Sentence examples for finite composition from inspiring English sources

Definition 10 We say that a function is elementary if it is a finite composition of rational, algebraic, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic and inverse hyperbolic functions.

Assume that X and Y are ANRs in normed spaces with ({mathcal{E}}(Y neq0), and let (Phi Xrightrightarrows Y) be a map admitting a decomposition as a finite composition of u.s.c.s.c

Advances in Chemical Engineering, 23, 63 170) we can confine all geometric manipulations when proposing alternative reactive distillation processes to a finite composition domain by combining the vectors in a different order.

We show how to carry out all geometric constructions entirely within a finite composition domain by decomposing the total stoichiometric coefficient vector into product and reactant stoichiometric coefficient vectors.

(X_{rho}) is compact non-empty and the map (Psi_{rho}) is l.s.c. and has non-empty compact convex values on (X_{rho}); the restriction of the map Φ to (X_{rho}) admits a decomposition as a finite composition of u.s.c.s.c

Assume, furthermore, that (existsrho_{0}>0) such that (forallrho geq rho_{0}): (iii) (X_{rho}) is compact non-empty and the map (Psi_{rho}) is l.s.c. and has non-empty compact convex values on (X_{rho});   (iv) the restriction of the map Φ to (X_{rho}) admits a decomposition as a finite composition of u.s.c.s.c

Given a class of maps, denotes the set of maps (nonempty subsets of ) belonging to, and the set of finite compositions of maps in.

To see the relationship between zeros of polynomials with integer coefficients and M, note that finite compositions f σ | k ( z ) of the maps in F λ give rise to polynomials of the form f σ | k ( z ) = ( λ z ) k + ∑ l = 0 k − 1 ( σ l + 1 − 1 ) λ l, where each coefficient ( σ l + 1 − 1 ) is 0 or 1.

However, two barriers are encountered when using matrix groups for finite motion composition in formulating topological models.

The other barrier comes from the incompetent to algebraically compute the finite motion composition result of matrix groups by using the Baker-Campbell-Hausdorff formula.

Moorhouse [7] considered the compactness of finite sum of composition operators on weighted Bergman spaces in the disk and gave a partial answer to the component structure of C ( A α 2 ).