Sentence examples for cusp condition from inspiring English sources

(19.13) is the celebrated Kato cusp condition.

The cusp condition only holds at simple singular points where only a single pair among ({0,ldotsdots,x_N}) coincides (in the atomic case).

(Kato cusp condition [325]) Let H be an atomic Hamiltonian and let (psi ) be an (L^2) eigenfunction for H. Let (varvec{x}=(x_1,ldots,x_N)).

Most modern variational calculations for atoms and molecules use basis elements that have the cusp condition, so this theorem is very influential.  .

frac{partial widetilde{psi }}{partial r}right| _{r=0} = -frac{Z}{2} psi (0,ldotsdots,x_N) end{aligned} (19.13). 1. (19.13) is the celebrated Kato cusp condition.

On the other hand, the variational parameter d will be determined using cusp conditions [33] which ensure that the local energy E L is finite.

A interesting alternate approach to understanding the Kato cusp conditions in terms of singularities at corners is found in Ammann et al. [11].  .

Since the simplest singularities, including Maxwell's sets, are the cusp singularities, cusp conditions for the total energy function of homogeneous deformations for incompressible materials in finite elasticity will be derived, compatible with strain jumping.

A revision in this wave function is the following functional form: exp a r + b r 2 1 + 2 Open image in new window which helps in satisfying Kato's cusp conditions, which have been stressed in the construction of an accurate wave function in the past.

Given that these structures are all located peripherally around the main tooth cusps, the conditions that promote the expression of one of them should also promote the expression of the others.

Comparison with ENLIL predictions of the solar wind environment suggest that Saturn's magnetosphere may have been in a compressed state during this cusp crossing, a condition that is known to be more conducive to magnetopause reconnection.