21,113 research outputs found
On certain non-unique solutions of the Stieltjes moment problem
We construct explicit solutions of a number of Stieltjes moment problems based on moments of the form (2rn)! and [(rn)!]2. It is shown using criteria for uniqueness and non-uniqueness (Carleman, Krein, Berg, Pakes, Stoyanov) that for r > 1 both forms give rise to non-unique solutions. Examples of such solutions are constructed using the technique of the inverse Mellin transform supplemented by a Mellin convolution. We outline a general method of generating non-unique solutions for moment problems
Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms
In this paper we study the problem of uniqueness of solutions to the Hartree
and Hartree-Fock equations of atoms. We show, for example, that the
Hartree-Fock ground state of a closed shell atom is unique provided the atomic
number is sufficiently large compared to the number of electrons. More
specifically, a two-electron atom with atomic number has a unique
Hartree-Fock ground state given by two orbitals with opposite spins and
identical spatial wave functions. This statement is wrong for some , which
exhibits a phase segregation.Comment: 18 page
Unique Solutions of Some Recursive Equations in Economic Dynamics
We study unique and globally attracting solutions of a general nonlinear equation that has as special cases some recursive equations widely used in Economics.Recursive equations, Intertemporal consumption
A Lagrangian approach for the incompressible Navier-Stokes equations with variable density
Here we investigate the Cauchy problem for the inhomogeneous Navier-Stokes
equations in the whole -dimensional space. Under some smallness assumption
on the data, we show the existence of global-in-time unique solutions in a
critical functional framework. The initial density is required to belong to the
multiplier space of . In particular, piecewise
constant initial densities are admissible data \emph{provided the jump at the
interface is small enough}, and generate global unique solutions with piecewise
constant densities. Using Lagrangian coordinates is the key to our results as
it enables us to solve the system by means of the basic contraction mapping
theorem. As a consequence, conditions for uniqueness are the same as for
existence
Quasibounded plurisubharmonic functions
We extend the notion of quasibounded harmonic functions to the
plurisubharmonic setting. As an application, using the theory of Jensen
measures, we show that certain generalized Dirichlet problems with unbounded
boundary data admit unique solutions, and that these solutions are continuous
outside a pluripolar set
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