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.     

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.     

Mathematical programming time-based decomposition algorithm for discrete event simulation

Mathematical programming has been proposed in the literature as an alternative technique to simulating a special class of Discrete Event Systems. There are several benefits to using mathematical programs for simulation, such as the possibility of performing sensitivity analysis and the ease of better integrating the simulation and optimisation. However, applications are limited by the usually long computational times. This paper proposes a time-based decomposition algorithm that splits the mathematical programming model into a number of submodels that can be solved sequentially to make the mathematical programming approach viable for long running simulations. The number of required submodels is the solution of an optimisation problem that minimises the expected time for solving all of the submodels. In this way, the solution time becomes a linear function of the number of simulated entities.     

Effects of proximity on the relaxation dynamics of flindersine and 6(5H)-phenanthridinone

The role played by the carbonyl group in the antenna system of a naturally occurring photochromic chromene, flindersine (FL), has been experimentally investigated and compared with that of a carbonyl group present in a structurally related unreactive heterocyclic compound, 6(5H)-phenanthridinone (PH). Through stationary and time-resolved absorption and emission techniques, the excited-state relaxation dynamics after UV irradiation were determined for FL and PH. The presence of a carbonyl group in both compounds entails the existence of two close-lying, strongly coupled electronic excited states, having n,pi* and pi,pi* character, respectively. Their coupling can be modulated by a careful choice of the solvent proticity and temperature. Moreover, in the case of strong coupling between the n,pi* and pi,pi* states, we have proved that the relaxation dynamics can involve transitions in which the upper of the coupled states acts as an intermediate for radiationless decay, bypassing the lowest emissive state, whereby the fluorescence quantum yield becomes a function of the excitation wavelength.     

HMDST as Useful Tool in Organic Synthesis: A Further Step in the Delivery of Sulfur Functionalities

Abstract

Bis(trimethylsilyl)sulfide (HMDST) was demostrated to be a very efficient reagent in the delivery of sulfur functionalities, allowing us to synthesize a wide range of thiocarbonyl compounds. The most reactive derivatives were trapped with suitable dienes, leading to the synthesis of different heterocyclic molecules with an high degree of chemo- and regioselectivity. Recently, the mildness of this methodology also allowed us to obtain particularly reactive thiooxocompounds, such as thioformylsilanes, α,β-unsaturated thioaldehydes, thioketones, thioacylsilanes, and thioacylstannanes.     

Self-, N2-, O2-broadening coefficients and line parameters of HFC-32 for ν7 band and ground state transitions from infrared and microwave spectroscopy

Hydrofluorocarbons have been used as replacement gases of chlorofluorocarbons, since the latter have been phased out by the Montreal Protocol due to their environmental hazardous ozone-depleting effects. This is also the case of difluoromethane (CH₂F₂, HFC-32), which nowadays is widely used in refrigerant mixtures together with CF₃CH₃, CF₃CH₂F, and CF₃CHF₂. Due to its commercial use, in the last years, the atmospheric concentration of HFC-32 has increased significantly. However, this molecule presents strong absorptions within the 8–12 μm atmospheric window, and hence it is a greenhouse gas which contributes to global warming. Although over the years several experimental and theoretical investigations dealt with the spectroscopic properties of CH₂F₂, up to now pressure broadening coefficients have never been determined. In the present work, the line-by-line parameters of CH₂F₂ are retrieved for either ground state or ν₇ band transitions by means of microwave (MW) and infrared (IR) absorption spectroscopy, respectively. In particular, laboratory experiments are carried out on 9 pure rotational transitions of the ground state and 26 ro-vibrational transitions belonging to the ν₇ band lying around 8.2 μm within the atmospheric region. Measurements are carried out at room temperature on self-perturbed CH₂F₂ as well as on CH₂F₂ perturbed by N₂ and O₂. The line shape analysis leads to the first determination of self-, N₂-, O₂-, and air-broadening coefficients, and also of line intensities (IR). Upon comparison, broadening coefficients of ground state transitions are larger than those of the ν₇ band, and no clear dependence on the rotational quantum numbers can be reported. The obtained results represent basic information for the atmospheric modelling of this compound as well as for remote sensing applications.     

Reproduction of exponential polynomials by multivariate non-stationary subdivision schemes with a general dilation matrix

We study scalar multivariate non-stationary subdivision schemes with a general integer dilation matrix. We characterize the capability of such schemes to reproduce exponential polynomials in terms of simple algebraic conditions on their symbols. These algebraic conditions provide a useful theoretical tool for checking the reproduction properties of existing schemes and for constructing new schemes with desired reproduction capabilities and other enhanced properties. We illustrate our results with several examples.     

Facile decoration of functionalized single-wall carbon nanotubes with phthalocyanines via "click chemistry"

We describe the functionalization of single-wall carbon nanotubes (SWNTs) with 4-(2-trimethylsilyl)ethynylaniline and the subsequent attachment of a zinc-phthalocyanine (ZnPc) derivative using the reliable Huisgen 1,3-dipolar cycloaddition. The motivation of this study was the preparation of a nanotube-based platform which allows the facile fabrication of more complex functional nanometer-scale structures, such as a SWNT-ZnPc hybrid. The nanotube derivatives described here were fully characterized by a combination of analytical techniques such as Raman, absorption and emission spectroscopy, atomic force and scanning electron microscopy (AFM and SEM), and thermogravimetric analysis (TGA). The SWNT-ZnPc nanoconjugate was also investigated with a series of steady-state and time-resolved spectroscopy experiments, and a photoinduced communication between the two photoactive components (i.e., SWNT and ZnPc) was identified. Such beneficial features lead to monochromatic internal photoconversion efficiencies of 17.3% when the SWNT-ZnPc hybrid material was tested as photoactive material in an ITO photoanode.