Sentence examples for following class of from inspiring English sources

It follows easily from Föllmer's pathwise Itô formula that for the following class of "basic admissible integrands" ξ, the Itô integral ({int _{r}^{t}}boldsymbol {xi }(s){,mathrm {d}}mathbf {S}(s)) exists for all t∈ [ r,u]⊂ [ 0,T] as the finite limit of Riemann sums in (2.4); see (Schied 2014, p. 86).

We consider the following class of unitary representationsπof some (real) Lie groupGwhich has a matched pair of symmetries described as follows: (i) SupposeGhas a period-2 automorphismτ, and that the Hilbert spaceH carries a unitary operatorJsuch thatJπ=J i.e.,selfsimilarity).

Geraghty [6] defined the following class of comparison functions.

It is natural to consider the following class of functions.

The following class of functions is used in [10].

In 1975 Matkowski introduced the following class of mappings.

In [7], Varošanec introduced the following class of functions.

Let us introduce the following class of mappings.

We introduce the following class of modified q-Bernstein polynomials.

In [22], Mubeen and Habibullah introduced the following class of fractional derivatives.

For our purpose, let us introduce the following class of optimal control problems [22].