Sentence examples for a wide class of functions from inspiring English sources

It is based on the fact that for a wide class of functions, all three definitions of the fractional derivatives are equivalent [4].

These differential equations model the dielectric properties of composites for a wide class of functions describing the interphase inhomogeneity and are shown to coincide with the equation obtained using DEDA [Yu KW, Gu GQ, Huang JP. Dielectric response of spherical particles of graded materials. cond-mat/0211532; 2002].

The gauge function is used to generalize the Riemann integral for a wider class of functions.

(K_{n}^{ast}(f;x)) allows a wider class of functions than the operator (K_{n}(f;x)).

By using the gauge function, the generalized mass function is defined so that it can be used for a wider class of functions on fractal sets.

In this article, we have provided a rigorous proof of the Hardy-Ramanujan theorem for a wider class of functions than was previously available.

In fact, Hardy had noted that the theorem should apply to a wider class of functions but had then provided the extension.

Comparing these statements with the results of Theorem 5 from paper [4], we see that if Φ is a non-negative function, then we have results for a wider class of functions Φ, i.e., for h-concave or h-convex functions.

We prove that the criterion of Yuan and Shu can be satisfied by a wide class of basis functions, including the well-known basis functions such as trigonometric and exponential polynomials.

It is known that a wide class of mathematical functions can be well approximated by rational functions of the form (4.1) (see, e.g. [ 37]).

The Smooth Sigmoid-Based Shrinkage (SSBS) functions introduced in [1] constitute a wide class of WaveShrink functions.