Correction could fail in the case has roots with higher multiplicity or the number of roots is smaller than it's degree.

In particular, they are not eigenfunctions of the total spin-squared operator, Ŝ, but can formally be expanded in terms of pure spin states of higher multiplicities (the contaminants).

Low temperature, starvation of the cells and high multiplicity of infection (MOI) are known to favor lysogeny (see later discussion).

Most multiple star systems known are triple; for higher multiplicities, the number of known systems with a given multiplicity decreases exponentially with multiplicity.

Systems with higher multiplicities are also generally hierarchical.

In high energy hadron reactions one distinguishes peripheral reactions with low multiplicity and central collisions with high multiplicity.

As the total number of degrees of freedom approaches infinity, the system will be found in the macrostate that corresponds to the highest multiplicity.

J774 macrophages were infected with M. paratuberculosis at high multiplicities of infection (30:1) and examined at various times post-infection (fig.

This causes b-jets to be wider, have higher multiplicities (numbers of constituent particles) and invariant masses, and also to contain low-energy leptons with momentum perpendicular to the jet.

Graeffe's method works best for polynomials with simple real roots, though it can be adapted for polynomials with complex roots and coefficients, and roots with higher multiplicity.