We have detected circumstellar absorption lines of the CN and CN Violet and Red System in the spectrum of the post-AGB star HD 56126. From a synthetic spectrum analysis, we derive a Doppler broadening parameter of b = 0.51 ± 0.04 km s, CN/CN= 38±2, and a lower limit of 2000 on CN/CN and CN/CN. A simple chemical model has been computed of the circumstellar shell surrounding HD 56126 that takes i...

Graininess is one of the important image quality metrics in the photographic quality. In this paper, we will report an investigation of our evaluation model for color graininess. In this evaluation model, overall image noise is predicted as a graininess index (GI) to the average lightness for each patch image, and the GI is calculated from two image noise metrics, the lightness noise (LN) and t...

The 2-adic valuation (highest power of 2) dividing the well-known Catalan numbers, Cn, has been completely determined by Alter and Kubota and further studied combinatorially by Deutsch and Sagan. In particular, it is well known that Cn is odd if and only if n = 2 k − 1 for some k > 0. The polynomial F ch n (321; q) = ∑ σ∈Avn(321) q ch(σ), where Avn(321) is the set of permutations in Sn that avo...

The principal inhibitory neurotransmitter in the mammalian cochlear nucleus (CN) is glycine. During age-related hearing loss (AHL), glycinergic inhibition becomes weaker in CN. However, it is unclear what aspects of glycinergic transmission are responsible for weaker inhibition with AHL. We examined glycinergic transmission onto bushy cells of the anteroventral CN in normal-hearing CBA/CaJ mice...

Inverse methods form the basis of biomedical imaging applications, especially when they involve optical and near infrared radiation where multiple scattering tends to blur an image. This paper summarizes some of the recent literature on optical property reconstruction and on the use of fluorescence-induced signals for imaging. NOMENCLATURE cn Speed of light at refractive index n D Diffusion coe...

We prove that the following pointwise inequality holds −∆u ≥ √ 2 (p + 1)− cn |x| a 2 u p+1 2 + 2 n− 4 |∇u|2 u in R where cn := 8 n(n−4) , for positive bounded solutions of the fourth order Hénon equation that is ∆u = |x|u in R where a ≥ 0 and p > 1. Motivated by the Moser iteration argument in the regularity theory, we develop an iteration argument to prove the above pointwise inequality. As fa...

A permutation π of [n] = {1, 2, . . . , n} is irreducible if π([m]) = [m] for no m ∈ [n], m < n, and it is connected if for no interval I ⊂ [n], 2 ≤ |I| ≤ n − 1, the image π(I) is an interval. We review enumeration of irreducible permutations and their appearances in mathematics. Then we enumerate connected permutations. Asymptotically, there are n!/e2 of them and exactly (for n > 2) their numb...

Some convenient limit properties of usual information criteria are given for cointegrating rank selection. Allowing for a non-parametric short memory component and using a reduced rank regression with only a single lag, standard information criteria are shown to be weakly consistent in the choice of cointegrating rank provided the penalty coefficient Cn → ∞ and Cn/n → 0 as n → ∞. The limit dist...