Sentence examples for denotes the composition of from inspiring English sources

In the equations above, (bigodot _{l=1}^{L}) denotes the composition of L functions.

where (bigodot _{l=0}^{L}) denotes the composition of L+1 functions.

φ ( 1 ) = 1 ; lim n → + ∞ φ n ( t ) = 1 for all t ∈ ( 0, 1 ), where φ n ( t ) denotes the composition of φ ( t ) with itself n times.

Hence, (varphicircpsi^{-1} phi =f), where (psi^{-1}) is the invarphicircpsi^{-1} phi =fnd (varphicirc psi^{-1}) denotes the composition of φ and (psi^{-1}).

If φ is a comparison function, then (i) φ ( 1 ) = 1 ;   (ii) lim n → + ∞ φ n ( t ) = 1 for all t ∈ ( 0, 1 ), where φ n ( t ) denotes the composition of φ ( t ) with itself n times.  .

Let Φ denote the composition of (Phi^) from diagram (10) and ψ̂.

For (beta in B), let (pi _beta ) denote the composition of the canonical projection (G longrightarrow G/N_beta ) with (phi _beta ).

By (D^{k}) we will denote the composition of (exactly) k differentiation operators, that is, if (fin H {mathbb {D}})), then D^{k} f=underbrace{Dbigl(Dbigl(cdots(D}_{ktext{-times}}f cdots bigr bigr).

At this level, variables that denoted the composition of the family were: children who were 1 year old or younger, and children who were 7 years old or younger, as well as adults 65 years old or older.

Hexagons denote the compositions of volcanic gases in the literature; SS: Showa-Shinzan (Mizutani and Sugiura, 1982), US: Usu (Giggenbach and Matsuo, 1991), MI: Miyakejima (Shinohara et al., 2003b), SI: Satsuma-Iwojima (Shinohara et al., 2002), KU: Kudryavy (Taran et al., 1995).

Here, ∘denotes the composition of functions.