Sentence examples for strong singularity from inspiring English sources

Since the strong singularity is removed in the weakly singular equation, the jump term of the field pressure expression in the very vicinity of the boundary disappears.

The Poisson Boltzmann equation (PBE) is one widely-used implicit solvent continuum model in the calculation of electrostatic potential energy for biomolecules in ionic solvent, but its numerical solution remains a challenge due to its strong singularity and nonlinearity caused by its singular distribution source terms and exponential nonlinear terms.

We find that the strong singularity is needed in the most recent papers associated to singular Liénard equation of repulsive type [30 35].

The results shed some light on the differences between a strong singularity and a weak singularity.

This is proved in the case of strong singularity and with a signed measure.

We also consider Hankel operators whose kernels have a strong singularity at some positive point.

When the latter has corners, for values inside the critical interval, unusual strong singularities for the electromagnetic field can appear.

The kernels N 1 and N 2 have strong singularities of order 1 y 0 2. The kernel N 3 has a polar singularity.

We investigated the main boundary value problems for harmonic functions in a simply connected plane domain with strong singularities on the boundary.

Also the ordinary differential equations with strong singularities under two-point boundary conditions are studied in the articles [30, 31] by Kiguradze.

The first step in studying the differential equations with strong singularities was made by Agarwal and Kiguradze in the article [29], where the linear ordinary differential equations under conditions (1.2), in the case when the functions (p_{j}) have strong singularities at the points a and b, are studied.