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The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
A general formalism was introduced for reorganization of QCD evolution equations and derivation of hierarchical solution to DGLAP equation. The hierarchical solution separates two types of parton emissions: the flavour changing emissions…
The family of fifth order nonlinear evolution equations is studied. Some traveling wave elliptic solutions are found. The classification of these exact solutions is given.
The Douglas--Rachford and Peaceman--Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable…
We present a geometric version of Quickest Change Detection (QCD) and Quickest Hub Discovery (QHD) tests in correlation structures that allows us to include and combine new information with distance metrics. The topic falls within the scope…
An algorithm for solving the random resistor problem by means of the transfer-matrix approach is presented. Preconditioning by spanning clusters extraction both reduces the size of the conductivity matrix and speed up the calculations.
Lambert's problem has been long studied in the context of space operations; its solution enables accurate orbit determination and spacecraft guidance. This work offers an analytical solution to Lambert's problem using the Koopman Operator…
We present the first global analysis of generalized parton distributions (GPDs) combing lattice quantum chromodynamics (QCD) calculations and experiment measurements including global parton distribution functions (PDFs), form factors (FFs)…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
We show how to approximate a solution of the first order linear evolution equation, together with its possible analytic continuation, using a solution of the time-fractional equation of order $\delta >1$, where $\delta \to 1+0$.
We reconsider the evolution equations for transverse momentum dependent distributions recently proposed by us and recast them in a form which allows the comparison with results recently appeared in the literature. We show under which…
We study gradient corrections to the transport equation for energetic light partons in dense QCD environments. In the diffusion limit, the transport dynamics is solely controlled by small-angle elastic scatterings, leading to transverse…
We derive the evolution equations of parton distribution functions appropriate in different kinematic regions in a unified and simple way using the resummation technique. They include the Gribov-Lipatov-Altarelli-Parisi equation for large…
In this article, we show that a technique for showing well-posedness results for evolutionary equations in the sense of [13] established in [16] applies to a broader class of non-autonomous integro-differential-algebraic equations. Using…
Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…
The formulas directly connecting parton distribution functions (PDFs) and fragmentation functions (FFs) at the next to leading order (NLO) QCD with the same quantities at the leading order (LO) are derived. These formulas are universal,…
In this paper we extend recent developments in computational optimal transport to the setting of Riemannian manifolds. In particular, we show how to learn optimal transport maps from samples that relate probability distributions defined on…
A NNLO analysis of certain logarithmic expansions, developed for precision studies of the evolution of the QCD parton distributions (pdf) at the Large Hadron Collider, is presented. We elaborate on their relations to all the solutions of…