Molecular weight effect on the obtainment of parallel and perpendicular orientation in thermotropic poly(diethylene glycol <Emphasis Type="Italic">p,p′</Emphasis>-bibenzoate)

Summary The effect of molecular weight on the uniaxial orientation process has been analyzed in two samples of thermotropic poly(diethylene glycol p,p′-bibenzoate), evaluating the influence of that parameter on the type of orientation obtained. Several strain rates and deformation temperatures have been tested in order to map out the conditions for obtaining the two different kinds of orientation. The results show that in the lower molecular weight PDEB sample (M_w=31200) it is rather easy to get exclusively perpendicular “anomalous” orientation, with the molecular axes aligned transversely to the stretching direction. However, it is extremely difficult to obtain 100% parallel “normal” orientation. On the contrary, either type of orientation or a mixture of them can be easily developed for the higher molecular weight PDEB sample (M_w=102900).     

Assessing continuous bivariate effects among different groups through nonparametric regression models: An application to breast cancer detection

In many applications, the joint effect of two continuous covariates on the target binary response may vary across groups defined by levels of a given factor. A testing procedure that would enable this type of surface-by-factor interactions to be detected has been designed. To accomplish this goal, a logistic generalized additive model (GAM) with bivariate continuous interactions varying across groups defined by levels of a factor is considered. A local scoring algorithm based on local linear kernel smoothers was implemented to estimate the proposed logistic GAM. Bootstrap resampling techniques were used for the purpose of testing for factor-by-surface interactions. Given the high computational cost involved, binning techniques were used to speed up computation in the estimation and testing processes. The adequacy of the bootstrap-based test was assessed by means of a simulation study. If a factor-by-surface interaction is detected in the model, it is then established that the use of the odds-ratio curves is very useful in obtaining a direct interpretation of the fitted model. The benefits of using this methodology when analyzing real data are illustrated by applying the technique to the outputs produced by a computerized system dedicated to the early detection of breast cancer.     

Manifold mapping: a two-level optimization technique

In this paper, we analyze in some detail the manifold-mapping optimization technique introduced recently [Echeverría and Hemker in space mapping and defect correction. Comput Methods Appl Math 5(2): 107—136, 2005]. Manifold mapping aims at accelerating optimal design procedures that otherwise require many evaluations of time-expensive cost functions. We give a proof of convergence for the manifold-mapping iteration. By means of two simple optimization problems we illustrate the convergence results derived. Finally, the performances of several variants of the method are compared for some design problems from electromagnetics.     

Thomas Fincke und die <Emphasis Type="Italic">Geometria rotundi</Emphasis>

Thomas Fincke (January 6^th, 1561–April 24^th, 1656), born in Flensburg (Germany), was one of the very most important and significant scientists in Denmark during the seventeenth century, a mathematician and astrologer and physician in the beginning of modern science, a representative of humanism and an influentual academic organizer. He studied in Strasbourg (since 1577) and Padua (since 1583) and received his M.D. in Basel (1587), he practised as a physician throughout his life (since 1587 or 1590) and became a professor at Copenhagen (1591). But he was best known because of his Geometriae rotundi libri XIIII (1583), a famous book on plane and spherical trigonometry, based not on Euclid but on Petrus Ramus. In this influentual work, in which Fincke introduced the terms tangent and secant and probable first noticed the Law of Tangents and the so-called Newton-Oppel-Mauduit-Simpson-Mollweide-Gauss-formula, he showed himself to be „abreast of the mathematics of his time“.      

Synthesis,characterization and properties of functionalized styrene–maleimide copolymers

New functionalized styrene–maleimide copolymers were prepared by free radical copolymerization of styrene (St) and N‐4‐carboxybutylmaleimide (NBMI) in chloroform, using 2,2′‐azobisisobutyronitrile (AIBN) as initiator. Monomer and copolymer characterization was carried out by ¹H‐ and ¹³C‐NMR. Copolymer composition was determined by elemental analysis and Fourier‐transform infrared (FTIR) spectroscopy. The glass transition temperature (from DSC) and the thermogravimetric analysis (TGA) of the copolymers were consistent with the thermal behavior and stability observed for alternating St–maleimide copolymers. St–NBMI copolymers crosslinked with divinylbenzene (DVB) were also synthesized and their cation exchange properties evaluated in order to assess the capacity of the new copolymers to bind metallic ions. Copyright © 2005 Society of Chemical Industry     

2,4,6‐Trichlorophenol and phenol removal in methanogenic and partially‐aerated methanogenic conditions in a fluidized bed bioreactor

A fluidized bed bioreactor (FBBR) was operated for more than 575 days to remove 2,4,6‐trichlorophenol (TCP) and phenol (Phe) from a synthetic toxic wastewater containing 80 mg L^?1 of TCP and 20 mg L^?1 of Phe under two regimes: Methanogenic (M) and Partially‐Aerated Methanogenic (PAM). The mesophilic, laboratory‐scale FBBR consisted of a glass column (3 L capacity) loaded with 1 L of 1 mm diameter granular activated carbon colonized by an anaerobic consortium. Sucrose (1 g COD L^?1) was used as co‐substrate in the two conditions. The hydraulic residence time was kept constant at 1 day. Both conditions showed similar TCP and Phe removal (99.9 + %); nevertheless, in the Methanogenic regime, the accumulation of 4‐chlorophenol (4CP) up to 16 mg L^?1 and phenol up to 4 mg L^?1 was observed, whereas in PAM conditions 4CP and other intermediates were not detected. The specific methanogenic activity of biomass decreased from 1.01 ± 0.14 in M conditions to 0.19 ± 0.06 mmolCH₄ h^?1 gTKN^?1 in PAM conditions whereas the specific oxygen uptake rate increased from 0.039 ± 0.008 in M conditions to 0.054 ± 0.012 mmolO₂ h^?1 gTKN^?1, which suggested the co‐existence of both methanogenic archaea and aerobic bacteria in the undefined consortium. The advantage of the PAM condition over the M regime is that it provides for the thorough removal of less‐substituted chlorophenols produced by the reductive dehalogenation of TCP rather than the removal of the parent compound itself. Copyright © 2005 Society of Chemical Industry