The electronic Schrödinger equation describes the motion of electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3 variables, three spatial dimensions for each electron. Approximating them is thus inordinately challenging. As is shown in the author's monograph [Yserentant, 2000, Springer (2010)], the regularity of the solutions, which increases with the number of electrons, the decay behavior of their...

The electronic Schrödinger equation describes the motion of
electrons under Coulomb interaction forces in a field of clamped
nuclei. The solutions of this equation, the electronic wave functions,
depend on 3 variables, three spatial dimensions for each electron.
Approximating them is thus inordinately challenging. As is shown in
the author's monograph [Yserentant,
,
Springer (2010)], the regularity of the solutions, which
increases with the number of electrons, the decay behavior...

The chemical master equation is a fundamental equation in chemical kinetics. It underlies the classical reaction-rate equations and takes stochastic effects into account. In this paper we give a simple argument showing that the solutions of a large class of chemical master equations are bounded in weighted
-spaces and possess high-order moments. This class includes all equations in which no reactions between two or more already present molecules and further external reactants occur...

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