Sentence examples for singular solutions from inspiring English sources

This paper also explores a systematic analysis for singularity properties and explicit singular solutions for corners of linear elastostatics.

In particular, near singular solutions exist and singularities are prevented from occurring in finite time by mechanisms akin to those in the evolution of vortex patches.

Geometric singularities, however, often give rise to singular solutions.

Our method requires little prior information of the singular solutions and can handle multiple singularities.

This class of differential equations has received all this attention, because it arises in the study of linear or nonlinear processes, including, for example, singular solutions of stationary or evolutionary equations, concentration of singularities in nonlinear PDEs, and Lane-Emden-Fowler-type equations with convection and singular potential.

In [1,2], a systematic analysis for singularity properties and particular solutions of linear elastostatics is explored, and the singular solutions for corners with the displacement or the free traction boundary conditions have been found.

These wars, like all wars, present complicated questions, ones that deserve sophisticated and honest answers, not boasts wrapped in singular solutions.

Let us consider examples with non-smooth and singular solutions.

We call "non-singular solutions" and "singular solutions" those in which det(W) ≠ 0 and det(W) = 0, respectively.

Using the mathematical method of Green's functions and the Fourier transform, exact, analytical, and non-singular solutions were found.

The non-singular solutions of equations (17) and (18) in the cylindrical coordinates ( r, φ, z ) with cylindrical symmetries = 0 and ( ∂ ∂ z ) = 0 are given by (19).