Unique Solutions to Hartree–Fock Equations for Closed Shell Atoms

Evolution System Approximations of Solutions to Closed Linear Operator Equations

ABSTRACT. With S a linearly ordered set with the least upper bound property, with g a nonincreasing real-valued function on S, and with A a densely denned dissipative linear operator, an evolution system M is developed to solve the modified Stieljes integral equation M(s, i)x = x + A((L)[sdgM(-, t)x). An affine version of this equation is also considered. Under the hypothesis that the evolufion...

1 Some closed form solutions to the Navier - Stokes equations

An algorithm for generating a class of closed form solutions to the Navier-Stokes equations is suggested, with examples. Of particular interest are those exact solutions that exhibit intermittency, tertiary Hopf bifurcations, flow reversal, and hys-teresis.

Closed Form Solutions for Linear Differential and Difference Equations

Finding closed form solutions of differential equations has a long history in computer algebra. For example, the Risch algorithm (1969) decides if the equation y′ = f can be solved in terms of elementary functions. These are functions that can be written in terms of exp and log, where “in terms of” allows for field operations, composition, and algebraic extensions. More generally, functions are...

Wigner's phase-space function and atomic structure: II. Ground states for closed-shell atoms.

Using closed orbits to bifurcate many periodic solutions for pendulum-type equations

For pendulum-like equations, perturbation-type arguments and topological tools provide the existence of external forces with many associated periodic solutions.  2003 Elsevier Inc. All rights reserved.