The test statistic of Williams is rewritten as the maximum of a finite number of standardized linear combinations of the means.
Next, the probability distribution of the peak sidelobe levels were identified by following a procedure in which the peak sideload level was determined as the maximum among a finite number of independent random sidelobe levels.
Moreover, when (S A,mathbf{b})) is nonempty, the principal solution (hat{mathbf{x}}) becomes the maximum solution and (S A,mathbf{b})) can be determined by the maximum solution and a finite number of minimal solutions.
Moreover, the Hessian at the global maximum (minimum) only possesses a finite number of negative (positive) non-zero eigenvalues and the sum of the corresponding eigenvalues is bounded from below (above).
Like most random-search algorithms, under assumptions that are easily satisfied, the SA algorithm earlier allows us to reach an arbitrary neighborhood (in terms of criterion value) of a global maximum of J α in a finite number of iterations almost surely; see, for example, 31.
Nash [4] firstly defined the best response correspondence and applied the Berge maximum theorem and Kakutani fixed point theorem to prove the existence of Nash equilibrium points in finite games, where finitely many players may choose from a finite number of pure strategies in finite-dimensional Euclidean spaces.
By definition there are a finite number of hash values, which would correspond to the maximum possible number of clusters in the data.
Due to the finite number of unit cells in real-world PhCs, the maximum reflectivity and the width of the PBG are strongly influenced by the number of unit cells and the contrast in refractive index between the layers.
As an alternative, we use non-parametric maximum likelihood (NPML) estimation where the distribution of β i is discrete on an unknown finite number K of mass points z k, with masses π k.
"So there's a finite number".
