Let X be a compact complex manifold and L → X a positive holomorphic line bundle. Assume that Aut(X,L)/C× is discrete, where Aut(X,L) is the group of holomorphic automorphisms of the pair (X,L). Donaldson [D] has recently proved that if X admits a metric ω ∈ c1(L) of constant scalar curvature, then (X,L) is Hilbert-Mumford stable for k sufficiently large. Since Kähler-Einstein metrics have cons...

The lattice hydrodynamic model is presented to take into account the passing effect in one-dimensional traffic flow. When the passing constant gamma is small, the conventional jamming transition occurs between the uniform traffic and kink density wave flows. When passing constant gamma is larger than the critical value, the jamming transitions occur from the uniform traffic flow, through the ch...

The use of " ideal " optimal test functions in a Petrov-Galerkin scheme guarantees the discrete stability of the variational problem. However, in practice, the computation of the ideal optimal test functions is computationally intractable. In this paper, we study the effect of using approximate, " practical " test functions on the stability of the DPG (discontinuous Petrov-Galerkin) method and ...

To deal with stochastic hybrid systems general state-dependent switching, we propose an approximation method by a sequence of piecewise constant type switching. The convergence rate in the Wasserstein distance is estimated terms difference between transition matrices. Our based on elaborate construction coupling processes Skorokhod’s representation theorem for jumping processes. Moreover, estab...