Related papers: On the solution to the NLO forward BFKL equation

Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…

We study the existence and localization of eigenvalue-eigenfunction pairs for parameter-dependent Neumann BVPs with a functional term. By reformulating the problems as a Hammerstein integral equation, we apply an existence and localization…

Analytic solutions for the energy eigenvalues are obtained from a confined potentials of the form $br$ in 3 dimensions. The confinement is effected by linear term which is a very important part in Cornell potential. The analytic eigenvalues…

For the incompressible Navier-Stokes equations in the 3D half space, we show the existence of forward self-similar solutions for arbitrarily large self-similar initial data.

Different definitions of integrability, as a rule, use linearization of initial equation and/or expansion on some basic functions which are themselves solutions of some linear differential equation. Important fact here is that linearization…

We derive explicit integral formulas for eigenfunctions of quantum integrals of the Calogero-Sutherland-Moser operator with trigonometric interaction potential. In particular, we derive explicit formulas for Jack's symmetric functions. To…

We prove existence of solution to a local fractional nonlinear differential equation with initial condition. For that we introduce the notion of tube solution.

We introduce a generating function for the coefficients of the leading logarithmic BFKL Green's function in transverse-momentum space, order by order in alpha_s, in terms of single-valued harmonic polylogarithms. As an application, we…

In this article we prove the existence of the Born approximation in the context of the radial Calder\'on problem for Schr\"odinger operators. The Born approximation naturally appears as the linear component of a factorization of the…

I prove the "folklore" result that the functional equation for a Lie group homomorphism can be solved by solving the corresponding differential equation.

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical…

We prove that a linear fractional operator with an asymptotically constant lower order term in the whole space admits eigenvalues.

This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…

An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be…

Details of the calculation of the non-forward BFKL kernel at next-to-leading order (NLO) are offered. Specifically we show the calculation of the two-gluon production contribution. This contribution was the last missing part of the kernel.…

We obtain the existence, uniqueness and regularity results for solutions to kinetic Fokker-Planck equations with bounded measurable coefficients in the presence of boundary conditions, including the inflow, diffuse reflection and specular…

We consider a generalization of a functional equation that models the learning process in various animal species. The equation can be considered nonlocal, as it is built with a convex combination of the unknown function evaluated at mixed…

In this work we applied a feed forward neural network to solve Blasius equation which is a third-order nonlinear differential equation. Blasius equation is a kind of boundary layer flow. We solved Blasius equation without reducing it into a…

This note describes the solution of the Helmholtz equation inside a nanotorus with uniform Dirichlet boundary conditions. The eigenfunction symmetry is discussed and the lower-order eigenvalues and eigenfunctions are shown. The similarity…

Systems of linear ordinary differential equations with the most general inhomogeneous boundary conditions in fractional Sobolev spaces on a finite interval are studied. The Fredholm property of such problems in corresponding pairs of Banach…