Sentence examples for case of the function from inspiring English sources

Figure 1, represent a typical case of the function on the right-hand side of (19).

However, the general case of the function and its relation with the zeta family does not seem to have been realized so far.

The 'Hill climbing' procedure is developed following the recommendations from [25] and [24], for finding the global extreme in the case of the function of three variables.

In the case of the function f z) defined and analytic in a certain region involving the interval [0,1], the problem was investigated by Wright [2], Kantorovich [3] and then Bernstein [4].

They proved the existence of positive solutions and dead core solutions (vanishing on a subinterval, ) of problem (1.3), and also covered the case of the function approximated by some regular function.

Noting that (|umapsto A0|_{Y_{p,mathbf{X}}}= |A0|_{ast}) for each (Ain Y_{p,mathbf{X}}), one can show (tmapsto A t 0in PAA (mathbf{X}^{ast} cap C_{u}(mathbb{R};mathbf {X}^{ast})) as in the case of the function (tmapsto[umapsto A t 0]) above with only some adaption of notations.

It is worth noting the following special or limit cases of the function Φ λ, μ ; ν ( z, s, a ).

There are two important special cases of the function E q ( x, a ) e q ( x ) = ∑ n = 0 ∞ x n ( q, q ) n, | x | < 1 (4).

In case of conflicts, the function of the complex structure is further examined by manual inspection.

For the radial form case of the Hamiltonian function, the characteristic function and the covariance matrix of the stationary response are calculated explicitly.

In particular, in case of the logarithmic function, the aggregate utility function appears to have relatively many local maxima.