Simulation and experimental research on polymer fiber mode selection polished coupler

Multimode dispersion is the main obstacle for high bandwidth in multimode optical fiber （MMF） communication system. Mode selection is an effective method to oppress multimode dispersion. We propose and investigate a kind of polymer optical fiber polished coupler. Beam propagation method （BPM） is employed to calculate the coupling coefficient of transmission modes in MMF coupler, and an output pattern from coupling branch is obtained. Analysis and experiment show that this coupler can select certain modes by changing polished depth, contact area, and intersection angle of two branches, which means that the device can be employed both as a mode selector and a sensor. In addition, simulation shows that five times bandwidth enhancement may be realized by selecting modes with the polymer fiber polished coupler.     

An approach of open-path gas sensor based on tunable diode laser absorption spectroscopy

Tunable diode laser absorption spectroscopy (TDLAS) is a new method to detect trace-gas qualitatively or quantificationally based on the scan characteristic of the diode laser to obtain the absorption spectroscopy in the characteristic absorption region. A time-sharing scanning open-path TDLAS system using two near infrared distributed feedback (DFB) tunable diode lasers is designed to detect CH4 and H2S in leakage of natural gas. A low-cost Fresnel lens is used in this system as receiving optics which receives the laser beam reflected by a solid corner cube reflector with a distance of up to about 60 m. High sensitivity is achieved by means of wavelength-modulation spectroscopy with second-harmonic detection. The minimum detection limits of 1.1 ppm·m for CH4 and 15 ppm·m for H2S are demonstrated with a total optical path of 120 m. The simulation monitoring experiment of nature gas leakage was carried out with this system. According to the receiving light efficiency of optical system and detectable minimum light intensity of detection, the detectable optical path of the system can achieve 1 - 2 km. The sensor is suitable for natural gas leakage monitoring application.     

On a conjecture of S.P. Robinson

In his thesis, S.P. Robinson made a conjecture concerning the polynomials

     

Bayesian Nonparametric Analysis for a Generalized Dirichlet Process Prior

This paper considers a generalization of the Dirichlet process which is obtained by suitably normalizing superposed independent gamma processes having increasing integer-valued scale parameter. A comprehensive treatment of this random probability measure is provided. We prove results concerning its finite-dimensional distributions, moments, predictive distributions and the distribution of its mean. Most expressions are given in terms of multiple hypergeometric functions, thus highlighting the interplay between Bayesian Nonparametrics and special functions. Finally, a suitable simulation algorithm is applied in order to compute quantities of statistical interest.     

Existence of limits of maximal means

For the class II(ℝ ^m ) of continuous almost periodic functionsf: ℝ ^m → ℝ, we consider the problem of the existence of the limit

On Some Generalizations and Refinements of a Ky Fan Inequality

In this paper, a Ky Fan inequality and an inequality by Wu and Wang [10] will be generalized. Some new and improved refinements of the Ky Fan inequality will be put forward.AMS Subject Classification (2000) 26D15     

Mixed means and inequalities of Hardy and Levin-Cochran-Lee type for multidimensional balls

Integral means of arbitrary order, with power weights and their companion means, where the integrals are taken over balls in centered at the origin, are introduced and related mixed-means inequalities are derived. These relations are then used in obtaining Hardy and Levin-Cochran-Lee inequalities and their companion results for -dimensional balls. Finally, the best possible constants for these inequalities are obtained.

     

The Functional Law of the Iterated Logarithm for the Empirical Process Based on Sample Means

Consider a double array of i.i.d. random variables with mean and variance and set . Let denote the empirical distribution function of Z_{1, n} ,..., Z _{N, n} and let be the standard normal distribution function. The main result establishes a functional law of the iterated logarithm for , where n=n(N) as N. For the proof, some lemmas are derived which may be of independent interest. Some corollaries of the main result are also presented.     

Lower estimate for the integral means spectrum for

In this paper we show that there exists a function bounded and univalent in the unit disk, such that ,

     

Two-weight norm inequalities for Cesàro means of Laguerre expansions

Two-weight norm inequalities are proved for Cesàro means of Laguerre polynomial series and for the supremum of these means. These extend known norm inequalities, even in the single power weight and ``unweighted' cases, by including all values of for all positive orders of the Cesàro summation and all values of the Laguerre parameter -1$">. Almost everywhere convergence results are obtained as a corollary. For the Cesàro means the hypothesized conditions are shown to be necessary for the norm inequalities. Necessity results are also obtained for the norm inequalities with the supremum of the Cesàro means; in particular, for the single power weight case the conditions are necessary and sufficient for summation of order greater than one sixth.