Related papers: Redundant Components in the 3 alpha Faddeev Equati…
This paper develops an enhanced finite element method for approximating a class of variational problems which exhibit the \textit{Lavrentiev gap phenomenon} in the sense that the minimum values of the energy functional have a nontrivial gap…
The variational method, within the Hamiltonian formalism of reformulated QED is used to determine relativistic wave equations for a system of three fermions of arbitrary mass interacting electromagnetically. The interaction kernels of the…
This paper focuses on phase retrieval from phaseless total-field data in biharmonic scattering problems. We prove that a phased biharmonic wave can be uniquely determined by the modulus of the total biharmonic wave within a nonempty domain.…
The relativistic Faddeev equation for three-nucleon scattering is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is achieved by…
A mechanism of disappearance and formation of the Efimov levels of the helium ^4He_3 trimer is studied when the force of interatomic interaction is changed. The resonances including virtual levels are calculated by the method based on the…
Conventionally, piecewise polynomials have been used in the boundary elements method (BEM) to approximate unknown boundary values. Since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for…
Recently the new method of the Cherenkov fields and loss factors of a point-like electron bunch passing through longitudinally homogeneous structures lined with arbitrary slowdown layers was proposed. It was shown that the Cherenkov loss…
Based on a three-potential formalism we propose mathematically well-behaved Faddeev-type integral equations for the atomic three-body problem and descibe their solutions in Coulomb-Sturmian space representation. Although the system contains…
Faddeev' equations are a set-theoretical and an operator forms of the star-triangle equation. Known solutions of the quantum star-triangle equation, related to the Faddeev equations, are based on various forms of the modular double of the…
Obtaining cross sections for nuclear reactions at intermediate energies based on the Glauber formulation has a long tradition. Only recently the energy regime of a few hundred MeV has become accessible to ab-initio Faddeev calculations of…
Using the generalized perturbation reduction method the Hirota equation is transformed to the coupled nonlinear Schr\"odinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is obtained.…
We outline a recently developed theory of impedance-matching, or reflectionless excitation of arbitrary finite photonic structures in any dimension. It describes the necessary and sufficient conditions for perfectly reflectionless…
We present a systematic account of the separation of the angular degrees of freedom from the nonrelativistic Schr\"{o}dinger equation for a three-body quantum system with arbitrary masses, charges, total angular momentum, and parity. The…
The relativistic Faddeev equation for three-nucleon scattering is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. The equation is solved through Pad\'e summation,…
The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation…
A finite element scheme for an entirely fractional Allen-Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, the Caputo fractional in-time derivative and the fractional Laplacian replace…
This paper establishes tahe existence and uniqueness of the nonlinear Knudsen layer equation with incoming boundary conditions. It is well-known that the solvability conditions of the problem vary with the Mach number of the far Maxwellian…
The idea of using Riedtmann's well-behaved functors to study compositions of irreducible morphisms has been explored in a number of articles. Here we introduce the concept of mesh-comparable components of the Auslander-Reiten quiver, which…
Relativistic wave equation of motion without redundant components for the particle having spin 3/2 has been considered. In order to show the newness a comparison with the known equations for the spin s=3/2 field is given. Therefore, the…
The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…