Sentence examples for sets of generating from inspiring English sources

To continue the study of this approach, in here, we state and prove that the presentation which has the minimal number of generators of the split extension of two finite monogenic monoids has different sets of generating functions (such that the number of these functions is equal to the number of generators) that represent the exponent sums of the generating pictures of this presentation.

In this paper, a finite characterization of CDL extensions using sets of generating defaults is given.

10.7554/eLife.04250.005 Figure 4. Two sets of generated synthetic data, one with spatially dependent connectivity and one without.

Based on above definition, we introduce the following definition in the setting of generating space of b-quasi-metric family.

Theorem 2.7 The inefficient but minimal presentation P M defined in (7) has a set of generating functions.

Theorem 2.12 The efficient presentation P M in (7) has a set of generating functions in terms of Stirling numbers as given in (13).

Inspired by the above definition, we introduce the (G_{bd} -cyclic-Kannan contraction in the settinG_{bd} -cyclic-Kannan of a b-dislocated metric family.

Corollary 3 The presentation P M in (12) has a set of generating functions in terms of Stirling numbers as given in (18).

If we use n weights (w_{1}, ldots, w_{n}) in the definition of the generating functions of Euler polynomials, then the symmetric group (S_{n}) naturally acts on a prescribed set of generating functions of the Euler polynomials.

Extreme pathways are a set of generating vectors that describe the conical steady-state solution space for flux distributions through an entire metabolic network.

Random error was added to the set of generated artificial data.