Sentence examples for required above from inspiring English sources

Even in the more refined results, namely Corollary 2.5 and Theorem 2.7, we see that some sort of additional hypothesis is required above and beyond the nonnegativity of the fractional difference.

Universal arrays represent a possible solution for re-sequencing of highly variable genes but increasing the probe length to above 10 nt increases the number of probes required above and beyond the capacity of a standard array.

What is required above all is a multilayered political strategy that reduces uncertainty and fosters stability.

These products required, above all, timely arrival of entire groups of parts, ready for on-site assembly.

"Any funding required above TfL's budget should be met by continuing support by government, who imposed this PPP structure on the tube and Londoners," said O'Toole.

YSPH students are eligible for Direct Unsubsidized Loans for graduate students of $33,000 per year and the Direct PLUS Loan for graduate students if additional loans required above that amount.

Two patients developed local recurrence of the tumour and also required above-knee amputation [24].

The most lucrative careers, such as law, medicine, technology and finance, all require above-average mental skills.

However the report noted that "unfortunately, the rain needed to reduce significant rainfall deficiencies in drought-affected areas is substantial and will require above-average rainfall over a prolonged period to completely remove deficits at longer timescales".

All the functions required in above above C++ codes are in define.h and defineOpto.h file.

It requires, above all, the possibility of winning.