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Olver and Rosenau studied group-invariant solutions of (generally nonlinear) partial differential equations through the imposition of a side condition. We apply a similar idea to the special case of finite-dimensional Hamiltonian systems,…
The modified evolution equation for parton distributions of Dokshitzer, Marchesini and Salam is extended to non-singlet Deep Inelastic Scattering coefficient functions and the physical evolution kernels which govern their scaling violation.…
We consider 3d Schrodinger operator with long-range potential that has short-range radial derivative. The long-time asymptotics of non-stationary problem is studied and existence of modified wave operators is proved. It turns out, the…
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…
For the Weyl-Heisenberg group, convolutions between functions and operators were defined by Werner as a part of a framework called quantum harmonic analysis. We show how recent results by Feichtinger can be used to extend this definition to…
In this work we investigate a 1D evolution equation involving a divergence form operator where the diffusion coefficient inside the divergence is changing sign, as in models for metamaterials.We focus on the construction of a fundamental…
We derive the LO DGLAP evolution equation for the full Mellin moments of the truncated at $x_0$ first moment of the nonsinglet parton distribution. This "moment of moment" approach allows to determine the small-$x_0$ behaviour of the…
Karlin and Altschul in their statistical analysis for multiple high-scoring segments in molecular sequences introduced a distribution function which gives the probability there are at least r distinct and consistently ordered segment pairs…
The Nekrasov partition function in supersymmetric quantum gauge theory is mathematically formulated as an equivariant integral over certain moduli spaces of sheaves on a complex surface. In ``Seiberg-Witten Theory and Random Partitions'',…
The N = 2, 4 superconformal symmetry constraints in d = 4 for four point functions of chiral primary 1/2-BPS operators are derived. The operators are described by symmetric traceless tensors of the internal R-symmetry group. A substantial…
Further results for conformal partial waves for four point functions for conformal primary scalar fields in conformally invariant theories are obtained. They are defined as eigenfunctions of the differential Casimir operators for the…
The Meta-Schr\"odinger algebra arises as the dynamical symmetry in transport processes which are ballistic in a chosen `parallel' direction and diffusive and all other `transverse' directions. The time-space transformations of this Lie…
We consider the anisotropic Shubin operators $(-\Delta)^m + \vert x\vert^{2k}$ acting on the space $L^2(\mathbb R^n)$, with $k, m \geq1$ some positive integers. We provide sharp quantitative estimates in Gelfand-Shilov spaces for the…
We propose a novel extension to symmetrized neural network operators by incorporating fractional and mixed activation functions. This study addresses the limitations of existing models in approximating higher-order smooth functions,…
We give a review of results on the operator-norm convergence of the Trotter product formula on Hilbert and Banach spaces, which is focused on the problem of its convergence rates. Some recent results concerning evolution semigroups are…
This paper advances the study of multivariate function approximation using neural network operators activated by symmetrized and perturbed hyperbolic tangent functions. We propose new non-linear operators that preserve dynamic symmetries…
We analyse the 3-point CFT correlators involving non-conserved spinning operators in momentum space. We derive a general expression for the conformal Ward identities defining the 3-point functions involving two generic spin $s$…
In this paper we define the Schwartz linear operators among spaces of tempered distributions. These operators are the analogous of linear continuous operators among separable Hilbert spaces, but in the case of spaces endowed with Schwartz…
We outline a general procedure on how to apply random positive linear operators in nonparametric estimation. As a consequence, we give explicit confidence bands and intervals for a distribution function $F$ concentrated on $[0,1]$ by means…
We develop a framework for the reconstruction of the non-forward kernels which govern the evolution of twist-two distribution amplitudes and off-forward parton distributions beyond leading order. It is based on the knowledge of the special…