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Using a recursive algorithm to solve the renormalization group equations of N=1 QCD (DGLAP), we describe the most general supersymmetric evolution of the parton distributions. The analysis involves the regular DGLAP evolution, a partial…
This work thoroughly examines several analytical tools, each possessing a different level of mathematical intricacy, for the purpose of characterizing the orientation distribution function of elongated objects under flow. Our investigation…
We derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
This paper is an edited and shortened version of Chapter 6 from the thesis of the author. First the one dimensional orthogonal derivative will be extended to the two-dimensional case. In the two-dimensional case we have to define the region…
Transverse-momentum-dependent parton distribution and fragmentation functions describe the partonic structure of the nucleon in a three-dimensional momentum space. They are subjects of flourishing theoretical and experimental activity. They…
The method is described and tested for analysis of statistical parameters of reduced neutron widths distributions accounting for possibility of coexistence of superposition of some functions with non-zero mean values of neutron amplitude…
The QCD evolution of the transversity distributions is investigated and compared to that of the helicity distributions. It is shown that they differ largely in the small-$x$ region. It is also proved that the evolution preserves Soffer's…
There are given characterizations of the exponential distribution by the properties of the independence of linear forms with random coefficients. Related results based on the constancy of regression of one statistic on a linear form are…
We study skew-orthogonal polynomials with respect to the weight function $\exp[-2V(x)]$, with $V(x)=\sum_{K=1}^{2d}(u_{K}/{K})x^{K}$, $u_{2d} > 0$, $d > 0$. A finite subsequence of such skew-orthogonal polynomials arising in the study of…
This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well known in the literature. The subdifferential formulas…
The consistent construction of scattering amplitudes for processes with off-shell initial partons and involving electro-weak interactions is addressed.
The parton distributions in the proton are evaluated dynamically using a nonlinear QCD evolution equation - the DGLAP equation with twist-4 (the GLR-MQ-ZSR) corrections - starting from a low scale $\mu^2$, where the nucleon consists of…
In the QCD the small~$x$ evolution of the interacting pomerons and odderons is studied with all angular momenta $l$ taken into account. The resulting system of coupled nonlinear evolution equations is formulated in the momentum space and…
Analytical expressions for the distribution of the length of chords corresponding to the affine invariant measure on the set of chords are given for convex polygons. These analytical expressions are a computational improvement over other…
Differential evolution indicators are introduced for 3D spatiotemporal imaging of micromechanical processes in complex materials where progressive variations due to manufacturing and/or aging are housed in a highly scattering background of…
We present an in-depth analysis of transverse momentum dependent (TMD) distributions of twist-three. In particular, we focus on evolution equations, symmetry relations, parameterization, interpretation, small-b asymptotic behaviour and the…
This paper studies the convergence properties the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple…
Predicting outcomes in external domains is challenging due to hidden confounders that potentially influence both predictors and outcomes. Well-established methods frequently rely on stringent assumptions, explicit knowledge about the…
We find that the evolution equation for the three-particle quark-gluon B-meson light-cone distribution amplitude (DA) of subleading twist is completely integrable in the large $N_c$ limit and can be solved exactly. The lowest anomalous…