Sentence examples for for these matrices from inspiring English sources

We give concise structural formulae for these matrices, and simple generating functions for them.

Determining an optimum design for these matrices is a difficult problem and is not pursued in this work.

The RI values for these matrices are calculated using Eq. 2 and the results are presented at the bottom of Table 8a d.

For these matrices, QM8 results in smaller quantization errors and higher bit rates, while QM1 corresponds to larger quantization errors and lower bit rates.

Point estimators for these matrices are usually used and they are evaluated using statistical inference methods and/or expert evaluation methods.

For these matrices, the strongest correlations are separated from the bulk of the value distribution.

For each of these matrices, we conducted analyses of complete plastomes (non-coding and protein coding) and protein-coding sequence (cds).

However, the use of these matrices for real-world applications is limited for several reasons: no fast matrix multiplication algorithm is available, huge memory requirements for large scale problems, difficult implementation on hardware, etc.

After benchmarking the performance of these matrices for apicomplexan proteins, we develop ApicoAlign a web server for finding orthologs and aligning apicomplexan proteins using a novel series of matrices.

In [5], they defined circulant matrices involving k-Lucas and generalized k-Fibonacci numbers and also investigated the upper and lower bounds for the norms of these matrices.

Finally, our aim was also to estimate the utility of these matrices for both rapid screening used in order to identify potential smokers and more accurate determination of the degree of exposure to tobacco smoke, especially that concerning pregnant women.