Sentence examples for under sums from inspiring English sources

Moreover, since e commutes with arbitrary sums, the full subcategory in ({text {Ho}}(mathsf{Ind},mathcal {C}_0)) spanned by objects (E') with ({text {Hom}}(E',widetilde{E})) is closed under sums, and then by Lemma 12.7, it coincides with the whole ({text {Ho}}(mathsf{Ind},mathcal {C}_0)).

Zhao et al. [22] investigated robust beamforming design of sum secrecy rate optimization under sum power constraint for multiple user-eavesdropper pairs, and a low complexity zero-forcing (ZF) beamformers is developed.

When speaking about some challenging physical conditions her foundation works under, Andrea sums it up by saying “the rewards of our work outweigh all the difficulties.”.

We present two methods for dynamically updating Minkowski sums under scaling, the first of which updates the sum under uniform scaling of arbitrary polygons and polyhedra, and the second of which updates the sum under non-uniform scaling of convex polyhedra.

Lawrence Summers, a former treasury secretary under Bill Clinton, summed it up well: "Incrementalism is not enough, we need full and fundamental reform.

We develop polynomial time algorithms for minimum cost network connection with paths or spanning trees under risk-sum constraints.

We consider the detection performance of the waveform under the sum power constraint and maximum individual power constraint.

All the existing beamforming designs in [1 19] were developed under a sum-power constraint across all transmit antennas.

However, in the cooperative case, power allocation can be clearly performed under either sum power constraint or individual power constraint for each user.

Several power optimization strategies were proposed to maximize the system throughput under a sum power constraint; a subchannel pairing scheme was further proposed to improve the system throughput.

As shown in Figure  1, the transmit power fluctuates as much as 4 W in the transmit antenna under the sum power constraint.