Sentence examples for bounded and the maximum from inspiring English sources

Moreover, (vert W_{1} vert ) is bounded, and the maximum of (lambda_{i}), (1 leq i leq p), decreases along the flow-lines of (W_{1}).

By the construction, (W_{1}) is bounded, and the maximum of (lambda _{i}(s)), (i=1, ldots, p), decreases along the flow lines of (W_{1}).

Furthermore, | W 1 | is bounded and the maximum of λ i 's decreases along the flow lines of  W 1. Proposition 3.4 For p ≥ 2, there exists a pseudo-gradient W 2 in V 2 ( p, ε ) such that ∀ u = ∑ i = 1 p α i δ ˜ i ∈ V 2 ( p, ε ), we have 〈 ∂ J ( u ), W 2 ( u ) 〉 ≤ − c ( ∑ i = 1 p 1 λ i n − 2 + ∑ i ≠ j ε i j + ∑ i = 1 p | ∇ H ( a i ) | λ i ), where c is a positive constant independent of u.

Furthermore, | W ˜ 1 | is bounded and the only case where the maximum of the λ i 's is not bounded is when a i ∈ B ( y l i, ρ ) ∀ i = 1, …, p with ( y l 1, …, y l p ) ∈ C n − 2 +.

Furthermore, we have | W 2 | is bounded and the only case where the maximum of λ i 's is not bounded is when a i ∈ B ( y l i, ρ ) ∀ i = 1, …, p with ( y l 1, …, y l p ) ∈ C n − 2 +.

The nodal pressure bounds and the pipeline maximum capacities can be found in [23].

Additionally, the elastically supported string critical speeds are bounded above, and the maximum critical speed is the upper bound of the divergent speed region.

Curvature (Fig. 2a), torsion (Fig. 2b) and climb angle ( Fig. 2c) functions are continuous and bounded by the maximum ({kappa _{mathrm{max}}}), ({tau _{mathrm{max}}}) and ({theta _{mathrm{max}}}) values, respectively.

We develop an upper bound and the maximum probability of overestimation when there is an infinite buffer size after each station.

In [10], it is shown that the cut-set bound and the maximum achievable DF rate for this MIMO relay channel can be obtained as the solutions of convex optimization problems, which also holds if a half-duplex constraint is imposed and frequency division duplex (FDD) with an average power constraint is considered.

The end-to-end delay is bounded by the maximum and minimum expected delay dmax and dmin, respectively.