Sentence examples for by the random variables from inspiring English sources

When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters.

Let H ( ε k * ) be the Hilbert space spanned by the random variables { ε k * }.

On the other hand, the occurrence of the ROIDs (x k-tau_{m}(k))) is characterized by the random variables (beta_{m}(k)) in a probabilistic way, which is more suitable for reflecting the network-induced phenomena.

Note that G ( x ) is a limit distribution of a residual waiting time of a renewal process generated by the random variables having the Weibull distribution with parameters ( α, 1 ).

Recalling that { X n, n ≥ 1 } is a sequence of random variables and F a b denotes the σ-field generated by the random variables X a, X a + 1, …, X b.

The elements of such a basis take the form ε k = ∫ T x ( t ) ϕ k * ( t ) F ( t ) d t a.s., and let H(ε k ) be the Hilbert space spanned by the random variables {ε k }.

Discretization of a stochastic program is usually performed by substituting the random variables by constant values.

(b Gaussian kernels obtained by changing the random variables of the kernels in (a).

Note that, by (29), the random variables concerned in (14) and (28) have finite moments of each order.

By redefining the random variables, we obviate the unrealistic dropout assumption.

The general form of these models is given by: (1) The random variables Z i are the latent variables representing the unexplained variation in each node.