Complete

Complete

Case Studies

Published in Arthur W. Lees, Vibration Problems in Machines, 2020

The modification, together with the introduction of damping in the second coupling, has proved very successful. The problem highlights the importance of designing a complete system, rather than just an assembly of components.

Optimal contraception control for a size-structured population model with extra mortality

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Journal Information

Published in Applicable Analysis, 2020

Rong Liu, Guirong Liu

Obviously, if is a fixed point of the map , then it is a solution of Equation (11) and vice versa. Define a new norm in by for some , which is equivalent to the usual norm. It is clear that is a Banach space; that is, is a complete metric space. Here for , . It is easy to see that maps into itself. Now, we show that is a contraction mapping on the complete metric space . For any , , we have Choose λ such that . Then is a contraction mapping on the complete metric space . By the Banach fixed-point theorem, owns a unique fixed point , which is the solution of Equation (11).

Path-based incremental target level algorithm on Riemannian manifolds

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Published in Optimization, 2020

Peng Zhang, Gejun Bao

Let be a sequence in the complete metric space . If is quasi-Fejér convergent to a set then is bounded and converges for all . If furthermore, a cluster point y of belongs to W, then .

Stochastic maximum principle for optimal control problem with a stopping time cost functional

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Published in International Journal of Control, 2022

Shuzhen Yang

Let be a continuous function on a complete metric space . Given and such that Then, there exists a such that and for all ,

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Case Studies

Optimal contraception control for a size-structured population model with extra mortality

Path-based incremental target level algorithm on Riemannian manifolds

Stochastic maximum principle for optimal control problem with a stopping time cost functional