Sentence examples for some singularities from inspiring English sources

Some singularities of the scalar potential are allowed.

The value ε is an infinitesimal number (ε ≤ 10−6) to avoid some singularities; it represents at the maximum only 1 μGal in the total gravity values.

However, this method may over-smooth the exact solution, it cannot effectively approximate the original solution when the exact solution has some singularities.

The structure of the extension equation is different from the one constructed in [4], in that the obstacle function has less regularity, and exhibits some singularities.

We study the existence and multiplicity of solutions for the three-point nonlinear boundary value problem, ;, where,, and are assumed to be positive and have some singularities, and is a positive parameter.

Finally, the authors in [6, 7, 10, 11, 22] use the Tikhonov regularization to identify the implied volatility, while it may over-smooth the exact solution and may not preserve the singularities of the solution well when the exact solution has some singularities.

The path could cross some singularity or diverge to infinity before reaching λ=1.

It is a well-known fact that systems that interact with themselves will develop into an equilibrium state, if there is such an equilibrium state, or else will develop towards some singularity.

All the previous BCD-based approaches left some singularity issue unattended as well as the convergence property unaddressed, our proposals are the first to provide a complete and provably-converging analytical solution.

Yield criteria for elastic-perfectly plastic solids, in particular, the Mises and Tresca ones, permit unlimited hydrostatic stresses, leading to some singularity in the classical Melan Koiter shakedown theory.

To avoid an infinite number of necessary conditions in the frame of classical solvability, we give a notion of a generalized solution to problem PK which can have some singularity at the point O.