Sentence examples for derivations first from inspiring English sources

A ℂ-linear mapping d: A → B is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ: A → X such that d a2) = ad(a) + δ(a)a for all a ∈ A. Generalized derivations and generalized Jordan derivations first appeared in the context of operator algebras [18].

(The order is unimportant: one can go through the derivation first and then follow the soundness proof).

As we are aware, the stability of derivations was first investigated by Jun and Park [10].

The current FCA includes 18 QC measures (see Table 6) that have often, but not exclusively, evolved based on experience in applying the analysis, rather than from derivations from first principles.

In order to continue with our derivations, we first define a local flight (LF) frame of reference for the radar as shown in Figure 4, where is defined as the unit vector pointing down from the radar's center of gravity to the center of the earth.

The answer is not trivial: derivations from first principles and analysis of the assumptions and approximations have been provided only recently for interactions with ionized impurities  [23] and with phonons  [24].

While standard in statistical theory, in the context of applying IDR models, this derivation was first given by Hutmacher et al. The derivation allows the interpretation of M t) in Eq. 1 as a physiological variable, and consequently, the mechanistic consistency of applying IDR models to M t).

Its abstract derivation was first discovered by Fuchssteiner and Fokas [1], while in the physical derivation of Camassa and Holm (see [2, 3]), the equation models unidirectional propagation of shallow water waves, and   represents the fluid velocity in the   direction, equivalently the height of the fluid's free surface above a flat bottom.

The derivation is first presented for the AW-XWVD followed by the S-transform.

The derivation focuses first on developing an upper limit for the dynamically recrystallized grain size.

Theoretical derivation is first given for a general three-dimensional formulation.