Related papers: Analytic Evolution of Singular Distribution Amplit…
The natural occurrence of singular spaces in applications has led to recent investigations on performing topological data analysis (TDA) in a stratified framework. In many applications, there is no a priori information on what points should…
We establish a sharp Adams-type inequality in higher-order function spaces with singular weights on $\mathbb{R}^n$. A sharp singular concentration-compactness principle, improving Lions' result, is also proved. The study distinguishes…
A new approach to global QCD analysis is developed. The main ingredients are two QCD-based evolution equations. The first one is the Balitsky-Kovchegov nonlinear equation, which sums higher twists while preserving unitarity. The second…
We revisit the evolution of generalised parton distributions (GPDs) at the leading order in the strong coupling constant $\alpha_s$ for all of the twist-2 quark and gluon operators. We rederive the relevant one-loop evolution kernels,…
We study the effects of quantum corrections on transverse momentum broadening of a fast parton passing through dense QCD matter. We show that, at leading logarithmic accuracy the broadening distribution tends at late times or equivalently…
We present a procedure of differential renormalization at the one loop level which avoids introducing unnecessary renormalization constants and automatically preserves abelian gauge invariance. The amplitudes are expressed in terms of a…
In this work, we present Con$^{2}$DA, a simple framework that extends recent advances in semi-supervised learning to the semi-supervised domain adaptation (SSDA) problem. Our framework generates pairs of associated samples by performing…
In this paper, we generalize the classical Yosida approximation by utilizing a nonstandard duality mapping to establish the existence and uniqueness of both (probabilistically) weak and strong solutions and demonstrate the continuous…
We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of…
In this paper, we study the leading-twist distribution amplitude (DA) of the heavy pseudoscalars (HPs), such as $\eta_c$, $\eta_b$ and $B_c$, within the QCD theory in the background fields. New sum rules up to dimension-six condensates for…
We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Class. Quantum Grav. 34, 045005 (2017), to the…
Two-dimensional (2D) Multiple Signal Classification algorithm is a powerful technique for high-resolution direction-of-arrival (DOA) estimation in array signal processing. However, the exhaustive search over the 2D an-gular domain leads to…
QCD evolution equations in $\text{MS}$-like schemes can be recovered from the same equations in a modified theory, QCD in non-integer $d=4-2\epsilon$ dimensions, which enjoys exact scale and conformal invariance at the critical point.…
We study duality in $\mathcal{N}=1$ supersymmetric QCD in the non-Abelian Coulomb phase, order-by-order in scheme-independent series expansions. Using exact results, we show how the dimensions of various fundamental and composite chiral…
The $Q^2$ evolution of polarised parton distributions at small $x$ is studied. Various analytic approximations are critically discussed. We compare the full evolution with that obtained from the leading-pole approximation to the splitting…
The supersymmetric evolution of the fragmentation functions (or timelike evolution) within N=1 $QCD$ is discussed and predictions for the fragmentation functions of the theory (into final protons) are given. We use a backward running of the…
We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest…
A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that…
We present a systematic study of higher-twist distribution amplitudes (DAs) of the B-meson which give rise to power-suppressed $1/m_B$ contributions to B-decays in final states with energetic light particles in the framework of QCD…
An analytical method is presented to solve generalized QCD evolution equations for the time development of parton cascades in a nuclear environment. Closed solutions for the spectra of produced partons with respect to the variables time,…