In [1], a new state sum model (the “balanced” model) was suggested as a quantum theory of gravity. In [2], a proposal was made to construct a geometrical interpretation of it, and to demonstrate that it gives general relativity in the classical limit. The purpose of this note is to make several advances in the interpretation of the balanced model. First, we outline a shortcoming of the definiti...

A switched sliding mode control strategy for a class of nonlinear uncertain systems is presented in this paper. It is characterized by an event– driven gain reduction mechanism which relies on a decomposition of the system state into regions. By enforcing sliding mode behaviors on a suitable set of sliding manifolds, while avoiding the generation of limit cycles, the proposed strategy proves to...

The continuum and semiclassical limits of isotropic, spatially flat loop quantum cosmology are discussed, with an emphasis on the role played by the Barbero–Immirzi parameter γ in controlling space-time discreteness. In this way, standard quantum cosmology is shown to be the simultaneous limit γ → 0, j → ∞ of loop quantum cosmology. Here, j is a label of the volume eigenvalues, and the simultan...

Abstract We show that even if a Hilbert space does not admit reproducing kernel, there could still be kernel function realizes the Riesz representation map. Constructions in spaces are Fourier transform of weighted L 2 {L}^{2} given. With mild assumption on weight func...

Abstract It is proved that the normalized $$L^2$$ L 2 metric on moduli space of n -vortices a two-sphere, endowed with any Riemannian metric, converges uniformly in Bradlow limit to Fubini–Study metric. This establishes, rigorous setting, longstanding informal conjectur...