A remark on the Hard Lefschetz Theorem for K\"ahler orbifolds

We give a proof of the hard Lefschetz theorem for orbifolds that does not involve intersection homology. This answers a question of Fulton. We use a foliated version of the hard Lefschetz theorem due to El Kacimi

Single-photon transport in a one dimentional waveguide coupling to a hybrid atom-optomechanical system

We explore theoretically the single-photon transport in a single-mode waveguide that is coupled to a hybrid atom-optomechanical system in a strong optomechanical coupling regime. Using a full quantum real-space approach, transmission and reflection coefficients of the propagating single-photon in the waveguide are ob- tained. The influences of atom-cavity detuning and the dissipation of atom on the transport are also studied. Intriguingly, the obtained spectral features can reveal the strong light-matter interaction in this hybrid system.Comment: 7pages, 8figure

Crucible cast from beryllium oxide and refractory cement is impervious to flux and molten metal

Crucible from a mixture of a beryllium oxide aggregate and hydraulic refractory cement, and coated with an impervious refractory oxide will not deteriorate in the presence of fused salt- molten metal mixtures such as uranium- magnesium-zinc-halide salt systems. Vessels cast by this process are used in the flux reduction of oxides of thorium and uranium

Non-fragile H∞ control with randomly occurring gain variations, distributed delays and channel fadings

This study is concerned with the non-fragile H∞ control problem for a class of discrete-time systems subject to randomly occurring gain variations (ROGVs), channel fadings and infinite-distributed delays. A new stochastic phenomenon (ROGVs), which is governed by a sequence of random variables with a certain probabilistic distribution, is put forward to better reflect the reality of the randomly occurring fluctuation of controller gains implemented in networked environments. A modified stochastic Rice fading model is then exploited to account for both channel fadings and random time-delays in a unified representation. The channel coefficients are a set of mutually independent random variables which abide by any (not necessarily Gaussian) probability density function on [0, 1]. Attention is focused on the analysis and design of a non-fragile H∞ outputfeedback controller such that the closed-loop control system is stochastically stable with a prescribed H∞ performance. Through intensive stochastic analysis, sufficient conditions are established for the desired stochastic stability and H∞ disturbance attenuation, and the addressed non-fragile control problem is then recast as a convex optimisation problem solvable via the semidefinite programme method. An example is finally provided to demonstrate the effectiveness of the proposed design method

Neural network prediction of geomagnetic activity: a method using local H\"{o}lder exponents

Local scaling and singularity properties of solar wind and geomagnetic time series were analysed using H\"{o}lder exponents $\alpha$. It was shown that in analysed cases due to multifractality of fluctuations $\alpha$ changes from point to point. We argued there exists a peculiar interplay between regularity / irregularity and amplitude characteristics of fluctuations which could be exploited for improvement of predictions of geomagnetic activity. To this end layered backpropagation artificial neural network model with feedback connection was used for the study of the solar wind - magnetosphere coupling and prediction of geomagnetic $D_{st}$ index. The solar wind input was taken from principal component analysis of interplanetary magnetic field, proton density and bulk velocity. Superior network performance was achieved in cases when the information on local H\"{o}lder exponents was added to the input layer.Comment: 17 pages, 7 figure