Sentence examples for necessary to be continuous from inspiring English sources

(a) The single valued map in Theorem 3.6 is not necessary to be continuous (see Example 2.12), but the continuity assumption is used in Theorem 3.2 [22, 25, 25] and Theorem 2.1 Ćirić and Ume [23].

We observe that this collocation solution is not necessary to be continuous on J.

In summary: for a function to have a derivative it is necessary for the function to be continuous, but continuity alone is not sufficient.

It is not, Dedekind stresses, necessary for space to be continuous in this sense, for "many of its properties would remain the same even if it were discontinuous".

This condition is necessary and sufficient for y to be continuous on [ 0, 1 ].

Therefore, it is not necessary to limit the material properties to be continuous for the present method.

Therefore, it is not necessary to limit the material properties to be continuous for the present formulation.

On the other hand, in order to run the proposed model, it was necessary to be taken advantage of continuous data because the fuzzy approach used to reduce the uncertainties that exist in the classic methods of data classification.

We know from such experience that patience is necessary, as are continuous refinements of the technique, and continuous revision of the right questions to ask.

In Theorem 1.3, it is not necessary to assume that and are continuous up to.

If the locations of two SNPs, i and j, respectively, resulting from the paired reads are on the same chromosome, we mask i and j in the second level hash tables, and then record the corresponding haplotype in this combined region (note that it is not necessary for it to be a continuous region because we may have another SNP k located between i and j).