Sentence examples for by using the inner from inspiring English sources

Then, the inequalities in inner product spaces are expandable to matrices by using the inner product between two matrices.

These are performed by using the Inner Outer impeller modeling technique coupled with the Multi Fluid Model (MFM) for the treatment of the dispersed phase.

To reduce the computational burden, a heuristic algorithm with polynomial time complexity for finding a unique (relative) reduct is designed by using the inner and outer significance measures of each criterion candidate.

Amplified DNA fragments were directly sequenced in both directions by using the inner primers by the dideoxynucleotide chain-termination method on a Li-COR DNA4200 sequencer (Li-COR Biosciences, Bad Homburg, Germany).

PCR products were purified by using the High Pure PCR Purification Kit (Roche Diagnostics GmbH) before sequencing, which was performed by using the inner PCR primers on an ABI automated sequencer and BigDye version 1.1 chemistry (both from Applied Biosystems, Darmstadt, Germany).

The first PCR was done by using 2 newly developed primers, Cap-parEcho-F (5′-TCHACWTGGATGMGRAARAC-3′) and Cap-parEcho-R (5′-TCYARYTCACAYTCYTCYTC-3′), which were designed outside the VP1 region, whereas the nested PCR was performed by using the inner primer pair, VP1-parEchoF1 and VP1-parEchoR1, described by Benschop et al. (8 ).

We can extend inequality (1.9) given in the previous section to matrices by using the Frobenius inner product as follows: Let.

For the design, Lamé's equation is used and the diameter ratios and interferences are determined by using the maximum inner pressure without yielding of rings after shrink fitting and during cold forging.

PCR products were purified on spin columns (Tiangen Biotech Co., Beijing, China) and directly sequenced by using the reported inner primers [25], [26] and BigDye Terminator v3.1 Cycle Sequencing Kit (Applied Biosystems, CA, USA) on a 3730 DNA sequencer (Applied Biosystems).

To calculate the EF, end-systolic and end-diastolic LV internal diameters were measured by M-mode using the inner edge technique at the level of the mitral leaflet tips in the parasternal long-axis view.

Hence the parameters of a T-S fuzzy system can be identified by solving equations constructed using the inner product between membership functions and a given target function.