Sentence examples for being a positive integer from inspiring English sources

Let (a_{1},ldots,a_{k}) be arbitrary complex numbers with k being a positive integer.

For the sake of simplicity, we will assume that the prototype filter length, denoted, is such that, with being a positive integer.

The least mean-fourth (LMF) [3] algorithm was also proposed later as a special case of the more general family of steepest descent algorithms [4] with 2k error norms, k being a positive integer.

In fact, for p (≥2) being a positive integer, we can find a function X ( x ) ∈ F and a positive real function M ( x ) satisfying lim sup x → ∞ X ( log M ( x ) ) log x = A ( 0 < A < ∞ ). and lim sup x → ∞ log p ( log M ( x ) ) log x = ∞ and lim sup x → ∞ log p + 1 ( log M ( x ) ) log x = 0.

In addition, (gamma_{ij}(s)) satisfies begin{aligned} gamma_{ij}(s) = textstylebegin{cases} gamma_{i}(s), & i=jtext{ and } 1leq i leq K leq N, c_{ij}, & text{otherwise}, end{cases}displaystyle end{aligned} (27) with (gamma_{i}(s)) being an arbitrary function of s and K being a positive integer.

In this section, we will consider the multiobjective noncooperative game in its strategic form Γ = ( X i, V i ) i ∈ I, where I = { 1, 2, …, n } is the set of players; every X i is the strategy set of the i th player and every V i : X = ∏ i ∈ I X i → R k i is the payoff function of the i th player with k i being a positive integer.

Let v be a positive integer and let K be a set of positive integers.

Let $X$ be the modular curve $X_0 N $, where $N$ is a positive integer.

Let υ be a positive integer, and K and M be two sets of positive integers.

Let q be a prime power and a be a positive integer such that a⩾2.

Further, is a positive integer.