On the classical Maki–Thompson rumour model in continuous time

In this paper, the Maki–Thompson model is slightly refined in continuous time, and a new general solution is obtained for each dynamics of spreading of a rumour. It is derived an equation for the size of a stochastic rumour process in terms of transitions. We give new lower and upper bounds for the proportion of total ignorants who never learned a rumour and the proportion of total stiflers who either forget the rumour or cease to spread the rumour when the rumour process stops, under general initial conditions. Simulation results are presented for the analytical solutions. The model and these numerical results are capable to explain the behaviour of the dynamics of any other dynamical system having interactions similar to the ones in the stochastic rumour process and requiring numerical interpretations to understand the real phenomena better. The numerical process in the differential equations of the model is investigated by using error-estimates. The estimated error is calculated by the Runge–Kutta method and found either negligible or zero for a relatively small size of the population. This pioneering paper introduces a new mathematical method into Operations research, motivated by various areas of scientific, social and daily life, it presents numerical computations, discusses structural frontiers and invites the interested readers to future research.     

Continuous monitoring of thermooxidative degradation products of polystyrene by membrane extraction with sorbent interface and gas chromatography

A novel method for the continuous monitoring of thermooxidative degradation products of polystyrene by membrane extraction with sorbent interface (MESI) and gas chromatography (GC) is developed. The results are compared with solid-phase microextraction-GC, which can extract gases, vapors, and aerosols. The volatile and semivolatile degradation products are identified by mass spectrometry. The membrane used in the MESI-GC analysis shows a high permeation for volatile aromatic hydrocarbons; a low permeation for corresponding volatile aldehydes; and no permeation for less volatile alcohols, acids, and degradation products with a high molecular weight, thus reducing significantly the number of compounds detected from MESI-GC. Sensitivity of the method depends on the time of trapping, which is limited by the breakthrough of the trap. By heating the trap at fixed intervals of time, consecutive gas chromatograms are obtained.     

Sulfinyl-mediated chirality transfer in diastereoselective Claisen rearrangements

[reaction: see text] The highly selective Claisen rearrangements of substrates bearing a sulfinyl moiety at C-5 allow for creation of up to two asymmetric centers and preserve a useful vinyl sulfoxide.     

Conformational selection of glycomimetics at enzyme catalytic sites: experimental demonstration of the binding of distinct high-energy distorted conformations of C-, S-, and O-glycosides by E. Coli beta-galactosidases

We show that the conformational features of the molecular complexes of E. coli beta-galactosidase and O-glycosides may differ from those formed with closely related compounds in their chemical nature, such as C- and S-glycosyl analogues. In the particular case presented here, NMR and ab initio quantum mechanical results show that the 3D-shapes of the ligand/inhibitor within the enzyme binding site depend on the chemical nature of the compounds. In fact, they depend on the relative size of the stereoelectronic barriers for chair deformation or for rotation around Phi glycosidic linkage.     

Renewal equations for option pricing

In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits.     

Nonlinear characterization with burst excitation of 1-3 piezocomposite transducers

Ultrasonic transducers made with 1-3 connectivity piezocomposites are frequently used in Medical applications and nondestructive testing. When the transducer is used for special applications as, for instance air-coupled transmission, it is necessary to compensate for the high difference of acoustic impedance between transducer and medium using high amplitude pulses to generate high acoustic signal. Thus, the nonlinear behavior of the transducer must be taken into account in similar application conditions. The newly developed method, which performs the nonlinear characterization with burst signal excitation near the thickness resonance frequency, is based on the measure of the current as well as the vibration velocity of the piezocomposite transducer. The current of the stationary response is measured before the end of the burst signal excitation. Burst excitation enables us to measure the nonlinear characterization without producing overheating in the transducers. The amplitude level dependence of mechanical losses tandelta(m) and the stiffness increases |Deltac/c(0)| have been studied, as well as the velocity dependence of a point of the transducer, measured with a laser vibrometer. In this method, the power level applied to the transducers can be higher than other nonlinear measurement methods, providing measurements of high accuracy.     

Multiplexing and transmission of RF signals using an optical fiber

Ultrasonic non-destructive testing systems designed to control huge structures normally use several transducers in the reception stage. To avoid increasing the cost of electronics, a multiplexer is used to send all received signals to the same processing module. Traditionally, transmission of such signals is carried out using copper cables. For special applications (i.e. continuous monitoring of nuclear plants) metallic cables are not suitable because of their high sensitivity to electromagnetic perturbations. Moreover, the multiplexing is made electronically. When the distance between the transducers and the reception unit is large and/or electromagnetic noise is important, signal degradation takes place. The proposed system implements the transmission and multiplexing of ultrasonic electrical signals obtained by means of broadband transducers (up to 1 MHz), using an optical fiber. Optical fibers are made of dielectric materials (silica or plastic) so they are inherently passive to electromagnetic noise. Wavelength division multiplexing is utilized for adding channels to the system by means of fiber optic couplers and different light sources. The wavelengths of the optical signals utilized are located far apart in the optical spectrum in order to avoid serious crosstalk in transmission. The limit to the number of multiplexed channels depends on the optical fiber selected, the spectrum of the light sources and the wavelength division multiplexers or couplers utilized.     

Nonlinear mechanical behavior of piezocomposites for ultrasonic transducers

A comparative study is carried out between the nonlinear behavior of a composite and the piezoceramic used to obtain it. This characterization is necessary for using the composite in power transducer applications. A study of the losses and the resonator stiffness variations has also been done. Both these effects, as well as the possibility of the frequency hysteresis, show different behavior in the composites, since the increases in the ceramics are different from those in the composites. In this study two measurement methods are used: principally the motional impedance increase with the motional current measurements. The results obtained are normalized in order to make them independent of the resonator size, and thus make the comparison between the composite and the ceramic easier. The figure of the mechanical loss tangent tan delta m versus the mean strain shows that the losses can be greater in the ceramic than in the composite for soft ceramics. The dependence behavior of the losses and stiffness variations versus the mean strain is studied for both resonators.     

Facile preparation of 3-substituted 2-quinazolinones via electrogenerated base

A new series of 3,4-disubstituted quinazolin-2-ones, with potential T-type calcium channel antagonist activity, and new 4-methylene-quinazolin-2-ones, promising catalysts as N-heterocyclic olefins, have been prepared in good yield by a simple reaction between 2-aminobenzophenone, or 2-aminoacetophenone, and cyanomethyl anion electrogenerated by acetonitrile reduction at a graphite electrode, followed by the addition of different organic isocyanates and subsequent heterocyclization.