Sentence examples for the definite function from inspiring English sources

However, the definite function(s) and mechanism of MAPs with respect to mitochondria or apoptosis have not been clarified yet.

Although the definite functions of the Gli family members are unclear, there is rising evidence for a predominantly transcription-activating function of Gli1 and Gli2 [ 13, 14].

While the definite functions of ABCA7 and ABCD4 are unknown, ABCC5 is a member of the MRP (multi-resistance protein) subfamily and may contribute to resistance of certain anti-cancer and anti-HIV drugs [ 42- 44].

Although the definite functions of the seven P450s and seven UGTs from B. chinense identified in the present study still have to be verified by further experiments, the isolation of their full-length cDNAs will be significant for elucidating their biofunctions in the growth and development of B. chinense.

The obvious difference of the proposed theory with the fractional Lyapunov direct theory is taking the integer derivative instead of the fractional derivative of the positive definite function V. Four examples are provided to illustrate the proposed theorem.

(See Chapter 5 in [9] for some basic properties of the positive definite function).

This measure is supported ϵ -away from A. Define the positive definite function F = μ ∗ ϕ ϵ / 2 which is supported in Ω (in fact ( ϵ / 2 ) -away from the boundary).

We will show that the positive definite function ϕ ϵ ∗ μ = ϕ ϵ ∗ G + h ϵ ( d - 1 ) / 2 ϕ ( x / ϵ ) (3 converges uniformly to f on R d as ϵ → 0. First, observe that ϕ ϵ ∗ G ( x ) = ϕ ϵ ∗ f ( x ) if dist ( x, ∂ Ω ) > 2 ϵ, hence ϕ ϵ ∗ G → f uniformly in R d, as both f and G are o ( 1 ) at distance 2 ϵ from the boundary (as ϵ → 0 ).

They encode the representation theory of the group via the positive definite functions on the group: positive definite functions correspond to cyclic representations and span these algebras as linear spaces.

For unitary representations we show that a vector v is smooth if the corresponding positive definite function ⟨π(g)v,v⟩ is smooth.

The semi-positive definite function V1 is dependent on first m state variables which can be steered along the given vector fields and V2 is dependent on the remaining n−m state variables which can be steered along the missing Lie brackets.