Sentence examples for basis and demonstrate from inspiring English sources

In Section 10 we study how relaxing the assumption of perfect square pulses reduces the performance of filters optimized in the Walsh basis, and demonstrate that these filter properties may be recovered in general by simply re-optimizing under the assumption of non-square pulses.

These results confirm previous hypotheses on a pan-genomic basis and demonstrate that our novel approach is entirely valid.

The relationships observed were similar whether contaminant levels were expressed as wet weight or on a lipid basis, and demonstrate strong consistency.

Results are presented on a district by district basis and demonstrate that self-reported uptake of drugs among adults varies considerably between and within districts.

This contrasting situation confirms that bone diagenesis must be treated on a site-by-site basis, and demonstrates that bioapatite is a reliable material to date skeletal remains in arid environments.

Public fury at BP's cost-cutting decisions, secrecy, limited liability, choice to use a highly toxic dispersant in staggering quantities, lack of public remorse and whatever else it has done in violation of its unwritten contract with humanity, has a legitimate basis, and demonstrates the extent to which corporations do what they want.

The relationships observed were similar, whether contaminant levels were expressed on a wet-weight or lipid-adjusted basis, and demonstrated reasonable consistency.

When the patient was nearly 5 years old he began performing pulmonary function testing (PFT) on a routine basis, and demonstrated normal lung function, without improvement following bronchodilator administration, during a month while he was off TSI (Table 2).

This represents a significant difference of 55% over the value obtained using PW basis set and demonstrates that SZP basis sets are unsuitable for accurate determination of valley splitting in these systems.

Amongst the variety of indicators commonly used to evaluate the eutrophication status, we chose a sub-sample for which a large number of measurements are available (see Section  2.2), and we define thresholds drawing on the Common Procedure (OSPAR 2005) as a basis to develop and demonstrate our methodology.

"This equipment will be able to make a record of some of the very challenging circumstances police officers are asked to deal with on a daily basis and then demonstrate, more effectively, the reality of policing our capital and our officers' professionalism," he said.