Sentence examples for defined provided from inspiring English sources

Then lim n → ∞ A 0 n ⊂ dom T so that the possibility of Ty being undefined is excluded and then Ty is defined provided that there is no finite or infinite jump discontinuities at y.

Indeed, in a way similar to the argument of Remark 3.2, iterative scheme (25) is well defined provided that for each n ≥ 0, the point z n belongs to U ( r ′ ) for some r ′ ∈ ( 0, r ).

The experimental strain data, together with a specific fatigue curved experimentally defined provided the input of a Finite Element Model of the repaired structure and resulted in the expected fatigue life of the repair metal-composite interface.

In this result, it is shown that a PWA system is stable inside the intersection of any level set for a local Lyapunov function and the design set where the function is defined, provided the flow points inwards at the boundaries of the intersection.

One also sees that products of two matrices of the given type is well defined (provided as usual that the column-index and row-index sets match), is again of the same type, and corresponds to the composition of linear maps.

Additional pigments bound by PsaA in close proximity to subunit PsaK (the structure of which is now almost completely defined) provided the first accurate description of this binding site and suggest a mechanism for energy transfer into the core antenna through the PsaK side.

(4) A user-defined wavelength-dependent scattering phase function can be defined, providing users with a unique framework for investigating phase functions beyond the more conventional Henyey-Greenstein approximation.

To searching this regard, the cost-optimal methodology based on the global cost was defined providing a tool to assess different nearly-zero energy scenarios.

An example of this kind of decisions during early design stages is the selection of the chemical process route, which, once defined, provides the guidelines for the process design.

The design structure reflexion matrices (DSRMs) that we have defined provide a complementary and succinct representation of the architecture and code for supporting qualitative and quantitative analysis, and likewise the refactoring of the architecture and code.

Finally, the gene expression differences associated with diabetic nephropathy were defined, providing a global view of both the pathogenic and protective pathways activated.