Boundary value problem for . I: Existence and uniqueness.
We study the evolution of pluri-anticanonical line bundles along the Kähler Ricci flow on a Fano manifold . Under some special conditions, we show that the convergence of this flow is determined by the properties of the pluri-anticanonical divisors of . For example, the Kähler Ricci flow on converges when is a Fano surface satisfying or . Combined with the works in [CW1] and [CW2], this gives a Ricci flow proof of the Calabi conjecture on Fano surfaces with reductive automorphism groups....
In this paper, the output synchronization control is considered for multi-agent port-Hamiltonian systems with link dynamics. By using Hamiltonian energy function and Casimir function comprehensively, the design method is proposed to overcome the difficulties taken by link dynamics. The Hamiltonian function is used to handle the dynamic of agent, while the Casimir function is constructed to deal with the dynamic of link. Thus the Lyapunov function is generated by modifying the Hamiltonian function...
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