Sentence examples for is unique provided from inspiring English sources

Suppose that the conditions in Theorem  2.1 are fulfilled and (b x,t geqslant0), then the bounded solution of Problem (1.1) is unique provided that the following condition holds (mathrm{H}_{3} quad textit{the function }f(s textit{ is decreasing in }sinmathbb{R}.

\, To justify the definition of logarithms, it is necessary to show that the equation :b^x = y \, has a solution x and that this solution is unique, provided that y is positive and that b is positive and unequal to 1.

The company describes its cooperation strategy: "Each of our relationships is unique, providing different benefits for the communities, such as a more stable future, or access to basic essentials like education, clean water and healthcare".

For every (tauin I_{epsilon,a_{0},a_{1}}), the forcing signal f and the shift α as above are unique, provided that the following constraint is required: (C) f is a piecewise affine forcing signal whose restriction (f|_{ 0,tau)}) has slope (1+epsilon) only on a subinterval whose left boundary is α.  .

The level of annotation in the RH/Day-6 mRNA cluster is low (~80% are unique), providing relatively few clues to the biochemical pathways that are transiently expressed during VEG development but in RH are permanently activated.

Moreover, the United States is unique in providing a right to a jury trial in IPR lawsuits, and juries are more likely than judges to favor patent holders.

Each descriptor is unique and provides different information about the molecule.

Finally, we prove that this limit is unique and provides the global solution to NLS equation with regard to (2 -(4)-(6).

Teachers tell us the combination of these three things is unique and provides them with the greatest ability to positively impact their teaching practice with getting in the way.

The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis on which the most accurate and reproducible measurements can be made.

Each DO animal is unique, which provides a highly recombinant population with a wide phenotypic variation.