Sentence examples for continuous partition from inspiring English sources

Let { β 0, β 1, …, β n } be a continuous partition of unity on X subordinated to the covering { V 0, V 1, …, V n }.

Since X is para-compact, there exists a continuous partition of unity {β0, β p : p ∈ LF(E)} for X subordinated to the open cover {V0, V p : p ∈ LF(E)}.

Since is paracompact, there exists a continuous partition of unity for subordinated to the covering (see Dugundji [22, Theorem VIII, 4.2]); that is, for any, and are continuous functions such that, for any, for all and for all and, is locally finite and for any.

Due to bandwidth fluctuations in the wireless environment, static partitionings in previous work are unsuitable for mobile platforms with a fixed bandwidth assumption, while dynamic partitionings result in high overhead of continuous partitioning for mobile devices.

In this note we discuss a novel graph partitioning problem, namely continuous graph partitioning, and we discuss its application to the design of surveillance trajectories for camera networks.

In continuous graph partitioning, each edge is partitioned in a continuous fashion between its endpoint vertices, and the objective is to minimize the largest load among the vertices.

We show that optimal trajectories can be designed via a continuous graph partitioning problem.

We show that the continuous graph partitioning problem is convex and non-differentiable, and we characterize a solution amenable to distributed computation.

Subsequently, as measured experimentally using the tomographical atom probe, continuous diffusional partitioning between the parent β- and product α-phases during isothermal annealing drives their compositions towards equilibrium.

The continuous graph partitioning problem naturally arises in the context of camera networks, where intruders appear at arbitrary locations and times, and the objective is to design camera trajectories for quickest detection of intruders.

Since any metric space is paracompact, there is a continuous locally finite partition of unity subordinated to the covering.