Point-like sources and the scale of quantum gravity

We review the General Relativistic model of a (quasi) point-like particle represented by a massive shell of neutral matter which has vanishing total energy in the small-volume limit. We then show that, by assuming a Generalised Uncertainty Principle, which implies the existence of a minimum length of the order of the Planck scale, the total energy instead remains finite and equal to the shell's proper mass both for very heavy and very light particles. This suggests that the quantum structure of space–time might be related to the classical Equivalence Principle and possible implications for the late stage of evaporating black holes are briefly mentioned.     

Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic γ : [0, 1] → M joining p and U whose endpoints are conjugate along γ. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.     

Improving the Performance of a Continuous Process for the Production of Ethanol from Starch

In a previous work, a continuous simultaneous saccharification and fermentation process to produce ethanol from cassava starch was studied, using a set of fixed-bed reactors. The biocatalyst consisted of glucoamylase immobilized in silica particles and co-immobilized with S. cerevisiae in pectin gel. Using 3.8 U mL^?1 _reactor and 0.05 g_{wet yeast} mL^?1 _reactor at start-up, starch hydrolysis was the rate-limiting step. Maximum ethanol productivity was 5.8 g_ethanol L^?1 h^?1, with 94.0% conversion of total reducing sugars (TRS) and 83.0% of the ethanol theoretical yield. In this work, the molar mass of the substrate and the biocatalyst particle size were reduced in an attempt to improve the bioreactor performance. The diameters of silica and pectin gel particles were reduced from 100 μm and 3–4 mm, respectively, to 60 μm and 1–1.5 mm, and the degree of substrate prehydrolysis by α-amylase was increased. The bioreactor performance was assessed for different loads of immobilized glucoamylase (2.1, 2.8, and 3.8 U mL^?1 _reactor), for the same initial cell concentration (0.05 g_{wet yeast.}mL^?1 _reactor). Feeding with 154.0 g L^?1 of TRS and using 3.8 U mL^?1 _reactor, fermentation became the rate-limiting step. Productivity reached 11.7 g L^?1 h^?1, with 97.0% of TRS conversion and 92.0% of the ethanol theoretical yield. The reactor was operated during 275 h without any indication of destabilization.     

Batch Experiments for the Determination of the Ti(IV,III) Couple Formal Potential in 1 mol⋅dm<Superscript>−3</Superscript> HCl, 2 mol⋅dm<Superscript>−3</Superscript> NaCl Medium at 25 °C

The determination of the Ti(IV,III) redox couple formal potential in 1 mol⋅dm⁻³ HCl, 2 mol⋅dm⁻³ NaCl medium at 25 °C through batch experiments involving the preparation of Ti(IV) and Ti(III) mixtures via the reaction of Ti(IV) with zinc amalgam, has been carried out with Emf measurements in order to verify the correctness of the previous value that the authors obtained by a coulometric-potentiometric investigation in the same conditions. The results from the two independent methods are in good agreement: (9±1) mV by the first method and (9±2) mV by the average batch result.     

Weak-type inequalities for higher order Riesz-Laguerre transforms

In this paper we study the weak-type (1,1) boundedness of the higher order Riesz-Laguerre transforms associated with the Laguerre polynomials. In particular, we obtain the boundedness for the Riesz-Laguerre transforms of order 2 and we find also the sharp polynomial weight ω that makes the Riesz-Laguerre transforms of order greater than two continuous from into L1,∞(dμα), being μα the Laguerre measure.     

On Twisted Fourier Analysis and Convergence of Fourier Series on Discrete Groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group C ^*-algebras of discrete groups. For amenable groups, Følner nets give the key to Fejér summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.     

Data mining by total ranking methods: a case study on optimisation of the "pulp and bleaching" process in the paper industry

Total order ranking methods are multicriteria decision making techniques used for the ranking of various alternatives on the basis of more than one criterion. The criteria, which are the standards by which the elements of the system are judged are not always in agreement, they can be conflicting, motivating the need to find an overall optimum that can deviate from the optima of one or more of the single criteria. Total order ranking methods are based on an aggregation of the criteria in a scalar function, i.e. an order or ranking index, which allow to sort elements according to its numerical value. Several evaluation methods which define a ranking parameter generating a total order ranking have been proposed in the literature. Four total order ranking methods are here described: Desirability functions, Utility functions, Dominance functions and Absolute Reference method. These methods have been compared to each other by applying them to a decision making problem in the paper industry. Various bleaching processes have been analysed and compared on the basis of multiple criteria, the aim being to find out best bleaching process among the ones proposed in the last years as alternative to chlorine bleaching process which is of high environmental impact due to the potential for chlorinated dioxin production.     

Anharmonic vibrational levels of the two cyclic isomers of SiC3

Using coupled-cluster approach full six-dimensional analytic potential energy surfaces for two cyclic SiC(3) isomers [C-C transannular bond (I) and Si-C transannular bond (II)] have been generated and used to calculate anharmonic vibrational wave functions. Several strong low-lying anharmonic resonances have been found. In both isomers already some of the fundamental transitions cannot be described within the harmonic approximation. Adiabatic electron affinities and ionization energies have been calculated as well. The Franck-Condon factors for the photodetachment processes c-SiC(3) (-)(I)-->c-SiC(3)(I) and c-SiC(3) (-)(II)-->c-SiC(3)(II) are reported.