Sentence examples for generalized differentiation from inspiring English sources

Loss of Dido3 expression nonetheless does not produce a generalized differentiation blockade, corroborated by the observation that Dido3ΔCT-RFP ES cells differentiate in response to retinoic acid and form all three germ layers in the teratoma assay.

Furthermore, we develop the necessary optimality conditions (see Theorem 4.4) for the problem (3.4) using generalized differentiation calculus of Mordukhovich.

Using the generalized differentiation calculus of Mordukhovich, the first-order necessary optimality conditions are established in the smooth setting.

Using the analysis tools from modern variational and generalized differentiation developed by Mordukhovich, first-order necessary and sufficient optimality conditions were established.

The generalized differentiation in our study is Mordukhovich's coderivative [4], which plays an important role in characterizations of metric regularity and openness properties of set-valued mappings; see [9] and the references therein.

Following Saigo et al. [18] and Saxena and Saigo [21], the left-hand sided and right-hand sided generalized differentiation for a power function are, respectively, given as follows (see, [24, p. 7, Eqs.

In a generalized vertical differentiation framework, the equilibrium line is exactly the same as the first-best socially optimal line.

Then the generalized fractional differentiation operators involving the Appell function F 3 in the kernel are defined as follows (see [20]): ( D 0 + α, α ′, β, β ′, γ f ) ( x ) = ( I 0 + − α ′, − α, − β ′, − β, − γ f ) ( x ) (1.7).

Secondary involvement of liver by lymphoma is relatively easier to diagnose on imaging due to the concomitant involvement of other organs especially spleen and generalized lymphadenopathy, although differentiation with disseminated granulomatous infection may sometimes be difficult.

The generalized concept of differentiation of distributions shifts the operations to test functions γ : R n × R + ⊃ G → R (G open) which are infinitely differentiable and have a compact support (meaning that for each γ there exists a closed and bounded subset K such that γ ( x, t ) = 0 for all x ∈ G ∖ K ).

The generalized expression of differentiation genes in this population is, at this moment, more difficult to explain.