Novel Optical Fiber Gas Sensor for On-line Measurement of Methane

Based on analysis of near infrared spectral absorption of methane,absorption type optical fiber methane gas sensor with high sensitivity using DFB LD as a source is demonstrated. Light source modulation harmonic measurement is presented in this paper. In order to eliminate the noise, the ratio of the fundamental and second-harmonic signals is used. The mathematical model of gas concentration harmonic measurement is built up.The detection result of methane concentration is also shown. Experiments have proved a sensitivity of 28×10-6.

Advances in shape measurement in the digital world

The importance of particle shape in terms of its effects on the behaviour of powders and other particulate systems has long been recognised, but particle shape information has been rather difficult to obtain and use until fairly recently, unlike its better-known counterpart, particle size. However, advances in computing power and 3D image acquisition and analysis techniques have resulted in major progress being made in the measurement, description and application of particle shape information in recent years. Because we are now in a digital era, it is fitting that many of these advanced techniques are based on digital technology. This review article aims to trace the development of these new techniques, highlight their contributions to both academic and practical applications, and present a perspective for future developments.

On quasi-similarity of subnormal operators

For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) in L2(v) and let Sv denote the operator of multiplication by the independent variable z on R2(K, v), that is, Svf = zf for every f∈R2(K, v). SupposeΩis a bounded open subset in the complex plane whose complement has finitely many components and suppose Rat(Ω) is dense in the Hardy space H2(Ω). Letσdenote a harmonic measure forΩ. In this work, we characterize all subnormal operators quasi-similar to Sσ, the operators of the multiplication by z on R2(Ω,σ). We show that for a given v supported onΩ, Sv is quasi-similar to Sσif and only if v/■Ω■σ and log(dv/dσ)∈L1(σ). Our result extends a well-known result of Clary on the unit disk.

Carleson Measures on Planar Sets

In this paper, we investigate what are Carleson measures on open subsets in the complex plane. A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles. We call a domain G multi-nicely connected if there exists a circular domain W and a conformal map ψ from W onto G such that ψ is almost univalent with respect the arclength on δW. We characterize all Carleson measures for those open subsets so that each of their components is multinicely connected and harmonic measures of the components are mutually singular. Our results suggest the extension of Carleson measures probably is up to this class of open subsets

On Pointwise Bounded Approximation

Let G be an open subset in the extended complex plane and let A（G） denote the algebra of all functions analytic on G and continuous on G. We call a domain multi-nicely connected if there is a circular domain W and a conformal map ~ from W onto G such that the boundary value function of φ is univalent almost everywhere with respect to the arclength on aW. Suppose that every component of G is finitely connected and none of the components of G have single point boundary components. We show that for every bounded analytic function on G to be the pointwise limit of a bounded sequence of functions in A（G）, it is necessary and sufficient that each component of G is multi-nicely connected and the harmonic measures of G are mutually singular. This generalizes the corresponding result of Davie for the case when the components of G are simply connected.

SOME BOUNDARY INCREASING PROPERTIES OF HARMONIC FUNCTIONS IN LIPSCHITZ DOMAIN

The object of this paper is to study the non-tangential increasing properties of positiveharmonic function u in Lipschitz domain by means of Martin representation theory. A necessaryand sufficient condition of the control of growth of u near any fixed boundary point is obtained.It is shown that the non-tangential increasing degree of u near a boundary point is exactlythe local degree of its representation measure with respect to the harmonic measure. Someexamples are given.