Sentence examples for denotes the common from inspiring English sources

Further L denotes the common Lipschitz constant of T and S, and I denotes the identity mapping on an arbitrary Banach space X.

Let biglVert T_{i}^{j}x-pbigrVert leq k_{i,j} |x-p|, quad forall x in C, p in F, where F denotes the common fixed point set of ({T_{n}}_{n=0}^{N-1}), (lim_{jrightarrowinfty}k_{i,j}=1) for all (0leq i leq N-1).

Given the L subjects or segments, the l th segment is generated by X l l ) ≈ A r ( l ) S r ( l ) + A h ( l ) S h ( l ) where A r ( l ) denotes the common bases which capture the intra and inter-subject variations and A h ( l ) denotes the individual bases which reflect the residual information.

This valuation has the additively separable structure (upsilon (s_{j})=x+s_{j}); here x denotes the common consumers' valuation of the homogeneous good independent of store quality, ( s_{j}) is the supermarket's level of services or quality (Wildenbeest 2011), and (p_{j}) is the basket's price.

Theorem 1. (Uniqueness of quadrilinear decomposition) [25] Consider that a matrix representation of X - is X = (A ◇ B ◇ C D T, where A ∈ C I × M, B ∈ C J × M, C ∈ C K × M and D ∈ C L × M are the four mode matrices of X -, and M denotes the common dimension.

Let us denote by (P_{l_1}=P_{s_1} cdot P_{s}) and (P_{l_2}=P_{s}2}cdothe_{s}) the failure probabilities of these two links, respectively, where (P_{s}) denotes the common SRLGs' failure probability between (l_1) and (l_2), and (P_{s_1}) ((P_{s_2})) is the non-overlapping SRLGs' failure probability of (l_1) ((l_1)).

(b) The black empty circles denote the common photoinduced current as a function of excitation wavelength.

Denote the common distribution and density of {X i : i ≥ 1} by F and f, respectively.

Thus, ϕ Tx t)=ϕ Rx t), and we denote the common phase noise process by ϕ(t).

They proved that if the sequence is bounded above from one, then the sequence generated by (1.5) converges strongly to, where denote the common fixed points set of.

Let (Gamma _{kl}) denote the common facet of (Omega _k) and (Omega _l), and note that (n_k{mid _{Gamma _{kl}}}=-n_l{mid _{Gamma _{kl}}}).