Dispersion Characteristics of Waveguide Arrays in Optical Spectrum Analyzers

Formulas for calculating the spectral characteristics of waveguide arrays, which are incorporated into waveguide spectrum analyzers based on planar waveguides, channel waveguides, and fiber optical waveguides, are derived taking into account the contribution of both the waveguide dispersion and the material dispersion to the dispersion factor. These formulas are used to study the dependence of the dispersion factor on the waveguide-system parameters for specific models of waveguide arrays. It is shown that consideration of contributions of the waveguide dispersion and material dispersion can affect profoundly the spectral characteristics of waveguide arrays.     

Tail probabilities of the limiting null distributions of the Anderson–Stephens statistics

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) z_i, i=1,…,n, Anderson and Stephens (Biometrika 59 (1972) 613–621) proposed testing procedures based on the statistics S_max=max_u S(u) and S_min=min_u S(u), where u is a unit vector and nS(u) is the sum of squares of u′z_i's. In this paper, we also consider another test statistic S_range=S_max−S_min. We provide formulas for the P-values of S_max, S_min, S_range by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.     

A Representation of a Family of Secret Sharing Matroids

Deciding whether a matroid is secret sharing or not is a well-known open problem. In Ng and Walker [6] it was shown that a matroid decomposes into uniform matroids under strong connectivity. The question then becomes as follows: when is a matroid m with N uniform components secret sharing? When N = 1, m corresponds to a uniform matroid and hence is secret sharing. In this paper we show, by constructing a representation using projective geometry, that all connected matroids with two uniform components are secret sharing     

Gradient‐enhanced one‐dimensional pulse schemes for quaternary and methylene carbon detection

Gradient‐enhanced pulse schemes are presented for the detection of quaternary and methylene carbons. The new pulse schemes permit the detection of quaternary and methylene (—CH₂) carbons or CH₂ carbons alone from a single experiment. Efficient suppression of CH and CH₃ carbons in all the pulse schemes is achieved by creating their antiphase magnetization and then dephasing using gradients. In the pulse schemes for detection of only CH₂ carbons, the quaternary carbons are also suppressed either by dephasing using gradients or by rendering them unobservable by retaining in longitudinal order. The experimental results of the gradient pulse schemes are demonstrated on cholesteryl acetate and cyclosporin A. These one‐dimensional techniques, because of their simplicity and the ease of performing the experiments, can be important for routine chemical applications. Copyright © 2003 John Wiley & Sons, Ltd.     

The Ends of Manifolds with Bounded Geometry, Linear Growth and Finite Filling Area

We prove that simply connected open manifolds of bounded geometry, linear growth and sublinear filling growth (e.g. finite filling area) are simply connected at infinity.     

Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -     

The solution of the neutron transport equation in a slab with anisotropic scattering

The neutron transport equation for a slab geometry with the extremely anisotropic scattering kernel is considered. The albedo and transmission factors are calculated using the variation method. The effect of the extremely anisotropic parameter on the variation of the slab albedo and transmission factor is calculated. The obtained results are compared with the published data.     

Polarization Sensitive Spectral Interferometric Optical Coherence Tomography for Biological Samples

A spectral interferometric optical coherence tomography (OCT) system which has polarization sensitivity is developed. This system reduces the mechanical scanning dimension by employing the principle of spectral interferometry, and measures a two dimensional cross-sectional image of biological tissue with one dimensional mechanical scanning. Sixteen OCT images with different polarization conditions are measured, and two dimensional distributions of each element of the Müller matrix of a sample to be measured are calculated.     

图的度序列不等式

用代数的方法证明了有关图度序列的几个不等式，并且得到了其相应的极图。