Sentence examples for by using limits from inspiring English sources

We present the necessary conditions for the existence of the Kolwankar Gangal local fractional derivatives (KG-LFD) and introduce more general but weaker notions of LFDs by using limits of certain integral averages of the difference-quotient.

Positive results were determined according to optical density and by using limits described for the PGL1 assay (13, 19 ).

Frequency equations of some simpler systems are also obtained from the general expression by using limiting processes.

This has been modelled in 3D cultured breast acini by using limiting dilutions of lentiviral infection [ 62].

However, the sensitivity of diagnostic tests is usually assessed by using limiting dilutions of recombinant DNA or genomic DNA derived from cell lines.

For other samples, individual incubation period of CJD-positive mice are presented; their infectious titers were estimated by using limiting dilution titration method (application of Poisson model) described by Brown et al (13 ).

Anticipating that the titer of scrapie infectivity in excreted urine would be low, we measured concentration by using limiting dilution titration, a method with which we have extensive experience quantitating TSE infectivity in blood and blood components.

In addition, we limited each search to a specific year by using the "Limits" function, which is incorporated in the search engine.

We mainly study the strong limit theorems for the log-optimal portfolio in the stock investment by using the limit properties for arbitrary random variables.

Interventions that reduced sedentary time by using TV limiting devices were shown to be effective for children but the results were limited for adults.

Since, for all and has closed graph, by using the limit presented above, we get that, that is,.