Separable asymptotic cost of evaluating elementary functions

The computational cost, in the bit model of computation, of the evaluation of a real function in a point is analyzed, when the number d of correct digits of the result increases asymptotically. We want to study how the cost depends on also when approaches a critical point for the function f. We investigate the hypotheses under which it is possible to give upper bounds on the cost as functions of “separated variables” d and , that is as products of two functions, each of one variable. We examine in particular the case of elementary functions. This revised version was published online in June 2006 with corrections to the Cover Date.     

On-Site Determination of Methylmercury by Coupling Solid-Phase Extraction and Voltammetry

A measurement and speciation procedure for the determination of total mercury (Hg_TOT), inorganic mercury (Hg_IN), and methylmercury (CH₃Hg) was developed and the applicability for on-site determination was demonstrated. A simple, portable sample pretreatment procedure was optimized to extract the analytes. Home-made columns, packed with a new sorbent material called CYXAD (CYPHOS 101 modified Amberlite XAD), were used to separate the two forms of the analyte. Hg_TOT and CH₃Hg were determined by anodic stripping voltammetry (ASV), using a solid gold electrode (SGE). Two certified reference materials (BCR-463 Tuna Fish and Tuna Fish ERM-CE 464) and eight fresh fishes were analyzed. Then, the results that were obtained following the optimized portable procedure were compared with the concentrations obtained, using a direct mercury analyzer (DMA). This quantification, using the two techniques, demonstrated the good performance of the proposed method.     

A Study on the Optically Active Polymer Poly‐β‐pinene

Poly‐β‐pinene (PBP) was obtained by radiation‐induced polymerization of monomer with γ radiation. The polymerizations were conducted both in vacuum and in the presence of air at different radiation doses up to 1–3 MGy. It was found that the presence of oxygen retards the polymerization rate and reduces the polymer yields and the radiation chemical yield suggesting that the polymerization mechanism involves free radicals. It is shown that PBP can also be obtained in low yields from β‐(‐)pinene polymerization with a free radical initiator. The chemical structures of the PBP radiopolymer and PBP obtained by a free radical initiator were studied by FT‐IR and ¹³C CP‐MAS NMR spectroscopy. The data shows that the PBP obtained have highly ordered structures, which is manifested also by the very high specific optical rotation which is about 3 times that of the starting monomer in the case of the radiopolymer and about 5 times in the case of the PBP prepared with the free radical initiator. In contrast, PBP obtained in high yields by cationic polymerization shows a very low specific optical rotation, much lower than that of the starting monomer and low regularity in chemical structure has been attributed to this polymer by FT‐IR and ¹³C CP‐MAS NMR spectroscopy. It is shown that PBP with high optical activity racemizes over an acidic catalyst.     

Synthesis of fullerene-silica hybrid materials

Fullerene/silica hybrid materials were obtained by radiation grafting on silica surface of toluene or decalin solutions of C₆₀. As determined by thermogravimetric analysis, the amount of C₆₀ grafted on silica surface was dependent from the radiation dose administered and independent from the C₆₀ concentration and the nature of the organic solvent. In absence of air, a dose of 48 kGy was sufficient to ensure a grafting level of 30% by weight of C₆₀ in the hybrid material. The fullerene/silica hybrid material shows a remarkable thermal stability, since the early decomposition starts above 300 °C as measured by DTG and DTA. The chemical structure of the fullerene/silica hybrid material was determined by FT-IR spectroscopy and with solid state ¹³C CP-MAS NMR. The potential application of such materials has been outlined.     

Separation of intact proteins on γ‐ray‐induced polymethacrylate monolithic columns: A highly permeable stationary phase with high peak capacity for capillary high‐performance liquid chromatography with high‐resolution mass spectrometry

Polymethacrylate‐based monolithic capillary columns, prepared by γ‐radiation‐induced polymerization, were used to optimize the experimental conditions (nature of the organic modifiers, the content of trifluoroacetic acid and the column temperature) in the separation of nine standard proteins with different hydrophobicities and a wide range of molecular weights. Because of the excellent permeability of the monolithic columns, an ion‐pair reversed‐phase capillary liquid chromatography with high‐resolution mass spectrometry method has been developed by coupling the column directly to the mass spectrometer without a flow‐split and using a standard electrospray interface. Additionally, the high working flow and concomitant high efficiency of these columns allowed us to employ a longer column (up to 50 cm) and achieve a peak capacity value superior to 1000. This work is motivated by the need to develop new materials for high‐resolution chromatographic separation that combine chemical stability at elevated temperatures (up to 75°C) and a broad pH range, with a high peak capacity value. The advantage of the γ‐ray‐induced monolithic column lies in the batch‐to‐batch reproducibility and long‐term high‐temperature stability. Their proven high loading capacity, recovery, good selectivity and high permeability, moreover, compared well with that of a commercially available poly(styrene‐divinylbenzene) monolithic column, which confirms that such monolithic supports might facilitate analysis in proteomics.     

An infinite precision bracketing algorithm with guaranteed convergence

The computational cost of a bracketing algorithm in the bit model of computation is analyzed, when working with a finite arithmetic of unbounded accuracy. The complexity measure used here is the number of bit operations, seen as a function of the required absolute error of the result. In this model the convergence of the classical bisection method (as well as that of any bracketing method which requires the function sign) is not ensured when no information on the behaviour of the function is available. A modified bisection algorithm with guaranteed convergence is proposed and an upper bound to its computational cost is given.     

Synthesis of polyarylacetylenes by γ‐ray‐induced polymerization of terminal alkynes. Nanostructures of ortho‐substituted derivatives

Terminal aryl alkynes RC₆H₄C?CH with substituents of different electronic properties and ring position (R = H, 4‐CF₃, 4‐OMe, 2‐CF₃, 2‐OMe, 2‐Me) were exposed to γ‐radiation (50–400 kGy) in organic solvents (hexane, 1,4‐dioxane, ethylacetate, methanol, tetrahydrofuran), at room temperature. The effects arising from substituent, solvent, dilution, and radiation dose allowed to define the conditions suitable for polymerization, which was favored in methanol at increasing dilution of the alkyne. Ortho‐substitution represented the key structural element in the substrate, and the derived polyarylacetylenes were characterized in detail, including gel permeation chromatography, thermal analysis, infrared, NMR, UV–vis, fluorescence, and scanning electron microscope spectroscopy. The results are consistent with the formation of irregular polymers mainly composed of trans‐transoid chains. Controlled aggregation of the polymers by means of an osmosis‐based procedure in solvent/non‐solvent mixtures allowed the formation of nanostructured materials, in particular of hollow nanospheres from THF/water. The methodology sets the basis for the development of γ‐rays‐induced polymerization of alkynes, in a transition metal catalyst‐free environment. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012