Related papers: Symmetric multivariate polynomials as a basis for …
We present a detailed study of the use of localized spherical-wave basis sets, first introduced in the context of linear-scaling, in first-principles density-functional calculations. Several parameters that control the completeness of this…
Orthogonal polynomials with respect to a weight function defined on a wedge in the plane are studied. A basis of orthogonal polynomials is explicitly constructed for two large class of weight functions and the convergence of Fourier…
I consider two identical quantum particles in two boxes. We can split each box, and thereby the wavefunction of each particle, into two parts. When two half boxes are interchanged and combined with the other halves, where do the two…
We compute the gravitational form factors (GFFs) of the pion and kaon using their light-front wave functions within the Basis Light-Front Quantization framework. The wave functions are obtained by solving a light-front effective Hamiltonian…
The general spin structure of the relativistic nucleon wave function in the $3q$-model is found. It contains 16 spin components, in contrast to 8 ones known previously, since in a many-body system the parity conservation does not reduce the…
The wave function in relativity is defined, in four-dimensional space, on a space-like three-dimensional plane. The plane, most close to the time-like region, is the light-front plane $ct+z=0$. Corresponding dynamical approach - the…
We produce the light-front wave functions (LFWFs) of the nucleon from a basis light-front ap- proach in the leading Fock sector representation. We solve for the mass eigenstates from a light-front effective Hamiltonian, which includes a…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
In this paper we study dual bases functions in subspaces. These are bases which are dual to functionals on larger linear space. Our goal is construct and derive properties of certain bases obtained from the construction, with primary focus…
Gyroscopic alignment of a fluid occurs when flow structures align with the rotation axis. This often gives rise to highly spatially anisotropic columnar structures that in combination with complex domain boundaries pose challenges for…
We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the wave front map becomes a functor into the…
We demonstrate that the partial wave decomposition of three-nucleon forces used up to now in momentum space has to be necessarily unstable at high partial waves. This does not affect the applications performed up to now, which were…
Across many areas of physics, multipole expansions are used to simplify problems, solve differential equations, calculate integrals, and process experimental data. Spherical harmonics are the commonly used basis functions for a multipole…
An algorithm is developed for efficiently constructing the Lorentz covariant effective three-point vertices of the decay of a particle into two daughter particles in which all the masses and spins of the three particles can be arbitrary.…
In this paper, we investigate the problem of finding tight linear lower bounding functions for multivariate polynomials over boxes. These functions are obtained by the expansion of polynomials into Bernstein form and using the linear least…
The pion electromagnetic form factor is calculated with a light-front quark model. The "plus" and "minus" component of the electromagnetic current are used to calculate the electromagnetic form factor in the Breit frame with two models for…
The structure of the pion wave function in the relativistic constituent quark model is investigated in the explicitly covariant formulation of light-front dynamics. We calculate the two relativistic components of the pion wave function in a…
The phenomena that cause a value of a polynomial function to be a bifurcation one are yet to be described when the fibers have dimension higher than $1$. In this note, the main result is the construction of a polynomial submersion function…
Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained…
We describe a model $\mathcal{M}_3^{comb}$ for the boundary of the connectedness locus $\mathcal{M}^{sy}_3$ of the parameter space of cubic symmetric polynomials $p_c(z)=z^3-3c^2z$. We show that there exists a monotone continuous function…