Sentence examples for the above formulae from inspiring English sources

The grip and the gauge parts are expressed separately in the above formulae.

Each of the above formulae mean that "whenever in the future \(p\) holds, \ q\) will hold within 3 time units later".

We shall make use of the above formulae (2.13), (2.14), (2.18) and (2.21) to give some closed formulae of sums of products of any number of Apostol-Bernoulli and Apostol-Euler polynomials and numbers in the next section.

The presence of the internal temperatures in all the above formulae prevents us from studying the quantities' variation with the internal entropy source ( dot{S}_{text{M}} ), as it was possible for the total system.

According to the above formulae, it may be concluded that v is the average speed of the nodes infecting the whole network, and propagation power expresses the risk of virus propagation in the network.

end{aligned} (8 It should be noted that in order to find numerical solutions by using the above formulae, one has to calculate among other functions, (g x,{varvec {theta }})) for different parameter vectors ({varvec {theta }}), which may stop the iterations of the algorithm because (g x,{varvec {theta }})) may not be defined for the corresponding ({varvec {theta }}) vector.

So, the q-integral in the above formula becomes.

To refine the above formula, we use the following observation.

The above formula gives a range in the data.

(d) Combining the above formula and (2.10), the result (d) is obvious.

Now, we can use the above formula in this regard.