2))$ of non-singlet structure functions at low x obtained fromDGLAP equations.
The rapidity dependence of the low-$p_t$ enhancement is shown to be a sensitive measure of the longitudinal source size for longitudinally expanding finite systems.
We formulate and numerically solve the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi~(DGLAP) evolution equations at next-to-leading order in perturbation theory directly for a basis of 6 physical, observable structure functions in deeply…
We consider systems of stochastic evolutionary equations of the $p$-Laplace type. We establish convergence rates for a finite-element based space-time approximation, where the error is measured in a suitable quasi-norm. Under natural…
Recent results from the HERA experiment H1 on the longitudinal stucture function $F_{L}$ of the proton are presented. They include proton structure function analyses with particular emphasis on those kinematic regions which are sensitive to…
We consider a Lindley process with Laplace distributed space increments. We obtain closed form recursive expressions for the density function of the position of the process and for its first exit time distribution from the domain $[0,h]$.…
In this paper we study the reductions of evolutionary PDEs on the manifold of the stationary points of time--dependent symmetries. In particular we describe how that the finite dimensional Hamiltonian structure of the reduced system is…
We report the results of including resummed splitting functions in the QCD evolution equations at small x, and discuss the predictions that follow for the deep inelastic structure functions. *Contribution at XXX Rencontres de Moriond, Les…
In this paper we prove strong unique continuation principle and unique continuation from sets of positive measure for solutions of a higher order fractional Laplace equation in an open domain. Our proofs are based on the…
We introduce an $L_q(L_p)$-theory for the quasi-linear fractional equations of the type $$ \partial^{\alpha}_t u(t,x)=a^{ij}(t,x)u_{x^i x^j}(t,x)+f(t,x,u), \quad t>0, \,x\in \mathbf{R}^d. $$ Here, $\alpha\in (0,2)$, $p,q>1$, and…
The validity of a previously proposed momentum space ansatz for threshold resummation of the non-singlet longitudinal structure function F_L is checked against existing finite order three-loop results. It is found that the ansatz, which is…
We show that the evolution equation of the effective potential in the auxiliary mass method corresponds to a leading approximation of a certain series. This series is derived from an evolution equation of an effective action using a…
As an extension to the Laplace and Sumudu transforms the classical Natural transform was proposed to solve certain fluid flow problems. In this paper, we investigate q-analogues of the q-Natural transform of some special functions. We…
We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for…
A new approach to $L_2$-consistent estimation of a general density functional using $k$-nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function $f$ of the densities…