Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter

In this work we study connections between various asymptotic properties of the nonlinear filter. It is assumed that the signal has a unique invariant probability measure. The key property of interest is expressed in terms of a relationship between the observation σ field and the tail σ field of the signal, in the stationary filtering problem. This property can be viewed as the permissibility of the interchange of the order of the operations of maximum and countable intersection for certain σ-fields. Under suitable conditions, it is shown that the above property is equivalent to various desirable properties of the filter such as

(a) uniqueness of invariant measure for the signal,

(b) uniqueness of invariant measure for the pair (signal, filter),

(c) a finite memory property of the filter,

(d) a property of finite time dependence between the signal and observation σ fields and

(e) asymptotic stability of the filter.

Previous works on the asymptotic stability of the filter for a variety of filtering models then identify a rich class of filtering problems for which the above equivalent properties hold.     

病毒感染群体动力学模型分析

本文构建并讨论了一类病毒感染的群体动力学模型,得到了模型存在轨道稳定周 期解的充分条件,较好地解释了在病毒持续感染者体内观察到的病毒载量波动现象.     

欧氏空间和球面子流形中Yang-Mills场的一类不稳定性结果

本文就欧氏空间和球面中紧致子流形的Yang-Mills场进行了讨论.得到了一类不稳定性结果.     

Optimally Stable Multivariate Bases

We show that the tensor product B-spline basis and the triangular Bernstein basis are in some sense best conditioned among all nonnegative bases for the spaces of tensor product splines and multivariate polynomials, respectively. We also introduce some new condition numbers which are analogs of component-wise condition numbers for linear systems introduced by Skeel.     

Optical and electric properties of Nb-doped anatase TiO2 single crystal

Nb-doped anatase TiO₂ single crystal has been grown by chemical vapour transport method. Raman spectra shows that the obtained crystal with Nb of 0.08 wt% has typical anatase structure. An absorption band was observed at around 2.2 eV, which seems to be due to the d-d transition in the conduction band. The electron paramagnetic resonance and electric resistivity measurements show that the doped niobium makes quite shallow donor level whose orbital is d_xy-like centered at the titanium position of anatase.     

An optical fibre pH sensor based on dye doped mesostructured silica

This paper describes the synthesis and optical pH sensing properties of a pH indicator dye activated mesostructured silica coated optical fibre. The pH-sensitive dye bromothymol blue was incorporated into the mesostructure sol precursor and thin films/coatings were used for pH-sensing applications without prior removal of the surfactant. The pH sensitivity range and operating wavelength were analysed by absorption measurements on layer dip-coated on glass slides. The pH sensing properties of coated optical fibre were tested by evanescent wave method. Experiments were carried out by using a series of solutions of known pH. No leaching was observed (except at very high pH) and an excellent reversibility was obtained between pH=2 and 5.     

Optical absorption of lithium metal vapor at high temperatures

Experimental results are reported for a unique spectroscopic device called the Plasma Spectroscopy Cell. Optical absorption of lithium metal vapor was observed at high density and temperature. Absorption spectra are analyzed using theoretical calculations of absorption cross sections for lithium-helium interactions, and singlet and triplet state transitions of diatomic lithium in the visible spectral range. This is believed to be the most complex example yet calculated in which absolute bound-bound, bound-free, free-bound, and free-free contributions for all possible optically allowed transitions are all included, in quite respectable agreement with experiment.     

A Stability Estimate for a Solution to a Three-Dimensional Inverse Problem for the Maxwell Equations

We consider the problem of determining dielectric permittivity and conductivity in the Maxwell equations. As additional information we prescribe the traces of the tangential components of the electromagnetic field on the lateral surface of a cylindric domain. We establish a stability estimate for a solution to the inverse problem and a uniqueness theorem.     

Convergence of Computational Methods and Stability of Self-Balanced Stresses under Shrinkage of Spherical Inclusions of a Damageable Material

Some iterative methods for calculating self-balanced stresses under shrinkage of a ball inclusion enclosed in a spherical matrix of a physically nonlinear damageable material. The stability of this system was studied using methods of catastrophe theory. It has been established that the beginning of divergence of the proposed iterative processes coincides with the moment of transition of the system to an unstable position of equilibrium.     

Low noise double pass L-band erbium-doped fiber amplifier

A new double pass long wavelength band erbium-doped fiber amplifier with enhanced noise figure characteristics is demonstrated. The noise figure is improved by about 2.6 dB with the incorporation of broadband conventional-band fiber Bragg grating (FBG) in between the two segments of erbium-doped fiber. By incorporating both the pre-amplifier and the FBG, the noise figure is further improved, which varies from 4.0 to 5.0 dB in the flat gain region from 1570 to 1600 nm. The gain varies from 32.0 to 33.4 dB within this region. The new amplifier with high gain and low noise figure can be useful as an inline amplifier in a wavelength division multiplexing transmission system.