Two new characterizations of carleson-newman Blaschke products

We present an extension of a result of Vasyunin by giving a characterization of finite products of interpolating Blaschke products B in terms of the minorization of B(z) by the distance of z to the zeros of B. We also characterize those Blaschke products that satisfy the hereditary weak embedding property.     

Infrared and Mössbauer studies of some diamine complexes with trimethyltin halides and dimethyltin dihalides

To obtain more structural information on complexes formed between alkyltin halides and bidentate ligands, the solid-state IR and Mössbauer spectra of the 1,2-ethanediamine and 1,4-butanediamine complexes of trimethyltin halides and dimethyltin dihalides were examined. The structures of the trimethyltin halide complexes were found to be trigonal bipyramidal with coplnar methyl groups. The dimethyltin dihalide complexes were octahedral with the methyl groups in the cis-positions and the halides trans to each other. However, there were no differences in the structures of the chloro and bromo complexes of either type.     

Bacterial growth response to photoactive quinones

Quinones are known producers of reactive oxygen species (ROS) that may be toxic in natural aquatic environments. In this study, the effects of parent quinones and their photodegradation products on bacterial growth were determined, and photochemical ROS formation rates were measured. Using (3)H-leucine incorporation to measure growth of the bacterium Pseudomonas aeruginosa and natural seawater bacterioplankton, growth inhibition was observed when samples were exposed to dichlone, chloranil and sodium anthraquinone-2-sulfonate (AQ2S). For seawater, compared with other quinones tested, dichlone showed the greatest toxicity in the dark, and AQ2S toxicity was greatest during simultaneous exposure to sunlight. Photodegraded chloranil and dichlone showed decreased toxicity compared with nonirradiated samples. For P. aeruginosa, AQ2S and its photodegradation products showed the greatest toxicity during simultaneous exposure to sunlight. Chloranil photodegradation products showed reduced toxicity compared with the parent compound during simultaneous exposure to sunlight. Dichlone was the only compound to show any toxicity to P. aeruginosa in the dark, and its photodegradation products were more toxic than the parent compound. Based on the results of dark and light controlled experiments measuring bacterial growth and estimated ROS production rates, ROS alone does not account for relative differences in toxicity between these quinones.     

Integrated optical temporal Fourier transformer based on a chirped Bragg grating waveguide

We experimentally demonstrate the first integrated temporal Fourier transformer based on a linearly chirped Bragg grating waveguide written in silica glass with a femtosecond laser. The operation is based on mapping the energy spectrum of the input optical signal to the output temporal waveform by making use of first-order chromatic dispersion. The device operates in reflection, has a bandwidth of 10 nm, and can be used for incident temporal waveforms as long as 20 ps. Experimental results, obtained through both temporal oscilloscope traces and Fourier transform spectral interferometry, display a successful Fourier transformation of in-phase and out-of-phase pairs of input optical pulses, and demonstrate the correct functionality of the device for both amplitude and phase of the temporal output.     

Application of Robust Optimization to the Sawmill Planning Problem

Optimization models have been used to support decision making in the forest industry for a long time. However, several of those models are deterministic and do not address the variability that is present in some of the data. Robust Optimization is a methodology which can deal with the uncertainty or variability in optimization problems by computing a solution which is feasible for all possible scenarios of the data within a given uncertainty set. This paper presents the application of the Robust Optimization Methodology to a Sawmill Planning Problem. In the particular case of this problem, variability is assumed in the yield coefficients associated to the cutting patterns used. The main results show that the loss in the function objective value (the “Price of Robustness”), due to computing robust solutions, is not excessive. Moreover, the computed solutions remain feasible for a large proportion of randomly generated scenarios, and tend to preserve the structure of the nominal solution. We believe that these results provide an application area for Robust Optimization in which several source of uncertainty are present.