Sentence examples for method they proved from inspiring English sources

By using bifurcation theory and the continuation method, they proved the following.

Using the Nehari manifold method, they proved (1.3) admits at least two solutions when ((mu, sigma )) belongs to a certain subset of ({ mathbb {R} }^{2}).

Using the Gel'fond-Baker method, they proved that all solutions ( x, y, z ) of (1.1) satisfy max { x, y, z } < exp ( exp ( exp ( 5 ) ) ).

By the Nehari manifold method, they proved that problem (1.6) admits at least a positive ground state solution for any (lambda>0) when (p tau +1)< q< m< p^=frac{pN}{N-p}).

Using the Nehari manifold method

A variant of Fisher criterion of D-LDA is expressed as follows W = arg max w W T S t W W T S w W (8). In this new LDA method, they proved that the most expressive vectors derived in the null space of the within-class scatter matrix using PCA are equal to the optimal discriminant vectors derived in the original space using LDA.

Their methods, if they prove to work for other cancers too, may revolutionise treatment.Dr Ellis and his team sequenced the whole genomes of both cancerous and normal tissue from 46 women with tumours of a type called oestrogen-receptor-positive breast cancer.

Like Friedrichs, both Kato and Rosenblum proved a time-dependent limit exists by first constructing objects with time-independent methods which they prove is the required limit.

After applying several separation methods they could prove the presence of PBDEs, HBCD and TBBPA in these samples.

In a letter to Tredinnick, Hunt thanked the MP for drawing his attention to the studies and said: "It is important we do not discount different methods of treatment if they prove to be effective and I asked the CMO to have them reviewed.

So far, this method has proved unsuccessful and it was mostly abandoned in the 1990s.