We prove lower semicontinuity and lower bounds for a Chen-Lubensky energy describing nematic/smectic liquid crystals with physically realistic boundary conditions. The Chen-Lubensky energy captures stable phases of the liquid crystal material, ranging from purely nematic or smectic states to coexisting nematic/smectic states. By including appropriate additional terms, the model includes the eff...

A renormalizable rigid supersymmetry for the four dimensional antisymmetric tensor field model in a curved space–time background is constructed. A closed algebra between the BRS and the supersymmetry operators is only realizable if the vector parameter of the supersymmetry is a covariantly constant vector field. This also guarantees that the corresponding transformations lead to a genuine symme...

The e ect from polarization of emitted wave fronts on the parameter estimation ac curacy for an array composed only of sensors sensitive to just one polarization direction has not been addressed in the literature this far Antennas with such characteristics are e g dipole or scalar antennas A vector sensor on the other hand is a sen sor whose output data consists of for the electromagnetic case ...

In this correspondence, we estimate the Hurst parameter H of fractional Brownian motion (or, by extension, the fractal exponent 9 of stochastic processes having 1/ f +‘-like spectra) by applying a recently introduced multiresolution framework. This framework admits an efficient likelihood function evaluation, allowing us to compute the maximum likelihood estimate of this fractal parameter with ...

We consider nite-state Markov chains that can be naturally decomposed into smaller \projection" and \restriction" chains. Possibly this decomposition will be inductive, in that the restriction chains will be smaller copies of the initial chain. We provide expressions for Poincar e (respectively, log-Sobolev) constants of the initial Markov chain in terms of Poincar e (respectively, log-Sobolev)...

Consider i.i.d. percolation with retention parameter p on an infinite graph G. There is a well known critical parameter pc ∈ [0, 1] for the existence of infinite open clusters. Recently, it has been shown that when G is quasi-transitive, there is another critical value pu ∈ [pc, 1] such that the number of infinite clusters is a.s. ∞ for p ∈ (pc, pu), and a.s. one for p > pu. We prove a simultan...

* This work is supported by NSF Grant #10672045 to Yu Kaiping Abstract—The key of fast identification algorithm of time-varying modal parameter based on subspace tracking is to find efficient and fast subspace-tracking algorithm. This paper presents a modified version of NIC(Novel Information Criterion) adopted in two-layer linear neural network learning for subspace tracking, which is applied ...