Sentence examples for hence by applying from inspiring English sources

Hence, by applying Lemma 2 to (U P)), we obtain the conclusion from (3.6).

Hence, by applying Lemma 4 to (h'(P)), we obtain (8).

Hence, by applying Theorem 3.1, we can see that equation (4.1) has at least one positive T-periodic solution.

Hence, by applying Theorem 3.2, we can see that Eq. (4.1) has at least one positive T-periodic solution.

Hence, by applying the operator U and U 2 T = T, we have X 2 = T ⊕ U T ∗.

Hence, by applying the chain rule, the expression of the equation in the new coordinate leads to the reduced equation.

As M increases, the benefit of the joint channel sensing of CSMATXRX becomes more evident; for M=4, CSMATXRX outperforms CSMARX by 40% and CSMATXby a factor 2. Hence, we conclude that by applying joint transmitter-receiver sensing in a network with M>1, the outage performance of CSMA can be improved beyond that of CSMARX.

Hence, the ratings were evaluated by applying weathering condition of rocks in each facet.

Hence, to overcome this problem by applying a single technique, image characteristics should be analyzed first, and based on these characteristics, images need to be separated into classes.

Hence, the detection performance, achieved by applying the multichannel NAMF to monostatic and bistatic data at different ranges, may be heavily influenced by this clutter diversity, especially by the behaviour of bistatic clutter.

The interlayer of the protonated titanate is significantly expanded by replacing the protons with bulky organic ions such as tetra-butylammonium ions (TBA+) [105], hence enabling the exfoliation process by applying a weak shear force in the liquid solution [105].