Sentence examples for methods provided that from inspiring English sources

Under some mild conditions on the potential V and nonlinearity W, we establish the existence of nontrivial semi-classical solutions via variational methods, provided that 0 < ε ≤ ε 0, where the bound ε 0 is formulated in terms of N, V, and W. MSC: 35J10, 35J20.

Estrogen-withdrawal is also prevented with some progestin-only methods, provided that ovarian activity is sufficiently suppressed.

The Quantitative Structure Property Relationships (QSPR) approach is one of the recommended methods, provided that they are developed within the rigorous guidelines proposed by the Organization for Economic Co-operation and DevelOrganization for Economic Co-operation

Comparing the time histories of the slip rate and the shear stresses, and the rupture time distribution obtained in the present FE simulations with those obtained by Day et al. (2005), we found that almost the same results were obtained by the present FE method as those by the FD and BI methods, provided that the appropriate mesh size and damping coefficients were used.

In the face of the changing climate and realizing the consequent adverse effects, rural communities in Afar continue applying a number of adaptation methods provided that they expect benefits out of their adaptation actions (Di Falco et al. 2011, 2012; Kato et al. 2011).

Computational methods, provided that they have been carefully validated, can play an important role in the structure determination process.

Data obtained by CZE are in line with "historical" data obtained by the compendial method, provided that peak integration is performed without time correction.

It is an easily reproducible method, providing that enough detail is given about how it was used.

Structured reporting is the optimised reporting method, provided that structured reporting tools do not impede radiologist productivity.

In 2007, an American College of Radiology (ACR) Intersociety Conference concluded that 1. Structured reporting is the optimised reporting method, provided that structured reporting tools do not impede radiologist productivity   2.

Some unstable solutions are obtained at higher level sets by Coron's topological method, provided that the minimizing solution does not exist.