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Context. The evolution of massive star-forming clumps that are progenitors of high-mass young stellar objects are often classified based on a variety of observational indicators ranging from near-infrared to radio wavelengths. Among them,…
Matching conditions are universal ingredients that describe how fragmentation functions change when heavy-flavour thresholds are crossed during the factorisation scale evolution. They are the last missing piece for a consistent description…
Time-fractional semilinear and quasilinear parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are considered, solutions of which exhibit a singular behaviour at an initial time of type $t^\sigma$ for any fixed…
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 $\delta \to 1+0$.
In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models…
In this work we study the asymptotic behavior of solutions for a general linear second-order evolution differential equation in time with fractional Laplace operators in $\mathbb{R}^n$. We obtain improved decay estimates with less demand on…
We establish trace and extension theorems for evolutionary equations with the Caputo fractional derivatives in (weighted) $L_p$ spaces. To achieve this, we identify weighted Sobolev and Besov spaces with mixed norms that accommodate…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
The $Q^2$ evolution of polarised parton fragmentation functions is discussed using Altarelli-Parisi evolution equations. The first moments of both polarised quark and gluon fragmentation functions are shown to behave in a similar fashion at…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…
Particle-mesh simulations trade small-scale accuracy for speed compared to traditional, computationally expensive N-body codes in cosmological simulations. In this work, we show how a data-driven model could be used to learn an effective…
An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For this problem, we give a simple and general…
We discuss the effect of QED corrections in the evolution of polarized parton distributions. We solve the corresponding evolution equations exactly to ${\cal O}(\alpha )$ and ${\cal O}(\alpha_s^2)$ in Mellin $N$-space, extending the…
In this paper we consider a sub-diffusion problem where the fractional time derivative is approximated either by the L1 scheme or by Convolution Quadrature. We propose new interpretations of the numerical schemes which lead to a posteriori…
Stochastic processes described by evolution equations in the universality class of the FKPP equation may be approximately factorized into a linear stochastic part and a nonlinear deterministic part. We prove this factorization on a model…
Factorization machine (FM) variants are widely used for large scale real-time content recommendation systems, since they offer an excellent balance between model accuracy and low computational costs for training and inference. These systems…
In this paper, the coupled fractional Ginzburg-Landau equations are first time investigated numerically. A linearized implicit finite difference scheme is proposed. The scheme involves three time levels, is unconditionally stable and…
Since the x dependence of the axial-anomaly effect in inclusive polarized deep inelastic scattering is fixed, the transformation from the $\bar{MS}$ scheme to different factorization schemes are not arbitrary. If the quark spin distribution…
We present new sets of nonperturbative fragmentation functions for D^*+- mesons, both at leading and next-to-leading order in the MS-bar factorization scheme with five massless quark flavors. They are determined by fitting the latest OPAL…
We show that a unified approach to the perturbative evolution of structure functions which sums all logarithms of Q^2 and 1/x at leading and next-to-leading order yields results in full agreement with the 1993 HERA data for F_2. This makes…