Sentence examples for discrete case for from inspiring English sources

While the continuous cases provide more intuitive extrema, derivation of the discrete case for higher moments is not as simple as deriving the continuous case and discretizing.

The results of Sections 2 and 3 are extendable directly to the discrete case for the sets and by replacing Lebesgue measures with discrete ones.

Now, consider another sequence that is related to by In the discrete case, for noninteger this is to be interpreted as a fractional sampling rate conversion as encountered in several areas of DSP.

The design of the teaching experiment articulates the static perspective of exponential covariation and a reformulation for the discrete case of the dynamic perspective of the covariation.

A remarkable generalization of the strong law of large numbers is the ergodic theorem: if X t), t = 0, 1,… for the discrete case or 0 ≤ t < ∞ for the continuous case, is a stationary process such that E[X(0)] is finite, then with probability 1 the average if t is continuous, converges to a limit as s → ∞.

In our earlier study [17], we have proposed a multi-stream HMM framework for the discrete case that integrate a stream relevance weight for each symbol in each state, and we have generalized the BW and the MCE/GPD training algorithms for this structure.

Our results unify and extend some continuous inequalities and for discrete case all are new.

On the contrary, in the 2 D discrete case inequality (1.2) holds for θ ∈ ( 0, 1 ] and also requires a logarithmic correction for θ = 0, see (1.6).

end{aligned} Using that fact the authors in [11] derived analogous results of Theorem 4.1 and Corollary 4.2 for discrete case.

Using that fact the authors in [11] derived the analogous results of Theorem 1.8 and Corollary 1.9 for discrete case, and here, similarly as in the previous section, we get the following results.

We want to check the expression derived by Van Nee in [8] for the conventional OFDM for the discrete case.