Sentence examples for denotes the identical from inspiring English sources

non-negative random variables such that Y and X in (1.1) are identically distributed, then S_{n} stackrel{d}sum_{j=1}^{N_{1}+N_{2}+cdots+N_{n}}Y_{j}, where (stackrel{d}) denotes the identical distribution.

The mapping (alphamathrm{id}_{X}+z) is a ≽-preserving self-mapping on X for every (zin X) and positive number α, where (mathrm{id}_{X}) denotes the identical mapping on X.

The condition inf Ω × R f u ′ ( x, u ) > − λ implies that zero is not an eigenvalue of Δ ϕ − f u ′ ( x, u ) ϕ = 0, so for every u ∈ W 2, 0 2 , the operator P ′ ( u ) = Δ u − f u ′ I is invertible and P is a local homeomorphism from W 2, 0 2 onto L 2 , where I denotes the identical operator.

(ii) The mapping (alphamathrm{id}_{X}+z) is a ≽-preserving self-mapping on X for every (zin X) and positive number α, where (mathrm{id}_{X}) denotes the identical mapping on X.   (iii) The norm (|cdot|) on X is compatible with the partial order ≽, that is, (|x|succcurlyeq|y|) implies (|x|geqslant| y|), where (|z|= zveemathbf{0})+ -zveemathbf{0})) for every (zin X) and 0 denotes the origin of X.  .

We denoted by l = 1.Nm ( = 3) the model, j = 1.Np the jth parameter in the parameter set of size Np and i = −Na.+Na the ith perturbation to each parameter, where Na is the number of positive/negative perturbations and i = 0 denotes the unperturbed parameter values (identical to the optimised reference parameters).

where R C denotes the number of tags per slot with identical colour.

where γ ∈ ( 0, 2 / L ) and L denotes the largest eigenvalue of the matrix A T A, I is the identical matrix.

where represents a series of independent and identical Gaussian random variables and the superscript denotes the vector transpose.

Here k sim denotes the number of overlapping positions where the reads have an identical base and k dissim is the number of positions where they are different.

The term in braces denotes the set of the pattern classes summarized in Table 3, including those which are identical after permutation of τ bits (pattern tolerance).

G(f d ) denotes the Fourier transform of the function which represents the antenna pattern and other time-variant characters (identical to all receiving antennas).